Rheology and Processing of Polymer Nanocomposites [1 ed.] 1118969790, 9781118969793

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RHEOLOGY AND PROCESSING OF POLYMER NANOCOMPOSITES

RHEOLOGY AND PROCESSING OF POLYMER NANOCOMPOSITES

Edited by SABU THOMAS RENE MULLER JIJI ABRAHAM

Copyright © 2016 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and speciically disclaim any implied warranties of merchantability or itness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of proit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Names: Thomas, Sabu, editor. | Muller, Rene, 1955- editor. | Abraham, Jiji, editor. Title: Rheology and processing of polymer nanocomposites / edited by Sabu Thomas, Rene Muller, Jiji Abraham. Description: Hoboken, New Jersey : John Wiley & Sons, Inc., [2016] | Includes bibliographical references and index. Identiiers: LCCN 2016007780| ISBN 9781118969793 (cloth) | ISBN 9781118969816 (epub) Subjects: LCSH: Rheology. | Plasticity. | Polymers. | Nanocomposites (Materials) Classiication: LCC QC189.5 .R524 2016 | DDC 620.1/92–dc23 LC record available at http://lccn.loc.gov/2016007780 Typeset in 10/12pt TimesLTStd by SPi Global, Chennai, India Printed in the United States of America 10 9 8 7 6 5 4 3 2 1

CONTENTS

List of Contributors 1 Materials for Polymer Nanocomposites

xiii 1

Jiji Abraham, Soney C. George, Rene Muller, Nandakumar Kalarikkal, and Sabu Thomas

1.1 1.2 1.3 1.4 1.5 1.6

Introduction, 1 Nanocomposite Framework, 3 1.2.1 Nanoscale Fillers, 3 1.2.2 Choice of Polymeric Matrices, 13 Recent Developments and Opportunities in the Area of Polymer Nanocomposites, 16 Challenges in the Area of Polymer Nanocomposites, 17 Relationships of Macroscopic Rheological Properties to Nanoscale Structural Variables, 18 Conclusion, 19 Acknowledgments, 20 References, 20

2 Manufacturing Polymer Nanocomposites

29

Yuvaraj Haldorai and Jae-Jin Shim

2.1 2.2

Introduction, 29 Nanoillers, 30 2.2.1 Structure and Properties of Clay, 31 2.2.2 Structure and Properties of Organically Modiied Clay, 32 2.2.3 Structure and Properties of CNTs, 33 v

CONTENTS

vi

2.3 2.4

2.5 2.6

Polymer Matrices, 36 Preparation of Nanocomposites, 37 2.4.1 In Situ Polymerization, 37 2.4.2 Solution Blending, 39 2.4.3 Melt Compounding, 42 2.4.4 Other Methods, 54 2.4.5 Supercritical CO2 Assisted Compounding, 55 Characterization, 58 Conclusions, 60 References, 61

3 Rheology and Processing of Polymer Nanocomposites: Theory, Practice, and New Challenges 69 Jean-Charles Majesté

3.1 3.2

3.3

3.4

3.5

3.6

Introduction, 69 Viscoelasticity of Nanocomposites, 72 3.2.1 General Trends, 72 3.2.2 Percolation Treshold, 75 3.2.3 Equilibrium Shear Modulus, 78 3.2.4 Validity of TTS Principle, 81 3.2.5 Quantifying Dispersion via Melt Rheology, 83 3.2.6 Payne Effect, 87 Flow Properties of Nanocomposites, 92 3.3.1 Steady-State Flow Curves: Relative Viscosity and Normal Stress Difference, 93 3.3.2 Flow-Induced Structure in Nanocomposites, 97 3.3.3 Elongational Flow, 99 Theory and Modeling of Nanocomposites Rheology, 103 3.4.1 Steady-State Viscosity, 104 3.4.2 Dynamic Rheology, 105 3.4.3 Elongational Rheology, 109 3.4.4 Payne Effect, 113 Processing of Nanocomposites, 119 3.5.1 Inluence of Blending Procedure, 119 3.5.2 Usual Processing Methods, 121 3.5.3 New Processing Routes, 124 Conclusion and Futures Challenges, 125 Acknowledgments, 127 References, 127

4 Mixing of Polymers Using the Elongational Flow Mixer (RMX®) Rigoberto Ibarra-Gómez and René Muller

4.1 4.2

Introduction, 135 Polymer Blends, 136

135

CONTENTS

4.3 4.4

4.5

4.6 4.7

vii

4.2.1 Capillary Number, Ca, 138 4.2.2 Rheology and Processing of Polymer Blends, 142 Polymer Nanocomposites, 147 4.3.1 Dispersion of Solid Additives, 148 Elongational Flow Mixer (RMX®), 151 4.4.1 RMX® Assembly and Operating Principles, 152 4.4.2 RMX® Flow Analysis by Numeric Simulation, 155 4.4.3 Estimation of Rheological Parameters in the RMX® via Capillary Rheometry, 156 RMX® Mixing of Polymer Blends, 158 4.5.1 Inluence of the RMX® Parameters on Mixing, 159 4.5.2 Inluence of the Viscosity Ratio, p, 165 4.5.3 Energy of Mixing: Performance Comparison, 168 4.5.4 Viscous Heating, 170 4.5.5 Effect of a Compatibilizer, 170 4.5.6 Rheology/Morphology Relationship, 172 Mixing of Polymer Nanocomposites, 173 Concluding Remarks, 182 References, 182

5 Rheology and Processing of Polymer/Layered Silicate Nanocomposites Masami Okamoto

5.1 5.2 5.3 5.4

5.5

5.6

Introduction, 187 Nanostructure Development, 189 5.2.1 Melt Intercalation, 189 5.2.2 Interlayer Structure of OMLFs and Intercalation, 190 Novel Compounding Methods for Delamination of OMLFs, 199 5.3.1 Solid-State Shear Processing, 200 Nanostructure and Rheological Properties, 202 5.4.1 Flocculation Control and Modulus Enhancement, 202 5.4.2 Linear Viscoelastic Properties, 205 5.4.3 Relaxation Rate and Crystallization, 210 5.4.4 Nonlinear Shear Response, 213 5.4.5 Analogy to Soft Colloids, 214 5.4.6 Reversibility of Network Formation Process, 215 5.4.7 Alignment of Silicate Layers in Networks, 218 Nanocomposite Foams, 222 5.5.1 Foam Processing Using Supercritical CO2 , 222 5.5.2 PLA-Based Nanocomposite Foams, 224 5.5.3 Polyethylene Ionomer-Based Nanocomposite Foams by MuCell® Injection Molding, 227 Future Prospects, 230 References, 230

187

CONTENTS

viii

6 Processing and Rheological Behaviors of CNT/Polymer Nanocomposites

235

Mohan Raja, Modigunta Jeevan Kumar Reddy, Kwang Ho Won, Jae Ik Kim, Sang Hun Cha, Han Na Bae, Dae Hyeon Song, Sung Hun Ryu, and Andikkadu Masilamani Shanmugharaj

6.1 6.2

6.3 6.4

Introduction, 235 Processing Techniques of Polymer/CNT Nanocomposites, 237 6.2.1 Solution Processing, 238 6.2.2 Dry Powder, Wet, and Partial Solution Mixing, 241 6.2.3 In Situ Polymerization, 242 6.2.4 Melt Blending, 249 Rheological Properties of Polymer/Carbon Nanotube Composites, 254 6.3.1 Dilute Regime, 254 6.3.2 Semidilute Regime, 255 Summary, 274 Acknowledgment, 274 References, 274

7 Unusual Phase Separation in PS Rich Blends with PVME in Presence of MWNTs 279 Priti Xavier and Suryasarathi Bose

7.1 7.2 7.3 7.4

7.5

Introduction, 279 Experimental Methods, 280 7.2.1 Materials and Sample Preparation, 280 7.2.2 Characterization, 281 Theory Background, 281 Results and Discussion, 284 7.4.1 Rheologically Determined Demixing Temperature, 284 7.4.2 Evolution of Morphology in the Blends in Presence of MWNTs, 286 Conclusions, 291 Acknowledgements, 291 References, 291

8 Rheology and Processing of Polymer/POSS Nanocomposites Krzysztof Pielichowski, Tomasz M. Majka, and Konstantinos N. Raftopoulos

8.1 8.2 8.3

Introduction, 293 Polyhedral Oligomeric Silsesquioxanes, 296 8.2.1 General Interactions between Polymer Matrices and POSS Particles, 297 Processing of Polymer/POSS Nanocomposites, 299 8.3.1 Polyolein/POSS Nanocomposites, 299

293

CONTENTS

8.4 8.5

ix

8.3.2 Polyamide/POSS Nanocomposites, 306 8.3.3 Polyurethane/POSS Nanocomposites, 309 8.3.4 Other Polymer/POSS Nanocomposites, 310 Rheological Behavior of POSS-Based Polymer Nanocomposites, 314 Conclusions, 318 Acknowledgments, 320 References, 320

9 Polymer and Composite Nanoiber: Electrospinning Parameters and Rheology Properties 329 Palaniswamy Suresh Kumar, Sundaramurthy Jayaraman, and Gurdev Singh

9.1 9.2 9.3

9.4 9.5 9.6

10

Introduction, 329 Electrospinning, 331 Electrospinning Process Parameters, 333 9.3.1 Solution Properties, 333 9.3.2 Operating Conditions, 335 9.3.3 Process Conditions, 336 Polymer-Based Nanoiber and its Rheology, 337 Nanoiber and its Polymer Composites, 348 Conclusion, 351 References, 351

Rheology and Processing of Inorganic Nanomaterials and Quantum Dots/Polymer Nanocomposites

355

Sneha Mohan, Jiji Abraham, Oluwatobi S. Oluwafemi, Nandakumar Kalarikkal, and Sabu Thomas

10.1 10.2 10.3

10.4 10.5

Inorganic Nanoparticle Filled Polymer Nanocomposites, 356 Fabrication of Inorganic Nanoparticle Filled Polymer Nanocomposites, 356 Why Rheological Study is Important for Polymer Nanocomposites, 357 10.3.1 Assessment of the Dispersion Quality, 358 10.3.2 Assessment of Processability, 358 10.3.3 Assessment of Correlation between Molecular Structure and Dynamics of Polymers (Structure–Property Relationship), 359 Rheology of Quantum Dot Based Polymer Nanocomposites, 359 Metal Oxide Nanoparticle-Based Polymer Nanocomposites, 366 10.5.1 Alumina, 366 10.5.2 Silica, 368 10.5.3 Titania, 372 10.5.4 Zinc Oxide, 376

CONTENTS

x

10.6

11

10.5.5 Ferrite Nanoparticles, 376 10.5.6 Calcium Carbonate, 377 Conclusion, 379 References, 379

Rheology and Processing of Laponite/Polymer Nanocomposites

383

Huili Li, Wenchen Ren, Jinlong Zhu, Shimei Xu, and Jide Wang

11.1 11.2 11.3

11.4

12

Introduction, 383 Rheology, 384 11.2.1 Linear Viscoelastic Properties, 384 11.2.2 Nonlinear Viscoelastic Properties, 387 Processing, 388 11.3.1 Melt Blending, 389 11.3.2 Solution Blending, 390 11.3.3 In Situ Polymerization, 392 Conclusions and Outlook, 399 Acknowledgement, 400 References, 400

Graphene-Based Nanocomposites: Mechanical, Thermal, Electrical, and Rheological Properties 405 Rachid Bouhid, Hamid Essabir, and Abou el kacem Qaiss

12.1 12.2 12.3

12.4

12.5 12.6

13

Introduction, 405 Graphene, 407 The Use of Graphene in Nanocomposite Materials, 408 12.3.1 Problematic, 410 12.3.2 Manufacturing Technique of Graphene-Based Nanocomposites, 411 Nanocomposite Characterization, 412 12.4.1 Structural Properties of Graphene Nanocomposites, 412 12.4.2 Thermal Stability, 414 12.4.3 Crystallization and Melting Properties, 416 12.4.4 Mechanical Properties, 418 12.4.5 Rheological Properties, 421 12.4.6 Electrical Properties, 423 Conclusion, 425 Future Perspective, 425 References, 426

Processing, Rheology, and Electrical Properties of Polymer/Nanocarbon Black Composites 431 Luís C. Costa and Manuel P. Graça

13.1

Introduction, 431

CONTENTS

13.2 13.3

13.4

14

xi

Experimental, 435 13.2.1 Sample Preparation, 435 13.2.2 Characterization Techniques, 436 Electrical Properties of Carbon Black Composites and Applications, 437 13.3.1 DC Conductivity, 437 13.3.2 AC Conductivity, 440 13.3.3 Positive Temperature Coeficient in Resistivity, 444 Conclusion, 447 References, 447

Rheology and Processing of Nanocellulose, Nanochitin, and Nanostarch/Polymer Bionanocomposites

453

Carmen-Alice Teacă and Ruxanda Bod̂irlau ̆

14.1 14.2

14.3 14.4

15

Introduction, 453 Biopolymers as Nanoillers for Polymer/Nanocomposites, 455 14.2.1 Nanocellulose, 455 14.2.2 Processing of Nanocellulose/Polymer Nanocomposites, 456 14.2.3 Nanochitin, 459 14.2.4 Processing of Nanochitin/Polymer Nanocomposites, 459 14.2.5 Nanostarch, 476 14.2.6 Processing of Nanostarch/Polymer Nanocomposites, 477 Potential Applications of Polysaccharide Nanoillers/Polymer Nanocomposites, 478 Conclusions and Future Perspectives, 481 References, 482

Rheology and Processing of Nanoparticle Filled Polymer Blend Nanocomposites Chongwen Huang and Wei Yu

15.1

15.2

15.3 15.4

Rheology of Polymer Blends, 491 15.1.1 Miscible Blends, 491 15.1.2 Immiscible Blends, 495 15.1.3 Partially Miscible Blends, 502 Effect of Nanoparticles on the Morphology of Polymer Blend, 509 15.2.1 Selective Distribution, 510 15.2.2 Phase Separation, 523 Rheology of Nanoparticles Filled Polymer Blend, 531 15.3.1 Viscoelasticity of Partially Miscible Systems, 531 15.3.2 Viscoelasticity of Polymer Blend Nanocomposites, 535 Summary, 540 References, 541

491

CONTENTS

xii

16

Rheology as a Tool for Studying In Situ Polymerized Carbon Nanotube Nanocomposites

551

Guo-Hua Hu, Philippe Marchal, Sandrine Hoppe, and Christian Penu

16.1 16.2

16.3

16.4

16.5

Index

Introduction, 551 Basic Principles of Rheokinetics, 552 16.2.1 Systemic Rheology: Couette Analogy/Mixer-Type Rheology, 552 16.2.2 A Couette-Type Rheoreactor for the Kinetics of In Situ Polymerization, 558 Rheokinetics of In Situ Polymerization of Carbon Nanotube/Monomer Systems, 560 16.3.1 Effects of the Presence of MWCNT on the Polymerization Kinetics, 560 16.3.2 Effect of the State of Dispersion of Carbon Nanotubes on the Polymerization Kinetics, 563 16.3.3 Inhibiting Effect of the MWCNT on the Polymerization Kinetics, 564 Rheological Percolation Threshold of Carbon Nanotube-Based Nanocomposites, 567 16.4.1 Experimental Procedures, 567 16.4.2 Percolation Threshold Observed by Mechanical Spectroscopy, 568 16.4.3 Electrical Percolation Threshold, 576 16.4.4 Determination of the Percolation Threshold by Mechanical Spectroscopy, 576 16.4.5 Electrical versus Rheological Percolations, 578 Concluding Remarks, 581 References, 581 587

LIST OF CONTRIBUTORS

Jiji Abraham, International and Inter University Centre for Nanoscience and Nanotechnology, Mahatma Gandhi University, Kottayam, Kerala, India Han Na Bae, Department of Chemical Engineering, Kyung Hee University, Yongin, Kyunggi-Do, South Korea Ruxanda Bodîrl˘au, “Petru Poni” Institute of Macromolecular Chemistry, Advanced Research Center for Bionanoconjugates and Biopolymers, Ia¸si, Romania Suryasarathi Bose, Department of Materials Engineering, Indian Institute of Science, Bangalore, India Rachid Bouhid, Institute of Nanomaterials and Nanotechnology, Composites and Nanocomposites Center, Polymer Processing Laboratory, Moroccan Foundation for Advanced Science, Innovation and Research (MAScIR), Rabat, Morocco Sang Hun Cha, Department of Chemical Engineering, Kyung Hee University, Yongin, Kyunggi-Do, South Korea Luís C. Costa, I3N and Physics Department, University of Aveiro, Aveiro, Portugal Hamid Essabir, Institute of Nanomaterials and Nanotechnology, Composites and Nanocomposites Center, Polymer Processing Laboratory, Moroccan Foundation for Advanced Science, Innovation and Research (MAScIR), Rabat, Morocco Soney C. George, Centre for Nano science and nanotechnology, Amal Jyothi College of Engineering, Kanjirappally, Kerala, India

xiii

xiv

LIST OF CONTRIBUTORS

Manuel P. Graça, I3N and Physics Department, University of Aveiro, Aveiro, Portugal Yuvaraj Haldorai, Department of Energy and Materials Engineering, Dongguk University, Seoul, Republic of Korea Sandrine Hoppe, Laboratoire Réactions et Génie des Procédés, Université de Lorraine – CNRS, Nancy, France Guo-Hua Hu, Laboratoire Réactions et Génie des Procédés, Université de Lorraine – CNRS, Nancy, France Chongwen Huang, Advanced Rheology Institute, Department of Polymer Science and Engineering, Shanghai Jiao Tong University, Shanghai, P. R. China Rigoberto Ibarra-Gómez, Department of Mechanical Properties and Tribology of Polymers, Institut Charles Sadron, CNRS-UPR 22, Strasbourg, France Sundaramurthy Jayaraman, Environmental & Water Technology Centre of Innovation (EWTCOI), Ngee Ann Polytechnic, Singapore Modigunta Jeevan Kumar Reddy, Department of Chemical Engineering, Kyung Hee University, Yongin, Kyunggi-Do, South Korea Abou el Kacem Qaiss, Institute of Nanomaterials and Nanotechnology, Composites and Nanocomposites Center, Polymer Processing Laboratory, Moroccan Foundation for Advanced Science, Innovation and Research (MAScIR), Rabat, Morocco Nandakumar Kalarikkal, International and Inter University Centre for Nanoscience and Nanotechnology, Mahatma Gandhi University, Kottayam, Kerala, India; School Pure and Applied Physics, Department for Physics and Chemistry, Mahatma Gandhi University, Kottayam, Kerala, India Jae Ik Kim, Department of Chemical Engineering, Kyung Hee University, Yongin, Kyunggi-Do, South Korea Palaniswamy S. Kumar, Environmental & Water Technology Centre of Innovation (EWTCOI), Ngee Ann Polytechnic, Singapore Huili Li, Key Laboratory of Oil and Gas Fine Chemicals, Ministry of Education and Xinjiang Uyghur Autonomous Region, College of Chemistry and Chemical Engineering, Xinjiang University, Urumqi, Xinjiang, People’s Republic of China Jean-Charles Majesté, Laboratoire Ingénierie des Matériaux Polymères, Univ Lyon, UJM-Saint-Etienne, CNRS, Saint-Etienne, France Tomasz M. Majka, Department of Chemistry and Technology of Polymers, Cracow University of Technology, Krakow, Poland Philippe Marchal, Laboratoire Réactions et Génie des Procédés, Université de Lorraine – CNRS, Nancy, France

LIST OF CONTRIBUTORS

xv

Sneha Mohan, Department of Chemistry, Cape-Peninsula University of Technology, Cape Town, South Africa René Muller, Rheology and Polymer Processing, Institut Charles Sadron, CNRS-UPR 22, Strasbourg, France Masami Okamoto, Advanced Polymeric Nanostructured Materials Engineering, Graduate School of Engineering Toyota Technological Institute, Nagoya, Japan Oluwatobi S. Oluwafemi, Department of Applied Chemistry, University of Johannesburg, Johannesburg, South Africa; Centre for Nanomaterials Science Research, University of Johannesburg, Johannesburg, South Africa Christian Penu, Laboratoire Réactions et Génie des Procédés, Université de Lorraine – CNRS, Nancy, France; TOTAL Research and Technology Feluy, Zone Industrielle Feluy, Seneffe, Belgium Krzysztof Pielichowski, Department of Chemistry and Technology of Polymers, Cracow University of Technology, Krakow, Poland Konstantinos N. Raftopoulos, Department of Chemistry and Technology of Polymers, Cracow University of Technology, Krakow, Poland Mohan Raja, School of Engineering, Jagran Lakecity University, Bhopal, Madhya Pradesh, India Wenchen Ren, Key Laboratory of Oil and Gas Fine Chemicals, Ministry of Education and Xinjiang Uyghur Autonomous Region, College of Chemistry and Chemical Engineering, Xinjiang University, Urumqi, Xinjiang, People’s Republic of China Sung Hun Ryu, Department of Chemical Engineering, Kyung Hee University, Yongin, Kyunggi-Do, South Korea Andikkadu Masilamani Shanmugharaj, Department of Chemical Engineering, Kyung Hee University, Yongin, Kyunggi-Do, South Korea Jae-Jin Shim, School of Chemical Engineering, Yeungnam University, Gyeongsan, Gyeongbuk, Republic of Korea Gurdev Singh, Environmental & Water Technology Centre of Innovation (EWTCOI), Ngee Ann Polytechnic, Singapore Dae Hyeon Song, Department of Chemical Engineering, Kyung Hee University, Yongin, Kyunggi-Do, South Korea Carmen-Alice Teac˘a, “Petru Poni” Institute of Macromolecular Chemistry, Advanced Research Center for Bionanoconjugates and Biopolymers, Ia¸si, Romania Sabu Thomas, International and Inter University Centre for Nanoscience and Nanotechnology, Mahatma Gandhi University, Kottayam, Kerala, India; School of

xvi

LIST OF CONTRIBUTORS

Chemical Sciences, Department for Physics and Chemistry, Mahatma Gandhi University, Kottayam, Kerala, India Jide Wang, Key Laboratory of Oil and Gas Fine Chemicals, Ministry of Education and Xinjiang Uyghur Autonomous Region, College of Chemistry and Chemical Engineering, Xinjiang University, Urumqi, Xinjiang, People’s Republic of China Kwang Ho Won, Department of Chemical Engineering, Kyung Hee University, Yongin, Kyunggi-Do, South Korea Priti Xavier, Department of Materials Engineering, Indian Institute of Science, Bangalore, India Shimei Xu, Key Laboratory of Oil and Gas Fine Chemicals, Ministry of Education and Xinjiang Uyghur Autonomous Region, College of Chemistry and Chemical Engineering, Xinjiang University, Urumqi, Xinjiang, People’s Republic of China Wei Yu, Advanced Rheology Institute, Department of Polymer Science and Engineering, Shanghai Jiao Tong University, Shanghai, P. R. China Jinlong Zhu, Key Laboratory of Oil and Gas Fine Chemicals, Ministry of Education and Xinjiang Uyghur Autonomous Region, College of Chemistry and Chemical Engineering, Xinjiang University, Urumqi, Xinjiang, People’s Republic of China

1 MATERIALS FOR POLYMER NANOCOMPOSITES Jiji Abraham International and Inter University Centre for Nanoscience and Nanotechnology, Mahatma Gandhi University, Kottayam, Kerala, India

Soney C. George Centre for Nanoscience and Nanotechnology, Amal Jyothi College of Engineering, Kanjirappally, Kerala, India

Rene Muller Rheology and Polymer Processing, Institut Charles Sadron, Strasbourg, France

Nandakumar Kalarikkal International and Inter University Centre for Nanoscience and Nanotechnology, Mahatma Gandhi University, Kottayam, Kerala, India; School of Pure and Applied Physics, M.G University, Kottayam, Kerala, India

Sabu Thomas International and Inter University Centre for Nanoscience and Nanotechnology, Mahatma Gandhi University, Kottayam, Kerala, India; School of Chemical Science, M.G University, Kottayam, Kerala, India

1.1

INTRODUCTION

Nanotechnology is technology concerning processes that are relevant to physics, chemistry, and biology taking place at a length scale of 1 divided by 1000 million of a meter [1]. Nanotechnology is a fast growing ield concentrated on the invention Rheology and Processing of Polymer Nanocomposites, First Edition. Edited by Sabu Thomas, Rene Muller, and Jiji Abraham. © 2016 John Wiley & Sons, Inc. Published 2016 by John Wiley & Sons, Inc.

1

2

MATERIALS FOR POLYMER NANOCOMPOSITES

of functional materials, smart devices and systems by controlling matter on the nanometer scale and the exploitation of novel phenomena and properties at that length scale [2]. Nanotechnology is so important because it is relatively cheap, safe, and clean and the inancial rewards are relatively very high [3]. Signiicant investments by industry, academia and government are being made with the hope that advances in nanotechnology will have an intense and positive effect on our lives [4]. Nanostructured materials are materials with a microstructure and the characteristic length scale of which is on the order of a few nanometers. They have attracted great interest in recent years because of the unusual mechanical, electrical and optical properties by the combination of bulk and surface properties with the overall behavior. The ield of nanotechnology obviously refers to polymer science and technology, which includes polymer-based biomaterials, nanoparticle drug delivery, miniemulsion particles, fuel cell electrode, polymer-bound catalysts, layer-by-layer self-assembled polymer ilms, electrospun nanoibers, imprint lithography, polymer blends, and nanocomposites. In the ield of nanocomposites, polymer matrix-based nanocomposites have become a prominent area of current research and development in the ield of nanotechnology [5]. Polymer nanocomposites are polymer matrix composites in which the illers are less than 100 nm in at least one dimension. When incorporating illers with polymers, the beneicial features of both can be combined. The beneicial features that can be contributed from the reinforcing iller include mechanical strength; chemical and thermal stability; and electrical, ferroelectric, magnetic, and diverse optical properties. Apart from their improved properties, these nanocomposite materials are also easily extruded or molded to near-inal shape, simplifying their manufacturing. This lightweight advantage could have signiicant impact on environmental concerns and other potential beneits. From the beginning of polymer chemistry, the technique of incorporating microillers into the polymer matrix is used. The quality of traditional composite materials is not comparable to recent nanocomposite materials because of the poor dispersion and poor interaction between microiller and polymer matrix. The interest in polymer nanocomposites has emerged for several reasons. First, nanoscale illers often have properties that are different from the bulk properties of the same material [6]. Owing to the small size of nanoillers in comparison to microillers, early failure can be prevented, leading to nanocomposites with enhanced ductility and toughness [7, 8]. It has also been shown that nanoparticles can increase the electrical breakdown strength [9] and have small optical scattering defects [10] due to their small size. Owing to the large surface area of the illers, nanocomposites have a large volume of interfacial matrix material with properties different from the bulk polymer [11, 12]. This chapter focuses on the materials for the polymer nanocomposite in detail. The state of the art, new challenges, and opportunities in the area of polymer nanocomposite systems will be discussed in this chapter. The recent developments in the area of polymer nanocomposites will be highlighted. The various unresolved issues and new challenges in polymer nanocomposites will also be discussed.

NANOCOMPOSITE FRAMEWORK

1.2

3

NANOCOMPOSITE FRAMEWORK

The composite is a material that is formed from two or more components according to the end application and desired properties. The irst component is called the matrix, which can be metallic, polymeric, or ceramic. It controls the major properties of the composite, holds the iller materials, protects illers from the surrounding environment and transfers load to the illers. The second component is the reinforcement material, which is usually added in small amounts compared to the weight of the whole mixture. Reinforcement can be of different forms such as particles, ibers, iller, lake, and lamina. The properties of the composite are closely related to concentration; distribution; orientation; and the nature, size, and shape of reinforcements [13]. 1.2.1

Nanoscale Fillers

By scaling the particle size down to the nanometer scale, it has been shown that novel material properties can be obtained. Nanoparticles are materials of two or more dimensions, with size in the range of 1–100 nm. Nanoparticles show unique size-dependent physical and chemical properties: the chemical composition and the shape of a nanoparticle also inluence its speciic properties. Nanoparticles can thus be classiied based on dimension, source, chemical nature, size, shape, and so on. However, one interesting classiication can be based on the dimension. The illers can be classiied into three groups depending on their shape. They are 1D nanoillers such as nanorods, ibers, or tubes with varying aspect ratios; 2D illers such as platelets with a thickness of the lower nanometer range and the dimensions in length and width far exceed the particle thickness; 3D nanoparticles, which are spherical in shape (Fig. 1.1). 1.2.1.1 Zero-Dimensional Nanoillers Silsesquioxanes are nanostructures having the empirical formula RSiO1.5 , where R is a hydrogen atom or an organic functional group such as an alkyl, alkylene, acrylate, hydroxyl, or epoxide unit [14]. Polyhedral oligomeric silsesquioxane (POSS) is a true hybrid inorganic/organic chemical composite that possesses an inner inorganic silicon and oxygen core (SiO1.5 )n and external

(a)

(b)

(c)

Figure 1.1 Classiication of nanoscale illers: (a–c) 1D, 2D, and 3D nanomaterials.

MATERIALS FOR POLYMER NANOCOMPOSITES

4

organic substituents that can feature a range of polar or nonpolar functional groups. POSS nanostructures have diameters ranging from 1 to 3 nm [15]. The incorporation of POSS moieties into a polymeric material can dramatically improve its mechanical properties (e.g., strength, modulus, rigidity) as well as reduce its lammability, heat evolution, and viscosity during processing. These enhancements can apply to a wide range of applications such as commercial thermoplastic polymers, high-performance thermoplastic polymers, and thermosetting polymers [16, 17]. Both monofunctional and multifunctional monomers of these types have been used to prepare commercial and/or high-performance thermoplastic polymers [18–20] and thermosetting polymers [21, 22]. Properties of POSS-containing polymer composites depend on the successful incorporation of POSS particles into polymeric matrices. Two approaches have been adopted to incorporate POSS particles into polymer matrices: (i) chemical cross-linking and (ii) physical blending (Fig. 1.2). Semiconductor nanocrystals especially have generated a lot of interest among researchers in the past decades due to their wide range of applications in photonics, electronics, and optoelectronics [23, 24]. For the fabrication of devices, quantum dots (QDs) have to be well dispersed and must be compatible with the supporting matrix while transferring it into a composite [25–27]. Polymers are found to be the ideal candidate for the same. These multicomponent materials usually possess the combined novel properties of both the nanoparticles and the polymer matrix [28, 29]. Due to the organophobic surface of the QDs, they tend to agglomerate inside the polymer matrix, so surface functionalization of QDs may be needed to enhance the dispersion of iller in the polymer matrix [30].

HO R R O R Si O O Si O Si Si R R O O R O O Si Si Si Si O O RO R OH HO HO O R OH O O R Si Si Si Si O O R O R Si Si Si O Si O O O R R R HO R

R

R

Si

O

O Si R

O O

R Si O Si R O R Si O Si O O O R R OSi O Si O O O R Si O Si R R T8 (c)

R Si O Si O O OR O R R O Si O Si Si Si O Si OO OO R O R Si R Si O Si O R R T10 (d)

Si

O

O

Si

(a) R

R O

Si

Si

O

R

O O

R

R

Si

Si R

(b) R O Si O R Si Si O Si R O O R O OO Si R Si O OSi OR Si R O O Si O O R Si Si O O R R Si O R T12 (e) R

R Si OH OH R O O Si Si O R OH O R Si OSi O O O R Si Si O R R (f)

Figure 1.2 Structures of silsesquioxanes [14]: (a) random structure, (b) ladder structure, (c–e) cage structures, and (d) partial cage structure.

NANOCOMPOSITE FRAMEWORK

5

1.2.1.2 One-Dimensional Nanoillers One-dimensional nanoillers are nanorods, ibers, or tubes with varying aspect ratios. Rod like nanoparticles can impart anisotropic properties to composite materials. Carbon iber reinforced polymer matrix composites form a special class of high-performance materials, which has received huge research attention in the past several decades because of the unique combination of properties such as lightweight, higher speciic strength, stiffness, rigidity, corrosion, and environmental resistance. They are synthesized from the pyrolysis of hydrocarbons or carbon monoxide in the gaseous state in the presence of a catalyst [31, 32]. Nanocarbon ibers have typical dimensions with an outer diameter of 50–200 nm, inner diameter of 30–90 nm, and length in the range of 50–100 μm. Carbon nanoibers (CNFs) are known to have wide-ranging morphologies from a disordered bamboo-like structure [33] to highly graphitized “cup-stacked” [34] structures where the conical shells of the nanoiber are nested within each other. Vapor-grown CNFs have been used to reinforce a variety of polymers, including elastomers [35, 36], thermoplastics such as polypropylene (PP) [37–40], polycarbonate [41, 42], nylon [43], and thermosets such as epoxy (Fig. 1.3) [45, 46]. (a)

100 nm (c)

(b)

10 nm

10 nm

Figure 1.3 TEM images of the nanoscale structure of carbon nanoibers showing (a) disordered bamboo-like structures, reproduced from Merkulov et al. [33] with permission of AIP Publishing; (b) highly graphitized sidewall of a cup-stacked nanoibers showing the shell tilt angle, reproduced from Endo et al. [34] with permission of AIP Publishing; and (c) a nesting of the stacked layers (insets: molecular models), reproduced from Endo et al. [44] with permission of AIP Publishing.

MATERIALS FOR POLYMER NANOCOMPOSITES

6

However, the literature about nanocomposites with nanorods mainly comprises the huge and promising ield of carbon nanotube (CNT) composites. Since their discovery by Iijima [47], they have attracted very much and are now being used for many fundamental and advanced applications. CNTs, basically consisting of sheets of graphite rolled up into thin cylinders, with Young’s modulus of about 1 TPa and tensile strength up to 63 GPa are considered to be ideal reinforcement materials. Multiwalled nanotube (MWNT) comprises a number of graphene layers coaxially rolled together to form a cylindrical tube. Each carbon atom within the atomic layer of a graphene sheet is covalently bonded to three neighboring carbon atoms. Three sp2 orbitals on each carbon form s-bonds with three other carbon atoms. One 2p orbital remains unhybridized on each carbon; these orbitals perpendicular to the plane of the carbon ring combine to form the �-bonds. The atomic interactions between the neighboring layers are the van der Waals forces [48]. The outer diameter of MWNTs is about 3–10 nm. The outstanding thermal and electric properties, combined with their high speciic stiffness and strength, and very large aspect ratios have stimulated the development of nanotube-reinforced composites for both structural and functional applications [49]. The irst polymer nanocomposites using CNTs as a iller were reported in 1994 by Ajayan et al [50]. Introducing CNTs to polymer matrices modiies mechanical [51], electrical [52], thermal [53], and morphological properties [54] of the produced nanocomposite (Fig. 1.4). Although CNTs have excellent properties, major challenges faced during the incorporation of nanoillers include their processing dificulty and tendency to form agglomerates [56, 57]. The ine dispersion of nanoillers in polymer has been still the most challenging task for their practical applications. Several strategies have been developed for the better dispersion of illers in the polymer matrix, which includes

(002)

(004) (002) 7 nm (a)

10 nm (b)

Figure 1.4 HRTEM images of MWNTs: (a) 18-nm-diameter nanotube produced at 675 ∘ C and (b) 180-nm-diameter nanotube produced at 775 ∘ C. The insets are the corresponding nanodiffraction patterns showing both tubes well graphitized at low synthesis temperatures. Reproduced from Andrews et al. [55] with permission of American Chemical Society.

NANOCOMPOSITE FRAMEWORK

7

covalent and noncovalent functionalization of CNT [58]. The nanotube–polymer interaction is believed to play an important role in determining the overall properties of the nanocomposites. Several studies have been reported based on surface-modiied CNT polymer nanocomposites [59–61]. The halloysite nanotubes (HNTs) is a kind of alumina silicate clay (Al2 Si2 O5 (OH)4 ⋅H2 O with 1:1 layer) having hollow micro- and nanotubular structure. It has been reported that HNTs have typical dimensions of 10–50 nm in the outer diameter and 5–20 nm in the inner diameter with 2–40 nm length [62, 63]. HNTs have high mechanical strength and modulus, and these features make it an ideal candidate for reinforcement in polymer nanocomposites. So many varieties of biological and nonbiological applications are recommended for HNT-based polymer nanocomposites [64]. 1.2.1.3 Two-Dimensional Nanoillers Two-dimensional illers are platelets with thickness of lower nanometer range and the dimensions in length and width far exceed the particle thickness. Typical illers used in polymer nanocomposites (PNCs) as platelets include layered silicates or layered double hydroxides (LDHs) such as graphene. The average interparticle spacing between layers depends on the extent of intercalation and mineral concentration, generally the higher the mineral concentration the smaller the spacing. The clay known as montmorillonite (MMT) consists of platelets with an inner octahedral layer sandwiched between two silicate tetrahedral layers [65]. The single layers have a planar structure with a thickness of about 1 nm and usually a length of several hundred nanometers. Due to the isomorphic substitution of Al3+ into the silicate layers or Mg2+ for Al3+ , the layers bear negative surface charges being compensated by inorganic cations adsorbed in the interlayer space. Because of their hydrophilic surface, natural layered silicates show poor miscibility with polymers. Thus, for the preparation of clay nanocomposites, the layers have to be separated from each other via ion exchange of the inorganic cations with organic cations such as alkylammonium ions [66]. Among the layered silicates, MMT is commonly used as reinforcement for the polymer–clay because it is an environmentally friendly material, which is readily available in large quantities with relatively low cost, and its intercalation chemistry is well understood. The use of organoclays as precursors to nanocomposite formation has been extended into various polymer systems including epoxys, polyurethanes, polyimides, nitrile rubber, polyesters, polypropylene, polystyrene (PS), and polysiloxanes [67–69]. In phase separated nanocomposites the polymer is unable to intercalate within the clay layers and the clay is dispersed as aggregates or particles with layers stacked together within the polymer matrix. Intercalated structures are self-assembled, well-ordered multilayered structures where the extended polymer chains are inserted into the gallery space of the clays. This leads to an expansion of the interlayer spacing. In an exfoliated structure, individual silicate sheets lose their layered geometry as a result of delamination and are dispersed as nanoscale platelets in a polymer matrix [70].

MATERIALS FOR POLYMER NANOCOMPOSITES

8

LDHs form a typical class of layered minerals that are frequently termed anionic clay minerals. LDHs can be of both natural origin and synthetically prepared in the laboratory. The general chemical formula for LDHs is [MII 1−x MIII (OH)2 ]x+ (An− )x/n ⋅yH2 O, where MII represents a divalent metal ion, for example, Mg2+ , Ca2+ , Zn2+ , and so on; MIII represents a trivalent metal ion, for example, Al3+ ,Cr3+ , Fe3+ , Co3+ , and so on; and An− represents an anion, for example, Cl− , CO3 2− , NO3 − , and so on. The anions remain in the interlayer region. The synthesis of nanosized LDH platelets can be generally classiied into two approaches: “bottom-up” and “top-down.” To date, the “top-down” synthesis is the most widely developed method. The delamination and reconstruction method is another promising technique for synthesizing organomodiied LDHs. One can obtain exfoliated LDH layers by this method, which subsequently aid in the dispersion of these layers into polymers. Since the charge density of LDH is very high, it requires the modiication of the LDH interlamellar environment and then selection of an appropriate solvent system, for example, ion-exchange intercalation of the LDH with anionic surfactant such as dodecyl sulfate (DDS). Delamination/exfoliation then occurs when it is dispersed in a highly polar solvent, which is able to solvate the hydrophobic tails of the intercalated anions (Fig. 1.5) [72]. The modiication of LDH materials is almost a requirement prior to the fabrication of elastomer composites because this process facilitates the intercalation of the elastomer chains, resulting in enhanced properties. The basic goal of the organic modiication process is to increase the interlayer spacing of LDH materials to make the intercalation of large species, such as polymer chains and chain segments, easier. It is believed that the anionic organic surfactants that have at least one anionic end group and a long hydrophobic tail are the best materials for serving the desired purpose [73]. Although there are many possible strategies to synthesize exfoliated polymer/LDH nanocomposites, generally the methods can be classiied into three principal options: (i) intercalation of the monomer molecules and in situ polymerization, (ii) direct intercalation of extended polymer chains, (iii) pre-exfoliation and followed by mixing with polymer, as shown in Figure 1.6a [74]. The use of modiied LDHs with elastomers substantially improves their mechanical, thermal, and optical properties. Even “smart properties” of elastomers, such as reversible thermotropic optical characteristics, have been realized with the use of LDH-based multifunctional additives in rubber formulations [75].

Oxidation Intercalation (l2/CHCI3) Brucite-like crystal

LDH crystal

Ion-exchange

Exfoliation

(NaCIO4)

(HCONH2)

LDH crystal

LDH nanosheets

Figure 1.5 Schematic illustration of topochemical synthesis and exfoliation of Co2+ –Fe3+ LDH. Reproduced from Renzhi et al. [71] with permission of American Chemical Society.

NANOCOMPOSITE FRAMEWORK

9

2D host material Monomer Δ, hv, e– (1)

(2)

In situ polymerization

(a)

Nanocomposite 2D host material

Polymer (1)

(2)

(b)

Exfoliated layers

(1)

(2)

Δ, hv, e–

(c)

Figure 1.6 Pathway of nanocomposite preparation by (a) monomer exchange and in situ polymerization, (b) direct polymer exchange, and (c) restacking of the exfoliated layers over the polymer. Reproduced from Leroux and Besse [74] with permission of American Chemical Society.

10

MATERIALS FOR POLYMER NANOCOMPOSITES

Natural lake graphite (NFG) is the polycrystalline form of carbon comprising layered planes containing hexagonal arrays of carbon atoms to form an atomically lat-stacked material in three dimensions. Covalent bonds bind the carbon atoms in the same plane together with van der waals forces between successive layers separated by 0.337 nm. Because of the very weak van der Waals forces, it is quite easy for small atoms, ions, and molecules to intercalate between the layers to form expanded graphite (EG) [76], graphite nanoplatelets (GNPs) [77], and graphene [78]. Expanded graphite (EG), a form of graphite intercalation compound (GIC), is fabricated from NFG through chemical or thermal expansion [79]. Nanosheets or platelets (GNPs) have proved their signiicance as strong, versatile, and inexpensive illers in composite materials [80]. A schematic representation showing all kinds of graphitic derivatives and their interdependence is given in Figure 1.6a–c. Since its discovery by Geim and Novoselov [81] and Novoselov et al. [82] in 2004, graphene has attracted in both academia and industry because it is one-atom thick and consists of sp2 carbon atoms arranged in a honeycomb lattice structure leading to exceptional in-plane functional and mechanical properties. The major fabrication methods of graphene include micromechanical cleavage [83]; chemical vapor deposition (CVD) [84]; and the oxidation, exfoliation, and reduction of graphite [85]. Two-dimensional graphene is an allotrope of carbon in which each carbon atom is bonded with another carbon by sp2 bonds. Here, carbon atoms are densely packed in a honeycomb crystal lattice with a bond length of 0.141 nm. Density of graphene is around 0.77 gm/cm3 , and a single-layered graphene is predicted to have a large surface area close to 2600 m2 gm. The important properties of graphene are given in Figure 1.7. Pristine graphene materials are unsuitable for intercalation by large species, such as polymer chains, because graphene as a bulk material has a pronounced tendency to agglomerate in a polymer matrix [86, 87]. The functional groups attached to graphene can be small molecules or polymer chains, and this can be performed using chemical methods [88–90]. Polymer–graphene nanocomposites show not only improved mechanical properties but also impressive functional properties, such as electrical (semi-)conductivity, unique photonic/optical transportation, anisotropic transport, low permeability, and luorescence quenching [91, 92]. A thorough investigation of the properties of various graphitic illers, such as NFG, expanded graphite (EG), GNP, and graphene, is undertaken by various researchers [93]. 1.2.1.4 Three-Dimensional Nanoillers Fullerenes pertain to the carbon molecules of C28 , C32 , C44 , C50 , C58 , C60 , C70 , C72 , C78 , C80 , and C82 [94]. They have many interesting properties, such as high surface area, porosity, thermal stability, nontoxicity, biocompatibility, and hydrophilic functionalization. Many of the polymer scientists tried to use this molecule as a building block to construct novel materials with unusual properties. Fullerene C60 and its polymeric composites have been demonstrated to possess interesting optoelectronic properties, photovoltaic, and optical limiting applications [95]. Carbon black, the amorphous form of carbon, is primarily used as commercial iller/additive of ultraviolet (UV) light stabilizer, antioxidant and antistatic agent in

NANOCOMPOSITE FRAMEWORK

11

Young´s modulus 1 TPa Fracture strength 125 GPa Optical transparency ~98%

Zero band gap material

Graphene properties

Thermal conductivity 5000 W m/K

Electrical conductivity 7200 S/m

Charge carrier mobility 200,000 cm2 V/s

Figure 1.7 Properties of graphene.

rubber industry, pigment or colorant in dye industry, conductive iller in polymer, and composite industry for semiconductive applications [96]. Carbon black has become one of the most widely used reinforcements in engineering applications of polymer-based composites due to its high temperature tolerance, elastic modulus and tensile strength, low weight, and thermal expansion [97]. Both high surface area and high degrees of porosity are the critical characteristics of carbon black that impart improvement in the overall performance at lower loadings in polymer composites [98–101]. 1.2.1.5 Metal Oxides Polymer nanocomposites containing surface-engineered metal oxide continuously offer new opportunities to enhance desired properties or functionalities such as optical transparency, ductility, lexibility, or molecular mobility [102, 103]. In order to prevent the agglomeration of these inorganic metal oxides in organic polymer matrix, various kinds of functional methods are adopted that include the use of surfactants [104] and silane coupling agents [105]. Polymer matrices reinforced with modiied inorganic nanoparticles combine the functionalities of polymer matrices, which include low weight and easy formability with the unique features of the inorganic nanoparticles. The nanocomposites obtained by

12

MATERIALS FOR POLYMER NANOCOMPOSITES

incorporation of these types of materials can lead to improvements in several areas such as optical, mechanical, electrical, magnetic, rheological, and ire retardant properties [106, 107]. Development of ceramic nanoparticles with improved properties has been studied with much success in several areas such as synthesis and surface science. Examples of ceramics are silica, alumina, titania, zirconia, silicon nitride, silicon carbide, and so on. Nanosized silica, SiO2 , has been widely used as iller in engineering composite. Some of the widely used methods to synthesize silica nanoparticles are sol–gel process, reverse microemulsion, and lame synthesis. The sol–gel process is widely used to produce pure silica particles due to its ability to control the particle size, size distribution, and morphology through systematic monitoring of reaction parameters. The chemical modiication of silica surface with organofunctional groups is an important step toward the preparation of silica–polymer nanocomposites. More precisely, the surface modiications have been reported to enhance the afinity between the organic and inorganic phases and at the same time improve the dispersion of silica nanoparticles within the polymer matrix. Surface modiication of silica nanoparticles can be carried out by using various types of silane coupling agents. Surface modiication makes the possibility to graft or conjugate the nanostructured silica with polymers or proteins for future applications in biotechnology and medicine such as dental illing composites, cancer treatment, and drug delivery ZnO is an inorganic iller and a semiconductor material existing in a diversity of structures. It is extensively used due to its distinctive optical, electrical, photocatalytic, optoelectronic, antibacterial, and dermatological properties [108, 109] Iron oxide (Fe2 O3 ), the most common oxide of iron, has important magnetic properties and is a convenient compound for the general study of polymorphism and the magnetic and structural phase transitions of nanoparticles. The existence of amorphous Fe2 O3 and four polymorphs (�, �, �, and �) is well established [110, 111]. Zirconium dioxide possesses excellent properties, namely high strength, high fracture toughness, excellent wear resistance, high hardness, and excellent chemical resistance. Hence, ZrO2 nanoparticles appear as an attractive option to be used as reinforcement of polymers, in order to produce composites with enhanced performance [112]. TiO2 is an example for inorganic iller. It has so many interesting properties making it a versatile one. Titanium dioxide is an inexpensive, nontoxic, and photostable inorganic material, which has good optical and photocatalytic properties for many applications [113]. Due to its high refractive index and ability to relect and refract or scatter light more effectively than any other pigment, titanium dioxide has for many years served and is still serving as a white pigment. It is also used to provide protection against UV effect because it is capable of absorbing UV light. Al2 O3 nanoparticles can be prepared by lame spray pyrolysis, reverse microemulsion, sol–gel, precipitation, and freeze drying [114, 115]. It has excellent optical, transport, mechanical, and fracture properties [116, 117]. It has applications in various ields such as wastewater and soil treatment by the removal of heavy metal ions and antimicrobial applications, ceramic ultrailters and membranes to remove pathogenic microorganisms, for gas separation, in catalysis and absorption processes and drug delivery [118, 119].

NANOCOMPOSITE FRAMEWORK

1.2.2

13

Choice of Polymeric Matrices

By taking the beneits of ininite number of monomers, oligomers, and chemicals available, we can tune the properties of matrices based on our desired application. Properties that can tuned or controlled include controlled hydrophobicity, ionizability, crystallinity, transparency, toughness, strength, densities, conductivity, and degradability [83, 120]. Polymers are giant molecules with molar mass ranging from several thousands to several millions and are composed of a large number of smaller parts joined together through chemical bonds. This era can be called as polymer age since polymer can be used for the production of various things, which includes plastic buckets, cups and saucers, children’s toys, packaging bags, synthetic clothing materials, automobile tires, gears and seals, electrical insulating materials, and machine parts, which has completely revolutionized the daily life as well as the industrial scenario. The word polymer is derived from Greek words poly meaning many and mers meaning parts or units of high molecular mass, each molecule of which consists of a very large number of single structural units joined together in a regular manner. The reaction by which the monomers combine to form a polymer is known as polymerization [121]. The polymerization is a chemical reaction in which two or more substances combine together with or without evolution of anything such as water, heat, or any other solvents to form a molecule of high molecular weight. The product is called polymer and the starting material is called monomer. 1.2.2.1 Classiication of Polymers Polymer is a generic name given to a vast number of materials of high molecular weight. These materials exist in countless forms and numbers because of very large number and type of atoms present in their molecule [122]. Polymer is the most widely used matrix material in composites. Polymers are lighter in weight, softer, and easier to be shaped than metals or ceramics. Polymers themselves are soft and have low strength, low electrical conductivity, and low thermal stability. Owing to their lighter weight and ease of manufacturing, polymers have many industrial applications (Fig. 1.8). Polymers can be generally classiied based on the following: 1) 2) 3) 4) 5)

Their origin – natural and synthetic Their structure Molecular forces Polymerization reaction Their steric structure

1.2.2.1.1 Classiication Based on Source There are three subcategories in this type of classiication. (i) Natural polymers: These polymers are found in nature such as in plants and animals. Examples are proteins, cellulose, starch, resins, and rubber. (ii) Semisynthetic polymers: These polymers are obtained by simple chemical treatment of natural polymers to change their physical properties, for example, starch and silicones. (iii) Synthetic polymers: The ibers obtained by the polymerization of simple chemical molecules in laboratory are synthetic polymers, for example,

MATERIALS FOR POLYMER NANOCOMPOSITES

14

Based on origin

Based on structure

Based on molecular forces

Based on mode of polymerization

Based on steric structure

Natural polymers

Homopolymer

Elastomers

Addition polymers

Isotactic

Semisynthetic

Heteropolymer

Thermoplastic

Condensation polymers

Syndiotactic

Synthetic

Thermosets

Atactic

Fibers

Figure 1.8

Classiication of polymers.

nylon, polyethene, polystyrene, synthetic rubber, polyvinyl chloride (PVC), Telon, and so on. 1.2.2.1.2 Classiication Based on Structure Polymers that are formed from single monomers are referred to as homopolymers and are produced from two or more monomers called heteropolymers or copolymers. Many of the well-known polymers are homopolymers such as polyethylene, polypropylene, and PVC; polymethyl methacrylate (PMMA); polystyrene; polytetralouroethylene (PTFE); and poly acrylonitrile. There are several types of copolymers that include alternating copolymer, random copolymer, block copolymer, and graft copolymer. 1.2.2.1.3 Classiication Based on Molecular Forces Mechanical properties of polymers such as tensile strength, toughness, and elasticity depend on intermolecular forces such as van der waals forces and hydrogen bonding. On the basis of these forces, they are classiied as elastomers, ibers, thermoplastics, and thermosetting polymers. An elastomer is a polymer with viscoelasticity (having both viscosity and elasticity) and very weak intermolecular forces, generally having low Young’s modulus and high failure strain compared with other materials [123]. They are lexible or “rubbery” materials that can readily be deformed and return rapidly to almost their original shape and size once released from stress, thus making them able to form reliable seals. A few “cross-links” are introduced in between the chains, which help the polymer to retract to its original position after the force is released as in vulcanized rubber. Natural and synthetic rubbers are common examples of elastomers. Fibers are the thread-forming solids that possess high tensile strength and high modulus. These characteristics can be attributed to the strong intermolecular forces such as hydrogen bonding. These strong forces also lead to close packing of chains and thus impart crystalline nature. They have much lower elasticity compared to

NANOCOMPOSITE FRAMEWORK

15

plastics and elastomers, for example, polyamides (nylon 6,6), polyesters (terylene), and so on. A thermoplastic or thermosoftening plastic is a plastic material, typically a polymer that becomes lexible or moldable above a speciic temperature and solidiies upon cooling [124]. In contrast to elastomers, plastics have a greater stiffness and lack reversible elasticity. Thermosetting polymers undergo certain chemical changes on heating and convert themselves into an infusible mass. The curing or setting process involves chemical reaction leading to further growth and cross-linking of the polymer chain molecules, thus producing giant molecules such as phenolic resins, urea, epoxy resins, and diene rubbers. 1.2.2.1.4 Based on Polymerization Reaction Chain-growth polymerization (or addition polymerization) involves the linking of molecules having double or triple carbon–carbon bonds. Unsaturated monomers that have extra internal bonds are able to break and link up with other monomers to form a repeating chain. Chain-growth polymerization is involved in the manufacture of polymers such as polyethylene, polypropylene, PVC, PMMA, PS, PTFE, polyacrylonitrile, and so on. Different forms of chain-growth polymerization include free radical polymerization, cationic addition polymerization, anionic addition polymerization, and coordination polymerization reactions. Step-reaction (condensation) polymerization is another type of polymerization. This polymerization method typically produces polymers of lower molecular weight than chain reactions and requires higher temperatures to occur. Stepwise reactions involve two different types of difunctional monomers that react with one another forming a chain. In this reaction, some of the atoms of the monomer are split off in the reaction as water, alcohol, ammonia, or carbon dioxide. Examples for condensation polymers are polyesters, polyamides, phenol–methanal plastics, polyurethanes, and so on. 1.2.2.1.5 Based on Steric Structure Another method of classifying polymers is by examining their steric structure. Polymers with side chains can be divided into two classes: one (stereoregular) that has a recurring pattern in terms of stereochemistry and the other (atactic) with no regular structure. Isotactic polymer: It is a type of polymer in which the characteristic groups are arranged in the same side of the main chain. A polymer is said to be syndiotactic if the characteristic groups are arranged in an alternate manner and it is called atactic if the characteristic groups are arranged in a random manner around the main chain. The scientiic and commercial progress in the area of polymer blends during the past decades was tremendous and was driven by the realization that by blending, new materials can be developed and can be implemented more rapidly and economically [125]. Interpenetrating polymer network (IPN) refers to multicomponent materials consisting of two or more cross-linked networks in which at least one is cross-linked in the presence of another [126]. IPN is emerging as a promising matrix to reinforce nanoillers [127]. Dendrimers are molecules with globular structure in

16

MATERIALS FOR POLYMER NANOCOMPOSITES

which well-deined branches radiate from a central core, becoming more branched and crowded as they move to periphery. These types of polymers have received considerable interest with applications that includes drug delivery agents, micelle mimics, and so on [128, 129].

1.3 RECENT DEVELOPMENTS AND OPPORTUNITIES IN THE AREA OF POLYMER NANOCOMPOSITES Polymer nanocomposites containing organic and inorganic nanoillers have attracted extensive interest from academic and industrial perspectives due to the unique characteristics of nanoparticles, including their large surface area, high surface reactivity, and relatively low cost. The POSS nanocomposites are composite materials reinforced with silica cages, ultraine illers of nanometer size, almost equal to the size of the polymer matrix. Several high-performance POSS nanocomposites can be used as light-emitting diodes, liquid crystals, photoresist materials, low dielectric constant materials, self-assembled block copolymers, and nanoparticles. QD-based polymer nanocomposites can be used to fabricate solar cells such as light-emitting diodes. By combining the excellent properties such as mechanical, electrical, and thermal properties of CNTs with polymers renders a vast range of potential applications. Large number of studies have been done to use these properties for industrial applications such as energy storage devices, electronics, sporting goods, automobiles, ilters, sensors, and so on. Due to heat absorbing capability, these nanocomposites can be used in aerospace industries as electromagnetic wave absorption materials [130]. Reinforcement of CNTs into epoxy could improve the mechanical properties such as strength, stiffness, and durability of materials that could be used for further industrial applications as sports goods, such as badminton rackets, golf and hockey sticks, and ski poles. CNT/polymer nanocomposites also play very signiicant role in automobile engineering. Polymer nanocomposites reinforced with HNTs possess highly increased tensile and lexural strength, elastic moduli, and improved toughness. HNT/polymer nanocomposites also exhibit elevated thermal resistance, lame retardancy, and unique crystallization behavior [131]. Due to the tubular microstructure and the biocompatibility of HNTs, nanocomposites of HNT/polymer have demonstrated good drug encapsulation and sustained release abilities, gaining them extensive use as tissue engineering scaffolds and drug carriers [132, 133]. Other than biomedical applications, HNTs have potential applications in high-performance composites for aircraft/automobile industries and environmental protection. Graphene-based PNCs represent one of the most technologically promising developments to emerge from the interface of graphene-based materials and polymer materials. Conductive graphene-based PNCs can ind applications in various ields such as ield effect transistors [134], solar cells (and other optoelectronic applications) [135], energy storage devices [136], and electromagnetic wave interference shielding and antistatic coatings [137]. The mechanical reinforcement achieved at low loadings of graphene offers potential uses in weight-sensitive aerospace and automotive applications, and improved barrier

CHALLENGES IN THE AREA OF POLYMER NANOCOMPOSITES

17

properties of graphene-illed composites suggest their use in packaging applications. An emerging research direction for graphene-based composites is focused on biomedical applications [138, 139]. Since the polymer/silica nanocomposites can not only improve the physical properties such as the mechanical properties and thermal properties of the materials but also exhibit some unique properties, which have attracted very much in many industries. Apart from common plastics and rubber reinforcement, many other potential and practical applications of this type of nanocomposite have been reported: coatings [140, 141], lame-retardant materials [142], optical devices [143, 144], electronics and optical packaging materials [145], photoresist materials [146], pervaporation membrane [146], ultrapermeable reverse-selective membranes, proton exchange membranes, and sensors [147, 148]. The incorporation of metal oxide nanoillers into organic matrices provides superior mechanical, optical, electronic, and thermal properties for the resulting organic–inorganic nanocomposite materials [149].

1.4

CHALLENGES IN THE AREA OF POLYMER NANOCOMPOSITES

Polymer nanocomposites are the excellent materials that ind various applications in our daily life. There is still a considerable uncertainty in theoretical modeling and experimental characterization of the nanoscale reinforcement materials, particularly nanotubes. Then, there is a lack of understanding of the interfacial bonding between the reinforcements and the matrix material from both analytical and experimental viewpoints. The improvement in properties and applications of these composites will depend on how effectively we can handle the challenges. Some key challenges are as follows: • The cost of nanoparticles and their availability are the challenges that remain to achieve good dispersion that pose signiicant obstacles to obtain improved properties to the nanocomposite materials. • The critical challenges lie in how to prepare structure-controllable nanomaterial with high purity, geometrical identity, and consistently dependable high performance and how to break up nanomaterial products to obtain isolated nanoparticles. • The next immediate challenge relates to the composite processing. The full exploitation of nanoiller-based nanocomposites will be determined both by the level of iller dispersion and alignment and by the cost-effective manufacturing of the inal material, then how to enhance load transfer from a matrix to iller reinforcement, and so on. Proper dispersion as well as good compatibility between iller and polymer is the main factor that controls the properties. • Among the many challenges as PNCs move beyond commodity plastic applications, precise morphology control is paramount [149]. Random arrangements of nanoparticles will not provide optimized electrical, thermal, or optical performance for many potential high-technology applications, such

MATERIALS FOR POLYMER NANOCOMPOSITES

18

•

•

•

•

as dielectric for electronic packaging, printed lexible electronics, engineered aerospace structural components, reconigurable conductive adhesives, and optical gratings to just mention a few. Most applications of nanocomposites with the exception of packaging materials are intended for long-term and/or outdoor use. It is well documented that inorganic illers often experimentally show a negative effect on the oxidative stability of the polymer independent of the structure, however, to a varying extent [150]. To moderate the negative inluence of illers on the (photo)oxidative stability, blocking of the active sites on the iller by the so-called iller deactivators or coupling agents is a potential solution. Through adjustment of the stabilizer composition and loading, it is possible to achieve protection of the polymer nanocomposite against oxidation and photooxidation to an extent as known from unilled polymers and needed for the individual application [151, 152]. One of the challenges in developing PNCs for advanced technology applications is a limited ability to predict the properties. Although the techniques exist to tailor the surface chemistry and structure of nanoparticle surfaces [153, 154], the impact of the nanoscale iller surface on the morphology, dynamics, and properties of the surrounding polymer chains cannot be quantitatively predicted. Other challenges include predicting the impact of heterogeneous iller distribution and iller geometries (e.g., wavy ibers). There are still many unresolved issues that need to be addressed theoretically and experimentally to harness the maximum beneits from nanomaterials in polymer composite systems. With the development of nanomaterials, the safety of nanomaterial is of special importance and the health hazards caused by many of these smart materials are of still unclear. It is generally agreed that small size means easy access to living organisms via inhalation or transdermally, and this may lead to an increased risk to living organisms.

1.5 RELATIONSHIPS OF MACROSCOPIC RHEOLOGICAL PROPERTIES TO NANOSCALE STRUCTURAL VARIABLES A direct consequence of incorporation of illers in molten polymers is a signiicant change in their steady shear viscosity behavior and the viscoelastic properties [155, 156]. Owing to the possibility to achieve thermodynamic equilibrium conditions, measurements of composition and condition dependencies of viscoelastic properties in the molten state are generally useful for theoretical prediction of the structure–property relationships in composite materials. As the iller nanostructure, the interparticle and polymer–iller interactions can all strongly inluence both linear and nonlinear viscoelastic behavior; rheology appears to be a suitable technique to obtain reliable experimental data on polymer nanocomposites. Rheological experiments can be used to probe the properties of the interfacial region more precisely. The loss modulus is sensitive to the distribution of relaxation times (relaxation spectra) of the polymer matrix. When nanoiller is added, the mobility of

CONCLUSION

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the polymer chains is altered and the relaxation spectra can either shift or broaden. Thus, rheology has been used in nanoscale composites to probe the extent, structure, and properties of the interfacial region [157]. Elastomers illed with nanoparticles show a solid-like behavior response, which includes a nonterminal zone of relaxation and a shear-thinning dependence of viscosity on particle concentration and/or dispersion. This behavior arises due to the formation of network structure by polymer–particle or/and particle–particle interactions. The strain dependency of the dynamic viscoelastic properties of elastomers is known as the Payne effect [158] and is well known in elastomers for 40 years. It is well established that rubber-like materials exhibit an appreciable change in their mechanical properties (stress softening) resulting from the irst tensile experiment. The well-known phenomenon known as Mullins effect [159] is due to following reasons: (i) physical disentanglement of rubber chains, (ii) decrease in the interactions between polymer molecules and iller surfaces, (iii) iller network breakdown, and (iv) chain scission of rubber molecules. On examining the viscoelastic behavior of PS/SiO2 , PP/MMT nanocomposites, both percolation threshold and limit of linearity decrease with an increase in the exfoliation state of organoclay platelets whereas they increase with the dispersion of fumed silica by surface grafting of end-tethered chains. From these results on thermoplastic nanocomposites, one could conclude that the iller networking is the primary structural variable controlling their viscoelastic properties. But in the case of elastomers, that is, polymers with long chains and sometimes with particular viscoelastic behavior, the iller network appears to be a second-order structural parameter affecting the viscoelastic response of the nanocomposite. Kalfus and Jancar [160] showed that the modulus recovery time was governed by the chain relaxation processes in the polymer matrix near the iller surface. As a result, in this study, iller agglomeration and/or network is less important representing only a second-order contribution to the nonlinear viscoelastic response of a nanocomposite. It is concluded that the linear and nonlinear rheological properties of polymer nanocomposites are consistent with a network structure of weakly agglomerated particles, which is combined with a mechanism of polymer chain relaxation at the iller surface vicinity governed by the polymer–particle interactions.

1.6

CONCLUSION

Polymer nanocomposites are materials possessing unique properties as new materials and used for academic research as well as for the development of innovative industrial applications. These materials possess characteristic properties of both polymer and iller. Various types of nanomaterials can be used as reinforcing illers in polymer nanocomposites based on their size, shape dimension, and surface area. In developing these composites, the nanomaterials have a strong tendency to form aggregates due to their large surface area, so in order to improve dispersion stability and compatibility with matrix, their surfaces should be modiied either by grafting polymers or by absorption of small molecules, such as surface-modifying agents. Polymer

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nanocomposites offer both great potential and great challenges, marking it as a vibrant area of work for years to come. The improvement and application of these composites will depend on how effectively we can handle the challenges. Nanocomposites represent one of the new classes of materials, but further research and development is needed before they gain signiicant position in the market.

ACKNOWLEDGMENTS The authors would like to thank Council for Scientiic and Industrial Research (CSIR), Delhi, DST Nano Mission India, for the inancial support.

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137. Liang JJ, Wang Y, Huang Y, Ma YF, Liu ZF, Cai FM, et al. Carbon 2009;47:922e5. 138. Wenrong Y, Kyle RR, Simon PR, Pall T, Gooding JJ, Filip B. Angew Chem Int Ed 2010;49:2114e38. 139. Shen H, Zhang L, Liu M, Zhang Z. Biomedical applications of graphene. Theranostics 2012;2(3). 140. Abdullayev E, Abbasov V, Tursunbayeva A, Portnov V, Ibrahimov H, Mukhtarova G, Lvov Y. Self-healing coatings based on halloysite clay polymer composites for protection of copper alloys. ACS Appl Mater Interfaces 2013;5(10):4464–4471. 141. Meera KM, Sankar RM, Murali A, Jaisankar SN, Mandal AB. Sol–gel network silica/modiied montmorillonite clay hybrid nanocomposites for hydrophobic surface coatings. Colloids Surf B Biointerfaces 2012;90(1):204–210. 142. Laufer G, Kirkland C, Cain AA, Grunlan JC. Clay–chitosan nanobrick walls: Completely renewable gas barrier and lame-retardant nanocoatings. ACS Appl Mater Interfaces 2012;4(3):1643–1649. 143. Kim Y, Chang J-H. Colorless and transparent polyimide nanocomposites: Thermooptical properties, morphology, and gas permeation. Macromol Res 2013;21(2):228–233. 144. Kunz DA, Schmid J, Feicht P, Erath J, Fery A, Breu J. Clay-based nanocomposite coating for lexible optoelectronics applying commercial polymers. ACS Nano 2013;7(5):4275–4280. 145. Sun YY, Zhang ZQ, Moon KS, Wong CPJ. Polym Sci B 2004;42:3849. 146. Cho JD, Ju HT, Park YS, Hong JW. Glass transition and relaxation behavior of epoxy nanocomposites. Macromol Mater Eng 2006;291:1155. 147. Jose T, George SC, Maya MG, Maria HJ, Wilson R, Thomas S. Effect of bentonite clay on the mechanical, thermal, and pervaporation performance of the poly(vinyl alcohol) nanocomposite membranes. Ind Eng Chem Res 2014;53:16820–16831. DOI: dx.doi.org/10.1021/ie502632p. 148. Korotcenkov G. Nanocomposites in Gas Sensors: Promising Approach to Gas Sensor Optimization. Handbook of Gas Sensor Materials Integrated Analytical Systems. Springer; 2014. p 181–184. 149. Kango S, Kalia S, Celli A, Njugunad J, Habibie Y, Kumar R. Surface modiication of inorganic nanoparticles for development of organic–inorganic nanocomposites—A review. Prog Polym Sci 2013;38:1232–1261. 150. Vaia RA, Maguire JF. Polymer nanocomposites with prescribed morphology: Going beyond nanoparticle-illed polymers. Chem Mater 2007;19:2736–2751. 151. Pfaendner R. Nanocomposites: Industrial opportunity or challenge? Polym Degrad Stab 2010;95:369e373. 152. Chmela S, Fiedlerova A, Borsig E, Erler J, Mülhaupt R. Photo-oxidation and stabilization of sPP and ipp/boehmite-disperal nanocomposites. J Macromol Sci 2007;44:1027e34. 153. Chin H, Solera PS, Horsey DW, Kaprinidis N, Sitzmann EV. Synergistic combinations of nano-scaled illers and hindered amine light stabilizers. US patent 7084197, assigned to Ciba Specialty Chemicals Corporation; 2006. 154. Ajayan PM, Braun PV, Schadler LS. Nanocomposite Science and Technology. Weinheim, Germany: Wiley-VCH Verlag GmbH & Co. KGaA; 2003. Chapter 2.

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155. Rong MZ, Zhang MQ, Ruan WH. Surface modiication of nanoscale illers for improving properties of polymer nanocomposites: A review. Mater Sci Technol 2006;22(7):787–796. 156. Cassagnau P. Morphology and viscoelasticity of PP/TiO2 nanocomposites prepared by in situ sol–gel method. Polymer 2008;49:2183. 157. Zhu A-J, Sternstein SS. Macromolecules 2002;35(19):7262–7273. 158. Payne AR. J Appl Polym Sci 1962;6:57. 159. Mullins L. Rubber Chem Technol 1969;42:339. 160. Kalfus J, Jancar J. J Polym Sci Polym Phys Ed 2007;45:1380.

2 MANUFACTURING POLYMER NANOCOMPOSITES Yuvaraj Haldorai Department of Energy and Materials Engineering, Dongguk University, Seoul, Republic of Korea

Jae-Jin Shim School of Chemical Engineering, Yeungnam University, Gyeongsan, Gyeongbuk, Republic of Korea

2.1

INTRODUCTION

Organic–inorganic nanocomposites have become a prominent area of current research and development in the ield of nanotechnology. Organic/inorganic nanocomposites are generally organic polymer composites with inorganic nanoscale building blocks. They combine the advantages of the inorganic material (e.g., rigidity, thermal stability) and the organic polymer (e.g., lexibility, dielectric, ductility, and processability). By combining the attractive functionalities of both components, nanocomposites are expected to display synergistically improved properties. The deining feature of polymer nanocomposites is that the small size of the illers leads to a dramatic increase in interfacial area compared to traditional composites. This interfacial area creates a signiicant volume fraction of interfacial polymer with different properties from those of the bulk polymer, even at low loadings [1–6]. Among the various nanoillers available, clay minerals, carbon nanotubes (CNTs), and silica nanoparticles are used more often to enhance the physical, mechanical, and thermal properties of polymers [7–13]. Therefore, polymer nanocomposites have Rheology and Processing of Polymer Nanocomposites, First Edition. Edited by Sabu Thomas, Rene Muller, and Jiji Abraham. © 2016 John Wiley & Sons, Inc. Published 2016 by John Wiley & Sons, Inc.

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attracted worldwide research interest over the past few decades to develop polymeric materials with improved/desired properties via the incorporation of these nanoscale materials into the polymer matrix. The uniform dispersion of nanoparticles produces an ultra-large interfacial area per volume between the nanoillers and host polymer. Fundamentally, the immense internal interfacial area and nanoscopic dimensions of nanoillers distinguish polymer nanocomposites from traditional composites and illed plastics. Therefore, new combinations of properties derived from the nanoscale structure of polymer nanocomposites provide opportunities to circumvent the traditional performance trade-offs associated with conventional reinforced plastics, epitomizing the promise of nano-engineered materials. New processing techniques that are effective on the nanoscale yet applicable to macroscopic processing are needed. Synthetic strategies for nanocomposites with a high homogeneity are, therefore, a challenge. Several attempts have been made for the synthesis of nanocomposites that can be classiied under two major categories: ex situ and in situ processes. In this chapter, the literature review examines the synthesis of polymer/inorganic iller nanocomposites using different techniques, such as the in situ method, solution blending, and melt compounding. The selected inorganic iller materials, such as clay and CNTs, as well as their composites, are discussed with the appropriate examples. In particular, melt compounding is discussed in detail because most polymer nanocomposites are manufactured using this technique on the industrial scale. Owing to the extensive research activities in this ield, a complete overview was not possible in this chapter. Instead, the focus is on a general overview of the techniques and strategies used to prepare nanocomposites. Selected examples that represent the different routes and systems will be described. More detailed descriptions of the speciic themes can be obtained from the related references.

2.2

NANOFILLERS

No precise deinition for nanoillers exists. Nanoillers are understood, in essence, to be additives in a solid form, which have a different composition and structure from the polymer matrix. Nanoillers are in the order of 100 nm or less in at least one dimension. Nanoillers are often added to enhance one or more of the properties of the polymer. Inactive illers or extenders raise the quantity and reduce the prices, whereas active illers result in targeted improvements in certain mechanical or physical properties. Common nanoillers include calcium carbonate, ceramic nanoillers, carbon black, CNTs, carbon nanoibers, cellulose nanowhiskers, nanoclays, gold particles, kaolin, mica, silica, silver nanoparticles, titanium dioxide, and so on. Owing to their impressive intrinsic mechanical properties, nanoscale dimensions and high aspect ratio, nanoillers, such as CNTs or nanoclays, are most promising because small amounts (1010 2 × 108 1.5 × 105 6 × 103 1.7 × 102

Source: Reproduced from Meincke et al. [146] with permission of Elsevier.

neat PA-6, the elastic modulus and yield strength of the composite were improved greatly (by approximately 214% and 162%, respectively) with the incorporation of only 2 wt% MWNTs. Zhang et al. [148] reported similar results for PA-6/MWNT nanocomposites. Siochi et al. [149] prepared PI/SWNT nanocomposite ibers by melt processing. SWNT alignment in the iber direction was induced by the shear forces present during the melt extrusion and iber drawing processes. This alignment resulted in signiicantly higher tensile moduli and yield stress in the PI/SWNT nanocomposite ibers compared to those values for unoriented nanocomposite ilms with the same SWCNT concentration. Kearns et al. [150] prepared PP/SWNTs composites in an internal mixer, equipped with a pair of high shear roller-type rotors. The temperature of the mixing chamber was set to 190 ∘ C and the blending time was 15 min. Once the polymer was molten, the appropriate percentage of CNTs was added. The obtained compounds were subject to compression at 200 ∘ C for 15 min. For a 1 wt% nanotubes loading, the iber tensile strength increased to 40% (from 9.0 to 13.1 g/denier). At the same time, the modulus increased to 55% (from 60 to 93 g/denier). Zou et al. [151] fabricated HDPE/MWNT composites by twin screw extrusion. In a typical procedure, CNTs were added to a solvent and sonicated for 1 h. The CNTs were then dried in a vacuum oven, broken into small pieces and mixed with PE. The mixture obtained was extruded using a co-rotating twin-screw compounding extruder. Finally, the composite was dried in an oven. At a critical MWNT concentration of approximately 1 wt%, the HDPE/MWNT composites showed considerably improved mechanical properties. Kanagaraj et al. [152] reported HDPE reinforced with CNTs using injection molding. As shown in Table 2.5, considerable improvement in the mechanical properties of the composites was observed when the volume fraction of the CNTs was increased. The composite reinforcement showed a good load transfer effect and interface link between the CNTs and HDPE. Tang et al. [153] reported similar results for HDPE/MWNT composite ilms. Manchado et al. [154] examined the dispersion of SWNTs in an iPP by shear mixing. The results indicated that the addition of a small amount of SWNTs leads to an increase in the rate of polymer crystallization with no substantial changes in the crystalline structure. As shown in Figure 2.9, the Young’s modulus and tensile

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TABLE 2.5 Mechanical Properties of the HDPE/CNT Nanocomposites CNT Content (vol%)

Young’s Modulus (GPa)

Strain at Fracture (%)

Toughness (J)

1.095 1.169 1.228 1.287 1.338

863.4 948.5 978.5 1020.4 1069

634.53 743.35 756.24 776.27 842.27

0.0 0.11 0.22 0.33 0.44

Source: Reproduced from Kanagaraj et al. [152] with permission of Elsevier.

38

36 1200 34 1000 32

Max strength (MPa)

Young’s modulus (MPa)

1400

Young’s modulus (MPa) Max strength (MPa) 800 0

2

4 6 8 SWCNT content (wt%)

10

30

Figure 2.9 Variation of Young’s modulus and yield strength as a function of SWCNT content in PP/SWCNT composites. Reproduced from Manchado et al. [154] with permission of Elsevier.

strength increased considerably in the presence of nanotubes. Similar results were observed by other researchers for PP/CNT composites [155–158]. The main disadvantage for melt blending is the high viscosity of the composite melt at high CNTs loadings. To overcome this disadvantage, Thostenson and Chou [159] reported a combination of solution and melt techniques. They initially dispersed MWCNTs in a solution of PS in tetrahydrofuran to prepare a ilm, and then extruded the cut ilm though a rectangular die. This approach, however, may lose the initial advantage of the melt blending method and draw it back to solution blending. 2.4.4

Other Methods

In addition to the three most widely used methods, some other methods have been developed, including co-vulcanization [160], electrospinning [161], solid-state intercalation [162–169], sol–gel [170], latex fabrication [171–174], and so on. These

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methods can provide unique properties of the nanocomposites and are useful in their speciic research area, but strict limitations of these methods restrict the wider applications. 2.4.5

Supercritical CO2 Assisted Compounding

In the search for new polymerization solvents, scientists have turned to supercritical luids (SCFs). Among the SCFs, supercritical carbon dioxide (scCO2 ), as a processing solvent, has made noticeable developments over the past decade and has been used extensively in a variety of applications, such as polymerization, polymer fractionation and extraction, impregnation, polymer foaming and blending, surface modiication, and coating and microlithography [175, 176]. A SCF is deined as the state of a compound, mixture or element above its critical pressure, Pc , and critical temperature, Tc , but below the pressure required to condense it into a solid. The properties of SCFs have been described frequently as having values between those of a gas and a liquid [177]. Under supercritical conditions, CO2 exhibits gas-like diffusivity and liquid-like density with zero surface tension. The high solvation power and rapid diffusion are especially beneicial to polymer processing and foaming technology. In addition, the critical point of CO2 is relatively low, 31 ∘ C and a pressure of 73.8 bar. Figure 2.10 shows the generic temperature–pressure phase diagram of CO2 [178]. Furthermore, CO2 is abundant at low cost; it is nontoxic, nonlammable, and environmentally benign. All these advantages make scCO2 a promising solvent for nanocomposite preparation.

100 Supercritical fluid region

Pressure (bar)

80

Critical point (31.1 °C, 73.8 bar)

60 Solid

Liquid

40

Vapor

20 Triple point (57 °C, 5.3 bar)

0 –100

–50

0 Temperature (°C)

50

100

Figure 2.10 Generic pressure–temperature diagram. Reproduced from Canelas and DeSimone [178] with permission of Springer.

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The technique using melt blending combined with scCO2 has been developed to prepare polymer/clay nanocomposites. In 2002, Manke et al. [179] developed a process that allows clay particles to be pretreated with scCO2 in a pressurized vessel and then depressurized rapidly into another vessel at atmospheric pressure to exfoliate the clay platelets. XRD conirmed the exfoliation of nanoclay. On the other hand, there was no statement regarding the exfoliation of nanoclay after being combined with the polymer via conventional melt blending. The same group [180] also reported a method to blend the polymer and clay using scCO2 . Both the polymer and clay were mixed separately with scCO2 and injected into the extruder through two individual hoppers. The temperature was maintained at the melting temperature of the polymer. They claimed that the clay layers exfoliated further when the melt mixture exited the extruder. No morphological or diffraction studies have been conducted to conirm the above statement. The use of scCO2 to reduce the melt viscosity and exfoliate the clay layers is an appealing approach for melt intercalation. The presence of scCO2 in the polymer phase will increase the inter-chain distance and free volume, as well as reduce the inter-chain interactions. Therefore, scCO2 leads to signiicant changes in the properties of polymers, such as lowering the interfacial tension and reducing the viscosity of the polymer melt. In the presence of CO2 , the melt viscosity of PS decreased, even with the addition of clay [181]. Ma et al. [182] achieved a relatively uniform dispersion of sepiolite in PP using scCO2 , even without the aid of maleated PP as a compatibilizer, which is in contrast to an earlier stated theory that a compatibilizer must be involved in melt intercalation for a nonpolar polymer. The authors suggested that the lower melt viscosity was responsible for reducing the breakage and improving the dispersion of the nanoclay. Because scCO2 is a good solvent and carrier agent for methacrylic acid (MA) [183], the interaction between scCO2 and MA affects the natural function of the compatibilizer. Hwang et al. [184] used scCO2 to improve the dispersion of MMT in PP nanocomposites prepared by twin screw extrusion. They observed improved thermal and mechanical properties. Three approaches for the preparation of PP/MMT nanocomposites by melt intercalation with the aid of scCO2 have been reported. The irst is the direct injection of scCO2 into a molten nanocomposite [185, 186]. The second is pretreating the organoclay in the presence of scCO2 before adding it to the melt [187]. The third is the injection of clay along with CO2 into the polymer melt [185, 188]. The effectiveness of clay dispersion between the conventional twin-screw extrusion and a novel single extrusion with the aid of scCO2 was compared. The authors conirmed that a twin-screw extruder, which provides suficient shear and intense mixing, is more effective for clay dispersion, and the improvement of exfoliation with the aid of scCO2 was observed. They also suggested that pretreating the clay with scCO2 prior to the extrusion might better improve the clay dispersion and exfoliation. Litchield et al. [189] reported that injecting the organoclay within a supercritical suspension into a single-screw extruder resulted in better dispersion. Horsch et al. [190] proposed a mechanism for how to delaminate clay layers using scCO2 . First, CO2 or its mixture with the polymers diffuses between the organoclay interlayers under supercritical conditions. This step should take suficient time to allow the polymer chains and CO2 to fully intercalate. Fast depressurization follows during which the CO2 expands dramatically and pushes the interlayers apart. Finally, the polymer chains

PREPARATION OF NANOCOMPOSITES

57

remain in the interlayers after CO2 is removed to prevent reformation of the layered structure. Recently, Chen et al. [191] developed an effective method to prepare PP/nanoclay composites with improved mechanical properties. A semicontinuous process using scCO2 was reported for processing polymer/clay composites with high clay loading (10 wt%) by reducing the collapse of the exfoliated clays. Two major modiications were involved in the new procedure: exfoliating the nanoclay directly into a hopper illed with polymer pellets followed by processing the composite immediately and then mixing the clay into the melt. This latter approach helped to minimize clay collapse when processing the composites with high clay loadings. The PP/nanoclay composite at 10 wt% nanoclay with improved clay dispersion was obtained with an increased modulus and tensile strength of 63% and 16%, respectively, compared to the pure PP matrix. They also compared their method with the other techniques, such as conventional melt blending, scCO2 -aided melt blending, and direct blending with sequential mixing. Figure 2.11 presents TEM images of the 10 wt% PP/MMT nanocomposites prepared using the four different processing methods. As shown in Figure 2.11a, the clay aggregation in the direct blended nanocomposite was signiicant with the addition of 10 wt% MMT. The system appears to have a phase-separated morphology with tactoids in the order of hundreds of individual clay layers. Apparently, the conventional melt intercalation is ineffective in exfoliating/intercalating the nanoclay at this high loading. A better clay dispersion can be

500 nm

500 nm

(b)

(a)

500 nm

(c)

500 nm

(d)

Figure 2.11 TEM images of 10 wt% MMT/PP nanocomposites processed by (a) conventional melt blending, (b) scCO2 -aided melt blending, (c) direct blending with sequential mixing, and (d) scCO2 -aided melt blending with sequential mixing method. Reproduced from Chen et al. [191] with permission of Elsevier.

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observed in the composite prepared by the scCO2 -aided melt blending method as shown in Figure 2.11b, but the size of the tactoid is still large. The morphology of the composite prepared by direct blending with the combination of sequential mixing (Fig. 2.11c) did not show a good dispersion of the nanoclay. The tactoids were smaller in size compared to Figure 2.11b. Sequential mixing might help avoid some further collapse of the silicate layers, but a good dispersion could not be obtained simply because the clays were not delaminated in the irst place. The best dispersion was observed in the nanocomposite prepared using the scCO2 -aided melt blending method with sequential mixing (Fig. 2.11d). The scCO2 -aided melt blending method was also extended to the synthesis of polymer/CNT nanocomposite. Few studies have reported the synthesis of polymer/CNT composites. Recently, Ma et al. [192] reported a method that used scCO2 to assist in the preparation of PP/CNT composites combined with batch melt mixing. In this method, the composite with a 3 wt% CNT loading was prepared by mechanically mixing the polymer melt and CNTs at a high temperature in an autoclave with the CO2 under supercritical conditions (150 bar and 200 ∘ C). Composites with lower concentrations were obtained by diluting this batch with a pure polymer. Through scCO2 -assisted mixing, the yield stress and Young’s modulus of the nanocomposites were increased by 33% and 6%, respectively. This improvement was mostly due to the reduced melt viscosity during mixing because scCO2 acted as a plasticizer. In addition, this method involved batch processing, which is a less preferable process compared to the scCO2 -aided continuous extrusion process. More recently, Chen et al. [193] reported improvements in the dispersion of CNTs, and the subsequent mechanical properties of CNT/poly(phenylsulfone) composites were obtained by applying the scCO2 -aided melt blending technique. The preparation process relied on the rapid expansion of the CNTs followed by melt blending using a single-screw extruder. The microscopy results showed improved CNTs dispersion in the polymer matrix and more uniform networks formed using scCO2 , which indicated that CO2 -expanded CNTs were easier to disperse into the polymer matrix during the blending procedure. They also compared the scCO2 -aided melt blending with the conventional melt blending technique. The CNT/polymer composites prepared using the conventional direct melt compounding methods did not show considerable improvement in the mechanical properties above the addition of 1 wt% CNTs because of their inability to adequately disperse the entangled CNTs into the polymer matrix. By combining the conventional melt blending method with the scCO2 technique, beneits from both sides can be expected, such as an excellent dispersion from scCO2 and the simplicity, fast speed, and industrial compatibility from the melt blending method.

2.5

CHARACTERIZATION

A range of characterization techniques have been used in polymer nanocomposite research [194, 195]. The commonly used powerful techniques include WAXD, small-angle X-ray scattering (SAXS), scanning electron microscopy (SEM), and TEM. SEM provides images of the surface features associated with a sample. On the

CHARACTERIZATION

59

other hand, there are two other microscopic techniques, scanning probe microscopy (SPM) and scanning tunneling microscopy (STM), which are indispensable in nanotube research [195]. SPM uses the interaction between a sharp tip and a surface to obtain an image. In STM, a sharp conducting tip is held suficiently close to a surface (typically ∼0.5 nm) so that electrons can “tunnel” across the gap. This method provides surface structural and electronic information at the atomic level. The invention of the STM inspired the development of other “scanning probe” microscopic techniques, such as atomic force microscopy (AFM). AFM uses a sharp tip to scan across a sample. Raman spectroscopy has also proven to be a useful probe of carbon-based material properties [195]. Owing to the easiness and availability, WAXD is a useful technique for characterizing the morphology of the polymer/clay nanocomposites because it enables the average basal spacing (distance between two clay platelets) to be calculated. WAXD of conventional or immiscible polymer/clay composites showed 2� values equal to the 2� values of pure modiied clay. This suggests that d-spacing of clay platelets in the polymer matrix does not change [194]. In addition, the 2� of polymer/clay occurs at a higher angle than for pure modiied clay and leads to a d spacing of clay platelets in the polymer matrix decreasing to a lower value, corresponding to the collapse of clay platelets [196]. In the intercalated polymer/clay nanocomposites, 2� shifts to a lower angle than the pure modiied clay. This was attributed to the increased d-spacing of the clay platelets due to the polymer entering into the clay platelets [194]. On the other hand, the dispersion of clay cannot be determined from WAXD because the intercalated clay may be present in a good or poor dispersion. Furthermore, diffraction peaks are not observed in exfoliated clay because the clay platelets are separated completely from each other and the spacing is simply too wide to observe by WAXD [194]. On the other hand, the disappearance of the diffraction peak from WAXD is not necessarily due to exfoliation; it may be due to the spacing of clay being too large to measure by WAXD. SAXS can be more informative and somewhat quantitative as explained by many authors [197, 198]. SAXS is useful when the layer spacing exceed 6–7 nm in the intercalated nanocomposites or when the layers become relatively disordered in the exfoliated nanocomposites. On the other hand, this technique has not been used widely except in a few laboratories probably because most laboratories do not have SAXS facilities or experience in interpreting the results. Other techniques, such as solid-state NMR and neutron scattering have also been used on a limited basis to explore clay dispersion [199, 200]. However, TEM allows a qualitative understanding of the internal structure, spatial distribution of the various phases, and views of the defective structure through direct visualization, in some cases of individual atoms. Although some structural features can be revealed by X-ray and neutron diffraction, direct imaging of the individual nanoillers is only possible by TEM and SPM. TEM is unique because it can provide a real space image of the atomic distribution in a nanocrystal and on its surface. TEM is a versatile tool that provides not only atomic resolution lattice images but also chemical information at a spatial resolution of ∼1 nm or better, allowing direct identiication of the chemistry of a single nanocrystal. The use of TEM is often

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criticized because it reveals the morphology in such a small region. On the other hand, this can be overcome by taking images at different magniications and from different locations and orientations until a representative picture of the morphology is established. For example, in the case of nylon-6-based nanocomposites, exfoliation is generally never complete and particles consisting of two, three, or more platelets can be observed [201]. In some cases, these platelets may be skewed relative to one another. Therefore, some particles may appear to be longer than the platelets really are. These issues should be considered when interpreting the quantitative analyses of the particle aspect ratios and when comparing the observed performance with that predicted by composite theory [201]. TEM, AFM, and SEM are also required to characterize the CNT dispersion or distribution in the polymer matrix. On the other hand, XRD has had relatively limited success in CNT research [195]. Raman spectroscopy is a useful technique for examining the bond vibrations of molecules in polymer/CNT nanocomposites. For thermal characterization and to study the cure behavior (typically for thermoset resin systems) of polymer nanocomposites, the most commonly used techniques include differential scanning calorimetry, thermogravimetric analysis, thermomechanical analysis, Fourier-transform infrared, dynamic modulus analysis, and rheometry.

2.6

CONCLUSIONS

This chapter reviewed the preparation and properties of clay and CNT-reinforced polymer composites. The properties achieved by nanocomposites will depend on the type of polymer, illers, surface interaction between iller and polymer, and the production method. Clay and CNTs are promising materials for blending with polymers with the potential to obtain nanocomposites of extraordinary mechanical, electrical, thermal, and multifunctional properties. The size scale, aspect ratio, and properties of nanoillers provide advantages in a variety of applications, including electrostatically dissipative materials; advanced materials with combined stiffness, strength, and impact for aerospace or sporting goods; composite mirrors; automotive parts that require electrostatic painting; and automotive components with enhanced mechanical properties. The various processing methods for producing these nanocomposites, such as in situ polymerization, solution processing, and melt blending were discussed; in particular melt blending was discussed in detail with examples. Some key results were summarized, relating to the mechanical and surface properties. To produce an exfoliated nanocomposite, some methods have assisted the exfoliation of nanoclay using scCO2 . Each technique to disperse nanoillers in polymer matrices has certain limitations. The scCO2 -assisted mixing was used successfully in the preparation of polymer/ clay and polymer/CNT nanocomposites. Relatively homogeneous dispersed and well-separated nanoillers were obtained throughout the polymer matrix. A better preservation of the nanoiller lengths was observed in scCO2 -assisted mixing. Studies of the mechanical properties showed a marked increase in Young’s modulus and tensile strength with the addition of nanoillers. More interestingly, techniques

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usually designed to achieve high-quality PP nanocomposites, such as the use of master batches, MA-grafted PP compatibilizers, or polymer-coated CNTs, were not required to achieve equivalent mechanical properties with scCO2 -assisted mixing. This review chapter is expected to provide readers in a wide range of backgrounds with a better understanding of the impact of various processing methods and illers (clay and CNT) on the properties of nanocomposites.

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3 RHEOLOGY AND PROCESSING OF POLYMER NANOCOMPOSITES: THEORY, PRACTICE, AND NEW CHALLENGES Jean-Charles Majesté Laboratoire Ingénierie des Matériaux Polymères, Univ Lyon, UJM-Saint-Etienne, CNRS, Saint-Etienne, France

3.1

INTRODUCTION

It has been well known for a century that the addition of nanoillers (mostly carbon black to rubber compounds) has a strong impact on the properties of materials. In past years, polymer nanocomposites have been developed as a new class of composites. For example, polymer-layered silicate nanocomposites have attracted a great interest as they can attain a higher degree of strength, thermal stability (ire-retardant applications), and barrier properties with very low nanoiller content (generally lower than 5%). Furthermore, fumed silica has also recently gained new interest since silica particles have become more important in tire, cosmetic, or biomedical applications. Finally, the development of new generation of nanocomposites illed with carbon nanotubes (CNTs) that exhibit excellent mechanical and electrical properties is promising. From a rheological point of view, a direct consequence of incorporation of illers in molten polymers is the signiicant change in the steady shear viscosity behavior and the viscoelastic properties. For example, the effect of strain dependence (nonlinearity effect) of the dynamic viscoelastic properties of illed polymers, often referred to as the Payne effect [1, 2], has been well known in elastomers for 40 years. Intensive discussions have been held thereupon, but the exact causes of this Rheology and Processing of Polymer Nanocomposites, First Edition. Edited by Sabu Thomas, Rene Muller, and Jiji Abraham. © 2016 John Wiley & Sons, Inc. Published 2016 by John Wiley & Sons, Inc.

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nonlinear effect, including thixotropic phenomenon, are still matter of investigations and controversial discussions. The level of iller dispersion is expected to play a major role in determining the iller effects on nonlinear responses of nanocomposites. Generally speaking, polymers illed with nanoparticles show a solid-like behavior response, which includes a nonterminal zone of relaxation, apparent yield stress, and a shear-thinning dependence of viscosity on particle concentration and dispersion. This particular rheological behavior arises from the presence of a network structure of solid particles. Actually, the controversial discussion, or at least the main debate in the open literature, is about the origin of this network structure: polymer–particle or/and particle–particle interactions. The difference stems from the main source of elasticity. For small strain, the elastic modulus describes how the network stores the mechanical energy of an applied load. Network elasticity is usually understood in terms of two extreme models: one is entropic and the other is enthalpic. Entropic gels are generally found when polymer chains bridge the particles. Thus, the difference in chain entropy resulting from chain stretching provides the restoring force for gel elasticity. On the other hand, the alternative energetic (enthalpic) model for elasticity is based on attractive or repulsive forces (van der Waals, H bond, etc.) between the nanoparticles itself. The combination of the different forces gives rise to a minimum free energy. When the iller structure is stretched, the bond length increases and the attractive force arises from the drive return to energy minimum. In both models, the elastic modulus of a gel is proportional to the number of elastically active bond in the network. Since the melt rheological properties of illed polymers are sensitive to the structure, concentration, particle size, shape, and surface characteristics of the illers, rheology offers original means to assess the state of the dispersion in nanocomposites and to investigate the inluence of low conditions upon nanoiller dispersion itself. This chapter is dedicated to the review of the present knowledge on rheology of polymer composites illed with nanoparticles (fumed silica, organoclays, CNTs, etc.). Consequently, a brief description of the structure of the new common illers is addressed in this introductory part. • Fumed silica is a inely divided amorphous silicon dioxide that can be seen at three main scales: primary particles of around 1–3 nm fused together in stable aggregates of around 100–250 nm and inally building up large micron-sized agglomerates, generally named clusters. Due to the large surface area (50–400 m2 /g) of these surfaces, the surface silanol functional groups (4–12 OH/nm2 ) and the surface siloxane interactions play a major role in the rheological impact of fumed silica. Actually, this cluster structure can be viewed as an assembly of primary particles in a structure having a fractal dimension. Due to their fractal structure and their high speciic area, fumed silica illers are subjected to aggregation and can consequently easily form a network of connected or interacting particles in the molten polymer. • With regard to organoclay-based nanocomposites, three-layered organization scales are generally differentiated: (i) the clay layers have a micron-size scale in the polymer matrix in the case of weak interaction and/or no appropriate

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shearing conditions; (ii) a few polymer chains are able to diffuse in the interlayer space, this structure is called intercalated; (iii) all the layers are homogenously dispersed as individual layers at a nanoscale, this structure is called exfoliated. Consequently, the exfoliation of organoclay layers increases the number of frictional interaction between the layers, which is consistent with the formation of a network structure of weakly agglomerated particles. Note that the recent developments in the linear and nonlinear viscoelasticity of silica and organoclays nanocomposites have been recently reviewed by Cassagnau [3]. • Graphene is a 2D sheet composed of sp2 carbon atoms and is expected to have tensile modulus and ultimate strength values similar to those of single-walled carbon nanotubes (SWNTs). Graphene sheets have been obtained using very different techniques (from micromechanical cleavage of graphite to more chemical routes as dissolution of graphite in chlorosulfonic acid) [4, 5]. From an industrial application point of view, the most promising method for large-scale production of graphene is based on the oxidation of graphite leading to graphite oxide. Given the shape and dimensions of single sheet of graphene, it belongs to the family of platelet nanocomposites such as organoclays. Exfoliated graphite oxide or graphene can therefore be classiied in fractal illers due to the long-range connectivity that arises from interparticle physical interactions. From a rheological point of view, nanocomposites illed with graphene behave very similarly compared to organoclay nanocomposites [6]. • CNTs are members of the fullerene structural family. Their name is derived from their size, since the diameter of a nanotube is in the order of a few nanometers while they can be up to several millimeters or even centimeters in length. Consequently, CNTs possess high lexibility, low density, and large aspect ratio. However, one of the most important challenges in polymer nanocomposite developments and applications is to obtain a homogeneous dispersion of CNT in polymer matrix by overcoming the van der Waals interaction between elementary tubes. A great level of activity in the domain of polymer nanocomposites illed with CNT is reported in the more recent scientiic literature. Several very interesting papers or review papers have been published recently [7–11] on CNT-based polymer nanocomposites. A lot of papers (too many to cite them) cover many aspect of nanocomposites science (microstructure, physical or chemical properties, etc.) and the large variety of shape or nature of the nanoparticles. The present chapter aims to focus on the generic rheology of polymer nanocomposites including iller percolations aspects, the use of rheology to get information on the microstructure, rheology (shear and elongational) for processing, the theoretical background for nanocomposites rheology, and inally the issue of polymer nanocomposites processing. No systematic investigation of the various existing illers has been done. In this chapter, each kind of iller has been selected in order to illustrate at best, the laws and the mechanisms that are discussed. This work intends to provide and to classify all the common rheological behaviors and theoretical approaches encountered for polymer nanocomposites. Moreover, only molten nanoilled polymers have been considered, and consequently

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rheological behavior near glass transition will not be addressed. Very speciic behaviors or processing issues according to the nature or shape of particles will treated in dedicated chapters. 3.2 3.2.1

VISCOELASTICITY OF NANOCOMPOSITES General Trends

Many authors have discussed on the connection that can be made between the iller morphology (structure, particle size, aspect ratio) and the melt viscoelastic properties of polymeric materials. When nanoillers are added to molten polymers, the general expected consequence is performance enhancement. The unique rheological properties of nanocomposites arise from the convergence of length scales where nanoparticle dimension (at least the smallest one), polymer characteristic length scale, and interparticle distance are of the same order of magnitude [12]. For instance, by comparing a microcomposite (particle volume ∼1 μm3 ) and a nanocomposite (particle volume ∼1 nm3 ) with the same volume fraction and nature of iller, the mean interparticle distance is smaller than three orders of magnitude, the total interfacial area increases by six orders of magnitude, and inally the number density of particles increases by nine orders of magnitude. These numbers depend on the aspect ratio of nanoparticles and must be viewed relative to the size of polymer molecules to capture the full potential impact of nanocomposites rheological properties. By considering the ratio of the interfacial volume to the particle volume, it can be easily shown that even a small volume fraction of nanoiller modiies the surrounding polymer properties. Moreover, the impressive value of the number density of particle favors the particles to percolate into 3D network in molten polymer matrix (even more for high aspect ratio). This network affects the whole viscoelastic behavior according to its strength. Generally speaking, the nature of the network, polymer–iller and/or iller–iller interaction, is inluenced by the thermodynamic interaction between the matrix polymer and the possible bounded molecules that physically or chemically attach themselves to the iller surface during the mixing process. The importance of polymer–particle interactions is ampliied in polymer nanocomposites such that the interface and the cooperativity between particles dominate the macroscopic properties. For instance, weak forces between particles (van der Waals) are more pronounced for nanometric particles because of the smaller average interparticle distance. Together with the increase of particle–particle interactions (for well dispersed systems), addition of nanoparticles largely increases rheological, mechanical, electrical, and many other bulk properties. In order to illustrate the impact of nanoiller on the viscoelastic properties, Figure 3.1a–c shows the variation of the linear complex shear modulus [G*(�) = G′ (�) + jG′′ (�), where G′ and G′′ are the shear storage and loss modulus, respectively] at different nanoiller concentrations, respectively: (Fig. 3.1a) linear low density polyethylene (LLDPE) illed with hydrophilic silica [13], (Fig. 3.1b) LLDPE illed with lamellar organoclay such as montmorillonite [14], and (Fig. 3.1d) polycarbonate (PC) illed multi-walled carbon nanotubes (MWNT)s [15].

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73

105

G′ (Pa)

104

103

102

101

100 0.01

0.1

1

10

100

ω (rad/s) (a)

105

G´ (Pa)

104 103 LLDPE MA2–1 MA2–2 MA2–3 MA2–5 MA2–8 MA2–10

102 101 100 0.01

0.1

1 ω (rad/s)

10

100

(b)

Figure 3.1 Variation of the complex shear modulus of nanocomposites at different nanoiller concentrations. (a) Storage modulus curves of LLDPE illed with x vol% of nanosilica A200 (T = 190 ∘ C) (◽) LLDPE, (○) x = 1 vol%, (⊗) x = 2 vol%, (∇) x = 3 vol%, and (◾) x = 4 vol%. Reproduced from Dorigato et al. [13] with permission of Express Polymer Letters. (b) LLDPE illed with layer organoclays (Storage modulus variation). Inset: MA-× means × phr of organoclay. Reproduced from Durmus et al. [14] with permission of Elsevier. (c) Polycarbonate illed with multi-walled carbon nanotube (storage modulus variation). Reproduced from Potschke et al. [15] with permission of Elsevier.

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MWNT %

T = 220 °C

106

G´ (Pa)

105

wt% MWNT 15 12.5 10 7.5 5.0 4.0 3.0 2.5 2.25 2.0

104 1.25 wt% 3

10

102

10–1

100

101

1.75 1.5 1.375 1.25 1.125 1.0 0.75 0.5 0.25 0.1 neat PC 102

ω (rad/s) (c)

Figure 3.1

(Continued)

Therefore, the general rheological trend for nanocomposites reported in most of the works is the appearance of a transition from a liquid-like behavior (G′ ∝ �2 and G′′ ∝ �1 ) to a solid-like behavior (G′ ∝ �0 = Ge ), that is, the apparition of a plateau (second plateau modulus) of the storage modulus at low frequency which is higher than the loss modulus (G′ /G′′ = tan � < 1). Remind that the irst plateau (rubbery modulus, G0N ) is attributed to the network of physical entanglements. Another signature of the liquid/solid transition is observed on the low curve of nanocomposite samples. For instance, Aubry et al. [16] clearly show the existence of two low behaviors above a critical volume fraction (∼1.5% for polyamide 12 illed with layered silica): a yield behavior at low shear rates, which depends strongly on the nanoiller content, and a shear-thinning behavior at high shear rates, which is nearly that of the matrix. The “yield” energy of the percolated network is of course linked to the nature of network but, surprisingly, rarely considered in the literature. One reason may be due to measurement dificulties as often wall slip will give similar plateau. Obviously, it is admitted that the increase in nanoiller concentration is driving this transition. However, the state of dispersion and/or the surface modiication of nanoillers is another parameter driving this transition and more generally transition from linear to nonlinear behavior (see Payne effect, Section 3.2.6). Filler–matrix interactions dictate the nature of shell formation around nanoillers. As a consequence, they play a direct role in the iller agglomeration and dispersion process and the nature of iller network. Numerous strategies in order to avoid iller agglomeration has been developed (polymer grafted

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75

nanoparticles – grafted to or grafted from) [17] but will not be addressed in this chapter. To summarize, from a rheological point of view, polymer nanocomposites provide combined advantages from colloidal dispersion and traditional composites. Regarding the spectacular increase of speciic interfacial area and number density of contacts between particles, rheology of polymer nanocomposites could resemble to colloidal dispersion. However, compared to classical colloidal dispersion, impact of Brownian motion on polymer nanocomposites structure is limited and Peclet number is generally high essentially due to greater viscosity of the suspending liquid. Consequently, aging or reorganization after low cessation is often slow kinetic processes and polymer nanocomposites are not real equilibrium systems but they are dynamically arrested systems. However, similar to traditional composites, a viscoelastic matrix is required for inal applications and rheological performance. In this case, polymer nanocomposites offer the great advantage to exhibit rheological reinforcement even at very low volume fraction of iller. This is completely not the case for traditional composites where reinforcement stems from hydrodynamic interaction that generally required a large amount of illers in order to target the same performances. 3.2.2

Percolation Treshold

The sol–gel transition (liquid to solid-like behavior) occurs during a random aggregation process of subunits into larger and larger aggregates at the macroscopic scale. Theoretically, the percolation threshold for spherical spheres without any interaction (hydrodynamic effect only) should be obtained for volume fraction above �c ∼ 0.16 and the jamming transition at the close packing volume fraction of �m ∼ 0.64. From a practical point of view, the increase in the effective particle volume fraction due to particle swelling or clustering from interparticle interaction leads to a drastic decrease in �c . For anisometric particles (rod-like or plate-like) such as nanoclay or clustering silica for instance, a geometrical approach, mainly based on excluded volume interactions, can be applied in the whole phase diagram to predict the average distances between particles and then the percolation threshold [18] The concept of effective ghost particles explains the decrease in the volume fraction for the percolation �c observed for anisometric particles. Scaling relations have been developed to provide the divergence of the properties at the percolation threshold arising from physical interactions. Actually, the sol–gel transition for nanocomposites in which the iller particle aggregates has the same features as chemical gelation, namely the divergence of the longest relaxation time and power law spectrum with negative exponent [19]. As a result, at the percolation threshold, storage and loss moduli have the same power law frequency dependency: G′ (�) ∝ G′′ (�) ∝ �Δ , where Δ is the relaxation exponent. Moreover, the loss tangent tan � (tan � = G′′ /G′ ) is independent on the frequency and is given by tan � = tan(Δ�/2). As shown in Figure 3.2, the fumed silica is aggregated in chain-like clusters of elementary silica particles, and these clusters at high concentrations lead to the formation of a percolation-like iller network. Furthermore, this percolation threshold was observed to be independent of the

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(a)

200 nm

1 µm

200 nm

1 µm

(b)

Figure 3.2 Transmission electronic microscopy on the nanocomposite illed with 6.6% v/v (a) and with 15.7% v/v (b) of silica particles. Observations at medium (left) and low (right) magniication are shown. The black zone corresponds to the silica and the gray to the polymer. Reproduced from Jouault et al. [20] with permission of American Chemical Society.

polymer chain regimes (entangled or Rouse regime). Inoubli et al. [21] observed for a polybutylacrylate nanocomposite illed with � = 0.025 that G′ and G′′ vary as Δ ≈ 0.5 in the intermediate part of the frequency spectrum. They reasonably estimated that � = 0.025 of the silica is very close to the percolation threshold. Moreover, Paquien et al. [22] concluded that percolation threshold values of fumed silica dispersed in polydimethylsiloxane (PDMS) are between � = 0.01 and � = 0.02. Regarding carbon black-illed SBR, Mongruel and Cartault [23] and Leboeuf et al. [24] observed a percolation threshold situated between � = 0.12 and � = 0.18 with Δ = 0.5. A different result (�c < 0.09) was found by Yurekli et al. on the basis of the linear viscoelastic analysis [25]. The percolation threshold of nanocomposites illed with organoclay platelets appears generally for a concentration below � = 0.01. For example, Loiseau and Tassin [26] obtained the formation of a gel above a critical volume fraction for the well-deined laponite particles dispersed into a PEO matrix on the order of �c = 0.002–0.004 depending on the protection of the particles. Regarding nanocomposites illed with CNTs, Du et al. [27], Zhang et al. [28], and Yearsley et al. [29] found percolation thresholds around �c = 0.012, �c = 0.005, and �c = 0.0014, respectively. As shown by Kalyon et al. [30, 31], percolation threshold actually depends on the dispersion state, which in turn depends on mixing method and energy

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77

input, speciically when interparticle interaction is high (clay/CNT) and there is no preferable polymer–particle interaction. As a consequence, regarding CNT, different percolation thresholds are likely to emerge following different mixing methods and procedures. Nevertheless, the rheological percolation threshold is actually inluenced by several nanoiller factors: aspect ratio, dispersion (processing methods, surface iller treatments, compatibilizing agents), orientation or alignment, and temperature. Figure 3.3 clearly shows that the linear viscoelastic response depends strongly on the silica particle interaction. Actually, the trends of storage modulus curves mean that the percolation threshold increases when the silica surface is modiied by polymer grafting. Assuming that the original silica network structure at the origin of the percolation threshold can be attributed to particle–particle interactions, these interactions are broken down with steric repulsion of grafted chains. Consequently, the percolation threshold will be observed at higher concentrations due to a better dispersion of silica particles [20, 33]. On the contrary, the percolation threshold was observed to decrease with increasing the exfoliation (dispersion at the tactoid scale) of nanocomposites illed with lamellar organoclays [26]. Actually, it is a clear fact that the type of surface treatment or compatibilization of organoclays play a crucial role considering both the effective volume fraction of immobilized shell and the enhancement of the dispersion state. Indeed, as aggregation of neat

106

G´ (Pa)

105

Unmodified silica

104 2 103 Polystyrene matrix

3 1 102 10–3

10–2

10–1

100

101

102

103

104

ω (rad/s)

Figure 3.3 Variation of storage modulus versus frequency of PS nanocomposite illed with 5 vol% of silica and PS-grated silica. References 1, 2, and 3 correspond to hydrodynamic diameter of PS-grated silica, respectively, 316, 144, and 181 nm (determined by dynamic light scattering). Master curve at T = 160 ∘ C. Reproduced from Bartholome et al. [32] with permission of Elsevier.

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nanoillers leads to the formation of anisotropic structures, surface treatment results in a better dispersion and the reduction of shape factor. Consequently, the increase in percolation threshold could be due to the change of anisotropic clusters (chain-like for instance) into isotropic particles. Regarding CNT-illed nanocomposites, such trends can be also expected. Indeed, the rheological behavior was reported to depend on nanotube dispersion, aspect ratio, and alignment under low. As mentioned earlier, by improving the CNT dispersion using functionalized single-wall nanotubes, Mitchell et al. observed that the percolation threshold dropped from 3 to 1.5 wt% in PS nanocomposites [34]. Wang et al. showed from polybutadiene/clay nanocomposite systems that the temperature can be a key controlling factor for the exfoliation and orientation–disorientation of clay particles [35]. Actually, the polymer–iller interactions can be temperature-sensitive and therefore the percolation threshold can be also temperature-sensitive. To conclude, the results on organoclays and CNTs are opposite to fumed silica and carbon black for which the critical threshold concentration is expected to increase with the dispersion of primary particles. Actually, this is coherent with the difference in the shape factor of primary particles. Improving the dispersion of silica or carbon black leads to roughly isotropic aggregates, which is completely the opposite for nanotubes or nanoclays. However, in both cases, the gel-like or solid-like behavior stems from the formation of a network of aggregated particles dominated by the particle–particle interactions. This inding will be conirmed later by studies on the Payne effect. 3.2.3

Equilibrium Shear Modulus

After the percolation threshold, the equilibrium shear modulus corresponds to the value Ge of the second plateau of the storage modulus at low frequency (Fig. 3.1). Actually, the modulus Ge represents the elastic energy stored and released by the iller network during one period of harmonic loaded strain or stress on the illed sample. This energy originates from the elastic interaction between illers structured in a 3D network [36]. Macroscopic deformation of this structure causes local solicitation at the aggregate level. The whole network’s response is the sum of each local contribution. Therefore, the modulus Ge can be expressed as the product of the local energy stored times the number of connections (per unit volume) between percolating entities. The growth of the value of Ge can be described as a function of the volume concentration � by (3.1) Ge ∝ (� − �c )t for � > �c Actually, detection of the percolation threshold parameters such as Ge seems to depend on very dificult and precise criteria, which cannot be experimentally validated. However, we observed in a previous work on silica nanocomposites [37] that the predicted power law dependency Ge ∝ (� − �c )t with t ∼1.5 is in agreement with some experimental results of the literature on carbon black-illed natural rubber [38], (t ∼1.56), which qualitatively agrees the analogy of de Gennes [39] using a percolation model of a random conductor network (t ∼1.9). Nevertheless, for PMMA illed

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79

with SWNT, Du et al. [27] found t ∼0.7. Unfortunately, this value is not universal. Krishnamoorti reported t ∼1.55 for CNT in PEO [40]. As extensively reported in the literature, the equilibrium elastic modulus (Ge ) scales with the iller volume fraction as following: Ge ∝ �m

(3.2)

It is expected that this power law exponent depends on particle–particle interaction. Indeed, the elasticity should increase more rapidly and the network becomes more resistive for elastomers illed with hydrophilic silica than for the hydrophobic ones. For example, Cassagnau [37] observed m = 4.5 for the suspension of hydrophilic silica in EVA copolymer. Paquien et al. [22] observed for silica suspension in PDMS that m decreased from m = 7.2 to m = 3.2 depending on the silica surface treatment (from hydrophilic to hydrophobic). Zhu et al. [41] observed the scaling law Ge ∝ �3.4 for polybutadiene illed with silica particles. Furthermore, Klüppel [42] and Heinrich and Klüppel [43] reported a power law close to Ge ∝ �3.5 for carbon black-illed rubber. From works of Moniruzzaman and Winey (Figure 14.9a of their work) on nanocomposites illed with SWNT, the following power law has been derived: Ge ∝ �1.35 . Furthermore, from the work of Poetschke et al. [44] on nanocomposites illed with CNTs, the respective power laws can be calculated: Ge ∝ �0.3 and Ge ∝ �2.0 . This great discrepancy between these power laws on nanocomposites illed with CNTs is mainly due to the nanotube nature (purity, aspect ratio, single wall, or multiwall) and their dispersion in the polymer matrix [45]. Furthermore, the scaling concept based on a fractal dimension is generally used to study the effect of interparticle forces on the elasticity of aggregated suspensions [46–48]. To model the size dependence, the aggregates of silica particles are described as fractal structure with a characteristic size �, which is the radius of the smallest particle containing N primary particles of radius a: ( )df � N(�) ≈ a

(3.3)

where df is the fractal dimension of the aggregate. Following this, the volume fraction of primary particle inside the aggregate is then: ( )df −3 � �≈ a

(3.4)

Finally, the variation of the equilibrium storage modulus versus the volume fraction of silica can be estimated according to the characteristics of the nonluctuating fractal structure [49] as follows: Ge ∝ �1.35

(3.5)

where df is the fractal dimension of silica clusters. Wolthers et al. found df = 2.25 for stearyl-coated silica particles [48]. Paquien et al. observed a fractal dimension

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df equal to 2.3 for unmodiied silica/PDMS composites [22]. Furthermore, they demonstrated that the fractal dimension is very sensitive to the surface modiication of silica as df can decrease to 1.4. However, Piau et al. for silica–silicone physical gel [49] and Cassagnau for EVA/silica composite systems [37] reported values close to 1.8. This great discrepancy between data is mainly due to the different nature of the samples superposed to the various sample histories in the different experiments as shown by Hobbie [45]. Heinrich and Klüppel have considered an alternative network structure that refers to a space-illing coniguration of kinetically aggregated iller clusters: the cluster–cluster aggregation (CCA) model [43]. This model is based on the assumption that the particles can luctuate around their mean position in a polymer matrix. Depending on the concentration of iller particles, a locculation process of particles or clusters leads to a iller network that can be considered as space-illing coniguration of fractal CCA clusters. From the calculation of the solid fraction of the fractal CCA clusters and assuming a rigidity condition for reinforcement of the polymer matrix, the authors derived the concentration dependence of the equilibrium elastic modulus: Ge ∝ �

3+df,B 3−df

(3.6)

where df,B ∼1.3 is the fractal dimension of the CCA cluster backbone and df ∼1.8 is the fractal dimension due to the characteristic self-similar structure of the CCA clusters. Note that such an expression was already derived by Buscall et al. [50] and Shih et al. [51]. It appears that for volume fractions above percolation threshold, rheological properties are clearly dominated by iller network and their fractal nature, which could lead to concentration–time–temperature superposition (TTS) [52–55]. Equation (3.6) predicts a power law Ge ∝ �3.5 conirmed by viscoelastic data obtained for carbon black illed rubbers [43]. In the case of fumed silica, Paquien et al. observed Ge ∝ �4.8−6.0 depending on the silica surface nature (from hydrophilic to hydrophobic) [22] and Cassagnau found Ge ∝ �4.5 for EVA nanocomposites illed with hydrophilic silica [37]. These scaling laws are very close to the values found by Piau et al. [49] on silica–silicone gels Ge ∝ �4.2 in agreement with a formulation of the nonluctuating fractal concept (Eq. (3.5)). Nevertheless, it must be pointed out that these power laws are generally measured at a lower constant frequency so that Ge may be not the truly equilibrium elastic modulus. Figure 3.4 shows that this plateau can increase with annealing time [56]. It means that the 3D network existing in the system is not stable and evolves with time. As a consequence, the accuracy and/or the validity of these power laws in some of the works are generally questionable. Furthermore, Ge must not be mistaken for the rubbery plateau modulus G0N at high frequency. The dependence of this modulus on the iller concentration is generally modeled with the Guth–Smallwood equation (for instance, see the work of Yurekli et al. [25] or all the numerous equations that are able to rely on the viscosity or moduli to the volume fraction by only taking into account hydrodynamic interactions. These laws are presented in Section 3.4 of this chapter.

VISCOELASTICITY OF NANOCOMPOSITES

81 105 Loss modulus G˝ (Pa)

Storage modulus G´ (Pa)

105

104 Time 103

102 10–2

10–1

100

101

102

104

103 Time 102 10–2

10–1

100

101

Angular frequency ω (rad/s)

Angular frequency ω (rad/s)

(a)

(b)

102

Figure 3.4 Time variations of storage modulus G′ (a) and loss modulus G′′ (b) of nanocomposite PP/PP-g-MA/MMT (85/10/5) at 200 ∘ C. The time increases from bottom to top. Reproduced from Zouari et al. [56] with permission of AIP Publishing.

These results can be completed with some works on thermoplastic nanocomposites illed with organoclays. Vermant et al. measured Ge ∝ �4.8−6.0 depending on polymer matrix [57], and Durmus et al. observed Ge ∝ �3.34−3.48 depending on the compatibilizer nature [14]. These scaling laws are close, or at least in the same order of magnitude, to those previously reported on silica nanocomposites. Note that these authors [14, 57] used the power law in Equation (3.6) to calculate df from experimental variation, which allowed them to discuss on clay dispersion with a less or more open fractal structure of the samples. Nevertheless, most of the studies have been focused on the power law variation of equilibrium modulus neglecting the importance of the front factor Gp of this power law (Ge = Gp �m ). As discussed by Heinrich and Klüppel, Gp is the averaged elastic bending–twisting modulus of the different kinds of angular deformation of the cluster units [43]. Actually, Gp depends on the dynamic relaxation regime of the polymer chains and consequently on the particle–particle and particle–polymer interactions. Furthermore, the effect of bound rubber on the elastic modulus can be expressed by introducing an effective solid volume of the clusters. If d is the particle size and Δ the bound rubber layer of a primitive spherical particle, they derived the following equation: ( ) 3+df,B 3−df (d + 2Δ)3 –6dΔ2 (3.7) � Ge = Gp d3 Consequently, more particular attention should be paid to this front factor as a master curve of the variation of the equilibrium modulus versus the effective volume 3 2 fraction �eff = (d+2Δ)d3–6dΔ � is expected. 3.2.4

Validity of TTS Principle

As above mentioned, in order to use the equilibrium shear modulus to characterize the dispersion, most of the studies dedicated to the investigation of the linear

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viscoelastic properties of nanocomposites assume that the sample structure does not change during small amplitude oscillatory shear experiments. Generally, stability is achieved when chemical or thermal treatments of the samples are carried out [58–60] or for long annealing time as illustrated in Figure 3.4. Under these conditions, no remarkable structural changes occur within the material, at least in the experiment time scale, for different temperatures. Thereby some authors showed that the phenomenological TTS principle applies and a master curve could be obtained to describe the rheological behavior of the nanostructured material on a broader frequency range than that allowed by the rheometer [59, 61]. In addition, from an Arrhenius it of master curves, a signiicant increase in low activation energy has been sometimes reported for illed samples [59] for polylactide/montmorillonite nanocomposites). This behavior might be attributed to the dispersion of intercalated and stacked montmorillonite layers in the PLA matrix [62]. In other words, for better dispersion state, interfacial area increases and so does the volume fraction of hindered polymer chain in the interaction with the montmorillonite layers. However, some authors found some failures by applying TTS, principally in the low-frequency range [56, 63–69]. They mentioned that the structure change within the nanocomposite results in a violation of the TTS principle. Reichert et al. have checked the validity of the TTS principle applied to extruded and injection-molded PP nanocomposite samples and concluded that the TTS principle is recovered after a suficient long thermal treatment (aging) to ensure that they are in a thermodynamically stable state [64]. Actually, such behavior was expected as it is typical for samples with properties changing during the experiments. Intrinsically TTS is valid for homogeneous system and assuming all relaxation modes have the same temperature dependence. The presence of nanoparticles induces heterogeneity. The fact that macromolecular chains close to the surface of nanoparticles are characteristically different from bulk (this issue is related to polymer/particle interaction) often leads to TTS failure. As shown in Figure 3.5, Zouari et al. showed that TTS principle can be recovered if, for each temperature, the rheological data are selected to provide the same nanostructure (the same yield stress value for instance) [56]. They went to the conclusion that the temperature dependence is only a property of the polymer. The nanoillers network does not have a temperature-dependent relaxation. The only relaxation process dependent on temperature is that of the polymer segments. In the same way, Triebel et al. concluded that PMMA illed with silica nanoillers behaves thermorheologically complex [63]. This behavior can be explained by the assumption of two processes within the composite that have different temperature dependences. Temperature only accelerates the formation of the particles network. From a practical point of view, only composites with intermediate aging kinetics (at least in the experimental timescale) are concerned by the problem of TTS violation. For very low viscosity matrices, aging is very fast and thermodynamic equilibrium is often reached. On the opposite, for very high viscous matrices, rotary diffusion coeficient of nanoparticles is suficiently low to limit network evolution with time. To conclude, whatever the viscoelasticity of the matrices, nanocomposite rheological behavior remains governed by the same physical phenomena, which are only

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83 105 Storage modulus G′ (Pa)

Storage modulus G′ (Pa)

105 104 103 102 101

10–2 10–1 100 101 102 Angular frequency ω (rad/s)

104

103

102

10–2 10–1 100 101 102 Reduced angular frequency ω aT (rad/s)

(a)

(b)

Figure 3.5 Curves obtained by TTS shift of the storage modulus G′ with frequency for three temperatures (◽: 220 ∘ C, •: 200 ∘ C, and ○: 180 ∘ C, reference taken at 180 ∘ C) at the same annealing time (a) and the corresponding curves at same yield stress (b). Reproduced from Zouari et al. [56] with permission of AIP Publishing.

accelerated with temperature increase. TTS principle is validated only when thermodynamic equilibrium of the 3D network is reached. 3.2.5

Quantifying Dispersion via Melt Rheology

The properties of illed polymers and nanocomposites are strongly linked to the adequate dispersion of the solid phase into a polymeric matrix. However, measuring the quality of dispersion in a nanocomposite is not an easy thing to do. Generally, one can distinguish two methods of evaluation. First, there is a “morphological” approach, which is mainly based on direct observations of both the sizes and the spatial distribution of illers. This approach covers a wide variety of techniques: scanning electron microscopy (SEM) [70], transmission electron microscopy (TEM) [71, 72], and scattering techniques such as X-ray diffraction (XRD) or small-angle X-ray scattering (SAXS) [73]. Although clearly dependent on the details of the nanoparticle, each of these methods can provide unique information on the state of dispersion, ranging from nanometer to micrometer in size scale; therefore, they are typically used in combination to provide detailed information on the hierarchical morphology usually present in nanocomposites [74]. These methods necessarily require the development of an analytical/numerical model to provide quantitative information regarding the dispersion. XRD is an invaluable method to provide a irst-cut examination of dispersion of layered compounds such as clays and graphene sheets because of the periodicity of the stacking and the disruption of the stack upon complete dispersion. XRD is also able to provide orientation information [75, 76]. On the other hand, small-angle X-ray and neutron scattering (SAXS and small-angle neutron scattering (SANS)) have been used to understand the dispersion of nanoparticles such as clays and nanotubes. The

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extensive SAXS and SANS studies on aqueous dispersions of laponite and montmorillonite, under both static and low conditions, enabled the generalization of the scattering theory for anisotropic nanoparticles to extract information on the dispersion and alignment of such layered silicate dispersions [77, 78]. Using analogies to the analysis of dispersed lamellar block copolymers, Vaia and coworkers further generalized this approach to develop a model that enables to determine quantitatively the extent of dispersion [79]. The following section focuses on the rheological properties of the material as a tool for quantifying dispersion. Measuring these macroscopic properties offers a global view of the material’s performance without the need of optical transparency, adequate scattering contrast, or conductivity. In particular, linear rheology is a technique generally used to assess the state of dispersion of nanocomposites directly in the melt state [3, 80]. Dispersion mechanisms of nanocomposites have been sometimes investigated using a combination of scattering (SAXS/ultrasmall-angle X-ray scattering (USAXS)) and rheological analysis. Like this, strong correlation between the local structure and the rheological behavior can be revealed [33, 73]. Moreover, such combination of techniques allows to deconvolve the effect of nanoparticles alignment to dispersion issues, which generally complicates the analysis of rheological data for anisotropic illers. Anyway, rheology offers a wide range of spectral investigation from particle network scale to the local motions of dispersed aggregates in the suspending matrix. For instance, Zhao et al. [66] for PS–clay nanocomposites have demonstrated a change of pattern in dynamic mechanical spectrum as a function of the degree of exfoliation. They showed that the number of particles per unit volume (actually a way to quantify the number of contacts between particles) is a key factor determining the characteristic response of nanocomposites. From a practical point of view, they proposed a schematic rheological response to the different level of clay dispersion shown in Figure 3.6 based on experimental data. PS matrix with a low level of clay particles gives a typical terminal relaxation behavior for polymer (G′ ∝ �2 ; G′′ ∝ �) with taking into consideration the possible hydrodynamic strain ampliication. Incorporation of more clay particles into the polymer would result in a change of the spectrum in the terminal relaxation regime (critical gel like behavior, both G′ and G′′ ∝ �Δ ). As the level of dispersion increases, the rheological response turns into a more solid-like behavior, especially at low frequencies (G′ > G′′ , G′ ∝ �0 ). Further increase in the clay dispersion would produce a response where G′ is greater than G′′ across all frequencies, indicating a fully percolated network structure. As discussed earlier, fractal dimension can be inferred from equilibrium shear modulus. However, real quantitative correlation between particle network structure and rheological properties are still not deined at this moment. Further information on the microstructure can be obtained by analyzing the high-frequency data. The low-frequency modulus mainly gives information about the aggregates or the 3D network of aggregates, the high-frequency response is dominated by the polymeric matrix contributions. Vermant et al. [57, 80] showed

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85

Hydrodynamic reinforcement ϕ ≪ ϕc

Percolation threshold ϕ ≈ ϕc G′

G′ φ

G′′

G′′

1 2

G′, G′′ ∝ ωΔ ω (rad/s)

ω (rad/s)

ϕc : percolation threshold; ϕm : close packing volume fraction Percolated clay network G′

G′ G′′

G′′

ω (rad/s) ϕc≪ ϕ< ϕm

ω (rad/s) ϕ>ϕc

Figure 3.6 The schematic representation of the speculated rheological response to the increase in the volume fraction of illers. Reproduced from Zhao et al. [66].

that, from a rheological point of view, high-frequency data are an interesting way to characterize dispersions. Actually, the higher moduli stem from an increase in the matrix contribution due to the hydrodynamic contributions. Hence, the volume occupied by the aggregates is probed, even when they are part of a network. High-frequency moduli, both G′ and G′′ , reveal similar trends, that is, an exponential-like increase when plotted versus volume fraction of nanoiller. The evolution of the relative high-frequency moduli can be described by a Krieger–Dougherty equation: G′HF rel

=

G′HF G′HF,m

[ ]−[�]�max � = 1− �max

(3.8)

where G′ HF refers to the high-frequency modulus of the nanocomposite, G′ HF,m is the high-frequency modulus of the matrix at the same frequency, � is the volume fraction, �max is the maximum packing fraction, and [�] is the intrinsic viscosity. Quantitatively, the nanocomposite structure enters through both [�], which depends on the shape of the basic clay units or primary aggregates, and �max , which depends on the hydrodynamic volume occupied by the aggregates and their shape. Thereby, different exfoliation and dispersion of the aggregates are probed by inferring these two parameters. Quantitative link with the aspect ratio Ar can be done using Brenner equation [81] for intrinsic viscosity for oblate spheroids ([�] ≈ 1.45 + 0.672Ar ). This provides a very good quantitative way to rank the

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86

different nanocomposites. It should be noted that quantitative estimation of aspect ratio from percolation threshold is also possible [82]. Recently, Galindo-Rosales et al. [80] have proposed a method in order to assess to the quality of dispersion by using nonlinear rheological data in a more straightforward manner comparing to the aforementioned methods. The strain sweep data for samples at a ixed particle loading above the percolation threshold can be exploited. Figure 3.8a shows a typical strain sweep for the nanoparticle dispersions from which a number of characteristic parameters can be deined. At low strains, the predominant elastic behavior originates from a 3D aggregate network as detailed earlier. Thereby, a plateau modulus at small strain amplitudes (G′ 0 ) can be deined. For samples above the percolation threshold, the viscous modulus increases up to a maximum value (G′′ max ) before decreasing (see Fig. 3.7a). The rise of G′′ is usually associated with the breakup/rebuilt mechanism of the particle network. The dissipation is increasing as particles and aggregates break loose. Therefore, G′′ max can be used as a measure for this dissipation. At a given (low) frequency, the ratio between the modulus at small strains G′ 0 and the maximum in the loss moduli as a function of the strain amplitude G′′ max gives a dimensionless parameter that is able to assess the strength of the network developed at rest (Fig. 3.7b). The maximum dissipation relects indirectly how the network breaks up into aggregates. This method has been tested on suspension of silanized silica nanoparticles in PDMS matrix. Different dispersion qualities have been obtained by using various sample preparation methods with different energy input (from mixing by hand (lowest 3.5

100

G′0

2.5

DQ

2.0 DQ

1.5 1.0 0.5

US U S H

T rest

0.0

G′,G″ (Pa)

(G′0/G″max)* (-)

3.0 10

1

γc

0.1 –2

0

2

4

6

8

10 12 14 16 18

G′ G″

G″max

0.1

1

10

(G″max)* (Pa)

γ (%)

(b)

(a)

100

1000

Figure 3.7 (a) Dynamic moduli at a ixed frequency (� = 0.5 rad/s1 ) as a function of strain amplitude for a colloidal suspension of silanized silica nanoparticles (SiO2 ) at 35 wt% after preshearing at 5 s−1 and a recovery for 7200 s. (b) Rescaled ratio G′ 0 /G′′ max as a function of G′′ max for the suspensions prepared at 35 wt% with particles from batch 2. Solid and dotted lines are the linear its to the slope and to the plateau, respectively. The marker US, U, S, and H corresponds to the sample preparation method, namely ultrasonic disperser (US), high shear Ultraturrax mixer (U), magnetic stirrer (S), and mixing by hand (H). Reproduced from Galindo-Rosales et al. [80] with permission of John Wiley and Sons.

VISCOELASTICITY OF NANOCOMPOSITES

Log shear modulus G*

modiication

87

Filler–iller interaction

In-rubber structure Hydrodynamic effects Polymer network γc

Log shear deformation

Figure 3.8 Different contributions to the complex shear modulus versus strain for polymers illed with iller at two levels of dispersion. Reproduced from Frohlich et al. [83].

energy) to ultrasonic disperser (highest energy)). It is noteworthy that the plot of G′ 0 /G′′ max versus G′′ max (Fig. 3.7b) has time as implicit parameter. The increase in G′ 0 /G′′ max suggests that the network develops. It can be observed that the slope is higher for the better dispersed suspensions. After a suficiently long enough resting time, the ratio (G′ 0 /G′′ max ) reaches an asymptotic value as is shown in Figure 3.7b. Interestingly, although both G′ 0 and G′′ max still evolve in time, the ratio G′ 0 /G′′ max remains constant that relects the same self-similarity of the structure. The better the dispersion quality, the higher will be the ratio between the elastic modulus of the unperturbed structure. Finally, it can be concluded that the plot in Figure 3.7b of the ratio G′ 0 /G′′ max versus G′′ max provides a convenient tool to compare dispersion quality using only a single volume fraction. 3.2.6

Payne Effect

The famous effect of strain amplitude dependence on the dynamic viscoelastic properties of illed polymers is often referred to as the Payne effect [1, 2]. Actually, the Payne effect was irst reported for carbon black reinforced rubbers and extensively studied on illed elastomers [43, 84] and thermoplastic composites [3, 24]. As previously discussed about the linear viscoelastic properties, the mechanism for reinforcement and nonlinearity can be based on two conceptual aspects. The concept of iller networking yields a good interpretation of the Payne effect for illed elastomers. For example, common features between the phenomenological agglomeration–disagglomeration and recent microscopic networking approaches (particle–particle interaction) were discussed by Heinrich and Klüppel [43]. The excess of dissipated energy is attributed to the breakdown of particle structure. Consequently, illed elastomers can be drastically modiied under deformation, and the viscoelastic properties are then governed by iller–structure breakdown and buildup. The notion of iller structure generally refers to a 3D network and space illing ininite cluster of aggregates. Payne effect was also observed even for

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RHEOLOGY AND PROCESSING OF POLYMER NANOCOMPOSITES

inite cluster of interacting particles. Leonov [85], Carrot et al. [86], and Majeste et al. [87] have considered the breakup of large agglomerates as being the origin of energy dissipation and loss of elasticity in illed polymers. Interestingly, Payne effect vanishes when no more agglomerates remain. Actually, such system can be considered as two-phase systems: dispersed phase of large agglomerates made of strong pure iller–iller interactions and a matrix of smaller dispersed aggregates which softly interact with each other via surface polymer shell. Then, the concept of iller–iller interaction breakdown is still valid whatever may be the extent of clusters. This inding was also supported by viscoelastic experiments showing that the linear low-frequency modulus of the composites decreased spectacularly when the particles were chemically treated with organosilane [88, 89] in order to suppress strong iller–iller interactions by reducing surface energy. The density of chains adsorbed in the bound polymer zone and their conformation at the iller surface are generally quite dificult to access even though measuring bound polymer is a simple technique in principle [90]. With regard to fumed silica, the adsorption of PDMS chains comes from the formation of hydrogen bonds between oxygen atoms belonging to chains skeletons and silanol groups on the surface of the illers. These observations reinforce the idea that the moduli and limit of linearity are related to the fraction of exfoliated layers or silica clusters that form a fractal structure. Figure 3.8 depicts these different contributions to the storage modulus and linear strain limit. Another argument generally put forward to explain the Payne effect is to consider the shift of the glass transition temperature induced by the presence of the illers for adsorbed polymer chains on the iller surface. Indeed, it has long been proposed that the polymer matrix in the vicinity of the iller is glassy especially for strong polymer/substrate interactions [91–94] while far from the interface the polymer is in the molten state. Then, when glassy layers around the iller overlap, spectacular reinforcement effects appear. Moreover, glassy layers play an essential role in both the dissipation mechanisms and the loss of elasticity under strain (Payne effect). Indeed, the glassy bridges are not permanent. They break or yield under applied load. The yielding of glassy bridges is one of the major sources of dissipation in the reinforcement regimes. Whatever the argument used to explain the Payne effect, the dissipation mechanisms are not enough considered even though they can capture the dynamics of breakup/rebuilding process under applied strain. The loss modulus (or the loss angle) is generally used to put in evidence energy dissipation under low in illed polymers. Contrary to the storage modulus that monotonically decreases with strain, three regimes for the dissipation are generally observed. At low deformations, the dissipation is dominated by dissipation in the polymer matrix [94] or by reorganization in agglomerates coniguration [87]. At intermediate deformation amplitudes, a maximum of G′′ is visible. The dissipation is governed by mechanisms of rupture and rebirth of iller–iller interaction (or glassy bridges) [86]. At larger deformation, the iller network is destroyed and the dissipation is concentrated in the polymer matrix. The amplitude of the maximum depends on the iller volume fraction, the structure of the network, the nature of the polymer/iller interface, or the iller–iller interaction.

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89

If the Payne effect has been deeply studied for carbon black and silica-illed nanocomposites, few works have been reported on the organoclay systems and the nonlinearity effect associated with tactoid illers is generally poorly discussed. Furthermore, as nanocomposites show thixotropic behavior, the value of the maximum strain deining the linear region depends on preshear history (intensity and time) of the composite so that rigorous experimental protocols must be applied [57]. 3.2.6.1 The Limit of Linearity As a consequence of the Payne effect, the limit of linearity � c decreases with increasing the volume fraction of particles according to the following general power law: �c ∝ �−�

(3.9)

Regarding silica particles, different experimental works [52, 95] reported on the (�) exponent values for low-viscosity liquid suspensions. For polymer nanocomposites, few power laws have been reported. According to works from Zhu and Sternstein [96] and Sternstein and Zhu [97], we found � = 2.4 and � = 3.0 for hydrophobic and hydrophilic silica, respectively. According to Cassagnau et al. [37], we calculated � = 1.7, as shown in Figure 3.9. Interestingly, Paquien et al. [22] observed that when the silica grafting ratio increases and the silica become more hydrophobic, the Payne effect is reduced in PDMS/silica nanocomposites, that is, the critical strain separating the linear and nonlinear regime increases with increasing the hydrophobic treatment of the silica. Such a result was also reported by Clement et al. who showed that the amplitude of the Payne effect is reduced by introducing a permanent treatment of the silica surface or a processing aid [98]. Only a few works have recently been reported on the nonlinearity of clay-illed nanocomposites. As expected, the maximum strain to which the linear viscoelastic domain extends was observed to be decreased with increasing clay concentration. Aubry et al. [16] irst observed �c ∝ �−1 in polyamide-12 layered silicate. Such a scaling relation was also reported by Devendra et al. [99] in the case of metallocene polyethylene montmorillonite composites. More recently, Durmus et al. [14] observed � = 0.85–1.1 in LLDPE/montmorillonite nanocomposites depending on the nature of the compatibilizer. Finally, Vermant et al. [57] showed � = 1.8–1.9 for the power variation of the limiting strain as a function of particle concentration. Interestingly, Lertwimolnun and Vergnes [100] and Letwimolnun et al. [101] showed that the linear viscoelastic domain, at the same concentration of organoclay, decreased with increasing the exfoliation degree of tactoids. Consequently, the decrease in linear viscoelasticity can be attributed to the difference in the degree of dispersion and more precisely the degree of exfoliation. As a consequence, it is clear that the exponent � cannot be considered as a universal parameter for the large variety of iller shapes. It comes that the shape factor, which controls the iller structure at a mesoscopic scale, must be taken into account. In this way, Shih et al. [51] developed a scaling theory for this limit of linearity � c considering the fractal dimension of the iller network. The critical strain values follow: 3+d

�c ∝ �

− 3−df,B f

(3.10)

RHEOLOGY AND PROCESSING OF POLYMER NANOCOMPOSITES

90 106

G′ (Pa)

105

8.6 6.6 Si% 3.4 2.3

104

EVA

103 10–2

10–1

100

101 Strain (%)

102

103

(a) 2 1.8

log(gc)

1.6 1.4

υ = 1.7

1.2 1 0.8 –1.7

–1.6

–1.5

–1.4 –1.3 log(Ф)

–1.2

–1.1

–1

(b)

Figure 3.9 Payne effect in fumed silica composites: limit of linearity. (a) Variation of the storage modulus versus deformation at different silica concentrations in a copolymer of ethylene and vinyl acetate. � = 10 rad/s, T = 140 ∘ C. Reproduced from Cassagnau et al. [37] with permission of Elsevier. (b) Power law on the limit of linearity � c .

The fractal dimension df ∼2 is universal for gel aggregate systems, whereas df,b , which depends on the number of particles per aggregates, strongly depends on the shape of illers (spherical or tactoids). Note that these power exponents are extremely sensitive to the experimental criteria used by the authors. Moreover, the two different scaling exponents for Ge and �c can be obtained from Equations (3.6) and (3.10). As a consequence, df,B and df can be calculated and compared or veriied with independent scattering data (especially df ). 3.2.6.2 Thixotropy and Aging Another important aspect in the mechanisms of nonlinear viscoelasticity in illed polymers is the restoration of moduli of the iller/polymer network following the destruction by a large strain perturbation.

VISCOELASTICITY OF NANOCOMPOSITES

91

Actually, the Payne effect is a reversible process and the material should undergo recovery of its original equilibrium structure. Under steady shear low, the gel-like particle structures are disrupted and take a long time to recover the original structure. This phenomenon, generally called thixotropy, is really a kind of viscoelasticity [102] but with a long relaxation time of a few hours. Quantifying thixotropic effects is not easy. The more common rheological experiments used to thixotropy in nanocomposites are transient shear low or stress relaxation. Thixotropic materials are very sensitive to low history. Indeed, small differences in low history occurring during sample loading may lead to signiicant differences in the behavior during the subsequent start-up of shear low. Therefore, very robust protocols are generally employed when studying these types of materials. One of the main dificulties remains to generate a reproducible initial structure. Typically, preshear lows are employed to erase structural history before any rheological measurements. Afterwards, it has been shown [103, 104] that thixotropic behavior is best studied by tracking the material response resulting from stepwise changes in shear rate or shear stress. Such experiments are more eficient to clearly separate the coupled effects of time and shear rate/stress. From a practical point of view, well-deined and reproducible initial condition is generated by shearing the sample at a speciic stress until a steady state is reached. Then, once a steady state is reached, the stress is suddenly reduced (step-down) or increased (step-up). The resulting viscosity transients show a monotonic evolution of the viscosity to a steady-state level. By comparing the timescales of the step-down and step-up experiments, different magnitudes are generally found. Usually, structure breakdown goes faster than structure buildup. The long-time viscosity evolutions observed in the transient rheological experiments are attributed to rearrangements of the aggregate structure as in thixotropic suspensions in general. In clay nanocomposite systems (or more generally in systems illed with anisotropic particles), two factors contribute to the structural evolution: the orientation of the tactoids and the aggregation due to strong thermodynamic interactions. Therefore, the timescales on which both reorientation of the multi-platelet clay particles and the buildup of the aggregates or even a network have to be separated. To do that, a combination of intermittent low reversal (IFR) and intermittent forward lows (IFF) are used [57, 61]. Indeed, Solomon et al. [61] observed a dependence of the stress overshoot on the rest time during IFR experiments. They clearly showed that a pronounced anisotropy of the microstructure can be inferred from the difference in response between IFF and IFR at short rest times. Increasing the resting time leads to anisotropy decrease, and the structure also becomes increasingly elastic with resting time. Again, rupture of an aggregate network gives rise to a rheological signature and conirms that nonlinearity effect is predominantly governed by the iller network breakdown (particle–particle interaction) combined with a second-order mechanism originating at the polymer–iller interface (polymer–particle interaction) [96]. Nevertheless, it must be pointed out that transient shear experiment can be only used to investigate the thixotropic behavior of liquid suspensions and the usual thermoplastic polymers. In the case of polymers showing more complex viscoelastic properties in the terminal relaxation zone (such as elastomers) combined with strong

92

RHEOLOGY AND PROCESSING OF POLYMER NANOCOMPOSITES

temporary elasticity, dynamic and subsequent dynamic experiments are generally preferred. In dynamic conditions, the strain amplitude dependence of the dynamic modulus is caused by a thixotropic change of the iller–network structure. Such process is accompanied by the recovery of the complex shear modulus, which is measured in the linear domain of viscoelasticity. Modulus recovery kinetics of elastomers illed with fumed silica have extensively been studied by the Sternstein’s group [96, 105]. They proposed that the recovery mechanism is based entirely on the dynamics of the iller–matrix interface and consequently on the physics of entangled chains (reptation of entangled chains). However, the agglomeration or network formation can be invoked especially at high iller concentration. Nevertheless, we reported in a previous paper [37] that the viscoelastic behavior of fumed silica particles dispersed in polymer organic solutions, from diluted solution to molten polymer, and the nonlinear behavior could be then imagined [37] to be associated with both mechanisms of chain disentanglements and iller network breakdown, depending on silica concentration, silica surface treatment, and amplitude deformation. To conclude, it is clear that nanocomposites exhibit time-dependent behavior, which compels to be cautious when performing rheological experiments. Generally speaking, concentrated suspensions of nanoillers exhibit aging under both oscillatory and shear low deformations. Moreover, the dynamic time sweeps under constant strain amplitudes indicate that the storage modulus increases more rapidly with time as the amplitude of the applied strain decreases. These observations have been conirmed by results obtained from the light scattering echo [106]. The local particle motions are essentially reversible at strain amplitudes lower than the yield strain. However, beyond a yield strain, irreversible changes in the particle positions, that is, yielding, are observed. This yield strains are found to correspond to the strains at which storage and loss moduli cross over that maintains the relation between the nonlinear behavior and the particle network evolution.

3.3

FLOW PROPERTIES OF NANOCOMPOSITES

As demonstrated in sections earlier, the presence of nanoparticles induces some new features in the linear or nonlinear viscoelastic properties of the polymer, such as the solid-like behavior at low frequencies or the thixotropic and recovery effects, or simply enhances its nonlinear behavior. Such observations have sustained a better understanding of the connections between microstructure and viscoelastic properties of rubber nanocomposites (although controversial discussion still remains) and have supported the development of models for the description and prediction of these properties (see Section 3.4). The following sections deal with the present knowledge and understanding of the inluence of nanoparticles on the low properties of a polymer matrix. From a practical point of view, polymer processing tools create steady state or transient low conditions in which the material experiences large deformations and large deformation rates. In such situations, illed polymers and more speciically nanocomposites exhibit complex rheological properties, so the description of their

FLOW PROPERTIES OF NANOCOMPOSITES

93

low behavior is still a challenge. From a fundamental point of view, this requires to understand how the nanoiller particles modify the properties of the polymer matrix. Due to the very nature of the low conditions, the inluence of the nanoiller nature or concentration on the shear viscosity, measured either in steady state or in transient conditions like those met in start-up experiments, is expected to be different from the effects described previously on viscoelastic properties measured in oscillatory shear. So, shear low will be addressed irst in this section and next will be the extensional low. 3.3.1 Steady-State Flow Curves: Relative Viscosity and Normal Stress Difference Nanoillers most commonly used with polymers are very different, speciically with regard to their interactions with the polymer, their aspect ratio, or their surface energy. However, they induce the same qualitative trends of the shear low properties. Data published by Aubry et al. [16], displayed in Figure 3.10, illustrate these features which can be summarized as follows: • At low shear rates (or stresses) and at low clay volume fraction, the apparent viscosity exhibits a plateau deining a Newtonian viscosity � 0 , and the dependence of the zero-shear viscosity on the volume concentration of particles can be described satisfactorily by hydrodynamic models as those used in suspension rheology. When increasing the iller concentration, the Newtonian plateau is no longer observed and yield behavior occurs (this point is developed further). • At large strain rates or stresses, a shear-thinning behavior is observed, and the viscosity is much less sensitive to the iller volume fraction than in the low shear rate range. η (Pa s) T = 200 ° C

104

103

10–3

10–2

10–1

100

101

102

–1

γ (s )

Figure 3.10 Steady shear viscosity as a function of shear rate at (•) 0%, (○) 0.25%, (◾) 0.5%, (◽) 0.75%, (▴) 1%. Reproduced from Aubry et al. [16] with permission of AIP Publishing.

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RHEOLOGY AND PROCESSING OF POLYMER NANOCOMPOSITES

From an experimental point of view, mainly due to low instabilities, it could dificult to measure the steady shear viscosity at high shear rates. Then, the shear viscosity can be estimated from the Cox–Merz relation [107] (� ∗ (�) = �(�) ̇ for � = �). ̇ For nanocomposites, it has been shown that Cox–Merz rule is invalid for high frequency (difference in iller orientation) and/or for high iller content (yield stress behavior). However, it is expected that this rule remains valid for low concentration of roughly spherical illers in polymer melts. As mentioned earlier, the incorporation of solid particles strongly inluences the low shear rate viscosity. At volume fractions below the percolation threshold, nanocomposites exhibit Newtonian behavior at low shear rates, and their relative Newtonian viscosity � 0r (ratio of � 0 (�) to the Newtonian viscosity of the matrix) conforms well to the second-order Einstein-type equation: �0r = 1 + [�]� + k([�]�)2

(3.11)

From the it of the previous equation to experimental data, it is possible to determine an intrinsic viscosity [�] and an interaction constant (k), which can be used as structure descriptors (Eq. (3.13)). The intrinsic viscosity [�] can be determined alternatively by itting the relative viscosity using a modiied Krieger’s semi-empirical equation replacing the effective maximum packing volume fraction by the viscosity percolation threshold �c , as proposed by Jeon et al. [108]: ]−[�]�c [ � �0r = 1 − (3.12) �c Knowing the intrinsic viscosity [�], the aspect ratio Ar (diameter/thickness) of the iller can be inferred [81, 109]: [�] = 2.5 + 0.025(1 + Ar1.47 )

(3.13)

Considering free rotation of anisotropic illers (rod, disks, etc.), a volume fraction of equivalent hard spheres can be found as a function of the reciprocal of the aspect ratio �eq ∝ 1∕Ar . Thereby, as this equivalent volume fraction obeys the usual critical volume fractions for spherical particles, namely the critical volume fraction at percolation �c and the maximum packing volume fraction �m , it is possible to infer roughly the apparent percolation threshold and the packing fraction for systems illed with nonspherical particles. In contrast to the preceding statement, when strain rates are high enough, illed polymers (even highly) demonstrate usual viscoelastic behavior as unilled polymeric liquids suggesting that the particles do not alter qualitatively the dynamics of the polymer chains. For high strain rate (where network contribution is limited), shifting of the curves over one another is possible. A single concentration shift factor f(�), analogous to the one used for Newtonian suspensions, can rescale viscoelastic functions of illed materials, which means predominance of hydrodynamic interactions [110, 111].

FLOW PROPERTIES OF NANOCOMPOSITES

T = 200 ° C

τ(Pa) 105

95

τy

104 Capillary rheometer

103 102 101 100

Rotational rheometer

10–1 –3 10

10–2

10–1

100

101

102

103

γ (s–1)

Figure 3.11 Steady shear stress as a function of shear rate at (•) 0%, (○) 0.25%, (◾) 1%, (◽) 1.5%, (▴) 2.5%, (Δ) 5%, (▾) 10%. Reproduced from Aubry et al. [16] with permission of AIP Publishing.

It has long been known that highly illed polymers exhibit yield stress. Figure 3.11 shows typical low curves for nanocomposites at various particle loading. Usually, two complementary techniques are used to assess the whole range of shear rates, namely rotational rheometer for low shear rate and capillary rheometer for the highest ones. Generally, two low behaviors are clearly found: a yield behavior at low shear rates, which is attributed to the iller network and depends strongly on the nanoiller content, and a shear-thinning behavior at high shear rates, which is nearly that of the matrix. As it stems from the same physics, yield stress correlates well with the evolution of linear viscoelastic properties such as the equilibrium shear modulus [51, 52]. Moreover, yield stress is the critical shear stress corresponding to the yield behavior of the network and the appearance of nonlinearities in the rheological response of the nanocomposite samples. Therefore, combining Equations (3.2) and (3.9), the yield stress � y scales with the iller volume fraction as following: �y = Ge �c ∝ �m �−� ∝ �m−�

(3.13)

The yield stress only appears in some rheological models as a parameter that takes into account the particle network contribution to the total stress. In this respect, Herschel–Bulkley’s equation: �y �= (3.14) + K �̇ n−1 �̇ provides the simplest approximation for the shear viscosity of concentrated suspensions of small particles in a power law luid. As aforementioned, very satisfactory master curves can be achieved with this model by applying separate shift factors to the contributions of either phase of the compound. The polymer contribution was

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96

described by the second term in Herschel–Bulkley’s equation and was treated with the classical temperature-dependent shift factor. The temperature dependence of the yield stress that resulted from the particle network was introduced via a vertical shift factor on the irst term. Rheological properties of illed polymer melts have been shown to be sensitive not only to the concentration but also to the structure, particle size, shape, and surface characteristics of the illers. In particular, these parameters inluence the dispersion and consequently the characteristics of the “iller network” resulting from interparticle interaction. The energy involved in these interactions drives the viscoelastic and low properties. Regarding the shear viscosity, it has been highlighted by numerical simulation [112] that the viscoelastic properties of the polymer matrix were strongly perturbed by the nanoparticles and depended on the nature of the nanoparticle–polymer interactions. Figure 3.12 depicts the effect of the nature of the nanoparticle–polymer interaction: attractive, neutral, or repulsive. Usual behavior (increase in relative shear viscosity) is found when attractive forces between particles are considered. Experimentally, this behavior has been encountered for the main majority of polymer nanocomposites without any treatment of particles surface for which aggregation leads to reinforcement. By modifying the surface and thus by enhancing the repulsive forces between particles, the very clear effect is to reduce signiicantly the shear viscosity (when nanoparticle size is similar to that of polymer coil) with respect to untreated particles [113] as predicted by computer simulation and experimentally veriied [114].

101 Attractive Neutral

ƞm/ƞ0

Repulsive

100

0.00

0.08 σc

0.15

Figure 3.12 Normalized polymer matrix viscosity as a function of speciic interfacial area � c . (� m and � 0 are polymer matrix viscosities in polymer nanocomposites and in pure polymer, respectively). Open and illed symbols are for Nb = 10 and Nb = 20 chains, respectively. The solid line is the expected behavior for conventional composites. The dashed lines serve to guide the eye. Estimated ±10% error bars for viscosities are shown. Reproduced from Smith et al. [112] with permission of AIP Publishing.

FLOW PROPERTIES OF NANOCOMPOSITES

97

Nevertheless, since all parameters vary simultaneously, especially the size of the agglomerates, the state of dispersion, the interparticle interactions, and the physicochemical nature of the particle–polymer interactions, no straightforward conclusion regarding the mechanisms of such reduction can be drawn. Finally, we turn to steady and transient irst normal stress difference N1 = � 11 –� 22 (subscripts 1 and 2 refer to low direction and gradient direction, respectively). The normal stress difference of polymer nanocomposites especially the transient normal stress difference has received much less attention than the shear viscosity. Only a few papers report measurements of the normal stress difference in shear lows [115–118]. According to the literature, the rigidity of the polymeric material increases in the presence of a solid particle (when the interaction between particles and polymer are cohesive), but it is not clear how the iller contributes to the elasticity. Many studies have shown that adding the iller reduces the elasticity of the composite. From a practical point of view, this is demonstrated by a reduction of the extrudate swell. Regarding the shear rate effects, qualitatively, similar results are obtained for the normal stress difference and the transient shear stress � + 12 , but the normal stress difference goes to its steady-state values slower than the shear stress. Similar to the shear stress, an overshoot in the normal stress difference is founded but its amplitude is lower. The question about the origin of this overshoot often arises. Eslami et al. [118] suggest that overshoot stems from transient mechanism of orientation of anisotropic particles in the low direction. At the beginning of the start-up low, the orientations of particles with high aspect ratio are nearly random. When the low is switched on, the randomly dispersed particles begin to orient in the low direction. Transition from the initial state of random orientation to another state of orientation in the low direction leads to the emergence of an overshoot in the shear stress and the normal stress difference. To conclude, it is admitted that in polymer nanocomposites, the normal stress difference has two origins similar to those claimed for linear viscoelastic properties: the polymer matrix and the particles. At low shear rates, the illers are not oriented and are structured into a 3D network, which itself helps to generate additional normal forces. At high shear rate, the network structure is destroyed and anisotropic particles (or clusters) are oriented in the low direction, which reduces the ability of polymer chains to return to their coil shape and consequently limit normal stresses generation. However, while the steady shear viscosity approaches that of the polymer matrix at high shear rate, the inverse dependence is observed for steady-state normal stress difference [118]. 3.3.2

Flow-Induced Structure in Nanocomposites

As we aforesaid in detail, the rheological properties of suspensions (even more for nanocomposites) are determined by the spatial organization of the particles, usually referred to as the microstructure. In quiescent conditions, in the absence of low, a wide range of organizations can be observed in different materials, depending on the relative values of Brownian, repulsive, and attractive forces [102, 119–121]. When Brownian forces dominate and the volume fraction is below the luid–solid threshold,

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the particles organize as in a disordered liquid. When the repulsive forces dominate, ordered crystalline structures can be obtained [122]. At low volume fractions, when the attractive forces dominate, the particles aggregate or gel into self- similar clusters with fractal structure [119, 123]. It should be noted that high polydispersity of nanoparticle size drastically limit ordered crystallinity in such a system. For noncolloidal suspensions, the behavior is mainly dominated by hydrodynamic interactions except for high iller volume fractions for which collisional effects, frictional effect, can appear. As a representative example, the case of fractal–cluster structure can be brought up. As demonstrated in Section 3.2, the fractal–cluster structure controls the linear viscoelastic rheological properties of aggregated dispersions [51, 55]. A low-frequency plateau of the storage modulus occurs and the effects of particle size and colloidal or noncolloidal interactions have been elucidated [47, 52, 124–126]. Some of the nonlinear rheological properties, such as the yield stress, correlate well with the evolution of the linear viscoelastic ones [51, 52]. These typical behaviors are observed close or above the luid–solid threshold and concentrate the majority of the effort in the ield. The case of the quiescent behavior of dilute suspensions has been already well understood. From a general point of view, at rest, literature [127] shows that the formation of highly anisotropic structures is not observed for both low and high volume fractions of isotropic illers whatever be their colloidal nature. The particle organization remains homogeneous at a large scale. However, it has been shown that entropy can lead to nematic state for anisotropic particles at a high concentration [53, 128]. Usually, structure distortion is observed when submitting the suspensions to low. Structure formation during low is strongly affected by the delicate balance among interparticle forces, Brownian motion and hydrodynamic interactions. The resulting nonequilibrium microstructure is a principal determinant of the suspension rheology. It is generally observed that it appears to be a correlation between the anisotropic microstructure and the rheological behavior (Fig. 3.13b). For instance, colloidal suspensions can develop as anisotropic and amorphous structures at low shear rates or elongation ratio. For silica/PDMS nanocomposites (in the aggregated state), Schneider and Göritz [129] found that the mass fractal dimension decreases due to the deformation (Fig. 3.13a). Due to the stretching, the aspect ratio of cluster increases up to 60. At high rates, clustering due to strong hydrodynamic forces leads to shear thickening rheology. Distortion of the microstructure will occur when the timescale associated with low is smaller than the timescale associated with local scale diffusion, that is, when the reciprocal of the shear rate is smaller than the time for diffusion (�̇ −1 < tDiffusion ). This constraint is equivalent to Péclet number larger than unity. Literature [127] often deals with the application of steady shear low to suspensions with repulsive interactions that induce a rich sequence of transitions to 1D, 2D, and 3D orders. In addition, short-range attractive interactions can lead to a luid-to-gel transition under quiescent suspensions. Application of low leads to orientation, breakup, densiication, and spatial reorganization of aggregates. Using a non-Newtonian suspending medium leads to additional possibilities for organization [127]. Once again, the difference between low and high iller content must be pointed up. Literature is widely focused on the microstructure distortion of highly illed

FLOW PROPERTIES OF NANOCOMPOSITES

3.0

dm

2.6 2.4

2.0

12

500

10

400

8

300

6

200

4 A

100

1.8 1.0

1.5

2.0 2.5 Elongation ratio

(a)

3.0

0

0

I

2

A - Anisotropic S(q) I - Isotropic S(q) 10

20

30 40 Time (s)

2

2.2

600

Stress (dyn/cm )

2.8

dm dm1 dm2

S(q)aq = 0.032

3.2

99

50

0 60

(b)

Figure 3.13 The different mass fractal dimensions as a function of the elongation ratio resulting from the three different q-ranges: full range, dm , that is, from the minimum q visible to approximately 0.2 nm−1 , dm1 from the range on the right-hand side of the minimum up to approximately 0.2 nm−1 , and dm2 from the range on the left-hand side of the minimum. Reproduced from Schneider and Göritz [129] with permission of AIP Publishing. (b) Comparison of the evolution of S(q) at low q with the stress evolution of organophilic silica-hexadecane at � = 0.035 at 3 s−1 . Reproduced from Varadan et al. [130] with permission of American Chemical Society.

colloidal or noncolloidal systems. However, one of the most outstanding results for diluted or semidiluted suspensions is the low-induced alignment of particles. This phenomenon, irstly reported by Michele et al. [131], refers to the alignment of noncolloidal spherical particles (60–70 nm) in viscoelastic luids to form long string-like structures that are oriented in the low direction in both steady shear and oscillatory shear lows. This phenomenon was observed only at high shear rates such that the ratio of the irst normal stress difference and the shear stress exceeded a certain critical value. Recently, from 2D simulations, Hwang et al. [132] have observed a typical transition in particle structures in a sequence: random, clustering, clustered string, and string formation, as the solvent viscosity lowers and the Weissenberg number increases. The point is that these structures are not stable and that changing the low can turn back the system to the homogeneous distribution. Anyway, this is the only rheological way to build large-scale anisotropic structures. 3.3.3

Elongational Flow

Elongational low situations are met in almost all rubber processing operations so that elongational rheology is an important issue to address. The methods developed to quantify elongational viscosity are based on different types of experiments: ilament stretching (i.e., “spinning,” in which the strain rate varies signiicantly with position, therefore leading to heterogeneous elongation of the sample), homogeneous stretching under constant elongation rate or stress, or at constant sample length, and

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convergent lows. All these approaches entail strong experimental dificulties, which explains that published data about extensional viscosity are very scarce compared to shear viscosity data. In ilament-stretching experiments (FiSER), steady-state lows hardly ever attained. Indeed, a steady elongational strain rate implies that test sample length should grow exponentially where no material can sustain indeinitely. (Homogeneous) stretching experiments are thus limited to low extension rates and small strains. At present, this technique is still in use with nanocomposites [133], but the rheometer originally designed by Meissner, based on the rotary clamp technique, has gained importance. This is mainly due to the fact that this rheometer allows the material to be elongated homogeneously within a zone of constant length between the clamps and that the stress and strain can be measured with accuracy and sensitivity. Moreover, large Hencky strains can be obtained, and the Hencky strain rate can be maintained constant by keeping the rotation speed of the rollers constant. New generation of devices able to apply well-controlled elongational low have also emerged 10 years ago. The device consists of two drums mounted on a system of gears and bearings connected to a drive shaft whose rotation results in the desired Hencky strains on the two drums, which rotate equally but in opposite directions. The ixture was mounted on a controlled-strain or controlled-stress rheometer. The maximum Hencky strain allowed is lower than the Meissner’s rheometer but, on the other hand, the range of strain rate is shifted toward the rate up to maximum 30 s−1 (compared to 1 s−1 for the Meissner rheometer). Commercial rheometers of this kind were used in recent studies of EVA–clay or PP–clay nanocomposites, as will be reported later. Finally, among all the “stretching” techniques, the Capillary Breakup Extensional Rheometer (CaBER) is able to quantify elongational properties of luids or semisolids. Apparent extensional viscosity � E can be determined by monitoring the evolution of the ilament diameter as a function of time. Generally, the addition of nanoillers in polymer matrix results in an enhancement of the elongational viscosity. Using CaBER, Wang et al. [134] have shown that silica nanoparticles in aqueous polyethylene oxide solution of high molecular weight were found to enhance the extensional low properties. Extensional viscosity enhancement was also observed for CNT dispersions as the result of orientation of CNT in the low direction during the stretch [135]. Chellamuthu et al. [133] investigated the extensional rheology of dispersions of fumed silica particles suspended in low molecular weight PPG using FiSER. They found that beyond critical extensional rate, a dramatic increase in strain hardening of extensional viscosity was observed similar to the thickening transition observed in shear but with a larger magnitude. Their results were direct observations of hydrodynamic clustering in extensional low. Using CaBER, the extensional rheology of fumed silica nanoparticles dispersed in an aqueous polyethylene oxide solution has been investigated by Khandavalli and Rothstein [136]. It was found that the addition of nanoclay particles to the polymer melt increases the elongation viscosity principally at low strain rates (Fig. 3.14). The dispersions showed strong strain-hardening behavior with thickening magnitudes

FLOW PROPERTIES OF NANOCOMPOSITES

Steady-state trouton ratio, ηE,∞/η0 ( )

200

10

180 8

160 140 120

6

100 80

4

60 40

2

20 0 2.5

3.0

3.5

4.0

4.5

5.0

0 5.5

Extensional relaxation time, λE (ms) ( )

101

Fumed silica nanoparticle concentration (wt%)

Figure 3.14 Steady-state Trouton ratio � E,∞ /� o ( ) and extensional relaxation time �E (▸) as a function of fumed silica nanoparticle concentration in 0.6 wt.% aqueous PEO solution (Mw = 6 × 105 g/mol). Reproduced from Khandavalli and Rothstein [136] with permission of AIP Publishing.

similar to that observed under shear. The trends in the magnitude of extensional hardening with particle and polymer concentration were found to be similar to shear. In some cases, extensional thickening of nearly 1000 times was observed. The increase in the strain-hardening behavior with increasing silica particle loading was attributed to increased bridging between particles and polymer chains and the development of a stronger interparticle network structure as was observed in the shear rheology and linear viscoelastic measurements. On the contrary, Xu et al. [137] found extensional thinning behavior for entangled nanoiber/glycerol–water dispersions using opposed jet device. This is likely a result of breakdown of entangled nanoiber network structure under extensional stress. In some cases, reduced strain hardening due to the presence of illers has been reported in the literature. For instance, Chan et al. [138] reported that the strain-hardening properties of high-density polyethylene or polystyrene were decreasing when adding glass ibers. Takahashi et al. [139] reported that LDPE composite systems, illed with glass ibers randomly dispersed, had strain-softening properties. Boyaud et al. [140] showed for polymer/polymer composites (the iller was a polymer dispersed phase below its glass or crystallization temperature) that strain hardening was considerably reduced and that strain softening appeared. The authors suggested that strain hardening of such composites was correlated to the homogeneity of the low at the iller interface. When the elongational low was disrupted in the interphase region so that the deformation around the particle was not homogeneous, strain softening occurred. Very few data can be found in literature concerning elongational viscosity of layered silicate composites, and most of them deal with ethylene-vinyl acetate (EVA)

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copolymer-based nanocomposites as in the papers by Bhattacharya and his coworkers [117, 141] and by La Mantia and Dintcheva [142]. The results reported by La Mantia and Dintcheva [142] with intercalated composites of EVA (14% VA) and montmorillonite, at loadings of 5% and 10%, show that, whatever the elongation rate, strain hardening is emphasized by the presence of the nanoiller. The extensional viscosity of the nanocomposites is higher than that of the neat polymer and increases with iller content. Similar to that observed for shear low, the effect of the nanoparticles is attenuated as the elongation rate increases. However, in some cases, the opposite is observed, as presented in Figure 3.15. The amplitude of the strain-hardening effect is reduced in the case of these exfoliated nanocomposites compared to pure polymer. Microstructural analysis of these strained samples by TEM showed that the extension of the material at large Hencky strains (beyond 3 in the present case), in which the nanoparticles were initially predominantly exfoliated, had resulted in a modiication of the dispersion, namely aggregation of the iller material and reformation of the so-called tactoids. This supports the attempt of the authors for a phenomenological explanation: in an exfoliated structure, the interactions between polymer and individual clay layers dominate over the interlayer interactions. The idealized morphology consists of a random dispersion of clay layers with different orientations, forming spheres or ellipsoids of clay surrounded by entangled polymer chains. Gupta et al. [117] assume that upon extension, causing axial stretching of the polymer chains, the interlayer distance decreases due to cross-sectional contraction of the sample, and electrostatic attraction develops between the edge surface of clay (not protected by organic coating) and the lat surfaces, providing a “house-of-cards” 1.00E-06

η+E(Pa s)

1.00E-05 3η° 1.00E-04

1.00E-03

1.00E-02 1.0E-01

EVA28 (strain rate = 1.0 1/s) EVA28 (strain rate = 0.5 1/s) EVA28 (strain rate = 0.11/s) EVA28–5% (strain rate = 1.0 1/s) EVA28–5% (strain rate = 0.5 1/s) EVA28–5% (strain rate = 0.1 1/s) 1.0E-00

1.0E-01

1.0E-02

Time (s)

Figure 3.15 Extensional viscosity proiles as a function of time for EVA28 (28% VA) and EVA28 nanocomposites at 130 ∘ C and at different elongation rates. Nanoiller is organomodiied bentonite, contents are in wt%. For clarity purposes, the viscosities of EVA28 with 2.5% and 5.0% nanoillers were multiplied by 10 and 50, respectively. Reproduced from Gupta et al. [117] with permission of Elsevier.

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network structure. van der Waals forces become stronger as clay layers get closer and locculated structures (face-to-face associations) eventually form. In conclusion, these results clearly illustrate the importance of the dispersion and polymer–iller interactions in the strain-hardening behavior of nanocomposites. In this respect, they can be compared with those obtained by Lee et al. [143] with polypropylene/layered silicate nanocomposites: only those composites containing maleic anhydride-grafted PP as a compatibilizer exhibited strain hardening, as a result from the presence of a 3D structure of exfoliated platelets strongly interacting with the polymer, and thus reducing the rate of polymer disentanglement.

3.4

THEORY AND MODELING OF NANOCOMPOSITES RHEOLOGY

In addition to experimental investigations, rheological modeling is important for the theoretical enlightenment of nanocomposite low problems. Constitutive equations, which describe the viscoelastic phenomena of polymeric liquids, have paid attention from scientiic community since many years. Practically, constitutive equations for polymeric liquids should describe both linear and nonlinear rheological behaviors such as shear thinning, normal stress differences, strain hardening, and time-dependent behavior. However, the complexity of constitutive equations may lead to numerical dificulties, and a universal model is still not available for the prediction of the whole experimentally observed rheological behaviors. This is mainly due to the complex interactions (particles/particles or polymer/particles) that control the macroscopic rheological response and the evolution of the microstructure or mesostructure during deformation. However, modeling of polymer nanocomposites rheological behavior has also received considerable attention. As we presented in the last section, the low characteristics of polymer nanocomposites depend on the size and shape of nanoparticles, volume fraction, interparticle interactions, and polymer–iller interactions. This large number of parameters forces to take into account a variety of physics (hydrodynamic interaction, low-induced orientation, dynamic clustering, elastic or viscous interaction, etc.), which is really tricky to integrate in one unique and universal constitutive equation. Generally, modeling attempts have been segmented according to the different rheological properties, low kinematics, iller anisotropy, and so on. Different models have been developed to capture and describe at best each of the different rheological property or behavior by introducing the relevant physics. On the other hand, improvement of numerical facilities has gained importance and is a powerful tool to solve complex constitutive equations even in complex lows and to provide physical insights into nanocomposites rheology [144–147]. So, modeling of the shear viscosity in steady lows will irst be addressed. Then the dynamics oscillatory shear lows will be regarded with respect to the microstructure of nanocomposites. As it is often encountered in processing circumstances, elongational low has paid great attention and the corresponding models will be presented. Finally, the different quantitative models of the Payne effect are detailed.

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3.4.1

RHEOLOGY AND PROCESSING OF POLYMER NANOCOMPOSITES

Steady-State Viscosity

As aforementioned, unlike the Newtonian behavior, for nanocomposites, strong thinning effects have been reported and generally the viscosity at high shear rates is almost independent of iller loading and comparable to that of the unilled polymer. This is reasonably attributed to the orientation of the layers in response to the applied shear deformation and the corresponding weak interactions between the polymer and the layered silicate. Another very unexpected inding is the reduction in viscosities arising from the incorporation of nanoparticles in the experiments [114, 148]. Authors have shown that this remarkable decrease in viscosity is attributed to the change of the free volume caused by the nanoparticles. For a better understanding of such inding, several computer simulation studies have been initiated toward this objective. Smith et al. [112] utilized molecular dynamics (MD) simulations to irstly investigate the viscoelasticity of model polymer nanocomposites. Inluence of the nanoparticle volume fraction, the speciic nanoparticle/polymer interfacial area, and the nature of the nanoparticle–polymer interaction has been investigated. In the simulations, the shear stress relaxation modulus, G(t), for each polymer nanocomposite was calculated by using the time autocorrelation function of the stress tensor. The viscosity � of each system was then calculated from Einstein’s relations: V ⟨P (t)P�� (0)⟩ kB T �� ⟨ ⟩ ∑∑ V 2 [A�� (t) − A�� (0)] � = lim t→∞ 12kB Tt � �≠�

G(t) =

A�� (t) − A�� (0) =

∫0

(3.15) (3.16)

t

P�� (t′ )dt′

(3.17)

where P�� (t) is an instantaneous value of the off-diagonal element of the stress tensor at time t, V is the volume of the system, kB is the Boltzmann constant, T is the temperature, and the brackets denote averaging over the whole trajectory and all six off-diagonal elements of the stress tensor. Results of the simulation have been already shown in Figure 3.12. Taking into account the nature of polymer–iller interaction in a modeling approach allows to conirm and to understand experimental indings for relative shear viscosity. Using the same coarse-grained polymer model for their simulation of shear rate dependence of viscosity of model nanocomposites, Kairn et al. [149] shown that although there are some signiicant differences in the scale between the simulated model polymer composite and the system used in the experiments (attributed to the consideration of only repulsive interaction between illers in the simulation), some important qualitative similarities in shear behavior are observed. Particularly, they conirm that when particles have the same size as the polymer coils, the particles act as a solvent or a plasticizer and the viscosity decreases, but if the illers are only slightly bigger than twice the size of the polymer chains, the viscosity increases with increasing iller concentration.

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Again, coarse-grained computer simulations have been used by Pryamitsyn and Ganesan to delineate the mechanisms governing the steady shear rheology of polymer–nanoparticle composites. Their results suggest the shear rheology of the composite is very similar to that of colloidal suspensions in a simple luid when polymer rheology, the particle-induced changes in the polymer rheology, and the polymer slip effects are accounted. At dilute and semidilute nanoparticle concentrations, the composite shear rheology is shown to be dominated by the shear thinning of the polymer chains, whereas for higher particle loads, the polymeric contribution to the rheology becomes much less important [150]. Without any weighty computing needs and only using classical concepts of polymer physics, an analytical model for illed concentrated solutions and polymeric melts have been proposed by Sarvestani et al. [151, 152] and compared to shear viscosity data. The dynamics of polymer chains is modeled using the Generalized Rouse Model, while the stick-slip process of the chain–iller interaction is modeled in a homogenized way through an additional friction force. As a whole, the model is purely frictional in nature. The focus has been on systems with nanoillers in which the energetic interaction of polymers and illers is strong. Interestingly, this model is the irst to introduce two mechanisms: entanglements and the process of attachment/detachment of chains from illers, which are assumed to play the most prominent role in the rheology of these materials. The agreement is good with experimental data, although some discrepancies exist in the highly nonlinear range of strain rates (surely due to the homogenized representation of the polymer–iller attachments and the dumbbell simpliication to capture the stick-slip process). The advantage of the model derives from its simplicity and conceptual unity. The parameters have transparent physical meaning. Another application of the basic concepts of the model has been developed to predict the linear viscoelastic behavior of polymer nanocomposites and is described further. 3.4.2

Dynamic Rheology

The irst models to estimate the dynamic rheological properties of polymer composites containing colloidal hard spheres in the limit of low shear rate have been proposed by Batchelor, Kerner, and Krieger–Dougherty. The impact of hard spherical inclusions on the viscoelastic properties is generally represented by the following generic equation: (3.18) G∗ (�) = G∗m ⋅ f (�) where G* and G* m are the complex shear modulus of the composite and of the matrix, respectively. The function f(�) differs according to the authors: Batchelor f (�) = 1 + 2.5� + 6.2�2 ]−[�]�m [ � Krieger-Dougherty f (�) = 1 − �m Kerner f (�) =

2 + 3� 2(1 − �)

(3.19a) (3.19b) (3.19c)

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RHEOLOGY AND PROCESSING OF POLYMER NANOCOMPOSITES

It can be easily noted that the proposed models were derived to take into account hydrodynamic interactions between rigid iller. Considering the case of low iller content (typically � ≤ �c ), it is possible to use the above-mentioned expressions in order to it complex shear modulus in both low and high frequency regions. However, in the case of iller loading above critical fraction for percolation, the relative complex shear modulus is largely underestimated especially in the low-frequency regime. As it could be expected, these models are unsuitable to catch the appearance of a yield stress. In the past decades, quite a variety of empirical non-Newtonian models have been proposed to solve this issue and to provide analytical expression for frequency dependence of the shear complex viscosity of nanocomposites. The irst attempt was done by deKee and Turcotte [153] who proposed a three-parameter model described by the following equation: � = �y �−1 + �1 e−t1 � (3.20) where � y is the yield stress. The limiting viscosity � 1 represents the zero-shear viscosity value when the solid network is absent, while t1 is a characteristic time related to the velocity of the viscosity drop at high frequencies. Characteristic time and limiting viscosity were presented by the authors as empirical parameters, with no evident physical meaning or correlation with material parameters. This model its very well the viscosity data in the low-frequency zone but fails at high frequencies. Mitsoulis et al. [154] modiied the so-called Herschel–Bulkley model to predict shear-thinning behavior of complex luids, with an expression reported in the following equation: � = k�n−1 + �y �−1 [1 − e−m� ] (3.21) where � y is the yield stress, n is the low behavior index, k and m depend on parameter n. Similar to the model of deKee and Turcotte, parameters have no physical meaning. Zhu et al. [155] proposed a modiication of the original deKee–Turcotte model in order to predict a inite value of the apparent viscosity when the shear rate approaches zero: � = �y �−1 [1 − e−m� ] + �1 e−t1 � (3.22) Recently, Dorigato et al. [13] have suggested a modiication of the original deKee–Turcotte expression in order to obtain a satisfactory itting of the rheological data in the high- frequency region. In particular, the following empirical equation is proposed: � � = �y �−1 + �1 e−t1 � (3.23) It can be noted that a new parameter � is introduced in order to improve the ability of the model to follow the nonlinear viscosity drop at high frequencies. Actually, all the previous models were proposed only on the basis of their itting capabilities. However, the model of Dorigato seems to be the most eficient to it experimental data in the case of LLDPE illed with fumes silica.

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In order to characterize changes in the rheology data induced by the addition of nanoparticles, various phenomenological spectral approaches have also been used [156–158]. These approaches allow to get a parametrization of the effect of nanoparticle addition. In this way, the BSW model by Baumgaertel et al. [159] is based on the fact that even a very complex relaxation process can always be described as a superposition of idealized Maxwell components with different characteristic relaxation times �, in this case implemented as a continuous relaxation spectrum H(�). Therefore, the complex shear modulus G*(�) can be calculated from the spectrum via G∗ (�) = Gelastic + i�

∫0

∞

H(�)(1 + i��)−1 d�

(3.24)

where Gelastic is the frequency-independent modulus (can be a complex), which may be used to describe the state of gelation in physically or chemically cross-linked materials. The high-frequency regime that has been shown to relect only hydrodynamic interaction between illers can be generally well described by the original ansatz proposed by Baumgaertel et al. for the spectrum H(�) [159]. On the other hand, to quantitatively include the possibility of gelation in the model (as a footprint of the particle network), a gel relaxation contribution Hgel (�) has to be added to the relaxation spectrum H(�). Several expressions have been suggested. Nusser et al. [157] deined this contribution in accordance with the literature by a self-similar relaxation pattern: Hgel (�) = Sgel ∕Γ(n) �−n

(3.25)

where Γ(n) is the gamma function, the amplitude Sgel represents the gel stiffness, and n is a relaxation exponent between 0 and 1. Gelfer et al. [158] have shown that the rheological behavior of nanocomposites below the gelation threshold could be described by the modiied Cole model, while the rheology of gel-like nanocomposites could be described by the log-normal model, which is deined by the following expression of the relaxation spectrum: H(�) = (2�� 2 )−1∕2 exp[−ln(�∕�0 )2 ∕(2� 2 )]

(3.26)

where �0 and � are parameters, whose physical signiicances have been described by Drozdov [160]. Even if such approaches do not bring any predictive insight into the macroscopic rheological behavior, the spectral decomposition gives the opportunity to highlight some microscopic mechanisms and the evolution of microstructure according to formulation or processing parameters. In this way, for PP/layered silicate nanocomposites, Kovacs et al. [156] have shown that silicate network initiates processes with long relaxation times, only detected by dynamic rheology. In a more predictive and theoretical approach, Sarvestani and Picu [151] proposed a molecular network model describing the viscoelasticity of polymer-based

RHEOLOGY AND PROCESSING OF POLYMER NANOCOMPOSITES

108

1000

F Bridging segment

100

G

Volume fraction = 12% Volume fraction = 6%

H

10

Loop

G'(ω) kBT

I

J

1 0.1

K

0.01

Polymer-iller junction (A-point)

0.001 0.001

0.01

(a)

0.1 ω τRN

1

10

(b)

Figure 3.16 (a) The internal chain-scale structure of the system. G, H, I, J, and K represent attachment points of a chain to two particles. Chain segments such as HI bridge illers. A large number of polydisperse loops (e.g., GH, IJ, and JK) and dangling ends (e.g., GF) are attached to each iller. (b) Prediction of Sarvestani’s model for the storage modulus G′ of nanoilled polymer systems at different iller volume fraction (� = 6%, 12%) with constant energetic polymer–nanoparticle interaction. Reproduced from Sarvestani and Picu [151] with permission of Elsevier.

nanocomposite and particularly the complex shear modulus. They considered the case of well-dispersed nanoparticles in an amorphous monodispersed homopolymers. Filler concentration and favorable energetic interactions between polymer and illers allow the formation of polymer–iller junctions. Under these conditions, a network of nanoparticles and adsorbed macromolecules is formed as depicted in Figure 3.16. The kinetics of this network is represented within the framework of the traditional transient network theories [161]. The evolution of the internal structure during deformation (represented by the distribution function for bridging segments ΨBi ) is governed by a convection equation: �ΨBi �t

=

−� ̇ + Gi (R, t) − Di (R, t) ⋅ (ΨBi R) �R

(3.27)

where Gi (R, t) and Di (R, t) represent the rate of generation and destruction of bridging segments per unit volume, respectively. The contribution of the dangling ends (the distribution function of dangling seg) is accounted for using a so-called elastic dumbbell model. ments ΨD i The model assumes that both segment types (bridged and dangled) contribute to stress production, and that this contribution may be expressed as a superposition of contributions: ∑ (TiB + TiD ) (3.28) T= i

where TiB and TiD represent the stress contribution of bridging and dangling strands of length (i) Kuhn units, respectively. These quantities are evaluated using the virial

THEORY AND MODELING OF NANOCOMPOSITES RHEOLOGY

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equation as: TiB = ⟨FiB R⟩B , TiD = ⟨FiD R⟩D

(3.29)

The brackets denote averaging over the respective coniguration space, that is, ⟨Qi ⟩j = j ∫ Ψi dR. Fi is the tension in the strand (i) that favor the detachment process (this force can be represented by using the Warner approximation to the inverse Langevin function). The evolution of the total stress is thus obtained using Equation (3.29) and by resolving the set of convection/diffusion equations. Several features of the model were demonstrated for applied steady and oscillatory shear deformation. Interestingly, it is observed that, to a large extent, the overall material viscoelasticity can be controlled by the lifetime of iller–polymer junctions. This model shows its capability to predict the transition to rubber-like behavior at low frequencies in case of very strong iller–polymer interactions. The advantage of the model derives from its simplicity and conceptual unity. The linear viscoelasticity behavior of composites of spherical nanoillers dispersed in polymer melt matrices has also been investigated using computer simulations (coarse grain approach) [110]. Overall, the particles can contribute to G′ (�) in three different ways: (i) The particle-induced effects on the polymer segments can modify the dynamics and relaxation spectrum of the polymers. (ii) Particle jamming effects can lead to slow relaxations and substantial enhancements in elasticity. (iii) The strain ield distortion caused by the presence of rigid inclusions can affect the overall modulus of the composite. 3.4.3

Elongational Rheology

It is dificult to predict the rheological properties in the elongational low based on shear properties because polymeric liquids show different rheological properties under elongational low compared to shear low properties. Moreover, elongational low is essentially nonlinear, and a more complex formalism to capture the evolution of the elongational properties is required. However, recent development in numerical techniques makes it possible to apply differential and even integral type of constitutive equations to both shear and elongational lows. We present, hereafter, various approaches from more or less phenomenological models to microscopic or mesoscopic based constitutive equations. Lee et al. [162] proposed to model elongational properties of PP/layered silicate nanocomposites prepared with or without compatibilizer using the so-called K–BKZ constitutive equation. The K–BKZ constitutive equation can calculate material functions from some rheological measurements. Practically, application of the model becomes successful through accurate determination of the viscoelastic parameters, for example, relaxation time spectrum and nonlinear damping function in a constitutive equation. When the time–strain separability can be assumed, a general form of the K–BKZ integral-type constitutive equation is given by t

�(t) =

∫−∞

m(t − t′ )[h1 (I1 , I2 )Ct−1 (t′ ) + h2 (I1 , I2 )Ct (t′ )]dt′

(3.30)

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where m(t − t′ ) is the memory function, Ct−1 (t′ ) and Ct (t′ ) are the Finger strain tensor and Cauchy strain tensors respectively. The damping functions h1 (I1 , I2 ) and h2 (I1 , I2 ) are written as a function of the irst invariant (I1 ) and second invariant (I2 ) of the Finger strain tensor. In order to simplify the damping functions h1 (I1 , I2 ) and h2 (I1 , I2 ), it is generally assumed that the ratio of the irst and second normal stress differences N2 /N1 is constant in shear low. This ratio can be deined as follows: b=

h2 N1 = N2 h1 –h2

(3.31)

where combination of Equations (3.30) and (3.31) yields t

�(t) =

∫−∞

m(t − t′ )h(I1 , I2 )[(1 + b)Ct−1 (t′ ) + bCt (t′ )]dt′

(3.32)

Nonlinear behavior in both shear or elongational should be captured using a proper damping function. Lee et al. [162] have tested two different types of damping functions. Wagner and Demarmels [163] suggested one type, and it was modiied by Feigl and Ottinger [164] (WD–FO model): h(I1 , I2 ) =

1 1 + �(I1 –3)n (I2 − 3)n

(3.33)

where � and n are parameters that control the response of the damping function in uniaxial elongational lows. Another model is proposed by Papanastasiou et al. [165] and modiied by Luo and Tanner [166] (PSM–LT model): h(I1 , I2 ) =

� (� − 3) + �I1 + (1 − �)I2

(3.34)

where � and � are nonlinear model constants to be determined from shear and uniaxial elongational lows. Although the WD–FO did not show the steady-state value and diverge to ininity at higher strain rates, the PSM–LT model agrees well with the experimental results in uniaxial elongational low. The PSM–LT model gives a good description of the experimental data and the steady-state viscosities in almost all the ranges of elongational rates. Especially, it also gives a quantitatively good it for outstanding strain hardening of compatibilized nanocomposites. It is more or less a tie between the two damping functions. However, the PSM–LT model has good applicability to the PP/layered silicate nanocomposites because possibility of stress divergence is much smaller than in the case of the WD–FO. Both models only provide simple and easy tractable way to predict elongational material functions from shear measurements that are more easy to obtain. However, all the parameters used in both models have no structural or microscopic origin so that the predictive skills are limited. In a more predictive way, Kagarise et al. [167] have developed a constitutive model for characterization of shear and extensional rheology and low-induced orientation

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of carbon nanoiber/polystyrene melt composites. The model is microstructurally based and aims at predicting the experimentally observed rheological behavior and evolution of nanoiber orientation. They seek to improve the understanding of how nanoparticle concentration and orientation affect the transient shear and transient uniaxial extensional low behavior of polymer/nanoparticle composites and how the nanostructure of the particles evolves during low. The constitutive model describes the total stress in the composite during low as the summation of the low-induced stress in the polymer and the low-induced stress caused by the presence of nanoibers. Moreover, an equation is dedicated to the prediction of the orientation evolution of the nanoibers, which affects the stress caused by the presence of nanoibers. The total stress reads p

Tij = −p�ij + 2�s Dij + Tij + TijCNF

(3.35)

where T p is the contribution of the polymer and TCNF is the contribution of nanoiber. The low-induced stress in the polymer is characterized by a ive-mode Giesekus model containing parameters for polymer viscosity, relaxation time, and mobility factor, � p , �, and �, respectively, which are determined from the properties of the polymer matrix. p DTij,m � � p p p Tij,m + �m (3.36) + m m (Tik,m Tkj,m ) = 2�p,m Dij Dt �p,m The low-induced stress caused by the presence of nanoibers TCNT is affected by the orientation of the nanoibers and is described by the following equation derived by Tucker [168]: TijCNF = 2[�s + �E ]�[ADkl aijkl + B(Dik akj + aik Dkj ) + CDij + 2Faij Dr ]

(3.37)

where � is the volume fraction of the nanoibers, � s and � E are the shear and extensional viscosities, respectively, and Dr is the rotary diffusivity due to Brownian motion. The coeficients A, B, C, and F are the shape factors (expressed in other works by Lozano et al. and Ma et al. [169–171]) that are functions of the particle aspect ratio r = L/D, with L being the particle length and D being the particle diameter. The evolution of nanoparticle orientation during low is captured by the second-order orientation tensor a and is described by the following equation: daij

1∕2

= (Wik akj − aik Wkj ) + �(Dik akj + aik Dkj − 2Dkl aijkl ) + 4CI IID (�ij − 3aij ) (3.38) Three unique parameters are required: �, aijkl , and CI . � is a shape parameter. The orientation predicted by the model depends on the value of the iber–iber interaction parameter CI . Wij and Dij are the skew and symmetric parts of the Eulerian velocity gradient, respectively, and IID is the second invariant of Dij . dt

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In a classical way, determination of model parameters for pure polymer was done using both small-amplitude oscillatory data and steady shear viscosity ones. Interestingly, the model parameters related to the presence of nanoibers have been determined from the TEM observation of iber orientation state. Therefore, the proper value of CI was determined from the comparison of model predictions with experimental measurements. To summarize, this model was shown to accurately predict the nanoiber concentration dependence of transient shear and transient extensional rheological behavior and nanoiber orientation development during low using a single set of model parameters. Moreover, the Trouton ratio of nanocomposites was accurately predicted by the model (except for iller fraction close to the percolation threshold, which was quite expected as agglomeration is not implemented in the model). The advantage of this constitutive model is that all model parameters can be determined from experimental measurements and have quite physical meaning. In order to capture the transient and coupled evolution of stress and orientation of anisotropic particle in polymer melt, Eslami and Grmela [172] have formulated a mesoscopic rheological model of a spatially homogeneous and isothermal suspension of completely exfoliated clay lamellae nanoparticles. They used an improved version of the so-called FENE-P dumbbells with an additional reptation term in combination with tensorial description of solid ellipsoid particles orientation to model the low properties of layered nanoparticles/polymer hybrids at homogeneous low ields. The formulation of the theoretical model at the mesoscopic level allows combination with other conformation tensors. Therefore, again, the total stress is assumed to be the summation of polymer matrix and nanoiller contributions. The state variables are two symmetric 3 × 3 tensors designated hereafter as C and A corresponding to polymer conformation and particle orientation states, respectively. They simply describe the extension of the polymer chains and the orientation of thin disks (layered organoclay particles), respectively. In the conformation tensor level, the state variable for the polymer chains is described by a 3 × 3 tensor C(t, s), which is the second moment of the distribution function: �(R, s)Ri Rj dR (3.39) Cij = ∫ A group of ellipsoid particles are represented by a probability distribution function �(p), deined as the probability for a particle being aligned within an angular range dp of the direction p is equal to Aij =

∫

pi pj �(p)dp

(3.40)

The overall free energy of the suspensions of ellipsoidal particles in the viscoelastic luids can be expressed by tensors C and A. Two equations governing the time evolution of the particle orientation and polymer conformation tensors have been derived [173]. As the complete set of equations is voluminous, we rather encourage readers to refer to the original paper [172, 174].

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The originality of this theoretical development lies in the fact that classical but arbitrary closure approximations are avoided by formulating the governing equations directly on the conformation tensor level. The disadvantage is, of course, that most of the parameters used at the conformation tensor level are more phenomenological than those used on the � level. However, the mesoscopic level of description appears to be a good compromise between microscopic details and overall simplicity of the governing equations. The results show a good agreement for start-up lows at higher shear rates and less satisfactory agreement at lower shear rates. For steady shear low, model predictions and experimental data are in good agreement specially in the case of small content of the nanoparticles. Actually, as aforementioned in the section dedicated to rheology of nanocomposites, the impact of the iller–iller or iller–polymer interactions vanish at high strain rate. It is generally observed that the matrix behavior governed the overall rheological behavior in such a range of strain rate. Therefore, the modiied FENE-P model has well captured the nonlinear rheology of the polymer matrix but seems to fail when particle networking has to be considered.

3.4.4

Payne Effect

Several interpretations have been proposed to explain the Payne effect. As we aforementioned, the most commonly adopted is based on iller network breakage. Thereby, several models based on these assumed mechanisms have been developed. The irst was proposed by Kraus [175, 176] in a quite phenomenological manner. Huber and Vilgis [177] have adopted the same interpretation of the Payne effect and attributed the phenomenon to the dynamical processes of breakage and reformation of the iller network. The model is however based on the fractal nature of the network. As the strain amplitude increases, the iller network breaks into smaller and smaller fractal entities. Majeste et al. and Carrot et al. [86, 87], based on the work of Leonov, proposed a model that account for the contribution of the large agglomerates of illers, which are actually heterogeneous locs of strong particle–particle interactions. Contrary to these models based on iller network, Maier and Goritz [178] have suggested that iller–polymer interaction is responsible to the Payne effect. In the same way, Merabia et al. [94] attributed this effect to the presence of glassy adsorbed polymer shell at the surface of nanoiller. Polymer interaction is responsible for strong and weak bonds that are able to break and rebuilt under strain or temperature. Clement et al. [98] have recently tested several of these quantitative models on polydimethylsiloxane (PDMS) networks illed with treated Aerosil A300 silica at variable temperature and various loadings. The main conclusion is that each model is able to account only for a part of the experimental results: Kraus and Huber–Vilgis for the variation of the Payne effect with iller volume fraction and Maier–Goritz for the inluence of temperature on the Payne effect. But neither of these quantitative models is able to it the whole set of experimental results on G′ and G′′ with a unique set of parameters. In agreement with a new interpretation of the Payne effect proposed by Wang et al. [179], the Payne effect in nanocomposites seems to stem from the two contribution iller–iller and iller–polymer interactions.

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From a modeling point of view, it is clear that Payne effect has paid much attention and numerous interpretations have been given. Particularly in the domain of reinforced elastomers, we invite readers to refer to the more exhaustive review of Heinrich and Klüppel [43]. In this section, we only propose to give more briely the details about the main aforementioned models in order to highlight the difference in the main physical concepts and their limits and advantages. 3.4.4.1

Models Based on Filler Network Breakage

3.4.4.1.1 The Kraus Model Kraus proposed a phenomenological model based on iller network breakage and reformation. In this model, G′ and G′′ have the following expression as a function of the shear strain �: G′ (�) − G′∞ = G′0 − G′∞ G′′ (�) − G′′∞ G′′0 − G′′∞

1 ( )2m

1 + �� c ( )m � 2 � c = ( )2m 1 + ��

(3.41a)

(3.41b)

c

where � c is the shear strain at which (G′ − G′ ∞ ) reaches half its value at � = 0. � c corresponds to the breakage of half the number of iller–iller contacts. The m parameter gives the shear strain sensitivity of the mechanism of network breakage. When compared to experimental results, all these parameters vary with silica loading. However, no physical interpretation can be given for this variation. G′ and G′′ curves cannot be itted with the same value of m. Moreover, as evidenced experimentally, the Payne effect should exist even when volume fractions are below the percolation threshold. This is not captured by the model just like the temperature inluence. 3.4.4.1.2 The Huber–Vilgis Model According to Huber and Vilgis [177], the Payne effect is related to the fractal nature of the nanoiller network characterized by its fractal dimension and connectivity (see previous sections). When the shear strain increases, the iller network breaks into smaller (likely fractal) entities. When the form is considered, the expressions proposed by Huber and Vilgis are very similar to Kraus’s ones: G′ (�) − G′∞ 1 = G′0 − G′∞ 1 + K 2 � 2m

(3.42a)

G′′ (�) − G′′∞ 2�K� m = ′′ ′′ G0 − G∞ 1 + K 2 � 2m

(3.42b)

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K and � are itting parameters that are considered to be able to capture the temperature effect. Although being very similar to Kraus expressions, this model has the advantage of giving physical meaning to the m parameter. Related to the fractal dimension and connectivity of the network, m should have a universal value for a given nature of iller. Therefore, according to Huber and Vilgis, Payne effect should be a universal effect independent of the polymer–iller interaction. Unfortunately, this is not what is experimentally observed. In addition, this model inherits all the other limitations of the Kraus model. 3.4.4.1.3 The Majeste–Carrot Model Majeste et al. [87] have shown that the viscoelastic behavior of highly illed polymer that melts in oscillatory shear can be well modeled by the Leonov model [85]. As aforementioned, the low-frequency behavior is conventionally associated with the presence of a iller network. However, the observation of a secondary plateau on the loss modulus remains anomalous in this frame since a real iller network should not be a dissipative system. The presence of the dissipative processes was attributed to the existence of agglomerates (locs of particles). Experiments within polymer matrices of the same chemical composition and nature but having very different rheological behaviors and therefore different dispersion capability have shown the correlation between agglomerates and dissipation within the system at low frequency [86]. Dissipation of energy was attributed to the rupture of agglomerates. This mechanism is strain and time dependent. Therefore, only a model associating a kinetic equation (which governs the state of partition of the agglomerates) with a viscoelastic equation can be able to describe this behavior. The Leonov model [85] has shown its capability to capture the low-frequency behavior of such systems. The governing equations for shear lows read the following: �p + �p �p d�p �p dt

d�p dt

=

�̇ � Zc p

+ �p = �̇

�p �p

Gp

(3.43a) (3.43b)

The number of partitions � p is subjected to a kinetic equation (3.43a). In the timescale of the relaxation of locs � p , the intensity of deformation � may overcome a critical intensity of elastic deformation Zc , and therefore, the loc breaks. The iller contribution � p to the stress is given by the viscoelastic equation of the Maxwell type (Eq. (3.43b)). However, for very low strain, in order to capture the asymmetric shape of G′′ curves, Majeste et al. [87] have added a new mechanism of reorganization of the agglomerates. They consider that locs can undergo deformation before rupture. The internal reorganization is introduced within the agglomerates as a dissipative mechanism. Applying the same formalism of Leonov but at a lower length scale, they predict dissipative mechanisms even for strains below the critical strain for loc rupture Zc .

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116 107

G',Φ = 0.252 G'', Φ = 0.252 G',Φ = 0.335 G'', Φ = 0.335

G', G'' (Pa)

106

105

104 10–2

10–1

100

101

Strain (%)

Figure 3.17 Comparison of theoretical prediction and experimental data of the complex shear modulus at � = 1 rad/s for volume fraction of 0.252 (illed symbols) and 0.335 (open symbols) as a function of strain. The full line represents Equation (3.44a). Reproduced from Majeste et al. [87] with permission of John Wiley and Sons.

The kinetic equation remains strain rate dependent. The expression for the complex shear modulus is given by G′ (�) = Gp 1+ ( G′′ (�) = Gp 1+

(

1 � Zc

� Zc

(

+

+

� Zc

1 N

+

1 N

)2

(3.44a)

)

1 N

)2

(3.44b)

where N is the complexity of the loc and Gp is its modulus. This improved model well describes both oscillatory and strain sweep experimental results without inlation in the adjustable parameters as shown in Figure 3.17. It only needs the use of the number of hopping particles in the locs (N), which could be obtained by microscopic observations. Consistent values of the numbers of hoping particles per locs were found in agreement with the distribution of particle size. 3.4.4.2

Model Based on Filler Polymer Interaction

3.4.4.2.1 The Maier–Goritz Model Maier–Goritz [178] proposed a molecular interpretation of the Payne effect by introducing that during elaboration process,

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polymer–iller favorable interaction can induce polymer adsorption at the iller surface. Two types of polymer–iller bonds were considered by Maier and Goritz: Stable bonds that involved strongly adsorbed chains on the iller surface and unstable bonds related to molecules dimly adsorbed ( i.e., the number of adsorbed monomers is low). The last unstable bonds are likely to break when large strain or stress is applied to the system or if the temperature is raised. Then, as stated by the theory of rubber elasticity, the elastic modulus is related to the cross-link density N of the illed network by G′ = NkB T

(3.43)

where kB is the Boltzmann constant and T is the temperature. The cross-link density stems from three contributions: The evolution of the storage modulus with strain is given by 1 1 + ��

G′ (�) = G′st + G′ust

(3.45)

c

0 kB T. with G′st = (Nc + Nst )kB T and G′ust = Nust ′ The G decrease with the strain amplitude is attributed to the progressive decrease in the number of unstable bonds, until it only remains stable bonds at the iller surface. Regarding the loss modulus, the following expression has been given:

′′

G (�) =

G′′st

+

G′′ust (

� �c

1+

� �c

)2

(3.46)

Interestingly, the Maier–Goritz model highlights the role of polymer–iller interface in the Payne effect. Compared to the Kraus and Huber–Vilgis models, it gives physical interpretation to temperature effects. The storage modulus decrease when temperature is raised is attributed to the decrease in unstable bonds. However, the model is not able to capture the strongly nonlinear variation of the number of polymer–iller bonds with iller volume fraction. Clement et al. [98] showed that such nonlinear variation is more in line with percolation law. In addition, the model does not give a satisfactory it for large deformation. 3.4.4.2.2 The Long–Sotta Model Long and Sotta [180] and Merabia et al. [94] proposed a model at the mesoscopic scale, in order to simulate the dynamical behavior of nanoilled elastomers in the high-temperature regime. This model represents a disordered elastic system made of hard spheres connected by harmonic springs. The parameters of the model are the connectivity n and the volume fraction �. Disorder is introduced by the dispersion of connectivity between rigid beads. The connection is essentially elastic and ensured by a layer of adsorbed chains at the iller surface. In addition, this layer is considered to be in the glassy state when the interaction between the matrix and the illers is suficiently strong. This glassy layer has the same physical

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origin as the Tg shift measured in thin polymer ilms. Long and Sotta proposed that the Tg shift at the distance z from an interface is of the form: ( ) � Tg (z) = Tg 1 + z

(3.47)

The value of � depends on the matrix–iller interaction (typically between 1 and 10 nm). When a strain is applied, the stress is concentrated in the glassy bridges. The local stress � results in a lowering of the local glass transition of the polymer given by ) ( � � − (3.48) Tg (z, �) = Tg 1 + z K where K is a constant that depends on the polymer. The glassy bridges are not permanent. Indeed, they break under applied strain. The breaking time is assumed to be equal to the local relaxation time �(z, �) at equilibrium. This dominant relaxation time � is by the William–Landel–Ferry (WLF) law of the corresponding polymer modiied by the Tg shift due to interfacial effects. In the same conceptual approach, the Payne effect is thus related to the life time of the glassy bridge. As this time is a function of both the stress and the temperature, the model is able to capture both main features of the Payne effect previously mentioned. Figure 3.18 depicts schematically the prediction of the model regarding the dissipation sources in the illed system. Three regimes for the dissipation are deined. At low deformations, the regime A is dominated by dissipation in the polymer matrix and dissipation in the glassy interfacial layers. At intermediate deformation amplitudes, regime B is dominated by rupture and rebirth of glassy bridges. At larger deformation amplitudes, regime C is dominated by the addition of matrix contribution and shearing of glassy layers.

G'' (x10 MPa)

1 0.8

B

0.6 0.4

A

C

0.2 0

0.001

0.01 2γ

0.1

1

Figure 3.18 Different regimes for the dissipation in strongly reinforced polymers. At low deformations, the regime A is dominated by dissipation in the polymer matrix and dissipation in polymer close to the glass transition. Regime B is dominated by rupture and rebirth of glassy bridges. Regime C is dominated by the addition of the same mechanisms as in regime A again. Reproduced from Merabia et al. [94] with permission of American Chemical Society.

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These concepts are implemented in a constitutive equation that is solved by numerical simulation. Qualitatively, the main concepts and general trends of the model are really convincing and attractive. The importance of local strain has also been found experimentally [54, 181]. Unfortunately, no systematic comparison with experimental data has been done yet. Apart from some quantitative estimation of the fraction of glassy layers in real highly illed systems suggested that the effect of glassy layers is quite overestimated.

3.5

PROCESSING OF NANOCOMPOSITES

The crucial inluence of the iller network on the viscoelastic and low properties of nanocomposites has been emphasized along the preceding sections. The features of this iller network are obviously due to the nature of the polymer and the chemical and physical characteristics of the iller and also to the extent of the dispersion achieved. Filler networking, that is, the creation of a secondary structure resulting from interparticle interactions (agglomeration), is governed by the iller–iller interaction, the iller–polymer interaction, and the distance between particles. Thus, the quality of the iller microdispersion results from a complex combination of thermodynamic factors (surface energies and interactions between materials), kinetic factors (diffusion mechanisms controlled basically by the polymer viscosity and the size of the particles), and the mechanical and thermal energy input from the mixing or processing operation. 3.5.1

Inluence of Blending Procedure

The processing of polymer nanocomposites via melt dispersion or melt intercalation is the most preferred method to produce polymer nanocomposites for commercial use owing to the absence of organic solvents, short processing times, and the compatibility with industrial manufacturing techniques. Particularly, regarding clay nanocomposites, the polymer is mechanically mixed with the clay in a two-step process. First, the transportation of the polymer chains inside the silicate layers with the help of a compatibilizer and the weakening of the bonding forces are important. Second, the exfoliation of the weakened layers under shear stress and homogeneous dispersion in the melt plays a decisive role. These two mechanisms can also take place parallel to each other. Regarding nanosilica illed polymers, the surface modiication has similar weakening effect on the iller–iller interaction and results in an improvement of the inal dispersion [32, 182]. Despite the importance of melt intercalation, the effects of processing conditions on the material’s properties are not studied very extensively. Generally, the processing parameters investigated in most of the various studies are the shear stress, the shear strain, the screw rotation speeds, and the residence time. Additionally, it can be noted that most studies lack a clear criterion for characterizing the mixing process. An indicator based on mixing energy, such as the speciic energy (in J/g) mentioned, for example, by Dimier et al. [183], might be of interest. This parameter is deined as

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∫0 M

Espe = 2�N

t

′

C(t )dt

′

(3.49)

where N is the rotation speed, t the mixing time, C the torque, and M is the mass introduced in the chamber. Speciic energy could be a means for helping in comparisons in the ield of composites in which effects from the matrix, iller, and morphology superpose in a very complex manner. As a general point of view, because of the various discrepancies in literature, the inluence of each parameter appears to be not yet identiied well. The dispersion state is inferred from direct local observation (microscopy), measuring macroscopic properties (mechanical, rheological, electrical, permeability) of the material and by using scattering techniques such as XRD or SAXS [73]. Actually, according to the given properties, a soft and short processing or an intensive and long processing (e.g., speciic energy) is more or less effective [184]. With respect to the speciic energy, an intensive and short processing should deliver the same results as soft and long processing, if their inluence is even. But, in reality, there is always one factor dominating (e.g., intercalation is a strongly time-dependent diffusion process). A long residence time during processing favors a more intercalated nanocomposite system, while more intensive shearing leads to the formation of more exfoliated systems [185, 186]. When intercalation or surface modiication is not the dominant process, the morphology of the dispersions and the rheological properties were studied, for example, by Modesti et al. [187]. It was found out for PP nanocomposites that the shear stress is much more important than the residence time because the diffusion process (dependent on the residence time) is not the controlling factor. Lertwimolnun and Vergnes [100] found similar behavior. The authors showed that the state of intercalation is globally unaffected by the processing conditions. The exfoliation was only improved by increasing shear stress, mixing time, and decreasing mixing temperature. This general behavior regarding the dispersion mechanism can be well predicted in the framework of hydrodynamic stress, which passes the cohesive forces inside the aggregates of particles. Even if weakening of cohesive forces is pretty often required, compared to the composites elaborated in a quiescent state, the effect of applied shear rates remains important to control the inal structure [188]. However, only hydrodynamic stress is never suficient to ensure good dispersion state of nanoparticles in polymer matrix especially when the viscosity is low. Franchini et al. [189] have shown that sepiolite-based epoxy networks were achieved through two key factors: the creation of appropriate iller–matrix interactions and the proper selection of the processing procedure and conditions. Classically, the irst processing strategy involved the chemical modiication of the nanoparticle surface and strong high shear mixing. For the second strategy, a dispersion method denoted “emulsion” processing method was developed to beneit from the high hydrophilic character of the non-modiied sepiolite. In any case, thermodynamic or chemical weakening of agglomerates is required to improve the eficiency of hydrodynamic forces. In addition, the “emulsion” process led to the formation of stronger physical gels, suggesting a better dispersion state of the sepiolite needles. As the clay is not

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modiied in this case, stronger clay–clay interaction can also be imagined. Finally, compared to other processing techniques as solvent casting or in situ polymerization, the melt processing appears not to be the adequate solution. For instance, Varela-Rizo et al. [190] have studied carbon nanoiber/PMMA nanocomposites with different concentrations using three different processing techniques. They show that suitable dispersion of carbon nanoiber is possible using the solvent method or in situ polymerization, in which also a covalent interaction between carbon nanoiber and PMMA produces a stronger restriction on the movement of the polymer chains, affecting the rheological response of the polymer, as well as creates a conductive carbon nanoiber network. Mohn et al. [191] went to the same conclusion for poly(lactide-co-glycolide) illed with spherical calcium phosphate nanoparticle. Actually, using melt compounding method, no rheological or electrical percolation was found in the concentration levels of the study. In such case, matrix low affects 3D iller network (shear forces orient the carbon nanoiber in low direction), which remains in a nonequilibrium state after processing due to high viscosity of the matrix and low diffusion coeficient. To summarize, considering the competition between the diffusion of compatibilizer and the hydrodynamic breakage of illers clusters, the predictions on the achievable structure versus processing conditions of nanocomposites are still dificult. In low-viscosity luids, hydrodynamic forces are not suficient to ensure dispersion, and weakening of iller agglomerates is strongly required [192]. In highviscosity matrix, transient low-induced anisotropic structures are often formed. The desired inal structure for application should then be obtained by subsequent aging of nanocomposites.

3.5.2

Usual Processing Methods

Extrusion is one of the most effective way to prepare nanocomposites and one of the most used processing technique. However, the role and importance of processing conditions in extrusion is the subject of very few articles. Generally, authors used various types of extruders including single screw [193], twin screw, co-rotating [194–196], and counter-rotating intermeshing screw conigurations [197]. It is commonly demonstrated that the clay exfoliation or intercalation in the single-screw extruder is poor compared to the other devices in spite of the relatively long residence time. Then, using a two-step process can improve the dispersion state: a solution-blended mixture is subsequently compounded in the melt state using a torque rheometer [198]. Another way of improvement of dispersion was evidenced by Sanchez et al. [193]. Clay concentration is the dominant factor over the processing conditions in order to obtain delaminated nanoclay structures. This can be explained in the classical framework by the increased viscosity. The higher shear stresses induced at higher viscosities promote the separation of tactoids. This was also observed by Lim et al. [198]. On the other hand, for the low clay concentration, the die with the lower ratio L/D = 20 seems to play a major role in the clay intercalation and exfoliation processes more evidently than the screw speed. They attributed this effect to the fact that the shear stresses are related inversely to

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the die length. Anyway, single-screw mixing process is not the proper tool to create nanocomposites. The addition of nanoillers in polymer matrix can lead to interesting and quite unexpected effect on the polymer processability. Sun and Li [199] has reported the effect of micro-diatomite/polyethylene glycol binary processing aids on the rheology of metallocene LLDPE. It was found that the binary processing aids can increase the shear-thinning behavior and decrease the melt viscosity signiicantly even when only a small amount of nanoclay is added. The reason for the melt viscosity reduction was attributed to the intercalation of PEG molecular chains into montmorillonite layers and the coating of illers. Therefore, the montmorillonite layers with PEG coating can slip in the matrix, reducing the friction. In addition, the onset of shark skin melt fracture of mLLDPE was delayed to higher shear rate [200, 201]. Vega et al. [202] have prepared a nanocomposite sample by melt mixing a high-density polyethylene (HDPE) with an in situ polymerized HDPE/MWNT master batch. Quite similar to the surface treatment of organoclays or standard illers, the adsorption process of the longest HDPE chains promotes that this fraction of molecules becomes “inactive” (unentangled) within the matrix, remaining immobilized onto the surface of the nanotubes and not contributing to the viscosity of the system. The existence of this fraction of unentangled/adsorbed chains onto the CNTs surface gives rise to some interesting phenomena in processing: They found lower values of the shear stress in extrusion and a delay of the defaults regime to higher shear stresses and rates (improvement of processability). In addition, the extrudate swell appeared to be reduced just as the melt strength, draw ratio, and viscosity in elongational low. However, the last effect cannot be generalized as a way to improve the processability for all processes. We will show hereafter that the enhancement of the elongational properties may be required for polymer processing operations such as ilm blowing, blow molding, or foaming [203, 204]. Injection of nanocomposites, after all, is not as tricky as for polymer illed with microillers. As nanosize particulates are far below the dimension of the molding parts (even microparts), nanocomposite low remains homogeneous in between the gap of the mold, and the issue of injecting nanocomposites mainly comes down to adjust or control the nonlinear rheological behavior at high shear rate. It is then noteworthy to recall that, in this range of shear rate, the whole rheological behavior is given by the polymer matrix but nevertheless, it was demonstrated that the surface functionalization of nanoparticles and nanoiller structure play an important role on the magnitude of the shear-thinning effect [184, 188, 189]. However, in the case of anisotropic particle, low orientation is affected by the type of processing used to form the test specimen (e.g., extrusion, injection molding). This is a separate issue from the degree of dispersion or exfoliation, which is usually determined in the mixing process and which still concentrates many efforts in the understanding of the physics underlying. Interestingly, the addition of clay seems to be an effective way to increase “melt strength,” which can be useful in some types of processing like foaming or blow molding. Ray et al. [62] have shown that under uniaxial elongational low, PLA/layered silicate nanocomposites exhibited very high viscosity and a tendency

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35

35

30

30 Percentage of extrudate swell

Percentage of extrudate swell

of strong strain-induced hardening. According to Okamoto et al. [205], these effects may originate from the perpendicular alignment of the silicate layers toward the stretching direction. Ray et al. claimed that such strain-induced hardening behavior is an indispensable characteristic for foam processing because of its capacity to withstand the stretching force experienced during the latter stages of bubble growth. In addition, they found that nanoilled PLA foam shows a smaller cell size and a larger cell density compared to that of pure PLA foam, suggesting that the dispersed silicate particles act as nucleating sites for cell formation. Di et al. [206] found the same trends that were attributed to the strong interaction between PLA and exfoliated organoclay layers, which lowers the molecular mobility of PLA and forms an interconnected structure within the PLA matrix. So, making polymer nanocomposites containing a low amount of organoclay has become an effective way to modify the processing behavior of polymer matrix. Reinforcing illers, in general, reduce the extrudate swell of polymeric materials. Generally admitted mechanisms for extrudate swell combine rearrangement of velocity proile at die exit, partial relaxation of entry tensile stress and recovery of strains associated with normal stress difference within the die. Upon addition of solid iller particles, extrudate swell is reduced not only due to their hydrodynamic effect and the reduction of polymer volume fraction but also due to the polymer–iller interactions, which develop generally higher viscosities at the expense of elasticity. This point can be illustrated by the work of Dangtungee et al. [207, 208] on isotactic polypropylene compounded with uncoated and stearic acid-coated CaCO3 nanoparticles in various iller loadings. They have shown that the percentage of extrudate swell increases with increasing apparent shear rate in a nonlinear manner, while it was found to have a linear relationship with the wall shear stress as shown in Figure 3.19. In addition, whatever be the nature of the interface between polymer and iller, the percentage of extrudate swell was found to be a decreasing function of the iller loading as expected in illed polymers.

25 20 15

Neat iPP 5 wt% 10 wt% 15 wt% 20 wt% 25 wt %

10 5 0 3E+4

4E+4

5E+4 6E+4 7E+4 8E+4 Wall shear stress (Pa)

9E+4

25 20 15

Neat iPP 5 wt% 10 wt% 15 wt% 20 wt% 25 wt%

10 5

1E+5

0 2E+4

3E+4

4E+4

5E+4 6E+4 7E+4 Wall shear stress (Pa)

8E+4

9E+4

1E+5

Figure 3.19 Percentage of extrudate swell as a function of wall shear stress for neat and iPP illed with (a) uncoated and (b) stearic acid-coated CaCO3 nanoparticles of various iller loadings, ranging from 5 to 25 wt%. Reproduced from Dangtungee et el. [207] with permission of Elsevier.

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3.5.3

New Processing Routes

Recently, carbon dioxide in supercritical luid conditions (scCO2 ) has been gaining popularity in research and industry as an environmentally friendly solvent and blowing agent in a wide range of applications [209]. Manke [210] and Mielewski [211] have patented a novel process utilizing scCO2 for exfoliating layered silicate and/ or graphite with or without polymer present. The liquid-like density and gas-like diffusivity of scCO2 allows it to penetrate the platelet galleries, while the large density change that the supercritical luid undergoes during instantaneous depressurization pushes the platelets apart. Horsh et al. [212] have shown that this method provides an interesting new way to disperse natural montmorillonite in a polydimethylsiloxane matrix. The resultant nanocomposites exhibit signiicant rheological improvements compared to melt-mixed benchmark. Nanocomposite is elaborated by processing clay/polymer solution in scCO2 followed by quick depressurization as illustrated in Figure 3.20. When compared to slowly depressurizing, it is clear that the dramatic CO2 expansion is a key factor in producing dispersion with this process [213]. Such new processing method not only allows improved clay dispersion but also promotes polymer–clay interaction. The results from this process appear to be comparable to or better than processes that use “custom-modiied” clays with in situ polymerization. Finally, photothermal effect (surface plasmon resonance) of metal nanoparticles can be productively used in a polymeric nanostructured material environment for generating signiicant localized heating when the nanoparticles are contained within a polymer composite. From a processing point of view, using the effect of localized heating may ultimately enable selective, in situ thermal manipulation of polymers for repair (i.e., self-healing from cracks, crazes, or tears) or enhancement and the performance of processing tasks such as annealing, thermally induced cross-linking, lamination, and shape memory actuation [214].

(a) Polymer + Clay

(b)

(c)

Polymer + Clay + scC02

Polymer + Clay +scC02 depressurize

Figure 3.20 Illustration of the supercritical carbon dioxide process. Polymer and clay are mixed together followed by a soaking period in scCO2 . The system is depressurized, and the expanding CO2 delaminates platelets. Reproduced from Manitiu et al. [213].

CONCLUSION AND FUTURES CHALLENGES

3.6

125

CONCLUSION AND FUTURES CHALLENGES

Since the rheological properties of nanocomposites are sensitive to the structure, particle size, shape, and surface characteristics of the nanoiller, the rheological tool is intensively used to assess the features of the dispersion of nanocomposites directly in the molten state. Obtaining the optimum properties for nanocomposites will usually require excellent dispersion of the nanoparticles (even in speciic cases, excellent isotropic dispersion may not be the desired morphology). Anyway, the tendency for nanoparticles (including platelets and ibers of nanoscale dimensions) to coalesce into macrosize agglomerates can seriously impact the achievable properties. When rather a hierarchical morphology is obtained such as those observed with percolation pathways in gel microstructure, scaling laws relating the rheological properties (equilibrium shear modulus, limit of linearity) to the iller loading have been extensively investigated and many modeling approaches provide fairly good description of the microstructure at rest. Most of the studies have been focused on the power laws variation of equilibrium modulus neglecting the importance of the front factor of these power laws. The future challenge is to take into account the intensity and the nature of the stress transmission across the iller network. The extreme sensitivity of the interaction forces to interparticle distance, the details of interparticle potential (e.g., deformation of the adsorbed polymer brush, van der Waals, hydrogen bonds), or the particle roughness on the strength of the 3D network of nanoparticles need to be further understood. Studies on these materials have been generally much more focused on microstructural analysis through rheological approach much less than nonlinear viscoelastic properties or low features. Determining sound rheological data in processing conditions still remains a challenge with such materials because of the fundamental knowledge on the inluence of iller particles (this is particularly the case for elongational lows). Research focused on understanding the intimate coupling between the low and the microstructure during the low of suspensions has greatly advanced through a combination of experimental techniques, theoretical developments, and numerical simulations. A major future challenge is to incorporate the microstructural features into constitutive descriptions of gelling nanoparticles rheology, which can also predict the nonlinear rheology relevant to processing operations involving nanoparticles. At present, the link between gel microstructure and rheology has only been described in qualitative terms. A link between micromechanical properties and aggregate structure under low has to be established. For the case of suspensions of spherical shape with an amorphous microstructure, the low-induced changes in the microstructure are well understood but some challenges lie ahead in the high Péclet regime [127]. For weakly aggregated suspensions of nanocomposites or largely anisotropic nanoparticles (which underwent low orientation), more work is needed to develop mechanistic understanding. As a consequence, very few constitutive models have been derived in spite of crucial need for the use in simulation software.

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Therefore, the next step in progress is the detailed comparison between experiment and direct simulation and is beginning to bear fruit. Much advancement has been made over the past years in computer modeling and simulation of polymer nanocomposites. Efforts concentrated mainly on the clariication of the interactions, local dynamics (diffusion), and equilibrium structure in particle–polymer nanocomposites for varying particle shapes, polymer architecture, and intermolecular interactions. This is a vast and singular topic that would deserve its own chapter to be wholly addressed. A very pertinent review article of Ganesan and Jayaraman [215] has detailed the main advances in theory and simulations in polymer nanocomposites. To summarize, three main theories have been developed in order to understand or predict structure and phase behavior in polymer nanocomposites consisting of polymer matrices and bare particles: PRISM theory (Polymer Reference Interaction Site Model), density functional theory (DFT), and self-consistent ield theory (SCFT). PRISM theory has been used extensively [216–219] to elucidate effective interactions and equilibrium structure in bare particle–polymer nanocomposites for varying particle shapes, polymer architecture, and intermolecular interactions. Moreover, results from PRISM theory show excellent agreement (some quantitative) with experiments and simulation results. To go further, there is a need for understanding spatial organization of the components of the composites near surfaces. There has not been much development in PRISM approaches to address this aspect and could be a direction for future development. Combination of DFT and SCFT approaches has led to signiicant advances in the understanding of the interaction and phase behavioral characteristics of polymer–nanoparticle mixtures. Such theories have been extended to multicomponent polymeric systems, and the structural results have been used to characterize the inluence of morphologies on mechanical properties [220, 221]. Possible next steps in this context should address similar issues in the context of anisotropic particles [222]. While pioneering early work of Balazs and coworkers [223] did consider the phase behavior of anisotropic particles mixed with polymers, their model was based on the combined SCFT + DFT approach [224, 225]. Extensions of the more rigorous hybrid modeling and/or DFT approaches have not been accomplished. On the side of simulation tools, coarse-grained tools have played an important role in advancing our understanding of the characteristics of polymer–nanoparticle mixtures. Such tools, especially MD (molecular dynamics) approaches, have been extensively used in studying the equilibrium (and more often, the dynamical) characteristics of polymer–nanoparticle mixtures. Such approaches enable to treat multibody interaction effects more accurately and can be used to study dynamical phenomena and access iner scale structural details of the polymer–monomers. The power of such simulations lies in their capacities to elucidate or conirm experimental issues, such as polymer structuring and its inluence on the dynamics of polymer segments near nanoparticle surfaces [226, 227] or the statistics of polymer conformations in nanoparticle systems [228]. Although much progress has been made over the past years in computer modeling and simulation of polymer nanocomposites, there still exists some room for improvement in this ield [229]. Since the introduction of anisotropic particles, such

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as clays, CNTs, and so on, with a good dispersion can always obtain better mechanical properties compared to that of the spherical nanoparticles, many efforts (with fairly encouraging success) have been made to simulate the overall rheological behavior at a mesoscopic scale but for low illers concentration. It seems now that more simulations should be carried out to investigate the behavior of fully exfoliated clays at high loadings (which required the implementation of particles interaction). Moreover, issues unique to polymer nanocomposites, such as the anisotropy of the illers, potentially long-ranged interparticle interactions (mediated by the polymers), and the dynamical and rheological response of the polymer matrix, do not have direct counterparts in the composites literature pertinent to micron-sized and larger particles. Hence, there is a need for the development of appropriate theoretical models and computational frameworks that can enable the study of nonequilibrium issues as well as the inluence of external ields on the structure and dispersion of nanoparticles in polymer matrices. In addition, as both theoretical and experimental investigations of the long-term unsolved “Payne” effect do not converge toward a unique interpretation, it is emphasized that more simulations should be carried out to elucidate this nonlinear viscoelastic phenomenon in polymer nanocomposites. So, it is believed that computer modeling and simulation will not only promote practical applications of polymer nanocomposites but also provide powerful tools in fundamental investigations of their rheological properties.

ACKNOWLEDGMENTS Prof P. Cassagnau is thanked for his stimulating discussion on the rheology of nanocomposites and for kindly reading the present chapter.

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4 MIXING OF POLYMERS USING THE ELONGATIONAL FLOW MIXER (RMX®) Rigoberto Ibarra-Gómez and René Muller Department of Mechanical Properties and Tribology of Polymers, Institut Charles Sadron, CNRS-UPR 22, Strasbourg, France

4.1

INTRODUCTION

As it is well known, predominant high shear contributions to dispersive mixing are common in conventional devices such as single-screw extruder (SSE), twin-screw extruder (TSE), and internal mixers. This is because shear low is easier to build up in a sustainable manner using relatively simple geometries compared to elongational low which, however, is also present at a different extent and whose contribution depends on the type of mixer. Nevertheless, shear stresses necessary for iller dispersion often involve ranges of high shear rates that considerably reduce the polymer viscosity in the shear-thinning zone, which demands high-energy inputs to reach a good dispersive eficiency. In addition, rotational motion (vorticity) is present in shear low unlike elongational low (irrotational low), situation that strongly accounts for a theoretically higher dispersive eficiency for the latter. Furthermore, elongational viscosity �e for viscoelastic luids may be several times higher than shear viscosity � � (Trouton’s ratio, �e = 3 for Newtonian luids), which promotes greater hydrodynamic stresses favoring dispersion of agglomerates or drops.

Rheology and Processing of Polymer Nanocomposites, First Edition. Edited by Sabu Thomas, Rene Muller, and Jiji Abraham. © 2016 John Wiley & Sons, Inc. Published 2016 by John Wiley & Sons, Inc.

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Utracki [1] resumes, in general, the following theoretical advantages of elongational low over shear low: 1) 2) 3) 4) 5)

Elongational low is orders of magnitude more energy-eficient than shear low. It generates better dispersive and distributive mixing. The heat build-up in extensional low is low. It does not cause reaggregation of solid particles reported for shear. It can be economically generated using convergent–divergent low geometry in either motionless or dynamic mixing devices.

An important set of properties of multiphase polymer systems, including polymer nanocomposites and blends, are intimately related to the state of dispersion and distribution of particles/droplets within a polymer matrix, that is, morphology. In this regard, mixing is the operation intended to bring together and homogenize two or more ingredients, hence rendering a mixture with a deined morphology, which provides a critical role in the overall processing of polymeric compounds at this stage. Fundamentally, mixing can be classiied as distributive (extensive) or dispersive (intensive). From a basic description, distributive mixing is characterized by spatial rearrangements of components originated from the convective motion, with or without increase in interfacial area, leading to uniformity. In polymer processing, distributive mixing is also named laminar convective mixing given the high viscosities of polymer melts. A permanent deformation or strain is usually imposed on the system by continuously shearing it or stretching it in a reoriented manner; in this way, the strain becomes the governing variable of distributive mixing. On the other hand, in dispersive mixing, it is involved the reduction of the size of droplets or agglomerates. The cohesive forces of these are needed to be overcome by the stress to effectively increase the interfacial area between components as to confer the maximum in properties. In this respect, the local stresses are in charge of the dispersion, playing a decisive role in the mixing operation. When it comes to processing of polymer nanocomposites and blends, a well-mixed system from both distributive and dispersive points of view is a central goal; however, dispersive mixing limits the overall process because of the unavoidable need for increasing the interfacial area. Therefore, great efforts are focused on how to improve the dispersive eficiency of mixing. It can be stated that, in general, the problem to create proper dispersive mixing is deined by the balance between the cohesive forces, holding agglomerates/aggregates or droplets together, and the disruptive hydrodynamic forces.

4.2

POLYMER BLENDS

In the mixing of liquid–liquid (viscoelastic) systems, polymer blends are considered a very important class of multiphase polymeric systems. In principle, properties of polymer blends can be customized leading to the development of new interesting

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materials that are often much easier to obtain than the materials produced through synthesis process or complex chemical modiication. From the basic concept of thermodynamics, multiphase systems are classiied as miscible or immiscible, and the condition for obtaining the former at a given temperature T is as follows [2–4]: ΔG = ΔH − TΔS ≤ 0

(4.1)

where ΔG, ΔH, and ΔS are the Gibbs free energy, heat, and entropy of mixing. It is clear from Equation (4.1) that an increase in temperature contributes to the establishment of the thermodynamic equilibrium for mixing since ΔS is usually positive. In addition, rising temperature favors molecular diffusivity, impacting positively on the rate of mixing. The vast majority of polymer blends are considered immiscible because the inal mixtures do not present homogenization at molecular levels; instead, they are characterized by distinguishable phases in a variety of morphologies, from which the most common involves either dispersed domains within a continuous phase (Fig. 4.1a) or co-continuous phases (Fig. 4.1b). Immiscibility leads to poor physical properties because of coalescence; therefore, a real improvement in the performance of a polymer blend with respect to the pristine components is only attained when morphology is stabilized. This is possible by using proper compatibilizing agents during compounding or by previous surface modiication of the constituent phases in such a way that the interfacial energy is lowered; thus, morphology is considered to be stabilized against postforming steps and/or end use. As expected, even though compatibilization is a key factor involved in the achievement of desired morphologies and

2 µm

2 µm (a)

(b)

Figure 4.1 Images from atomic force microscopy (AFM) of HDPE (50)/PP (40)/PS (10) wt/wt blends: (a) HDPE (dark domains) and PS (rounded clear particles) dispersed within PP (clear) matrix; and (b) co-continuos phases of HDPE and PP (PS rounded particle remains within the PP). Blends prepared by the elongational low mixer, RMX®. Reproduced from Mani et al. [13] with permission of Ecoindustry.

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properties in polymer blends, a list of parameters concerning concentration, physicochemical properties of components, and mixing procedures has to be addressed to have a better understanding of the overall production process of a polymer blend. Although the inluence of different parameters on the preparation of polymer blends will be discussed along this chapter, this will be done predominantly in the frame of RMX® mixer discussion, so we kindly encourage the reader to refer to classic treatises on polymer blends elsewhere [5–7]. Furthermore, interesting alternative approaches to compatibilization and morphology control of polymer blends have been applied recently with the advent of the nanotechnology. Targeted nanoillers have been introduced to polymer blends in order to attain controlled morphologies and compatibilization effects through selective location of the charge. Elias et al. [8] found that hydrophilic silica tended to decrease the size of ethylene-vinyl acetate (EVA) copolymer droplets in a polypropylene (PP)/EVA blend by means of preferential location of silica in the EVA dispersed phase. Istrate et al. [9], on the other hand, evaluated the mechanical properties of PP/polystyrene (PS) clay nanocomposites and observed dual clay effects as a compatibilizer and a reinforcing agent. More recently, the employment of carbon nanotubes (CNTs) and graphene nanoplatelets [10, 11] for morphology control in polymer blends have been reported. It has been generally observed in these works that inal morphology strongly depends, on one hand, on the mixing sequence, that is, one-step mixing, iller introduction into either of the components or the two phases partly illed and, on the other hand, on a more fundamental basis such as the balance of interaction energies between components, speciically wetting parameters [12]. Taguet et al. [12] present a complete review on polymer blends morphology, stabilization, and control by nanoillers introduction. Speciically, the melt processing of polymer blends into useful products involves important technological challenges, derived from a series of factors that play key roles as much in processing as in the inal performance of polymer blends, which have to be strongly considered in their design: • • • • • • • 4.2.1

Concentration ratio Compatibility of polymeric phases Viscosity ratio Glass transition and melting point Rheological properties/viscoelasticity Degradation stability Mixing/processing type (low geometry) Capillary Number, Ca

In the absence of inertial effects (high Reynold’s number), as it is indeed the case of blending of polymer melts, a fundamental phenomenon in mixing, that is, the dynamics of drop deformation and breakup within a low ield, is governed by two

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dimensionless numbers, p and Ca. The parameter p is the ratio of the viscosity of the dispersed phase (�d ) to that of the continuous phase (�c ), p = �d /�c . The capillary number, Ca, according to the classic works by Taylor [14, 15] and Grace [16], deines the interval of p where dispersed droplets are prone to burst and breakup within a continuous phase under the inluence of a certain type of low ield. The capillary number describes the balance, during the mixing process, between the hydrodynamic stresses generated by the viscous low (the forces tending to deform and break up the dispersed droplet) and the interfacial stresses (which tends to preserve the droplet’s integrity); thus, for Newtonian luids: ̇ � �r (4.2) Ca = 0 Γ where �0 is the viscosity of the continuous phase, �̇ is the shear rate, r is the initial droplet radius, and Γ is the interfacial tension. If the shear rate is replaced by an elongation strain rate �,̇ the inluence of elongational low ields on mixing is also addressed. During mixing, Ca decreases with time, starting at high values where big droplets and low interfacial area generate passive interfaces, which leads to quite low local ̇ As the interfacial stresses, Γ∕r, compared to an initial value of shear stress, �0 �. process continues, signiicant deformation of droplets under low takes place and the local length scale of the system is decreased, favoring the role of the interfacial stresses and the diminishing of Ca. This stage is particularly characterized by the appearance of elongated drops or threads of the dispersed phase, a phenomenon known as striation or afine deformation. The subsequent increasing deformation over time leads to the appearance of active interfaces [3] and interfacial disturbances (named Rayleigh’s disturbances [17]), a phenomenon that inally results in the disintegration of the thread into small droplets (Fig. 4.2). At this point, interfacial stresses are about the same magnitude order as shear or elongational stresses and Ca assumes a

Ca >> Cacrit

Ca ~ Cacrit

Figure 4.2 Depiction of the evolution of Rayleigh’s disturbances for a Newtonian thread in a quiescent Newtonian matrix as interfacial stresses and shear stresses.

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Cacrit

critical value, Cacrit . The pioneer work by Taylor [14] gave a irst insight into the critical conditions to droplet breakup under shear low for Newtonian luids. The author found Cacrit ∼ 1 at p ∼ 1. From the point of view of the overall mixing process, it can be said that high values of Ca (Ca ≫ Cacrit ) are characteristics of an initial stage of predominantly distributive mixing that depends on the total strain (being the product ̇ As long as Ca becomes Cacrit , stresses are of strain rate and time, in shear, � = �t). high enough to promote dispersive mixing. For a determined system, Cacrit depends on both p and the type of low. On the one hand, p governs the dynamics of the deformation and the time to breakup, but on the other, the type of low, shear versus elongational, strongly points out to dispersive eficiency. About Grace’s results, behavior of Cacrit as a function of p clearly differs from one type of low to another (Fig. 4.3). In the whole range of p displayed, Cacrit is much lower in elongational low than in shear low. The use of elongational low widens the window of p to quite higher values than unity, whereas for shear low, Cacrit goes to ininity at p ∼ 4. Hence, it is clear that elongation is the more effective mode of deformation in relation to droplets breakup. In this regard, particle orientation in the mainstream as exhibited by each type of low is a key point to account for the differences in dispersive eficiency. Simple shear low is said to have a rotational character, that is, a drop subjected to this type of low will tend to rotate in the direction of the stream lines. Therefore, to favor dispersive eficiency in shear low somewhat counteracting the rotational component, the drop must acquire an ideal particular orientation. Accordingly, an angle of 45∘ with respect to the main direction of strain is adopted by the drop longest axis (assuming an ellipsoid) to develop maximum deformation prior to breakup. However, elongational low has no rotational component; hence, a drop put inside this type of

Simple shear

2D elongation

Breakup

No breakup p (�d /�c)

p=1

Figure 4.3 Depiction of the critical capillary number for droplet breakup as a function of viscosity ratio in simple shear and planar elongational low.

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low experiments an orientation of its longest axis in the direction of the main deformation. In order to quantify the differences just described, an estimated eficiency parameter, ef (the scalar product of the principal direction of strain and the transient drop orientation), illustrates the capacity of shear and elongational lows to deform the drop until breakup (Fig. 4.4) [3]. In elongation, ef approaches to 1 irrespective of the initial orientation as a result of the drop alignment with the main axis of strain. By contrast, in shear low, e quickly reaches 1 as long as the drop orientation gets 45∘ f

relative to the direction of strain; afterwards, it decreases to a constant value because of the rotation. It is precisely this predominant rotation character of shear low at high p that explains the asymptotic behavior of Cacrit in Grace’s results. In practice, the global dispersive eficiency in simple shear low may be increased by repeatedly reorienting the droplet to the relative position of maximum deformation and it is, actually, the way in which several conventional devices accomplish the mixing action. Applicable as well to elongation strain, this is a process generally known as “folding.” This is easier to attain in shear low compared to elongational low since the former is able to quickly generate and sustain longer than the latter. This is why the design of mixers with increasing elongational low contributions to the effectiveness of mixing is a quite complex task. However, the inherently higher dispersive eficiency of elongational low over shear low (especially for systems of high interest such as polymer blends at high p values), along with practical processing concerns such as reduced viscous heating, makes the search for predominant elongational mixers an area of great activity. In addition to the discussion about dispersion mechanism, an important issue inherently associated with the practice of mixing in polymer blends is the phenomenon of coalescence [3, 4]. In fact, a real mixing process is better characterized by the competence between dispersion and coalescence and, in the end, the inal morphology depends on the balance of this mechanisms. Therefore, the use of

1

1

ef

0.71 ef Elongation

0

ε (a)

Simple shear 0

γ (b)

Figure 4.4 Depictions of the eficiency coeficients, ef , for (a) elongational and (b) simple shear lows.

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compatibilization [18] methods is usually mandatory to obtain a inal compound of the desired performance. 4.2.2

Rheology and Processing of Polymer Blends

Although current mixing and processing devices operate under predominantly shear low, they differ in the extent of elongation low contribution to the mixing process. Actually, based on its fundamental superiority on dispersive eficiency with respect to shear, explained earlier, elongational strain is continuously trying to be implemented in processing equipment. However, beyond the direct contributions of the low geometry to dispersive eficiency, in practice, the overall mixing performance also depends strongly on a critical mechanism consisting of reorientation of material and multiple passage of this through points of high-stress regions in a mixer. This is intended to develop strain enough by the “folding” process and ultimately getting the high stresses needed to perform the dispersive action. It was mentioned earlier that total strain depends directly on strain rate and time or residence time; therefore, mixing and processing equipment design has the ultimate premise, about dispersive eficiency, of promoting regions of high stresses (direct inluence of low geometry) where reorienting and multiple passage of material is present (inluence of strain and residence time distributions). From these fundamental requirements, two important practical issues arise: 1) Repeatedly applying high shear stresses leads to signiicant heat build-up because of viscous dissipation. In this regard, elongational low promotes dispersive mixing at lower viscous heating and risk of affectation on material integrity. 2) Simple shear low is very easy to develop and sustain; thus, energy and power consumption initially involved are relatively lower compared to any extensional low, only in a straightforward comparison. In general, mixing/processing equipment is classiied as batch and continuous. The former comprises the well-known internal batch mixers, from which the Banbury type is among the most popular. The second group comprises the single-screw extruder (SSE), twin-screw extruder (TSE) and the wide spectrum of alternative systems. In the most of internal batch mixers (non-intermeshing type), iller agglomerates or polymer drops actually experience shearing between rotors and inside wall of the chamber, but the zone of high shear stress and possible extensional low contributions is found mainly at the narrow tip clearance between the tip of the rotor and the inner surface of a chamber. The shear stress, predominant in internal mixers, depends on the rotor speed, the viscosity of the compound, and tip clearance. Shear stress is directly proportional to the irst two variables, whereas it has an inverse relationship with the last one, from which the factor of rotor design comes up to play a major role since it deines the balance of low contributions and, hence, inal eficiency. Internal mixers are designed to force the mixture to pass, repeatedly, through the zones of high

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shear stress where dispersive mixing takes place, making it prone to viscous heating and potential degradation; thus, accurate temperature control is needed. In the end, the dispersion quality in this kind of equipment depends on mixing type, rotor speed, temperature, and rotor geometry. SSE, which is the most widely used machine in polymer processing, reports a satisfactory performance in melting and pumping, but its mixing capability is rather limited. The cross-low component traveling down the channel is said to promote distributive mixing in SSE because of a stirring effect by circulating the luid from the top to the bottom of the channel, and vice versa. However, this mixing component is not enough to attain effective dispersion when breaking up of the dispersed phase is involved, as in the case of agglomerates or polymer drops where van der Waals forces or interfacial tension have to be surpassed. In this sense, a great constraint of SSE to generate dispersive mixing is the limited number of high stress points; indeed, the only high-shear region is the light clearance where elongational low is practically absent. In addition, most of the material does not experience enough repeated passage through these high-stress zones. A number of modiications or complementary accessories are applied constantly to screws in order to improve distributive and dispersive mixing. Among them, the introduction of pins in the low channel (pin barrel extruder, QSM) is a simple and popular option since it augments the eficiency of the cross-low mixing by splitting the low so as to cause reorientation of the luid surfaces. On the other hand, all kinds of mixing heads, from the classic Maddock type to the CRD mixing section, Figure 4.5, have been designed over the past decades with the aim of meeting

(a)

(b)

Figure 4.5 Typical mixing heads for SSE: (a) Maddock Courtesy of James Frankland and (b) CRD. Adapted from http://www.google.com/patents/US6709147.

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dispersive mixing requirements: high-stress zones and multiple passages through them. Nonetheless, from the wide range of mixing heads available today, only few of them develop sustainable elongational low as the main component in the dispersive mechanism. As an example, in the CRD system, the elongational mixing is achieved in two methods [19]: 1) The wedge shape of the pushing lank in the mixing lights induces an extensional deformation of the pool melt between the screw and the barrel. 2) Tapered slots within the lights sum up for elongational low and, additionally, contribute to dispersive mixing. The high contribution of elongational low to mixing also reports an important decrease in viscous heating, that is, less affectation of the compounds integrity. Certainly, a critical point to consider when it comes to the use of mixing heads is that pressure losses are high and it could limit the inal extruder throughput. In addition, energy input may increase signiicantly. Despite the generalized use of SSE with improved mixing capabilities, nowadays, TSE are by far the most popular mixing devices. This is mainly because these devices combine a high pumping capacity (throughput) with tooling versatility (wide spectrum of shear to elongational low contribution). TSE are classiied, in general, as intermeshing or non-intermeshing type as well as co- and counter-rotating systems. From the point of view of mixing capabilities, distributive mixing is per se improved in TSE since low is continuously reoriented in its passage from one screw to another. Additionally, back-low may be present at a different extent as an important requirement for multiple passages. However, the eficiency on dispersive mixing may vary signiicantly depending on the extruder type and particular arrangements of mixing elements (kneading elements). It is remarkable the singular “lego-like” or modular design that TSE possess at present to quickly tune up a wide range of mixing needs (Fig. 4.6). Actually, this versatility is one of the main advantages of TSE against any other type of mixer. Briely, intermeshing-type devices offer a higher degree of dispersive mixing than nonintermeshing mixing since high-stress zones are also developed in the intermeshing region (leak lows) because of a high shearing and calendering effect (expansion and contraction of the mass). Regarding turning direction, nevertheless, counter-rotating intermeshing, more eficient dispersion, in principle, than co-rotating one, is limited to low speed because the largely stressed material tends to be concentrated between the screws provoking that, at high speeds, some screw zones deprive from a melt bed necessary for proper performance of the device. On the other hand, co-rotating TSE are able to attain very high speeds because the mass low, unlike counter-rotating TSE, follows inward and outward motions with respect to the intermeshing zone, allowing to an even distribution of the melt and less heating. Among TSE, this is, by far, the option most picked up in plastics’ compounding.

POLYMER BLENDS

Conveying zones

145

Adaptable mixing zones (kneading elements)

Figure 4.6 Modular adaptability of a TSE. Distributive and dispersive eficiencies depend on both the number of mixing segments and the particular design.

Non-intermeshing TSE, for its part, allows to privilege strong distributive low ields by virtue of the existence of open channels. In these devices, the stress ields are weak in comparison to the intermeshing types. Although classiication of TSE involves important performance differences in relation to mixing, most of them are considered, comparatively, low-energy input devices. Finally, a popular modiied version of a TSE system is the Farrel Continuous Mixer (FCM). Actually, the operation principles of this kind of mixer resemble more properly with those of an internal mixer than a TSE. The FCM is mainly built by two large lobe-type nonintermeshing rotors turning in a counter-rotating manner. The most important high-stress zones are formed, just as in internal mixers, in the tip clearance, where high shear and extensional deformation occur because of the highly wedge-shaped rotor wings. Repeatedly, the melt pass over circumferentially through these zones enhancing greatly the dispersive mixing while in the region of rotor–rotor interaction, the material interchange within the wide gap promotes distributive low. The FCM even though comprises a partially conveying zone, it is not designed for low transportation; therefore, the auxiliary assistance of conventional extruders and gear pumps is usually required in the whole mixing/processing line. As stated earlier, capillary number rules the basic mechanisms of mixing phenomenon of liquid–liquid systems in general. However, in relation to non-Newtonian luids such as polymer melts and, particularly, polymer blends, additional fundamental effects as that of viscoelasticity have to be taken into account in order to do both, a proper mixer design and useful structure–property relationships, that hold for the development of the morphology as a function of basic physicochemical quantities. In this respect, advances in the ield of polymer blend rheology have allowed to employ emulsion models to derive quantitative relationships between linear rheological properties on the one hand and interfacial properties on the other. Among them, the Palierne model [20] may account for viscoelastic behavior of matrix and

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146

inclusions, effects of inite concentration, distribution of size, and composition of the inclusions, as well as interfacial tension effects. Two general cases can be basically addressed by the Palierne model: 1) Dilute system, where interactions between deformations of neighboring particles are neglected. 2) Finite concentrations, where the strain seen by a given particle is not the macroscopic strain but is modiied by the deformation of neighboring particles. In the two cases, the complex shear modulus, G∗ (�), of the emulsion can be written as a function of the particle radius R, the volume fraction Φ of inclusions, the complex moduli G∗m (�) and G∗d (�) of matrix and dispersed phase, and the interface properties including the static interfacial tension � and the dynamic contributions � ′ (�) and � ′′ (�); accordingly, for the dilute case: ) ( 5 E(�) ∗ ∗ G (�) = Gm (�) 1 + Φ (4.3) 2 D(�) where E = 2(G∗d − G∗m )(19G∗d + 16G∗m ) + +

48� ′ � 2� ′ 8� + (5G∗d + 2G∗m ) + (23G∗d − 16G∗m ) R R R2

4� ′′ (13G∗d + 8G∗m ) R

(4.4)

D = 2(G∗d − 3G∗m )(19G∗d + 16G∗m ) + +

48� ′ � 32� ′′ (� + � ′ ) 40� ∗ (Gd + G∗m ) + + R R2 R2

2� ′ 4� ′′ (23G∗d + 32G∗m ) + (13G∗d + 12G∗m ) R R

(4.5)

All frequency-dependent quantities E, D, G∗m , G∗d , � ′ , and � ′′ have to be taken into account at the same frequency (�). For the case of inite concentrations, Equation (4.3) becomes ∗

G (�) =

⎛ 1 + 3 Φ E(�) ⎞ 2 D(�) ⎟ ⎜ 1 − Φ E(�) ⎟ ⎝ D(�) ⎠

G∗m (�) ⎜

which indeed reduces to Equation (4.3) at small Φ values.

(4.6)

POLYMER NANOCOMPOSITES

147

Speciic results on the application of the Palierne model can be found in the work by Graebling, Muller, and Palierne [20].

4.3

POLYMER NANOCOMPOSITES

Since the feasibility to produce polymer nanocomposites was validated by the Toyota group laboratories more than two decades ago, the science and technology behind the current methods to elaborate this type of compounds have been greatly challenged. Extensive and intensive research on how to obtain polymer nanocomposites in a more controlled and sustainable way has been done ever since, and it is still today a subject to be consolidated. With the aim of accomplishment, two main general approaches are continuously revisited: melt processing and in situ chemical/solvent techniques, the latter being employed in early works from the Toyota group and representing, so far, the most successful routes to produce polymeric compounds with iller inclusion in the range of nanometers. Nevertheless, despite their promising results, important limitations arise concerning chemical or solvent approaches: the use of monomers and/or solvents, laborious procedures, small amounts of inal material, and limited capability to expand to a larger scale. Because of this, melt compounding continues to be a strong alternative to produce polymer nanocomposites in a more reliable manner, even though results obtained by this method have been not that remarkable. However, the great interest in melt compounding lies in that it presents very signiicant advantages such as the use of continuous, semicontinuous, and batch processes that yield high production of material; operation relatively simple and economic, and, very important, the use of solvents is usually avoided. The accelerated increase in the research in polymer nanocomposites is well justiied since novel and promising nanoillers are in the spotlight of materials science. The basic feature to exploit in nanostructured compounds is the exposed high surface area when nanoillers are dispersed to the minimum primary particles (exfoliation). Theoretically, this dispersion state is the base to provide the maximum in physical properties imparted by the nanocharge to the system. From basic polymer reinforcement to functional materials where more specialized and tuned characteristics are sought for, we can nowadays ind illers at the nanoscale with a vast number of properties. In recent past, different types of silicates, that is, montmorillonites have been intensely studied as polymer reinforcing systems and gas barrier. Currently, nanoillers with more complex properties call the attention of scientist. This is the case of CNTs, nanowires, graphene, quantum dots, and so on, which imparts a wide range of properties such as high strength and lightweight, high electrical conductivity at very low percolation threshold, and optical and magnetic performance. Nevertheless, the scientiic and technological challenge when it comes

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to polymer nanocomposites is still lying in the dificulty to attain proper dispersion of the nanoillers. This is why the search for eficient mixing procedures for these compounds is nowadays a critical subject. 4.3.1

Dispersion of Solid Additives

Particularly, a widely accepted sequence for the dispersion of solid additives into a polymer matrix is as follows: 1) Incorporation and wetting of the iller 2) Rupture of solid agglomerates and/or aggregates 3) Separation of the resulting fragments to the point where reagglomeration will not occur 4) Distribution of the separated fragments throughout the polymeric matrix 5) Aggregation or networking depending on the particular system. Although ideal mixing, in terms of dispersion quality, considers steps 1–4 to be achieved, it is generally agreed that the rupture or deagglomeration step is the limiting one, especially regarding polymer nanocomposites. As it was stated earlier, appropriate conditions to agglomerate dispersion are determined by the balance between the cohesive forces, holding agglomerates/aggregates together, and the disruptive hydrodynamic forces. In this regard, a hard research prevails in the direction of eficiently dispersing current challenging “nanoillers,” conformed in the initial undispersed state either by tightly compacted clusters and aggregates or by crystals structured in a sheet-like manner, susceptible of undergoing exfoliation when subjected to shear and/or elongational low at the appropriate stress level. A series of representative works focused on the role of these low geometries on mixing can be found in the literature [21–24]. In this respect, in a classical work by Tadmor [21], he used an analytical approach to derive speciic relationships deining the force necessary, exerted in shear and elongational low ields, to separate an agglomerate. The agglomerate was modeled as a dumbbell consisting of two unequal beads connected by a rigid connector. The dumbbell approach allows to depicting a more schematic view of the agglomerate rupture under the inluence of a low ield, that is, as a result of the viscous drag on each of the beads a certain force develops in the connector, which depends on the magnitude of the viscous drag and on dumbbell orientation. When these forces exceed a certain critical value, which equals the attractive cohesive forces, the beads break apart. Accordingly, the maximum force estimated to separate the beads from the dumbbell, subjected to shear low, is described as follows: Fmax = 3�(��)r ̇ 1 r2

(4.7)

where � is the viscosity, �̇ is the shear rate, and r1 and r2 are the radii of the beads. The maximum force is, thus, proportional to the shear stress (��). ̇ On the other hand,

POLYMER NANOCOMPOSITES

149

the maximum force for the application of a steady elongational low in the connector corresponds to Fmax = 6���r1 r2 (4.8) where � is the rate of elongation. On the way down to obtain Equations (4.7) and (4.8), an important remark about the disrupting force orientation is pointed out: for shear low, the maximum force has to be oriented at 45∘ angle to the direction of shear, whereas in elongational low the force is aligned in the direction of low. In addition, from the equations it can be seen that, at the same deformation rate, the force exerted by elongational low doubles the force from shear low. Nevertheless, in practice, high shear rates are much easier to obtain than high elongation rates; thus, appropriate conditions to make valid what is concluded from Equations (4.7) and (4.8) are not easy to attain. This is an important reason why most dispersive mixers are based on shear dispersion. In another theoretical approach, Manas-Zloczower et al. [22] analyzed agglomerate rupture in linear low ields, employing four low geometries: simple shear; pure elongation, uniaxial extension, and biaxial extension. The eficiency of each type of low is compared on the basis of power and time requirements to achieve a given degree of dispersion. The authors indicate that a minimum value of low strength, which depends on the geometry of the bulk low ield, is required for the rupture of the agglomerate. The low geometry is indeed classiied in terms of the forces acting to rupture the agglomerate, relative to the tensile strength of the agglomerate, by a single dimensionless parameter, Z: Z=

���̇ �

(4.9)

where � is a scalar related to the geometry of the breakup process, � is the viscosity of the suspending luid, �̇ is the applied shear rate, and � is the tensile strength of the agglomerates. For each low geometry, there is a minimum value of the parameter Z required for the rupture to occur, that is, the values corresponding to the condition at which hydrodynamic stresses trying to disrupt the agglomerate overcome the cohesive forces holding it together. The plane of the fracture is oriented perpendicular to the principal axis of strain for each low ield. The range of Z values leading to agglomerate rupture as a function of the low ields is as follows: Simple shear Pure elongation Uniaxial extension Biaxial extension

Z≥2 Z≥1 Z ≥ 0.5 Z≥1

From the point of view of determining stress critical conditions for the rupture process, it can be say, in a broad sense, that the parameter Z, in the area of solid dispersion into low ields, is analogous to the capillary number, Ca, for droplet breakup in viscous media.

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Regarding eficiency results, it was found that, based on time–energy balance, biaxial extension and pure elongation low ields reported by far the best results in comparison to simple shear. From an experimental approach, Utracki et al. [24] have qualitatively addressed the importance of elongational low contributions to melt compounding of polymer/organoclay nanocomposites. In his work, dealing with polystyrene (PS)/montmorillonite compounds, since the low ield during melt mixing is assumed to affect the degree of clay exfoliation, three different mixing heads were attached to the end of a SSE, each producing different low pattern: pure shear (smooth cylinder), pure elongation (sharp grooved cylinder), and elongation/shear (lat grooves). It was shown that the device providing elongation/shear low patterns generates the higher degree of dispersion and mechanical properties of the inal nanocomposites. Particularly, the analysis of exfoliation in clays has been addressed from a theoretical and practical point of view in works as those of Bandyopadhay et al. [25] and Cho et al. [26]. In this literature, estimation of delamination forces is carried out strongly considering platelet orientation in the models. Authors in both papers propose the next relationship to obtain the van der Waals’ forces associated with the cohesive strength between two square platelets: Fvan der Waals =

Acpc 6�

(

1 2 1 + − d3 (d + 2h)3 (d + h)3

) L2

(4.10)

where d is the spacing between the two platelets, h is the thickness of the platelet, Acpc is the Hamaker constant when the polymer is present between the two platelets, and subscripts c and p represent clay platelet and polymer, respectively, and L is the length of the platelet. Speciically, Bandyopadhay et al. [25] estimated the shear stress developed in a TSE, considering it in a suitable range to cause clay delamination or exfoliation. Authors point out that both dispersive and distributive mixings contribute to the delamination process: the former breaks up the large particles and the latter is responsible for the homogeneous delamination of those particles. Polymer diffusion within the stacks galleries is critical for the exfoliation to occur; this is promoted by temperature rising. However, Cho et al. [26] proposed models to estimate the dispersive force needed to separate two platelets under shear and elongational low. They concluded, according to the model, that exfoliation is a function of shear rate, viscosity of the matrix, the Hamaker constant, overlapped fraction, gallery spacing, and aspect ratio. In addition, the stress ratios are strongly dependent on the angle that the platelets make with the horizontal plane, and also tactoids with more clay layers can be broken more easily. In addition to the popular employment of nanoclays in polymer nanocomposites, another system of high growing impact is that of polymer/graphite/graphene nanocomposites which were derived from the advent of graphene in the last decade [27]. Graphite is one of the most common forms of carbon and, as silicates, its

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151

layered structure makes it a natural iller candidate for the elaboration of polymer nanocomposites. It has the susceptibility to undergo exfoliation under proper conditions, that is, to render pristine tactoids into graphite nanoplatelets (GNP, several layers stacks) and/or graphene. Nowadays, there is a large volume of work in the literature devoted to describe different ways to sustainably obtain GNP and graphene from graphite, in their basic and modiied versions (named, in general, chemically modiied graphene, CMG). Derived from such research, a series of graphitic materials are to be considered as precursor or structural illers for the elaboration of polymer nanocomposites, that is, expanded graphite (EG), graphite intercalation compounds (GIC), graphite oxide (GO), graphene oxide (G-O), functionalized graphene sheets (FGS), chemically reduced GO (R-GO), thermally reduced GO (TrGO), polymer-modiied GO (P/GO), and others [28, 29]. Regarding the methods to elaborate polymer/graphite/graphene nanocomposites, casting or solution methods are still more successful than melt processing in rendering nanostructured materials. Two important examples are given by Stankovich et al. [30] and Brinson and coworkers [31]. However, advantages of the melt processing, as stated earlier, make it a ield of research of increasing interest [32–37].

4.4

ELONGATIONAL FLOW MIXER (RMX®)

In the last decades, new mixing devices have been developed to create strong elongational low to improve dispersive mixing. As mentioned earlier, developments have been principally applied to the existing continuous systems such as SSEs and TSEs where a critical feature is the multiple passage of the material through the points of high stresses, which compensates for the dificulty to reach critical rates of strain needed for breakup. Nevertheless, the idea of promoting elongational low for enhancing mixing eficiency has given place to the development of devices speciically designed to generate elongational low, either for the particular analysis of the low ield or intended for mixing. In particular, Meller and coworkers [38] studied the deformation and breakup of dispersed droplets in molten polymer blends of different viscosities. They used a capillary rheometer equipped with dies having different entry proiles and showed that the mixing eficiency in the converging low zone was dependent on both the shape of the convergence and the low rate. These types of works have enabled some actual authors to revisit and to bring back old mixer designs as those of Hausman [39] and Westofer [40] concerning the concept of low between two opposite chambers through a small diameter die. Mackley and coworkers [41] adapted this geometry to design the so-called multipass rheometer in which the inluence of the number of passes through the central die on the rheological properties can be studied. Recently, Son et al. [42] have shown that the concept of multipass rheometer can be adapted to design a batch mixer in which an unlimited number of convergent/divergent lows can be applied to the material to be mixed.

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152

4.4.1

RMX® Assembly and Operating Principles

The architecture of an RMX® prototype for melt mixing is presented in Figure 4.7. The main assembly comprises two opposite cylindrical chambers communicated by a central mixing element (capillary die) interchangeable at different possible L/D ratios. Within the chambers, two pistons are hydraulically driven by a servo valve at a controlled speed in the range of 3–180 mm/s, which using a 3.2-cm-diameter cylinder represents a volumetric low Q between 2.4 and 125 cm3 /s. The maximum pressure is limited by the power of the hydraulic station. The current version can reach around 300 bars. This device allows us to work with a variable volume of material (between 10 and 100 cm3 ). Regarding the RMX® operation, in Figure 4.8a, the feeding step is carried out by injecting the melt into one of the chambers. Next, during mixing as in Figure 4.8b, the material is induced to pass from one chamber to another throughout the mixing element by means of the reciprocating pistons, in a back and forth manner.

a e

b

c

d e

f

c

d

a b

Figure 4.7 Three-dimensional view of the RMX®: (a) chamber, (b) piston with seal, (c) mixing element, (d) feeding unit for melts, (e) feeding channel for liquids, and (f) optional mold. Reproduced from Bouquey et al. [43] with permission of John Wiley and Sons.

ELONGATIONAL FLOW MIXER (RMX®)

153

(a)

(b)

(c)

Figure 4.8 Schematic operation of the RMX® mixer: (a) feeding, (b) mixing, and (c) discharge. Reproduced from Bouquey et al. [43] with permission of John Wiley and Sons.

An unlimited number of convergent/divergent lows at the entrance and exit of the die can thus be produced at different speeds, allowing to repeatedly generate elongational low in an eficient manner. Finally, in the discharge step as in Figure 4.8c, the material is ready to be either extruded or molded, expelled by one of the pistons. A mixing sequence is deined simply by the piston velocity (v) and number of cycles (N). Pressure in one of the chambers is continuously measured during the mixing sequence by a pressure transducer, making it a central output variable to be followed up as related to viscosity changes. In this regard, Figure 4.9 shows a mixing sequence of 10 cycles, clearly identiied in terms of pressure peaks during the gathering of data. Figure 4.9a correspond to a mixing sequence where a mixing element of L/D = 14 was used, whereas in Figure 4.9b the L/D was changed to 7. The difference in pressure is readily observed. Furthermore, pressure variation during the global mixing sequence due to chemical or physical changes can be followed up in this way. In relation to Figure 4.10, speciic behavior of the pressure for each cycle is obtained when this is followed up as a function of piston displacement. This allows to accurately differentiate in a more detailed procedure, pressure loses from cycle to cycle. Because of the mixing principle of the RMX®, there exist operation conditions where phenomenon of viscous heating may be relevant. In this respect, the increment in temperature (ΔT) due to viscous heating during RMX® mixing can be estimated from the ΔP measurements [41], using the calculation for an adiabatic temperature rise, so as to have ΔP (4.11) ΔT = �PLA CpPLA On the other hand, as ΔT ∝ � �̇ [44], viscous heating effects may be smoothed by balancing the L/D ratio of the central die and linear speeds.

MIXING OF POLYMERS USING THE ELONGATIONAL FLOW MIXER (RMX®)

154 200 180 Pressure (bars)

160 140 120 100 80 60 40 20 0 0

100

200

300 400 Data acquistion (a)

500

600

140

Pressure (bars)

120 100 80 60 40 20 0 0

100

200

300 400 Data acquistion (b)

500

600

Figure 4.9 Maximum pressure reached by cycle in an RMX® mixing sequence for an HDPE/PP/PS blend at N = 10 and v = 10 mm/s, employing mixing elements of (a) L/D = 14 and (b) L/D = 7. Reproduced from Mani et al. [13] with permission of Ecoindustry.

In a broad sense, dificulties commonly found in conventional mixers to generate high elongational strain rates are overcome by the RMX® because of its simple geometry; it also means that a correlation between the linear speed of pistons and the shear/elongational strain rates in the mixing element is readily estimated using speciic rheological data of the material. On bringing that together with the capability of multiple passages, appropriate conditions for the enhancement of the dispersive eficiency are fulilled in a good extent. On the other hand, the totality of the mass to be mixed passes through the elongational strain zones (convergence/divergence areas) at a large range of elongation rates (wide time spectrum for the material to be subjected to elongational strain) given the wide range of linear speeds.

ELONGATIONAL FLOW MIXER (RMX®)

155

250

Pressure (bars)

200

150

100

50

0

80

90

100

110

120

130

140

150

160

Piston displacement (mm)

Figure 4.10 Pressure trajectory as a function of piston displacement in an RMX® mixing sequence for an HDPE/PP/PS blend at N = 10, v = 10 mm/s, and mixing element L/D = 14. The total displacement in millimeters depends on the volume of material (in the example, 40 g). Reproduced from Mani et al. [13] with permission of Ecoindustry.

4.4.2

RMX® Flow Analysis by Numeric Simulation

A numerical simulation of the low within the RMX® characterizes the relative contribution of elongational and shears lows during operation [43]. The low was assumed to be axisymmetric, and the volume within both chambers and in the mixing element was discretized with a structured mesh. A nonslip boundary condition was imposed on the walls and surface of the pistons, and the pistons moved with a constant velocity parallel to the axis. The total volume was conserved during the simulation. To solve this problem, we used a inite volume code (CFD-ACE) that allowed us to solve the continuity and Navier–Stokes equations for an incompressible luid [45]. From the viscosity/shear rate curves, the parameters of a Carreau-type equation were identiied for each polymer and were taken into account in the simulation under the assumption that the material followed a generalized Newtonian equation of state [46]. Because the geometry was in motion, remeshing of the volume was required at each time step. The solver compressed the cells on one side and expanded them on the other side. The mesh displacement was taken into account in the calculations with the ALE method (simple interpolation). The low geometry was characterized by a scalar parameter (�) deined by Astarita [47]: Ωrel (4.12) � =2 Ωrel + D

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MIXING OF POLYMERS USING THE ELONGATIONAL FLOW MIXER (RMX®)

χ 0

1

2

χ 0

1

2

Figure 4.11 Mapping of the low by Astarita’s parameter. Reproduced from Bouquey et al. [43] with permission of John Wiley and Sons.

where D is the magnitude of the strain rate tensor and Ωrel is the magnitude of the relative rate of the rotation tensor (Ω − W, where Ω is the vorticity tensor and W is the tensor giving the rate of rotation of the eigenvectors of D). With this deinition, � is an objective quantity whose values are in the range of 0–2. � = 0 corresponds to pure elongational low, � = 1 corresponds to simple shear low, and � = 2 corresponds to rigid body motion. Figure 4.11 shows a mapping of Astarita’s parameter (�) in the volume of the mixer with a mixing element of L/D = 5. As expected, the low was nearly elongational in the contraction and expansion zones close to the mixing element and was purely simple shear in the middle of the die. Once the velocity ield was determined, we could also estimate the mapping of the elongational strain rate in the convergent and divergent zones. The values along the axis of symmetry are shown in Figure 4.12 for v = 10 mm/s (Q = 7 cm3 /s). Very high values of the elongational strain rate were found close to the mixing element, but the corresponding residence times were very short because of increasing luid velocity. 4.4.3 Estimation of Rheological Parameters in the RMX® via Capillary Rheometry Since the RMX® coniguration is analogous to capillary rheometer geometry, corresponding shear rates at the different piston speeds are easily calculated applying the

ELONGATIONAL FLOW MIXER (RMX®)

157 200 150

ε (s–1) 100 50

–3.0E–02

–2.0E–02

0 0.0E +00

–1.0E–02

1.0E+02

–50

2.0E+02

3.0E+02

X (m)

–100 –150 –200

Figure 4.12 Elongational strain rate dv/dx (s−1 ) along the x-symmetry axis. Reproduced from Bouquey et al. [43] with permission of John Wiley and Sons.

Rabinowitsch equation to non-Newtonian low: �̇ =

4Q 3n + 1 ⋅ 4n �R3

(4.13)

where �̇ is the true or corrected shear rate, Q is the volumetric low, R is the radius of the die or mixing element in the RMX®, and n is the low power index obtained by capillary measurements. In order to estimate elongational strain rate in the RMX® at a certain value of shear rate, irstly, it is necessary to obtain elongational properties from capillary measurements using the Cogswell approach [48]: 9 (n + 1)2 �e = ⋅ ⋅ 32 � 3 (n + 1) ΔPe 8 � �̇ = e �e

�e =

(

ΔPe �̇

)2 (4.14) (4.15) (4.16)

where �e is the elongational viscosity, � is the shear viscosity, ΔPe is the entrance pressure drop, �̇ is the shear rate and �e and �̇ are the elongational stress and elongational strain rates, respectively.

MIXING OF POLYMERS USING THE ELONGATIONAL FLOW MIXER (RMX®)

158 1000

Elongational strain rate (1/s)

100 Convergence ratio barrel/die: 15/2 Convergence ratio barrel/die: 15/1 10

1

0.1 1

10

100

1000

10 000

100 000

Shear rate (1/s)

Figure 4.13 Estimation of elongation strain rate in the RMX® using capillary data obtained at similar convergence ratio of capillary die for a blend HDPE/PP/PS. Reproduced from Mani et al. [13] with permission of Ecoindustry.

In this way, by using same or similar convergence ratios, Φc /Φd (diameter of the reservoir to that of the die), in both, the capillary rheometer and the RMX®, it is possible to ind an estimated value of �̇ in the RMX® from a certain value of �̇ according to the relationship showed graphically in Figure 4.13. In the RMX®, ranges of shear and elongational strain rates are easily expanded or reduced by using different L/D ratios of the mixing element. 4.5

RMX® MIXING OF POLYMER BLENDS

Up to now, different systems of polymer blends have been successfully treated by means of the RMX®. Among many particular aspects to consider, in general, two important reference points have been relevant to an objective evaluation of the inal performance of the mixer: 1) Mixing performance at high viscosity ratio of blends since dependency of mixing eficiency on elongational low contributions becomes more prominent at high p. 2) Mixing eficiency of the RMX® (morphology) in comparison to other mixers at the same speciic energy input.

RMX® MIXING OF POLYMER BLENDS

159

With respect to morphology, to fully characterize a polymer blend, the application of both qualitative and quantitative analyses is recommended. The well-known microscopy techniques for qualitative characterization are scanning electron microscopy (SEM), transmission electron microscopy (TEM), and atomic force microscopy (AFM). The information obtained by this method is used to carry out quantitative morphology analysis through the calculation of the number-averaged diameter, Dn , volume-averaged diameter, Dv , and polydispersity (PDI). Accordingly, ∑ i ni dni Dn = ∑ (4.17) i ni ∑

Dv = ∑ PDI =

4 i ni dni 3 i ni dni

(4.18)

Dv Dn

(4.19)

Dn simply represents the arithmetic mean of particle size, where the number of particles is rather privileged over the frequency of speciic classes (small, medium, or large size). Dv , on the other hand, takes into account the size classes. 4.5.1

Inluence of the RMX® Parameters on Mixing

In a pioneer work, mixing performance of the RMX® and the resulting morphological data on polystyrene (PS)/polymethylmethacrylate (PMMA) blends were extensively analyzed [43]. Speciic qualitative inluence of the number of cycles on the morphology of the blend is evidenced in Figure 4.14.

10 µm (a)

10 µm (b)

Figure 4.14 TEM images at two different values of N for 10/90 PS/PMMA blends (v = 10 mm/s), L/D = 5: (a) 10 and (b) 40. Reproduced from Bouquey et al. [43] with permission of John Wiley and Sons.

MIXING OF POLYMERS USING THE ELONGATIONAL FLOW MIXER (RMX®)

160

According to Figure 4.14, after 10 cycles, a complex morphology with large PS domains containing PMMA inclusions was observed. When N is increased to 40 cycles, a homogeneous and well-dispersed morphology is obtained, from which the average particle diameters could be determined. Figure 4.15, on the other hand, presents the overall effect of N on morphology, in terms of morphology parameters Dn and Dv , at different ratio L/D of the mixing element. As N increases, the average particle values tend to reach a plateau, which indicates steady-state blend morphology. Furthermore, small particles were present from the early steps of the mixing process, and increasing N led to the progressive breakup of the largest particles and to a reduction of the particle size polydispersity. From the same Figure 4.15, it is possible to discuss the effects of L/D on Dn and Dv . L/D = 5 led to a much iner dispersion, which indicated that in this particular combination of material and mixing parameters, the shear low contribution enhanced by a longer die played an important role in the deformation process. The signiicance of this contribution, though, is not easy to be explained given the complexity of the transitional phenomenon that is elongational to shear low geometry. Firstly, initial droplets size is critical when it comes to the extent of total deformation. Accordingly, larger droplets (as it is assumed in the irst stages of mixing) undergo larger deformation, that is, thick elongated ilaments [49, 50], which require times to breakup higher than the residence time reached in the solely convergent zone. Although this zone promotes intense elongational low and, hence, high deformation, in the irst stages of mixing droplets would require more time to attain the total deformation

Average particle diameter (µm)

1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

50

100 150 Number of cycles (N)

200

Figure 4.15 Dn and Dv (μm) versus N for 90/10 PS/PMMA blends (v = 10 mm/s, temperature = 210 ∘ C): (◽) L/D = 5 (long die), Dn ; (▵) L/D = 1.5 (short die), Dn ; (◾) L/D = 5, Dv ; and (▴) L/D = 1.5, Dv . Reproduced from Bouquey et al. [43] with permission of John Wiley and Sons.

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needed to undergo rupture (e.g., by ilament instability). This seems to be accomplished only by the contribution of shear low, say, an appropriate die length. For a short die, the residence time is supposedly very small, and we could assume that the elongated droplets reached the divergent low zone in the downstream chamber before breakup and therefore eventually recovered their initial size. Secondly, since the blend system studied in Figure 4.15 does not comprise the use of compatibilizing agents, the mechanisms and inal balance of droplet breakup and coalescence phenomena turn out to be particularly dependent on the low geometry contributions. This seems to be illustrated by the work of Miroshnikov et al. [49] on measuring coalescence in lows through converging channels for an incompatible PMMA/PS blend. They found that in the convergent zone, Ca surpasses Cacrit (condition for the droplet breakup to occur); however, collision frequency of the dispersed droplets is also simultaneously increased and, thus, coalescence takes place in a signiicant way. As a consequence, large droplets are present continuously in the convergent zone, which, again, would make the role of the shear contribution or die length quite signiicant. In order to further explain the dependence of droplets collision probability on mixing parameters, that is, droplets size and deformation rate, it is needed to approach the theory of ilm drainage between colliding drops [3]. Briely, at a given deformation rate, small droplets are more likely to coalesce than the large ones because the lattened area between them is consequently smaller; thus, the time for the matrix ilm drainage and droplets contact is shorter. A signiicant increase in the deformation rate leads to a global increase in the lattened area, which requires long times for ilm drainage; therefore, coalescence tends to be suppressed. Back on the particular case of the RMX® and the contributions of elongational and shear low on the inal morphology, it has to be added that elongational low is also generated at the exit or divergence of the die (see Figs 4.11 and 4.12). This inal deformation stage would also contribute to enhance the overall ilament breakup process in the RMX®. Of course, since the RMX® operates in a dynamic mode, the evolution of the morphology over time would also determine the exact role of the contributions of each type of low and the speciic signiicance of the die length during the different stages of the mixing process. For the sake of complement, it is known that a well-compatibilized blend system presents additional and important phenomena by virtue of interface stabilization, which makes droplet breakup dynamics to follow a kind of different mechanism. In this case, it is recently found that the interaction between a pair of droplets of the dispersed phase does not end up in coalescence but rather in a “pushing/squeezed” mechanism in the constriction zone, which strongly contributes to the known droplets deformation processes [51]. Results in the same direction, about L/D signiicance, were also founded in blends of polypropylene (PP) (at two different melt low index) and ethylene propylene diene monomer (EPDM), prepared also by the RMX® (Fig. 4.16) [52]. Two mixing elements are also compared here: a 4-mm-diameter die (L/D = 7) and a 2-mm-diameter

MIXING OF POLYMERS USING THE ELONGATIONAL FLOW MIXER (RMX®)

162 6

L/D = 7 Dn

5

Dv

L/D = 14 Dn Dv

Dn, Dv (µm)

4 3 2 1 0 0

5

10

15

20

25

Number of cycles (N)

Figure 4.16 Dn and Dv (μm) as a function of N in the RMX® (T = 200 ∘ C and Q = 21 cm3 /s) for PP/EPDM 80/20 (wt/wt%) blends: (Δ) Dn (L/D = 7), (▴) Dv (L/D = 7), (◽) Dn (L/D = 14), and (◾) Dv (L/D = 14). Reproduced from Rondin et al. [52] with permission of John Wiley and Sons.

die (L/D = 14) of same length but of different diameter. The evolution of Dv is an accurate indicator of the dispersive mixing eficiency as it takes more into account the presence of large remaining EPDM droplets. Consequently, homogeneously dispersed morphologies will have a lower Dv than heterogeneous ones with the same values of Dn . For both mixing elements, a decrease in the EPDM particle diameter is observed with an increase in the number of cycles and a plateau size is reached, indicating steady-state blend morphology for both mixing elements. The plateau value for Dv is around 1 mm, which is consistent with the sizes reported in the literature for this type of blend [53]. For the blends elaborated with the L/D = 14, only 10 cycles are necessary to reach the plateau size, whereas it takes the double amount of cycles with L/D = 7. In terms of mixing times, steady-state morphology is obtained very early as it takes only 1 min to perform 10 cycles. The dispersive mixing eficiency of the L/D = 14 can be explained, again, by higher shear and elongational contributions to the overall deformation–breakup process based on Rayleigh’s instabilities [54]. Droplets undergo maximum elongation at the entrance and exit of the die leading to an instable thread that may breakup into a line of smaller droplets. Moreover, the reduction of the die diameter can signiicantly enhance the elongational rate at the entrance/exit [55]. Of course, larger L/D unavoidably leads to higher viscous heating of the molten polymers; thus, attention must be paid in this respect. The effect of different L/D ratio is addressed as well in Figure 4.17, which presents the morphology of a blend of high-density polyethylene (HDPE)/polypropylene (PP)/polystyrene (PS), 50/40/10 (wt/wt%) obtained from the RMX®.

RMX® MIXING OF POLYMER BLENDS

4.0 µm

163

4.0 µm (a)

(b)

Figure 4.17 AFM images of an HDPE/PP/PS-50/40/10 (wt/wt%) blend obtained by RMX® at 200∘ C, v = 3 mm/s, and N = 5: (a) L/D = 7 (Φ = 4 mm) and (b) L/D = 14 (Φ = 2 mm). Reproduced from Mani et al. [13] with permission of Ecoindustry.

The dark regions correspond to HDPE while the clear ones to PP. On the other hand, PS is dispersed in big elongated particles. As observed, in Figure 4.17a, using a diameter, Φ = 4 mm (lowest shear and elongational strain rate, �̇ = 16 s−1 and �̇ = 563 s−1 ), a homogeneous and co-continuous phase morphology is likely to appear by virtue of the concentration ratio of the majority phases HDPE/PP close to 1 and combined effects of speed and high viscosity ratio (p ∼ 4). Large PS particles, however, indicate that stresses at this level of strain are not still high enough to render a well-dispersed morphology. This state changes drastically when the polymer blend is subjected to a much higher shear and elongational strain rates just by reducing the diameter of the mixing element by the half, Φ = 2 mm (strain rates unfold several times, �̇ = 112 s−1 and �̇ = 4500 s−1 ). The morphology of Figure 4.17b is quite homogeneous and presents domains of HDPE and PP in the order of less than 1 μm. PP particles (ellipsoids) are indeed signiicantly reduced in size and also well distributed all over the visual ield. With respect to the inluence of v or Q for PS/PMMA blends (Fig. 4.18), as soon as N exceeded approximately 50, Dn was almost independent of Q and t and had a very small value of approximately 0.1 μm. On the other hand, Dv decreased both with N up to at least 200 cycles and with Q. This result is again in agreement with a breakup mechanism based on droplet elongation and further breakup by interfacial instability. This mechanism produced a signiicant number of very small droplets even in the early stages of blending that were responsible for the small initial values of Dn . The later decrease in Dv was attributed to remaining larger drops that broke up progressively as t increased. Again, for the system HDPE/PP/PS, Figures 4.19 and 4.20 show the inluence of v (Q) on the morphology. However, as will be noticeable, this inluence also depends on the L/D ratio of the mixing element. In Figure 4.19, using a mixing element of L/D = 7

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Average particule diameter (µm)

164

0.4 0.3 0.2 0.1 0

0

50

100 150 Number of cycles (N)

200

Figure 4.18 Dn and Dv (μm) of PMMA/PS blends versus N at different v/Q values, temperature = 210 ∘ C: (▵) Dn at 5 mm/s, (▴) Dv at 5 mm/s, (◽) Dn at 10 mm/s, (◾) Dv at 10 mm/s, (○) Dn at 20 mm/s, and (•) Dv at 20 mm/s. Reproduced from Bouquey et al. [43] with permission of John Wiley and Sons.

4.0 µm

4.0 µm

4.0 µm (a)

(b)

(c)

Figure 4.19 AFM images of an HDPE/PP/PS-50/40/10 (wt/wt %) blend obtained by RMX® at 200 ∘ C, v = 3 mm/s, N = 5, L/D = 7. (a) 3 mm/s, (b) 10 mm/s, and (c) 30 mm/s. Reproduced from Mani et al. [13] with permission of Ecoindustry.

4.0 µm

4.0 µm (a)

4.0 µm (b)

(c)

Figure 4.20 AFM images of an HDPE/PP/PS-50/40/10 (wt/wt %) blend obtained by RMX® at 200 ∘ C, v = 3 mm/s, N = 5, L/D = 14. (a) 3 mm/s, (b) 10 mm/s, and (c) 30 mm/s. Reproduced from Mani et al. [13] with permission of Ecoindustry.

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(Φ = 4 mm), from low to medium speed, morphology change from co-continuous pattern to a dispersed HDPE phase (dark tone, high viscosity phase). Afterwards, at even higher speed, coalescense seems to appear changing the morphology to a much more discrete dispersed HDPE domains within a continuous PP phase. In spite of this, dispersion of the high viscosity phase into the minor one is still effective, but according with the observations there seems to exist an apparent optimum speed (shear to elongational contributions) related to a maximum dispersing eficiency. A possible explanation to this behavior is the high relaxation time of the highly elastic dispersed phase that cannot develop strain enough at high shear rates. When the L/D is increased to 14 (Φ = 2 mm), however, morphology changes over speed from a homogeneous, very well-dispersed mixture to inally coarsed co-continuous pattern (Fig. 4.20). Certainly, in the case of high shear rates, viscous heating could play a major role in such a way that morphology may not depend only on the balance between hydrodynamic and interfacial forces. 4.5.2

Inluence of the Viscosity Ratio, p

Rheological information about pristine components of the polymer blend is needed � to estimate appropriate viscosity ratios ( p = �d ), that is, the range of shear rates of c interest. In Figure 4.21, based on dynamic tests, p and elasticity ratios are obtained for blends PP/EPDM in the shear-thinning zone, which usually represents the region of conventional melt mixing and processing. Figure 4.22 illustrates the role of p on the morphology evolution of blends of PP/EPDM elaborated by the RMX®. Although signiicant particle size reduction is observable in Dv and PDI at high p, the global mixing eficiency is still closely linked to L/D ratio. An interesting initial observation is that the blend at p = 0.8 and L/D = 14 presents the lowest average particle size even in the earliest stage of mixing. Since values of p around and below 1 are related to droplet breakup in the domain of shear rate, according to classical Grace’s work, we could expect that the well-developed shear low and higher residence time in the long die allow for a direct and higher contribution of shear low on droplet breakup with respect to p = 2, keeping L/D as well as the elongational contribution the same. Again, according to Grace’s work, blends at p = 2 probably reach or fall beyond the eficiency limit of shear low to promote droplet breakup, resulting in a lower dispersion eficiency in the early stages of mixing. Over time, average droplets size is equalized for both p values at L/D = 14. On the other hand, there is remarkable difference in average droplets size between blends at different p using the short die. The much lower size for the case of p = 0.8 suggests one more time that shear-driven droplet breakup appears to signiicantly contribute to morphology, whereas for p = 2, as stated earlier with respect to the inluence of die length (Fig. 4.15), the short die does not allow for the suficient deformation and residence time to achieve small droplets eficiently in the range of mixing time or

166

MIXING OF POLYMERS USING THE ELONGATIONAL FLOW MIXER (RMX®) 100 000

η* (Pa S)

10 000

1000 PP(2) 100 0.01

0.1

PP(12) 1

EPDM-P 10

100

ω (rad/s)

(a) 100 000

G' (Pa)

10 000 1000 100 10 PP(2) 1 0.01

0.1

PP(12) 1

EPDM-P 10

100

ω (rad/s)

(b)

Figure 4.21 (a, b) Complex viscosity �* and storage modulus G′ of PP with two different melt low index, MFI, and EPDM at 200 ∘ C: (⬧) PP (MFI:2), (◾) PP (MFI:12), and (▴) plasticized EPDM. Guided lines are for the Carreau-Yasuda itting. Reproduced from Rondin et al. [52] with permission of John Wiley and Sons.

cycles employed. As can be seen, it is the only case where stable morphology is not attained. A general trend found is that, regardless the p value, the larger the die length, the higher the dispersion eficiency, other parameters being kept constant. According to the precedent observations and particularizing the operational principle of the RMX®, we can suggest that depending on the viscosity ratio of the blend, capillary low within the die would contribute in two forms to the inal morphology: (i) by directly taking part of the deformation/droplet breakup process, for the case of low p [56], thus, making the shear low contribution as signiicant as the elongational low contribution and, (ii) by enhancement of deformation and residence time at high p where elongational low contribution is clearly predominant. PDI values are

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Dv (µm)

12 10

p = 0.8

8

p=2

L/D = 7 L/D = 14 L/D = 7 L/D = 14

6 4 2 0 0

5

10

15

20

25

Number of cycles (N) (a) 12 p = 0.8

10

PDI (–)

8

p=2

L/D = 7 L/D = 14 L/D = 7 L/D = 14

6 4 2 0 0

5

10

15

20

25

Number of cycles (N) (b)

Figure 4.22 (a) Dv as a function of the number of cycles and (b) PDI as a function of the number of cycles done in the RMX®. (T = 200 ∘ C and Q = 21 cm3 /s) for PP/EPDM 80/20 (wt/wt%) blends at different viscosity ratios and L/D. Reproduced from Rondin et al. [52] with permission of John Wiley and Sons.

represented in Figure 4.22b. It is also evident the inluence of L/D especially at the highest viscosity ratio p = 2. Another example of a high p system is as illustrated by Figure 4.23 where viscosity � is obtained for the three components of the blend HDPE/PP/PS-50/40/10 (wt/wt%). In Figure 4.23, when a common shear-thinning region is reached, estimated � p = �HDPE ∼ 4. As it is prospected, the main interest lies on dispersing a high viscosPP, PS ity component (HDPE) within a low viscosity one (PP or PS), proving the eficiency of the elongational low contribution at high p.

168

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100000

Viscosity (Pa s)

10000 HDPE PP PS

1000

100

10

1 0.01

0.1

1

10

100

Shear rate (1/s)

Figure 4.23 Viscosity of pristine polymer to be mixed into a blend HDPE/PP/PS by RMX® mixing. Reproduced from Mani et al. [13] with permission of Ecoindustry.

PS PP

HDPE 4.0 µm

4.0 µm (a)

(b)

Figure 4.24 AFM images of HDPE/PP/PS systems: (a) extruded and compression molded and (b) after RMX® mixing. Reproduced from Mani et al. [13] with permission of Ecoindustry.

Figure 4.24 shows the change in morphology for the system HDPE/PP/PS from a coarsen morphology before RMX® treatment to a high dispersion of the components at even the mildest condition in the mixer in terms of v and N. 4.5.3

Energy of Mixing: Performance Comparison

Because of the impossibility to directly compare dispersive eficiency between mixers in terms of typical mixing conditions, an important quantity of reference used to this

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169

purpose is the speciic mechanical energy input (SMEI). This is actually an indicator of the RMX® performance with respect to another mixing system. Comparison of morphology at the same SMEI was carried out between RMX® and a Haake internal mixer for polymer blends PP/EPDM [52]. Corresponding images are presented in Figure 4.25. SMEI (J/g) for every mixer is calculated as follows: SMEIRMX =

ΔP ⋅ Q ⋅ t m

Haake Rheomix 600

(4.20)

RMX (L/D = 14) a2

p = 0.8

a1

6 µm

6 µm (a) b2

p=2

b1

6 µm

6 µm (b)

Figure 4.25 SEM images at equivalent speciic mixing energies. (a) PP (MFI = 2)/ EPDM-60/40 (wt/wt%) blends: (a1) Haake Rheomix 600 (v = 50 rpm, t = 6 min, SMEI = 405 J/g) and (a2) RMX® (L/D = 14, N = 10, t = 1 min, SMEI = 408 J/g); (b) PP (MFI = 12)/EPDM-P 60/40 (wt/wt%) blends: (b1) Haake Rheomix 600 (v = 50 rpm, t = 6 min, SMEI = 260 J/g) and (b2) RMX® (L/D = 14, N = 10, t = 1 min, SMEI = 272 J/g). Reproduced from Rondin et al. [52] with permission of John Wiley and Sons.

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where ΔP is the pressure drop between the up- and downstream chambers, Q is the volume low rate, t is the mixing time, and m is the total mass of material introduced. SMEIHaake =

∑ Ωi ⋅ Ti ⋅ ti i

m

(4.21)

where Ωi is the rotor rotation speed (rad/s) and Ti is the measured torque inside the chamber (N m). For the samples in Figure 4.25, the concentration ratio is changed to 60/40, and L/D = 14 was taken as a reference since a very ine dispersion of the high viscosity minor phase was obtained in the RMX® in the case of a concentration ratio 80/20. Morphology results are clearly inclined to a better mixing performance of the RMX® even at the lowest p. Indeed, an even poorer quality of mixing in the Haake Rheomix 600 is obtained when p is increased, where coarsening of the dispersed phase seems to be more evident. 4.5.4

Viscous Heating

It has been already discussed earlier on the inluence of L/D ratio of the mixing element on the morphology of blends. An inherent issue linked to this aspect, as a direct consequence of the back and forth motion principle of the RMX®, is the different levels of viscous heating or temperature increment (ΔT) mainly as a function of the shearing component. As it was inferred earlier, in spite of the central role of elongational low on the RMX® eficiency, an appropriate L/D value is necessary in order to count with enough shear contribution; in this sense, larger L/D dies have reported the best results when it comes to quality of dispersion. Nevertheless, the higher ΔP reached at larger L/D ratios represents higher amounts of viscous heating and, depending on the system to be mixed, caution has to be taken in the selection of the central die or mixing element to avoid possible degradation or even high rheological variations during mixing. Therefore, a suitable balance between L/D ratio and ΔT increment has to be made on this matter. Figure 4.26 presents temperature increments (ΔT) at different piston speeds using different L/D ratios (same diameter, Φ = 2 mm, different length) for the blend system HDPE/PP/PS. The twofold effect, from increasing speed and L/D, on viscous heating is clearly observed. It is noteworthy that extreme points render a similar ΔT, this is, at (v = 30 mm/s, L/D = 3.5) and (v = 3 mm/s, L/D = 14), ΔT ∼ 58 ∘ C, thus, question arises on the speciic weight of every parameter, v and L/D, on morphology. So far, L/D appears to have a more deinite role on the quality of mixing. 4.5.5

Effect of a Compatibilizer

The effect of a compatibilizer iller/polymer in the quality of dispersion has been also addressed for the RMX® [57]. In Figure 4.27, a morphology comparison (at same SMEI) between a Haake internal mixer and the RMX® is realized for samples

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Piston speed (mm/s)

30

10

L/D = 3.5 L/D = 7 L/D = 14

3

0

20

40

60

80

100

ΔT (°C)

Figure 4.26 Temperature increment at three different piston speeds and L/D ratio for blends HDPE/PP/PS obtained by RMX®. Reproduced from Mani et al. [13] with permission of Ecoindustry.

(a)

(b)

Figure 4.27 Morphology comparison between (a) Haake internal mixer and (b) RMX® at the same mixing energy for PBT/PP compatibilized blends. Top photographs, without maleic anhydride; bottom, 5 wt/wt% maleic anhydride. Reproduced from Bouquey et al. [57] with permission of MIXPLAST.

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prepared with and without maleic anhydride as compatiblizer, in a blend system of PBT/PP coming from plastic wastes. Regardless of the use of the hydrophilic agent, the RMX® shows again a better dispersion and homogeneity than the internal mixer. Under the effect of the compatibilizer, the RMX® reports a signiicant reduction in the particle size of PBT (clear phase), and an even distribution, while in the case of the Haake mixer, even though an improvement is noticeable, large PBT particles and poor homogeneity are evident. The lower interfacial energy provided by the compatibilizer favors the dispersion mechanisms over the coalescence of phases especially in the domains of elongational low. 4.5.6

Rheology/Morphology Relationship

As was indicated earlier, results from dynamic tests on polymer blends can be additionally exploited in the framework of theoretical rheology/morphology relationships, from which, the Palierne model [20] is one of the most used. Figures 4.28 and 4.29 are the examples of this application for PP/EPDM blends obtained by the RMX®. In Figure 4.28, a good agreement is obtained between the experimental data and the Palierne model. However, the characteristic “elbow” observed at low frequency because of the shape relaxation of the EPDM droplets is not observed for the itting curve in the considered frequency range and should be expected at lower frequency. This could be because of the fact that a simpliied model was used here and that does not completely take into account of the droplet size distribution. It has also to be mentioned that the different volume–average radii Rv measured and implemented into the model do not change the itting curve behavior (gray and black lines). 100000

G',G''(Pa)

10000

PP(2)/EPDM-P 80/20 σ = 0.3 mN/m R v = 0.36 µm

1000

100

G'

G''

Haake Rheomix 600 ® RMX 10 0.01

0.1

1 ω (rad/s)

10

100

Figure 4.28 G′ (white symbols) and G′′ (black symbols) for a PP(FMI = 2)/EPDM 80/20 (wt/wt%) blend elaborated in the Haake Rheomix 600 (v = 50 rpm, t = 6 min) and in the RMX® (L/D = 14, N = 10). Gray and black lines correspond to the moduli itting of the respective Palierne model, and dash lines represent the matrix moduli. Reproduced from Rondin et al. [52] with permission of John Wiley and Sons.

MIXING OF POLYMER NANOCOMPOSITES

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100 000 PP(2) / EPDM-P 60/40 σ = 0.3 mN/m R v = 0.53 µm

G',G'' (Pa)

10 000

1000 G' G'' 100 0.01

0.1

1

10

100

ω (rad/s)

Figure 4.29 G′ (white symbols) and G′′ (black symbols) for a PP(FMI=2)/EPDM 60/40 (wt/wt%) blend elaborated in the Haake Rheomix 600 (v = 50 rpm, t = 6 min) and in the RMX® (L/D = 14, N = 10). Gray and black lines correspond to the moduli itting of the respective Palierne model, and dash lines represent the matrix moduli. Reproduced from Rondin et al. [52] with permission of John Wiley and Sons.

For higher concentration of the EPDM phase, the Palierne model is no longer reliable as the originally separated droplets start to percolate in order to create a three-dimensional network (Fig. 4.29). Also the plasticizer may diffuse toward the interface that may result in interfacial tension gradients, which are outside the scope of the simpliied Palierne model. This co-continuous morphology can be better modeled by the Doi and Ohta model [55], which was extended by Lee and Park [58]. Castro et al. recently built a model empirically based on the previous ones [59]. The main assumption of this model is that elasticity in a blend of incompatible polymers is produced from both components and also from the interfacial tension �, which in combination with speciic interfacial area Q (per unit volume) deines the magnitude of the elastic stresses.

4.6

MIXING OF POLYMER NANOCOMPOSITES

Although the RMX® has shown remarkable results as mixer for polymer–polymer multiphase systems, as discussed earlier, its use has been expanded to the area of polymer nanocomposites where promising results can be found. As an example, RMX® has been applied to achieve micro- and nanoscopic reinement of GNP within a polystyrene (PS) matrix and compare results, with other processing methods, with a high voltage application of the nanocomposites [60]. In this regard, graphene-based illers are, on the one hand, creating a wealth of

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MIXING OF POLYMERS USING THE ELONGATIONAL FLOW MIXER (RMX®)

new opportunities and, on the other hand, also challenges for their use in polymer matrices. Their technological application is far from being fully understood and established. Experience with a similar disruptive technology, CNTs, shows that carbon nanoparticles may eficiently impart desirable behavior to polymers, for example electroactivity, such as electrical conductivity, piezoelectricity, photorefractivity, and others [61–64]. Similarly, it may be expected that graphene-based polymer nanocomposites will be among the fastest growing applications of graphene [65]. Properties and applications of graphene-based polymer nanocomposites have been overviewed recently, for example, by Kim et al. [66], Potts et al. [67], and Sengupta et al. [29]. In Figure 4.30, typical microscopic morphologies resulting from different manufacturing methods of conductive nanocomposites, including RMX®, are shown. Good light transparency of PS matrix facilitates imaging and both iller particles on the surface and somewhat below are seen and appear white since the iller particles relect light, while the matrix appears gray. Black spots are voids. In this work, optical microscopy has been used to evaluate the amount of large agglomerates present in the composites. Large agglomerates are highly undesirable in the material for at least two reasons: (i) they increase the electrical percolation threshold; (ii) they reduce the electrical stability in a high voltage application.

200 μm

(a)

200 μm

(b)

200 μm

(c)

200 μm

(d)

Figure 4.30 Optical microscopy images of morphologies resulting from different manufacturing methods: (a) Brabender mixing chamber, (b) Haake microcompounder, (c) RMX compounder, and (d) solvent-based preparation. A 5 wt% GNP was used in all cases. Reproduced from Oxfall et al. [60] with permission of John Wiley and Sons.

MIXING OF POLYMER NANOCOMPOSITES

175

0.6

Area fraction

0.5 0.4 0.3 0.2 0.1 0

1 2

3 4 5

50–100

1 2

3 4 5

100–250

1 2

3 4 5 >250

Agglomerate size (μm2) 100–250

Figure 4.31 Histogram representing various manufacturing methods employed to prepare the 5 wt% composition: (1) mixing chamber, (2) roll milling, (3) microcompounder, (4) elongational low, (5) solvent processing. Reproduced from Oxfall et al. [60] with permission of John Wiley and Sons.

As shown in Figure 4.31, the smallest amount of large microagglomerates and simultaneously the largest amount of small microagglomerates are produced in the composite manufactured by elongational low mixing using processing conditions of 5 (wt/wt%) at N = 31.2, v = 40 mm/s, and SMEI = 395 J/g. At the referred concentration, mixing conditions different from this are also reported but eficiency is actually not as high. A similar morphology is measured for the solvent prepared material. Both manufacturing methods give much higher microdispersibility compared to the other manufacturing methods for the present system and experimental parameters. Particularly, the microdispersibility imparted by microcompounding is lower than that by elongational low mixing and is higher than that by Brabender mixing chamber processing and two-roll milling/calendering. It is remarkable that high microscopic dispersibility of GNP in PS, practically the same as in solvent processing, can be obtained by melt processing when elongational low mixing is employed. It was also found that from the group of processing conditions in the RMX®, the highest mixing energy gives the better performance. In Figure 4.32, independent of the processing method, iller networking seems to deine the response of the low frequency moduli. However, at both 5 and 10 (wt/wt%) concentrations, solvent method tends to prevail over the rest of the group. A possible stronger interaction polymer/GNP in the solvent because of better diffusivity of polymer molecules may account for the higher stiffness as shown in Figure 4.32. In fact, electrical conductivity measurements correlate in a good way with that observed

MIXING OF POLYMERS USING THE ELONGATIONAL FLOW MIXER (RMX®)

176

106 105

G' (Pa)

104 103 102 101 100

10–3

10–2

10–1 100 Frequency (Hz) (a)

101

102

10–3

10–2

100 10–1 Frequency (Hz) (b)

101

102

106 105

G' (Pa)

104 103 102 101 100

Figure 4.32 G′ versus frequency of materials processed using various manufacturing methods. (a) 5 wt% and (b) 10 wt%: (⬧) mixing chamber, (▴) roll milling, (◾) microcompounder, (•) elongational low, and (x) solvent processing. Reproduced from Oxfall et al. [60] with permission of John Wiley and Sons.

about frequency measurements since solvent method reports the higher conductivity for both concentrations while elongational low gets the second place in this property at the higher mixing energy (SMEI) conditions. In another work, RMX® was also employed to obtain graphite/polymer nanocomposites [68]. Graphite is one of the most common forms of carbon and, as silicates, its layered structure makes it a natural iller candidate for the elaboration of polymer nanocomposites. It has the susceptibility to undergo exfoliation under proper conditions, that is, to render pristine tactoids into graphite nanoplatelets (GNP, few layers

MIXING OF POLYMER NANOCOMPOSITES

177

stacks) and/or graphene, and this is, indeed, precisely the challenge to overcome when polymer nanocomposites starts out from graphite as iller. Polylactic acid (PLA) was selected as matrix by virtue of its growing popularity as ecofriendly polymer; nevertheless, it represents also a challenging material from the processing point of view because of the high susceptibility to thermomechanical degradation. Indeed, as mentioned earlier, the design of the RMX® allows to an easy coniguration and control of mixing conditions in such a way that degradative processes are able to be followed up. In Figure 4.33, the complex viscosity of a formulation of expanded graphite (EG) at 3 (wt/wt%) in PLA is evaluated after several mixing conditions in the RMX®. It is evident that average weight molecular weight (Mw) of PLA is in general highly sensitive to the thermomechanical process but especially at high values of v and, of course, to the combined effect of increasing v and N. In fact, evidence of degradation during mixing, supporting the observed in Figure 4.33, was encountered in results from Figure 4.34, which illustrates the pressure behavior as the mixing sequence evolves for a sample at high v, v = 40 mm/s, N = 10. Pressure lowers at each cycle pointing out to high thermomechanical effects on PLA integrity. In spite of the different extents of chain scission in PLA, the eficiency on dispersive mixing of the RMX® led to the elaboration of polymer nanocomposites with

Complex viscosity (Pa s)

1.00E+04

1.00E+03

PLA control, Mw = 157,000 g/mol 10 mm/s 40 cycles, Mw = 118,000 g/mol 20 mm/s 10 cycles, Mw = 135,500 g/mol 40 mm/s 10 cycles, Mw = 106,000 g/mol 40 mm/s 20 cycles, Mw = 94,500 g/mol

1.00E+02 0.1

1 10 100 Angular frequency (1/s)

1000

Figure 4.33 Complex viscosity as a function of frequency for processed samples of neat PLA at different RMX mixing conditions. Reproduced from Ibarra-Gómez et al. [68] with permission of John Wiley and Sons.

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178

1.40E+07 Forward

1.20E+07

P (Pa)

1.00E+07 8.00E+06 6.00E+06 4.00E+06 2.00E+06

Backward

0.00E+00 0

0.01

0.02 0.03 0.04 Piston displacement (m)

0.05

Figure 4.34 RMX® pressure trajectory during the mixing sequence of neat PLA at 40 mm/s and 10 cycles. Reproduced from Ibarra-Gómez et al. [68] with permission of John Wiley and Sons.

morphologies at particle sizes between nanoscale and microscale magnitude orders as was revealed by TEM in Figure 4.35. These morphology results were also the base to perform a comparison of the RMX® with a Haake® internal mixer. Figure 4.36 presents micrographs from the two mixing devices at the lowest (62 J/g) and highest (246 J/g) energy inputs used in the RMX. In both cases, direct comparison evidences a less homogeneous EG particles distribution and signiicantly higher particle size for the internal mixer blends. Furthermore, inal RMX® nanocomposites presented remarkable improvement in elastic modulus as described by Table 4.1. A general remarkable increase in elastic modulus, from 20 up to 38%, was found. It must be recalled that a ixed concentration of only 3 wt/wt% of EG has been used; therefore, only the inluence of mixing on properties is addressed. In a closer look to the effects, the particular results and comparison between different RMX conditions point out to several scenarios that would have to do with the issue of molecular weight role in polymer reinforcement. As it has been stated earlier, Mw changes at every commanded mixing condition. About this matter, it is known that, under proper compatibility between components, high molecular weight and viscosity of the polymeric matrix lead to the generation of high shear and elongational stress needed to effectively disperse and/or exfoliate the iller particles [69, 70],

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179

2 μm

2 μm

(b)

(a)

2 μm

2 μm

(c)

(d)

Figure 4.35 TEM images of (a) reference sample, (b) 10/20, (c) 10/30, and (d) 10/40. 10,000× (bar = 2 μm). Reproduced from Ibarra-Gómez et al. [68] with permission of John Wiley and Sons.

thus improving mechanical properties through the high increase in interfacial area. But, on the other hand, low molecular weight promotes better chain diffusion into particle galleries (interlocking) what is said to also promote reinforcing and exfoliation [71, 72]. In the present case, this could be better explained starting out from samples at extreme v/N conditions. For example, sample at the mildest condition, 10/10, expected to have the highest molecular weight, presents the second largest E′ increment, around 31%. On the other hand, sample at the highest speed, 40/10, with the lowest Mw of the series surprisingly presents the largest E′ increment, 38%. Evidently, reinforcement mechanisms in terms of molecular weight role are different, suggesting for the irst one a predominant shear/elongational stress contribution to dispersion and reinforcement and, for the second one, a more diffusional, molecular interlocking phenomenon. Although samples just described seem to adhere in a

180

MIXING OF POLYMERS USING THE ELONGATIONAL FLOW MIXER (RMX®)

2 μm

2 μm

(b)

(a)

2 μm

2 μm

(c)

(d)

Figure 4.36 TEM characterization: (a, b) photographs of internal mixer sample and RMX sample 10/10, respectively, at 62 J/g. (c, d) photographs of internal mixer sample and RMX 10/40, respectively, at 246 J/g. 10,000× (bar = 2 μm). Reproduced from Ibarra-Gómez et al. [68] with permission of John Wiley and Sons.

greater extent to one mechanism or another, it is dificult to discuss in more detail on mechanisms for samples at relatively medium conditions, having among them a similar E′ increment of about 20%. In this point, the work by Bousmina [72] gives an important insight: it points outs to a balance between mechanical stresses and diffusion process that requires rather low to medium viscosity as to favor the best level of exfoliation in, for example, clay-based nanocomposites. In fact, in Figure 4.37, corresponding to the X-ray characterization, we can observe very important differences in peak intensities as a function of mixing conditions. In this respect, diffraction peak intensity is related to the amount of graphitic layers that scatter, it means, to the mass fraction of crystalline phase [73]. Thus, differences observed may obey to the development of different dispersion patterns, even partial exfoliation, as a function of mixing [74], where the reference sample is expected to present a much more agglomerated or preserved iller microstructure, which coincides with the highest peak.

MIXING OF POLYMER NANOCOMPOSITES

TABLE 4.1

181

Physical Properties of PLA/EG Nanocomposites

Sample (v/N)

E′ (MPa)

% ΔE′

Tg (∘ C)

2750 3600 3350 3400 3300 3400 3800

30.9 21.8 23.6 20 23.6 38.2

60 65 64 65 64 63 61

PLA ref 10/10 10/20 10/30 10/40 20/10 40/10

9000 8000 7000

4000 3500 3000 2500 2000 1500 1000 500 0

3 mm/s 1cycle (REF) 10 mm/s 10 cycles 10 mm/s 20 cycles 10 mm/s 30 cycles

6000

10 mm/s 40 cycles

Counts

20 mm/s 10 cycles

5000

0

10

20

30

40

40 mm/s 10 cycles

4000 3000 2000 1000 0 25.5

25.7

25.9

26.1

26.3

26.5

26.7

26.9

Diffraction angle 2𝛷 (º) Figure 4.37 XRD diffractograms showing the graphite characteristic peak for PLA/EG samples at different RMX® mixing conditions. The inset shows the general pattern of all samples, in order to point out that the amorphous character of the PLA matrix was preserved. Reproduced from Ibarra-Gómez et al. [68] with permission of John Wiley and Sons.

182

MIXING OF POLYMERS USING THE ELONGATIONAL FLOW MIXER (RMX®)

In the present system, a range of viscosities coming up from the mixing process and resultant degradation favor different balances between the two mechanisms just described, diffusion and stress-dependent dispersion/exfoliation and, thus, reinforcement. In spite of the aim to ponder the importance of low geometry in dispersion, it is not possible to assess so far the punctual role of elongational low contribution since the drastic effect of viscous heating in PLA produces signiicant changes in the rheology of the system in the very same mixing sequence, speciically, the elongational to shear low ratios. It is remarkable, nevertheless, that good morphology/properties of nanocomposites are attained in a relatively small window of experimental conditions, and using an extremely sensitive polymer represents a solid starting point to continue doing new and promising research on this ield.

4.7

CONCLUDING REMARKS

The present results and discussion have given a signiicant insight about the versatility and eficiency of the RMX® mixing device, especially when it comes to polymer blends. Both dispersive and distributive mixing of polymer blends of even high viscosity ratios have proven to be achieved. However, more fundamental work is still to be done in order to fully elucidate the mixing mechanisms with respect to the wide spectrum of variables implied. Operation principles of the RMX® address important limitations encountered in conventional mixing systems as the dificulty to generate intense elongational low ields and the enough number of passages of material through high stresses points, particularly elongational stresses, to attain a good quality of dispersion. Shear low contributions, though, proved to be critical during the dispersion process since these are involved just in the deformation or deformation/breakup process of droplets depending on the viscosity ratio of the blends. Signiicant indings point out to an optimum central die length, which adds to the overall ilament deformation, providing also residence times enough for the droplet breakup to occur. The RMX® mixer has been so far commercialized for pilot plants and academic purposes; however, continuous work has been carried out in order to scale up the device for industrial operations through fundamentally passing from the current batch type to a semicontinuous or continuous operation.

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5 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES Masami Okamoto Advanced Polymeric Nanostructured Materials Engineering, Graduate School of Engineering, Toyota Technological Institute, Nagoya, Japan

5.1

INTRODUCTION

A decade of research has shown that nanostructured materials have the potential to signiicantly impact growth at every level of the world economy in the 21st century. This new class of materials is now being introduced in structural applications, such as gas barrier ilm, lame retardant product, and other load-bearing applications. Of particular interest is recently developed nanocomposites consisting of a polymer and layered silicate because they often exhibit remarkably improved mechanical and various other properties [1–6] as compared with pure polymer or conventional composites (both micro- and macrocomposites). These concurrent property improvements are well beyond what can be generally achieved through the preparation of micro-/macrocomposites. Polymer/layered silicate nanocomposites (PLSNCs) have become the focus of academic and industrial attention [7–17]. The number of scientiic publications was searched from Web of Science™ using the following keywords: polymer, clay, and nanocomposites. Figure 5.1 shows the total number and its distribution of selected articles. In the last 4 years, the articles have increased over 350 per each year, in which a signiicant amount of work has been done on various aspects of PLSNCs. However, complete delamination of layered

Rheology and Processing of Polymer Nanocomposites, First Edition. Edited by Sabu Thomas, Rene Muller, and Jiji Abraham. © 2016 John Wiley & Sons, Inc. Published 2016 by John Wiley & Sons, Inc.

187

188 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES 4000

350

Articles per year

3500

300

Total articles

3000

250

2500

200

2000

150

1500

100

1000

50

500

Total articles

Articles per year

400

0

0 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 Year

Figure 5.1 Selected articles based on Web of Science™ (accessed February 07, 2014) using keywords: polymer, clay, and nanocomposites.

silicate nanoillers in continuous polymer matrix is still a challenging issue because it could not be satisfactorily attained. Gardolinski and Lagaly [18] described a very distinctive deinition of delamination and exfoliation with the aim of avoiding the controversial use of these terms. Exfoliation is deined as the decomposition of large aggregates into smaller particles, whereas delamination denotes the process of separation of the individual layers of the particles at the nanoscale. To the best of our knowledge, so far, the complete delamination is not feasible after melt intercalation with an appropriate shear. Only a few examples of this type can be found in the literature [19–21]; however, many published photographs show very small regions in the melt compound where partial exfoliation occurred [7–17]. Delamination of stacked layered nanoillers in polymeric nanocomposite is the ultimate target for controlling better overall materials’ properties. Thus, we are far from the goal of understanding the mechanisms of the nanostructure control and the preparation of the PLSNC with discrete dispersion of the layered nanoillers. From this reason, a novel preparation method is currently in progress. The chapter reviews current research trends on PLSNC materials, including strategies for fabrication of the PLSNCs possessing discrete dispersion of the nanoillers. Another major challenge is an understanding of the thermodynamic issue associated with the nanocomposite formations, especially in the direct melt intercalation of macromolecule into nanogalleries [22–26]. A primary progress in PLSNCs, a nylon-6/layered silicate hybrid [5, 27] reported by Toyota Central Research & Development Co. Inc. (TCRD), was successfully prepared by the in situ polymerization of �-caprolactam in a dispersion of montmorillonite (MMT). The silicate can be dispersed in a liquid monomer or in a solution of monomer. The synthetic strategy and molecular design were irst explored by TCRD with nylon-6 as the matrix polymer. This new class of material is now being

NANOSTRUCTURE DEVELOPMENT

189

introduced in structural applications, such as gas barrier ilm and other load-bearing applications [5]. PLSNCs and their self-assembly behavior have been approached to produce nanoscale polymeric materials. Additionally, these nanocomposites have been proposed as model systems to examine polymer structure and dynamics in conined environments [28–30]. In order to understand the processability of these materials, that is, the inal stage of any polymeric material, one must understand the detailed rheological behavior of these materials in the molten state. Understanding the rheological properties of PLSNC melts is not only important in gaining a fundamental knowledge of the processability but also helpful in understanding the structure–property relationships in these materials. Although rheological measurement is an indirect probe, it is a well-established approach to probe the interaction between nanoiller and polymer matrix and the time-dependent structure development. In addition, more clear nanoscale and mesoscale structure development of the systems could be provided when combined with X-ray/light scattering experiments and electron microscopy. The original mesoscale structure in PLSNCs consists of randomly oriented delaminated individual layers or tactoids of layers. This randomly distributed nanoiller forms a “clay network” structure (percolation ininite network [20, 21]), which is mediated by polymer chains and clay–clay interactions, responsible for the linear viscoelastic response observed in PLSNC melts. This mesostructure, which is intrinsically disordered metastable state and out of equilibrium, and offers an apt analogy to soft colloidal glasses and gels, was extensively discussed [31–47]. To our regret, however, the existence of percolated clay network structure, which is ignored in a vast literature as always, is responsible for the linear viscoelastic response, crystalline capability, and lammability observed in PLSNC melts. In this chapter, we also intend to highlight the mesostructure development in PLSNC melts with the primary focus on low behavior and an analogy to soft glassy dynamics [32]. 5.2 5.2.1

NANOSTRUCTURE DEVELOPMENT Melt Intercalation

Since the possibility of direct melt intercalation was irst demonstrated [48], melt intercalation has become a preparation of the intercalated PLSNCs. This process involves annealing, statically or under shear, a mixture of the polymer and organically modiied layered nanoillers (OMLFs) above the softening point of the polymer. During annealing, the polymer chains diffuse from the bulk polymer melt into the nanogalleries between the layered illers. In order to understand the thermodynamic issue associated with the nanocomposite formation, Vaia et al. [28, 49] have applied mean-ield statistical lattice model and found conclusions based on the mean-ield theory nicely agreed with the experimental results. The entropy loss associated with the coninement of a polymer melt is

190 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES

not prohibited to nanocomposite formation because an entropy gain associated with the layer separation balances the entropy loss of polymer intercalation, resulting in a net entropy change near to zero. Thus, from the theoretical model, the outcome of nanocomposite formation via polymer melt intercalation depends on energetic factors, which may be determined from the surface energies of the polymer and OMLFs. Nevertheless, we have often faced the problem that the nanocomposite shows ine and homogeneous distribution of the nanoparticles in the polymer matrix (e.g., poly(l-lactide) (PLA)) without a clear peak shift of the mean interlayer spacing of the (001) plane as revealed by wide-angle X-ray diffraction (WAXD) analysis [50]. Furthermore, we sometimes encounter a decrease in the interlayer spacing compared with that of pristine OMLF, despite very ine dispersion of the silicate particles. For this reason, information on the structure of the surfactant (intercalant)–polymer interface is necessary to understand the intercalation kinetics that can predict inal nanocomposite morphology and properties of overall materials [23, 51–53]. 5.2.2

Interlayer Structure of OMLFs and Intercalation

5.2.2.1 Nanoillers In characterizing layered silicate including layered titanate (HTO), the surface charge density is particularly important because it determines the interlayer structure of intercalants as well as cation-exchange capacity (CEC). Lagaly proposed the method consisting of total elemental analysis and the dimension of the unit cell [54]: Surface charge∶ e− ∕nm2 = �∕ab

(5.1)

where � is the layer charge (1.07 for HTO, 0.66 for synthetic luorine hectorite (syn-FH), and 0.33 for MMT. a and b are cell parameters of HTO (a = 3.782 Å, b = 2.978 Å [55]), syn-FH (a = 5.24 Å, b = 9.08 Å [56]), and MMT (a = 5.18 Å, b = 9.00 Å [23]). For syn-FH, however, about 30% of the interlayer Na+ ions are not replaced quantitatively by intercalants because it is not active for ion-exchange reactions [56]. For HTO, only 27% of interlayer H+ (H3 O+ ) is active for ion-exchange reactions [50]. The remaining part is the nonactive sites in the HTO. Thus, the incomplete replacement of the interlayer ions is ascribed to the intrinsic chemical reactivity. The characteristic parameters of three nanoillers are also summarized in Table 5.1 [23]. HTO has a high surface charge density of 1.26 e− /nm2 compared with those of syn-FH (0.971 e− /nm2 ) and MMT (0.780 e− /nm2 ). From these results, we can estimate the average distance between exchange sites, which is calculated to be 0.888 nm for HTO, 1.014 nm for syn-FH, and 1.188 nm for MMT, respectively. This estimation assumes that the cations are evenly distributed in a cubic array over the silicate surface, and that half of the cations are located on the one side of the platelet and the other half reside on the other side. 5.2.2.2 Molecular Dimensions and Interlayer Structure The calculated models of the intercalant structures are presented by Okamoto et al. [23] (Fig. 5.2). For octadecylammonium (C18 H3 N+ ), obtained molecular length, thickness, and width

NANOSTRUCTURE DEVELOPMENT

191

TABLE 5.1 Characteristic Parameters of Nanoillers Parameters

HTO

MMT

syn-FH

Chemical formula H1.07 Ti1.73 O3.95 ⋅0.5H2 O Na0.66 Mg2.6 Si4 O10 (F)2 Particle size (nm) ∼100–200 ∼100–200 ∼800 BET area (m2 /g) ∼2400 CECa (meq/100g) ∼200 (660) ∼120 (170) 1.26 0.971 e− (charge/nm2 ) 2.40 2.50 Density (g/cm3 ) 2.3 1.55 Refractive index (n20 D ) pH 4–6 9–11

Na0.33 (Al1.67 Mg0.33 ) Si4 O10 (OH)2 ∼100–200 ∼700 ∼90(90) 0.708 2.50 1.55 7.5–10

Methylene blue adsorption method. The values in the parenthesis are calculated from the chemical formula of nanoillers. Source: Reprinted with permission from [23] © 2006, Wiley-VCH.

a

are 2.466, 0.301, and 0.301 nm, respectively. Since the length of all alkyl units are more than 2 nm, these spacings (distance between exchange sites) of 0.888–1.188 nm do not allow parallel layer arrangement such as lat-lying chains [54] in each gallery space of the nanoillers. All the intercalants are oriented with some inclination toward the host layer in the interlayer space to form an interdigitated layer. This is suggested as parafin-type layer structure proposed by Lagaly, especially in case of clay minerals of high surface charge [54]. WAXD patterns for three OMLF powders are presented in Figure 5.3. The mean interlayer spacing of the (001) plane (d(001) ) for the HTO intercalated with qC14 (OH) (HTO-qC14 (OH)) obtained by WAXD measurements is 2.264 nm (diffraction angle, 2� ≅ 3.90∘ ). The appearances of small peaks observed at 2� ≅ 7.78∘ , 11.78∘ , and 15.74∘ were conirmed that these relections were due to (002) up to (004) plane of HTO-qC14 (OH). HTO-qC14 (OH) surprisingly well-ordered suprastructure proved by WAXD with diffraction maxima up to the fourth order is due to the high surface charge density of the HTO layers. However, syn-FH and MMT, which have low surface charge density compared with that of HTO, show less-ordered interlayer structure. That is, the coherent order of the silicate layers is much lower in each syn-FH and MMT intercalated with surfactants. From WAXD results, we can discuss the interlayer opening that is estimated after subtraction of the layer thickness value of 0.374 nm for HTO [55], 0.98 nm for syn-FH [56], and 0.96 nm for MMT [54]. This is an important point for the following discussion on the interlayer structure. The illustration of a model of interlayer structure of the qC14 (OH) in gallery space of the HTO is shown in Figure 5.4. For nanoillers with high surface charge density, the intercalants can adopt a coniguration with an orientation where the alkyl chains are tilted under the effect of the van der Waals forces, which decreases the chain–chain distance. For this reason, the angle � should be directly related to the packing density of the alkyl chains. The value of � decreases until a close contact between the chains is attained, giving an increase in the degree

192 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES

(a)

(b)

(c)

Thickness Width

(d) Intercalant

C18H3N+

C18(CH3)3N+

2C18(CH3)2N+

qC14(OH)

Length (nm)

2.466

2.601

4.766

2.090

Thickness (nm)

0.301

0.372

0.434

0.374

Width (nm)

0.301

0.372

0.318

0.881

Figure 5.2 Molecular dimensions of intercalants: (a) octadecylammonium (C18 H3 N+ ); (b) octadecyltrimethylammonium (C18 (CH3 )3 N+ ); (c) dioctadecyldimethylammonium (2C18 (CH3 )2 N+ ); and (d) N-(cocoalkyl)-N,N-[bis(2-hydroxyethyl)]-N-methylammonium cations (qC14 (OH)). Reproduced from Yoshida and Okamoto [23] with permission of John Wiley and Sons.

NANOSTRUCTURE DEVELOPMENT

8000

193

d = 2.264nm (001)

6000 4000

d = 1.135 nm d = 0.751 nm (002) d = 0.563 nm (003) (004)

2000 0

Intensity/a.u.

HTO-qC14(OH)

d = 2.063 nm

6000

syn-FH-qC14(OH)

(001)

4000

d = 1.027 nm 2000

(002)

0 MMT-qC14(OH)

6000 4000

d = 1.855 nm d = 0.930 nm (002)

(001)

2000 0

0

5

10 2θ (°)

15

20

Figure 5.3 WAXD patterns of HTO, syn-FH, and MMT intercalated with qC14 (OH)+ . Reproduced from Yoshida and Okamoto [23] with permission of John Wiley and Sons.

of the crystallinity of the intercalants into the nanogalleries. To estimate the tilt angle �, they combined the molecular dimension, interlayer spacing, and loading amount of intercalant in the layers, which was calculated from thermogravimetry analysis (TGA). The characteristic parameters are summarized in Tables 5.2 and 5.3. Note that HTO exhibits large value of layer opening accompanied with large values of � and endothermic heat low ΔH due to the melting of the intercalants in the galleries when compared with those of syn-FH and MMT. This indicates that HTO leads to a highly interdigitated layer structure, and the interlayer opening becomes more uniform compared with MMT and syn-FH (possessing lower surface charge density). From this fact, we can observe well-deined diffraction peaks up to (004) plane (see Fig. 5.3). The entropic contribution of the intercalants, which leads to the entropy gain associated with the layer expansion after intercalation of the polymer chains, is not signiicant because of the interdigitated layer structure. 5.2.2.3 Correlation of Intercalant Structure and Interlayer Opening For the interdigitated layer structure in MMT, alkyl chain length, that is, C18 H37 , CH3 , and (CH2 )2 OH in the amine structure, changes the interlayer opening. That is, when we compare different intercalants having same long alkyl chain (i.e., C18 H3 N+ and

194 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES HTO-qC14(OH) – OH

– OH

Ti-O

N+

N+ CH 3

CH3 1.889 nm

N+

CH3

CH3

N+ α

HO –

HO –

Ti-O

0.888nm (0.794 nm2/charge)

Figure 5.4 Illustration of a model of the interlayer structure of intercalant N-(cocoalkyl)N,N-[bis(2-hydroxyethyl)]-N-methylammonium cation (qC14 (OH)) in gallery space of layer titanate (HTO). The average distance between exchange sites is 0.888 nm calculated by surface charge density of 1.26 e− /nm2 . For qC14 (OH), the obtained molecular length, thickness, and width are 2.09, 0.881, and 0.374 nm, respectively (see Fig. 5.2). The tilt angle � of the intercalants can be estimated by the combination of the interlayer spacing, molecular dimensions, and loading amount of intercalants when the alkyl chains are adopted all-trans conformation. Reproduced from Yoshida and Okamoto [23] with permission of John Wiley and Sons.

TABLE 5.2 Comparison of Characteristic Parameters Between HTO, syn-FH, and MMT Prepared with qC14 (OH)

Layer opening (nm) Tilt angle � (∘ ) Organic content (wt%) Tm a (∘ C) ΔHa (J/g)

HTO-qC14 (OH)

syn-FH-qC14 (OH)

MMT-qC14 (OH)

1.889 64.4 39.6 108.3 214.5

1.083 31.1 30.4 111.3 141.2

0.895 25.3 32.5 97.7 138.6

The melting and heat low of qC14 (OH)+ Cl− are 35.8 ∘ C and 69.8 J/g, respectively. Source: Reprinted with permission from [23] © 2006, Wiley-VCH.

a

C18 (CH3 )3 N+ ), three methyl (CH3 ) substituents instead of hydrogen (H) disturb the contact with silicate surfaces. The value of � decreases until close contact between the ammonium cations and silicate surfaces is attained, giving a decrease in the interlayer opening (=d(001) ) (see Table 5.3). In cases where the intercalant has two long alkyl chains (i.e., 2C18 (CH3 )2 N+ ), the packing density of the alkyl chains is reduced and sterically limited to nanogalleries. Consequently, MMT-2C18 (CH3 )2 N+ exhibits large interlayer opening accompanied with low crystallinity of the intercalant (ΔH ∼ 130 J/g) compared with

NANOSTRUCTURE DEVELOPMENT

195

TABLE 5.3 Comparison of Characteristic Parameters MMT-Based OMLF Prepared with C18 H3 N+ , C18 (CH3 )3 N+ , and 2C18 (CH3 )2 N+

Layer opening (nm) Tilt angle � (∘ ) Organic content (wt%) Tm a (∘ C) ΔHa (J/g)

C18 H3 N+

C18 (CH3 )3 N+

2C18 (CH3 )2 N+

1.350 33.2 35.5 69.9 177.7

1.011 22.9 29.5 69.5 189.6

1.540 40.1 39.8 44.0 129.7

The melting and heat low of C18 H3 N+ , C18 (CH3 )3 N+ , and 2C18 (CH3 )2 N+ are 83.8 ∘ C and 95.6 J/g; 103.5 ∘ C and 161.2 J/g; and 37.0 ∘ C and 54.6 J/g, respectively. Source: Reprinted with permission from [23] © 2006, Wiley-VCH.

a

MMT-C18 H3 N+ and MMT-C18 (CH3 )3 N+ . Accordingly, we observe disordered diffraction peak of (001) plane of MMT-2C18 (CH3 )2 N+ in the WAXD analysis (see Figure 1 in Ref. [51]). We have to pay attention to the molecular size of the substituents instead of H attached to the nitrogen for the better understanding of the interdigitated layer structure and direct polymer melt intercalation. This feature has been observed in the results of OMLFs intercalated with various intercalants (such as octadecyldimethylbenzylammonium, (n-hexadecyl)tri-n-butylphosphonium, nhexadecyltriphenylphosphonium cations) [22]. 5.2.2.4 Nanocomposite Structure Figure 5.5 shows the results of transmission electron microscopy (TEM) bright ield images of polylactide (PLA)-based nanocomposites, in which dark entities are the cross section of intercalated MMT layers. The organically modiied MMT content in all nanocomposites was 4 wt%. From the TEM images, it becomes clear that there are some intercalated-and-stacked silicate layers in the nanocomposites. Yoshida et al. estimate the form factors obtained from TEM images, that is, average value of the particle length (L), of the dispersed particles and the correlation length (�) between them [23]. From the WAXD patterns, the crystallite size (D) of intercalated-and-stacked silicate layers of each nanocomposite is calculated by using Scherrer equation. The calculated value of D (≅ thickness of the dispersed particles) and other parameters for each nanocomposite are presented in Table 5.4. For PLA/MMT-C18 (CH3 )3 N+ , L and D are in the range of (200 ± 25 nm) and 10.7 nm. On the other hand, PLA/MMT-C18 H3 N+ exhibits a high value of L (450 ± 200 nm) with a large level of stacking of the silicate layers (D∼21 nm). � Value of the PLA/MMT-C18 (CH3 )3 N+ (80 ± 20 nm) is lower than the value of PLA/MMT-C18 H3 N+ (260 ± 140 nm), suggesting that the intercalated layers are more homogeneously and inely dispersed in the case of PLA/MMT-C18 (CH3 )3 N+ . The number of the stacked individual silicate layers (≡D/d(001) +1) is 5 for PLA/MMT-C18 (CH3 )3 N+, and � value of this nanocomposite is one order of magnitude lower compared with those of PLA/MMT-C18 H3 N+ and PLA/MMT-2C18 (CH3 )2 N+ , suggesting that intercalated silicate layers are more homogeneously and inely dispersed.

196 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES

500 nm (a)

500 nm (b)

300 nm (c)

Figure 5.5 Bright ield TEM images of PLA-based nanocomposites prepared with (a) MMT-C18 H3 N+ , (b) MMT-C18 (CH3 )3 N+ , and (c) MMT-2C18 (CH3 )2 N+ . The dark entities are the cross section and/or face of intercalated-and-stacked silicate layers and the bright areas are the matrix. Reproduced from Yoshida and Okamoto [23] with permission of John Wiley and Sons.

Although the (initial) interlayer opening of MMT-C18 (CH3 )3 N+ at 1.011 nm is smaller than MMT-C18 H3 N+ at 1.350 nm and MMT-2C18 (CH3 )2 N+ at 1.540 nm, the intercalation of the PLA in these different OMLFs gives almost same basal spacing after the preparation of the nanocomposites. Note that the existence of sharp Bragg peak in PLA-based nanocomposites after melt extrusion clearly indicates that the dispersed silicate layers still retain an ordered structure after melt extrusion.

NANOSTRUCTURE DEVELOPMENT

197

TABLE 5.4 Form Factors of Three Nanocomposites Obtained from WAXD and TEM Observations Nanocomposites

PLA/MMT-C18 H3 N+

PLA/MMT-C18 (CH3 )3 N+

PLA/MMT-2C18 (CH3 )2 N+

d001 (nm) Δ Opening (nm) Final layer opening (nm) D (nm) (D/d001 ) + 1 L (nm) � (nm)

3.03 0.72 2.07

2.85 0.879 1.89

2.95 0.45 1.99

20.9 7.9 450 ± 200 260 ± 140

10.73 4.8 200 ± 25 80 ± 20

14.71 6.0 655 ± 121 300 ± 52

Source: Reprinted with permission from [23] © 2006, Wiley-VCH.

In Table 5.4, they summarized the layer expansion after preparation (=Δ opening) of three nanocomposites or after subtraction of the initial layer opening. For same MMT with different intercalants (e.g., comparison between MMT-C18 (CH3 )3 N+ and MMT-2C18 (CH3 )2 N+ ), the layer expansion of the former (0.879 nm) exhibits a high value compared with that of the latter (0.45 nm) in PLA-based nanocomposites. In other words, the smaller interlayer opening caused by the coniguration with small tilt angle (� = 22.9∘ for C18 (CH3 )3 N+ ) promotes the large amount of the intercalation of the polymer chains. Accordingly, PLA/MMT-C18 (CH3 )3 N+ exhibits a iner dispersion of the nanoillers compared with PLA/MMT-2C18 (CH3 )2 N+ and PLA/MMT-C18 H3 N+ as discussed earlier (Fig. 5.5). A more interesting feature is the absolute value of Δ opening. According to the molecular modeling, the width and thickness of the PLA are 0.76 and 0.58 nm (Fig. 5.6). This may suggest that the polymer chains could not penetrate into galleries in case of MMT-2C18 (CH3 )2 N+ when we compare the apparent interlayer expansion (=Δ opening).

PL-oligomer Width 0.393 nm

3.376

3.933

Thickness 0.338 nm

Figure 5.6 Molecular dimensions of PLA backbone using the molecular dynamics program (MM2 in Quantum CAChe) in consideration with van der Waals’ radii. Optimization of structure is based on the minimization of the total energy of the molecular system.

198 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES

Now it is necessary to understand the meaning of the interlayer expansion in the intercalated nanocomposites. As discussed earlier, we have to take the interdigitated layer structure into consideration. This structure may suggest that the different orientation angle could adopt when the polymer chains penetrate into the galleries, giving a decrease in the basal spacing after intercalation. At the same time, this structure apparently provides a balance between the polymer penetration and different orientation angle of the intercalants. That is, we have to pay attention to intercalation of the polymer chains into the galleries from the result of the change of the basal spacing as revealed by WAXD. Presumably the penetration of the polymer chain is prevented or reduced by the steric limitation of the coniguration with a high value of � (e.g. � = 40.1∘ for MMT-2C18 (CH3 )2 N+ ). Accordingly, we sometimes observe small interlayer expansion and encounter a decrease in the interlayer spacing after melt intercalation. As shown in Table 5.4, the initial interlayer opening depends on the interlayer expansion (=Δ opening) after melt intercalation. The smaller initial opening leads to the larger interlayer expansion and gives almost the same inal interlayer opening. This feature has been observed in the results of other nanocomposites prepared by different OMLFs intercalated with different surfactants [25, 26]. From this result, the entropic contribution of the intercalants, which leads to the entropy gain associated with the layer expansion after intercalation of the small molecules and/or polymer chains, may not be signiicant due to the interdigitated layer structure. Presumably the penetration takes place by pressure drop within the nanogalleries, nanocapillary action, generated by the two platelets. As reported in the literature [22–26], the pressure drop (Δp) into the nanogalleries, which makes the polymer penetration more dificult, should be discussed. The estimated pressure difference (∼24 MPa) is much larger than the shear stress (∼0.1 MPa) during melt compounding [22, 23]. This suggests that shear stress has little effect on the delamination (exfoliation) of the layer. This is the main reason with the intercalated structure reported by so many nanocomposite researchers who can prepare only intercalated (not exfoliated) nanocomposites via simple melt extrusion technique [7–17]. A novel compounding process is currently in progress. Solid-state shear processing is an innovative technique to delaminate the layered illers [24, 26, 57]. Compared to OMLFs, nanocomposite structure is dificult to model using atomic scale molecular dynamics (MD) because the intercalated polymer chain conformation is complex and can hardly be in the equilibrium state. However, Pricl et al. [58] explored and characterized the atomic scale structure to predict binding energies and basal spacing of PLSNCs based on polypropylene (PP) and maleated (MA) PP (PP–MA), MMT, and different alkylammonium ions as intercalants (Fig 5.7). From a global interpretation of all these MD simulation results, they concluded that intercalants with smaller volume are more effective for clay modiication as they improve thermodynamics of the system by increasing the binding energy. On the other hand, intercalants with longer tails are more effective for intercalation and exfoliation processes, as they lead to higher basal spacing. Additional information is necessary to predict more reasonable nanostructure of PLSNCs; some literature [59–61] related to the conined polymer chains within the silicate galleries by using coarse-grained MD simulation appeared.

NOVEL COMPOUNDING METHODS FOR DELAMINATION OF OMLFs

(a)

199

(b)

Figure 5.7 Three-component model used for basal spacing simulations, consisting of two layers of MMT with K+ cations (stick model), four molecules of trimethylammonium cation (a) or dimethylstearylammonium cation (b) (stick and ball model), and one molecule of maleated PP (PP-MA) (ball model). Reproduced from Toth et al. [58] with permission of Elsevier.

5.3 NOVEL COMPOUNDING METHODS FOR DELAMINATION OF OMLFs Some methods for the delamination of OMLFs were conducted by using supercritical CO2 (sc-CO2 ) [62]. The effect of sc-CO2 fed to the tandem extruder on the dispersion of organically modiied MMT with different intercalants into nylon-6 matrix was examined. In the absence of sc-CO2 , pressure improved the MMT delamination by reducing the free volume of the polymer and increasing the interaction between chains and ultimately increasing the viscosity. Using sc-CO2 did not improve the clay dispersion due to the decrease in the melt viscosity. Another interesting approach for the delamination of OMLFs is an ultrasound in the preparation of nanocomposites. The effect of the in situ ultrasound on the polymer/MMT melt phase is reported [63]. An effective method to enhance the dispersion, intercalation, and exfoliation of OMLFs in thermoplastic-based nanocomposites is reported. The same experiment was done in another report for polypropylene (PP)-based nanocomposite preparation

200 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES

[64]. The maximum power output and the frequency of the ultrasonic generator are 300 W and 20 kHz, respectively. They described the ine dispersion of silicate layers in PP matrix after ultrasonic treatment (100 W). However, the ultrasonic oscillations exhibited a little effect on the delamination of OMLFs as revealed by TEM observation. Thus, the compounding with an assist from sc-CO2 luids and ultrasonication did not improve the state of the nanoiller dispersion once a critical morphology was established. That is, the dispersion of the nanoiller in the polymer matrix is governed by judicious choice of OMLF. Although the intercalation technology of the polymer melt is developed along with the current industrial process, such as extrusion and injection molding, we have to develop more innovative compounding process especially in the preparation of the nanocomposites possessing discrete dispersion of the nanoillers. In this regard, Saito et al. [24, 26] have reported solid-state processing of poly(p-phenylenesulide) (PPS)-based nanocomposites to delaminate the stacked layered iller in the polymer matrix. The mixture of PPS and organically modiied layered iller (OMLF) (95:5 wt/wt) was subjected to the processing using thermostated hot-press at ambient temperature of 150 ∘ C, below Tm of PPS (i.e., PPS matrix is still at the solid state), and applying pressures of 7, 14, and 33 MPa for 30 s. The mixture exhibited disorder and delaminated layer structure with the thickness of 40–80 nm into PPS matrix. The solid-state processing led to the delamination of the silicate layers and attained the discrete dispersion. Similarly, Wang et al. [65–67] reported the exfoliation of talc illers by solid-state shear processing using pan-type mill to prepare PP/talc nanocomposites, in which the delamination of talc illers was not achieved in the nanocomposite as revealed by TEM images. Wakabayashi et al. [68] demonstrated that a continuous scalable solid-state shear pulverization (SSSP) could result in unmodiied well-dispersed graphite in PP, leading to a 100% increase in modulus as compared with neat PP. High shear and compressive forces result in repeated fragmentation and fusion of polymer in the solid state producing an excellent mixing and dispersion of nanoillers in the nanocomposites [69]. There are several factors that play important roles in producing exfoliated nanocomposites: (i) chemical afinity (or compatibility) between the surface of OMLF and polymer matrix, (ii) melt viscosity of the polymer matrix, and (iii) capillary pressure drop within the nanogalleries [24, 26]. The capillary pressure drop plays a very important role in controlling the effective mixing between OMLFs and polymer to attain the delamination. The solid-state shear processing may be an innovative technique to delaminate the layered illers in overcoming the pressure drop (Δp) within the nanogalleries. Therefore, successful delamination of OMLFs could broaden the scope of application of this procedure. 5.3.1

Solid-State Shear Processing

Solid-state processing for the preparation of polypropylene (PP)-based nanocomposites having inely dispersed layered illers was conducted [57]. The mixture of PP and OMLF (95:5 wt/wt) was subjected to the processing using alumina mortar heated at 65 ∘ C, below Tm of PP (i.e., PP is still at the solid state), and ground for 8 h before melt compounding.

NOVEL COMPOUNDING METHODS FOR DELAMINATION OF OMLFs

201

50 µm (a) A

P

50 µm (b)

Figure 5.8 POM images of the mixture: (a) unprocessed sample and (b) after solid-state processing for 8 h. Both micrographs were taken at 180 ∘ C just after annealing for 30 s. The insets in each image are a computed FFT spectra of the micrograph. Reproduced from Saito and Okamoto [57] with permission of Elsevier.

Figure 5.8a shows the polarizing optical microscopy (POM) image of the mixtures prepared by melt compounding and annealing at 180 ∘ C for 30 s. It is clear from the POM images that stacked-and-agglomerated structure of layers is evident in the melt compounded sample, whereas a good dispersion appears in the processed sample for 8 h (Fig. 5.8b). The fast Fourier transform (FFT) pattern shows weak scattering with isotropy (halo) as compared with that of unprocessed sample (i.e., melt compounded sample). This indicates that the particle size of the dispersed nanoiller becomes smaller during solid-state processing. The dispersion state in the nanometer scale was directly observed via TEM analysis.

202 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES

Figure 5.9 shows the results of TEM bright ield images and their FFT patterns of the melt compounded mixtures corresponding to the POM experiments, in which dark entities are the cross section of the layered nanoillers. The large agglomerated tactoids of about 3 μm thickness are seen in Figure 5.9a (unprocessed sample). On the other hand, in Figure 5.9b, layers of nanometer-sized thickness were straggled in the observation area. Figure 5.9c shows disorder and delaminated silicate layer structure with the thickness of 3–7 nm and length of 50–200 nm (average thickness of 5.8 nm and length of 67 nm). This is a very interesting observation of the discrete silicate layers. They attempted to apply a phenomenological formulation for the breakup of mineral particles (Rittinger’s law): dE = −b

[

] 1 dD Dn

(5.2)

where E is the energy for breakup, D is the mean diameter of particles, and the parameter b and n are the breakup coeficients, which depend on processing condition and materials [70]. The mixing torque T is constant throughout the processing so that the input energy E is proportional to residence time t, that is, E ∝ T ⋅ t. Hence, Equation 5.2 can be rewritten as T ×t ∼

1 Dn−1

(5.3)

The effect of the different applying torque and residence time on the delamination behavior of the OMLF was discussed [57].

5.4 5.4.1

NANOSTRUCTURE AND RHEOLOGICAL PROPERTIES Flocculation Control and Modulus Enhancement

Most of the nanocomposite researchers obdurately believe that the preparation of completely exfoliated structure is the ultimate target for better overall properties. However, these signiicant improvements are not observed in every nanocomposite systems, including systems where the silicate layers are near to exfoliated [71]. While from the barrier property standpoint, the development of exfoliated nanocomposites is preferred always. On the other hand, nylon-6-based nanocomposite systems are completely different from other nanocomposite systems as discussed [21]. In Figure 5.10, Okamoto summarized the clay content dependence of dynamic storage modulus (G′ ) of various types of nanocomposites obtained under well below Tg of the matrices. Einstein coeficient (kE ) derived by using Halpin and Tai’s theoretical expression modiied by Nielsen is shown in this igure, and it represents the aspect ratio (Liller /diller ) of the dispersed MMT particles without intercalation. From Figure 5.10, it is clearly observed that poly(butylene succinate)(PBS)-based

NANOSTRUCTURE AND RHEOLOGICAL PROPERTIES

203

500 nm

(a)

(b)

(c)

500 nm

100 nm

Figure 5.9 Bright ield TEM images of (a) unprocessed sample, (b) and (c) sample prepared by solid-state processing for 8 h. The dark entities are the cross section and/or face of intercalated-and-stacked silicate layers, and the bright areas are the matrix. The insets in (a) and (c) are a computed FFT spectrum of the micrograph. Reproduced from Saito and Okamoto [57] with permission of Elsevier.

204 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES 10

Gʹnanocomposite/Gʹmatrix

PLACN1 PLACN2 PLACN3 PLACN4 PLACN5 PLACN6

160

70

15

T = 20 °C

T = 0 °C

T = –50 °C 1 1

0.1

10

N6CN1.6 N6CN3.7 PBSCN1 PBSCN2 PBSCN3 PBSCN4 PBSCN5 PBSCN6

100

Vol% of clay ′

′

Figure 5.10 Plots of Gnanocomposite ∕Gmatrix versus vol% of MMT for various nanocomposites. The Einstein coeficient kE is shown with the number in the box. The lines show the calculated results from Halpin and Tai’s theory with various kE .

nanocomposites (PBSCNs) show very high increment in G′ compared to other nanocomposites having the same content of clay in the matrix. N6CNs are the well-established, exfoliated, nylon-6-based nanocomposites. PLACNs are becoming established intercalated-and-locculated PLA-based nanocomposites, while PBSCNs are intercalated-and-extended locculated nanocomposites systems [45, 46]. Due to the strong interaction between hydroxylated edge–edge groups, the MMT particles are some time locculated in the polymer matrix. As a result of this locculation, the length of the MMT particles increases enormously and hence overall aspect ratio. For the preparation of high molecular weight PBS, diisocyanate [OCN-(C6 H12 )-NCO]-type end-groups are generally used as a chain extender. These isocyanate end-groups’ chain extenders make urethane bonds with hydroxy-terminated low molecular weight PBS, and each high molecular weight PBS chain contains two such kinds of bonds. These urethane-type bonds lead to a strong interaction with silicate surface by forming hydrogen bonds and hence strong locculation. For this reason, the aspect ratio of dispersed clay particles is much higher in the case of PBSCNs compared to all nanocomposites, and thus high enhancement of modulus. This behavior with the help of classical rheological theory of suspension of conventional iller reinforced systems can be explained. According to this theory [72], the rotation of iller is possible when volume fraction of clay �iller < �critical ≅ (aspect ratio)−1 . All PBSCNs studied here follow this relation except PBSCN4 (MMT = 3.6 wt%), in which �iller ≫ (aspect ratio)−1 . For this reason in PBSCN4, rotation of dispersed intercalated-and-locculated stacked silicate layers is completely hindered and only translational motion is available and hence shows very high modulus. This behavior is clearly observed in dynamic storage modulus measurements under the molten state [45].

NANOSTRUCTURE AND RHEOLOGICAL PROPERTIES

5.4.2

205

Linear Viscoelastic Properties

Dynamic oscillatory shear measurements of polymeric materials are generally performed by applying a time-dependent strain of �(t) = �o sin(�t) and the resultant shear stress is �(t) = �o [G′ sin(�t) + G′′ cos(�t)], with G′ and G′′ being the storage and loss modulus, respectively. Generally, the rheology of polymer melts strongly depends on the temperature at which the measurement is carried out. It is well known that for the thermorheological simplicity, isotherms of storage modulus (G′ (�)), loss modulus (G′′ (�)), and complex viscosity (|� ∗ |(�)) can be superimposed by horizontal shifts along the frequency axis: bT G′ (aT �, Tref ) = bT G′ (�, T) bT G′′ (aT �, Tref ) = bT G′′ (�, T) |� ∗ |(aT �, Tref ) = |� ∗ |(�, T) where aT and bT are the frequency and vertical shift factors and Tref is the reference temperature. All isotherms measured for pure polymer and for various PLSNCs can be superimposed along the frequency axis. In case of polymer samples, it is expected that at the temperatures and frequencies at which the rheological measurements were carried out, the polymer chains should be fully relaxed and should exhibit characteristic homopolymer-like terminal low behavior (i.e., curves can be expressed by a power law of G′ (�) ∝ �2 and G′′ (�) ∝ �). The rheological properties of in situ polymerized nanocomposites with end-tethered polymer chains were irst described by Krishnamoorti and Giannelis [33]. The low behavior of poly(�-caprolactone) (PCL)- and nylon-6-based nanocomposites differed extremely from that of the corresponding neat matrices, whereas the thermorheological properties of the nanocomposites were entirely determined by the behavior of matrices [33]. The slope of G′ (�) and G′′ (�) versus the aT � is much smaller than 2 and 1, respectively. Values of 2 and 1 are expected for linear monodispersed polymer melts and a large deviation especially in the presence of a very small amount of layered silicate loading may be due to the formation of network structure in the molten state. However, such nanocomposites based on the in situ polymerization technique exhibit fairly broad molar mass distribution of the polymer matrix, which hides the structure relevant information and impedes the interpretations of the results. To date, the melt state linear dynamic oscillatory shear properties of various kinds of PCNs have been examined for a wide range of polymer matrices including nylon-6 with various matrix molecular weights [34], PS [35], polystyrene (PS)–polyisoprene (PI) block copolymers [36, 37], PCL [38], polypropylene (PP) [31, 39–42], polylactide (PLA) [43, 44], and poly(butylene succinate) (PBS) [45, 46]. In the linear viscoelastic regime, a big change in terminal (low frequency) region from liquid-like response to a solid-like response was observed for all PCNs (G′ (�) ∼ G′′ (�) ∝ �0 ), ascribed to the formation of a volume spanning mesoscale OMLF (organoclay)

206 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES

network above the mechanical percolation threshold [42]. The terminal rheology is sensitive to organoclay loading and the extent of exfoliation/intercalation in the polymer matrix. A typical example of the linear dynamic viscoelastic master curves for the neat PLA and various PLA-based nanocomposites (PLACNs) with different organoclay loading [44] is shown in Figure 5.11. The linear dynamic viscoelastic master curves were generated by applying time–temperature superposition principle and shifted to a common temperature Tref using both frequency shift factor aT and modulus shift factor bT . The moduli of the PLACNs increase with increasing clay loading at all frequencies �. At high �’s, the qualitative behavior of G′ (�) and G′′ (�) is essentially the same and unaffected with frequencies. However, at low frequencies, G′ (�) and G′′ (�) increase monotonically with an increase in organoclay content. In the low frequency region, the curves can be expressed by the power law of G′ (�) ∝ �2 and G′′ (�) ∝ � for neat PLA, suggesting that it is similar to those of the narrow molecular weight (Mw ) distribution homopolymer melts. On the other hand, for aT � < 5 rad/s, viscoelastic response (particularly G′ (�)) for all the nanocomposites displays significantly the diminished frequency dependence as compared with the matrices. In fact, for all PLACNs, G′ (�) becomes nearly independent of low aT � and exceeds G′′ (�), which is the characteristic of the materials exhibiting a pseudosolid-like behavior. The slope values of the terminal zone of both neat PLA and PLACNs are estimated at lower aT � region ( is observed during low in both cases as compared with initial quiescent state (before shearing). Presumably this is due to the hydrodynamic forces, which promote alignment of the organoclay networks because of the large dimensions of the networks. Under �̇ = 0.5 s−1 (corresponding to unabated viscosity regime), the gradually decrease in < � 2 > and increase in �� upon imposition of shear are observed. Simultaneously, the value of < � 2 > is jumped upward and then remains almost at a constant value during low, where �� also maintains a constant value of 400 nm, indicating that the anisotropy in the system is developed. Upon cessation of shear at 750 s, on the contrary, < � 2 > increases with time and inally levels off at 1300 s with �� of 250 nm. On the other hand, < � 2 > does not become zero, and developed orientation

NANOSTRUCTURE AND RHEOLOGICAL PROPERTIES

cessation (t = 750 s)

Shear

γ~ 0.5 or 60 s –1

0 imposition (t = 50 s)

4

217

3

450 (t = 0)

2

630

302 ξη / nm

700 747

527 250

102

1 0 0.4

γ~ 0.5 s –1

400

(a) ξδ / nm

690

0.2 0

ξη / nm

450 (t = 0)

3

446

2

430

(b)

1

102

0 0.4

450

γ~ 60 s –1

ξδ / nm

0.2 0 0

400

800

1200

1600

Time (s)

Figure 5.19 Time variation of and upon imposition/cessation of steady shear under low (=0.5 s−1 ) and high �̇ (=60 s−1 ) conditions. Debye–Bueche equation is applicable in anisotropic shear low ield for dense suspension [83]. Reproduced from Okamoto et al. [81] with permission of The Society of Rheology, Japan.

of the network with �� of 690 nm in the shear ield is stable even upon cessation of shear. The anisotropy gradually develops with time, forming relatively stable oriented networks, which are stable even after the cessation of the shear. In the case of �̇ = 60 s−1 , < � 2 > slightly decreases upon imposition of shear but �� does not change and agrees well with the value of the initial quiescent state during low. For the anisotropy, during shear low, < � 2 > appears stable with �� of 450 nm and upon cessation of shear its disappears suddenly, suggesting that such aligned, orientated network structure in the high shear ield is lability (not stable) as compared with that under weak shear low. Furthermore, following the large deformation, the slippage and/or rotation takes place at an interface between the network domains, resulting in the shear-thinning behavior that is observed in this condition [84]. This

218 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES

feature may resemble the rotation of the grains in block copolymer melt under uniaxial deformation [85]. In PLSNC melts, however, the network structure is easily destroyed (ruptured) by deformation due to the polymer chain entanglement as discussed by Solomon et al. [39]. The structure disorder creates energy barriers that prevent reorganization/ reconstituting of networks into states of lower free energy. In dynamics for a typical soft glassy material, slow degree of freedom is taken into account [32, 86]. The jamming is a common property of the complex luids. In the presence of stress, the viscosity is given by the distribution of relaxation times of the networks of “slow mode.” Imposition of shear is considered to change the energy landscape and allows for the system to access new metastable states [87]. For this reason, the imposition of weak shear (� = 0.5 s−1 ) (much smaller than yield stress) is considered as shear rejuvenating conditions (� (�∶ ̇ t) ∝ t0.5 ), meaning that the longest relaxation time of the slow mode decreases in time. Accordingly, the initial network structure grows with time, accompanied by an increase in �� . Upon cessation of shear, aging begins anew because low alters the energy landscape, new metastable state is now accessible, and the system evolves spontaneously, accompanied by a increase in �� and a decrease in �� . This suggests that an aging of the system (i.e., the reconstituting in between networks) starts and a steady state is inally reached. In the case of large deformation (�̇ = 60 s−1 ), those energy barriers become greater the longer a system is aged such that the longest relaxation time continuously increases. As a result, upon cessation of shear, thermal motion alone is insuficient to mediate complete structural relaxation. Therefore, the network may become trapped in a higher energy state (almost constant value of �� ). Brownian forces alone are unable to change the energy barriers created by such oriented organoclay network structure because the estimated rotational Brownian motion of the hectorite platelets is about 10−2 s at 25 ∘ C. Such discussion on energy landscape appears to be entirely valid for the experimental results as well as for isotropic particle dispersion in a Newtonian luid matrix [86]. 5.4.7

Alignment of Silicate Layers in Networks

The organoclay platelets orient in both shear and elongational low ields. A second question is how the platelets are oriented during the low direction. Lele et al. [41] reported the in situ Rheo-X-ray investigation of low-induced orientation in syndiotactic PP/layered silicate nanocomposite melt. The clay platelets rapidly oriented and remained at a constant orientation in the long-time regime (∼1500 s). The orientation of silicate layers and nylon-6-base nanocomposite (N6CN) using ex situ small-angle X-ray scattering (SAXS) is examined [76]. The clay layers, due to their higher aspect ratio, were predominantly oriented in “parallel” orientation (with layer normals along the velocity gradient direction) at different times following LAOS.

NANOSTRUCTURE AND RHEOLOGICAL PROPERTIES

219

Kojima et al. [88] have found three regions of different orientations in the injection molded bar as a function of depth. Near the middle of the sample, where the shear forces are minimal, the clay platelets are oriented randomly and the nylon-6 crystallites are perpendicular to the silicate layers. In the surface region, shear stresses are very high, so both the clay layers and the nylon-6 crystallites are parallel to the surface. In the intermediate region, the clay layers, presumably due to their higher aspect ratio, still orient parallel to the surface and the nylon-6 crystallites assume an orientation perpendicular to the silicate. Medellin-Rodriguez et al. [89] reported that the molten N6CN samples showed planar orientation of silicate layers along the low direction, which is strongly dependent on shear time as well as on clay loading, reaching a maximally orienting level after being sheared for 15 min with �̇ = 60 s−1 . In contrast, the orientation occurs by the “normal” to the clay surface, aligning the low direction through vorticity during shear. Okamoto et al. conducted the transmission microscopic (TEM) observation for the sheared N6CN3.7 (clay loading = 3.7 wt%) with �̇ = 0.0006 s−1 for 1000 s [90]. The edges of the silicate layers lying along the z-axis (marked with the arrows (A)) or parallel alignment of the silicate edges to the shear direction (x-axis) (marked with the arrows (B)) rather than random orientation in the matrix is observed, but in fact, one cannot see these faces in this plane (Fig. 5.20). Here, it should be emphasized that the planar orientation of the silicate faces along the x–z plane does not take place prominently. For the case of rapid shear low, the commonly applicable conjecture of the planar orientation of the silicate faces along the shear direction irst demonstrated to be true by Kojima et al. [88]. In uniaxial elongational low (converging low) for a PP-based nanocomposite (PPCN4) (clay loading = 4 wt%), the formation of a house-of-cards structure is found by TEM analysis [91, 92]. The perpendicular (not parallel) alignment of clay platelets with large anisotropy toward the low direction might sound unlikely, but this could be the case especially under an elongational low ield, in which the extensional low rate is the square of the converging low rate along the thickness direction, if the assumption of afine deformation without volume change is valid. Obviously under such conditions, energy dissipation rate due to viscous resistance between the platelet surface and the matrix polymer is minimal when the platelets are aligned perpendicular to the low direction. Figure 5.21 shows double logarithmic plots of transient elongational viscosity �E (�̇ 0 ; t) against time t observed for N6CN3.7 and PPCN4 with different Hencky strain rates �̇ 0 ranging from 0.001 to 1.0 s−1 . The solid curve represents time development of the threefold shear viscosity, 3�0 (�; ̇ t), at 225 ∘ C with a constant shear rate −1 (�̇ = 0.001 s ). First, the extended Trouton rule, 3�0 (�; ̇ t) ≅ �E (�̇ 0 ; t) [93], as well as an empirical Cox–Merz relation (� (�) ̇ = |� ∗ |(�)) [94], fails for both N6CN3.7 and PPCN4 melts, as opposed to the melt of ordinary homopolymers. In �E (�̇ 0 ; t) at any �̇ 0 , N6CN3.7 melt shows a weak tendency of strain-induced hardening as compared to that of PPCN4 melt. A strong behavior of strain-induced hardening for PPCN4 melt was originated from an aging phenomenon characteristic of reconstituting of the

220 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES y (Shear gradient)

y

x (Flow)

x

O z (Neutral)

z

(A)

(A)

(B)

(A) (B)

100 nm

Figure 5.20 TEM image in the x–z plane showing N6CN (clay loading = 3.7 wt%) sheared at 225 ∘ C with �̇ = 0.0006 s−1 for 1000 s. The x-, y-, and z-axes correspond to low, shear gradient, and neutral direction, respectively. Reproduced from Okamoto [90] with permission of Rapra Technology.

networks through the perpendicular alignment of the silicate platelets to the stretching direction. From TEM observation (Fig. 5.20), the N6CN3.7 forms a ine dispersion of the silicate platelets of about 100 nm in Lclay , 3 nm thickness in dclay , and � clay of about 20–30 nm between them. The � clay value is a one order of magnitude lower than the value of Lclay , suggesting the formation of rigid network domain structure of the dispersed clay platelets in end-tethered polymer chains. This suggests that both slow (�̇ = 0.001 s−1 ) and rapid (�̇ = 1.0 s−1 ) elongational low rates are unable to erase the energy barriers created by in situ polymerization condition. Accordingly, the longest relaxation time in the network may still remain constant. This tendency was also observed in PPCN7.5 melt having higher content of clay (=7.5 wt%).

NANOSTRUCTURE AND RHEOLOGICAL PROPERTIES

108

221

N6CN3.7 225 °C

106 –1

ε*o/s 1.0 0.5 0.1 0.05 0.03 0.01 0.005 0.001 3*ηo (cone-plate; 0.001 s –1)

4

10

η (Pa s)

102

100

(a) PPCN4 150 °C

106

104

102

(b) 100 10–1

100

101

102

103

Time (s)

Figure 5.21 Time variation of elongational viscosity �E (�̇ 0 ; t) for (a) N6CN3.7 melt at 225 ∘ C and for (b) PPCN4 at 150 ∘ C. The solid line shows three times the shear viscosity, 3�E (�; ̇ t), taken at a low shear rate �̇ = 0.001 s−1 on a cone–plate rheometer. Reproduced from Okamoto [90] with permission of Rapra Technology.

SANS is useful in determining the orientation of the organoclay under shear because of contrast matching to clay (MMT) in D2 O [77]. In an aqueous dispersion of hectorite (3 wt%) and poly(ethylene oxide) (PEO) (2 wt%), the platelets were oriented in the low direction with the surface normal in the neutral direction (Fig. 5.22) [77]. It is quite possible that the dispersed organoclay platelets attain not only parallel alignment but also perpendicular or even transverse alignment during shear and elongational low ields. The aqueous clay (kaolinite) suspensions have been investigated both in the quiescent state [95] and under shear low using SANS [96]. Some 20 years ago, van Olphen [92] pointed out that the electrostatic attraction between the layers of natural clay in aqueous suspension arises from higher polar force in the medium. The intriguing features such as yield stress thixotropy and/or rheopexy exhibited in aqueous suspensions of natural clay minerals may be taken as a reference to the

222 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES Neutral direction Flow direction

Gradient direction

al nti

am

be

ge

n Ta

l dia

am

be

Ra

Figure 5.22 Couette-type shear cell for SANS and the model for real-space orientation of the oriented clay platelets in the cell. The reference coordinate frame is anchored in the tangential beam. Reproduced from Scmidt [77] with permission of American Chemical Society.

present PLSNCs. More detailed surveys on various types of experiments can also be available in the literature [97–104]. 5.5

NANOCOMPOSITE FOAMS

Flow-induced, internal, structural change occurs in both shear and elongational low, but differs from each other, as judged from the above results on �E (�̇ 0 ; t) and 3�0 (�; ̇ t) (see Fig. 5.21). Thus, with the rheological features of the PLSNCs and the characteristics of each processing operation, tactics should be selected for a particular nanocomposite for the enhancement of its mechanical properties. For example, the strong strain-induced hardening in �E (�̇ 0 ; t) is the requisite for withstanding the stretching force during the processing, while the rheopexy in ̇ t) suggests that for such PLSNCs, a promising technology is the processing in 3�0 (�; conined space such as the injection molding where shear force is crucial. 5.5.1

Foam Processing Using Supercritical CO2

PP-based nanocomposites have already been shown to exhibit a tendency toward strong strain-induced hardening. This strain-induced hardening behavior is an indispensable characteristic for foam processing due to its capacity to withstand

NANOCOMPOSITE FOAMS

223

the stretching force experienced during the latter stages of bubble growth. On the basis of this result, the irst successful nanocomposite foam, processed by using supercritical (sc)-CO2 as a physical foaming agent, appeared through a pioneering effort by Okamoto et al. [105, 106]. A small amount of nanoillers in the polymer matrix serves as nucleation sites to facilitate the bubble nucleation during foaming. Novel nanocomposite foams based on the combination of new nanoillers and sc-CO2 lead to a new class of the materials. The process consists of four stages: (i) saturation of CO2 in the sample at desired temperature, (ii) cell nucleation when the release of CO2 pressure started (supersaturated CO2 ), (iii) cell growth to an equilibrium size during the release of CO2 , and (iv) stabilization of cell via cooling process of the foamed sample. Figure 5.23 represents the scanning electron microscopy (SEM) images of neat PP-g-MA and various PPCNs foam conducted at various temperatures under a pressure of 10 MPa. From the SEM images, it is clearly observed that except for PPCN4 (MMT = 4 wt%) and PPCN7.5 foams prepared at 130.6 ∘ C, all others exhibit nicely closed-cell structures with cells having 12 or 14-hedron shapes. The formed cells show their faces mostly in pentagons or hexagons, which express the most energetically stable state of polygon cells. To understand the complex mechanism of physical foaming, Taki et al. studied the dynamic behavior of bubble nucleation and growth in the batch foaming of PP-based nanocomposites [107]. Employing image-processing techniques, the bubble nucleation and growth rate for different nanocomposites are analyzed from the series micrographs. Together with the solubility and diffusivity of CO2 into PP matrix, the mechanism of nanocomposites foaming is investigated. Clay content (wt%) 7.5

4

2

0

200 µm 130.6 °C

134.7 °C

139.2 °C

143.4 °C

Temperature (°C)

Figure 5.23 SEM images for PP-MA and various PPCNs foamed at different temperatures. Reproduced from Nam et al. [106] with permission of John Wiley and Sons.

224 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES Valve 1

Pump

Buffer cylinder Chiller Microscope with high-speed digital camera Pressure sensor

Needle valve

Sapphire windows Computer Temperature controller

Valve 2

CO2 cylinder

Cartridge heater Backlight

Figure 5.24 A schematic diagram of the visual observation apparatus for batch physical foaming. Reproduced from Taki et al. [107] with permission of John Wiley and Sons.

Figure 5.24 shows a schematic diagram of the visual observation apparatus for batch physical foaming. It consists of a high-pressure cell, a gas supply line, and a pump with a gas cylinder. The high-pressure cell is made of stainless steel and has two sapphire windows on the walls. The C-shape stainless steel is used for a spacer. A signal processing board (DITECT, Japan; HAS-PCI) is installed so as to acquire series of micrographs into a computer online. The bubble growth rate is quantiied by measuring the temporal change in the cross-sectional area of each bubble. Figure 5.25 shows the representative growth rate of the bubbles born at the designated time in PP-g-MA and nanocomposite foaming. Since the change in cross-sectional area of bubbles can be approximated by a linear function of time as mentioned earlier, the bubble growth observed by micrographs is a mass transfer-controlled process. Therefore, it can be said that the clay content changes the mass transfer rate of CO2 from the matrix polymer to bubbles. The clay particles decrease the diffusivity of CO2 while keeping the solubility of CO2 the same in matrix polymer. Particularly, owing to the clay-induced diffusivity depression, the increase in clay content depresses the mass transfer of CO2 from matrix polymer to the bubbles. As a result, the bubble growth rate is decreased. 5.5.2

PLA-Based Nanocomposite Foams

By means of a batch process in an autoclave, the foam processing of neat PLA and two different types of PLA-based nanocomposites (PLACNs) has been conducted using sc-CO2 as a foaming agent. The cellular structures obtained from various ranges of

NANOCOMPOSITE FOAMS

225

Representative average growth rate (µm2/s)

12 000

10 000 PPMA PPCN2

8 000

PPCN4 PPCN7.5

6 000

4 000

2 000

0 2.5

3.0

3.5

4.0

4.5

5.0

5.5

Time elapsed after the pressure release starts (s)

Figure 5.25 Representative average growth rates for PP-MA and nanocomposite foaming. Reproduced from Taki et al. [107] with permission of John Wiley and Sons.

foaming temperature–CO2 pressure were investigated by using SEM and TEM [108]. The incorporation with OMLF induced heterogeneous nucleation because of a lower activation energy barrier compared with homogeneous nucleation as revealed by the characterization of the interfacial tension between bubble and matrix. The grown cells having diameter of ∼200 nm were localized along the dispersed clay particles in the cell wall. The dispersed clay particles acted as nucleating sites for cell formation and the cell growth occur on the surfaces of the clays. The PLACNs provided excellent nanocomposite foams having high cell density from microcellular to nanocellular. Figure 5.26 shows the relation of relative modulus (Kf /Kp ) against relative density (�f /�p ) of neat PLA and nanocomposite foams, taken in the directions parallel (a) and perpendicular (b) to the low, respectively. To clarify whether the modulus enhancement of the nanocomposite foams was reasonable, we applied the following Equation 5.7 proposed earlier by Kumar [109] to estimate relative moduli with various foam density: Kf = Kp

(

�f �p

(

)4 −

�f �p

(

)2 +

�f �p

) (5.7)

where Kp and Kf are the modulus of pre-foamed and post-foamed samples, respectively. The solid line in the igure represents the it with Equation 5.7. The neat PLA foams do not show any difference between two moduli (Fig. 5.26a and b). On the other hand, for PLACN foams, the relative moduli exhibit a large value compared

226 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES 2.5 PLA PLA/MMT-ODA PLA/MMT-SBE

1.5

f

K /K

p

2

1 0.5 0

0

0.2

0.4

0.6

0.8

1

0.6

0.8

1

ρf / ρp

(a)

2.5

1.5

f

K /K

p

2

1 0.5 0

(b)

0

0.2

0.4

ρf / ρp

Figure 5.26 The relation of relative modulus (Kf /Kp ) against relative density (�f /�p ) of neat PLA and PLA-based nanocomposite foams, taken in the directions parallel (a) and perpendicular (b) to the low.

with the theoretical one. The dispersed clay particles in the cell wall align along the thickness direction of the sample. In other words, the clay particles arrange due to the biaxial low of material during foaming. The clay particles seem to act as a secondary cloth layer to protect the cells from being destroyed by external forces. In the directions perpendicular to the low, the relative modulus of PLA/MMT-ODA and PLA/MMT-SBE foams appears higher than the predicted value even through at the same relative mass density in the range of 0.7–0.85 (see Fig. 5.26a). This upward deviation suggests that the small cell size with large cell density enhances the material property as predicted by Weaire [110]. This may create the improvement of mechanical properties for polymeric foams through PLSNCs.

NANOCOMPOSITE FOAMS

227

More detailed surveys on the various types of nanocomposite foaming can also be available in the literature [111–114]. 5.5.3 Polyethylene Ionomer-Based Nanocomposite Foams by MuCell® Injection Molding To understand the correlation between foamability and melt rheology of polyethylene-based ionomers having a different degree of neutralization and the corresponding nanocomposites, Hayashi et al. [115] have conducted the foam processing via a batch process in an autoclave and microcellular foam injection molding (FIM) process using the MuCell® technology. They have discussed the obtainable morphological properties in both foaming processes. All cellular structures were investigated by using ield emission SEM. The competitive phenomenon between the cell nucleation and the cell growth including the coalescence of cell was discussed in the light of the interfacial energy and the relaxation rate as revealed by the modiied classical nucleation theory and rheological measurement, respectively. The FIM process led to the opposite behavior in the cell growth and coalescence of cell as compared with that of the batch process, where the ionic cross-linked structure has a signiicant contribution to retard the cell growth and coalescence of cell. The mechanical properties of the structural foams obtained by FIM process were discussed. Figure 5.27 shows the typical results of scanning electron microscope (FE-SEM) images of the fracture surfaces of the structural foams processed at two different conditions under FIM process. All structural foams consist of two compact polymer skin layers enclosing a foamed core. As well as the upper side at bottom side the layer thickness (skin layer thickness %) is measured at four points and averaged. However, in the case of MC-2 condition (density reduction of 5%) for nanocomposites (ionomer/clay 20/0/58 and ionomer/clay 20/3/78), the second layer is observed at the end of skin layer to the center area of the foamed core. The cell size in this area exhibits much smaller (∼10–30 μm) than that of the foamed core. The characteristic features of the obtained foams are presented in the literature. In the case of MC-1 (density reduction of 10%), all foams exhibit larger cell size and smaller cell density as compared with those of MC-2 condition (density reduction of 5%) except ionomer 3/89. This indicates that the different processing conditions have rather pronounced effect on the morphology of the structural foams. The coalescence effect in the cellular core is a dominant factor rather than the promoting nucleation due to the low viscosity of the materials with an sc-N2 of 0.2 wt% at 215 ∘ C. For this reason, the FIM process in this study leads to a bigger cell size and a smaller cell density as compared with that of batch process. The development of solidiied skin layer can be explained easily by heat transfer. However, the skin layer thickness has no signiicant difference between these processing sets including injection molding of their solid.

Ionomer 0/55

Schematic picture

MC-1

Ionomer 3/89

MC-2

MC-1

Ionomer/clay 20/0/58

Ionomer/clay 20/3/78

MC-1

MC-2

MC-1

MC-2

500 µm

Skin Core

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(bʹ)

(cʹ)

(dʹ)

(eʹ)

(fʹ)

(gʹ)

100 µm

(aʹ)

Figure 5.27 Typical results of FE-SEM images of the fracture surfaces of the structural foams processed at two different conditions under FIM process. (a)–(g) are skin layers enclosing the foamed core, and (a′ )–(g′ ) are center areas of the foamed core. Reproduced from Hayashi et al. [115] with permission of Elsevier.

228

NANOCOMPOSITE FOAMS

229

Interestingly, the FIM process leads to the opposite behavior in the cell growth and coalescence of the cell as compared with that of the batch process, where the ionic cross-linked structure has a signiicant contribution to retard the cell growth and coalescence of cell. The speciic dynamic storage modulus (G′ ) at –50 ∘ C and the speciic thermal expansion coeficient (�) in the temperature range of –150 to 0 ∘ C of solids and foamed materials obtained by FIM process are summarized in Figure 5.28. In the case of solid, there is a signiicant increase in G′ and decreasing in � for all nanocomposites as compared with that of ionomers. After structural foaming prepared by MC-1 condition, all nanocomposite foams exhibit much higher enhancement in G′ (200% for ionomer/clay 20/0/58, 210% for ionomer/clay 20/3/78) than those of the structural foam of the corresponding ionomers. This is due to the mechanistic reinforcement by the dispersed OMLF particles in the cell wall [105]. The dispersed OMLF particles seem to act as a secondary cloth layer to protect the cells from being deformed by external forces. At the same time, the reduction of the thermal expansion coeficient in the nanocomposite foams seems to stem from the mechanical constraint by the dispersed OMLF particles [116]. For this reason, all nanocomposite foams show a significant reduction of � value, and the value decreases by 66% for ionomer/clay 20/0/58

1

Specific Gʹ/GPa/kg/m3

T = –50 °C 0.8 0.6

Solid MC-1 MC-2

0.4 0.2 0

104 Specific α /mm/mm °C/kg/m3

(a) 0

T = – 150 to 0 °C

2 1.5 1 0.5 0

Ionomer 0/55

Ionomer 3/89

Ionomer/clay 20/0/58

Ionomer/clay 20/3/78

(b)

Figure 5.28 (a) Speciic dynamic storage modulus (G′ ) at –50 ∘ C and (b) speciic thermal expansion coeficient (�) in the temperature range of –150 to 0 ∘ C of solids and foams. Reproduced from Hayashi et al. [115] with permission of Elsevier.

230 RHEOLOGY AND PROCESSING OF POLYMER/LAYERED SILICATE NANOCOMPOSITES

and 53% for ionomer/clay 20/3/78 with MC-1 condition as compared with their structural foam of the ionomers. Unfortunately, in this study, no samples perpendicular to the mold-illing direction have been investigated.

5.6

FUTURE PROSPECTS

For an improved understanding of the soft glassy dynamics in PLSNC melts, we have described some recent results concerning the mesoscale OMLF (organoclay) network structure and its reversibility in the light of melt rheometry with a combination of scattering experiment and electron microscopy. We have studied the dynamics in PLSNC melts; however, it is dificult to discuss the intrinsic feature of the networks. Although our experimental results are still weak evidence to discuss the mesoscale structural development in PLSNC, many studies ignore the existence of percolated organoclay networks and its intrinsically metastable state and out of equilibrium. Once a percolated network is formed, the networks retard crystalline capability and enhance thermal stability as well as modulus [30, 117]. This study is the scope for the future for designing high-performance PCN materials and their processing, in which the correlation between the mesoscale network structure and macroscopic properties will be a probe via an innovative methodology such as three-dimensional TEM and fast scanning Fourier transform infrared (FTIR) imaging.

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6 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES Mohan Raja School of Engineering, Jagran Lakecity University, Bhopal, Madhya Pradesh, India

Modigunta Jeevan Kumar Reddy, Kwang Ho Won, Jae Ik Kim, Sang Hun Cha, Han Na Bae, Dae Hyeon Song, Sung Hun Ryu and Andikkadu Masilamani Shanmugharaj Department of Chemical Engineering, Kyung Hee University, Yongin, Kyunggi-Do, South Korea

6.1

INTRODUCTION

Since the birth of polymer science in the 1830s, these materials have dominated the market in terms of their versatility for product applications. These materials have unique properties such as low density, reasonable strength, lexibility, and easy processability. However, the mechanical properties of these materials are inadequate for many engineering applications. Various kinds of illers such as carbon black, silica, metal particles, glass, and boron ibers are used to enhance the strength and stiffness of these polymer materials [1–3]. However, signiicantly high iller loading is required to achieve the desired mechanical property of the polymer that in turn affects the processability characteristics and the cost of manufacture. So as to achieve high mechanical properties at lower iller loading, nanoillers that have nanometer size (∼100 nm) at least in one dimension are often used. This nanoiller-reinforced polymer matrix is termed as polymer nanocomposite that has received signiicant Rheology and Processing of Polymer Nanocomposites, First Edition. Edited by Sabu Thomas, Rene Muller, and Jiji Abraham. © 2016 John Wiley & Sons, Inc. Published 2016 by John Wiley & Sons, Inc.

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236 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES

attention in recent years. The global consumption of nanocomposites is estimated to rise from 119 million kilogram in 2010 to about 330 million kilogram in 2016. Indeed, these materials have a big potential for applications in the automotive and aerospace industry as well as in construction, electrical applications, and food packing. Since the discovery of carbon nanotubes (CNTs) by Iijima in 1991 [1, 4], considerable effort has been focused on using this special kind of iller in polymer-based composites [5, 6]. CNTs are one-dimensional carbon nanostructures with high aspect ratios (L/D) of 1000 or more although their diameter is close to molecular dimensions. They are classiied as single-walled carbon nanotubes (SWCNTs) (Fig. 6.1a)

(a)

(b)

5 nm

5 nm (c)

(d)

Figure 6.1 Schematic representations of (a) single-wall carbon nanotubes (SWCNTs); (b) multi-wall carbon nanotubes (MWCNTs); transmission electron micrographs of (c) SWCNTs and (d) MWCNTs. Reproduced from Eatemadi et al. [7] with permission of Open Access.

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TABLE 6.1 Comparative Properties of Carbon Nanotube and Graphite Property Speciic gravity Elastic modulus Strength Resistivity Thermal conductivity Magnetic susceptibility Thermal expansion Thermal stability Speciic surface area

Carbon Nanotubes 3

Graphite 3

0.8 g/cm for SWCNT; 0.8 g/cm for MWCNT ca. 1 TPa for SWCNT; ca. 0.3–1 TPa for MWCNT 50–500 GPa for SWCNT; 10–60 GPa for MWCNT 5–50 Ω cm 3000 W/m K 22 × 106 EMU/g Negligible >700 ∘ C (in air); 2800 ∘ C 10–20 m2 /g

2.26 g/cm3 1 TPa

50 Ω cm 3000 W/m K1 −1 × 106 K−1 450–650 ∘ C (in air)

or multi-walled carbon nanotubes (MWCNTs) (Fig. 6.1b) depending on the number of concentric cylindrical shells of graphene sheets coaxially arranged around a central hollow core with interlayer separations close to that of the interlayer distance in graphite (0.34 nm). SWCNTs consist of single cylindrical shell of graphene sheet with diameter varying in the range of 0.4–3 nm (Fig. 6.1c). Alternatively, MWCNTs consists of several concentric graphene layers with the inner diameter diverged from 0.4 to a few nanometers and outer diameter in the range of 2–30 nm (Fig. 6.1d) [7–9]. The comparative properties of CNT and graphite are summarized in Table 6.1. MWCNTs are electrically conductive due to the graphite lattice, whereas SWCNTs behave as conductors or semiconductors depending on the chirality of the graphite sheets [8]. Studies showed that CNTs have a unique combination of mechanical, electrical, and thermal properties that make nanotubes as excellent candidates to substitute or complement the conventional nanoillers in the fabrication of multifunctional polymer nanocomposites. Potential applications of polymer/CNT nanocomposites include energy storage and energy conversion devices, sensors, ield emission displays, radiation sources, hydrogen media, nanometer-sized semiconductor devices, probes, interconnects, coatings, encapsulates, and structural materials [9].

6.2 PROCESSING TECHNIQUES OF POLYMER/CNT NANOCOMPOSITES The effective utilization of CNTs in fabricating polymer nanocomposites strongly depends on the homogeneous dispersion of CNTs throughout the matrix without destroying their integrity. Furthermore, good interfacial bonding is also required to achieve signiicant load transfer across the matrix–CNT interface, a necessary

238 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES

condition for improving the mechanical properties of the composites. The dispersion states of CNTs in the polymer matrix are often inluenced by three main mechanisms of interaction between the polymer matrix and the CNTs: (a) Micromechanical interlocking (b) Chemical bonding between the nanotubes and the matrix (c) Weak van der Waals bonding between the iber and the matrix. While, the local nonuniformity on the CNT surface, including varying diameter and nonhexagonal defect induced bends/kinks on the CNT surfaces contributed to the polymer–CNT adhesion by micromechanical interlocking, improved interfacial interaction through ionic or covalent bonding contributed to the polymer–CNT adhesion through chemical bonding technique. Alternatively, though not a signiicant polymer–CNT adhesion, it is also slightly induced by weak van der Waals forces present on the CNT surfaces. Generally, it is a dificult task of getting ine dispersion of CNTs in a polymeric matrix as they have strong van der Waals forces due to its large surface area, which in turn result in CNT aggregation in the polymer matrix [10]. Several processing methods available for fabricating polymer/CNT composites include solution mixing, melt blending, and in situ polymerization (Fig. 6.2). In addition, dry powder mixing and surfactant-assisted mixing techniques are also being widely adopted to obtain intimate mixing of CNTs with polymer matrices. 6.2.1

Solution Processing

The most familiar method for preparing polymer/CNT nanocomposites involves the mixing of CNTs and polymer using a suitable solvent. The common method for preparing polymer/CNT composites has been to mix the nanotubes and polymer in CNTs

Solvent

CNTs

Dispersion

Monomer

Polymer Exfoliation

CNTs

Evaporation

Polymer

Mixing

Melt blending

Polymerization

Polymer nanocomposite

Polymer nanocomposite

Polymer nanocomposite

(a)

(b)

(c)

Curing agent

Solvent

Figure 6.2 Schematic representations on various processing types of polymer–CNTs composites: (a) solution mixing; (b) melt mixing; (c) in situ polymerization.

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a suitable solvent before evaporating the solvent to form a composite ilm. The beneit of solution blending is the rigorous mixing of CNTs with polymer in a solvent that facilitates the effective debundling of CNTs leading to a ine dispersion. Almost all solution processing methods are based on a general theme, which can be summarized as follows: 1) Dispersion of nanotubes in either a solvent or polymer solution by energetic agitation. 2) Mixing of nanotubes and polymer in solution by energetic agitation. 3) Controlled evaporation of solvent or by pouring in nonsolvent leaving a composite ilm. In general, agitation is provided by magnetic stirring, shear mixing, relux, or the most commonly ultrasonication. Sonication can be provided in two forms: mild sonication in a bath or high-power sonication using a tip or horn. Both organic and aqueous media have been used to produce polymer/CNT composites [11–15]. An early example of solution-based composite formation is described by Jin et al. [16], in which they used inely dispersed MWCNT in chloroform solvent and poly(hydroxy amino ether) (PHAE) polymer. In the initial step, MWCNTs produced by arc discharge were dispersed in chloroform by sonicating for 1 h. In the second step, poly(hydroxy amino ether) (PHAE) was then dissolved in the MWCNT chloroform dispersion and subjected to another hour of sonication. The resulting suspension was then poured into a Telon mold and dried in ambient conditions overnight in a fume-hood leading to free standing composite ilms with reasonably good CNT dispersion at high loading levels, namely, 50 wt% [11, 16]. Qian et al. [17] prepared polystyrene composite ilm by ultrasonication to disperse catalytic MWCNT in toluene and the subsequent blending of polystyrene in toluene. Shaffer and Windle [18] prepared poly(vinyl alcohol) (PVOH) composite ilm with nanotube loading as high as 60 wt% by blending PVOH solution and chemically modiied catalytic MWCNT dispersion using aqueous medium. Mixing was achieved by further sonication before drop casting to form ilms. A representative scanning electron microscopy (SEM) image of PVOH/CNT composite is included in Figure 6.3a. Ruan et al. [19] followed a similar method but used magnetic stirring and sonication to disperse the MWCNTs in xylene solvent and reluxing condition to mix the nanotubes and crystalline polymer such as ultrahigh molecular weight polyethylene (UHMWPE). Figure 6.3b,c showed the low and high magniications of transmission electron microscopy (TEM) images of cryo-microtomed solution processed UHMWPE/MWCNT composite ilms [19]. Several interesting observations can be made from these micrographs. First, the MWCNTs appear to disperse in the form of 1-μm-diameter clusters. These clusters appear to be the center for PE crystal growth. Second, a magniied view of the clustered region shows that the MWCNTs are fully dispersed as individual nanotubes, although some are entangled together in the form of random arrays. No rope-like regions are observed, implying that the solution mixing is effective in separating the MWCNTs. Although sonication-assisted solution processing of polymer/CNT nanocomposites is an

240 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES

100 nm

(a)

(b)

(c)

Figure 6.3 (a) Scanning electron microscopy (SEM) image of MWCNT-PVOH nanocomposites. Reproduced from Shaffer et al. [18] with permission of John Wiley and Sons. (b and c) TEM images of the undrawn 1 wt% MWCNT-UHMWPE nanocomposites. (b) A global view showing the macroscopic distribution of the embedded CNTs and their effects on PE crystallization. No staining was applied but the PE phase displays a clear lamellar structure radiating from the clustered CNTs. (c) A magniied view of one of the clustered CNT regions displaying the dispersion of CNTs as individual tubes. Some clusters on the nanoscale show local entanglements between CNTs. Reproduced from Ruan et al. [19] with permission of Elsevier.

eficient technique to produce high-performance composites with relatively ine dispersion of CNT in the matrix, prolonged sonication resulted in the CNT rupture, which in turn shorten the tube length (i.e., aspect ratio of CNT), and thus resulted in poor composite performance [20]. It should be pointed out that solution processing relies on the eficient dispersion of nanotubes in the relevant solvent. The choice of solvent is generally made based on the solubility of the polymer. However, pristine nanotubes cannot be well dispersed in most solvents. To get around this problem, a number of groups have used an additive such as a surfactant to disperse the nanotubes before mixing with the polymer solution [21–23]. The most common choices of the surfactant are the derivatives of sodium dodecyl sulfate (SDS). This technique results in excellent dispersion, with no derogatory effects on ilm properties observed. In a similar technique, the pH of the dispersion is controlled by the addition of HCl, thus resulting in good dispersion and wetting [24]. However, the major drawback associated with the surfactant-assisted solution processing is the existence of the surfactant in the nanocomposite ilms that in turn deteriorate the transport properties of resultant composites. Bryning et al. [25] prepared epoxy/SWCNT nanocomposites using the surfactant-assisted solution processing, and they showed that the thermal conductivity of composite is much lower if surfactant is used for SWCNT dispersion. Although solution processing is an eficient technique in preparing polymer/CNT composites, slower evaporation rate of solvent during composite preparation often leads to CNT aggregation in the composite ilms. To overcome this problem, polymer/CNT suspension can be kept on a rotating substrate [26] or can be dropped on a hot substrate [27] to expedite the evaporation step during the polymer nanocomposite preparation. Alternatively, coagulation technique developed by Du et al. [28] is yet another method, which involves pouring of polymer/CNT suspension into an excess

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of nonsolvent. This lead to entrapment of CNTs by precipitating polymer chains, which in turn prevents the CNTs from bundling. 6.2.2

Dry Powder, Wet, and Partial Solution Mixing

Although solution processing is an eficient technique for preparing inely dispersed CNT in the polymer nanocomposites, it has certain demerits, that is, it requires large amount of solvents for composite preparation. Moreover, many polymers are not soluble in the solvents used for nanoiller dispersion. In contrast to the solution processing, dry, wet, or partial solution mixing is an eficient technique for the preparation of polymer/CNT composites for certain systems (Fig. 6.4) [29a]. Dry powder mixing process is the eficient technique for the preparation of polymer/CNT composites, resulting in a conductive network with segregated morphology [29b]. Grady et al. [29b] prepared UHMWPE/SWCNT composites by dry powder mixing process in the presence of silica catalyst, resulting in the formation of segregated morphology with electrical percolation threshold as low as 0.14%. Figure 6.5 showed scanning electron micrographs of UHMWPE/SWCNT composite consisting spatial ordering with interconnected conductive CNT pathways [29b].

Neat polymer particle

Add iller particles, mix

Add non-soluble solvent+iller; mix and dry

Add partially soluble solvent+ iller;mix,dry

Consolidate particles

Consolidate particles

Consolidate particles

Dry mixing

Wet mixing

Partial solution mixing

Add soluble solvent+iller; mix and dry

Complete solution mixing

Figure 6.4 Schematic representations of various process models. Reproduced from Balogun and Buchanan [29a] with permission of Elsevier.

242 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES

(a)

(b)

Figure 6.5 Scanning electron micrographs (SEM) of SWCNT-UHMWPE with 5% iller: (a) and (b) represent the same sample imaged at different magniications. Reproduced from Grady et al. [29b] with permission of John Wiley and Sons.

Partial solution mixing (PSM) utilizes a polymer compatible solvent, which causes polymer swelling, as a vehicle for iller dispersion over the polymer surfaces. In this process, the polymer core remains largely unaffected by the solvent, but the iller phase is dispersed throughout the soft, swollen polymer surface structure. Such a structure is expected to exhibit stronger matrix particle bonding and a deined interfacial iller phase concentration (Fig. 6.4). Finally, wet mixing is the polymer processing, which uses a noncompatible solvent as vehicle to disperse the nanotube illers over the surfaces of the larger polymer particles. The solvent is such that it neither dissolves the polymer nor causes appreciable swelling of it (Fig. 6.4). However, these techniques often produce nonuniformity in the distribution of iller around the polymer particles due to the effects of the van der Waals force (Fig. 6.4). This nonuniformity is typically replicated in the iller distribution proile of the composite after molding [30], and usually negatively affects the uniformity of the electrical properties. 6.2.3

In Situ Polymerization

In situ polymerization has been intensively explored for the last few years for the preparation of polymer-grafted CNTs and subsequent processing of the corresponding polymer composite materials. The main advantage of this method is that it enables grafting of polymer macromolecules onto the walls of CNTs. Although the methodologies for the preparation of polymer/CNT composites are broadly classiied as “grafting to” [31] and ‘grafting from” [32] approach, in situ polymerization is the “grafting from” approach in which initiator or monomer was bonded to the CNT surface followed by the polymerization of monomers on the surface. In addition, it is a very convenient processing technique, which allows the preparation of nanocomposites with high CNTs loading and very good miscibility with almost each polymer matrix. This technique is particularly important for the preparation of insoluble and

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thermally unstable polymers, which cannot be processed by other processing techniques. Depending on required molecular weight and molecular weight distribution of polymers, various types of polymerization techniques, namely, radical, chain transfer, radical, anionic, and ring-opening metathesis polymerizations can be used for in situ polymerization. Initially, in situ radical polymerization was applied for the synthesis of poly(methyl methacrylate) (PMMA) with MWCNTs nanocomposites using free radical initiator such as 2,2′ -azobisisobutyronitrile (AIBN) [33–35]. According to Jia et al. [33], �-bonds in CNTs were initiated by AIBN and therefore nanotubes could participate in PMMA polymerization leading to a strong interface between the MWCNTs and the PMMA matrix. Yang et al. [35] synthesized hairy rod-like nanostructures of polystyrene-grafted MWCNT with a coating thickness of 8–10 nm by surface-initiated free radical polymerization using AIBN initiator, styrene monomer, and vinyl group grafted CNTs (MWCNT-CH = CH2 ). Alternatively, Park et al. [36] proposed a novel surface-initiated polymerization process in which they grafted UV photoinitiator, that is, benzoyl peroxide using chemically modiied MWCNTs followed by the polymerization of active monomer such as styrene leading to the formation of polystyrene-grafted MWCNTs. Figure 6.6a showed the schematic representation of the synthesis steps used by Park et al. [36]. SEM (Fig. 6.6b,c) and TEM (Fig. 6.6d) images of the pristine and polymer grafted CNTs revealed the

R

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1 µm SE

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(b)

(a)

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1 µm SE 24–Nov–09 INHA WD17.4mn15.0kV ×50k

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10 m

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Figure 6.6 (a) Reaction scheme of polymer-grafted MWCNTs via free radical graft polymerization (FRGP); scanning electron microscopy (SEM) images of (b) pristine MWCNTs; (c) MWCNTs-PS; and (d) HR-TEM images of MWCNT-PS. Reproduced from Park et al. [36] with permission of Elsevier.

244 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES

successful grafting of polystyrene by a signiicant rise in the average diameter of the MWCNTs. They have also successfully prepared various other polymer-coated MWCNTs, namely, poly(methyl methacrylate) (PMMA), poly(butyl methacrylate) (PBMA), and poly(2-hydroxy ethyl methacrylate) apart from polystyrene system. Alternatively, Wu et al. [37] adopted in situ emulsion polymerization technique under microwave radiation using potassium persulfate as initiator for the preparation of polymer-wrapped MWCNTs (PS and PMMA). TEM results showed the successful wrapping of amorphous PS (Fig. 6.7a) and PMMA (Fig. 6.7b) layers although it is not uniformly coated on the nanotube surface. Both the polymer-wrapped CNTs when dispersed in chloroform showed excellent optical limiting behavior in comparison to the pristine MWCNT in chloroform solvent. In contrast to the earlier reports, in situ polymer composite by grafting of polymers on CNT surface without disrupting the original nanotube structure can be achieved by anionic polymerization using carbanions introduced CNTs (Fig. 6.8a,b) [38]. Addition of carbanions such as secondary butyl lithium ion on the SWCNT not only debundled the aggregated CNTs but also acted as the initiator for anionic polymerization of styrene monomer leading to the formation of polystyrene chains on the CNT surface. This attachment of polymer chains enhances the bulk polymer–CNT adhesion and thereby ine dispersion of CNT with the existence of individual tubes in the matrix. Viswanathan et al. [38] corroborated the presence of individual tubes without change in structural integrity using atomic force microscopy (AFM) characterization (Fig. 6.8c,d). Various polymer grafted CNTs including polyisoprene (PI), polystyrene (PS), poly(ter-butyl acrylate) (PtBA), poly(ter-butyl acrylate-methyl methacrylate) (P(tBA-MMA), poly(N-vinyl carbazole) (PVK) were also successfully synthesized using via in situ anionic polymerization [39–42]. In situ polymerization leading to polymer grafted CNTs with well-controlled molecular weight and thickness can be achieved by surface initiated atom transfer radical polymerization (SI-ATRP). In comparison with the anionic polymerization approach, the atom transfer radical polymerization approach displays at least three merits: (i) both styrene and acrylate/acrylamide monomers can be directly used as

10 nm

10 nm (a)

(b)

Figure 6.7 Transmission electron microscopy (TEM) images of (a) polystyrene (PS) wrapped MWCNTs and (b) poly(methyl methacrylate) (PMMA) wrapped MWCNTs. Reproduced from Wu et al. [37] with permission of Elsevier.

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– Li

+

–

– Li+

Li +

(b)

(a) 10.0 nm

1.00

nm

–1.00

0

5.0 nm

0 0.30 µm

0.0 nm 0

2 µm (c)

(d)

Figure 6.8 Schematic (not to scale) of carbanion formation and subsequent initiation of polymerization: (a) section of SWCNT sidewall showing sec-butyl lithium addition to a double bond (gray arrow indicates the bond to which it adds) and formation of anion via transfer of charge, (b) the carbanion attacks the double bond in styrene, which in turn transfers the negative charge to the monomer. Successive addition of styrene results in the formation of living polymer chain. (c) Tapping mode atomic force microscopy (TMAFM) image of a polystyrene-grafted SWCNT/polystyrene ilm. (d) AFM height proile of an individual nanotube of diameter ∼0.8 nm. Reproduced from Viswanathan et al. [38] with permission of American Chemical Society.

the raw materials; (ii) the initiating sites in the reaction system remain constant after the graft polymerization and puriication of the products, so it is convenient to further perform block copolymerization and chain extension; and (iii) it presents an access to prepare the polymers with a functional group in each repeating unit such as poly(hydroxyethyl methacrylate) (PHEMA) [43]. The general strategy for grafting polymers on CNT surface via SI-ATRP involves (i) grafting of alkyl halide initiator

246 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES O

O 1) HNO3, SOCl2, 2) HOCH2CH2OH

O

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4) CuBr/PMDETA

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MMA, 60°C Br

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MWCNT-Br

(a)

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n OCH3 Br

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O Br

Br O

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O 3) Br

O

O

MWCNT-PMMA

3.8 nm 14 nm 10 nm

10 nm

10 nm (b)

(c)

(d)

Figure 6.9 (a) Schematic representation of surface-initiated atom transfer radical polymerization (SI-ATRP) of polymer brushes on MWCNT surfaces; TEM images of pristine MWCNT (b) PMMA-grafted MWCNTs (c and d) [c, monomer: MWCNT-Br 1:1; monomer: CuBr: N,N,N′ ,N′′ ,N′′ -pentamethylene diethylenetriamine ratio, 5:1:1; temperature, 60 ∘ C; time, 20 h; d, monomer: MWCNT-Br 10:1; monomer: CuBr: N,N, N′ ,N′′ ,N′′ -pentamethylene diethylenetriamine ratio: 50:1:1; temperature, 60 ∘ C; time: 30 h]. Reproduced from Kong et al. [43] with permission of American Chemical Society.

onto CNT and (ii) grafting of polymers using initiator grafted CNT, copper halide, ligand, and monomers [43]. Figure 6.9a showed the schematic representation of PMMA grafted MWCNTs via SI-ATRP. TEM results revealed that the PMMA layer wrapped on the CNT with varying thickness can be achieved by adjusting feed ratio (Monomer: MWCNT-Br) (Fig. 6.9b,c). Polymer coated SWCNTs consisting of CNT core surrounded by a “hair-like” corona of lexible polymer chains, which in turn improving its dispersibility and adhesion has been termed as hairy nano-objects by Wu et al. [44]. Controlled synthesis of poly(n-butyl acrylate) polymer by SI-ATRP on the CNT surface as shown in Figure 6.10a resulted in the formation of hairy brushes [44]. Tapping-mode atomic force microscopy (TMAFM) provided the direct evidence of the “hairy nanorod” nature of the grafted SWCNTs with more insights into the uniformity of grafted chain lengths and grafting density (Fig. 6.10b,c). Wu et al. [44] reported that the grafting densities of the hairy polymer brushes on the SWCNTs are in the range of ∼1.0–10.0 chains per nanometer. Shanmugharaj et al. [45] reported various polymer grafted CNTs, namely, polystyrene (PS), poly(styrene-co-acrylonitrile) (SAN), and polyacrylonitrile (PAN) using SI-ATRP. Water-dispersible stimuli responsive MWCNTs were also prepared by grafting poly(N-isopropyl acrylamide) chains from the nanotube surface via SI-ATRP [46]. The advantage of this procedure was that grafting proceeds in

PROCESSING TECHNIQUES OF POLYMER/CNT NANOCOMPOSITES

Br

H2N

OH HO Isoamyl nitrite 60 °C

n

247

O

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OH n

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Figure 6.10 (a) Functionalization of pristine SWNTs and ATRP of n-butyl acrylate from such functionalized SWCNTs and (b) TMAFM height images of SWCNT-BA-1 (DP of BA = 218): (a) original height; inset: phase image. Image size: 830 × 830 nm2 . Pixel size: 1.62 × 1.62 nm2 . (b) Image after reconstruction (grafting densities of regions A: 1.6, 2.1, and 1.2 chains/nm2 ). Reproduced from Wu et al. [44] with permission of John Wiley and Sons.

aqueous media and at room temperature. In situ nitroxide-mediated polymerization (NMP) is an alternative radical polymerization technique, which is usually used to prepare polymer grafted CNTs with controlled molecular weight and distribution. Datsyuk et al. [47] reported an in situ NMP of MMA onto double-walled carbon nanotubes (DWCNTs). The main advantage of this two-step synthetic route is that it does not involve any CNT pretreatment or functionalization. In the irst step, short chains of poly(acrylic acid) (PAA) or polystyrene (PS) were polymerized in situ in the presence of NMP initiator. In the second step, the presence of the stable nitroxide radical on CNTs surface makes it possible to reinitiate the polymerization of different monomers. Zhao et al. [48] carried out NMP of styrene on the surfaces of MWCNTs initiated by an MWCNT-supported initiator (MWCNT-TEMPO). A copolymer, polystyrene-b-poly(vinyl pyridine) (PS-b-P4VP), was also grafted to MWCNTs by further polymerization of 4-vinyl pyridine initiated by MWCNT–PS. Although in situ polymerization using SI-ATRP is a successful technique to graft amorphous polymers such as polystyrene onto CNT surfaces, these are not viable techniques to graft crystalline polymers, namely, polyethylene or polypropylene. Alternatively, in situ metallocene polymerization using anchored Ziegler–Natta catalyst (MgCl2 /TiCl4 ) at the surface of oxidized SWCNTs was used for in situ

248 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES

polymerization of ethylene monomer leading to the formation of polyethylene [49]. Philip et al. [50] reported in situ functionalization of MWCNTs by polyaniline (PANI) by oxidation polymerization. The oxidized CNTs were activated by thionyl chloride and reacted with para-phenylene diamine in the next step. The tubes were shown to be almost of uniform diameter. Wu et al. [51] studied the mechanical and thermal properties of hydroxyl functionalized MWCNTs with acrylic acid grafted poly(trimethylene terephthalate) (PTT) nanocomposites and showed a signiicant enhancement in thermal and mechanical properties of PTT matrix due to the formation of ester bonds between –COOH groups of acrylic acid grafted PTT and –OH groups of MWCNTs. Kumar et al. [52] synthesized poly(p-phenylene benzobisoxazole)/SWCNT (PBO/CNT) composite materials by in situ polymerization of rod-like PBO polymers in the presence of SWCNT, which was further subjected to dry-jet wet spinning technique to yield high-strength composite ibers. In situ polymerization was also very useful and successful method for the synthesis of polyamide-based CNTs, polymer nanocomposites, which involves the usage of ring-opening or condensation polymerization. In situ hydrolytic polymerization of �-caprolactam in the presence of pristine and carboxylated CNTs resulted in the formation of nylon-6-modiied MWCNTs [53]. In another work, Gao et al. [54] reported new improved chemical processing technology that allows the continuous spinning of nylon-6/SWCNT (PA6/CNT) ibers by the in situ ring-opening polymerization of caprolactam in the presence of SWCNT (Fig. 6.11). This process results in a new hybrid material with characteristics of both the iber and the matrix, with an excellent compatibility between the SWCNTs and nylon-6. Recently, Shabanian et al. [55] reported an effective in situ direct polycondensation process to synthesize polyamide grafted using monomers such as adipic acid and 4,4-diaminodiphenylsulfone in the presence of pristine or ethylene diamine grafted carbon nanotubes (EA CNT) (Fig. 6.12a). They corroborated CNT entanglement is absent on using ethylene diamine modiied CNT for in situ polycondensation reaction, when compared to pristine CNT (Fig. 6.12b,c). SWCNT-reinforced polyimide nanocomposites were synthesized by in situ polymerization of diamine and dianhydride in the presence of sonication. This process enabled uniform dispersion of SWNT bundles in the polymer matrix. The resultant SWNT–polyimide nanocomposite ilms were electrically conductive (antistatic) and optically transparent with signiicant conductivity enhancement (10 orders of magnitude) at 0.1 vol% loading [56]. Recently, Wu et al. [57] reported in situ synthesis of poly(3,4,9,10-perylenetetracarboxylic dianhydride ethylene diamine)/SWCNT composites, which could be used as organic cathode materials for lithium-ion batteries. They have reported that loading of SWCNT in polyimide enhanced the rate capability, and the capacity was increased from 10 to 115 mA h/g at 2 ∘ C. Epoxy nanocomposites comprise the majority of reports using in situ polymerization methods, where the pristine and chemically modiied CNTs were irst dispersed in the resin followed by curing of the resin with the hardener [58–62]. Zhu et al. [61] prepared epoxy nanocomposites by the technique using carboxylated end-cap SWCNTs and an esteriication reaction to produce a composite with improved tensile modulus. Choi et al. [62] reported that curing characteristics are signiicantly

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H O

O NH

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+ H3N

Initiation 250 °C

CN H

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Termination

O

H C N

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O (a)

COO–

Nitrogen

Polymer iber

(b)

3 cm (c)

(d)

(e)

Figure 6.11 (a) Synthesis of nylon-6 SWCNT composite by ring-opening polymerization of caprolactam in the presence of SWCNTs. (b) Schematic of the iber spinneret setup. (c) Photograph of the spinneret setup. (d) Photograph of the composite iber. (e) SEM image of cross-sectional fracture of the composite iber. Reproduced from Gao et al. [54] with permission of American Chemical Society.

altered by the addition of pristine or modiied CNT in the epoxy nanocomposites. It is important to note that as polymerization progresses and the viscosity of the reaction medium increases, the extent of in situ polymerization reactions might be limited. 6.2.4

Melt Blending

While solution or in situ polymer processing is a valuable technique for both nanotube (CNT) dispersion and composite formation, it is completely unsuitable for industrial scale processes. For industrial applications, melt processing is a preferred choice because of its low cost, uniform mixing, and simplicity to facilitate large-scale production for commercial applications. Melt mixing is often used to produce polymer nanocomposites based on thermoplastic polymer as matrixes that get soften on

250 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES

H 2N

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H2N OH

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NH2

TPP/NMP CaCl2 Poly amide/FCNT nanocomposite (PA-FCNT)

DMAc Insoluble

Soluble

Polyamide-pristine CNT

100 nm

(b)

FCNT-sPA:

FCNT-/PA:

Long chain of PA (/PA)

Short chain of PA (sPA) PA:

O S O

N H

NH O

O n

Polyamide-EA CNT

(a)

100 nm

(c)

Figure 6.12 (a) Synthesis of polyamide/functionalized carbon nanotube (FCNT) composite (PA–FCNT), FCNT–short-chain PA and FCNT–long-chain PA, TEM images of (a) polyamide-pristine CNT composites and (b) polyamide-ethylene diamine-g-CNT composites. Reproduced from Shabanian et al. [55] with permission of Royal Society of Chemistry.

heating. The temperature used for melt processing of polymer/CNT nanocomposites depends on the polymer type, whereas the amorphous polymer needs to be processed above their glass transition temperature, the processing temperature of semicrystalline polymers has to be ixed above its melting temperature to induce softening. In general, melt processing involves the melting of polymer pellets to form a viscous liquid followed by the incorporation of additives, such as CNTs to the melt by shear mixing. Bulk samples can then be fabricated by molding techniques such as compression molding, injection molding, or extrusion. Polymer nanocomposites based on poly(methyl methacrylate) (PMMA) loaded with 26 wt% loading of MWCNT using laboratory mixing molder processed at 200 ∘ C was earlier reported by Jin et al. [63]. The prepared composites were then compression molded (under 8–9 MPa at 210 ∘ C) in a hydraulic press to give composite slabs with good dispersion of MWCNT even at higher concentration. Successful industrial scale preparation of polymer nanocomposites by melt

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processing involved two steps: In the irst step, polymer needs to be blended with higher loading of CNTs using high shear mixer to form masterbatches. This step is followed by the incorporation of the neat polymer in the masterbatches to form lower mass fraction samples in the second step. Finally, compression molded samples prepared using above composites showed signiicant improvement in the properties due to the enhanced CNT dispersion. Andrews et al. [64] showed that commercial polymers such as high-impact polystyrene (PS), polypropylene (PP), and acrylonitrile–butadiene–styrene (ABS) could be processed with MWCNT using this dilution technique. Polycarbonate (PC) nanocomposites illed with MWCNTs was successfully prepared by diluting PC masterbatches followed by extrusion process using circular die to prepare the test samples with excellent nanotube dispersion [65]. TMAFM results of PC/MWCNT nanocomposites are shown in Figure 6.13. Height and phase images of PC nanocomposite masterbatches loaded with 15% of MWCNT showed interconnected MWCNT in the PC composites (Fig. 6.13a,b). Alternatively, dilution of PC masterbatches with neat polycarbonate polymer resulting in 1–2 wt% MWCNT loading amount showed either homogeneous dispersion of curved nanotubes (1 wt% MWCNT) or interconnected morphology (2 wt% MWCNT) depending on the MWCNT loading amount in the PC matrix (Fig. 6.13c–f). Injection molding technique has been successfully implemented for preparing test samples based on polymer blend nanocomposites of polyamide (nylon-6) and ABS polymer with excellent electrical conductivity at lower MWCNT loading (4–6 wt%) by Meincke et al. [66]. They have processed the nylon-6/ABS polymer blend-based MWCNT nanocomposites using twin-screw extruder at 260 ∘ C, and the resultant extrudate was broken up into pellets and injection molded to form test samples with good nanotube dispersions [66]. Raja et al. [67] reported melt processable shape memory polymer blend nanocomposites based on polyurethane (PU) and poly(lactic acid) (PLA) illed with pristine and chemically modiied MWCNTs. Very recently, melt processable phenoxy nanocomposites illed with MWCNTs showing extremely low percolation threshold (pc ∼ 0.20 wt%) was reported by Zhang et al. [68]. In some cases, shear mixing can be dificult as the nanotube powder tends to stick to the walls of the mixer. To overcome this challenge, a combination of solution and melt techniques can be used [69]. Thostenson and Chou initially dispersed MWCNT in a solution of polystyrene (PS) in tetrahydrofuran (THF), which was drop casted to form a ilm [69]. The obtained ilms could be formed by compression molding, or alternatively the nanotubes could be aligned by drawing the sample direct from the extruder. In both cases, very good adhesion and wetting were observed [69]. For many applications, ibers are more suitable than bulk materials. In addition, iber production techniques tend to be suited to the alignment of nanotubes within the iber. A number of studies have focused on the production of composite ibers by melt processing. Haggenmueller et al. [70] used a complicated production process of composite ibers based on poly(methyl methacrylate) (PMMA) and SWCNT, which involved the usage of solution casting and multiple step melt processing. Alternatively, Sandler et al. compared ibers made from polyamide-12 with a range of illers: arc-MWCNT prepared by arc discharge, vapor grown carbon ibers (VGCF), and both aligned and entangled MWCNT prepared by chemical vapor deposition

252 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES

0

Data type Height Z range 200.0 nm

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Data type Height 4.00 µm Z range 100.0 nm (e)

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Figure 6.13 Tapping mode atomic force microscopy (TMAFM) images of (a, b) PC with 15 wt% MWCNT (Masterbatch); (c, d) PC with 1 wt% MWCNT; (e, f) PC with 2.0 wt% MWCNT. Reproduced from Poetschke et al. [65] with permission of Taylor & Francis.

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(CVD) [71]. In the irst step, polymer pellets and nanotube powder were mixed in a twin-screw microextruder, and the resulting extrudate was chopped and fed into a capillary rheometer with 1-mm die. Fibers were spun at 0.5 m/s to produce a inal iber diameter of 125 μm. The observed dispersion and alignment were very good for the MWCNT prepared by CVD. However, the MWCNTs prepared by arc discharge were less well dispersed. In addition, voids were seen in the ibers fabricated from arc-MWCNT (Fig. 6.14). El Ghanem et al. [72] studied the effect of MWCNT on the dielectric behavior of the ABS nanocomposites. They have also studied the effect of DC-bias on the dielectric behavior ABS at various loading amount of MWCNTs, and they reported that DC-bias had more pronounced effect on the dielectric behavior of nanocomposite with low iller content, ≤5 wt%, while for the highly illed nanocomposites (MWCNT ≥10 wt%), the effect of DC-bias was insigniicant. Although melt blending is a simple and effective technique, usage of high shear forces for CNT dispersion also leads to nanotube fragmentation. So an optimum shear stress is required to achieve the desired dispersion at the lowest possible damage of

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×700 10 µm

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Figure 6.14 SEM images of the nanocomposite ibers containing (a) 10 wt% carbon nanoibers (CNF), (b) 10 wt% entangled catalytically grown nanotubes (eCGCNT), (c) 5 wt% aligned catalytically grown nanotubes (aCGCNT), and (d) 5 wt% arc-grown carbon nanotubes (AGCNT). Reproduced from Sandler et al. [71] with permission of Elsevier.

254 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES

CNTs. Processing temperature is another critical parameter in melt processing, which needs to be optimized without degrading the polymer intrinsic properties.

6.3 RHEOLOGICAL PROPERTIES OF POLYMER/CARBON NANOTUBE COMPOSITES If eficient and economically viable bulk processing of polymer/CNT composites is to be realized, in-depth understanding of the rheological aspects of the polymer nanocomposites is required. Therefore, rheology or low properties of polymer/CNT composites are extremely rich, diverse, and lie between those of the pure polymer rheology and the rheology of colloidal suspensions [73]. The rheological behavior of polymer/CNT composites is often inluenced by ive important parameters of CNT microstructure, such as its dispersion state, network structure, aspect ratio, concentration, and its orientation state in the polymer matrix. In the following sections, the rheological aspects of the various processing techniques of polymer/CNT composites have been discussed. CNT dispersion in polymer matrix is a spatial property, whereby the individual nanotubes are spread with the roughly uniform number density throughout the continuous supporting matrix [73]. CNT dispersion in polymer matrix involves separation and then stabilization of CNTs. Effective separation requires the overcoming of the intertube van der Waals (VDW) attraction. Depending on the tube shape/sizes and the orientation of tubes with respect to each other, such an attraction can act within a spacing of a few nanometers [74]. For closely packed tubes, the surface adsorption or wetting by the polymer, both require a temporary (partial) exfoliation state. Although they may appear very different in nature, they are both governed by the transfer of physical shear stress that breaks down the bundles. The rheological characterization under suspension or melt state provides more insights into the dispersion states of CNTs in polymer solution or polymer melts. Rheological response of polymer/CNT suspension or melt depends on the volume fraction of nanotube in the polymer, and generally they are classiied as (i) dilute, (ii) semidilute, and (iii) concentrated regimes depending on the nanotube concentration. Cone and plate and oscillatory rheometer are widely applied to understand the rheological properties of polymer/CNT composites under suspension or melt state [74, 75]. 6.3.1

Dilute Regime

An understanding of the phase behavior of rod-like molecules was initially developed by Onsager [76], modiied by Flory [77], and subsequently by Doi and Edwards [78]. Briely, in this formalism, the dilute regime is deined as � < L−3 , where � is the number density of rods. In terms of a volume fraction (�/100) of nanotubes, the dilute regime is deined as �L3 ≈ (4/�)(L/d)2 �/100 ≤ 1.0 [75, 79]. Physically, in this regime, dispersed CNT can be treated as isolated particles and there are relatively few neighboring tubes within the region of overlap; hence, interactions between the nanotubes are negligible. Under isolated condition in dilute regime, CNT, which is having

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255

a deinite aspect ratio, rotates slowly when its long axis is nearly parallel to the low direction in the absence of Brownian motion. This rotation is often termed as a Jeffrey orbit, which has practical implications in ield low fractionation of CNTs by length or pressure-driven Poiseuille low in a narrow channel (microluidic devices) [80]. Unfortunately, there is almost no report available focusing on the dilute regime rheology of CNTs dispersed in polymer matrix and possibly since the viscoelastic response of the polymer would far exceed that of the dispersed CNTs. For such dilute dispersions, the reduced viscosity depends linearly on the CNT concentration and the relaxation time is independent of CNT concentration, both of which are in accordance with the theory developed for dynamics of dilute Brownian rods [79, 81]. By measuring the zero-shear viscosity of individual SWCNTs stabilized in polymer surfactants, the aspect ratio of CNTs can be determined. Nicholas et al. [82] determined the length of the SWCNTs by determining the zero-shear viscosity of the dilute suspensions of polymer surfactant-stabilized SWCNTs and by correlating the rotational relaxation time, which is independent of concentration as they are not interacting in dilute regime. At this point, it is also relevant to discuss briely the nature of individual CNTs dispersed a viscous polymer matrix. In viscous polymer medium, Brownian force is active that tends to bend a 1D object such as CNT depending on the characteristic persistence length (LP ), which is the ratio of bending stiffness (�) to thermal energy (LP = �/kB T where kB T is thermal energy). If the length of a nanotube inside a network is shorter than LP , then it essentially appears as rigid rod; whereas, if the length of the nanotube segment in the network is longer than LP , then it behaves as a semilexible rod. There is considerable debate on the values of LP for isolated CNTs as well as in networks of nanotubes. While the individual SWCNTs inside the CNT network of CNT-solvent suspension exist as semilexible rods, MWCNTs dispersed in polydimethylsiloxane (PDMS) polymer exist as rigid rod in the concentrations ranging between the dilute and semidilute regime [83, 84]. 6.3.2

Semidilute Regime

The semidilute regime is very broad, being deined by the somewhat vague relations cL3 ≫ 1 and cL2 a ≤ 1. From a rheological perspective, this is by far the richest window of concentration for CNT suspension [79]. The state of dispersion can be quantiied through the percolation threshold (Øc in volume %). For instance, Øc is measured via the concentration of CNTs where linear viscoelastic properties of the nanocomposite change from liquid-like to solid-like transition. Structurally, the earliest network spanning path (or backbone connectivity) is developed at this concentration. For example, polymer melt or a solution under the application of small-amplitude linear oscillatory shear, the low-frequency (�) storage, and loss ′ modulus (G′ and G′′ , respectively) exhibits terminal behavior with G′ ∼ �2 and ′′ G ∼ �, respectively. Equivalently, the magnitude of the complex viscosity (|�*|) is independent of frequency (i.e., Newtonian behavior). Incorporation of CNTs in the polymer gradually transforms the liquid-like terminal behavior to solid-like nonterminal behavior (i.e., both G′ and G′′ are independent of � as � → 0) (Fig. 6.15a; in

256 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES 107

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Figure 6.15 (a) Storage modulus G′ of nanotube-illed polycarbonate at 260 ∘ C. (b) Complex viscosity versus nanotube content at different frequencies (inset). Schematic of (left) isolated nanotube dispersion below the percolation threshold, (center) onset of percolation, the matrix spanning backbone connectivity is marked white, and (right) fully grown network. (c) Schematic of CNTs–polymer nanocomposites in which the nanotube bundles have isotropic orientation. (Top) At low nanotube concentrations, the rheological and electrical properties of the composite are comparable to those of the host polymer. (Bottom) The onset of solid-like viscoelastic behavior occurs when the size of the polymer chain is somewhat large to the separation between the nanotube bundles. Reproduced from Chatterjee and Krishnamoorti [75] with permission of Royal Society of Chemistry.

this speciic example, CNTs are dispersed in polycarbonate, an engineering polymer) [75, 85]. Equivalently, the low-frequency complex viscosity diverges with |�*| ∼ 1/�. The evolution of structural properties of the nanocomposites as a function of CNT concentration follows a typical sigmoidal dependence [75, 85, 86]. Figure 6.15b displayed the variation of complex viscosity |�*| as a function of nanotube content for a series of polycarbonate/CNT nanocomposites, where the different regimes are apparent [85]. At low CNT concentration (i.e., Ø < Øc ), individual CNTs act as dispersed, isolated objects, and the mechanical properties (in this case |�*|) are expressed as a perturbation due to the dispersed objects of the matrix properties (described by Guth’s

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modiication of Einstein’s viscosity relationship) [87]. Close to and beyond the geometrical percolation of the nanotubes, Ø ≥ Øc , the development of the percolative network occurs, and the resulting network superstructure dominates the mechanical response and structural properties following typical power-law scaling with concentration (Ø − Øc ). At high concentrations, on the other hand, the addition of nanotubes results in the aggregation of the tubes and weakens the composition dependence of the reinforcement. The striking characteristic in the semidilute regime is the emergence of an elastic nanotube network, which is often inluenced by CNT microstructure, such as its dispersion state, network structure, aspect ratio, and orientation state apart from its concentration. Signiicant research has been reported on the inluence of CNT microstructure, such as its dispersion state, network structure, aspect ratio, and orientation state apart from its concentration on the rheological properties of the polymer/CNT composites [88–95]. Rheological property measurement under suspension state of epoxy nanocomposites illed with 0.5 wt% of pristine MWCNT revealed that storage (G′ ) and loss modulus (G′′ ) determined by frequency sweep method are of two orders of magnitude higher especially at low-frequency region for the suspension prepared by ultrasonication (sample B) in comparison to epoxy/MWCNT suspension prepared by magnetic stirring (sample A) (Fig. 6.16a). Relatively better dispersion of MWCNT in epoxy composites prepared by the ultrasonication is attributed to the presence of microaggregates with sizes in the range of 1–3 μm along with some separated MWCNTs (TEM result, Fig. 6.16b), whereas larger aggregates with sizes ranging 1–500 μm exist in the epoxy systems prepared by magnetic stirring (TEM result, Fig. 6.16c). Another interesting observation is the formation of rubbery plateau in the storage modulus (G′ ) with a higher value of loss modulus (G′′ ) at low frequencies and a crossover of storage modulus G′ at higher frequencies for epoxy/MWCNT suspension prepared by ultrasonication (Fig. 6.16a) [89]. According to Fan and Advani, appearance of Newtonian rubbery plateau of G′ at low frequencies is an indication of the development of an entanglement or network in the liquid. Presence of large aggregates of MWCNT in epoxy/MWCNT suspension behaves more like particle suspension (sample A), which in turn exhibits low low resistance (lower viscosity and G′ ), when compared to the epoxy/MWCNT suspension having microaggregates as well as separated MWCNTs in the system (sample B). They corroborated the frequency-dependent rise of storage (G′ ) and loss modulus (G′′ ) and its crossover at higher frequencies for epoxy/MWCNT suspension prepared by ultrasonication to the rise in elastic component due to the formation of interconnecting MWCNT network from the well-separated MWCNT in the epoxy system [89]. Similar trend is observed in steady shear viscosity (�), which showed signiicant rise at lower shear rates of epoxy/MWCNT suspension prepared by ultrasonication, when compared to epoxy system prepared by magnetic stirring [89]. The effect of the aspect ratio of the MWCNT on the rheological property of epoxy nanocomposites was also investigated by Fan and Advani by using the acid-treated MWCNT for nanocomposite preparation. Acid treatment of MWCNT resulted in a signiicant reduction in the aspect ratio (� = 0.025 × 103 ∼ 0.1 × 103 ) when compared to pristine MWCNT (� = 0.5 × 103 ∼ 103 ). According to their observation, storage and loss

258 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES 1000

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0.01000 1000

100.0

Ang. frequency (rad/s) (a)

MWNT aggregates

MWNT

0.2 µm

(b)

0.2 µm (c)

Figure 6.16 (a) Frequency dependence of storage (G′ ) and loss modulus (G′′ ) of epoxy-MWCNT suspension (0.5 wt%) prepared by magnetic mixing (sample A) and ultrasonication (sample B), TEM images of MWCNT in epoxy using (b) ultrasonication and (c) magnetic stirring. Reproduced from Ran et al. [89] with permission of AIP Publishing.

modulus (G′ & G′′ ) of low aspect ratio MWCNT-illed epoxy nanocomposites are relatively lower in the range of frequency in comparison to the high aspect ratio MWCNT-illed epoxy system, and this fact is attributed to the relatively better dispersion in the former compared to the latter. Yokozeki et al. [90] studied the effect of weight average CNT length prepared by ball milling on the shear viscosity of epoxy composites, and they corroborated a signiicant decrease in shear viscosity with increasing CNT length. On contrary, Song and Youn [91] reported that a well-dispersed MWCNT in epoxy matrix showed a decrease in G′ , over the range of frequency, when compared

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to the less dispersed state. They claimed that the MWCNT agglomerates in the poorly dispersed epoxy nanocomposites act as large particles as if higher iller loading were present. The agglomerates trap polymer resin in the void between CNTs, and the nanocomposites behave as if it had lower volume fraction of polymer matrix. This contradictory report could be explained by the presence of different dispersion microstructures as shown in Figure 6.17. Song and Youn [91] also observed that the poorly dispersed epoxy/MWCNT nanocomposites showed higher shear viscosity in comparison to the well-dispersed epoxy system and they corroborated stronger non-Newtonian behavior in the former compared to the latter. Chatterjee and Krishnamoorti [92] corroborated that CNT exists as mass fractal networks (fractal dimension in the range of 2–3) with hierarchal morphologies in polymer solution (Fig. 6.18). A schematic of the network structure conjectured and veriied by experiments in semidilute dispersions of CNTs in a polymer is shown in Figure 6.18a. Using ultrasmall and small-angle neutron scattering techniques, they revealed that the CNTs in a polymer matrix are bounded by the percolation event (at the lower limit) and the isotropic–nematic transition (at the upper limit) in the semidilute regime (Fig. 6.18b) [93]. The average loc size (R) is found to be the order of a few microns (typically � critical ), the stress relaxation behavior exhibits a strain softening with the shape of the relaxation spectrum being preserved, suggesting the applicability of time–strain separability (i.e., G(t, �) = G(t) × h(�), where G(t) is the linear relaxation modulus and h(�) is the damping function); (iii) For still higher deformations (� ≫ � critical ), the shape of the relaxation spectrum is no longer preserved and time–strain superposability is no

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longer valid. Chatterjee and Krishnamoorti [75, 93] reported the strain amplitude-dependent relaxation curve for SWCNT-based PEO nanocomposites (�SWNTs = 0.7 vol%, Ø/Ø c ∼7.0, PEO MW = 8k) (Fig. 6.20). Beyond percolation, that is, Ø > Øc , the elastic shear modulus increases with increasing CNT loading: G′ 0 ∼ Ø� . Concurrently, the shear sensitivity of the stress relaxation behavior and the underlying shear sensitivity of the structural elements increase with increasing CNT loading with the critical strain for the onset of nonlinear behavior scales as � critical ∼ Ø−� . These observations suggest that with increasing 106 100

104

h(γ)

G(t) (dynes/cm2)

γ≤ = 0.003 0.10 0.15 0.30 0.50 0.80 1.00

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100 γlocal

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Figure 6.20 (a) Representative stress relaxation behavior for CNTs loading � = 0.7 vol% in PEO (Mw = 8000 Da) as a function of the applied bulk strain amplitude. For low-amplitude strain (� ≤ 0.003 where � critical = 0.003), linear behavior is observed followed by a time–strain superposable zone (gray curves, 0.003 ≤ � ≤ 0.03). At higher strain amplitude (� > 0.03), time–strain superposability is violated (black curves). (b) Damping function h(�) required for the time–strain superposition for different nanocomposites is plotted against the applied or bulk strain (� bulk ). Deviation from h(�) = 1.0 marks the onset of nonlinearity. With increasing nanotube loading, an earlier onset of nonlinear response (i.e., lower � critical ) is observed. (c) The local strain dependence of h(�). The onset of the shear thinning is observed at � local ∼ 0.1 and is similar to other nanocomposite systems with short-range interactions. Therefore, at and around 10% deformations, the nanocomposite network starts to low. Reproduced from Chatterjee and Krishnamoorti [75] with permission of Royal Society of Chemistry.

264 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES

CNT loading, the polymer nanocomposite gets stiffer and more fragile [75, 93]. For dispersions of CNTs in PEO, 3 ≤ Ø/Øc ≤ 10, Chatterjee and Krishnamoorti reported � = 4.3 ± 0.6 and � = 2.3 ± 0.2 [93]. For fractal networks well above the percolation threshold (� ≫ �c ) where the interactions between the locs dominate over those within a loc (i.e., the strong link regime), the concentration scaling exponents for the elasticity and critical strain can be expressed as � = (D + db )/(D − df ) and � = (1 + db )/(D − df ), where db and df are the backbone and fractal dimensions of the network, respectively, and D is the value of the Euclidian dimension [97]. For many CNT dispersions, db is found to be ∼1.0, indicating that CNTs are rod-like objects, at least on a local length scale, in these nanocomposites [93]. The fractal dimension (df ) of the nanotube network deduced from the rheological measurements conirms mass fractal network and is in good agreement with those obtained from independent neutron-scattering measurements [93]. These internally consistent scaling of G′ 0 and � critical with nanotube concentrations indicate that (i) the weak and relatively short-range interactions between nanotubes and multiple pathways between percolating paths dominate the network properties, and (ii) the tube–tube bonding, rather than bending or stretching, is the origin of network elasticity observed in such nanocomposites. On the other hand, the shear sensitivity of the network structure captured through the damping function, h(�), when scaled by the concentration shift factor [98], f(Ø), collapses onto a single master curve (Fig. 6.20b,c) [� local = � bulk f(Ø)]. The concentration shift factor is deined as f(Ø) = G′ (�, Ø)/G′ (�, Ø = 0) = G′′ (�, Ø)/G′′ (�, Ø = 0) = 1 + 0.67(�Ø/100) + 1.62(�Ø/100)2 . Such a form for the concentrationdependent shift factor explicitly accounts for the change in the bulk “linear” viscosity due to the dispersion of anisotropic objects. However, extension of this notion to describe the scaling of the nonlinear deformation in such nanocomposites suggests that the effective deformation of the suspension of particles in this intermediate regime of strain amplitudes is “afine.” Mathematically, it suggests that for Ø ≫ Øc , concentration scaling of any linear memory function can be written as M0 (t, Ø) = f(Ø)M0 (t, Ø = 0) [75]. Therefore, the factorized nonlinear memory function for self-similar particle network appears to be consistent with the concentration scaling of the material function [99]. In fact, such a local strain controlled deformation is valid for fractal systems dominated by weak short-range interaction [75], whereas it fails where long-range interactions [100] (due to ionic, H-bonding, and polymer-bridged gels) dominate the development of structure. Finally, the time–temperature–composition superposition suggests that above the percolation threshold, both the linear and nonlinear viscoelasticity are dominated by the network superstructure. In fact, the nonlinear viscoelastic regime can be broadly divided into two regimes. In regime 1, the network deformation is reversible and the superposition principle holds. In contrast, in regime 2, the deformation is irreversible or permanent and the recovery process is extremely sluggish [75]. 6.3.2.2.2 Steady Shear Properties The steady shear response of polymer/CNT nanocomposites has important consequence on the potential processability of the materials. In this context, the steady shear viscoelastic behavior of various

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polymer/CNT nanocomposites with CNT concentrations in the semidilute regime has been critically reviewed in this chapter. Considering the production chain starting from melt mixing to the extruded semiinished goods or injection-molded plastic parts, Alig et al. [101] reported elaborately the rheological responses of polymer/CNT composites, which in turn depend on the iller network and also corroborated its inluence on the mechanical and electrical properties. To achieve polymer/CNT composites with enhanced electrical conductivity, the initial agglomerates (Fig. 6.21a) of the iller have to be irst well dispersed in the polymer matrix (Fig. 6.21b). During the second processing or shaping step (extrusion, injection molding, compression molding), the inal iller network is formed by secondary agglomerates or clusters (Fig. 6.21c), which then determines the electrical properties. It has been experimentally established that the so-called secondary agglomeration of CNT can occur in the quiescent melt as well as under shear deformation (Fig. 6.21d,e). The secondary agglomeration leads to the formation of inhomogeneous conductive iller networks (including “hierarchical iller structures”) and is considered to be a key process for understanding the dependence of electrical conductivity on thermal and rheological prehistory (Fig. 6.21f). Elastic networks such as those formed by CNT dispersions in a polymer matrix are expected to exhibit a yield stress and best evidenced through their steady shear behavior (Fig. 6.22a) [75, 102]. For CNT concentrations much in excess of the percolation threshold (Ø ≫ Øc ), application of steady shear (from rest) typically results in a stress overshoot (independent of the polymer matrix itself), which equilibrates to a steady-state value (� ∞ ) at long times. Note that overshoot responses of the stress, resulting from the elastic network of the CNTs, are absent, when Ø < Øc . In fact, this claim is further supported by a calculation of a nondimensional Peclet number that is greater than 1 and indicates that convective transport dominates the dynamic processes and that shear rate controls the structure. The Cox–Merz rule, which provides numerical relation between steady shear viscosity (�) at comparable shear rates/frequencies and dynamic viscosity (�*), do not quantitatively agree for CNT suspensions in a polymer matrix (Fig. 6.22b) [103]. Although the linear complex dynamic viscosity, �*, represents the quiescent or near-quiescent-state structure, the steady shear viscosity, �, represents the steady-state structure at a ixed shear rate during shear low. A good agreement between � and �* is observed at low shear rates, suggesting that this may be a useful way to measure low viscosities at low shear rates. On the other hand, � is almost two to three orders of magnitude lower in comparison to �* at higher concentrations and at higher shear rates. Although the failure of the Cox–Merz rule has been observed for many systems, including in some cases monodisperse polymers [104], the breakdown of the Cox–Merz rule for these nanocomposites (while being obeyed for the polymer itself) suggests a breakdown of the superstructure when large displacements are imposed on them during steady shear low [75]. It is hypothesized that the network superstructure under steady shear, initially, rearranges locally to accommodate the displacement [75, 102]. The stress increase is a manifestation of the structural changes that result from the aggregation due to

266 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES

1 µm

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Figure 6.21 TEM images of different MWCNT arrangements in a polycarbonate matrix: (a) initial agglomerates; (b) well-dispersed MWCNTs; and (c) secondary agglomerates. (d, e) Time-dependent conductivity for initially agglomerated and well-dispersed composites of MWCNT (0.6 vol%) in PC under steady shear deformation (d�/dt = 0.02 s−1 for 1 h) and during quiescent annealing after shear at 230 ∘ C (inset: schematics show the state of nanotube dispersion and the measuring cell with the sample). (f) Schematic representation of the differences between the conductivity (“electrical network”) and rheological properties (mechanical active iller network): The shaped nanotubes are represented by black lines and the polymer chains by gray lines. To symbolize the contact resistance, an “electrical equivalent circuit” was taken, whereas the viscoelastic coupling between CNTs via polymer chains is represented by a “dash pot” for local friction and an “entropic spring.” Reproduced from Alig et al. [101] with permission of Elsevier.

RHEOLOGICAL PROPERTIES OF POLYMER/CARBON NANOTUBE COMPOSITES

0.3 1.0

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Figure 6.22 (a) Representative transient shear stress response obtained during start-up of steady shear measurements for an SWCNT–PEO dispersion (�/�c = 5.0). For all shear rates, the stress data exhibit an initial overshoot arising from the shear-induced cluster aggregation, and in the long time, the network breaks to reach a steady state. Solid lines are model its to the experimental data as described in Ref. [101]. Reproduced from Chatterjee and Krishnamoorti [102] with permission of American Chemical Society. (b) Comparison of the complex and steady shear viscosities as a test for the Cox–Merz rule. The nanocomposites fail to obey the Cox–Merz rule presumably because of an alteration in the mesoscale structure during steady low. Reproduced from Chatterjee and Krishnamoorti [102] with permission of American Chemical Society.

collisions of clusters and formation of new bonds across clusters [75, 102]. For times greater than the time corresponding to the maximum in the stress, the fractal network breaks and the effective stress supported by the network reduces. Thus, the overshoot stress, or the maximum stress (� max ), is analogous to a yield stress beyond which the network starts to low [75]. The time required to attain the maximum stress (tmax ) is independent of CNT loading and only a function of shear rate [102]. Therefore, the shear stress data when scaled in terms of the network yield stress and are plotted against a dimensionless shear strain collapse onto a master curve [105]. For strains beyond the maximum shear stress, the fractal network breaks up (bonds are broken) and the system lows until a steady shear viscosity is obtained. The steady-state low behavior is governed by an establishment of equilibrium between bond-breaking and bond-formation processes [106]. Despite extensive rheological property measurements to corroborate the properties of polymer/CNT composites, there is a lack of systematic study on melt low instabilities, which usually occurs in extrusion processing of polymer/CNT composites. The optimum throughput condition for extrusion processes of polymer/CNT composites will be limited by the appearance of these instabilities. It has been shown that the melt low instabilities are reduced by increasing the amount of CNTs although without a quantitative evaluation about this effect [107]. By using a capillary rheometer with a novel detection system for melt low instabilities and two polyethylenes having

268 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES

different topologies (polyethylene with long-chain branching, PE-LCB; polyethylene with short-chain branching, PE-SCB), Palza et al. [107] characterize the melt low instabilities, namely, spurt, sharkskin, and gross melt fracture in polymer/CNT composites with varying MWCNT amount ranging from 0.05 to 12 wt%. The shear rate for the onset of the spurt instability decreases with increasing loading amount of MWCNT in the PE-LCB matrix (Fig. 6.23a). Similarly, the effect of the MWCNT on the sharkskin instability of polyethylene/carbon nanotube (PE-SCB/CNT) composites processed at a shear rate of 472 s−1 has been investigated by Palza et al. [107]. Morphological characterization of the extrudates using SEM revealed a reduction in sharkskin instability at low CNT content, whereas it increases at higher loading amount (Fig. 6.23b–e) and they corroborated it to the physical interaction between the polymer and nanoiller. Alternatively, the bulk distortion due to the melt fracture instability at high shear rate (1054 s−1 ) slightly reduced on loading MWCNT in the polymer matrix (Fig. 6.23g–i).

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Figure 6.23 (a) Flow curve for PE-LCB and its composites with high amount of MWCNTs measured at 190 ∘ C (arrows indicate the onset of the spurt instability); (b–e) SEM images showing the effect of MWCNTs on the surface morphology of PE-SCB composites processed at a shear rate of 472 s−1 (under these conditions, the samples develop sharkskin instability); (f–i) SEM images showing the effect of MWCNTs amount on the surface morphology of PE-SCB composites processed at a shear rate of 1054 s−1 (under these conditions, the samples develop gross melt fracture. Insets in (b) and (d) demonstrate detailed morphological changes occurring with increasing MWCNTs amount). Reproduced from Palza et al. [107] with permission of Elsevier.

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6.3.2.2.3 Elongational Flow Properties In contrast to the shear low, there are only a few reports on the extensional low behavior of polymer/CNT composite melts or suspensions [108, 109]. It is necessary to understand the elongational low behavior in order to develop proper processing conditions for the production of nanocomposite ibers, ilms, bottles using melt spinning, ilms blowing, and blow molding techniques. The transient elongational behavior of polymer/CNT melts was irst studied by Handge and Pötschke [108], who had previously also investigated the orientation of PC/MWCNT composites by melt spinning [109]. In their study, Handge and Pötschke [108] compared the transient elongational viscosity of pure and 2 wt% MWCNT-loaded PC composites at 190 ∘ C, measured using uniaxial elongational rheometer, and revealed that the addition of CNT moderately modiied the time dependence and the value of the elongational viscosity. The authors corroborated that the stress of the PC matrix is much higher than the stress caused by the CNTs so that small stresses are necessary to deform the CNT network arrangement. They also discussed that this result in elongational low compares well with the high-frequency behavior of polymer/CNT composites where the complex modulus (G*) is mostly determined by the viscoelasticity of polymer matrix. Pötschke et al. [110] observed enhanced elongational viscosity at various strain rates on loading 5 wt% MWCNT in polypropylene (PP) in comparison to pure PP. Signiicant improvement in elongational viscosity led to an enhanced melt strength and to an improved foamability of the PP matrix with the inclusion of nanotubes. Handge and Pötschke [111] reported transient recovered stretch (�r ) of polycarbonate/carbon nanotube (PC/CNT) composites, which is composed of two contributions: (i) the molecular driven recovery to an isotropic coiled state and (ii) at larger timescales, the surface tension driven recovery. Loading of CNTs in polymer matrix does not lead to signiicant variation in the average retardation times of the macromolecules. On inclusion of CNT in the PC matrix, the recovered stretch values does not vary signiicantly at lower Hencky strain rates, whereas it is dramatically reduced when the Hencky strain rates are equal or higher than 0.3 s−1 in comparison to the �r values of the PC. The authors pointed out that their recovery data indicate that the arrangement of CNTs produced a yield stress and prohibited large extensions of the macromolecules during extension [111]. 6.3.2.3 Shear-Induced Orientation During composite processing, such as injection or compression molding, the suspension undergoes a modest amount of shear as it is pushed into a mold. The shear low has been known to orient the short ibers in the direction of the shear or stretching. Shear-induced alignment of ibers in the shear direction exhibits lower viscosity when compared to randomly oriented iber suspension as they experience lower resistance [112]. This phenomenon could be extended to the nanoscale in polymer/CNT suspensions, where the shear-induced alignment of CNTs could contribute to the shear-thinning behavior of polymer/CNT composites [113]. Du et al. [114] created different degrees of PMMA-aligned CNT suspensions and found that suspensions with aligned CNTs showed lower G′ and

270 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES

G′′ . Shear low will also reduce the viscosity as the alignment of CNT increases, thus exhibiting shear-thinning behavior. Alternatively, Yang et al. [115] reported temperature-dependent rheological properties under steady shear conditions for MWCNT core–shell nanostructures consisting of MWCNT as hard cores and hyperbranched poly(urea-urethane) (HPU) trees as soft shell (Fig. 6.24i). TEM results revealed the successful coating of HPU on MWCNTs with an average polymer thickness as high as 14.5 nm (Fig. 6.24ii). They have reported the variation of viscosity with shear rates at two different temperatures (20 ∘ C and 80 ∘ C), and they corroborated that these HPU grafted MWCNT core–shell structures exhibited typical shear-thickening behaviors at low shear rates and behaved as Newtonian

Hyperbranched polymers

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MWCNT Hyperbranced Poly (urea-urethane) Intramolecular H-bond Intermolecular H-bond Proton-donor Proton-acceptor

Figure 6.24 (i) Schematic representation of hyperbranched poly(urea-urethane) (HPU)-grafted MWCNT. (ii) TEM image of HPU-grafted MWCNT. (iii) Solution rheology of HPU-grafted MWCNT at two different temperatures (20 and 80 ∘ C). (iv) Rheological mechanism of the HPU-functionalized MWCNTs in their solutions. Reproduced from Yang et al. [115] with permission of American Chemical Society.

RHEOLOGICAL PROPERTIES OF POLYMER/CARBON NANOTUBE COMPOSITES

271

luids at high shear rates on carrying out the experiments at low temperature (20 ∘ C). Alternatively, these core–shell nanostructures showed typical shear-thinning behavior at low shear rates and behaved as Newtonian luids at high shear rates on carrying out the experiments at high temperature (80 ∘ C) (Fig. 6.24iii). They have corroborated this contradictory behavior at two different temperatures to the (i) interplay of intramolecular and intermolecular hydrogen bonding at varying rates and (ii) disentanglements and orientation of polymer chains and MWCNTs as shown in schematic reaction mechanism (Fig. 6.24iv). Alignment or orientation of the CNT can be done by shear or elongational low ields or electrical ields [75]. In this chapter, we limit our discussion on orientation of CNTs or CNT locs under shear low and elongational low ield and their impact on different rheological properties such as shear stress, normal stress, and so on [75]. In semidilute concentration regime, under weak shear, CNTs aggregate along the vorticity direction (Fig. 6.25i). The aggregation of the CNT in the vorticity

Top plate

(i)

500 µm

Flow

Helical band (HB)

(ii)

Isotropic CNT aggregates Moving bottom plate

Figure 6.25 (i) The formation of cylindrical locs aligned along the vorticity direction. The micrograph was collected for shear rate = 0.5 s−1 , gap = 180 μm, and time = 600 s. Direction of low is vertical as indicated. For this optical micrograph, vorticity alignment of CNT locs is clearly visible. (ii) Schematic diagram of the growth mechanism. A nucleus rotates within the steady shear and captures initially isotropic aggregates of nanotubes. The nanotubes are then wound helically to form a cylinder with long axis perpendicular to the direction of low. Reproduced from Ma et al. [108] with permission of Springer. (iii) Photos of extrudates of pure iPP and CNT/iPP melt (7.4% mass fraction) at 210 ∘ C under different shear rates. The diameter and length of capillary die were 1 and 32 mm, respectively. iPP at 100 s−1 , mean diameter of 1.34 mm (a); iPP at 500 s−1 , mean diameter of 1.46 mm (b); iPP at 1000 s−1 , mean diameter of 1.67 mm (c); iPP at 2000 s−1 , mean diameter of 1.82 mm (d); 7.4% mass fraction CNT/iPP at 100 s−1 , mean diameter of 1.18 mm (e); 7.4% mass fraction CNT/iPP at 500 s−1 , mean diameter of 1.38 mm (f); 7.4% mass fraction CNT/iPP at 1000 s−1 , mean diameter of 1.54 mm (g); 7.4% mass fraction CNT/iPP at 2000 s−1 , mean diameter of 1.66 mm (h). The gray circle in the igure shows the size of the capillary die for comparison. The minimum scale of the ruler at the downside of the igure is 1 mm. The relative measurement uncertainty of the extrudate diameter was estimated to be about 1%. Reproduced from Xu et al. [116] with permission of American Chemical Society. (iv) Models about deformations of low aspect ratio CNT/iPP and high aspect ratio CNT/iPP networks under steady shear. Reproduced from Xu et al. [116] with permission of American Chemical Society.

272 PROCESSING AND RHEOLOGICAL BEHAVIORS OF CNT/POLYMER NANOCOMPOSITES (iii)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(iv) Low aspect ratio CNT

Low shear rate

High shear rate

High aspect ratio CNT

Low shear rate

Figure 6.25

High shear rate

(Continued)

direction is observed when the interloc or interparticle attractions are comparable to hydrodynamic forces. Therefore, there is a inite range of shear rates over which the vorticity alignment of CNT locs is realized. If the shear rate is too high, then the CNT aggregates break up and align along the low direction. Rheo-optical measurements suggest that the origin of cylindrical locs and their vorticity alignment are primarily a mechanical and geometrical phenomenon. The gap height (h) at which shear is applied inluences both the formation kinetics and the inal diameter of the cylindrical structure. The timescales over which such anisotropic structures form depend on both the shear rate and gap height (h) where small h and high �̇ facilitate their formation. Ma et al. [117] reported a schematic growth mechanism of

RHEOLOGICAL PROPERTIES OF POLYMER/CARBON NANOTUBE COMPOSITES

273

vorticity band structure induced by MWCNTs aggregates in the epoxy matrix due to its alignment perpendicular to the shear low (Fig. 6.25ii). As an alternative, Hobbie and coworkers proposed that inelastic instability of nanotubes is responsible for vorticity alignment [118]. Analogous to Weissenberg’s rod-climbing effect [119], for soft aggregates surrounded by a less viscous luid in low–gradient plane, hoop stress leads to elongation in the vorticity direction along with somewhat compression in the radial direction of the cylinder. However, this argument does not provide any insight into the role of coninement on the growth of the structure and dependence of structural dimensions on the gap between the plates. The vorticity alignment of CNT locs is associated with a negative normal stress difference, where the effect has been explained through a competition between low-induced orientation and thermodynamically driven nematic state [118]. Furthermore, for CNT dispersions in low viscosity media, there is a timescale associated with the −ΔN development (equivalent to vorticity elongation timescale), which decreases with increasing shear rate and gap (h) between the plates [117]. In contrast, there is an instantaneous development of −ΔN in MWCNT-based polypropylene (PP) nanocomposites under shear low [116, 119]. Positive ΔN is observed when the CNT loading in PP is below the percolation threshold, � < �c , and it becomes large and negative for the CNT loading greater than percolation threshold (� > �c ). While the underlying causes behind the observation of −ΔN in PP/MWCNT are not completely clear, it is assumed that both the large-scale deformation of the network (� > �c ) and the local-scale deformation of individual tube are responsible. Physically, the network structure gets distorted under shear low where the network tilts rather than elongates due to presence of stiff nanotubes (Fig. 6.22iii,iv) [118]. It has also been reported that the sign of ΔN depends on the CNT aspect ratio in PP/CNT nanocomposites. For low aspect ratio CNTs, the volume fraction for network formation is high, and in that case the mesh size (� ∼ Ø−1/2 ) is too small to accommodate rotational distortion [116]. Therefore, −ΔN is only observed for tubes with high aspect ratio or a good state of dispersion. One remarkable consequence of negative ΔN is the impact on nanocomposite processing. Extrusion of high molecular weight polymers results in die-swelling, which is an outcome of their positive normal stress difference. On the contrary, polymer/CNT nanocomposites with an overall negative ΔN exhibit die contraction behavior (Fig. 6.25iii,iv). Although the reduction in extrudate swell is well known for polymers with inorganic illers, the speciic importance in polymer/CNT nanocomposites lies in the iller-loading content. Generally, for spherical particles, this is observed at a high volumetric iller loading (>0.3 vol%) [75, 120]. In contrast, such a reduction is observed for CNT-based polymer nanocomposites at much lower loading (100 ∘ C) or molecular size of the individual components. These blends exhibit unique phase separation mechanisms such as aggregating nucleation and growth (ANG), coalescence induced viscoelastic phase separation (C-VPS), transient gel induced viscoelastic phase separation (T-VPS), and so on, other than the nucleation and growth and the spinodal decomposition mechanisms [5]. The individual components are weakly interacting (weakly negative �); hence, the thermorheological complexity in this particular blend is due to the change in the conformational entropic contribution to the polymer miscibility [6, 7]. In this work, the phase separation behavior in off-critical blends of PS/PVME (90/10, wt/wt) has been studied in the presence of MWNTs by shear rheology [8, 9] and the morphology development was evaluated from POM (polarized optical microscopy). The study is quite intriguing and unique in this case as the faster component (i.e., PVME) has higher molecular weight compared to that of the slower component (PS).

7.2 7.2.1

EXPERIMENTAL METHODS Materials and Sample Preparation

Atactic polystyrene (PS) of weight average molecular weight (Mw ) of 35 kDa and PDI of 2.0 was procured from Sigma Aldrich (USA). Polyvinyl(methyl ether) (PVME) of 80 kDa was obtained from Tokyo Chemical Industry Co., Ltd (Japan) and was obtained as a 30% solution in water. Extreme care was taken to prevent the oxidation of PVME. This was conirmed by the transparent nature of the sample that becomes slight yellowish on oxidation [10]. Analytical grade solvents were obtained commercially and used as received. Glass transition temperature of PS and PVME are 70∘ C and −26∘ C, respectively. Neat PS/PVME blends 90/10 (wt/wt) was prepared by shear mixing (Ultra-Turrax® T25) in toluene at 8000 for 45 min. In the case of blends with nanoparticles, the MWNTs were initially dispersed in toluene using a probe sonicator (Hielscher UP400S). The composite solution was then dried under vacuum at room temperature for 2 days and at 60 ∘ C for 2 days. PVME in water forms an LCST

THEORY BACKGROUND

281

system, in which phase separates at 37 ∘ C [11]. Hence, complete drying of PVME was ensured by its constant weight and it was checked prior to blend preparation. 7.2.2

Characterization

POM was carried out using Olympus BX51, Japan. It is itted with an automated hot stage (Linkam THMS600). The samples were spin coated (2 wt/vol% in toluene) on a glass coverslip. The morphological development as a function of temperature was recorded using a CCD camera (ProgRes C3, Germany) mounted on the microscope. The samples were scanned at a heating rate of 1 K/min from 80 ∘ C. A stress-controlled Discovery Hybrid Rheometer (DHR-3 from TA Instruments) was used to study the viscoelastic properties of the blends. The geometry used in the measurement was parallel plate (25 mm diameter) with 1 mm gap. To detect the onset of phase separation in the blends, isochronal dynamic temperature ramp measurements at a heating rate of 0.5 K/min were performed from the single homogeneous phase (80 ∘ C) to the phase-separated regime (160 ∘ C). A constant frequency (0.1 rad/s) in the terminal regime was chosen. The strain amplitude used was within the linear viscoelastic regime. In order to prevent thermal degradation or adsorption of moisture, all measurements were carried out under nitrogen atmosphere.

7.3

THEORY BACKGROUND

The variation in the viscoelastic properties in the vicinity of phase separation has been studied by certain scaling laws proposed by Fredrickson–Larson [2] and Onuki [12]. The integration over a vector space gives the dynamic storage and loss moduli as given in Equations (7.1) and (7.2).

G′′ =

2kB T� k0 15� 2 ∫0

{

}2 �S0 −1 (k) dk �k2 }2 { k6 S0 2 (k)�(k) �S0 −1 (k) dk �2 + 4�2 (k) �k2

k T�2 k0 k6 S0 2 (k) G = B 2 15� ∫0 �2 + 4�2 (k) ′

(7.1)

(7.2)

Here, �(k) = k2 /S0 k(�), S0 (k) is the static structure factor, �(k) is the Onsager coeficient, k is the wave vector, and kB is the Boltzmann coeficient. The value of structure factor S0 (k) was found out by de Gennes [13] by a mean-ield approximation method in the random-phase approach. Later, Ajji and Choplin derived expressions for G′ , G′′ , using the value of structure factor obtained by the above method. It is given as

UNUSUAL PHASE SEPARATION IN PS RICH BLENDS

282

1 1 1 = + − 2� S0 (k) ΦN1 g1 (k) (1 − Φ)N2 g2 (k)

(7.3)

where Φ is the volume fraction of polymer 1, Ni denotes the number of statistical segments, and gi (k) is the Debye function and the formula for the Onsager coeficient �(k) calculated by Binder: 1 1 1 = + �(k) Φa1 2 W1 g1 (k) (1 − Φ)a2 2 W2 g2 (k)

(7.4)

where ai denotes the statistical segment length of the species i and Wi is the orientation rate given by Wi = 3�kB T∕�i (7.5) where � i is the monomeric friction coeficient. The integrals in Equations (7.1) and (7.2) converge, and structure factor decreases to zero at the terminal regime. Hence, storage and loss modulus in the terminal regime are calculated as 1∕2

⎧ ⎛ 2 )1∕2 R2′ ⎞⎫ ( � �02 kB ⎪ ⎪ 1 ⎜ Rg1 ′ g 2 01 ⎟ Gcf (�) = + + [2(� s − �)]−5∕2 ⎬× ⎟ ⎜ 1920� ⎨ 3 ∅N (1 − ∅)N ∅N (1 − ∅)N 1 2 1 2 ⎪ ⎝ ⎠⎪ ⎭ ⎩ (7.6) T�2

−1∕2

⎧ )1∕2 2 R2′ ⎞⎫ ( � �02 kB T� ⎪ 1 ⎛⎜ Rg1 ⎪ g 2 01 ′′ ⎟ + + [2(� s − �)]−5∕2 Gcf (�) = ⎬ × ⎟ ⎜ 240� ⎨ 3 ∅N (1 − ∅)N ∅N (1 − ∅)N 1 2 1 2 ⎪ ⎝ ⎠⎪ ⎭ ⎩ (7.7) where � s is the interaction parameter at the spinodal, Rgi is the radius of gyration for 2∕6 the species i, R2gi = Ni ai . Equations (7.6) and (7.7) have been used to derive a ratio that eliminates monomeric friction coeficient and (� ). This ratio is also supposed to show a frequency dependency. [ 2 ] ′ a2 2 −3 G 30� a1 + (� S − �) ∕2 = 2 ′′ k T 36Φ 36(1 − Φ) G B

(7.8)

As these equations are valid in the terminal regime, the frequency dependence in the terminal regime is given as G′ ∼ �2 and G′′ ∼ �. The interaction parameter is given as � = A + B∕T

(7.9)

THEORY BACKGROUND

283

Hence, a relation of the following nature is obtained (

G′′ 2 TG′

where C is given by

( C=

) 2∕3

45� kB

B = C

) 2∕3 [

(

a21 ∅

1 1 − TS T

+

)

a22

(7.10) ]

1−∅

(7.11)

The homogeneous regime is characterized by the linear region at the higher temperature and the intercept on the 1/T axis is taken as the Ts . The spinodal decomposition temperature Ts is calculated by taking the reciprocal of the intercept to the 1/T ( ′′ )2∕3 G axis from the plot of G×T versus (1/T). The length scale of the concentration luctuation is called correlation length. The data obtained from isochronal temperature ramp measurements can be used to understand the contribution of the correlation length (�) of the concentration luctuation to the evolving stresses and can be derived from the isochronal temperature sweeps. The � is given by �=

−1 a′′ [Φ(1 − Φ)(� − � S )] ∕2 6

(7.12)

where � is the interaction parameter, � S is the interaction parameter at spinodal temperature (Ts ), and a′′ is the characteristic length. The individual length segments are given by the equation: a2 a22 a′′ 2 = 1+ Φ(1 − Φ) Φ 1 − Φ [ ] 1∕3 k T G′ �= B 30� G′′ 2

(7.13) (7.14)

The relation between � and the structure factor is given by S(k) =

S(0) 1 + � 2 k2

(7.15)

The total scattering structure factor for an interacting polymer blend is given by inverse additivity of the scattering structure factor. It is given as 1 1 1 = + − 2� S(q) NA �A SA (q) NB �B SB (q)

(7.16)

By putting in the values of scattering length and other constants, the above equation can be modiied as kN 2� 1 1 + − = S(q) NA �A �A SD UA NB �B �B SD UB �0

(7.17)

UNUSUAL PHASE SEPARATION IN PS RICH BLENDS

284

Expansion of the above equation in the Ornstein–Zernike forms S(q) = S(q = 0)∕[1 + � 2 (T, �)q2 ] � 2 (T, �) =

b2 36

[�A �B (� s − �)−1

(7.18) (7.19)

In the vicinity of phase separation, �(T, �) may have a scaling form as often observed in critical luctuation phenomenon: �(T, �) = �(�)�−n

(7.20)

where � = (T−Tc /Tc ) and n = 1/2 as per mean-ield model. 7.4 7.4.1

RESULTS AND DISCUSSION Rheologically Determined Demixing Temperature

The demixing temperature in the PS/PVME blends was obtained by performing an isochronal temperature sweep measurement. The phase separation, in general, is characterized by a distinct nature for its various low parameters. The phase separations in block copolymers and the polymer blends are specially characterized by discontinuities in the dynamic parameters such as complex modulus, complex viscosity, and so on [14]. This was proposed by Bates [15] for explaining the drastic change in the viscoelastic properties associated with the order–disorder transition in block copolymers. The same method was adopted by various groups in determining the demixing temperature of PS/PVME blends [16–19]. The change in the slope of the G′ with temperature plot gives us an idea about the concentration luctuation induced, and the formation of the interface will contribute to an additional elasticity to the system and thereby an additional relaxation mechanism. The dynamic elastic modulus (G′ ) as a function of temperature for the control PS/PVME (90/10 wt/wt) neat blend and blend with 0.25% and 0.5% MWNTs are shown in Figure 7.1a–c. The temperature ramp was performed from the homogeneous region to temperature above the demixing temperature to ind the demixing temperature. G′ decreases with an increase in temperature in the homogeneous region, similar to the case of a homopolymer. This is due to thermally assisted Brownian motion. In the vicinity of phase separation temperature, the mobility is overpowered by the thermodynamic effects and, thereby, resulting in an increase in the G′ . It has been observed that G′ is more sensitive for learning about phase separation. The loss modulus (G′′ ) shows a similar trend as that of G′ , however, with a lag. The responses associated with these changes are of elastic nature because of the stresses generated due to interfacial driven elasticity. PS/PVME is a dynamic asymmetric blend and thereby characterized by an abrupt jump in the storage modulus value due to the increased concentration luctuation associated with these samples. The present analysis is to understand the effect of MWNTs on the concentration luctuation and demixing in the off-critical blends. The demixing temperature in

RESULTS AND DISCUSSION

285

105

Gʹ (Pa)

PS/PVME 90/10

104

103 95

100

105

(a)

110

115

120

125

130

135

Temperature (°C)

105

Gʹ (Pa)

PS/PVME 90/10 with 0.25% MWNT

104

90

100

(b)

110 120 Temperature (°C)

130

105

Gʹ (Pa)

PS/PVME 90/10 with 0.5 wt% MWNT

104

100 (c)

110

120

130

Temperature (°C)

Figure 7.1 Isochronal dynamic temperature ramp performed at � = 0.1 rad/s, 1% strain with 0.5 ∘ C/min heating rate for (a) 90/10 PS/PVME neat blends and blend with (b) 0.25 wt% MWNT and (c) 0.5% MWNT.

286

UNUSUAL PHASE SEPARATION IN PS RICH BLENDS

off-critical compositions is far off from the critical temperature, and the concentration luctuation is weaker compared to that of the critical compositions. The demixing in off-critical blends of PS/PVME (90/10) is characterized by a deviation from the linear proile of storage modulus unlike the case of critical compositions such as 60/40 PS/PVME [9, 20]. This is similar to the phase separation in dynamically symmetrical blends like PMMA/SAN wherein the correlation length of the concentration luctuation is weak [9, 20]. The rheological phase separation temperature is taken as the deviation from the linearity in G′ versus temperature proile. So, according to this analysis, the phase separation temperature has not altered with the addition of MWNTs. The correlation length is calculated near the critical point from the rheological data using Equation (7.14). The variation in � for the control blends and with 0.25 and 0.5 wt% MWNTs is given in Figure 7.2a–c. The correlation length rapidly increases due to the increase in the local concentration luctuation. The temperature where the correlation length increases rapidly can hence be regarded as the binodal temperature. It has been observed that the apparent binodal temperature (Tb ) almost remained unaltered in presence of MWNTs. In Figure 7.3, the reciprocal square of correlation length (� −2 ) is plotted versus temperature for various blends investigated here [21]. A straight line interpreting � −2 = 0 can be taken as the spinodal decomposition temperature. It has been found that the addition of MWNTs did not alter the spinodal decomposition temperature. Due to the absence of any speciic interaction in these particles, the polymer conformational behavior is only affected by the geometric constraints on the surface of MWNTs. By the addition of particles, the Flory Huggins theory can be modiied by adding a compositional penalty on the composition variation [22]. The conformational relaxation of the individual chains is retarded by the transient network structure. This is purely of a dynamic origin as it not related to any equilibrium constraints. Long-range spatial correlation induces highly cooperative motions causing slow entangled dynamics. 7.4.2

Evolution of Morphology in the Blends in Presence of MWNTs

The effect of MWNTs on the evolution of morphology is studied in situ in a POM as the blends transit through the metastable and the unstable regimes of the phase diagram. It has been studied that ilm thickness has an effect on the phase separation of the sample. Hence, the thickness was chosen such a way as to nullify its effect on the mechanism of phase separation [23, 24]. The samples were homogeneous at the start of the scan at 80 ∘ C. As the temperature increases, phase separation is characterized by the appearance of smaller domains. The contrast seen in the images is due to the difference in refractive index of each of phases: (PS = 1.592, PVME = 1.467 with respect to air). Hence, PVME appears brighter in comparison to PS [25]. This has been explained in detail in our previous works [26, 27]. PVME molecules get preferentially adsorbed to the MWNTs despite being more polar than PS [28]. PVME has high dispersive solubility parameter PVME (� d = 7.1 MPa compared to that of PS (� d = 1.1 MPa1/2 )

RESULTS AND DISCUSSION

30

287

PS/PVME 90/10 + 0.25 wt% MWNT

25

ξ (Å)

20

15 Tb 105 °C 10

5

90

100

110 120 Temperature (°C)

130

(a) 25

PS/PVME 90/10 + 0.5 wt% MWNT

20

ξ (Å)

15

10

Tb 110 °C

5

0

100

110

120

130

Temperature (°C) (b)

Figure 7.2 Variation of correlation length as a function of temperature for (a) 90/10 PS/ PVME blend with (b) 0.25 wt% MWNT and (c) 0.5% MWNT.

even though the solubility parameter of PVME (� = 22.6 MPa /2 ) is comparable to that of PS (� = 19.2 MPa1/2 ). This is the reason for the selective localization. Figure 7.4a1 –a3 shows the POM images of neat PS/PVME (90/10, wt/wt) blends, with 0.25% MWNTs (Figure 7.4b1 –b3 ) and 0.5% MWNTs (Figure 7.4c1 –c3 ). It is interesting to note that in earlier studies, viscoelastic phase separation has been reported as the dominant mechanism in off-critical compositions, unlike the one investigated here with lower molecular weight of PS compared to that of PVME. 1

UNUSUAL PHASE SEPARATION IN PS RICH BLENDS

288 5

PS/PVME 90/10

1/ξ2 × 103

4 3 2 1 Ts 110 °C

0 2.56

2.58

2.60

2.62

1/T × 103 K–1

(a)

6 PS/PVME 90/10 + 0.25 wt% MWNT

1/ξ2 × 103

4

2

0

Ts 114 °C 2.58

2.60

2.62

2.64

2.66

1/T × 103 K–1

(b) 10

PS/PVME 90/10 + 0.5 wt% MWNT 8

1/ξ2 × 103

6 4 2 0 2.550 (c)

Ts 114 °C 2.575

2.600 1/T × 103 K–1

2.625

2.650

Figure 7.3 Reciprocal square correlation length versus 1000/T for (a) 90/10 PS/PVME neat blends and blend with (b) 0.25 wt% MWNT and (c) 0.5% MWNT.

RESULTS AND DISCUSSION

289

a1

115 °C

a2

130 °C

a3

165 °C

b1

115 °C

b2

130 °C

b3

165 °C

c1

115 °C

c2

130 °C

c3

165 °C

Figure 7.4 POM images for 90/10 PS/PVME blend with and without MWNTs during early (a1 , b1 , c1 ); intermediate (a2 , b2 , c2 ), and late (a3 , b3 , c3 ) stages of phase separation. The top row is for neat 90/10 PS/PVME blends. The middle and the bottom rows are for 90/10 PS/PVME blends with 0.25 and 0.5 wt% MWNTs, respectively. (The darker phase represents PS and the brighter phase corresponds to the PVME phase; scale bar corresponds to 20 μm).

In dynamically asymmetric blends, the phase separation generally leads to the formation of a transient gel of the slower component. VPS takes place in these cases because of the long relaxation time of the slow component, which cannot catch up with the deformation rate of the phase separation itself and often manifest into interconnected network-like structure especially in slower component-rich phase. In this study, the molecular weight of the slower component-rich phase is signiicantly lower than the faster component (PVME). The latter is observed to form sponge-like structure. In the control blends, as the temperature increases, microscopic droplets of PS start to appear. The brighter PVME phase is also seen evolving around the PS phase. It is interesting to observe that in the intermediate stage (130 ∘ C) of phase separation, PVME, despite being the minor component, forms an interconnected network. PVME is more viscoelastic than PS and forms a transient gel-like structure that later coarsen to form droplets, which is very different from the usual viscoelastic phase separation. At 115 ∘ C, the cases of control blend as well as the blends with MWNTs (0.25% and 0.5%) have been characterized by the presence of droplets of PVME. So it can be concluded that the thermodynamic demixing temperature is more or less

290

UNUSUAL PHASE SEPARATION IN PS RICH BLENDS

unaltered in the presence of MWNTs. However, it is observed that the addition of 0.25% and 0.5% MWNTs has delayed the phenomenal transient structures and, more importantly, retained them even in the late stage of phase separation. AFM studies on certain other compositions of the same blend show [9] that MWNTs are selectively localized in the PVME phase. Hence, selective localization of MWNTs in the PVME phase can alter the elasticity of the component and thereby effectively change the mechanism of phase separation in the blend. Both the control blends and the blends with 0.25% MWNTs were characterized by the transient gel-like behavior in the intermediate stage of the phase separation. Even though both of these cases were characterized by the formation of the intermediate network, there is a difference in the size of the domain that is mentioned as the viscoelastic length. The intermediate stage is called a volume-shrinking stage, and it was observed that a mechanical stress is generated in the weaker part of the network that further resulted in break up to form droplets. It was observed that in the case of MWNTs, the formation of the interconnected network and also thereby the subsequent break up to form droplets was signiicantly delayed although the rheologically determined demixing temperature did not alter much (discussed in the next section). It was studied that the addition of nanoparticles can alter the viscoelasticity of the blend and the evolving morphology [29]. It is envisaged that transient gel formation, break up to form droplets, and so on are signiicantly inluenced by the interaction between the constituent polymers and can be quantiied by rheological measurements [30]. The interesting rheological responses and the morphological development in this blend are due to the difference in the relaxation time of the two polymers. Tanaka [31] in his works has explained about the anomalous phase separation phenomenon exhibited by dynamic asymmetric blends. These principles were applied in the PS/PVME blends by Xia et al. recently [32]. According to these studies, the characteristic length of the morphology developed during the phase separation has been related to the elasticity as G ∼ kB Tm ∕a3

(7.21)

� ∼ a2 ∕Da ∼ 6��a3 ∕kB T

(7.22)

where Tm is the characteristic ordering temperature (can be considered as phase separation temperature), “a” is the characteristic length scale (can be related to the domain size), � t is the characteristic timescale, Da is the diffusion constant, kB is the Boltzmann constant, T is the absolute temperature and, � is the viscosity. The faster and the slower component in the dynamic asymmetric blend causes an obvious size discrepancy between them, which is of the order 103 –104 . The characteristic length that was mentioned in the above section is of a pure rheological origin. Diffusion and viscoelastic effects are the factors that contribute to the characteristic length. A relationship between viscosity and � ve is given as, �(k) = �s +

�m 2 k2 1 + �ve

(7.23)

REFERENCES

291

This equation was proposed in the case of polymer in a solvent, where �s and �m are given as solvent and macroscopic viscosity respectively. This can be further approximated as (7.24) �ve = (�m ∕�s )1∕2 �b here � b is the blob size [33, 34]. The viscoelastic length in a polymer–polymer solution depends on the viscosity ratio of the components. The selective localization affects the viscosity of the phases and thereby the � ve . It is clear that there is a direct relation for the blend morphology to the low behavior of the blend. So, the overall blend behavior can be very well analyzed by rheology.

7.5

CONCLUSIONS

Viscoelastic properties and the evolution of morphology in off-critical blends of PS/PVME have been studied here systematically. It has been observed that at this particular composition, the blends exhibit unusual demixing characterized by a network formation of the faster component in the intermediate stages of phase separation, as observed from POM. This phenomenal transient microstructures altered signiicantly in the presence of MWNTs. The dynamic low parameters and also various mean-ield approximation methods suggest no signiicant change in the demixing temperature in the presence of MWNTs. There is a scope of an interesting investigation by altering the surface phenomenon of MWNTs (by grafting polymer of varying chain length), and the change in the viscoelastic properties can be assessed. ACKNOWLEDGEMENTS The authors gratefully acknowledge Department of Science and Technology, India, for the inancial support.

REFERENCES 1. Fredrickson GH, Larson RG. J Chem Phys 1987;86(3):1553. 2. Larson R, Fredrickson GH. Macromolecules 1987;20(8):1897. 3. Shenoy AV. Rheology of Filled Polymer Systems. Springer Science & Business Media; 1999. 4. Utracki LA. Polymer Blends Handbook. Kluwer Academic Publishers; 2002. 5. Yeganeh JK et al. RSC Adv 2014;4(25):12809. 6. Schneider HA. Polymer 1989;30(5):771. 7. Tanaka H. Adv Mater 2009;21(18):1872. 8. Xavier P, Bose S. Phys Chem Chem Phys 2014;16(20):9309.

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Xavier P, Bose S. J Phys Chem B 2013;117(28):8633. Petri HM et al. Macromol Chem Phys 1995;196(5):1453. Suzuki M, Hirasa O. Responsive Gels: Volume Transitions II. Springer; 1993. p 241. Onuki A, Taniguchi T. J Chem Phys 1997;106(13):5761. De Gennes PG. Scaling Concepts in Polymer Physics. Cornell University Press; 1979. Ajji A, Choplin L. Macromolecules 1991;24(18):5221. Bates FS. Macromolecules 1984;17(12):2607. Gharachorlou A, Goharpey F. Macromolecules 2008;41(9):3276. Khademzadeh Yeganeh J et al. RSC Adv 2012;2(21):8116. Xia T et al. Macromol Chem Phys 2010;211(20):2240. Kapnistos M et al. Macromolecules 1996;29(22):7155. Yu W et al. Polymer 2011;52(12):2693. Han CC et al. Polymer 1988;29(11):2002. Karim A et al. Macromolecules 1998;31(3):857. Wang H et al. Langmuir 2001;17(9):2857. Müller-Buschbaum P et al. Macromolecules 2000;33(13):4886. Polios IS et al. Macromolecules 1997;30(15):4470. Xavier P et al. Phys Chem Chem Phys 2014;16(39):21300. Bharati A et al. J Phys Chem B 2014;118(8):2214. Yurekli K et al. Macromolecules 2004;37(2):507. Xavier P et al. Phys Chem Chem Phys 2014;17:14972–14985. Sadiku-Agboola O et al. Mater Sci Appl 2011;2:30. Tanaka H. arXiv preprint arXiv:1307.1518; 2013 Xia T et al. RSC Adv 2014;4(63):33431. Tanaka H. Phys Rev Lett 1993;71(19):3158. Takahashi Y et al. Macromolecules 1994;27(22):6476.

8 RHEOLOGY AND PROCESSING OF POLYMER/POSS NANOCOMPOSITES Krzysztof Pielichowski, Tomasz M. Majka and Konstantinos N. Raftopoulos Department of Chemistry and Technology of Polymers, Cracow University of Technology, Krakow, Poland

8.1

INTRODUCTION

The organic–inorganic (O–I) nanohybrid materials are novel composite materials consisting of both organic and inorganic components, chemically interconnected with each other. Among the most promising O–I nanoparticles, we ind the polyhedral oligomeric silsesquioxanes (POSS). They are an important topic of research in the past few years, especially as reactive illers in polymer nanocomposites. Many application areas have emerged for this kind of materials, including biomaterials [1–3], dielectric materials [4–8], catalysts [9–11], organic light-emitting diode devices [12–14], and fuel cell and battery membranes [15–17]. Polymer nanocomposites attract large scientiic and technological interest because of their considerably improved properties as compared to the conventional composites [18–20]. These nanomaterials can be produced with both thermoplastic and thermoset polymers as matrices [21, 22] and a variety of nanoparticles such as carbon nanotubes, nanosilica, or nanoclays [23–25] as illers. Thermoset nanocomposites ind their use mostly in the shipbuilding and coating industry as well as in the automotive or packaging sectors. Thermoplastic polymer nanocomposites can be obtained in several ways; however, the most common and eficient method is melt intercalation [21–29]. Rheology and Processing of Polymer Nanocomposites, First Edition. Edited by Sabu Thomas, Rene Muller, and Jiji Abraham. © 2016 John Wiley & Sons, Inc. Published 2016 by John Wiley & Sons, Inc.

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By every approach, a critical concept for the successful production of polymer nanocomposites is the dispersion of the particles, often involving the grafting of polymer friendly groups – the “compatibilizers” – on the surface of otherwise polymer-repellent structures. Hybrid organic–inorganic particles, such as the POSS, intrinsically possess such organic groups, with the additional advantage that they can be properly tailored to each speciic matrix. A step further is that the organic groups may not only be physically soluble to the matrix but also bond on its chains, providing an organic–inorganic hybrid material with truly molecular dispersion of the rigid nanoparticles. This unique property differentiates POSS from conventional nanoillers [30–34] and has attracted to them a lot of attention from the scientiic community. The incorporation of POSS in thermoplastic or thermoset polymers can affect the thermal, oxidative, and dimensional stability of many polymer resins, resulting in improvements in properties, including increased glass transition temperature Tg, decomposition temperature Td , and mechanical modulus M, reduced lammability, and increased gas permeability. Depending on the number of POSS functional groups, different architectures of POSS/polymer composite can be obtained. A variety of copolymers with POSS units attached as dangling blocks to the polymer backbone have been synthesized [35–45] by monofunctional and difunctional POSS. The resulting materials represent a new category of polymers characterized by the presence of bulky POSS nanoparticles. The common feature of these materials is an increase in Tg and thermal stability as the POSS content increases. Incorporation of multifunctional POSS into polymer systems has been investigated with different polymers [46–52]. In these cases, single-phase polymer networks with molecularly dispersed POSS are often formed with the O–I moieties acting as a chemical cross-links. But no deinite effect of POSS on network properties has been established. The Tg may increase [52], remain steady [46], or – strikingly – decrease [49, 50], despite the cross-linking. The rubbery modulus increases due to a high cross-link density, and thermal stability increases with POSS content, although, often due to changes in the overall morphology of complex polymeric systems such as polyurethanes, the mechanical modulus may as well decline [52]. A more convenient method of incorporating POSS into organic polymers is physical blending. Since each POSS molecule has a Si8 O12 core covered with alterable organic side groups, it is believed that better dispersion may result from increased interaction of compatible side groups and the host polymer [53–55]. Blanski et al. [55] studied the dispersion of POSS in polystyrene (PS). They found that by altering the organic side groups to more compatible phenethyl groups, POSS molecules can be fully dispersed into PS. The surface hardness of the PS/styrenyl POSS ilm increased by 30%. Molecularly dispersed POSS behave as a weak cross-linker in polymer melts and accelerate the crystallization rate of the host polymer [56]. Matejka et al. [49] studied the effect of POSS with various topological locations in a network on its structure and properties. These authors incorporated monofunctional, multifunctional, and nonfunctional POSS into epoxy networks and observed that POSS pendant on a network chain showed a strong tendency toward aggregation and crystallization. The crystalline domains thus act as physical cross-links, leading to very

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strong reinforcement. The mechanical properties are affected mainly by POSS–POSS interactions while the POSS-network chain interactions are of minor importance. POSS have dimensions comparable with the size of segments of polymer chains and can restrict their mobility at the molecular level. Restraining the mobility of polymer chains leads to elevation of the glass transition temperatures and to an enhancement of stress–strain characteristics. In addition, POSS molecules have shells of a nearly spherical shape and are able to effectively reduce the viscosity of polymer systems; that is, their action is similar to that of plasticizers. The introduction of POSS into the side units of polymer chains can suppress the ability of POSS molecules to aggregate and to form nanocrystals [46, 57]. The aggregation of POSS is prevented by long organic spacers that link the POSS molecules to polymer chains, as well by the size of the POSS molecules themselves, which impedes the formation of crystalline regions. In the case of differences in the reactivity of functional groups of the POSS and the organic monomer, the aggregates formed in the polymer matrix can contain a considerable amount of unreacted POSS molecules [58]. As a result, the majority of POSS molecules that aggregate into nanocrystals in this polymer are not bound to the polymer and do not exert a signiicant effect on the thermomechanical characteristics of the samples. The incorporation of POSS molecules has an effect on the structural organization of polymer chains. A change in the relative amount of POSS units in poly-�-caproamide leads to alteration in the structure of polymer crystals with the prevalence of �-or � forms [59]. DSC studies showed that the crystallinity of PEO is reduced with an increase in the amount of POSS units. At Mn values of 1000 and 2000 for PEG, the DSC curves do not exhibit the PEO melting endotherm [60]. It has been observed that the presence of POSS facilitates a considerable depression of the melting point of the crystalline phase of the organic constituent [36] and leads to Tg elevation for the amorphous phase [61]. In the case of POSS with bulky peripheral groups, the complete suppression of the segmental mobility of organic moieties can take place. Along with the glass transition temperature, the onset temperature for the degradation of the polymers is increased as a result of incorporation of POSS [62, 63]. The incorporation of POSS molecules substantially enhances the thermo-oxidative stability of polyoleins owing to the formation on the polymer melt surface of a layer of POSS nanoparticles, preventing the underlying polymer layers from degrading. So far, it has been shown that polymer nanocomposites containing POSS have been synthesized by various techniques including chemical grafting [64], copolymerization [40, 65], and melt blending [66, 67]. In this chapter, we will focus on the latter approach. We will start by describing the various POSS particles available at laboratory or industrial scale. Then, we will explore the main processing methods of polyolein, polyamide, polyurethane, and other polymer matrices such as melt blending, extrusion, injection molding, and compression molding. The design of a successful processing protocol is closely related to the rheological properties of the processed nanocomposite; therefore, it is essential to understand the effects of POSS on the rheological properties of the matrices. This will be the topic of last section before we conclude with a summary and an outlook to future research.

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8.2

POLYHEDRAL OLIGOMERIC SILSESQUIOXANES

The term silsesquioxane refers to the molecules, whose chemical structure follows the basic composition of Rn Sin O1.5n . POSS are polyhedral silsesquioxane molecules featuring a Si atom at each vertex of a polyhedral cage. The shape of the cage is typically cubic (n = 8), but cages of 6–12 vertices are often reported. The Si vertices are interconnected with – O – linkages. The R-group – the so-called “vertex group” – is attached to each of the Si atoms and is pretty much tailored to the speciic application. The vertex group may be as simple as a hydrogen atom, or as an inert organic group such as alkyl, phenyl, or isobutyl, or even carry a reactive group such as hydroxyl, carboxyl, or an unsaturated bond. The nature of those cage substituents determines to a large extent the compatibility of the particle to the matrix, possible chemical reactions, and thus the inal structure of the nanocomposite. As expected, it will directly or indirectly alter, to an extent, the mechanical, thermal, optical, and other physical properties [68–77]. The molecular architecture of silsesquioxanes can be classiied into four categories (Fig. 8.1): random structure (a), ladder structure (b), caged structure (c, d, e), and partial caged structure (f) [77, 79–96]. The caged structures – both complete and partial – are deined as POSS. POSS cages are typically synthesized by hydrolytic condensation. The polyhedral Si–O core of completely condensed POSS cages is usually formed by a hydrolytic condensation of trifunctional monomers of the type XSiY3 where X is a suitable organic substituent that will form the vertex group and Y is a highly reactive substituent such as Cl or an alkoxy [30]. Incompletely condensed cages with OH groups in the “missing” corner have also attracted some interest both as standalone particles,

HO R R R Si O Si O R Si RO Si O O O R O O Si Si Si SiO O R OH RO HO OH HO OR O O R Si Si Si Si O O R O R Si Si O Si Si O O O R R HO R R

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(e) T12

R Si OH R O O OH Si SiO R OH O Si O R O Si O R O Si Si O R R

(f)

Figure 8.1 Structures of POSS. (a) Random structure, (b) ladder structure, (c–e) cage structures, and (f) partial cage structure. Reproduced from Kuo et al. [78] with permission of Elsevier.

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to be introduced “as-is” in matrices, and as precursors for fully condensed cages with a differing eighth vertex group. In this case, of particular interest are reactions of trisilanols with ligand-deicient trivalent-metal complexes because of the inability of these trisilanols to support trigonal planar coordination environments that usually lead to more complex structures [30]. The capping with a suitable eighth group is easily achieved by a subsequent reaction with an XSiY3 compound as described earlier. 8.2.1 General Interactions between Polymer Matrices and POSS Particles POSS, like other highly symmetric molecules, including dendrimers, interacts with the polymer host in the three dimensions of the surrounding space. From the microscopic point of view, the characteristic size of the POSS particle of ∼1.5 nm can be compared to the dimensions of polymeric segments, and the incorporation of POSS moieties into linear polymer chains and/or polymer networks will modify the local molecular interactions, molecular topology, and segmental mobility. These microand nanoscopic modiications are manifested in the macroscopic physical properties and performance, such as mechanical modulus, strength, glass transition temperature, thermal stability, and dimensional stability [97]. Regardless of the preparation approach, the dispersion and self-assembly of POSS moieties inside the host polymer are the key factors affecting the inal physical properties. The dispersion depends on the thermodynamic interactions between POSS and the polymer matrix. If the POSS–polymer interaction is favorable compared to the POSS–POSS interaction, POSS moieties will disperse well; otherwise POSS will aggregate. Unlike a illed system or blend, however, proper functionalization of POSS may limit aggregation due to covalent attachment to the polymer backbone or an appropriate choice of nonreactive vertex groups may prevent aggregation beyond a scale of approximately one radius of gyration [98–102]. Naturally, the resulting effect on physical properties will vary with the POSS dispersion or the aggregation level. Therefore, it is of primary importance to understand the nanostructure–property–processing relationships for given systems in order to successfully tailor properties to intended applications [98–102]. Most inorganic silicas or ceramics are immiscible in organic polymer systems because of low level of speciic interactions within these organic/inorganic hybrids and the negligibly small combined entropy contribution to the free energy of mixing. Speciic intermolecular interactions are generally required to enhance the miscibility of polymers and inorganic particles; such interactions include hydrogen bonding, dipole–dipole interactions, and acid/base complexation [103]. Depending on the number of POSS functional groups, four architectures of polymer/POSS nanocomposites can be obtained (Fig. 8.2) [104]: • Nonreactive POSS molecules dispersed in a polymer matrix as iller. • Bead type – a POSS core with two reactive functional groups is incorporated into the backbone of a polymer.

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Nonfunctional POSS

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Figure 8.2 General polymer/POSS architectures. Reproduced from Kuo et al. [78] with permission of Elsevier.

• Pendant type – these are POSS molecules with a single reactive functional group and can be polymerized as a monomer or co-monomer. • Network or cross-linked type – these are synthesized by the polymerization of a POSS cage containing multifunctional polymerizable groups that will form 3D networks. Copolymerization, grafting, and blending are useful methods yielding polymer–POSS multifunctional hybrid materials with intermediate properties between those of the organic polymers and of ceramics [34, 68].

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8.3

299

PROCESSING OF POLYMER/POSS NANOCOMPOSITES

The processing routes of typical polymer nanocomposites reinforced with 1D, 2D, or 3D nanoillers, and their technological characteristics were described in Ref. [105]. As it was mentioned earlier, in this chapter, we focus on polymer/POSS composites processing, rheology, and interactions between polymer matrix and iller.

8.3.1

Polyolein/POSS Nanocomposites

Polyoleins can be divided into three main types: polyethylene, polypropylene, and polyisobutylene, which are subdivided into several grades. From these “big three,” the greatest demand is for the irst two materials. Polyethylene (PE) is a consumer polymer, with a variety of applications, including polymer ilms, containers, pipes, toys, and others. Polyethylene has valuable properties in addition to its low cost, such as the ease of recycling, nontoxicity, good processability, and good chemical resistance. Signiicant efforts have been done to improve its properties by using different types of illers including POSS. Reactive or nonreactive POSS have been incorporated into polyethylene by different methods; however, only few attempts to produce PE/POSS nanocomposites by melt blending have been reported. In the following, we will describe recent studies on the incorporation of POSS into polyethylene matrix via melt blending using different types of machines [106–108]. Polypropylene (PP) has also many processing advantages, for example, excellent cost/performance balance, versatile properties, good processability, and low density. For these reason, it is widely used in many applications. However, more than 50% of all manufactured polymer resins need to be illed with inorganic illers to get the desired properties. Polypropylene is often combined with different illers such as calcium carbonate, clay, and carbon black. Recently, POSS particles have also been incorporated into PP via chemical incorporation or physical blending [109–112]. PE/POSS and PP/POSS nanocomposites have been prepared by using an internal mixer (Fig. 8.3a) or a single-screw extruder (Fig. 8.3b). The internal mixer is used for uniform mixing of small amounts of components in the laboratory scale. This is the one of the two melt blending methods to obtain PE/POSS nanocomposites. The heart of mixer is a mixing chamber, where mixing or shearing is made by two counter-rotating horizontal rotors. Before mixing, all materials should be dried in an oven. Drying temperature should not exceed 80 ∘ C in accordance with appropriate Materials Data Sheet to avoid thermal degradation. For a mixing chamber with 45 cm3 volume, about 35 g of the components in total (polyoleines, POSS) can be inserted and blended for about 10–15 min, at an angular speed of 50–100 rpm and at different mixing temperatures in the range of 175–270 ∘ C [113, 114]. PE/POSS and PP/POSS nanocomposites can be also prepared by melt blending in a single-screw extruder with L/D value of, for example, 20:1 [115–117], and with screw speed of 80–100 rpm [105, 115–117]. POSS nanoparticles should be partially melted at 220–270 ∘ C in polyolein matrices [21, 105, 115–120]. The

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Figure 8.3 Schematic presentation of polymer/POSS composites melt blending using (a) internal mixer and (b) screw extruder.

average temperatures of feed zone, compression zone, metering zone, and die for the polyolein/POSS nanocomposite samples prepared are reported in Table 8.1. The extrudate, after passing through a cooling bath, is fed into a conveyor belt and pelletized to a length of 0.4–5 mm by a pelletizer so that it can be easily compressed and injection molded at a later stage. The typical parameters for injection and compression molding are summarized in Table 8.2. The processability by injection molding and compression molding of polyolein/POSS nanocomposites was compared together. During injection molding, torque, and load of the compounder motor, a measure of the pressure is generated

TABLE 8.1 Zone Temperatures of Extruder for Different Polyolein/POSS Nanocomposites [117–120]

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TABLE 8.2 Examples of Parameters of Injection Molding Carried Out by Boy 30A Injection-Molding Machine and Compression Molding [117–123] Polyethylene Injection molding in laboratory scale Zone 1 (∘ C) Zone 2 (∘ C) Zone 3 (∘ C) Nozzle (∘ C) Mold temperature (∘ C) Injection speed (%) Injection pressure (Bar) Back pressure (Bar) Back pressure time (s) Cooling time (s)

200 215 215 220 60 50 60–105 55–90 12–15 15 Polypropylene Compression molding in laboratory scale Press temperature (∘ C) 200 Preheating time (s) 480 Pressure time (s) 200–300 Inert atmosphere No Pressure (bar) 100 Cooling time (s) 300

Polypropylene 200 215 215 220 60 35 40 45 15 45

in the mixer, where the pressure is generated as a result of design of the mixer. For a constant volume of material compounded and a ixed screw speed, the pressure generated is proportional to the viscosity of material. The lower the pressure, the lower the viscosity, and the easier the material is to process. During compression molding, a preheated polymer composite is placed into an open, heated mold cavity. The mold is closed with a top plug and the pressure is applied to force the material to contact all areas of the mold. Throughout the process, heat and pressure are maintained until the polymer has cured. While the compression molding process can be employed nanocomposites with both thermosets or thermoplastics matrices. Most applications use thermoset polymer/POSS nanocomposites. Advanced composite thermoplastics can also be compression molded with unidirectional tapes or woven fabrics. Compression molding process of polymer/POSS nanocomposites is mainly used in order to improve barrier properties. The ilms subjected to the permeability tests are amorphous in order to discriminate the barrier effect of the illers and do not take into account the one of the crystallites. In PP nanocomposites, it has been observed that the permeability increases when the SiO2 particles are not compatibilized due to the formation of voids around the nanoparticles through which gases could freely evacuate [124–126]. Compression molding is considered as a large-volume and high-pressure processing method designed for molding complex, high-strength objects. And with its short cycle time and high production rate, many organizations in the automotive industry have chosen compression molding to produce parts.

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In the following, we will discuss melt blending of POSS in polyoleins. Joshi et al. prepared a system of HDPE/octamethyl POSS by melt mixing and investigated its rheology and viscoelastic behavior [113]. POSS particles act as lubricants at lower concentrations of 0.25% and 0.5% and decrease the viscosity of the polymer. This effect is related to the ine distribution of POSS molecules in the polymer matrix and to interactions between HDPE chains and POSS molecules, which lead to a decrease in the polymer chain entanglements. At higher concentrations (>2%), POSS starts aggregating and hinders the chain mobility and thereby increases the viscosity. Moreover, the rheological results showed that above 5% of POSS gelation occurs at low shear rate, while at low POSS, contents of 0.25% and 0.5% storage modulus improve signiicantly as compared to the pure polymer. It is suggested that POSS is dispersed in the amorphous phase of the polymer matrix, whereas the crystallinity decreases with a further increase in POSS content by 10% [113]. In 2007, Joshi and Butola studied the isothermal crystallization of HDPE-octamethyl POSS [114]. They observed that the POSS molecules are dispersed at the nanoscale up to 1% in the matrix and act as nucleating agent, while by increasing the POSS content, the molecules start to agglomerate forming POSS crystals. The researchers also claim that only when POSS is dispersed at the molecular level, it acts as a nucleating agent and affects the crystallization mechanism. Lim et al. melt blended high-density polyethylene (HDPE)/POSS functionalized by low concentrations of octamethyl, octaisobutyl, and octaphenyl group [115]. It was found that there is no big difference between the solubility parameters of POSS nanoillers and HDPE. The solubility parameters are much smaller for octaisobutyl-POSS than for the other types of POSS. From this, the authors assumed that there is better interaction between HDPE and octaisobutyl POSS. The thermal and morphological properties of the melt-mixed blends of high-density polyethylene/ethylene-vinyl acetate copolymer with octaisobutyl POSS were reported in Ref. [108]. Octaisobutyl POSS showed a different behavior depending on the loading. At low concentration (1%), the POSS particles formed a nanodispersion in the polymer matrix with average dimensions of 150 nm, while aggregation occurred at higher concentrations (5%), which indicates that the solubility limit of POSS is around 1%. On the other hand, the presence of EVA promotes the aggregation of POSS. Hato’s group studied the thermal and thermomechanical properties of LLDPE with three different amounts of octamethyl POSS, 5%, 7.5%, and 10% [127]. These nanocomposites were prepared by the melt mixing method using a batchmixer. The results showed that POSS was distributed homogeneously in micrometric scale in LLDPE, which led to improved elastic storage modulus at higher POSS concentrations because of the formation of 3D network-like structures. In 2011, Hato et al. reported the rheological properties of the melt-state viscoelastic properties of LLDPE illed with varying octamethyl POSS loading [128]. Frequency sweep tests showed no signiicant improvement in the storage and loss modulus in the presence of octamethyl POSS particles. Also the nanocomposites showed the characteristic behavior of liquid-like materials at which both moduli change with frequency. It was suggested that this behavior is related to the weak interaction between the LLDPE

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matrix and POSS particles, which results in lubrication of the polymer matrix in the molten state. However, the complex viscosity of the nanocomposites is almost the same in all POSS loadings, which is also related to the absence of the interaction between octamethyl POSS particles and LLDPE matrix [128]. Melt-mixed blends of polyethylene with octa(ethyloctadeca-10,13 dienoamide) silsesquioxane were recently reported by Nguyen and coworkers [123]. These blends were applied to paperboard by compression coating. The results showed micron-sized (10–20 μm) dispersion with the addition of 1–40% of POSS, and, furthermore, increasing the amount of nanocages caused continuous decrease in the melt low index. This indicates an increase in the melt viscosity of the nanocomposites. The mechanical properties of nanocomposites reduced with increasing POSS content. A number of interesting articles related to the preparation of PP/POSS hybrid materials by melt blending have been published over the past decade, aiming at improving polymer properties and understanding the structure–property relationships. PP/POSS nanocomposites are often produced by two competing methods, that is, reactive blending and physical melt blending [129–133]. Reactive blending has proven to be a key technology in the polymer industry and is regarded as an eficient method for the continuous polymerization of monomers and for the chemical modiication of existing polymers in the absence of solvents. Compared with the physical blending composites of PP/POSS, reactive blending composites have better mechanical and thermal properties [129]. The structure, morphology, crystallization, and melt behaviors are also changed because of the graft reaction. This reactive blending method is a simple and effective approach to prepare POSS-grafted polymers without rigorous reaction environment of polymers [129, 131]. Before blending, PP and POSS should be dried at 70 ∘ C under vacuum for about 12 h. Reactive mixture consists of three materials: PP, POSS, and a reactive component. In Ref. [131], 0.1 wt% of dicumyl peroxide (DCP) has been used as a reactive component. The mixture was blended at 180 ∘ C and 60 rpm for 8 min. THF or boiling xylene may be used as solvents to improve good distribution of iller and to provide an appropriate reaction medium. Then composite was removed and compression was molded in a press at 190 ∘ C for 20 min (preheat 15 min and then mold for 5 min), and inally cold-pressed to get samples for testing. Physically blended composites of PP/POSS were prepared without DCP but with a compatibilizer, which is usually a maleic anhydride grafted PP (PP-g-MA). The reactive blending composites were resolved in reluxing xylene, precipitated, and washed by acetone (alternatively, cold chloroform could be used), the precipitate is resolved and precipitated at least three times and dried at 80 ∘ C for 12 h and thought as POSS-grafted PP (POSS-g-PP) (Fig. 8.4) [131]. The effect of POSS carrying different alkyl substituents on the morphological and thermal properties of PP was studied in Ref. [110]. The results showed differences in the morphological properties of nanocomposites, prepared via melt blending, by increasing the alkyl chain lengths, which depend strongly on the chemical compatibility with the polymeric matrix. Microaggregates (10–20 μm) of octamethyl POSS appeared in the matrix, even at low loadings (3% and 5%). On the other hand, no

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(b)

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Figure 8.4 SEM images of PP/POSS composites: (a) physical blending composites; (b) reactive blending composites; and (c) POSS-g-PP. Reproduced from Zhou et al. [131] with permission of Elsevier.

POSS aggregates in the PP/octaisobutyl POSS nanocomposites were found. Instead, regular crystals with average dimensions of about 500 nm were formed. Pracella et al. [134] investigated the melt crystallization behavior in isothermal and nonisothermal conditions for the same PP/POSS nanocomposites with different alkyl substituents and varying amounts of iller (Fig. 8.5). They found that the length of the alkyl groups affects the nucleation activity of POSS, which, in turn, inluences the iller dispersion in the PP matrix. The results

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Figure 8.5 Polarizing optical micrographs of growing spherulites: (a) PP/OM3 ; (b) PP/IOB10 molten samples during isothermal crystallization at Tic = 130 ∘ C. Reproduced from Pracella et al. [134] with permission of John Wiley and Sons.

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showed low compatibility between PP and octamethyl POSS, the particles acted as nucleating agent on all loading amounts. On the contrary, octaisooctyl POSS retards the crystallization kinetics due to the ine dispersion of this iller in the matrix. In the case of octaisobutyl POSS, two different behaviors appear, which depend on the iller content in the matrix: at low loading (3%), the nanodispersion of the iller hinders the PP crystals growth; and by increasing the iller contents to 10%, it acts as nucleating agent. A further study on these nanocomposites was performed by Baldi and coworkers [67]. The results showed that the mechanical properties of the POSS nanocomposites are affected by the length of the POSS alkyl chains. The reinforcing action was observed for POSS particles carrying short alkyl chains such as octamethyl POSS. Reduction was observed in the mechanical properties with a decrease in Young’s modulus and the mechanical strength obtained in the presence of long alkyl chain such as octaisobutyl and isooctyl POSS. Furthermore, Zhou [135] prepared PP/octaaminophenyl POSS nanocomposites using PP-g-MA as compatibilizer. The size of POSS agglomerates was reduced from submicron size in the nanocomposites prepared without compatibilizer to nanometric size in the systems with compatibilizer. This enhancement in the dispersion is attributed to the interaction between the amine group of octaaminophenyl POSS and the carbonyl groups of PP-g-MA. The degree of crystallinity of PP decreases in the presence of octaaminophenyl POSS. It is assumed that the polymer chain mobility is retarded by octaaminophenyl POSS, which has a nucleating effect on the addition of PP-g-MA. Moreover, it was observed that the melting temperature increases as compared to that of the corresponding PP and PP/octaaminophenyl POSS. The rheology showed that the complex viscosity for the PP/PP-g-MA/octaaminophenyl POSS nanocomposites is lower than that of the PP/octaaminophenyl POSS nanocomposites with the same octaaminophenyl POSS content, and this might be due to the weak POSS–POSS interaction and interface slipping. The use of PP-g-MA as a compatibilizer considerably increases matrix/iller adhesion; however, the mechanical properties are in some examples only slightly improved in comparison with composites without compatibilizer. The interaction between POSS and the PP matrix in the presence of compatibilizer results in more eficient transfer of mechanical stresses, leading to more eficient distribution of mechanical efforts. The composites processed without PP-g-MA display rather unstable behavior under inert gas atmosphere, while in oxidative atmosphere, thermal degradation parameters show no signiicant variation [135]. Fina et al. [112] investigated the effect of three different organic groups (methyl, vinyl, and phenyl) in the POSS structure on the mechanical properties, thermal stability, and combustion properties of melt-blended PP/POSS nanocomposites. It was found that the addition of vinyl POSS leads to maximum increase in Young’s modulus, yield stress, and elongation at break due to the ine distribution of POSS in the matrix as well as due to the chemical interactions between polypropylene chains and the POSS organic groups. Moreover, incorporation of 5% methyl POSS results in a 15% reduction in Young’s modulus and yield strength values compared with the pure polymer, while the elongation at break remains unaffected. The reduction in mechanical properties is related to the aggregation of methyl POSS molecules, which act

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as weakening points in the polymer matrix. In the case of phenyl POSS, the results showed that POSS form aggregates in micron size at 5% POSS loading and decreases the mechanical properties with increasing POSS content. 8.3.2

Polyamide/POSS Nanocomposites

Polyamide (PA)/POSS nanocomposites can be prepared by several approaches: • physical melt blending using one type of PA matrix and POSS iller; • physical melt blending using two types of polymer matrices and POSS iller; • physical melt blending using one type of PA matrix and one type of POSS modiied clay; • solution mixing using PA pellets dissolved in solvent and POSS iller; • ine dispersion in the PA matrix by mixing �-caprolactam with silsesquioxane followed by lactam hydrolytic polymerization; • ine dispersion in the PA matrix by mixing �-caprolactam with silsesquioxane followed by lactam quasi-adiabatic anionic polymerization in bulk; • ine dispersion in the PA matrix by mixing �-caprolactam with silsesquioxane followed by lactam isothermal anionic polymerization in the bulk; • ine dispersion in the PA matrix by mixing �-caprolactam with silsesquioxane followed by lactam anionic suspension polymerization in quasi-isothermal conditions; 8.3.2.1 Physical Melt Blending Using One Type of PA Matrix and POSS Filler Dasari obtained PA/trisilanol phenyl POSS nanocomposites by melt blending method using a twin-screw extruder with L/D = 30 [136]. Extrusion process was performed within the temperature range of 210–245 ∘ C at screw speed of 300 rpm. The extruded pellets were oven-dried and then molded into standard 100 × 100 × 3 mm plates using a injection-molding machine with the barrel and mold temperatures maintained at 240 and 50 ∘ C, respectively. The holding pressure was 60 MPa, while the holding and cooling times were 10 and 25 s, respectively [136]. By the aforementioned procedure, the following materials were prepared: • • • •

neat polyamide-6; polyamide-6/POSS nanocomposite; polyamide-6/organoclay nanocomposite; polyamide-6/POSS/organoclay nanocomposite.

The good nanodispersion of the clay – with platelets oriented to the low direction – was not affected by the addition of POSS. The O–I particles, on the other hand, showed ellipsoidal domains along the low direction with major and minor axis ca. 200 and 100 nm, respectively. Interestingly though, some clay platelets penetrated the POSS domains. The introduction of POSS did not improve lammability as compared to the organoclay nanocomposite.

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Jeziórska et al. [121] reported that POSS particles were uniformly dispersed in polyamide-6 by melt blending in a twin-screw extruder (D = 42 mm, L/D = 6) at a barrel temperature of 230 ∘ C and a screw speed of 60 rpm. Incorporation of POSS promotes modiication of the polyamide-� crystal structure, resulting in an increase in crystallization temperature and the crystallization rate of the polyamide matrix. Mechanical tests showed that the presence of POSS resulted in increased strength and signiicantly improved elongation at break relative to that in the neat PA6. 8.3.2.2 Physical Melt Blending Using Two Types of Matrices and POSS Filler Poly(2,6-dimethyl-1,4-phenylene oxide) (PDPO)/polyamide-6 blend is a typical incompatible blend and PDPO has higher melt viscosity than PA6 [137, 138]. Co-continuous morphological structure can be obtained only at a high content of PDPO. It is considered that the blends with co-continuous morphology can exert the optimum eficiency of blend components [139]. Polystyrene or synthetic luorine mica was added to PDPO/PA6 blends in order to achieve continuous structure by adjusting the viscosity ratio [140, 141]. The addition of polystyrene makes the mechanical properties of the blends much worse, while the continuous structure of poly(2,6-dimethyl-1,4-phenylene oxide)/polyamide-6 blends reinforced with synthetic luorine mica was not always stable during melt mixing. The melt viscosity of polyamide can be increased by chain extension [142–144]. In order to increase the viscosity of PA6 to meet that of PDPO, POSS were introduced into these blends, which could lead to branching or even cross-linking of polyamide-6. With increasing content of POSS, the morphology of PDPO/PA6/POSS composites changed from droplet/matrix to continuous structure accompanied by phase inversion, which could be mainly attributed to the change in rheological behavior of blend components. POSS acted as an effective chain extension and cross-linking agent for PA6 and was mainly located in the polyamide phase of the blends. 8.3.2.3 Physical Melt Blending Using One Type of PA Matrix and One Type of POSS Modiied Clay Montmorillonite (MMT) is one of the most commonly used clay minerals. Its properties – high cation-exchange capacity, good swelling ability, and ease for modiication, make MMT a versatile iller in numerous composite materials [105, 145–148]. MMT is a useful platform that can be functionalized by, for example, POSS derivatives containing short alkyl ammonium chains. Systems with dual-surfactant modiied clays based on POSS with an additional alkylammonium surfactant are reported in the literature. Introduction of ammonium cations decrease the surface energy of inorganic silicate and increase the interlayer spacing, making thus intercalation possible [148–150]. Research has been conducted mainly on PA6-based nanocomposites with MMT [105, 145–148, 150–154], while relatively few studies on layered silicate nanocomposites have involved other polyamides, such as polyamide-11 [155, 156] and polyamide-12 [157–159]. Polyamide-12 possesses much longer aliphatic chains and a lower melting point and mechanical strength than PA6, but it shows good lexibility, low density, high

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impact resistance, chemical resistance, impermeability, and thermal stability [157]. Zhao et al. reported modiication of organo-montmorillonites by two types of POSS surfactants and also the combination of POSS and an alkylammonium-based second surfactant [160]. PA12/MMT nanocomposites were prepared by melt compounding. Two types of POSS-modiied montmorillonites (aminopropylisooctyl-POSS/MMT and octaammonium-POSS/MMT) were prepared via an ion-exchange process. Low exchange ratios were found for both POSS-modiied MMTs, which could be due to the rigidity and larger molecular size of POSS. 8.3.2.4 Solution Mixing Polyamide pellets were dissolved in triluoroethanol (TFE) for at least 24 h (1.0 g of polyamide in 20 ml of TFE). Next POSS was added to the solution and stirred for at least 48 h. After mixing, the mixture was transferred into an ultra-plate watch-glass and maintained at 25 ∘ C. Later on, the ilms were dried in a vacuum oven at 80 ∘ C for more than 12 h to allow the TFE solvent to evaporate and subsequently kept in a desiccators before use [161]. 8.3.2.5 Hydrolytic Polymerization In Rico’s work [162], polyamide was synthesized by hydrolytic polymerization at high temperature (270 ∘ C); mixtures of initiator, caprolactam, and POSS were introduced at room temperature into a glass polymerization vessel and kept at the polymerization temperature by placing the vessel in a heated aluminum block for 4 h. When the reaction was completed, the vessel was quickly cooled to room temperature under nitrogen stream. 8.3.2.6 Quasi-Adiabatic Anionic Polymerization in the Bulk A double-walled glass reactor was illed with caprolactam and immersed in an oil bath kept at the temperature of 155 ∘ C [162]. Initiator was formed in situ by the addition of NaH when caprolactam temperature was around 100 ∘ C. Finally, when the temperature of 155 ∘ C was reached, either heptaisobutyl-propylcarbamoylcaprolactam-POSS or cyclohexylcarbamoyl-caprolactam was added as the activator. After completion of the reaction, generally reached in less than 2 min, the glass vessel was removed from the oil bath and quickly cooled at room temperature [162]. 8.3.2.7 Isothermal Anionic Polymerization in the Bulk Polymerization reaction was carried out in a stainless steel mold, with a disk-shaped die [162, 163]. The mold, immersed in an oil bath kept at the polymerization temperature of 155 ∘ C, was previously connected with a vacuum pump by using a three-way valve and then illed with the molten reaction mixture under a pressure of dry nitrogen. After 600 s, which is a time more than adequate to reach reaction completion under all chosen conditions, the mold was quickly cooled by immersion in a cold water bath [162, 163]. 8.3.2.8 Anionic Suspension Polymerization in Quasi-Isothermal Conditions The polymerization reaction was carried out in a cylindrical glass reactor. The reactor was illed with polyisobutene, then it was immersed in an oil bath thermostated at 155 ∘ C. The reactant mixture was prepared in another glass vessel kept at 95 ∘ C and injected into the reactor with the aid of a dry nitrogen stream under moderate

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pressure. After 600 s, the mixture of polyisobutene, polyamide-6, POSS catalytic residues, unreacted caprolactam, and low molecular mass species was carefully washed with petroleum benzine in order to ensure a quick cooling, as well as to dilute the highly viscous suspending medium [162]. 8.3.3

Polyurethane/POSS Nanocomposites

Polyurethanes (PUs) are versatile polymeric materials and their physical properties are governed by the microphase separation between their hard and soft segments. Incorporation of POSS particles should reinforce the PU matrix and alter the degree of microphase separation [15, 164–168]. In a consequence, polyurethanes reinforced with silsesquioxanes can form hard, abrasion-resistant coatings with high thermal stability [169, 170]. Polyurethane formation can be monitored in situ to obtain the structural information during the gelation process. The technique investigates the connectivity of polymers as a function of time, temperature, and composition by measuring storage and loss modulus during gelation. The gel point of polymer during the gelation process can be determined by rheological experiments. This moment is reached at a critical degree of cross-linking, when the largest connected cluster diverges to ininity. The relaxation behavior at gel point shows a self-similar pattern [171]. Among various works on PU/POSS materials, Hsiao et al. [45] prepared polyurethane/POSS nanocomposites through the reactions of POSS derivative featuring one corner group substituted by either a hydridomethylsiloxy group (hydridoPOSS) or a 3-(allylbisphenol-A)propyldimethylsiloxy group. A polyurethane system using an organic biodegradable PDLA soft block and an inorganic diol-POSS hard block was obtained by Mather et al. [172]. Janowski and Pielichowski [164] synthesized polyurethane/POSS nanocomposites using MDI with polytetramethylene glycol, 1,4-butanediol, and diol-POSS, whereby Turri et al. [173, 174] synthesized a linear PU/POSS nanocomposite through a diol-functionalized POSS macromer; this nanocomposite exhibited signiicantly enhanced surface hydrophobicity and decreased surface energy relative to that of polyurethanes. Neumann et al. [175] and He et al. [176] synthesized a POSS macromer with eight reactive isocyanate groups ((NCO)8 -POSS) through hydrosilylation of m-isopropenyl-R,R-dimethylbenzyl isocyanate with Si–H bonds of Q8M8H. The incorporation of octafunctional POSS in polyurethane ilms resulted in higher thermal stability and cross-link density. Aqueous polyurethane dispersions with functionalized POSS were prepared through homogeneous solution polymerization by Nanda et al. [177]. The use of acetone as the initial polymerization solvent enabled the facile incorporation of both diamineand diol-functional POSS monomers. A Brabender-type mixer was applied for the preparation of PU/POSS nanocomposites by melt blending [178]. Thermoplastic polyurethane (TPU) (Elastollan® C85A, BASF) was melt-mixed with 10 wt% of poly(vinylsilsesquioxane) using a Brabender mixer operating at 50 rpm for 10 min at 180 ∘ C under nitrogen low. Mass loss calorimetry results reveal a large reduction of the peak of heat release rate (PHRR) in TPU/POSS composites as compared to virgin TPU, and the protection

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occurs via an intumescent mechanism. The intumescent material was found to be composed of ceramiied char made of silicon network in a polyaromatic structure. This material acts as a thermal barrier at the surface of the substrate limiting thus the heat and mass transfer as evidenced by lowered HRR. Monticelli et al. proposed a novel method to prepare PU/POSS hybrids by melt reactive blending [179]. This approach is based on the reaction between OH-functionalized POSS molecules and the isocyanate functional groups, which are formed directly during the melt blending process through a controlled scission of the polyurethane matrix. TPU/POSS systems were prepared at 220 ∘ C under inert gas atmosphere for 10 min by mixing the pristine polymer (Elastollan® 1185A, BASF) and POSS (octaisobutyl or trans-cyclohexanediolisobutyl POSS) at concentrations from 2 to 20 wt%. Authors observed an increase in glass transition temperature and better surface water wettability, evidenced by the decrease in water contact angle from 95∘ for neat TPU to 70∘ in TPU/POSS (10 wt%) nanocomposite. Lopes et al. [180] also proposed a method to prepare PU/POSS composites and explained how the thermal behavior can relect in rheological properties of dispersed systems of PU/POSS type. The addition of POSS caused higher intrinsic viscosities as the amount of silsesquioxane was increased. Composites tended toward a linear pseudoplastic behavior, with a higher amount of POSS leading to higher intrinsic viscosities at all shear rates evaluated. Building-in of POSS into the TPU backbone produced a signiicant change in the viscosity – the viscosity increased linearly with POSS, corroborating the reinforcing eficiency of POSS in the TPU backbone. The non-Newtonian behavior of TPU/POSS composites was postulated in which the viscosity at low frequencies is considerably higher than that obtained at high frequencies. The POSS moieties limit the movement of lexible domains due to probable formation of silicate layers, which is evidenced by an increase in viscosity. Similar effect was found by Nanda et al. in another PU/POSS hybrid system [177]. 8.3.4

Other Polymer/POSS Nanocomposites

As we already mentioned, both thermoplastic and thermoset polymer matrices are used to obtain polymer/POSS nanocomposites. Of course, POSS molecules are mostly used to enhance polymer properties by incorporating them into the polymer matrix via physical blending or copolymerization [78, 181]. One major difference between the physical blending and copolymerization is that the macroscopic phase separation between the POSS particles and the polymer matrix that occurs in the physical blends is absent (or considerably limited) in the systems with covalent bonding [182]. A few selected examples will be presented in the following sections. 8.3.4.1 POSS-Epoxy-Based Nanocomposites The phase behavior of POSScapped poly(ethylene oxide) incorporated into diglycidyl ether of bisphenol A epoxy was investigated by Zeng and Zheng, where 4,4-methylenebis(2-chloroaniline) was used as a curing agent [183]. Poly(ethylene oxide)-capped POSS forms about 60 nm spherical aggregates in the epoxy matrix, whereby the morphologies of

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POSS-containing epoxy resin-based O–I hybrids depend on the functional groups of the POSS particles [184, 185]. For instance, incorporation of octanitrophenyl-POSS in diglycidyl ether of bisphenol A lead to a phase separation, since the components are not miscible to each other. The two-phase morphologies, with a uniform dispersed domains, resemble to some extent the phase-separated microstructures induced by polymerization. On the other hand, incorporation of the octaaminophenyl-POSS lead to a homogeneous nanocomposite, as octaaminophenyl is compatible with diglycidyl ether of bisphenol A. 8.3.4.2 POSS-Methacrylate-Based Nanocomposites Methacrylate-based polymers ind many applications because of the ease of processing and high modulus. In order to improve the thermal and mechanical properties, POSS could be introduced to polymer backbone covalently via free radical polymerization or through atom transfer radical polymerization. Pyun [186] synthesized POSS-containing ABA triblock copolymers possessing a soft poly(n-butyl acrylate) middle segment and glassy poly(methacrylate-POSS) outer segments. Successful incorporation of octavinyl-POSS into poly(methyl methacrylate) polymer was also found to be effective in improving the glass transition temperature of the polymer nanocomposite [187]. In Table 8.3, typical melt blending conditions of poly(methyl methacrylate)/POSS nanocomposites are presented. In Ref. [188], researchers worked on POSS for their processing with supercritical carbon dioxide (scCO2 ) and applications in polymers. POSS with CO2 -philic functional groups can be solubilized in scCO2 , and polymers can be modiied with these nanocages by supercritical luid processing. Prior to polymer processing studies, the solubility of functionalized POSS cages in scCO2 was measured. The cloud point measurements have exhibited complete solubility of the hybrid structures in the supercritical luid. Researchers have constructed pressure versus composition solubility curves at moderate temperatures and pressures, and have thermodynamically modeled the solubility data using the Peng–Robinson equation of state. Based on the solubility data, they have conducted POSS-CO2 processing of polymethyl methacrylate (PMMA) sheets at conditions where hybrid nanocages are completely soluble in supercritical CO2 . Morphological and microstructural analyses of POSS-CO2 -processed polymer sheets showed that functionalized POSS can be embedded into foamed PMMA, and the polymer surface can be coated successfully with these nanoscale inorganic/organic hybrid cage structures using supercritical carbon dioxide. TABLE 8.3 Typical Melt Blending Conditions of Poly(Methyl Methacrylate)/POSS Nanocomposites [186, 187] Drying Temperature (∘ C) 100

Drying Time (h)

Mixing Temperature (∘ C)

Stirring Rate (rpm)

Mixing Time (s)

24

180

60

480

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8.3.4.3 POSS-Polyoxymethylene Nanocomposites Polyoxymethylene (POM) is an important thermoplastic polymer commonly used to replace metal or alloy products in engineering applications because of its dimensional stability, stiffness, and corrosion resistance. However, its low impact toughness and moderate heat resistance restrict the number of novel applications [189]. The incorporation of amino-functionalized POSS molecules into a polyoxymethylene matrix via melt blending techniques improves the thermal stability of the polymer [189]. Monosilanolisobutyl POSS was added to polyoxymethylene via direct melt blending, and the morphology and thermomechanical behavior of the composite were studied [190]. It was found that the hydrogen bond interaction was not able to prevent aggregation of POSS molecules in the polymer matrix; however, they led to monosilanolisobutyl-POSS domains of micron-scale dimensions. The low content of monosilanolisobutyl-POSS led to antiplasticization effect, while higher POSS content cause a decrease in the storage modulus of the nanocomposites relative to the pristine polymer. Sánchez-Soto et al. produced nanocomposites by melt mixing the three types of POSS molecules with polyoxymethylene. A poor dispersion of glycidylethyl-POSS and poly(ethylene glycol)-POSS molecules within the matrix was observed, with the presence of some particles of 1–20 μm sizes. As authors suggested, these particle sizes were due to the formation of nanospherical aggregates, indicating the phase separation effects. The best dispersion was observed within the polymer matrix, when aminopropylisobutyl-POSS was used as a iller. In this system, only a few submicrometer-sized aggregates were detected, conirming an almost completely homogeneous microstructure due to high miscibility between aminopropylisobutyl-POSS and POM macromolecules. Authors ascribe this high compatibility to similar polarity between amine end-groups of the POSS molecules and ether groups of the polyoxymethylene chain, as well as to hydrogen bond interactions between ether oxygens of POM and hydrogen atoms of functionalized POSS [189]. 8.3.4.4 POSS-Styrene-Based Nanocomposites Incorporation of POSS into styrene-based polymers was found to inluence the nanostructure of the composites. In Fu et al.’s work, POSS has been incorporated into cylindrical structures formed by styrene–butadiene–styrene triblock copolymer through the hydrosilylation technique [64]. POSS particles containing a silane functional group were grafted covalently onto poly(butadiene) blocks. The investigation revealed that the triblock copolymer cylindrical structure lost its long-range order due to the incorporation of POSS [191, 192]. Hao incorporated phenyl-POSS particles into polystyrene (PS) through the solution blending method [193]. A homogeneous transparent phenyl-POSS-containing PS nanocomposite ilm was produced, showing a uniform POSS distribution up to 40 wt% of iller loading. Phenyl surface functional groups of POSS favorably interact with polystyrene, and uniform dispersion of POSS even at high loadings is possible [194].

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8.3.4.5 POSS-Rubber Nanocomposites Processing of rubber/POSS nanocomposites is different from other polymer/POSS nanocomposites. In this case, the natural or synthetic matrix is mixed with nanoadditives by special rolling mills. This process consists of several parts, which are described earlier. First, with an appropriate shore, hardness is subjected to a pre-plasticizing with a selected quantity of nanoiller. This initial pre-plasticizing is performed by a rolling mill delivering warmed punches within a temperature range of 160–200 ∘ C and within appropriate gap between the rollers. The harder the matrix, the smaller the gap that should be used. It should be noted that the initial processing should take no longer than 15 min. In the next step, the rubber/POSS blend receives the initial shape of the product. If the proiles are obtained, a single-screw extruder is used. Then, the composite is subjected to vulcanization. Depending on the rubber, vulcanization is carried out using sulfur or metal peroxides. During vulcanization, high temperatures are applied and then the proile is cooled in a cooling bath illed with calcium nitrate. If a compression press is utilized, then vulcanization takes place in a heated mold and the whole process lasts from a few to several minutes. On a laboratory scale, a mixer is often used instead of a rolling mill [195]. For instance, Joshi et al. [196] prepared nanocomposites of polydimethylsiloxane (PDMS) with functionalized fumed silica and nonreactive POSS as illers by blending in a planetary mixer. Fumed silica was functionalized by aliphatic and aromatic groups to study the iller–iller interactions with the aliphatic and aromatic POSS illers and consequently their inluence on the properties in the PDMS matrix. Aliphatic and aromatic iller combinations showed more aggregated structures. Moreover, aliphatic POSS despite of good dispersion at higher loadings acts as lubricant, which is attributed to the disturbance in the PDMS–silica iller interaction and also the iller–iller interaction within fumed silica. The thermal stability of the aromatic functionalized illers improves due to the thermally stable phenyl groups. Chen et al. [197, 198] also prepared a series of novel polydimethylsiloxane (PDMS)/DVPS hybrid materials as room temperature vulcanized (RTV) silicone rubbers. The chemical incorporation of novel POSS into hydroxyl-terminated PDMS by hydrolytic condensation reaction was veriied by attenuated total relection infrared spectroscopy. The results exhibited enhanced effects on the thermal stability and mechanical properties as compared to the PDMS polymer prepared with tetraethoxysilane (TEOS). They observed improvements in thermal properties that could be attributed to the effective 3D network structures resulting from the structure of DVPS. The thermal degradation of the RTV silicone rubbers in nitrogen was also monitored by TG coupled with FTIR, and the degradation residues were also characterized by FTIR. It was found that the POSS cross-linker facilitated the formation of cross-links in the char residues. The improvement in mechanical properties could be attributed to the synergistic action of the structure of 3D multi-arm cross-linking agent being a vinyl-POSS derivative, the plasticization of self-cross-linking vinyl-POSS derivative and perfect distribution of vinyl-POSS derivative.

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8.4 RHEOLOGICAL BEHAVIOR OF POSS-BASED POLYMER NANOCOMPOSITES Rheology is a scientiic discipline dealing with deformation and low of materials. During the last years, research focuses in the micro- and nanoscale, so it is called micro- and nano-rheology, respectively. Rheological experiments reveal information about the low behavior of liquids and the deformation behavior of solids. These experiments are done using a (micro)rheometer [199]. Two types of rheometers are used in rheological investigations nowadays: • rotational rheometers; • oscillatory rheometers. Liquids and solid materials can be investigated using both rheometers. Rotational tests are performed to characterize the viscous behavior of materials, while creep and viscoelastic behavior as well as relaxation tests can be carried out using oscillatory rheometers [199]. Investigation of the rheological properties in the molten state is fundamentally important to understand the processability and structure–property relationships of polymer composite systems. These properties are strongly dependent on the degree of dispersion of the iller particles in the polymer matrix (Fig. 8.6) [114, 115, 121, 200, 201], while that of the polymer melt strongly rely on the temperature of

9 92% increase Tensile strength (MPa)

8

7 PEPB 6 PEPM 5 PEPP 4 0

0.5

1 POSS content (wt%)

1.5

2

Figure 8.6 Tensile strength curves of PE/POSS nanocomposites with different contents of POSS. PB – octaisobutyl–POSS; PM – octamethyl–POSS; PP – octaphenyl–POSS. Reproduced from Lim et al. [115] with permission os Elsevier.

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measurement [202]. Therefore, studies of the rheological behavior of a polymer matrix reinforced with iller particles, where the POSS nanoparticle size allows interactions with the polymer matrix at the molecular scale, are of crucial importance. Some examples of the inluence of processing conditions on rheological properties of different polymer nanocomposites reinforced with POSS will be shown in the following. Kopesky et al. [202] found that tethered POSS within entangled poly(methyl methacrylate) (PMMA) reduced the rubbery plateau modulus (G0N ) of the neat PMMA. Wu’s group [203] reported on the linear viscoelastic properties of entangled random copolymers from styrene and isobutyl-POSS. A dramatic reduction in the (G0N ) values of the copolymers caused by the addition of isobutyl-POSS particles was observed. Such behavior suggested a strong dilatation effect on the entanglement density caused by the presence of isobutyl-POSS. The rheological properties of polyethylene/octamethyl-T8-POSS nanocomposites were investigated by Joshi et al. [114]. POSS acted as lubricating agent at lower POSS contents and reduced the complex viscosity (�*) of the nanocomposites, while high POSS loadings showed an increase in the viscosity. The presence of POSS particles caused gelation in the PE matrix at concentrations higher than 5 wt%. In Zhou’s work [204], the rheological behavior of polypropylene/octavinyl-POSS composites, prepared through reactive and physical blending in the presence of DCP, was investigated. It was reported that the �* of the physically blended composites decreased at a lower POSS content and increased with increasing POSS content. The samples showed a liquid-like rheological behavior after nanocomposite formation due to the strong particle–matrix interaction. In the case of the reactive blending, the composites showed a solid-like rheological proile at the low-frequency region when the nanoiller content was higher than 1 wt%. Kim et al. [205] reported on the rheological behavior of poly(ethylene terephthalate) (PET)/POSS nanocomposites carried out at 280 ∘ C. They used two types of POSS to prepare the composites: disilanol- and trisilanol-POSS particles. An increase in the amount of trisilanol-POSS molecules in the PET matrix increased the �* at low frequencies; the opposite behavior was observed at high frequencies. This behavior was due to a shear-thinning effect. Similar effect was observed in the case of PET/disilanol-POSS nanocomposites, with a slight difference in �* with increasing the POSS content. This behavior indicated strong interfacial interactions between the polymer matrix and the particles. Fu et al. [206] studied the rheological properties of nanocomposites prepared from an ethylene–propylene copolymer and octaisobutyl POSS particles. Their investigation revealed a transition from liquid-like rheological behavior in the pure ethylene–propylene copolymer to solid-like rheological behavior for the POSS composites. The rheological behavior of neat ethylene–propylene copolymer resin was typical of polymer melts having a negative slope in tan � over the entire frequency range. The introduction of POSS molecules drastically changed the ethylene–propylene copolymer rheology: slope of the tan � became positive in the low-frequency region (Fig. 8.7). The gelation process of polyurethane/POSS systems was investigated by Zhang et al. [207] using isothermal time-resolved mechanical spectroscopy at 40, 60, 70, and 80 ∘ C. For the sample processed at 40 ∘ C, typical dependence was found when

RHEOLOGY AND PROCESSING OF POLYMER/POSS NANOCOMPOSITES

316 100

Gel point

tan δ

10

160 °C EP1_00 EP1_B_20 1 0.1

1

10

100

ω (rad/s)

Figure 8.7 tan � value versus � for EPI/POSS nanocomposite containing 20 wt% octaisobutyl-POSS molecules at 160 ∘ C. The hypothesized dotted line represents the gel point. Reproduced from Fu et al. [206] with permission of Elsevier.

the curing time was less than 12,500 s, G′ increased gradually as time increased. This was attributed to the increase in branching during the gelation process [208]. When curing time was higher than 12,500 s, G′ kept increasing and the speed of rotor was slower than that of the initial stage. For the sample processed at 80 ∘ C, when the curing time was less than 5000 s, a substantial increase was observed in G′ with increasing curing time. In this region, the cross-linking structure formed rapidly. When curing time was higher than 5000 s, G′ became independent of curing time, which meant that the equilibrium modulus was reached and the cross-linking structure was constructed permanently. It was also reported that the gel stiffness was also decreased as POSS concentration increased. This indicated that the critical gel became soft at high curing temperature and high POSS concentration. Presumably less bonds were necessary to form the critical gel at higher POSS concentration. In the literature, POSS/POSS interactions determining solid-like behavior have been reported, but only for signiicantly higher POSS loadings, with both tethered and untethered POSS. For instance, in polystyrene/POSS copolymers, solid-like behavior was reported only for POSS loadings 42 wt% [39, 206]. Various models have been proposed to explain modiications of macromolecules’ dynamics in the presence of POSS, including sticky reptation and association effects [39, 206, 209–211], inertial effects [39], and particle-to-particle interactions [206]. Considering the low-grafted POSS concentration and the presence of small amounts of unreacted POSS, the most compelling explanation for the results discussed here may be based on the model proposed by Kopesky et al. (Fig. 8.8) [209]. Jones et al. [212] reported the properties of polyphenylsulfone with two types of POSS: dodecaphenyl-POSS and trisilanolphenyl-POSS. It was seen that there is a reduction in the torque during processing with increasing POSS loading. The authors

RHEOLOGICAL BEHAVIOR OF POSS-BASED POLYMER NANOCOMPOSITES

317

(a)

3 nm

(b)

(c)

Figure 8.8 Schematic of the illed copolymer blend. At low loadings of untethered-POSS (black circles), most of the tethered-POSS groups are present in an unbound state (open circles). However, a kinetic exchange takes place whereby a particular chain (represented by the dashed line) may contain (a) an “active” tethered-POSS group (gray circle), which forms a thermodynamic association with a nanocrystallite of untethered-POSS. This temporary association may (b) break, thus allowing the chain to reptate freely before (c) a different tethered-POSS group on the same chain forms an association with the nanocrystallite. This kinetic exchange between an associated and a dissociated state leads to the dramatic slowdown in the relaxation processes in the copolymer matrix. Reproduced from Kopesky et al. [209] with permission of American Chemical Society.

suggested that this is related to POSS melt transitions, as both POSS types were in the liquid state during the extrusion of the material from 375 to 400 ∘ C. The capillary rheometry data indicated that the apparent viscosity decreases with small loading of POSS (Fig. 8.9). In Bhadu et al.’s work [213], the authors studied the rheological behavior of poly(trimethylene terephthalate)/trisilanolphenyl-POSS nanocomposites prepared

RHEOLOGY AND PROCESSING OF POLYMER/POSS NANOCOMPOSITES

318

Apparent viscosity (Pa s)

PPSU 0.5% Dp-POSS 1.0% Dp-POSS 2.5% Dp-POSS 5.0% Dp-POSS 7.5% Dp-POSS 10.0% Dp-POSS

1000

100

10

100

1000

10000

Shear rate (1/s)

Figure 8.9 Log–log plot of � ap as a function of the POSS concentration as measured by the capillary rheometry of the Dp-POSS composites (PPSU – thermoplastic polyphenylsulfone; Dp-POSS – closed-cage dodecaphenyl polyhedral oligomeric silsesquioxane). Reproduced from Jones et al. [212] with permission of John Wiley and Sons.

via melt blending. They found a decrease in the torque during the extrusion of the nanocomposites compared with the neat polymer, as well as decrease in the shear viscosity at low POSS concentration due to the lubrication effect of POSS. It was reported that at high POSS contents, the reduction in the shear viscosity decreases. The trisilanolphenyl-POSS nanoparticles improve the pseudoplasticity of the polymer matrix and increase the shear-thinning behavior due to the better distribution of the nanoiller [213]. Structure–property relationships of polystyrene/POSS nanocomposites with closed and open-cage POSS carrying different organic groups were studied by Dintcheva et al. [214]. The rheological properties of the nanocomposites depend on the type of the POSS organic group and the inorganic framework. The complex viscosity and the storage and loss moduli of all nanocomposites samples were smaller than that for the pristine PS, but the reduction of the complex viscosity for the nanocomposites with an open cage was larger than with closed cage (Fig. 8.10). Compared with the closed POSS cage, the open silsesquioxane cage is more lexible, which leads to an enhanced reduction of the frictional effect between the polymer chains. 8.5

CONCLUSIONS

Polymer/POSS nanocomposites witness a spectacular growth in the last decade as they show designed chemical, mechanical, or thermal properties required in materials science applications. They can be obtained by melt blending techniques

CONCLUSIONS

319

106 PS IB-PS IO-PS TSIB-PS TSIO-PS TSPH-PS

Complex viscosity (Pa s)

105

104

103

102 10–1

1

10 Frequency (rad/s)

102

103

Figure 8.10 Flow curves of polystyrene and polystyrene-POSS nanocomposites (PS – polystyrene; IB-PS and TSIB-PS – i-butyl-POSS-polystyrene; IO-PS and TSIO-PS – i-octyl-POSS-polystyrene; TSPH-PS – phenyl-POSS-polystyrene). Reproduced from Dintcheva et al. [214] with permission of Budapest University of Technology and Economics.

that require proper selection of processing equipment and process conditions. Depending on these conditions, different structures and morphologies at the nanoscale can be obtained that lead to various chemical and physical properties. The relationships among processing, structure, and property of polymer/POSS hybrid materials are still developed, and this chapter reports on the latest capabilities of synthesis and processing of different types of polymer matrix with POSS particles, showing examples of processing inluence on basic rheological properties of these nanocomposites. Rheology and processing of polymer/POSS nanocomposites include silsesquioxane-containing materials based on polyoleins, polyamides, polyurethanes, styrene- and methacylate-based (co)polymers, poly(oxymethylene), epoxies, and selected polymer blends and copolymers. Various effects of POSS particles on the rheological behavior of polymer melt, including lubrication, particle–matrix interactions, and cross-linking, were described. Polymer/POSS nanocomposites have tremendous potential for application in automotive, electronics, and biomedicine due to their multifunctional “hybrid” chemical and physical properties. Indeed, higher glass transition and usage temperature increased thermal stability and lowered oxygen permeability; enhanced mechanical properties and lame resistance were observed in published research

320

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indings. However, the development and applicability of silsesquioxane-containing macromolecular materials depend on both understanding of rheological behavior and on the use of eficient and properly designed processing technologies on industrial scale. There are several key challenges encountered in preparing POSS-containing polymer nanocomposites, including tendency to aggregation of silsequioxane nanoparticles and expensive large-scale production. However, eficient processing methods have been developed to incorporate POSS moieties into polymer matrices either by in situ polymerization or by melt mixing. For the obtained well-deined hybrid materials, structure–property relationships are still to be found which is of primary importance for tailoring polymer/POSS hybrids for speciic applications. On the other hand, particle–polymer interactions play a crucial role in POSS-containing polymer nanocomposites and contribute to the control of morphology and molecular dynamics. Compared with traditional composites, for hybrid materials, it is even more challenging to determine the composition, strength, and functionality of the interfacial region of organic–inorganic phases. Another challenging issue is scaling up of the production processes to fabricate larger quantities of POSS nanocomposites on industrial scale. At present, it is dificult to predict which, if any, market sector would not be able to beneit from the hybrid materials technology. It can be expected that various sectors such as aerospace, automotive, packaging, electronics, and biomedical will proit from a new range of silsesquioxane-based nanomaterials. The timescale for some of these sectors is a long-term prospect requiring strict testing and validation procedures.

ACKNOWLEDGMENTS Authors acknowledge funding by the National Science Centre in Poland under contract No. DEC-2011/02/A/ST8/00409.

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9 POLYMER AND COMPOSITE NANOFIBER: ELECTROSPINNING PARAMETERS AND RHEOLOGY PROPERTIES Palaniswamy Suresh Kumar, Sundaramurthy Jayaraman, and Gurdev Singh Environmental & Water Technology, Centre of Innovation (EWT COI), Ngee Ann Polytechnic, Singapore

9.1

INTRODUCTION

Rheology is based on the fundamental physical relationships about low and deformation of materials under applied forces, and the term was coined by Bingham in 1920 [1]. The term “rheology” was originated from the Greek word “rheos” meaning “lowing” or “streaming.” Viscosity is one of the most important low properties that represent the resistance to low or resistance to shearing. Most of the materials exhibit complex rheological properties, whose solution viscosity are varying depending on the external conditions such as stress, strain, timescale, and temperature. In general, rheology involves measurements in controlled low, mainly the viscometric low in which the velocity gradients are nearly uniform in space. In these simple lows, there is an applied force where the velocity is measured, or vice versa. They are called viscometric and are used to deine an effective shear viscosity � from the measurements � = �xy ∕�

Rheology and Processing of Polymer Nanocomposites, First Edition. Edited by Sabu Thomas, Rene Muller, and Jiji Abraham. © 2016 John Wiley & Sons, Inc. Published 2016 by John Wiley & Sons, Inc.

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where � xy is the shear stress (measured or applied) and � is the shear rate (applied or measured). Viscosity is measured in Pa s (Pascal second). Rheology in polymer is not just about viscosity but also about another important property of polymer, namely the elasticity. The modulus of elasticity is deined as G = �xy ∕� where � is the strain or the angle of shearing deformation. G is measured in Pa (Pascal). G is one of the elastic moduli, known as the storage modulus, as it is related to the amount of recoverable energy stored by the deformation. G for most polymeric luids is in the range 10–104 Pa, which is much smaller than that of solids (>1010 Pa). However, for high polar solutions, the rheological properties are greatly dependent on the physical interactions between polymer chains, which are greatly inluenced by solvent, temperature, molecular weights, and concentrations of polymer. In the past few decades, numerous measuring techniques have been proposed to determine the interfacial rheological parameters of luids and semisolid dispersions. Rheological properties mainly measured from bulk sample deformation using a mechanical rheometer or on a microscale by using a microcapillary viscometer or an optical technique such as microrheology. However, all these measuring techniques have advantages and limitations with respect to the operating range, sensitivity, and suitability for measuring different interfaces. Therefore, there is a need to study the rheological properties of different polymers and its composites to understand the unique functional properties. Figure 9.1 shows the fundamental physical relationships of materials rheology. The mechanical, thermal, and electrical properties of the nanocomposite ibers are greatly dependent on the orientation and the dispersion of the particles within the polymer matrix. Recently, polymer and composite nanoibers represent an emerging class of biomimetic nanostructures that have shown tremendous promising applications, such as in water iltration/treatment, battery separator, reinforcing materials, wound dressing, tissue scaffolding, and advantageous drug delivery systems. Processing Properties

Rheology

Structure

Figure 9.1

Processing

Fundamental physical relationships of materials rheology.

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techniques such as self-assembly, phase separation, and electrospinning have been adapted for the synthesis of different multifunctional polymer nanocomposites. Among them, electrospinning is very eficient due to its versatility, lexibility, and ease of iber production. Fabrication of polymer and its composite nanoibers through electrospinning process has received huge attention due to its versatility and easy process. Studies have revealed that electrospun polymer iber with distinctive polymer molecules can generate iber with very few nanometers. Understanding the rheological properties of the polymer solutions is signiicant because they offer a critical clue to determine the optimum processing conditions in the electrospinning process. The rheology mainly depends on the polymer molecular characteristics such as molecular weight, polydispersity, and the degree of branching. These molecular properties of the polymer play a vital role in determining iber initiation and stabilization. Hence, the rheological characteristics are decisive in the electrospinning process and are used as a predictive tool for the success of electrospinning.

9.2

ELECTROSPINNING

Electrospinning is a simple, reproducible, and scalable one-step technology for the preparation of different nanoibers and nanostructures (such as ceramic, composite, and polymer) with controllable morphology from solutions of both natural and synthetic polymers. The irst documented patent of electrospinning of a polymer solution into iber was patented by Cooley and Morton in 1902 [2]. The applied electrostatic forces are employed to produce nanoibers with a controllable morphology and diameter (micrometer to nanometer) by optimizing the polymer solution rheology. By altering the iber diameter from micrometers (mm) down to submicrometers or even nanometers (nm), the iber possesses characteristics such as very large surface area to volume ratio, lexibility in surface functionalities, and superior mechanical performance (stiffness and tensile strength) compared with any other known form of the material. Basically, electrospinning system consists of three major components: (i) a high-voltage power supply, (ii) a spinneret, and (iii) a grounded collecting plate (usually a metal screen, plate, or rotating mandrel). Typically, electrospinning techniques involve the use of a high-voltage electrostatic potential (5–30 kV) ield to charge the surface of the polymer solution droplet and thus induce the ejection of a liquid jet through a spinneret (single, multi-spinneret, or co-axial). Figure 9.2a shows the schematic image of typical electrospinning setup and its process parameters inluencing the nanoiber morphology and (b) the visual images of multiple parallel electrospinning jets [3, 4]. During the electrospinning process, an applied electric ield is subjected to the end of the capillary tube, which contains the solution luid that is held by its surface tension. When the intensity of the electric ield is increased, the hemispherical surface of the luid at the tip of the capillary tube (needle) elongates to form a conical shape called the Taylor cone. Eventually, when the charge repulsion exceeds the solution surface tension, then a jet of solution is ejected from the Taylor cone toward the grounded target substrate.

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F Air Liquid

Air

Interfacial viscosity

Viscosity

Liquid

Collector Polymer solution

Pump HV Needle to collector distance

°C Applied voltage

Conductivity

100 80 60 40 20 0 −20

ϕv

(a)

5 cm Linear region Whipping region

(b)

Figure 9.2 Schematic image of typical electrospinning setup and its process parameters inluencing the nanoiber morphology. Reproduced from Pelipenkp et al. [3] with permission of Elsevier. (b) Visual images of multiple parallel electrospinning jets and the resultant linear and whipping regions of the jets. Reproduced from Roman et al. [4] with permission of American Chemical Society.

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TABLE 9.1 Different Solvent and Its Physical Properties for Fiber Formation Solvent

Boiling Point (∘ C)

Surface Morphology

64.7 66 77.1 78.3 100 153

Fiber with small diameter Smooth and beaded, ribbon-like ibers Smooth and ribbon-like ibers Smooth iber, nanoporous Beaded ibers with small diameter Smooth and beaded

Methanol Tetrahydrofuran Ethyl acetate Ethanol Water Dimethyl formamide

The discharged polymer solution jet undergoes an instability and elongation process, which allows the jet to become continuous and thin. During the process, the solvent evaporates leaving behind only charged polymer nanoiber on collector. The electrospinning process is governed by a variety of forces including the Coulomb force between the charges on the jet surface, the electrostatic force due to the external electric ield, the viscoelastic force of the solution, the surface tension, the gravitational force, and the frictional force due to air drag [5]. Electrospun nanoibers can be easily controlled to meet the performance requirements of various applications by controlling the electrospinning conditions, such as the viscosity and electrical conductivity of the polymer solution, collector geometry, and the volatilization degree of the solvents. In addition, the solution feed rate, applied potential, distance between the needle tip and collector, other environmental conditions (temperature and relative humidity) are needed to be carefully controlled in order to obtain well-aligned ibers with optimized diameter. Table 9.1 shows the different kinds of solvent and its physical properties for iber formation [6–12].

9.3

ELECTROSPINNING PROCESS PARAMETERS

The major challenge of the electrospinning process lies in the optimization of the parameters to achieve desirable nanoiber morphology and properties. Electrospinning parameters are very important to understand the rheology behavior of polymer solutions into nanoibers or turn them to different forms of 1D morphologies. In general, typical electrospinning processes are inluenced by three main parameters. 9.3.1

Solution Properties

Polymer concentrations play an important role in the iber formation during the electrospinning process based on uniaxial stretching of a charged jet. Surface tension and viscosity of a polymer play a signiicant effect on rheological properties of the polymer solution, which ultimately decides the spinnability of the solution into nanoibers. When the polymer concentration is too low, electrospraying occurred due to the effect of the applied voltage and surface tension of the polymeric solution, which results in beads formation instead of smooth ibers. At an increased polymeric concentration, as

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the viscosity increases the chain entanglement between polymeric chains improves and regular nanoibers are formed. However, at very high concentrations, the viscosity of the solution becomes exceedingly high, disrupting the low of the polymer solution through the capillary that results in the deformation of iber structure into spindle-like structure. Park et al. have reported on the optimization of the nanoiber morphology by changing the solution concentration (5–30 wt%). Figure 9.3 shows the morphology of electrospun ibers with respect to different solution concentration, which lead to different morphologies from beads to iber mats. Molecular weight of the polymer also has an important effect on morphologies of electrospun iber, which relects the entanglement of polymer chains in solutions [13]. Similarly, Wang et al. have reported for the irst time on high-temperature electrospinning approach to produce ultrathin polyacrylonitrile (PAN) ibers with a diameter lower than 100 nm. From the experimental observation, it is noted that the decreasing in PAN concentration and/or increasing in solution temperature result in a progressive reduction

(a)

(b)

(c)

(d)

(e)

(f)

(g)

Figure 9.3 Morphology of electrospun ibers at various PVAc concentrations: (a) 5 wt%, (b) 8 wt%, (c) 10 wt%, (d) 15 wt%, (e) 20 wt%, (f) 25 wt%, and (g) 30 wt% (applied voltage, 15 kV; low rate, 100 μl/min; distance, 10 cm). Reproduced from Park et al. [13] with permission of Elsevier.

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of the iber diameter. As the temperature of the PAN solutions was increased, both viscosity (� o ) and surface tension (�) were decreased, but solution conductivity (k) was enhanced [4]. The choice of right solvent is also very critical for a particular polymer to solubilize and be transformed into nanoibers through electrospinning. Generally, it has been observed that an increase in solution conductivity results in a substantial decrease in nanoiber diameter, and it has been shown that the radius of the nanoiber jet is inversely related to the cube root of the electrical conductivity of the solution. 9.3.2

Operating Conditions

An electric ield either lower or higher than critical value will result in beaded morphologies or even inhibit polymer jet initiation. In general, with an increase in the applied voltage beyond a critical value, the nanoiber diameter decreases initially and then increases after a deinite point. The low rate of the polymer solution through a capillary inluences the nanoiber diameter, porosity, and geometry of the electrospun nanoibers. When the spinning low rate increased, the available polymer volume was high, which increased the nanoiber diameter along with an increase in pore size. It was observed that an increase in low rate simultaneously increased the electric current and decreased the surface charge density. However, at very high low rate, the nanoibers were unable to dry completely before reaching the collector and higher beads were observed. It is noted that the changes in nanoiber morphology are also explained with the combination of solvent evaporation rate and beads formation during the capillary breakup of viscoelastic luid. In the case of capillary breakup, the force of liquid connection stretching is gravitational force, whereas in case of electrospinning, it is the electrostatic force due to the applied electric ield. The solidiication process is decelerated and the liquid in the electrospun jet has more time to low when RH is increased. Figure 9.4 Collector Jet fusion on collector

E

Jet solidiication

D

Jet solidiication

RH C Jet solidiication

B A

Jet solidiication

Jet development

Figure 9.4 Schematic representation of electrospun jet development under various RH conditions. Reproduced from Pelipenkp et al. [3] with permission of Elsevier.

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shows the schematic representation of electrospun jet development under various RH conditions [3]. So far, different kinds of spinneret collectors (such as foils, metals, and rotating drums) are adopted to produce random and aligned nanoibers. Due to inexpensive and easy availability, aluminum (Al) foil is used as collector electrode generally. The collector and distance between collector and spinneret tip is considered one of the critical parameters for nanoiber formation and optimized distances ensure the nanoibers without beads. Generally, rotating drum collectors are used to produce aligned nanoibers with uniform thickness. The low rate of the solution from the syringe is also an important process parameter as it inluences the jet velocity and the material transfer rate. With a lower solution feeding rate, smaller ibers with spindle-like beads are formed and vice versa. 9.3.3

Process Conditions

Ambient parameters (such as temperature, humidity, and air velocity) are variable, which affect the morphology and nanoiber formation. Temperature has an effect on the average diameter of the nanoibers because it is related to evaporation rate of the solvent and rigidity of the polymer chain. Report suggested that the increase in temperature during spinning process exhibits reduced iber diameter due to decrease in solution viscosity, surface tension, and conductivity. The effects of relative humidity are also strongly coupled to other process parameters and operating conditions. Putti et al. reported that the surface turns from smooth iber to porous or crater-like structure with the change in temperature and relative humidity (RH). Figure 9.5 shows

30%

40%

50%

Relative humidity 60% 70%

80%

90%

20 °C

Temperature

25 °C

30 °C

35 °C

40 °C

10 μm

Figure 9.5 SEM images of polycaprolactone (PCL) ibers spun from a 15 wt% solution at different temperatures and relative humidity (RH). Reproduced from Putti et al. [14] with permission of Elsevier.

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the SEM images of polycaprolactone (PCL) ibers spun from a 15 wt% solution at different temperatures and relative humidity (RH) [14]. Similarly, Casper et al. have demonstrated that the electrospinning process with humidity less than 25% produced smooth ibers without any surface features. However, when the humidity increased above 30%, pores begin to form on the surface of the iber. Increasing the amount of humidity causes an increase in the number of pores on the surface, the pore diameter, and the pore size distribution [15]. Upon optimization, all solution and spinning key parameters, electrospun ibers typically exhibit porous structure with high surface-to-volume ratio with better physical and mechanical properties than any other nanostructured material. So far, more than 100 polymers have been investigated and formulated for electrospun nanoibers with polymers of natural origin being generally favoring different kinds of polymeric nanoibers (such as polyvinyl alcohol (PVA), polyacrylonitrile (PAN), polyvinylidene luoride (PVDF), polyvinylpyrrolidone (PVP), polyethylene glycol (PEG), and polystyrene (PS)). These nanoibers found multifunctional applications in energy (as battery separators, solar cell, fuel cell) [16, 17], environmental (water iltration), and biological applications (such as controlled drug delivery, wound healing, and tissue engineering) [18–22]. Rheological characteristics still play an important role due to the larger diameter of the jet. During jet thinning, interfacial characteristics prevail due to the signiicant increase in the surface-to-volume ratio (S/V = 4D−1). The jet diameter (D) is reduced from approximately 1 mm (inner diameter of the needle used) to a few hundred nanometers or less (diameter of the obtained nanoibers). Moreover, solvent evaporation creates a concentration gradient in polymer molecules, leading to a more pronounced effect of the interfacial characteristics. To simulate the increase in polymer concentration during jet solidiication and to evaluate the changes of G′ and G′′ that occur due to solvent evaporation, the rheological measurements of polymer solutions were performed. This chapter focuses on to bring rheology characteristics of different polymeric nanoibers and nanocomposites.

9.4

POLYMER-BASED NANOFIBER AND ITS RHEOLOGY

Polymer nanoibers represent an emerging class of biomimetic nanostructures with distinctive electrical, mechanical, optical, and electrical properties. Over the past few years, many researchers have investigated various parameters affecting morphology and diameters of electrospun PVA ibers, for example, solution concentration, solution low rate, degree of hydrolysis, applied electrical potential, collection distance, ionic salt addition, molecular weight of PVA, pH, surfactant addition, and the type of collector. However, the rheological behavior of the polymer solution plays a crucial role in the electrospinnability for any solution. Most researchers discussed on the polymer solution viscosity for smoother nanoiber, but rheological factors such as the elastic (G′ ) and plastic (G′′ ) moduli are hardly discussed. Commonly used natural polymers in tissue engineering are collagen, gelatin, hyaluronan, chitosan, gelatin, and alginate. Among all, chitosan and alginate-based nanoibers have demonstrated promising functionality such as biocompatibility and biodegradability properties for

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tissue engineering. These polymers (such as chitosan, alginate, and sodium alginate) alone cannot be electrospun from aqueous solution due to its ionic characters, high viscosity at low concentration, and water solubility. However, these drawbacks can be overcome by blending an electrospinnable polymer (such as PEO or PVA), which can improve the spinnability properties. Nanoibers prepared from PVA using the electrospinning process have received a great deal of attention over the past decade due to their outstanding characteristics and their applicability in the ield of biomedicine, coupled with their innovative preparation. Klossner et al. have successfully developed chitosan-based defect-free nanoibers via electrospinning by optimized blending chitosan and PEO solutions. Klossner et al. observed that even with very low chitosan concentrations, the solution became highly viscous and unable to get smooth electrospun ibers. However, by increasing the blend polymer (chitosan + PEO) concentration reduced the beads formation. After increasing the chitosan to PEO ratio from 2:3 to 8:9 and increasing the overall polymer concentration from 3.0 to 3.4 wt% resulted in defect-free nanoibers with a diameter of only 62 nm (Fig. 9.6a–f). However, the zero shear rate viscosity (� 0 ) of these solutions decreased signiicantly after which attributed to phase separation of the two-component solutions. Figure 9.6g corresponds to the zero shear rate viscosity (� 0 ) of chitosan/PEO solutions measured as a function of time [23]. Similarly, McKee et al. have reported that linear and branched poly(ethylene terephthalate-co-ethylene isophthalate) (PET-co-PEI) copolymers were electrospun from semidilute unentangled, semidilute entangled, and concentrated solutions under identical conditions and determined the effects of concentration regime and molecular topology on electrospun iber morphology [24]. Rošic et al. have reported correlations between the rheological parameters of solutions composition of chitosan-PEO and alginate-PEO blends for electrospinnability. The conductivity and surface tension of the solutions clearly showed that the surface tension of blends remained nearly unchanged regardless of the solution composition, whereas the conductivity correlated with the proportion of chitosan or alginate in the blends. For chitosan, smooth nanoibers were observed when the content of chitosan in the blends was 10% or less, whereas alginate solution with 30% content produces smooth iber without beads [25]. Figure 9.7a–b shows the interfacial viscosity, storage (G′ ), and loss (G′′ ) moduli as a function of solution composition of chitosan–PEO and alginate–PEO blends. However, for alginate, PEO blends, the solutions having concentrations of alginate up to 30% were in the irst region and those up to 60% were in the second region. With 70% alginate, the parameters started to decrease, although division into three regions remains consistent because the parameter values remain above those of the other two regions. Saquing et al. reported on the sodium alginate-PEO blend nanoibers through electrospinning process. The incorporation of carrier PEO polymer reduced the electrical conductivity and surface tension of the alginate solution, aiding in iber formation [26]. At a maximum of 70 wt%, alginate content was achieved for 2000 kDa PEO but the iber diameter dramatically increased due to increased viscosity at this concentration. With increasing alginate concentration in the blends (reduced ability to form ibers), the viscosity decreased dramatically

POLYMER-BASED NANOFIBER AND ITS RHEOLOGY

(a)

(b)

(c)

(d)

(e)

(f)

4 × 103

Total polymer: 3 wt%; CS:PEO 1:1 Total polymer: 3 wt%; CS:PEO 3:2 Total polymer: 4 wt%; CS:PEO 5:3 Total polymer: 4.2 wt%; CS:PEO 5:2

3 × 103

η0 (cP)

339

2 × 103

103

0 0

5

10 15 Time (days) (g)

80

Figure 9.6 (a–f) Electrospun chitosan–PEO nanoibrous structures illustrating the effect of acetic acid concentration, chitosan–PEO ratio, and total polymer concentration. (g) Zero shear rate viscosity (� 0 ) of chitosan/PEO solutions measured as a function of time. Reproduced from Klossner et al. [23] with permission of American Chemical Society.

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20

4

15

3

10

2

5

1 0

0 20 40 60 80 100 Chitosan in CH: PEO blends (% w/w) Interfacial G′ Interfacial G″ Interfacial viscosity 0

(b)

6 1.0 4 0.5

2

Interfacial viscosity (mPas)

Interfacial G′ or G″ (mPa)

8

1.5

0 20 40 60 80 100 Alginate in ALG: PEO blends (% w/w) Interfacial G′ Interfacial G″ Interfacial viscosity 0

0

Alginate/PEO Alginate/PEO/Triton

15

10

5

0

(d)

0

20

40

60

80

100

60

80

100

40 60 80 Alginate content (%)

100

10 Alginate/PEO Alginate/PEO/Triton

8 6 4 2 0 0

(e)

10

2.0

Viscosity (Pa *s)

25

5

Electrical conductivity (mS/cm)

30

6

20

40

Alginate/PEO Alginate/PEO/Triton

60 Surface tension (mN/m)

7

Interfacial viscosity (mPas)

(c)

Interfacial G′ or G″ (mPa)

(a)

50 40 30 20 0

20

Figure 9.7 Interfacial viscosity, storage (G′ ), and loss (G′′ ) moduli as a function of solution composition of (a) chitosan : PEO and (b) alginate : PEO blends. (c–e) Viscosity, electrical conductivity, and surface tension of low-viscosity alginate and PEO blends in the absence and presence of triton. Reproduced from Rošic et al. [25] with permission of Elsevier; Reproduced from Saquing et al. [26] with permission of American Chemical Society.

(Fig. 9.7c–e), indicating that the addition of PEO aids electrospinnability in part by increasing the viscosity of the resulting solution. Rošic et al. have successfully developed smooth nanoibers using PVA solutions in the concentration range from 8% to 12% (w/w). These nanoibers exhibited Newtonian behavior, have viscosities in the range from 0.2 to 1.3 Pa s, with a strong predominance of bulk and interfacial plasticity over elasticity, conductivity from 0.45 to 0.6 mS/cm, a surface tension from 63 to 70 mN/m, and Rg equal to 2.2 ± 0.1 nm [27]. Roman et al. reported as a function of applied voltage for PEO solutions of differing viscosity. In general, the iber velocity cannot be changed instantaneously due to the effect of viscosity, and rather it must occur over a inite length scale. In this case, the electric ields created the driving force that generated a velocity (v) gradient along the plate which resulted in the cone jet. Due to the system viscosity, it quickly reached

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steady state where the driving and viscoelastic forces (per volume) balance [4]. | �E | | dP | | d2 v | �v | | | | | = |� | dx | | dz2 | = �0 E | �x | ≅ 3a2 | | | | | | where P is the pressure (the electrostatic pressure P = 1/2�0 E2 , with E the electric ield) and � is the viscosity. The viscoelastic force pulls back against and balances the force due to the gradient in pressure. Abbasi et al. have reported on the relationship between the rheological properties of nylon-6,6 solutions and their nanoiber morphology behavior. The diameter and uniformity of the nanoibers were found to be dependent on the viscosity. Moreover, the average diameter of electrospun nanoibers was found to be dependent on zero shear rate viscosity and normalized concentration (c/cn ) in a power-law relationship with exponents of 0.298 and 0.816, respectively [28]. Härdelin et al. have reported on the synthesis of cellulose nanoibers from ionic liquids through electrospinning process. The zero shear rate viscosity as a function of cellulose concentration showed that all the solutions were in the entangled semidilute regime, where the polymer concentration was large enough for signiicant overlap necessary for chain entanglement [29]. Xu et al. have successfully synthesized PEO composite nanoiber mats by using cellulose nanocrystals (CNCs) and cellulose nanoibers (CNFs) as reinforcement nanoillers. Mechanical properties of the nanoiber mats were signiicantly improved by the addition of low concentrations of CNCs and CNFs. The increases in mechanical properties of the nanoiber mats were primarily caused by the reinforcing effects of CNCs or CNFs on the individual nanoibers [30]. Detailed mechanical properties (such as Young’s modulus, tensile strength) of PEO/CNC and PEO/CNF iber mats are shown in Table 9.2. Terada et al. reported the improved functionality of nanoibers by incorporating polyelectrolyte at optimized potential. Author had observed the defect-free iber formations at optimized voltages of −14 and −16 kV, whereas beaded ibers were formed at lower or higher voltages. Thus, the uniform defect-free smooth nanoibers could be obtained within a certain applied voltage window in the cathodic electrospinning trials, but not in the anodic electrospinning trials [31]. Sousa et al. have successfully TABLE 9.2 Mechanical Properties of PEO/CNC and PEO/CNF Nanoiber Mats [30] Filler PEO CNCs

CNFs

Filler Young’s Tensile Strain at Fracture Content (wt%) Modulus (MPa) Strength (MPa) Failure (%) Toughness (kJ/m3 ) 0 1 4 7 10 1 4 7 10

20 ± 1 72 ± 20 56 ± 20 50 ± 10 22 ± 3 44 ± 9 51 ± 10 24 ± 10 20 ± 3

1.6 ± 0.2 3.5 ± 0.6 2.9 ± 0.4 1.9 ± 0.2 1.3 ± 0.2 2.1 ± 0.1 2.2 ± 0.3 0.8 ± 0.2 1.2 ± 0.3

152 ± 31 204 ± 30 185 ± 11 87 ± 12 71 ± 7 119 ± 25 197 ± 10 86 ± 18 75 ± 12

232 ± 20 702 ± 45 448 ± 16 153 ± 11 84 ± 3 400 ± 40 513 ± 16 72 ± 22 86 ± 9

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synthesized agar-based nanoibers by co-blending polymer such as PVA (10 wt% starting solution), which improved the solutions viscoelasticity and improved the solutions spinnability [32]. Agar/PVA solutions were prepared with different mass ratios (100/0, 50/50, 40/60, 30/70, 20/80, and 0/100) and electrospun at various sets of electrospinning conditions and showed potential opportunities for the fabrication of agar-based biomaterials. Chuangchote et al. have synthesized electrospun PVA nanoiber mats with or without the incorporation of carbon black (CB) nanoparticles [33]. Incorporation of CB (1–10% based on the weight of PVA) in 10% w/v PVA solution did not affect the morphology, but they only affected the irregularity of the as-spun ibers. The incorporation of CB affected both the mechanical and the electrorheological properties of the as-spun PVA/CB iber. While their Young’s modulus was found to increase, both the tensile and the elongation at the break of the as-spun iber mats were found to decrease, with the addition and increasing amount of CB. Zhao et al. have reported electrospinning performance of perluorosulfonic acid (PFSA), PVP, and PFSA/PVP blends with various PFSA/PVP ratios [34]. The electrospinnability of PFSA/PVP/DMF solutions were manipulated by changing the ratio of PFSA to PVP and the total polymer concentration of the mixed solutions. It was noted that the spinnability of PVP solutions increased with the increase in polymer concentration. However, electrospinning of pure PFSA solutions in DMF at a broad concentration range of 5–52 wt% produced only droplets on the aluminum foil collector in spite of the increase in concentration. However, for a ixed total concentration of the mixed polymer solutions exhibited, an increasing weight percentage of PVP or increasing the total polymer concentration with a ixed PFSA/PVP ratio improved the electrospinnability of the PFSA/PVP/DMF

C

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Figure 9.8 (a) Electrospun samples from PFSA/PVP/DMF solutions with different compositions (I – droplets region, II – beaded ibers region, III – ine ibers region) and (b) mixing the two endpoint solutions of the line using principles of balance. Reproduced from Zhao et al. [34] with permission of John Wiley and Sons.

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solution. Figure 9.8a,b shows the detailed PFSA/PVP/DMF solutions with different composition and blend solutions prepared using principles of balance. Gelatin has been used widely at bulk state in foods for thickening and stabilizing purposes. Recently, Okutan et al. have synthesized electrospun gelatin nanoibers at different 7% and 20% solution concentration. The electrical conductivity, surface tension, consistency index, and low behavior index of the gelatin solution at 20% were 4.77 mS/cm, 34.91 mN/m, 1.37 Pa sn , and 0.93, respectively. The range of nanoiber diameters increased with the applied voltage. Wang et al. have successfully electrospun poly(butylene terephthalate) (PBT)-based ibers, and rheological studies revealed the concentration (�, volume fraction) dependence of zero shear rate viscosity (� o ) to be � o ∼ �3.87 in the entangled solution regime, and the entanglement concentration (�e ) was 7.84 vol%. Diasa et al. have reported the rheological behavior of poly(�-caprolactone) (PCL) solutions to produce nanoscale iber meshes by using glacial acetic acid (AA) with triethylamine (AA/TEA) at different concentrations (1.5, 3, 6, 9, and 11 wt%) [35]. The critical concentration (c*) of about 10 wt% for PCL/AA and 9.6 wt% for PCL/AA/TEA was optimum to produce nanoiber meshes without beads. Jin et al. fabricated poly(3,4-ethylenedioxythiophene) (PEDOT) nanoiber mats by electrospinning combined with in situ interfacial polymerization [36]. The prepared PEDOT nanoiber mats exhibited superior mechanical properties with tensile strength, Young’s modulus of 8.7 ± 0.4 and 28.4 ± 3.3 MPa, respectively. The PEDOT iber be restored to its original shape even after serious twisting and crimping. Combined with these properties, PEDOT nanoiber showed an outstanding electrical conductivity of 7.8 ± 0.4 S/cm1 , which make the PEDOT nanoiber mats the promising candidates in biotechnology applications. McKee et al. reported polyelectrolyte rheological behavior of poly(2-(dimethylamino)ethyl methacrylate hydrochloride) (PDMAEMA⋅HCl) by electrospinning process [37]. The aqueous PDMAEMA⋅HCl solutions displayed classic polyelectrolyte behavior with � sp ∼ C0.6 in the semidilute unentangled regime and speciic viscosity (� sp ) ∼ C1.5 in the semidilute entangled regime. Solution rheological studies revealed that PDMAEMA⋅HCl in an 80/20 w/w water/methanol co-solvent displayed polyelectrolyte behavior based on the scaling relationship between � sp and concentration in the semidilute untangled and semidilute entangled regimes. A qualitative comparison of the concentration dependence of � sp for 0.1 and 2.0 wt% PDMAEMA⋅HCl was obtained despite the lack of SEC molar mass information (Fig. 9.9a). From the experimental observation, it was noted that the value of entanglement concentration (Ce ) increased from 1.0 to 8.0 wt%, and CD increased from 10 to 20 wt% as the initiator concentration was increased. The average iber diameter continued to increase from 280 to 480 nm as the PDMAEMA⋅HCl concentration was increased from 10 to 14 wt% (Fig. 9.9b). Polyamide-6 (nylon-6) is a biodegradable, biocompatible, and synthetic polymeric material having good mechanical properties. Pant et al. reported the morphology of the two types of ibers (nano and sub-nano size) arranged with spider-net-like structure using single polymer nylon-6 by electrospinning at different applied voltage (12, 22, and 32 kV) [38]. FESEM images of the mats at different applied voltage

POLYMER AND COMPOSITE NANOFIBER

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Figure 9.9 (a) Inluence of molar mass and concentration on the viscosity of PDMAEMA⋅HCl and (b) the corresponding FESEM images of electrospun PDMAEMA⋅HCl ibers. Reproduced from McKee et al. [37] with permission of American Chemical Society.

POLYMER-BASED NANOFIBER AND ITS RHEOLOGY

(a)

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Figure 9.10 FESEM images of electrospun nylon-6 nanoibers mats at different voltages: (a) m12 (12 kV); (b and d) m22 (22 kV); and (c and e) m32 (32 kV); and (f) typical tensile stress–strain curves of electrospun nylon-6 mat. Reproduced from Pant et al. [38] with permission of Elsevier.

conirmed the formation of nanoibers with diameters around 8–29 nm and arranged in a spider-net-like structure thick nanoibers of about 80–292 nm (Fig. 9.10a–e). It was found that the nanoibers mat of nylon-6 as the function of applied voltage had more surface-to-volume ratio with higher mechanical strength, which was mainly due to the formation of spider-net-like structures by means of stronger hydrogen bonds (Fig. 9.10f). Similarly, Wang et al. have reported electrospun-based nylon-4,6 nanoibers using polyelectrolyte as base solution and examined the iber

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0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10

α-CD

0.35 Viscosity (pa s)

Viscosity (pa s)

formation with change in solution concentration. Based on the solution rheology, the concentration of the entangled regime and the concentrated regime (øD ) were 1 and 10 wt% and yielded bead-free smooth nanoiber of diameter around 49 nm with minimum polymer concentration (10 wt%) [39]. Celebioglu et al. successfully produced nanoibers from native cyclodextrins (CDs) of α-CD and β-CD via electrospinning technique [40]. Experimental observation showed that at very lower CD concentrations, beaded nanoibers with beads were obtained, whereas smooth nanoibers were observed at optimal concentrations (such as 160% and 150% (w/v)) for α-CD and β-CD, respectively. It was noted that the high solution viscosity and viscoelastic solid-like behavior of CD solutions played a key role for the electrospinning of smooth nanoibers. The viscosity of CD solution for the same concentration was being independent of shear rate indicating that the CD systems show the characteristic of a Newtonian luid. In addition, the solution viscosity of CDs increased with the increasing CD concentration due to the presence of higher number of aggregates and their growing sizes (Fig. 9.11). Bajaj et al. successfully synthesized ibers of poly(amide-co-imide)/poly (trimellitic anhydride chloride-co-4,40-methylene dianiline) (PAI/PTACM) blends at different blending ratios [41]. It was noted that the increase in PAI resin content had a signiicant increase in diameter of the nanoibers, whereas the PTACM resin played an important role in determining the morphology and electrospinnability of nanoiber webs. The close relationship was found to exist between the viscosity of the blended solutions and the diameter of the blended nanoiber. The shear viscosity of the PAI/PTACM blending solution was found to be decreased upon increasing the PTACM resin content as the PTACM resin acted as a lubricating agent. With higher PTACM resin content, along with the reduction in the diameter of the PAI/PTACM blend nanoibers, the bead-on-string phenomenon was observed due to the much lower viscosity and molecular weight of PTACM resin. Chisca et al. reported solution rheology of electrospun aromatic polyimide ibers based on 3,3,4,4′ -benzophenonetetracarboxylic dianhydride (BTDA)

10 20 30 40 50 60 70 80 90 100 Shear rate (1/s) (a)

β-CD

0.30 0.25 0.20 0.15 0.10

10 20 30 40 50 60 70 80 90 100 Shear rate (1/s) (b)

Figure 9.11 Viscosity versus shear rate graphs of (a) α-CD solutions and (b) β-CD solutions. Reproduced from Celebioglu et al. [40] with permission of Elsevier.

POLYMER-BASED NANOFIBER AND ITS RHEOLOGY

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(a)

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Figure 9.12 (a) SEM image of the polyimide morphology at different solution concentrations and (b) speciic viscosity concentrations with the corresponding developed morphology. Reproduced from Chisca et al. [42] with permission of American Chemical Society.

and 3,3′ -dimethyl-4,4-diaminodiphenylmethane (MMDA) at different solution concentration [42]. From SEM images, it was observed that at lower concentration, 15% exhibited the formation of a beaded structure with the diameter size in the range of 2−5 μm; whereas at the highest concentration, 30% exhibited defect-free polyimide ibers with the diameter in the range of 0.60−0.85 μm (Fig. 9.12). The changes in the slope of speciic viscosity dependence on the concentration from 1.11 to 4.42 at the critical entanglement concentration Ce is equal to 18.3% (Fig. 9.12b). These modiications also enhanced the low energetic barrier and the solution consistency, inducing a stability of the jet during electrospinning. Modiication of chain interactions in solution relected in a sudden increase of low energetic barrier and consistency index values from 3.56 to 10.28 kJ/mol and 0.19 to 1.09 Pa sn , respectively. Few reports suggested that the temperature had a profound effect on the rheological properties of the solutions through the formation of physical structure. Chae et al. investigated the effects of measuring temperature on the rheological properties of PVDF in dimethyl acetamide (DMAc) solvent with three different concentrations (30, 50, and 70 ∘ C) [43]. The nanoiber web prepared at 14 wt% PVDF/DMAc solutions

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showed the decrease in average diameter from 167.95 to 96.05 nm with an increase in spinning temperature from 30 to 70 ∘ C, which was due to the higher dynamic viscosity and lower loss tangent. In the dilute concentration regime, intrinsic viscosity was decreased with increasing temperature over the range of 30–70 ∘ C, but Huggins constant was increased from 0.301 to 0.345. Park et al. demonstrated the fabrication of conducting PMMA–PEDOT nanoiber mats by a dual process using the electrospinning and oxidative polymerization (OP) methods [44]. The PMMA–PEDOT nanoiber mats exhibited a ine coating of PEDOT on the PMMA nanoibers, leading to good electric conductivity. The high speciic surface area of the PMMA nanoiber mats provided suficient routes for exposing the EDOT monomer to the oxidant; this led to the presence of PEDOT throughout the surface and pores of PMMA nanoiber mats, resulting in a high electrical conductivity.

9.5

NANOFIBER AND ITS POLYMER COMPOSITES

Polymer nanocomposites have provoked great interest in materials science and engineering for their wide potential applications in energy storage devices, electronics, sensors, and aerospace vehicles. Since the discovery of carbon nanotubes (CNTs), intense investigation has been conducted on polymer reinforced by single-walled carbon nanotubes (SWCNTs), multi-walled carbon nanotubes (MWCNTs), and carbon nanoiber (CNF) materials in the ield of composite materials. By relatively incorporating small loadings of CNFs in a polymer matrix resulted in excellent electrical, thermal, and mechanical characteristics. Until now, the majority of research in 1D iber-based polymer composites has been motivated by the importance of several key factors including the rheological behaviors for the development of multifunctional materials. Among these, CNTs and CNFs, both possessing similar properties, have been widely investigated as a proper alternative to enhance the mechanical properties, thermal stability, and the electrical conductivity. For instance, the incorporation of a relatively small content of CNTs signiicantly improved the host material properties by an order of 1010 as this is far from the conductivity of the CNT ilm, 5700 S/m. Sandler et al. studied nanoreinforced ibers of a semicrystalline high-performance PEEK containing up to 10 wt% CNFs. The CNFs were found to be well aligned with the direction of low during processing, and nanocomposite stiffness, yield stress, and fracture strength improved with respect to neat polymer. Upon addition of nanoibers, a signiicant increase in the degree of crystallinity of the matrix was also observed [45]. Xuyen et al. fabricated the CNT-anchored polymer nanoiber mats by in situ spraying of CNTs [46]. An improvement in conductivity of the composite mat with high catalytic current (3400 mA/cm2 /mg Pt) with long-term stability was observed. Gao et al. reported uniform adsorption of CNTs on electrospun polymer nanoiber surfaces by ultrasonication process [47]. It was observed that the maximum weight loss rate of the polyurethane (PU) nanoibers increased from 360.7 to 397.7 ∘ C after CNT adsorption, which was attributed to the uniform dispersion of CNTs as well as the strong interaction between the CNTs and the polymer nanoibers. Paleo et al. reported on the incorporation of two different

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CNFs in PP matrix by twin-screw extrusion under the same processing conditions [48]. The electrical conducting composites based on CNFs showed liquid-like to solid-like transition, which led to the plateaus for G′ , G′′ at low frequencies, whereas the electrical isolating composites based on CNFs remain practically unaltered in their rheological behavior when compared with the pure PP composites. The rheological threshold itted from G′ /G′′ was found to be ∼0.5 vol%, slightly higher than electrical percolation threshold ∼0.4 vol%. Similarly, Kumar et al. have synthesized electrospun ibers from PP/CNF composites possessing superior modulus and compressive strength with respect to the pure polymer at only 5 wt% of CNFs [49]. Gauthier et al. noted that the reinforcement of rubbery matrices by CNFs and the mechanical performances revealed a linear increase in the modulus measured above and below the glass transition temperature for nanoiber content up to 10 wt% [50]. Miyazono et al. reported rheological behavior and morphology of PS/CNF composites in their melt phase [51]. The results suggested that both shear and extensional viscosities increase with increasing nanoiber concentration. Viscosity measurements of the PS/CNF composites in the linear regime showed the ratio of the transient extensional viscosity to the transient shear viscosity to be 3.8–4.6 (MB composites) and 5.8 (SC composites), which was greater than Trouton’s ratio of 3. Bangarusampath et al. reported PEEK/MWNT composites containing up to 17 wt% iller [52]. Linear viscoelastic measurements showed that both complex viscosity and moduli increase with increasing MWNT concentration. The storage modulus G0 exhibited a dramatic increase in seven orders of magnitude around 1 wt%, leading to a solid-like low-frequency behavior at higher loadings; the effect can be attributed to the network formation at a rheological percolation threshold. The electrical response was also dominated by percolation effects, increasing by nearly 10 orders of magnitude from 10−11 to 10−1 S/cm, on the addition of only 2 wt% MWNTs. In contrast, the thermal conductivity and tensile elastic modulus of the composites increased linearly with nanotube content, rising by 130% and 50%, at 17 wt% MWNTs, respectively. Nataraj et al. synthesized electrically conducting CNF mats with diameters ranging from 100 to 300 nm. Different amounts of heteropolyacids (HPAs) were incorporated, namely, silicotungstic acid (SiWA) and silicomolybdic acid (SiMoA) into PAN precursor by electrospinning technique. Electrical conductivity of the CNF mats increased with increasing concentrations of HPAs. Thermal analysis of CNFs showed a strong exothermic peak, for 1 wt% of HPAs, peaks shifted gradually to lower temperatures with increasing concentration of 3 and 5 wt% HPAs. The unusual shift was attributed to higher loadings and the density of the acid sites decreased, which could be mainly due to the decomposition of HPAs into its constituent oxides. The optimal HPA concentration of 5 wt% seemed to be responsible for enhancements of morphological and physicochemical properties of developed CNFs. Tsou et al. have studied both polyelectrolyte and neutral polyamide-6 (PA6) solutions for electrospinning, and their spinnability was correlated with their rheological properties. The effects of the average molecular weight on PA6 and the addition of carbon nanocapsule (CNC) nanoparticle on solution rheology were investigated. Homogeneous PA6 solutions illed with CNCs exhibited more elastic

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behavior than unilled solutions due to the presence of the CNC–CNC network apart from the entangled network of PA6 chains [53]. Tensile properties of electrospun ibers have not been widely investigated due to the dificulties in handling nanoibers and measuring low load for deformation. Recently, Doustgani et al. reported the mechanical properties of electrospun PCL: nano-hydroxyapatite (nHA) composite nanoiber with an applied voltage of 18 kV, 7.5% nHA concentration with an electrode distance of 10 cm, and low rate of 0.6 ml/h exhibited a tensile strength and module of 5.4 ± 0.1 and 12.4 ± 0.22 MPa, respectively [54]. It was noted that the tensile strength increased initially with increasing nHA concentration and then decreased by further increase in the process parameter. Spinning distance showed a decreasing effect on the mechanical properties of electrospun ibers. Shorter spinning distance and applied voltage resulted in stronger iber formation with improved mechanical properties. Recently, there has been a great interest in the unique mechanical, electrical, chemical, and optical properties that can be achieved by combining the advantages of metal nanoparticles and polymer nanoibers. Metal nanoparticle-illed polymer nanoiber composites were prepared by a two-step process in which metal nanoparticles such as silver or gold were synthesized and dispersed into the electrospinning solution. Shi et al. reported the synthesis of silver nanoparticle-illed nylon-6 nanoibers by electrospinning, which showed an excellent ibrous structure (iber diameter of 50–150 nm), with narrow size of 2–4 nm silver nanoparticles uniformly dispersed throughout the nylon-6 matrix [55]. Silver nanoparticle (Ag NP)-illed nylon-6 nanoibers provided a steady and prolonged silver-ion release. Antibacterial assays showed that these nanoibers have over 99.9% inhibition eficiency to Bacillus cereus and almost 99.9999% to Escherichia coli. Celebioglu et al. synthesized size-tunable Ag-NP incorporated into electrospun nanoibers in which in situ reduction of silver salt (AgNO3 ) to Ag-NP was carried out in an aqueous solution of PVA [56]. The size of Ag-NP was ∼8 nm and some Ag-NP aggregates were observed for PVA/Ag-NP nanoibers. The sizes of Ag-NP decreased from ∼8 nm down to ∼2 nm within the iber matrix without aggregation were attained for PVA/hydroxypropyl-beta-cyclodextrin (HPβCD) nanoibers, which acted as additional reducing and stabilizing agent in order to control size and uniform dispersion of Ag-NP. Similarly, Fouda et al. reported that the Ag-NP-embedded carboxymethyl chitosan (CMCTS)/PEO nanoibers exhibit excellent antimicrobial activity compared with nanoibers without Ag-NPs and with Ag-NPs [57]. Zhao et al. fabricated clay/CNF hybrid sheets (0.05 and 0.20 wt%) of Cloisite Na+ clay and integrated onto the surface of laminated composites such as traditional continuous iber mats through vacuum-assisted resin-transfer molding process [58]. The ire performance of the laminated composites was evaluated with cone calorimeter tests under an external radiant heat lux of 50 kW/m2 . Clay/nanoiber hybrid sheets survived on the combustion surface of composites and signiicantly reduced the heat release rate by ∼60.5%. The protective clay layer reduced the heat release rates, and the nanoiber network reinforces the clay layer against the air bubbling and melt low of the products degraded from the polymer resin. The Cloisite Na+ clay layer was strengthened by the nanoiber network, and acted as a perfectly continuous barrier to O2 supply and as a pyrolyzed fuel to the combustion surface of composites.

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Toskas et al. have reported ceramic silica (SiO2 ) hybrid nanoibrous membranes by adding high molecular weight PEO into the silica sol. The viscosity of polymer solutions was related to the intermolecular interactions among the polymer chains and enhanced the formation of the silica nanoibers. The initial dynamic viscosity of 3 wt% PEO used in this study was measured to be 407 mPa s, whereas that of 4 wt% PEO giving unbeaded nanoibers was 1550 mPa s. The conductivities of the spin-dopes that were governed by the PEO solution conductivity, measured 1350 μS/cm, and decreased down to 5.5 μS/cm for the SiO2 /PEO 96/04 wt solution were observed [59].

9.6

CONCLUSION

This chapter gives a summary of the electrospinning process and rheology properties that involved in synthesizing of smooth polymer and composite nanoibers. The rheological behavior of the electrospinning solution inluences the nature of the iber, morphology, and its importance in synthesizing polymeric and composite nanoibers. The electrospun nanoibers and nanocomposites have found applications in areas including iltration, biomedicine, scaffolds for artiicial organs, clinical medicines, thickeners, surfactants, emulsiiers, energy conversion, and environmental remediation and are further being explored. The insights and highlights of polymer and composite electrospinning nanoibers will provide an interesting and useful view of the rapidly developing area of nanoibers in the ield of materials science and technology.

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30. Xu X et al. Comparison between cellulose nanocrystal and cellulose nanoibril reinforced poly(ethylene oxide) nanoibers and their novel Shish-Kebab-like crystalline structures. Macromolecules 2014;47(10):3409–3416. 31. Terada D et al. Transient charge-masking effect of applied voltage on electrospinning of pure chitosan nanoibers from aqueous solutions. Sci Technol Adv Mater 2012;13(1):015003. 32. Sousa AMM et al. Electrospinning of agar/PVA aqueous solutions and its relation with rheological properties. Carbohydr Polym 2015;115:348–355. 33. Chuangchote S, Sirivat A, Supaphol P. Mechanical and electro-rheological properties of electrospun poly(vinyl alcohol) nanoibre mats illed with carbon black nanoparticles. Nanotechnology 2007;18(14):145705. 34. Zhao J et al. Evaluation of electrospun nanoiber formation of perluorosulfonic acid and poly (N-vinylpyrrolidone) through solution rheology. J Mater Sci 2011;46(23):7501–7510. 35. Diasa JR, Antunesb FE, Bártolo PJ. Inluence of the rheological behaviour in electrospun PCL nanoibres production for tissue engineering applications. Chem Eng Trans 2013;32:6. 36. Jin L et al. A facile approach for the fabrication of core-shell PEDOT nanoiber mats with superior mechanical properties and biocompatibility. J Mater Chem B 2013;1(13):1818–1825. 37. McKee MG et al. Solution rheological behavior and electrospinning of cationic polyelectrolytes. Macromolecules 2005;39(2):575–583. 38. Pant HR et al. Effect of successive electrospinning and the strength of hydrogen bond on the morphology of electrospun nylon-6 nanoibers. Colloids Surf A 2010;370(1–3):87–94. 39. Wang C, Jheng J-H, Chiu F-C. Electrospun nylon-4,6 nanoibers: Solution rheology and Brill transition. Colloid Polym Sci 2013;291(10):2337–2344. 40. Celebioglu A, Uyar T. Electrospinning of nanoibers from non-polymeric systems: Electrospun nanoibers from native cyclodextrins. J Colloid Interface Sci 2013;404:1–7. 41. Bajaj B et al. Effect of new poly(amide-co-imide)/poly(trimellitic anhydride chlorideco-4,4[prime or minute]-methylenedianiline) blends on nanoiber web formation. J Mater Chem 2012;22(7):2975–2981. 42. Chisca S et al. Morphological and rheological insights on polyimide chain entanglements for electrospinning produced ibers. J Phys Chem B 2012;116(30):9082–9088. 43. Chae DW, Kim MH, Kim BC. Temperature dependence of the rheological properties of poly(vinylidene luoride)/dimethyl acetamide solutions and their electrospinning. Korea Aust Rheol J 2010;22(3):229–234. 44. Park H et al. Conducting polymer nanoiber mats via combination of electrospinning and oxidative polymerization. Polymer 2013;54(16):4155–4160. 45. Sandler J et al. Carbon-nanoibre-reinforced poly(ether ether ketone) ibres. J Mater Sci 2003;38(10):2135–2141. 46. Xuyen NT et al. Three-dimensional architecture of carbon nanotube-anchored polymer nanoiber composite. J Mater Chem 2009;19(42):7822–7825. 47. Gao J, Hu M, Li RKY. Ultrasonication induced adsorption of carbon nanotubes onto electrospun nanoibers with improved thermal and electrical performances. J Mater Chem 2012;22(21):10867–10872.

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48. Paleo AJ et al. Rheological and electrical analysis in carbon nanoiber reinforced polypropylene composites. J Polym Sci B 2013;51(3):207–213. 49. Kumar S et al. Synthesis, structure, and properties of PBO/SWNT composites. Macromolecules 2002;35(24):9039–9043. 50. Gauthier C et al. Reinforcement effects of vapour grown carbon nanoibres as illers in rubbery matrices. Compos Sci Technol 2005;65(2):335–343. 51. Miyazono K et al. Shear and extensional rheology and low-induced orientation of carbon nanoiber/polystyrene melt composites. J Appl Polym Sci 2011;119(4):1940–1951. 52. Bangarusampath DS et al. Rheology and properties of melt-processed poly(ether ether ketone)/multi-wall carbon nanotube composites. Polymer 2009;50(24):5803–5811. 53. Tsou S-Y et al. Rheological aspect on electrospinning of polyamide 6 solutions. Eur Polym J 2013;49(11):3619–3629. 54. Doustgani A et al. Optimizing the mechanical properties of electrospun polycaprolactone and nanohydroxyapatite composite nanoibers. Compos B 2012;43(4):1830–1836. 55. Shi Q et al. One-step synthesis of silver nanoparticle-illed nylon 6 nanoibers and their antibacterial properties. J Mater Chem 2011;21(28):10330–10335. 56. Celebioglu A et al. One-step synthesis of size-tunable Ag nanoparticles incorporated in electrospun PVA/cyclodextrin nanoibers. Carbohydr Polym 2014;99:808–816. 57. Fouda MMG, El-Aassar MR, Al-Deyab SS. Antimicrobial activity of carboxymethyl chitosan/polyethylene oxide nanoibers embedded silver nanoparticles. Carbohydr Polym 2013;92(2):1012–1017. 58. Zhao Z et al. Fire retardancy of clay/carbon nanoiber hybrid sheet in iber reinforced polymer composites. Compos Sci Technol 2009;69(13):2081–2087. 59. Toskas G et al. Inorganic/organic (SiO2)/PEO hybrid electrospun nanoibers produced from a modiied sol and their surface modiication possibilities. ACS Appl Mater Interfaces 2011;3(9):3673–3681.

10 RHEOLOGY AND PROCESSING OF INORGANIC NANOMATERIALS AND QUANTUM DOTS/POLYMER NANOCOMPOSITES Sneha Mohan Department of Chemistry, Cape Peninsula University of Technology, Cape Town, South Africa; International and Inter University Centre for Nanoscience and Nanotechnology, Mahatma Gandhi University, Kottayam, Kerala, India

Jiji Abraham International and Inter University Centre for Nanoscience and Nanotechnology, Mahatma Gandhi University, Kottayam, Kerala, India

Oluwatobi S. Oluwafemi Department of Applied Chemistry, University of Johannesburg, Johannesburg, South Africa; Centre for Nanomaterials Science Research, University of Johannesburg, Johannesburg, South Africa

Nandakumar Kalarikkal International and Inter University Centre for Nanoscience and Nanotechnology, Mahatma Gandhi University, Kottayam, Kerala, India; School Pure and Applied Physics, Department for Physics and Chemistry, Mahatma Gandhi University, Kottayam, Kerala, India

Sabu Thomas International and Inter University Centre for Nanoscience and Nanotechnology, Mahatma Gandhi University, Kottayam, Kerala, India; School of Chemical Sciences, Department for Physics and Chemistry, Mahatma Gandhi University, Kottayam, Kerala, India

Rheology and Processing of Polymer Nanocomposites, First Edition. Edited by Sabu Thomas, Rene Muller, and Jiji Abraham. © 2016 John Wiley & Sons, Inc. Published 2016 by John Wiley & Sons, Inc.

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10.1 INORGANIC NANOPARTICLE FILLED POLYMER NANOCOMPOSITES Blends of polymers and nanoparticles (NPs), commonly called “polymer nanocomposites” (PNCs), have garnered much attention due to the possibility of dramatic improvement of polymeric properties with the addition of a relatively small fraction of nanoparticles [1]. Structure–property relations between the matrix and the iller and the effect of composite processing in affecting such relations have dominated our understanding of multiphase, multicomponent polymeric materials for a considerable period of time. Inexpensive inorganic substances are widely used as illers to improve mechanical and thermal properties of polymers and polymer composites; to decrease shrinkage and internal stresses during fabrication of polymer articles; to increase thermal conductivity, thermal stability, lame resistance; and, not of least importance, to improve cost-effectiveness. PNCs based on inorganic nanoparticles (NPs) are emerging as an important class of multiphase, multicomponent materials with unique sets of structure–processing–property correlations [2]. The crucial question appearing at realization of nanocomposites concept consists in: “Why nanoillers reinforce polymer with a high eficacy?” There are different versions of answer to this question. All of them are based on superhigh interfaces in such systems, but the angle of vision is different. The main reinforcing effect comes from polymers due to the absorption of macromolecules onto external (e.g., nanoparticles) or internal (intercalated layered silicates) surfaces of nanoparticles, realization of their “non-natural” conformations, formation of dense adsorption layers, and separation of conformations between volume and adsorbed layers. The extend of reinforcement depends on the uniformity of dispersion of illers inside the matrix, and this depends on the eficiency of the mixing technique used for the preparation of that composite system. Solidiication of precursors by cooling (thermoplastics) or cross-linking (reactive resins) leads to “freezing” of these conformations for amorphous polymers or to speciic crystallization behavior for semicrystalline polymers. The term “speciicity” in this case means that depending on macromolecular conformations in liquid precursor, the inal crystalline structure of polymer in solid nanocomposites will be changed. In other words, the introduction of nanodimensional particles modiies the structure of polymer. All these events take place at a minor content of nanoillers, which is less than percolation threshold, and at higher concentration, there is possibility to form arming network by the aggregation of nanoparticles. Based on the above-mentioned concept, the reinforcing effect should be especially expressed at homogeneous distribution of particles. However, all of them, due to high interfacial energy and presence on the surface of functional groups, inclined to form aggregates. 10.2 FABRICATION OF INORGANIC NANOPARTICLE FILLED POLYMER NANOCOMPOSITES Inorganic nanoparticles have opened new strategies for developing a wide range of novel multifunctional materials. Some of them are summarized in Table 10.1.

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TABLE 10.1 Different Routes for the Preparation of Inorganic Nanoparticle Filled Polymer Nanocomposites Method

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Solution processing

Nanoiller is dispersed Faster de-aggregation in a solvent and and dispersion of mixed with a iller. polymer solution by Composites with mechanical mixing, uniform iller magnetic agitation, dispersion or high-energy sonication. Finally a composite can be obtained by vaporizing the solvent

In situ Nanoiller is mixed Composites with polymerization with monomers or uniform dispersion pre-polymers and and improved polymer properties nanocomposites can be obtained by polymerizing the monomers or pre-polymers Melt blending

Temperature assisted mixing of nanoparticle and polymer

Disadvantage Solvent removal is a critical issue. Excess sonication for the dispersion of iller can cause the decomposition of illers

Polymerization process is usually accompanied by a viscosity increase that hinders manipulation and limits load fraction. Solvent removal is a problem

Environmentally It may reduce the friendly, economical aspect ratios of and suitable for nanoiller due to mass production high shear force and thus preventing them to achieve a low percolation threshold and high conductivity of the composites

10.3 WHY RHEOLOGICAL STUDY IS IMPORTANT FOR POLYMER NANOCOMPOSITES PNCs are distinguished from traditional composites by the signiicantly increased interfacial surface area between dispersed nanoparticles and polymer chains in the case of former. In addition, the relatively low concentration of anisotropic nanoparticles at which percolation occurs and the orientational and positional correlation between particles even at low volume fractions of nanoparticles have profound inluences on the rheological properties and processing of these materials [3]. Therefore,

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rheology or low properties of PNCs are extremely rich and diverse and lie between those of the pure polymer (melt) rheology and the rheology of colloidal suspensions. 10.3.1

Assessment of the Dispersion Quality

Properties of nanocomposites are greatly affected by the degree of iller dispersion achieved during mixing operations [4]. Without proper dispersion, the material will not offer improvement in properties over the conventional composites. Therefore, a key challenge in processing nanoparticle-based materials is to control and evaluate the quality of dispersion. Measuring the quality of dispersion by optical methods such as microscopy and light scattering only investigates the local microstructure. In addition, they are either labor intensive or may yield data that are dificult to analyze. The rheological properties, both the linear and nonlinear ones, are sensitive to changes in the particulate microstructure, which integrated overall length scales. Rheological measurements have hence been used for different types of nanocomposite systems as a complementary or indirect technique to monitor the quality of dispersion [5]. One of the advantages of rheology is that using samples of macroscopic dimensions offers an integrated picture of the composite material with increased data reliability, compared to other methods using smaller samples that are in microscale range. Above the percolation threshold, the state of dispersion can be evaluated from the volume fraction dependency of the plateau modulus and the critical strain that limits the linear response regime [6]. The microstructure can be evaluated using scaling laws for fractal aggregate networks. Additionally, changes in the high frequency moduli were also considered as a mean to assess dispersion quality because they enable one to determine the effective hydrodynamic volume of the particles and aggregates over the entire range of concentrations [7]. In analyzing rheology data, it is important to evaluate the effects of low history and the resulting thixotropic response. Pre-shearing protocols that allow suficient rest times between sample loading and experiments are ways in which, at least, reproducible initial conditions can be obtained. 10.3.2

Assessment of Processability

From an application point of view, melt rheological properties are very important for processing of polymer-based nanocomposites. Also, rheometry is a powerful tool for inspecting the internal microstructure of PNCs. Filler network has a crucial inluence on the viscoelastic and low properties of nanocomposites. The features of this iller network depend not only on the nature of the polymer and the chemical and physical characteristics of the iller but also on the extent of the dispersion achieved. Filler networking, that is, the creation of a secondary structure resulting from interparticles’ interactions (agglomeration) is controlled by the iller–iller interaction, the iller–polymer interaction, and the distance between particles. Thus, the quality of the iller microdispersion results from a complex combination of thermodynamic factors (surface energies and interactions between materials), kinetic factors (diffusion mechanisms controlled basically by the polymer viscosity and the size of the particles), and the mechanical and thermal energy input from the mixing or processing operation.

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10.3.3 Assessment of Correlation between Molecular Structure and Dynamics of Polymers (Structure–Property Relationship) Dynamic melt rheometry is a powerful tool to inspect the effect of inorganic iller on the motion and relaxation of polymer chains. The viscoelastic properties of PNCs are determined by a combination of the mesoscopic structure and the strength of the interaction between the polymer and nanoiller. The mesoscopic structure depends not only on the strength of polymer/iller interaction but also on the intrinsic viscoelastic properties of the matrix in which the nanoillers are dispersed. Due to this kind of internal structure, PNCs have provided important characteristics of the static and dynamic properties of conined polymer including viscoelastic properties. Based on the results of DMTA and melt rheometry, a mechanism was suggested that the mobility and relaxation of macromolecular chains were retarded by the geometric coninement of the organoclay network by Wang et al. [8]. The correlation between the mesoscopic iller network structure and the macroscopic properties in isotactic polypropylene/organic montmorillonite clay (iPP/OMMT) nanocomposites has been systematically investigated (Fig. 10.1). It is identiied that the impact of nanodispersed OMMT tactoids and layers on the mobility of polymer chains is weak before the construction of a percolated iller network, which is dominant in determining the macroscopic properties of investigated composites. Once such a percolated iller network is formed, the role of the molecular weight of iPP becomes less important and iller network determines the macroscopic properties of the composites as evidenced from rheological study.

10.4 RHEOLOGY OF QUANTUM DOT BASED POLYMER NANOCOMPOSITES Semiconductor nanocrystals, also known as quantum dots (QDs), with dimensions close to the Bohr radius (aB) of the electron–hole pair, have got considerable attention in scientiic research because of their unique size-dependent optical properties. A QD is a semiconductor nanoparticle that ranges from 2 to 20 nm in diameter. Traditionally, QDs are made of chalcogenides (selenide or sulphate) of metals such as cadmium or zinc (e.g., CdSe and ZnS), but QDs composed of other materials also exist. The salient property of a quantum dot is that it absorbs ultraviolet (UV) light and emits the light in the visible spectrum [9]. This ability for a particle to receive one type of signal and produce a different type of signal is unique among nanoparticles and has been used in the areas of data storage and sensing devices. The color of the quantum dot in visible and UV light is dictated by the size of the dot. For example, a QD particle of 2 nm will appear blue in visible light and glow green under UV light, and when QD particle of 7 nm will appear as orange in visible light which appear as red under UV light (Fig. 10.2). These materials retain some of the familiar properties of bulk semiconductors and also have absorption and emission spectra that are tunable with particle size [11–13]. Their remarkable photostability and spectral tunability via size control are beneicial for tunable light source in various applications.

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105 104

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Figure 10.1 Linear melt-state rheological properties as a function of oscillatory frequency: (a) storage modulus, G′ and (b) loss modulus, G′′ . Reproduced from Wang et al. [8] with permission of Elsevier.

QDs in the III–V family are valued mainly in the application of their optical and electronic properties, such as high-frequency (high-speed) electronic devices, high-frequency light-emitting devices, and light detectors with high eficiency. Measurement tools for the study of optical properties of QDs include photoluminescence, time-resolved photoluminescence, and the temperature change experiments that come with the power changes in the optical excitation or pumping or the cryogenic systems, and these may obtain the radiation photon spectra of the e-hole recombination from spectral data and the relaxation mechanism and time of its carriers, life information, and other device-related parameters. For many applications, either the surface of the QDs must be chemically engineered or the QDs must be embedded in a solid matrix. The stability of the nanocrystals in solution is limited by the stability of the ligand at the QD surface.

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Figure 10.2 Size-tunable luorescence spectra of CdSe quantum dots (a) and illustration of the relative particle sizes (b). From left to right, the particle diameters are 2.1, 2.5, 2.9, 4.7, and 7.5 nm. Reproduced from Smith and Nie [10] with permission of Royal Society of Chemistry.

Polymer-coated QDs were thought to be more stable as compared to QDs coated with small organic ligands. Additionally, by using polymers, multiple and diverse chemical functionalities can be introduced at the QD surface. The success of approaches based on the direct functionalization of the QD surface lies in the ability of the QDs to retain the luminescence properties after functionalization. The polymers at the QD surface may also play an interfacing role between the QDs and the surrounding matrix. For example, electron-transfer processes between the QDs and the surrounding matrix are essential in a range of optoelectronic devices such as solar cells. Functionalization of the QD surface with electroactive polymers is therefore explored with the aim of facilitating the charge transfer across the QD/polymer interface. A number of strategies were developed to obtain polymer-coated QDs. Hydrophobic interactions between the nanocrystals’ surface ligands and polymers are for instance used to create a thin polymeric coating on the QD surface. This approach does not involve ligand exchange reactions and is therefore expected not to interfere with the optical properties of the QDs. Other methods of QD functionalization include the attachment of macromolecules directly onto the QD surface via multiple or single bonds, or polymerization of polymeric chains directly from the QD surface. All the latter methods require an intermediate ligand exchange step and usually lead to changes in the photophysical properties of the QDs. Since most synthetic polymeric materials are transparent in the visible part of the electromagnetic spectrum, they are often employed as

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matrices for nanocomposite materials for optical applications [14, 15]. Apart from playing the role of the matrix, polymers provide mechanical and chemical stability to the nanocomposite material. Additionally, polymers may prevent nanocrystal agglomeration and offer processability into technologically relevant structures such as thin ilms, or micro- and nanospheres [16]. Despite many advantages that a combination of QDs with polymeric materials has to offer, the development in this ield of research has been relatively slow. The main dificulties encountered include poor compatibility of the QDs with the polymers and deterioration of the electronic or optical properties of the QDs after conjugation with the polymers [17]. To improve the stability of the QDs in the polymer spheres, the nanocrystals can be directly coupled to the polymer matrix [18]. The coupling can be realized by using functionalized polymers able to bind to the nanoparticle surface or by employing functionalized surfactants. Thiol-modiied polystyrene (PS) microparticles have been used to immobilize CdS or CdS/ZnS nanoparticles [19, 20]. The resulting CdS–PS hybrid spheres were, however, not stable against photoirradiation, and fusion of the nanoparticles was found to occur inside the polymer spheres. Such fusion of the nanoparticles leads to a broadening of the size distribution, as well as to the deterioration of the photophysical properties. Coating the QDs with a ZnS shell or encapsulating the CdS–PS particles with an in situ prepared polyurethane shell has been found to suppress the undesirable CdS growth. Atabey et al. [21] investigated the rheological behavior of polyvinyl alcohol (PVA) and its nanocomposite ibers illed with different concentrations of CdSe and ZnS quantum dots prepared via electrospinning process and found that pure PVA solution was more viscous than the PVA/QDs dispersions. Addition of 5 wt% octadecylamine-coated QDs led to dramatic decrease in viscosity values due to the uniform dispersion of nanoparticles in polymer matrix, which reduces the tendency toward uncontrolled locculation (Fig. 10.3). Composites have been modeled using a power-law equation: ( )n �(u) �=K (10.1) �(y) where � is the shear(stress, ) K is the low consistency index and can be related to the �(u) luid viscosity, and �(y) is the shear rate, the value n determines the low behavior. Here at low loading of QDs, system behaves like Newtonian luid, and at higher loading there is a tendency to change from Newtonian to non-Newtonian behavior. K values are quite consistent with viscosity curves depending on the QDs loading. Mahmoudifard et al. studied the effect of QD concentration on the viscosity of polyvinyl alcohol nanocomposites [22]. They claimed that at low concentration, QDs act as a spacer between polymer chains and thus reduction on viscosity was observed compared to pure PVA solution. But at higher concentration of QDs due to the entanglement of polymer chains around QD particles or QDs aggregation, the increase in viscosity occurs. Effect of polymer concentration on linear viscoelastic behavior of PMMA/QD nanocomposites was studied by Wei et al. [23]. The viscosity increases with increasing the PMMA loading and decreases with the addition of QDs when compared with that of the neat PMMA solution.

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Figure 10.3 (a) Shear stress versus shear rate and (b) viscosity versus shear rate of neat PVA solution and PVA/QDs dispersions and SEM images of 0% QDs, 1.0% QDs, and 5% QDs in PVA. Reproduced from Atabey et al. [21] with permission of SAGE.

Electrospinning is a very useful technique to produce uniform polymer nanoibers. But it is really a challenge to electrospin elastomers into stable microibers and nanoibers because of their low glass transition temperature and viscous surface, which make the as-spun ibers merge quickly into large ibers or even a continuous thin ilm. Ionic liquid can be used as a solvent for electrospinning of elastomer/QD composites [24]. Vistamaxx 6202 propylene-based elastomer (VM) with an ethylene content of 15 wt% was mixed with octadecylamine-capped CdSe/ZnS QDs using toluene as a solvent to prepare its PNC ibers. Ionic liquid was added into one set to improve the ionic conductivity of the sample. On analyzing the rheological data, it is seen that all the composites with ionic liquid show higher viscosity compared to those without ionic liquid. Addition of nanoparticles to polymer leads to a dramatic decrease in viscosity up to a particular concentration of QDs after which the viscosity increases. This is because of a dilution effect rather than entanglement owing to their faster diffusion, which provides constraint release and leads to viscosity reduction. The unusual viscosity reduction in the spherical QD-suspended elastomer solutions is beneicial for the nanocomposite processing and manufacturing for several potential applications (Fig. 10.4). Wei et al. [23] studied the rheological behavior of poly(methyl methacrylate) (PMMA)-CdSe/ZnS quantum dots (QDs) nanocomposite ibers with various iller

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Figure 10.4 Viscosity versus shear rate of the solutions (a) without IL and (b) with 1 wt% IL and shear stress versus shear rate of the solutions (c) without IL and (d) with 1 wt% IL. Reproduced from Zhu et al. [24] with permission of Elsevier.

loading and fabricated via a simple electrospinning method. The PMMA-QD nanocomposite ibers were fabricated from the PMMA solutions with PMMA concentration of 8, 10, 12, 18, and 22 wt% and QD concentration of 0.04, 0.06, 0.08, and 0.1 wt% (against the neat polymer). Rheological studies revealed a pseudoplastic behavior of both pristine PMMA and PMMA-QD solutions. Figure 10.5a,b shows the viscosity and shear stress as a function of the shear rate for the PMMA and PMMA/QD solutions. The viscosity increases with increasing the PMMA loading (Figure 10.12a). With the addition of QDs to the PMMA, the viscosity decreases when compared with that of the neat PMMA solution. The shear stress versus shear rate plot does not follow a linear relationship (Figure 10.12b), in the PMMA and PMMA/QD solutions, which is the characteristic of Newtonian luids. The curve obtained shows the pseudoplastic nature of the polymer solution, in which viscosity decreases with increased stress [26]. Elliott et al. [27] studied the effect of QDs on the photopolymer PolyJet on the 3D printing property of the material. Results show that the printability was not signiicantly affected by the presence of quantum dots in mass concentrations less than or equal to 0.5%.

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Surface tension (mN/m)

The nanosuspensions were deposited via inkjet to demonstrate the feasibility of creating optically unique artifacts. Surface tension is the force present at the interface of two luids caused by the attraction between similar molecules. Surface tension is signiicant in determining the jettability of a luid, and both the size and the concentration of the nanoparticles matter when determining the effect of particles on the surface tension of a luid. The data in Figure 10.6 reveals that the addition of QDs in 0.5 wt% did cause an increase in surface tension. The viscosity of a luid is the luid’s resistance to deformation. With a high viscosity, the luid has a high resistance to deformation. A luid with high viscosity requires more energy to eject from an inkjet nozzle (Fig. 10.7). Experimental results showed an average of 0.15% increase in viscosity, with the average measured viscosity of the control polymer and the suspension with the highest QD loading (0.5 wt%) being 0.01982 ± 0.0012 and 0.01985 ± 0.0015 Pa s,

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Figure 10.6 Surface tension at varying concentrations of QD’s. Reproduced from [27] with permission of Amelia Elliott.

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Figure 10.7 Viscosity of QD’s + photopolymer. Reproduced from [27] with permission of Amelia Elliott.

respectively. Figures 10.3–10.6 shows one standard deviation from the average viscosity (of three samples each) collected for pure polymer highlighted in gray. As shown, the average viscosity for all sample concentrations lies within one standard deviation from the average viscosity found for pure polymer. Although an increase average viscosity can be seen for the 0.02 wt% sample, the overlap of the error bars signiies that there is no signiicance in this higher average value.

10.5 METAL OXIDE NANOPARTICLE-BASED POLYMER NANOCOMPOSITES Metal oxides can adopt a vast number of structural geometries with an electronic structure that can exhibit conductor, semiconductor, or insulator character. In technological applications, oxides are used in the fabrication of microelectronic circuits, sensors, piezoelectric devices, fuel cells, coatings for the passivation of surfaces against corrosion, and as catalysts [28]. In order to expand the area of application, metal oxides are used to prepare various polymer metal oxide nanocomposites with unique properties. 10.5.1

Alumina

Alumina nanoparticles are one of the best choices as illers in a broad range of polymer nanocomposites. Alumina nanoparticles are low in cost and can be easily functionalized. They have been used as illers with a broad choice of polymer matrices such as epoxy, poly(methyl methacrylate), polystyrene, and poly(vinyl ester) [29–31]. According to Khumalo et al., addition of unfunctionalized synthetic boehmite alumina (BA) practically did not inluence the thermal (melting and crystallization) and rheological properties of the pure PEs [32]. But BA worked as a powerful thermo-oxidative stabilizer for polymer. The melt rheology of the PE/BA nanocomposites was well matched with that of the parent PEs. They concluded

METAL OXIDE NANOPARTICLE-BASED POLYMER NANOCOMPOSITES

367

that this type of behavior is very beneicial for the processing of nanocomposites as their melt viscosity practically does not change with either type or amount of BA. Rheological and morphological analyses of addition of surfactant in the styrene–butadiene–styrene (SBS) had a great inluence on the spatial orientation of microdomains, which leads to morphological changes for the composites [33]. Rheological study of bisphenol E cyanate ester/alumina nanocomposites shows that both complex viscosity and storage modulus increase with an increase in alumina loading. Pseudoplastic or “shear-thinning” behavior of each composite is not only due to the formation of hydrogen bonds between hydroxyl groups of neighboring particles formed under low shear, which are broken under high applied shear, but also due to the physical entanglement and agglomeration of nanoparticles. “Shear-thinning” behavior is more pronounced at higher iller loadings, where the distance between particles is reduced and particles are more likely to agglomerate. Einstein’s equation [34] for the viscosity of a suspension of rigid spherical particles is (10.2) � = �m (1 + kE �f ) where � and � m are the viscosity of the suspension and suspending matrix liquid, respectively, �f is the volume fraction of iller, and kE is Einstein coeficient given by kE = 2.5 +

VL VS

(10.3)

where VS is the actual volume of the spheres in a typical agglomerate and VL is the volume of the matrix luid that is entrapped within the agglomerate or on its surface. Einstein equation shows a very good agreement with experimental results at lower iller loading. Many modiications to Einstein equation have been proposed mainly by Roscoe and Mooney equations. The Roscoe equation [35] is given by ) ( �f (10.4) � = �m 1 − �max where �max is the maximum volume fraction possible and its value ranges from 0.37, for random close packing (agglomerated), to 0.74, for hexagonal close packing. The Mooney equation [36] shows very good agreement between experimental and theoretical values of viscosity over the entire concentration range and is given by ( ) kE �f (10.5) � = �m exp 1 − �f∕�max The viscosity of epoxy/alumina suspensions at a shear rate of 100 s−1 shows that the best it is given by the Mooney model �max of 0.37 and kE of 16.4. The experimental viscosity of the composite is much higher than that predicted by the Roscoe model. This is due to the strong interaction between alumina and epoxy via hydrogen bonding of cyanate groups in epoxy with the hydroxyl groups on the alumina surface (Fig. 10.8).

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0.18 BECy/alumina suspension Roscoe (ϕmax = 0.601) 0.16

Roscoe (ϕmax = 0.37) Mooney (ϕmax = 0.601, kE = 2.5) Mooney (ϕmax = 0.37, kE = 16.4)

η (Pa s)

0.14

0.12

0.10

0.08 0.00

0.02

0.01

0.03

ϕr

Figure 10.8 Viscosity at a shear rate of 100 s−1 versus volume fraction of nanoparticles. Lines represent the different theoretical models. Reproduced from Sheng et al. [37] with permission of John Wiley and Sons.

10.5.2

Silica

Silica as a nanoiller is well studied and has seen wide applications as an agent to reinforce and modify the rheological properties of liquids, adhesives, and elastomers [38, 39]. Rheological studies of polystyrene/silica by Vaziri et al. showed that viscosity decreases with an increase in silica loading due to good chain/nanoparticle surface interaction, which is the result of high surface area of nanoparticles [40]. The decrease in melt viscosity of poly(propylene) through the addition of a minute amount of silica nanoparticles is attributed to the unique effect of “selective adsorption of high molar mass polymer chains” on the surface of the nanoillers [41]. Adsorption of high molar mass chains on the surface of nanoparticles eventually leads to a reduction in entanglement density, therefore enhancing the lowability or reducing the viscosity (Fig. 10.9). The concept of selective adsorption of high molar mass polymer chains on nanoiller surface may lead to a possible breakthrough by changing the classical power-law relationship, � � (Mw)3.4 , between molar mass of the polymer and the viscosity of polymeric materials. Temperature effects on the rheological behavior of uncured epoxy resin with different loadings of SiO2 conirm a low viscosity, thus a large processing window exists prior to the initiation of cure. As loading increases, the curing response shifts to lower temperature. The onset temperature is taken from

METAL OXIDE NANOPARTICLE-BASED POLYMER NANOCOMPOSITES

Reaction temperatures TONSET TMAX 10.0% 118 °C 160 °C 166 °C 5.0% 123 °C 170 °C 1.0% 132 °C 172 °C 0.0% 137 °C

104 103 102 η* (Pa s)

369

101 100 10–1 10–2

60

80

100

120 140 Temperature (°C)

160

180

200

Figure 10.9 Viscosity versus temperature data from a series of SiO2 /Epon862/W nanocomposite samples. The onset temperature is taken from the crossing of tangent lines representing the minimum viscosities and the trend at the steepest part of the curves (tangent lines not shown). The maximum temperature was taken as the maximum of the derivative of the viscosity proile, �*. Reproduced from Chen et al. [42] with permission of Elsevier.

the crossing of tangent lines representing the minimum viscosities and the trend at the steepest part of the curves 10 wt% as a function of temperature [42]. Effect of surface modiication of silica nanoparticles on the rheological behavior of melt compounded functionalized ethylene-octene copolymer (EOC) nanocomposites were investigated by Bailly et al. [43]. Both functional groups grafting on polymer surface and iller modiication improve the interaction between these two. Fractal-like composite structure agreed with the exponents determined through small-angle oscillatory shear rheometry (SAOS). The effect of polymer/iller interactions on the rheological properties is provided through experiments on frequency sweeps, time sweeps, and strain sweeps. Both frequency sweep and stress sweep measurements showed that the values of the moduli at low frequencies scaled with the volume fraction according to a power-law relation, which is consistent with the presence of a fractal structure. Time-sweep experiments showed that the composites were prone to aggregation in the absence of chemical interactions between iller and hosting polymer. Inluence of polymer–particle and particle–particle interactions on the viscoelastic properties of nanocomposite materials is investigated using narrow molecular weight distribution poly(ethylene oxide) (PEO) containing isotropic silica nanospheres [44]. The iller networking mechanism was proposed to explain the improved viscoelastic

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response of the illed composites. First, conined polymer shells surrounding silica nanoparticles make the effective particle volume fraction much higher than the real particle volume fraction. Second, silica particles are strongly bridged with adsorbed PEO molecules, forming a temporary polymer–particle network. The long-time response of PEO/silica nanocomposite melts with small-amplitude step shear strains shows two distinct relaxation modes: a fast mode believed to arise from relaxation of “free” PEO molecules in the matrix and second mode believed to arise from relaxation of the iller structure. It is possible to estimate the effective polymer–particle interphase thickness from the decreases in damping behavior. The magnitude of the tan � peak decreases with increasing iller content. If the damping of the rigid iller is neglected, the decrease in damping as a result of replacing polymer with iller is given by tan �c = tan � m (1 − �f )

(10.6)

where tan � c is the damping of the composite and tan � m is the damping of the matrix [45]. A correction parameter, P, is introduced if there is signiicant decrease in damping factor as a result of strong interaction between iller and matrix [46]. tan �c = tan � m (1 − P�f )

(10.7)

The effective interfacial thickness of the interphase between the polymer and particle, ΔR, is related to P by ( ) ΔR 3 P= 1+ (10.8) R where R is the radius of the particles in question. Using Equations 10.7 and 10.8, interphase thickness can be calculated. There is a general decreasing function of ΔR with respect to volume fraction, possibly indicating that as volume fraction increases, there is a greater extent of overlap in the interphase regions due to increasing nanoparticle agglomeration (Fig. 10.10). Several rheological parameters such as Payne effect, percolation threshold, and elastic effects are theoretically and experimentally studied for silica reinforced ethylene vinyl acetate by Cassagnau et al. [47] The Payne effect refers to the effect of strain dependence of the dynamic viscoelastic properties of illed polymers in amorphous state above Tg . For a particular frequency, the storage modulus decreases with increasing deformation from a linear plateau value to a lower plateau at high amplitude of the deformation, whereas the loss modulus exhibits a pronounced peak. The nonlinear behavior (Payne effect) can be associated with both mechanisms of chain disentanglements and iller network breakdown depending on silica concentration and amplitude deformation. The structure–property correlations of PNCs can be related to the two main reinforcement effects: the iller network contribution and a iller–polymer matrix effect. The mechanical response of the material at low deformation is investigated by Jouault et al. using ARES oscillatory shear plate–plate rheometer and

METAL OXIDE NANOPARTICLE-BASED POLYMER NANOCOMPOSITES

371

106

8.6

105

6.6 G′ (Pa)

Si%

3.4 2.3

104 EVA

103 10–2

10–1

100

101

102

103

Strain (%)

Figure 10.10 Variation in storage modulus with strain rate. Reproduced from Cassagnau [47] with permission of Elsevier.

dynamical mechanical analysis, DMA [48]. Low deformation measurements are interesting because the microstructure of the ilms shows much less alteration. Time–temperature superposition was applied to analyze the long range effect of rheology. According to Williams–Landel–Ferry (WLF) equation log(aT) =

C1 (Tref − T) C2 + T − Tref

where aT is the multiplicative factor, Tref is the reference temperature of the master curve (in our case 143 ∘ C), T is the temperature of the measurement, and C1 and C2 are the WLF parameters. The variations of the elastic modulus and loss modulus were analyzed as a function of the product of the pulsation � (rad/s), by the factor aT of time–temperature superposition to a reference temperature of 143 ∘ C for all composites, which varies in silica loading. It is observed that at high pulsation �aT > 100 rad/s, whatever the silica volume fraction, the behavior of the nanocomposite is very close to the one of the PS matrix. At intermediate and low frequencies, differences appear. At �aT > 10 rad/s, this is limited to a progressive increase in G′ with silica fractions, analogous to elastic reinforcement as expected. But in the lowest pulsation regime, �aT < 1 rad/s, a much more differentiated behavior is observed: adding silica greatly increases the terminal times. So it is concluded that with longer time spans (than the matrix terminal time) and small deformation (1%), a more surprising mechanical signature appeared below the silica volume fraction threshold for connectivity: the material exhibited an additional elastic contribution with very long terminal times (Fig. 10.11).

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372

107

105 G′ (Pa) 0% G′ (Pa) 1% G′ (Pa) 2% G′ (Pa) 3% G′ (Pa) 4% G′ (Pa) 5%

103 10–3

10–1

101 . ω aT (rad/s) (a)

103

G″ (Pa)

G′ (Pa)

107

105 G″ (Pa) 0% G″ (Pa) 1% G″ (Pa) 2% G″ (Pa) 3% G″ (Pa) 4% G″ (Pa) 5%

103 10–3

10–1 101 . ω aT (rad/s) (b)

103

Figure 10.11 Elastic shear modulus G′ (a) and G′′ (b) as a function of pulsation �, using time–temperature superposition (T0) 143 ∘ C) coeficient aT deined in the text, for different volume fractions of silica in the composite (0%, 1%, 2%, 3%, 4%, and 5% v/v). Reproduced from Jouault et al. [48] with permission of American Chemical Society.

Rheological properties of polypropylene (PP)/ethylene–propylene–diene terpolymer (EPDM)/silicon dioxide (SiO2 ) ternary composites produced by two processing steps have shown that fabrication method has great inluence on the rheological behavior of nanocomposites [25]. Two-step processing method made the solid-like behavior occurred at an earlier stage compared with that of a one-step processing method, also, the higher elastomer content facilitated the formation of the iller–network structure (Fig. 10.12). 10.5.3

Titania

TiO2 has emerged as one of the most fascinating and interesting materials of the present era. It captures the attention of physical chemists, physicists, material scientists, and engineers in exploring many of its wonderful properties such as semiconducting and catalytic properties [49]. The low properties of PP–TiO2 composites have been studied as a function of the particle iller size by Acierno et al. [50]. Signiicant increases of both the elastic and the viscous moduli have been noticed for the nanocomposite, while negligible effects have been identiied for the microcomposite. The presence of TiO2 nanoparticle clusters observed through electron microscopy seems to be responsible for the rheological behavior of nanostructured formulations. Rheological analysis of LDPE/TiO2 master batch and LLDPE/LDPE composites shows that as TiO2 nanoparticles were introduced in the form of master batch where they are pre-dispersed in a low molecular weight LDPE viscosity, the resulting nanocomposites decreased compared to unilled one [51]. This will be beneicial to the ine dispersion of LDPE/TiO2 master batch in LLDPE/LDPE composite ilms

METAL OXIDE NANOPARTICLE-BASED POLYMER NANOCOMPOSITES

4×108

105

4×106

105

0 min 10 min 20 min 30 min

1000 800 600

4×104

0.2

0.3

G′ (Pa)

0.1

0.4

ω (rad/s)

1/2

103

102

10–1

100 101 ω (rad/s) (a1)

0 min 10 min 20 min 30 min

104

1/2

1/4 200 0.1

0.2

0.3

0.4

ω (rad/s)

1/2

103

102

102

G′ (Pa)

G′ (Pa)

G′ (Pa)

104

0 min 10 min 20 min 30 min

400

1/2

4×102

373

0 min 10 min 20 min 30 min

10–1

100 101 ω (rad/s) (b1)

0 min

η* (Pa s)

η* (Pa s)

0 min

104

10 min 20 min 30 min

104

103

10–1

100 101 ω (rad/s) (a2)

102

102

10 min 20 min 30 min

103

10–1

100 101 ω (rad/s) (b2)

102

Figure 10.12 Frequency-dependent viscoelastic properties of PP/EPDM/B-SiO2 (80/20/3) composites at different mixing time: (a) one step; (b) two steps: (1) storage modulus (G0 ) and (2) viscosity (�*). Reproduced from Yang et al. [25] with permission of Elsevier.

during the latter blow-forming process. On comparing the non-Newtonian index curves of the composites, they exhibit different variety rule of non-Newtonian index before and after the intersection. The lower non-Newtonian index shows a stronger viscoelastic behavior of the melting composites. Moreover, the non-Newtonian index of LDPE/TiO2 master batch decreases slightly compared to that of LLDPE/LDPE composites, indicating that LDPE/TiO2 master batch has a relatively steady viscoelastic behavior. It is reported that the introduction of TiO2 nanoparticles inluences the processability of HIPS slightly. At a low TiO2 content, it seems to improve the rheological behavior. Further analysis indicates that this is owing to the further dispersion of TiO2 nanoparticles induced by shear [52] (Fig. 10.13). Effect of surface functionalization on TiO2 nanoparticles has been investigated by several researchers [53, 54]. The introduction of surface-coated particles remarkably increases the shear viscosity of the composite melts in the low shear rate region due to the strong interfacial interaction. The surface coating endows the composite with a stronger shear-thinning behavior compared to that with uncoated nano-TiO2 . ER luids are suspensions consisting of particles with high dielectric constant and low

RHEOLOGY AND PROCESSING OF INORGANIC NANOMATERIALS AND QUANTUM

374

LLDPE/LDPE (weight ratio = 3:1)

Non-newton index n

1.0

LDPE/TiO2 master batch TiO2wt.–%=20

0.8 0.6 0.4 0.2 0

500 1000 1500 2000 2500 Shear rate γ (s−1)

Figure 10.13 Flow index versus shear rate with different composites and SEM image of TiO2 nanoparticles dispersed randomly in LLDPE/LDPE/TiO2 composite ilms. Reproduced from Wang et al. [51] with permission og John Wiley and Sons.

conductivity dispersed in an insulating liquid medium whose rheological properties can rapidly and reversibly vary upon application of an external electric ield. One-dimensional polyaniline/titanate (PANI/TN) composite nanotubes, which were synthesized by in situ chemical oxidative polymerization directed by block copolymer, were used as a dispersed phase in electrorheological (ER) luids, and the ER properties were investigated under both steady and dynamic shear [55] (Fig. 10.14). Figure 10.15 shows the low behavior for both composite nanotube-based luids

102 102 0.0kV/mm 1.0 kV/mm 2.0kV/mm 3.0kV/mm

1

101 0.0kV/mm 1.0kV/mm 2.0kV/mm 3.0kV/mm

100

102 101 0.0 kV/mm 1.0 kV/mm 2.0 kV/mm 3.0 kV/mm

100 100

101

102 −1

Shear rate (S )

103

Shear viscosity (Pas)

Shear stress (Pa)

10

100

0.0kV/mm 1.0 kV/mm 2.0kV/mm 3.0kV/mm

102 101 100 10−1

100

101

102

103

−1

Shear rate (S )

Figure 10.14 Flow curves for PANI/TN-1 (b, d) and PANI/TN-2 (a, c) based luids under different electric ield strengths. Reproduced from Cheng et al. [55] with permission of John Wiley and Sons.

METAL OXIDE NANOPARTICLE-BASED POLYMER NANOCOMPOSITES 6

Epoxy

2 wt% u-Fe3O4

5 wt% u-Fe3O4

Epoxy 7

15 wt% u-Fe3O4 Viscosity (Pa s)

Viscosity (Pa s)

10 wt% u-Fe3O4

5

375

2 wt% f-Fe3O4

10 wt% f-Fe3O4

5 wt% f-Fe3O4

15 wt% f-Fe3O4

6

5

4 4

400 600 Shear rate (1/s) (a)

200

800

1000

200

7

8

Solid symbol: u-Fe3O4

Open symbol: f-Fe3O4 Viscosity (Pa s)

Viscosity (Pa s)

1000

6

53.58 1/s 211.3 1/s 579.4 1/s 1000 1/s

5

800

Solid symbol: u-Fe3O4

Open symbol: f-Fe3O4 6

400 600 Shear rate (1/s) (b)

4 25 °C 70 °C 120 °C

2

4

0 0

2

4

6 8 10 Fe3O4 loading (wt %) (c)

12

14

200

400 600 Shear rate (1/s) (d)

800

1000

Figure 10.15 Viscosity versus shear rate of epoxy resin suspensions illed with different loadings of (a) �-Fe3 O4 NPs and (b) f-Fe3 O4 NPs at 25 ∘ C; (c) effect of surface functionalization on the viscosity of Fe3 O4 /epoxy nanocomposite suspensions with different loadings under different shear rates at 25 ∘ C; (d) Effect of temperature on the viscosity of epoxy resin suspensions with a Fe3 O4 particle loading of 15 wt%. Reproduced from Gu et al. [56] with permission of American Chemical Society.

under different electric ield strengths. Without an electric ield, both luids show a slight deviation from the Newtonian luid. In the presence of an electric ield, the shear stress increases abruptly showing a yield behavior of a Bingham luid, and the viscosity exhibits a strong shear-thinning behavior. Meanwhile, the shear stress and shear viscosity of both luids increase with an increasing electric ield strength at the same shear rate. Viscoelastic measurements also indicate that the storage modulus is larger than the loss modulus in the linear viscoelastic region, and the chain structures formed by polarizable particles become more elastic and stiffer with increasing electric ield strength. On comparing the viscoelastic properties of Nitrile rubber reinforced with different illers such as TiO2 , Ca3 (PO4 )2 , and layered silicate, it is observed that the storage modulus of the composites increased with the addition of iller due to the enhancement in stiffness of the material. The damping behavior was found to decrease as a function of iller loading, and this was due to the restricted movement of the polymer segments. The higher surface area-to-volume ratio factor

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RHEOLOGY AND PROCESSING OF INORGANIC NANOMATERIALS AND QUANTUM

of the layered silicate resulted in the better interaction between the polymer matrix and the iller, which resulted in the change in glass transition temperature [57]. 10.5.4

Zinc Oxide

Dynamic rheometry using a parallel-plate rheometer showed that the rheological moduli of the nano-ZnO reinforced polypropylene nanocomposites increased with an increase in nanoiller concentration and this increase was greater in the high-frequency region [58]. There was an increase in complex viscosity of the nanocomposites with increasing the nanoiller concentration. Moreover, the rheological behavior of nanocomposites is more sensitive to nanoparticle concentration at low frequencies. All of the models used for prediction of melt viscosity underestimated the viscosity of nanocomposites; however, the Einstein equation was in agreement with experimental values. 10.5.5

Ferrite Nanoparticles

An understanding of the rheological properties of composites is of great importance because it provides a critical clue to determine the processing conditions in a real polymer processing such as extrusion and injection molding. The effects of ferrite nanoparticle loading, surface functionality, and temperature on both the viscosity and storage/loss modulus of liquid epoxy resin suspensions and the physicochemical properties of the cured solid PNCs are systematically investigated by Gu et al. [56] Viscosity increases with increasing NP loadings and decreases with increasing shear rates. The G′ and G′′ increase with increasing NP loadings. The surface functionalization can make Fe3 O4 NPs uniformly dispersed in the polymer matrix and has more obvious effects on the G′ than on G′′ . The viscosity of pure epoxy resin decreases with increasing temperature. At high temperature, the obvious phase separation between �-Fe3 O4 NPs and epoxy monomers is observed during the viscosity measurement, which increases the resistance of the laminar motion of the liquid, thus, the viscosity of epoxy resin suspension with �-Fe3 O4 NPs is higher than that of epoxy resin suspension with f-Fe3 O4 NPs, indicating that a better compatibility between f-Fe3 O4 NPs and epoxy resin. The decrease in viscosity of composites with the addition of nanoparticles because of retarded chain mobility due to the physical association between them was clariied in the Casson plot showing that the yield stress was increased with ferrite content [59]. The yield behavior caused by some physical association between PET and ferrite nanoparticle is well evidenced by adopting the following Casson plot: ′′1∕2

G′′1∕2 = Gy ′′1∕2

+ K�1∕2

(10.9)

stands for yield stress and K is the constant. where Gy Higher loadings of iller show nonzero positive intercept in the plot. In particular, with a loading of 5 wt% and above, yield stress is notably increased with ferrite content, suggesting that the nanoparticles over a critical level produce a signiicantly

METAL OXIDE NANOPARTICLE-BASED POLYMER NANOCOMPOSITES

377

10

8

(G″)1/2 (Pa)1/2

6

4

2

0 0.0

0.2

0.4

0.6

0.8 1.0 1.2 ω1/2 (rad/s)1/2

PET

G″y= 0

PET-0.1

G″y= 0.0016

PET-1

G″y= 0.17

PET-5

G″y= 1.02

PET-10

G″y= 4.93

PET-20

G″y= 13.62

1.4

1.6

1.8

2.0

Figure 10.16 Effect of ferrite content on the yield stress of PET. Reproduced from Chae et al. [59] with permission of Elsevier.

increased heterogeneity in the polymeric systems. Magnetorheological characteristics of ferrite nanoparticles illed polymer nanocomposites have been discussed in different studies [60, 61] (Fig. 10.16).

10.5.6

Calcium Carbonate

Calcium carbonate illed thermoplastic PNCs show variation in rheological behavior depending on iller concentration and iller modiication [62–65], and there was an increase in complex viscosity of the nanocomposites with increasing nanoiller concentration. Moreover, the rheological behavior of nanocomposites is more sensitive to nanoparticle concentration at low frequencies. From the dynamic mechanical measurements, the storage modulus of the composites improved upon addition of nanoillers even for small amounts. At room temperature, the illed composites showed an increase in comparison to virgin polymer. For the illed composites, glass transition temperature shifted to the right hand indicating good iller matrix adhesion [66]. Many theoretical models are proposed to compare experimental values of complex viscosity with theory, among them Roscope equation was the nearest to experimental values in the case of nano-CaCO3 illed polypropylene nanocomposites [67].

RHEOLOGY AND PROCESSING OF INORGANIC NANOMATERIALS AND QUANTUM

378

Rheological study of polypropylene (PP) by incorporating ethylene–octene copolymer (POE) and nanosize calcium carbonate reveals that POE exhibits slightly lower viscosity than PP at a shear rate (of 60 s−1 ) indicating that POE is more likely to wrap the nanoillers during melt mixing [68]. The addition of CaCO3 nanoparticles into POE signiicantly raises the viscosity of POE, leading to a higher viscosity ratio between the elastomer and the matrix. It means that premixing of POE with CaCO3 might be detrimental to the dispersion of POE in PP. However, the higher viscosity of the dispersed POE particles would retard their coalescence. Ternary systems containing nanoparticles exhibit more viscosity than binary systems It indicates that the interaction between the components is increased due to the addition of nanoparticles. In addition, the ternary composites have similar storage moduli as that of neat PP, which again suggests good compatibility between the components (Fig. 10.17).

107

η* (Pa s)

η* (Pa s)

106 105 10

103

4

103 10–1 (a)

104

POE/CCR (5/2.5) POE/CCR (5/7.5) POE/CCR (5/17.5) PP POE

100

101 ω (rad/s)

102

102

PP/POE (95/5) PP/POE/CCR (95/5/2.5) PP/POE/CCR (95/5/7.5) PP/POE/CCR (95/5/17.5) PP/POE/CCM (95/5/7.5) PP/POE/CCM (95/5/2.5) PP/POE/CCR (95/5/2.5)-a PP POE

10–1

101

100

102

ω (rad/s)

(b)

105

G′ (Pa)

104 103 PP/POE/CCR (95/5/7.5) PP/POE/CCM (95/5/7.5) PP/POE/CCR (95/5/2.5) PP/POE/CCM (95/5/2.5) PP/POE/CCR (95/5/2.5)-a PP/POE (95/5/) PP POE

102 101

100 102 (c)

103

104

105

G″ (Pa)

Figure 10.17 Complex viscosity versus shear rate at 220 ∘ C for (a) PP, POE, and POE/nano-CaCO3 , and (b) PP, POE, and PP/POE/nano-CaCO3 . Logarithmic plots of G′ versus G′′ for the PP and its binary and ternary composites at 220 ∘ C. Reproduced from Ma et al [68] with permission of Elsevier.

REFERENCES

10.6

379

CONCLUSION

Rheological characterization of PNCs is very important in order to understand the viscoelastic low behavior of the system. It gives an overall idea about how the addition of various illers inluences the structure–property relationship. Addition of nanoillers usually led to dramatic decrease in viscosity values of the neat polymer due to the uniform dispersion of nanoparticles in polymer matrix which reduces the tendency toward uncontrolled locculation. At low loading of illers, the polymer iller composite systems usually behaves like Newtonian luid, and at higher loading there is a tendency to change from Newtonian to non-Newtonian behavior. REFERENCES 1. Hanemann T, Szabó DV. Polymer-Nanoparticle Composites: From Synthesis to Modern Applications. Materials 2010;3:3468–3517. 2. Starr FW, Douglas JF, Glotzer SC. Origin of particle clustering in a simulated polymer nanocomposite and its impact on rheology. J Chem Phys 2003;119:1777. 3. Du F, Scogna RC, Zhou W, Brand S, Fischer JE, Winey KI. Nanotube Networks in Polymer Nanocomposites: Rheology and Electrical Conductivity. Macromolecules 2004;37:9048–9055. 4. Dzenis Y. Structural Nanocomposites. Science 2008;319:419. 5. Galindo-Rosales FJ, Moldenaers P, Vermant J. Assessment of the Dispersion Quality in Polymer Nanocomposites by Rheological Methods. Macromol Mater Eng 2011;296:331–340. 6. Song Y, Youn J. Assessment of the Dispersion Quality in Polymer Nanocomposites by Rheological Methods. Carbon 2005;43:1378–1385. 7. Vermant J, Ceccia S, Dolgovskij M, Maffetone P, Macosko C. Inluence of dispersion states of carbon nanotubes on physical properties of epoxy nanocomposites. J Rheol 2007;51:429–450. 8. Wang K, Liang S, Deng J, Yang H, Zhang Q, Fu Q, et al. The role of clay network on macromolecular chain mobility and relaxation in isotactic polypropylene/organoclay nanocomposites. Polymer 2006;47:7131–7144. 9. Efros AL, Rosen M. The electronic structure of semiconductor nanocrystals. Ann Rev Mater Res 2000;30:475–521. 10. Smith AM, Nie S. Chemical analysis and cellular imaging with quantum dots. Analyst 2004;129:672–677. 11. Alivisatos AP. Semiconductor Clusters, Nanocrystals, and Quantum Dots. Science 1996;271:933–937. 12. Kim SM, Yang H. Radiative decay of surface-trapped carriers and quantum yield in CdSe nanocrystal quantum dots. Curr Appl Phys 2011;11:1056–1059. 13. Dabbousi BO, Rodriguez-Viejo J, Mikulec FV, Heine JR, Mattoussi H, Ober R, Jensen KF, Bawendi MG. (CdSe)ZnS Core-Shell Quantum Dots: Synthesis and Characterization of a Size Series of Highly Luminescent Nanocrystallites. J Phys Chem B 1997;101:9463–9475.

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11 RHEOLOGY AND PROCESSING OF LAPONITE/POLYMER NANOCOMPOSITES Huili Li, Wenchen Ren, Jinlong Zhu, Shimei Xu and Jide Wang Key Laboratory of Oil and Gas Fine Chemicals, Ministry of Education and Xinjiang Uyghur Autonomous Region, College of Chemistry and Chemical Engineering, Xinjiang University, Urumqi, Xinjiang, People’s Republic of China

11.1

INTRODUCTION

Polymer nanocomposites are materials in which a iller phase is dispersed in a polymer matrix. Improvements in solvent resistance, ionic conductance, heat resistance, gas permeability and lammability are observed in the polymer nanocomposites [1–5]. Polymer nanocomposites based on inorganic nanoclay are emerging as an important class of multiphase and multicomponent materials with superior mechanical, thermal, and barrier properties [6–9]. Although montmorillonite (MMT) [10–12] is by far the most commonly used layered silicate in the synthesis of clay/polymer nanocomposites, Laponite has attracted a great deal of attention in recent years due to good dispersion and small size (1 nm thick and 25–40 nm large) [13–20]. Furthermore, Laponite, as a synthetic trioctahedric hectorite clay, offers a great advantage over natural clay of being chemically pure and free from external contaminants. These features make Laponite a good candidate for the synthesis and application of nanocomposites. A great attention and signiicant interest have been paid for understanding structure–property relations for polymer nanocomposites. Currently, numerous procedures for the preparation of polymer nanocomposites Rheology and Processing of Polymer Nanocomposites, First Edition. Edited by Sabu Thomas, Rene Muller, and Jiji Abraham. © 2016 John Wiley & Sons, Inc. Published 2016 by John Wiley & Sons, Inc.

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have been proposed. The key issue is that dispersion and compatibility of Laponite in the polymer matrix must be effectively controlled through adjusting the preparation conditions so as to ensure the performance requirements of nanocomposites. In addition, rheology of Laponite-illed polymer nanocomposites has been widely investigated due to the sensitivity toward nanocomposite structure and its predicting processability. As the iller nanostructure, the iller–iller and polymer–iller interactions can strongly inluence both linear and nonlinear viscoelastic responses [21]. Accordingly, quantitative understanding of the rheological properties of such nanocomposites is important for mastering the process parameters that lead to controlled microstructure, which in turn enables control of the end-use properties. In this chapter, three methods including melt blending, solution blending, and in situ polymerization are mainly introduced. 11.2

RHEOLOGY

For more than a decade, the percolation of Laponite within polymer matrix affects the rheological properties of polymer nanocomposites. The rheological properties of the polymer-based nanocomposites are furthermore inluenced by their internal construction and the strength of interactions between the components. The dynamic response of polymer nanocomposites can be classiied into two parts: linear and nonlinear. Linear and nonlinear rheological responses of these Laponite/polymer nanocomposites are carried out using two simple controlled approaches: small-amplitude oscillatory shear (SAOS) and large-amplitude oscillatory shear (LAOS), respectively. Oscillatory shear based on small strains is presented by SAOS, which is a common method for probing the linear viscoelastic properties of Laponite/polymer nanocomposites because of the irm theoretical background and easy implement. However, in some processing operations, the deformations can be large and rapid: it is therefore the nonlinear material properties that control the system response. LAOS experiments seek to probe the Laponite/polymer nanocomposites in the nonlinear viscoelastic regime. LAOS tests allow setting amplitude and frequency independently. LAOS experiments are presently considered as one of the most promising instrument to investigate the nonlinear viscoelastic behavior of Laponite/polymer nanocomposites, which is capable of covering a wide range of conditions. Due to the microstructural state of the material changing periodically along the LAOS experiment, the interpretation of LAOS results becomes rather inconvenient and dificult. 11.2.1

Linear Viscoelastic Properties

Recently, the linear viscoelastic properties of Laponite/polymer nanocomposites have been studied for a wide range of polymeric matrix such as poly(ethylene oxide) (PEO) [22, 23], poly(ethylene glycol) (PEG) [24, 25], poly(acrylic acid) (PAA) [13], poly(l-lactide) (PLLA) [26], polyacrylamide (PAM) [27, 28], polyurethane (PU) [29], polystyrene (PS) [30], poly(N-isopropylacrylamide) (PNIPAm) [31], microibrillated cellulose (MFC) [32], maleated polyethylene (PEMA) [33], poly(styrene-co-butyl acrylate) (poly(St-co-BA)) [34], pluronic

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F127/diphenyliodonium-2-carboxylate monohydrate (PAG) [35], and so on. In general, the addition of Laponite strongly inluences the rheological behaviors of nanocomposites. The viscoelastic behaviors are sensitive to the structure, particle size, shape, and surface characteristics of the silicate phase. Laponite suspensions are known to age with time up to an arrested phase even for very low concentrations. The long-term aging can be inluenced by the introduction of polymers, which in turn has an effect on the rheology of Laponite/polymer systems. Linear oscillatory rheology of Laponite with and without the addition of PEO was shown to age up to 100 days by Baghdadi [36]. The storage modulus (G′ ) of neat Laponite lower than 3 wt% aged for more 1000 days with no apparent stagnation. Adding low concentrations of PEO resulted in a similar aging response of G′ as neat Laponite. Above a critical ratio, � (predicted by models of soft glassy systems [37, 38]), of the free polymer chains in solution to the total Laponite surface area, the PEO dynamics dominated at high frequencies. It appeared that the dynamics of this complex Laponite–PEO system was governed by the parameter �. On the other hand, Zulian [39] showed that arresting phenomena between Laponite particles were hindered when PEO was added, and thus slowing of the aging dynamics with increasing PEO concentration was observed. A possible mechanism was progressive coverage of the clay surface by polymers, which grow with increasing PEO concentration. The dynamic mechanical rheological behavior of Laponite/polymer nanocomposites has been extensively studied over the past several years [32, 33, 40–43]. Variation in dynamic mechanical rheological properties can be explained well on the basis of the combination of partly exfoliated, intercalated, and aggregated structures of the nanoclay inside the polymer matrix. The resulted G′ and loss modulus (G′′ ) are a function of elastic properties and viscosity performance of the Laponite/polymer nanocomposites, respectively. For another, dissipation factor (tan �) represents for the heat loss energy during the deformation. In general, for Laponite nanocomposites, an increase is observed in G′ with increasing clay loading [22, 44–48]. The observed behaviors can be attributed to the strong interaction or increased cross-linking density between polymer chains and clay platelets [22, 31]. The interaction can be further enhanced by the use of reactive clay modiier [44] or polymer modiier [49]. Mishra [50, 51] investigated the inluence of modiication of surface of clay platelets by ionic, covalent, and dual modiication techniques on the dynamic rheological behaviors of polyurethane (PU) nanocomposites, respectively. The G′ of PU/Laponite nanocomposites by ionic modiication of surface of clay platelets was lower than that by covalent modiication. At the same time, the G′ was improved by 172.8% (with Laponite RD modiied by octyltrimethoxysilane (OS) followed by cetyltrimethylammonium bromide (CTAB)) and 85% (with Laponite RD modiied by CTAB followed by OS), respectively, as compared to that of the neat PU. Dynamic rheological behaviors of PU nanocomposites have something to do with the dispersion of modiied Laponite. On the other hand, based on the change in the number of active functional groups (tethering) on the dual-modiied Laponite surface, Mishra [52] prepared successfully novel thermoplastic polyurethane (TPU)–dual modiied clay nanocomposites by ex situ and in situ techniques in novel tubular, elliptical, and spherically aggregated morphologies of clays together with the hard segments of TPU as in Figure 11.1.

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(a)

PU

Spherical pattern

50 nm (b)

E3cOSL

E3cAPL

(c)

Tubular morphology 50 nm

50 nm (d)

50 nm

I3cOSL

Spherical aggregate

50 nm

Elliptical morphology

(e)

I3cAPL

Spherical aggregate

Figure 11.1 TEM images of neat PU, ex situ, and in situ prepared PU–clay nanocomposite [52]. (I3cAPL = TPU with 3% of cAPL prepared by in situ technique (cAPL: Laponite RD modiied by CTAB followed by 3-aminopropyltriethoxysilane (AP); E3cAPL = TPU with 3% of cAPL prepared by ex situ technique; E3cOSL = TPU with 3% of cOSL prepared by ex situ technique (cOSL: Laponite RD modiied by CTAB followed by OS); I3cOSL = TPU with 3% of cOSL prepared by in situ technique). Reproduced from Mishra et al. [52] with permission of Elsevier.

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Ex situ prepared nanocomposites showed better tensile properties than the in situ prepared nanocomposites. Nanocomposites based on cOSL (with lower degree of tethering) exhibited better mechanical and rheological properties along with thermal stability as compared to its cAPL (with greater extent of tethering) counterpart. The percentage improvement in tensile strength and elongation at break of the ex situ prepared nanocomposites with the modiied clay having lesser tethering were found to be 67% and 208%, respectively. In addition, the dependency behavior of G′ on clay content is found to be strongly inluenced by both the clay size and the type of modiier [29, 45, 49]. For large-sized clay, that is, MMT, a monotonic decrease in G′ is observed instead with increasing clay content, irrespective of the clay modiier used [45]. Further to the increase in the clay content, the G′ of Laponite/polymer nanocomposites may decrease due to the presence of excess of unafiliated/intercalated aggregates [32]. It is worth mentioning that, in the case of nanocomposite hydrogel, G′ is usually higher than G′′ over a wide range of frequencies due to solid-like character after gelation [53]. Oscillatory shear rheology is also widely used in the analysis of linear viscoelastic behavior of nanocomposites [54]. The linear viscoelasticity behaviors of Laponite/PEO system have been intensively investigated. A threshold PEO molecular weight (Mw) leading to the G′ minimum was suggested to separate the two opposite effects of PEO molecular weight (Mw) on the gelation and/or glass transition in Laponite suspensions without addition of salts: the interparticle bridging by high-Mw PEO and reduction in the effective volume fraction by depletion force of low-Mw PEO [36, 55]. In contrast, the adsorption of PEG on the Laponite platelets in the suspension containing NaCl was enhanced for the PEG with lower Mw to inhibit the gelation [56, 57]. In addition, different preparation methods made an effect on the viscoelastic properties. Small amplitude oscillatory measurements in the linear viscoelastic region revealed a signiicant disparity in the plateau moduli for the solution and melt prepared Laponite/PEO nanocomposites [58]. This behavior can be qualitatively explained using the analogy with the dispersion by shearing in polymer blends having wide difference in viscosities. For Laponite/PAA nanocomposite hydrogel, G′ and G′′ increased monotonically by increasing the amount of both Laponite and acrylic acid (AA). The intersection point in the curve of G′ and G′′ as a function of frequency shifted to a low frequency with an increasing Laponite content, suggesting a longer relaxation time and higher cross-linking degree between polymer chains and Laponite sheets [13]. 11.2.2

Nonlinear Viscoelastic Properties

The LAOS rheology is intensively accepted during recent years in studying nonlinear behavior of complex luids. As usual, linear viscoelastic properties are characterized using SAOS, but LAOS with a larger strain amplitude is exploited to manifest nonlinear viscoelastic properties, where G′ and G′′ are dependent on both frequency and strain amplitude, of Laponite/polymer nanocomposites. The quantitative description methods of LAOS are Fourier transformation methods, stress decomposition, and graphical analysis by drawing a Lissajous curve. The studies on nonlinear viscoelastic

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properties of the Laponite/polymer nanocomposites are not as many as on their linear viscoelastic properties. LAOS rheology of Laponite suspension containing PEG and NaCl showed that an increase in PEG Mw or decrease in PEG concentration enhanced the nonlinear viscoelasticity of the clay suspension showing macromolecule effect [54]. The relative intensity of third harmonic relected the delicate difference in the nonlinear viscoelasticity induced by added PEG with different Mw and concentrations, which was hardly distinguished by conventional dynamic strain sweep. The minimum and large strain rate viscosities from the Lissajous curve were found to be sensitive to the nonlinear viscoelasticity. This nonlinear behavior of the PEO-Laponite system [59] was illustrated by the Lissajous phase plots for large strain amplitudes of 500%. It was observed that the response was initially linear, went through a nonlinear regime and again became linear after the structure relaxation had inished. The non-linearity of the Lissajous phase plots calculated by Pozzo indicated a more sensitive structure existed during the relaxation.

11.3

PROCESSING

In polymer-based nanocomposites, reinforcement of polymer with nanoillers exhibits new functionality and more predominant properties. The properties of polymer nanocomposites based on clay are directly affected by their structure. Depending on the way the nanoclays are dispersed within the polymer matrix, the following cases can be considered [60]: phase separated nanocomposites, intercalated nanocomposites, and exfoliated nanocomposites. Exfoliated nanocomposites show the largest improvement of the mechanical properties, whereas intercalated ones display a moderated increase and deintercalated ones display the smallest increase. Ruggerone [61] found that signiicant increases in the storage and tensile moduli were observed on Laponite addition of Laponite/PS nanocomposites. In detail, the increases in the glassy state were correlated with the extent of exfoliation of Laponite in the Laponite/PS nanocomposites, while in the rubbery state (160 ∘ C) they were more dependent on the overall Laponite content. The elaboration of exfoliated nanocomposites is a key point to clay/polymer nanocomposites. In a broad sense, dispersion of Laponite is favored by Laponite polymer phase miscibility as well as an effective Laponite exfoliation during processing. Currently, three main processing categories are used to achieve the exfoliation of the nanoclays within the polymer matrix: melt blending, solution blending, and in situ polymerization. These processes may be used individually or in combination with each other in order to achieve the desired structure of Laponite/polymer nanocomposites. On the other hand, Laponite/polymer nanocomposites as intrinsically anisotropic materials exhibit the ability to orient Laponite in response to externally applied low. Due to the quiescent mesoscale structure, the controlled viscoelastic properties of such nanocomposites appear to be used in the special application. Schmidt et al. [62] examined the inluence of steady shear on the orientation of Laponite in an aqueous solution of PEO using low birefringence and small-angle neutron scattering

PROCESSING

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(SANS). The platelets are oriented in the low direction with the surface normal in the neutral direction. 11.3.1

Melt Blending

Melt blending is used to prepare Laponite/polymer nanocomposites by mechanically mixing thermoplastic polymers with Laponite in the melt phase under shear. The intercalation of Laponite can be achieved by the force of enthalpic interaction between polymers and individual silicate layers. This method is attracting much more attentions since it is solvent-free, simple, and straightforward way to prepare Laponite/polymer nanocomposites. However, two problems need to be solved when making Laponite nanocomposite by melting blending: (i) Laponite is hard to exfoliate without hydration in water; (ii) Laponite is hydrophilic but most thermoplastic polymers are hydrophobic. Ion exchange of the interlayer sodium cations by a cationic surfactant such as alkylammonium, CTAB, octadecyltrimethylammonium bromide (C18TAB) [63], and dimethyldihydrogenated tallow ammonium chloride [33] or phthalocyanine [64] is a common method to increase the interlayer distance. Another effective method is to covalently functionalize the Laponite through a condensation reaction of silanol groups on the silicate edge with monoalkoxysilanes or trialkoxysilanes (Fig. 11.2) [65]. After covalently functionalized with silanes, the Laponite surfaces are modiied from hydrophilic to hydrophobic; therefore, the compatibility with polymers in melting phase is enhanced [66, 67]. O Si O O

NH2

or

O

or

NH2

Si

O Si O O

APES + Sodium laponite

APS

Si O

+ − Na+ − Na+ − Na+ Na − − Na+ − − − − − Na+ − − + Na − − Na+

Si R

TPS

O

O Si

R = H, NH2 O Si

O Si

R R R

R

Figure 11.2 Schematic representation of a sheet of Laponite whose silanol groups have been reacted with alkoxy silanes. Reproduced from Wheeler et al. [65] with permission of American Chemical Society.

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RHEOLOGY AND PROCESSING OF LAPONITE/POLYMER NANOCOMPOSITES

The most extensively studied Laponite/polymer nanocomposites via melt blending are Laponite/PEO composites [23, 68–72]. The hydrophilic nature of PEO presents an important advantage when preparing intercalates of PEO and hydrophilic silicate clay platelets [70]. PEO was found to intercalate between the clay platelets, and the adsorbed macromolecules were completely amorphous [73]. Other Laponite/polymer nanocomposites such as Laponite/poly(vinyl chloride) (PVC) composite [64], Laponite/nylon-6 composite [74], and Laponite/polyethylene (PE) composite [33, 68] were also reported. In Laponite/nylon-6 melt blending system, the surface of Laponite promotes the formation of �-phase crystallites that can further stabilize these crystallites at high annealing temperature, while bulk nylon-6 can stabilize only �-phase crystallites [74]. It should be mentioned that once the Laponite surface is saturated, the excess of the polymers behaves like the pure one. The temperature is chosen so as to achieve optimum viscosity in the polymer melt, which is able to withstand shear from the compounder, and also allows good mixing with the iller. 11.3.2

Solution Blending

In the solution blending method, Laponite, as well as polymers, is dissolved in solvent together to make nanocomposites. Laponite can disperse and hydrate into water easily at low concentration (about 2 wt%). This property greatly widens the application of Laponite since polymer solutions are more lexible than polymers in melting phase. There are several circumstances that Laponite needs to be modiied in solution blending process. One of circumstances lies in preparing high Laponite content solutions (above 2 wt%), and in such high clay content the particles tend to form “house of cards” structures resulting in physical gels. Tetrasodium pyrophosphate is typically used to decrease the viscosity of Laponite by adsorbed onto the cationic edges of the Laponite [28, 75]. The other circumstance lies in preparing organic Laponite solutions, as we all know that the hydrophilic Laponite cannot disperse in any organic solvents. In organic solvent, Laponite exists in the form of tactoids with two or three clay sheets held together by long-range attractive forces [66]. Hydrophobization of the Laponite by silane is also used in order to make Laponite containing organic solutions [51, 76] (Table 11.1). One recent interesting progress in solution blending is supramolecular hydrogels made by Laponite and macromolecules with multiple adhesive termini [53, 88, 89]. Wang et al. [88] irst reported a noncovalent approach preparing nanocomposite by mixing water, Laponite, molecular binder, and sodium polyacrylate (ASAP) together. Owing to multivalency provided by the dendronized or linear structure, the guanidinium ion groups in the molecular binder strongly adhere to the clay nanosheets dispersed by ASAP, cross-linking them together to form a 3D network [89] (Fig. 11.3). Laponite composite made by supramolecular forces, may provide many interesting applications. Solution casting procedure is often used to make ilms, and it brings out by casting aqueous dispersions of Laponite and polymer mixtures onto the plate. It can get nanocomposites with high Laponite content because the clay concentration

PROCESSING

391

TABLE 11.1 Chemicals Used for Laponite Modiication in Solution Blending Interaction Mechanism

Laponite Modiiers

Effect

Adsorption

PEO [77–81] PEG [82] Tetrasodium pyrophosphate [28, 75]

Intercalation

1-Methylimidazolium hydrogen sulfate [83] Dequalinium chloride salt [83] Trimethylene glycol di-p-aminobenzoate [84] 4-Benzylaniline [84] CTAB [29, 51, 85] Dodecylamine hydrochloride [29, 41] Dihydrogenated tallow dimethylammonium chloride [86] C18TAB [87] Octyltrimethylammonium bromide [87] Octyltrimethoxysilane (OS) [51] Triethoxysilane-modiied PEG [76]

Intercalation or hydrophobization

Electrostatic interaction Ionic exchange

Covalent bond

CNSASAP

Reduce viscosity

Hydrophobization

Molecular binder

(a)

(b)

(c)

Figure 11.3 Hydrogelation by mixing Laponite (CNS as shown) and molecular binders in water. (a) Schematic representation of the mechanism of hydrogelation. (b, c) Pictures of supramolecular hydrogels. Reproduced from Tamesue et al. [89] with permission of American Chemical Society.

392

RHEOLOGY AND PROCESSING OF LAPONITE/POLYMER NANOCOMPOSITES

increases with the solvent evaporation. As this technique requires a homogeneous casting solution, it is usually made by nonionic polymers such as poly(vinyl alcohol) (PVA), starch, PAM, and cellulose [90–92]. Ionic polyelectrolytes, such as polyvinylpyrrolidone (PVP) and PAA, tend to coagulate with Laponite and are not suitable to this method. The incorporation of nanoparticles into engineering thermoplastic affords engineers an opportunity to synthesize polymer nanocomposites that potentially rival the most advanced materials in nature. Development of these materials is dificult because thermodynamic and kinetic barriers inhibit the dispersal of inorganic, often hydrophilic nanoparticles in hydrophobic polymer matrices. Zulian and coworkers [39] outlined a novel solvent-exchange approach to eficiently exfoliate Laponite in commercial thermoplastic polyurethane (TPU) elastomers. This requires the use of two solvents, A and B, that meet four criteria: (i) solvent A must fully disperse the hydrophilic clay; (ii) solvent B must dissolve the polymer matrix and not cause reaggregation of the nanoclay; (iii) solvents A and B must be fully miscible; and (iv) solvent B must have a higher boiling point than solvent A. Solvents with high dipole moments and dielectric constancies are found to be the most suitable B solvents. This solvent-exchange method allows Laponite to mix into block copolymers with polar constituents such as TPU effectively to develop high-performance materials. 11.3.3

In Situ Polymerization

In general, in situ polymerization is an extensively used processing for the preparation of Laponite/polymer nanocomposites. For the irst time, Okada [93] has synthesized nylon-6/clay nanocomposites from caprolactam monomers using the in situ polymerization technique. Distinguishing from the melt blending and solution blending, monomers are used in the in situ polymerization technique. Thereafter, the monomers are converted into polymers in the dispersion of Laponite by conventional or living free-radical polymerization [94], and the initiator is initiated by external stimulation such as photochemical, thermal activation, and so on. With the nanoparticles dispersed uniformly in the polymer matrix, the Laponite nanoparticles would confer excellent physical and mechanical properties. According to the dispersed state of monomer in medium, the method can be divided into several categories, namely, homogeneous polymerization (bulk and solution polymerization) and heterogeneous polymerization (emulsion polymerization and suspension polymerization). 11.3.3.1 Homogeneous Polymerization These homogeneous polymerization reactions can be performed either in bulk or in solution. In bulk polymerization, Laponite directly disperses in the monomer and initiator without any solvent. Bulk polymerization is suitable for the laboratory research [95]. The problems needed to be solved are how to exclude the reaction heat. Because of this disadvantage, industrial application of this method is limited. The solution polymerization reactions can be performed either in water or in organic solvents. Most of the Laponite/polymer nanocomposites prepared in water are nanocomposite hydrogels (NC gels) irst reported by Haraguchi, which are derived from monomers such as acrylamide (AM) [96–99], N-isopropylacrylamide

PROCESSING

393

(a)

(b)

(c) Clay Monomer KPS TEMED

(d)

(e)

Figure 11.4 Schematic representations of the model structures for the reaction solution and the mechanism of forming organic/inorganic network structure in an NC gel. (a) Aqueous solution consisting of clay and NIPAm. Here, the formation of house-of-cards structure does not form. (b) Reaction solution consisting of clay, NIPAm, potassium persulfate (KPS), and N, N, N′ , N′ -tetramethylethylenediamine (TEMED). (c) Radical formation near the clay surface in the reaction solution. (d) Formation of clay–brush particles. (e) Formation of organic/inorganic networks. In the models, only a small number of monomer (polymer), KPS, and TEMED are depicted for simplicity. Reproduced from Haraguchi et al. [105] with permission of American Chemical Society.

(NIPAm) [31, 42, 49, 94, 100], vinylpyrrolidone [101], and N,N-dimethylacrylamide (DMA) [102–104] using Laponite as cross-linker (Figure 11.4). All monomers reported above are nonionic on account of the precipitation of Laponite in ionic monomers dispersions [106]. Till now, there had been limited success in the preparation of ionic NC gels. To avoid the aggregation of Laponite in ionic monomers, nonionic monomers (i.e., NIPAm or AM) were usually added to pre-adsorb on Laponite followed by copolymerization with ionic monomers (sodium methacrylate (SMA) [107] or 2-(dimethylamino)ethyl methacrylate (DMAEMA) [108] or sodium acrylate (SA) [109]). However, aggregation would be observed when content of ionic monomers was more than 1–10 mol% of nonionic monomers. It seems that this can avoid the aggregation of Laponite to a certain degree. In the other case, supernatant of agglomerated acid-activated Laponite XLS in AA had to be used to prepare the hydrogel [110]. Recently, a transparent and tough ionic NC gel was prepared successfully via in situ copolymerization of AA and 2-acrylamido-2-methylpropanesulfonic acid (AMPS) in Laponite dispersion. Synergistic effect of acylamino and sulfo groups of the ionic AMPS can dramatically improve the miscibility of ionic monomers with Laponite (Fig. 11.5) [14]. In addition, speciic sulfobetaine monomers were found to be well dispersed in the aqueous Laponite dispersion and thus formed mechanically tough ionic NC hydrogels after free-radical polymerization [111].

394

RHEOLOGY AND PROCESSING OF LAPONITE/POLYMER NANOCOMPOSITES

H2O

AMPS

AA SO3− SO3 SO3 SO3

SO3−

SO3− − SO3 SO3 SO3

SO3−

Polymerization Laponite

SO3−

AMPS

AA

Poly(AMPS-co-AA)

Figure 11.5 Proposed mechanism for the ionic Laponite/poly(AMPS-co-AA) NC gels [14]. Reproduced from Chen et al. [14] with permission of Elsevier.

On the other hand, for hydrophobic Laponite/polymer nanocomposites, because of the aggregation of the unmodiied Laponite in the organic solvents, it is necessary to convert these Laponite into organophilic to make them compatible. In general, its state of dispersion in polymers can be improved through modifying the surface of Laponite. The major categories of clay modiications reported include ionic and covalent modiication techniques as mentioned in melt or solution blending [112–116]. For the outstanding mechanical properties and rheological characteristics of Laponite/polymer nanocomposites, the dual-modiied Laponite [117] prepared by both ionic and covalent modiications are used. The dual-functional Laponite/TPU is synthesized by in situ technique, and dual-functional Laponite was irst modiied by a condensation reaction with silane-coupling agents, such as 3-aminopropyltriethoxysilane (AP) [52], g-methacryloxypropyltrimethoxysilane (MPTS) [118], and OS, followed by cation-exchange reaction with quaternary ammonium salts, such as CTAB. The nanocomposites showed different morphologies compared with solution blending method (Fig. 11.6). 11.3.3.2 Heterogeneous Polymerization Heterogeneous polymerization techniques for Laponite/polymer nanocomposites involve emulsion and suspension polymerization. In contrast, suspension polymerization is seldom reported possibly due to the large size of the resultant composites. For the irst time, Lee [119] prepared the nanocomposites by a simple technique of emulsion polymerization using methyl methacrylate (MMA) monomer and MMT. Roughly speaking, emulsion polymerization is a process in which monomers were dispersed in the water and emulsiied into the emulsion state in the effect of emulsiier, just like surfactants, then triggered by the initiator. The addition of surfactant molecules are usually used for the stabilization of the monomer droplets, and the subsequent monomer polymerization is carried out in the water phase. These techniques can easily bring forth controlled morphology than solution or bulk polymerization.

PROCESSING

395

Si

Si

+

NR3

O R

N

C

O

NR3 +

H

O

NR3 +

N

C

O

O

NH2

O OH O

O R

O

N

C

NH2

O

H

H

R

N

C

R O

N

O R

O

Si

Si

NR3 + O

OH

O R

+

NR3

O

Si

Si

NR3 + O

O

O

C

N

C

O

H O

H O

O R

H

N

C

O

H

(a)

(b)

(c) Si

+ NR3 NR3 +

NR3 + O

Si

O

O

NR3 +

O O

C

NR3 O +

O

Si

O

Si

O

O

+ NR3

Si

NH

O

Si

C

O

NH

C

NH

O

NH O

O R

N

NH

C

O

H

C

O R

O N

O

O

H

R

NH

C

N

C

O

H

O

O R

N

C

O

H

(d)

(e)

Figure 11.6 Possible mechanisms for the development of different types of structures [52]. (a) TPU; TPU/Laponite nanocomposites prepared by (b, c): solution blending (d, e) in situ technique. Reproduced from Mishra et al. [52] with permission of Elsevier.

The species of the emulsion polymerization can be divided into the following categories: conventional emulsion polymerization, miniemulsion polymerization, and soap-free emulsion polymerization. In order to increase interfacial interactions and control particle morphology, a great deal of matter has been performed to modify the Laponite particles using three categories, namely, cationic exchange, covalent modiication, and adsorption of polar polymers’ surface modiication. From another perspective, based on the modiier’s participation in the next polymerization reactions, it can be divided into “reactive” and “nonreactive” modiiers. The extent of clay exfoliation was strongly dependent on the reactivity of the clay modiier. A nonexhaustive list of functional molecules used in Laponite/polymer nanocomposites synthesis through conventional emulsion polymerization is given in Table 11.2.

396

Poly(ethylene oxide) monomethylether methacrylate

Reactive

�-Methacryloyloxypropyl dimethylethoxysilane

�-Methacryloyloxypropyl trimethoxysilane

Poly(ethylene glycol) monomethylether methacrylate

Nomenclature

Modiier

O

O

O

O

O O

O 1000

O(CH2)3 Si(CH3)2(OCH2CH3)

O(CH2)3 Si(OCH3)3

(O CH2 CH2)nOCH3

O

Chemical Formula

MPDES

MPS

PEGMA

PEOMA

Abbreviation

Styrene, butyl acrylate

Styrene, butyl acrylate

Styrene

Styrene

Monomers

[121–123]

[121]

[61]

[120]

References

TABLE 11.2 Chemical Structures of Organic Modiiers Used to Functionalize Laponite During the Synthesis of Laponite/Polymer Nanocomposites through Conventional Emulsion Polymerization

397

Nonreactive

Dodecylbenzenesulfonic acid sodium

2,2-Azobis(2-methyl propionamidine) hydrochloride

2-Methacryloyloxyethyl trimethylammonium chloride

3-Methacryloyloxypropyl trimethoxysilane

N

Cl− H

N+

CH3

+

CH3

N

CH3

OMe

CH3

Si

CH3(CH2)10CH2

H

H2N

H3C

MeO

MeO

N

O O

O

CH3

H CH3

O

N

O

S

O ONa

NH2

H

Cl− +

DBS

AIBA

MADQUAT

MPTMS

Acrylonitrile, butadiene, and styrene

Styrene, butyl acrylate

Styrene, butyl acrylate

Styrene, butyl acrylate

[125, 126]

[123, 124]

[123]

[122, 123]

398

RHEOLOGY AND PROCESSING OF LAPONITE/POLYMER NANOCOMPOSITES

The size of Laponite/polymer nanocomposites of about 100 nm diameter in miniemulsion polymerization [34, 44, 45, 127] is smaller than the composites produced by the conventional emulsion polymerization. Furthermore, the biggest breakthrough of the miniemulsion polymerization over the conventional emulsion polymerization is that clays can be effectively encapsulated inside the polymer nanocomposite particles. However, encapsulation of clay using emulsion or miniemulsion polymerization methods was usually achieved with low clay content (typically G′′ ).

422

GRAPHENE-BASED NANOCOMPOSITES: MECHANICAL, THERMAL, ELECTRICAL

Storage modulus, G′ (Pa)

105 104 103 Neat PP 0.2 wt% 0.5 wt% 1 wt% 1.5 wt% 2 wt% 3 wt%

102 101 100 10–1

(a)

10–2

10–1

100 Frequency (Hz)

101

102

Loss modulus, G″ (Pa)

104

103

Neat PP 0.2 wt% 0.5 wt% 1 wt% 1.5 wt% 2 wt% 3 wt%

102 101 100 10–2

(b)

10–1

100 Frequency (Hz)

101

105

1 wt% 1.5 wt% 2 wt% 3 wt%

Viscosity, η∗ (Pa s)

Neat PP 0.2 wt% 0.5 wt% 104

103

10–2 (c)

102

10–1

100 Frequency (Hz)

101

102

Figure 12.7 The melt rheological measurement as function of GNs content and frequency: (a) storage modulus (G′ ), (b) storage modulus (G′′ ), and (c) complex viscosity (�*). From Ref. [18]. Reproduced with permission of John Wiley and Sons.

NANOCOMPOSITE CHARACTERIZATION

423

The complex viscosity (�*) of a thermoplastic polymer contains usually two distinct behaviors: the Newtonian behavior and rheoluidifying behavior (shear thinning). The irst behavior is observed at low frequencies and is characterized by the independence of the viscosity with frequency. In contrast, the rheoluidifying behavior is found in high frequencies and is characterized by the linear decrease in viscosity with increasing frequency. Figure 12.7c shows the evolution of the complex viscosity as a function of frequency and graphene content. It was observed that the complex viscosity increases with increasing graphene content. The neat PP shows the Newtonian at low frequency (≤1 Hz), and the shear-thinning behavior at high frequencies (≥1 Hz). When GNs content is 1 wt%, the Newtonian plateau began to disappear, indicating that the nanosheets began to form a continuous network. And when GNs content is greater than 1.5%, the Newtonian behavior is completely disappeared. This is accompanied by the formation of GNs networks in the PP matrix and the transition from liquid-like to solid-like viscoelastic response [67]. It can be seen that the rheological percolation threshold is close to the GNs content of 1 wt%. These measurements were performed in order to characterize the quality of the dispersion GNs in the PP matrix, the degree of interfacial interaction between GNs and PP chains, and the determination of the rheological percolation threshold structure. From the analysis of the obtained results in terms of rheological measurements for nanocomposites based on graphene nanosheets and PP at different GNs content and at different frequencies, important information may be concluded. However, the increase in elastic modulus with increasing GNs content, which is accompanied by a similar increase in complex viscosity through a passage from a luid-like behavior to the elastic behavior (the threshold percolation), is related to the following: + The good dispersion/distribution of the individual graphene nanosheets in the PP matrix. + Strong interactions between dispersed graphene nanosheets and PP chains. These interactions may be generated by the presence of a good compatibility between polymer interface and graphene nanosheets. 12.4.6

Electrical Properties

It is known that the properties of neat polymer are improved by the incorporation of rigid and higher electrically conductive illers such as graphene, clay, or other carbon derivatives (carbon illers). Graphene-based polymer nanocomposites show a higher thermal, mechanical, electrical, gas barrier, and lame-retardant properties compared to the neat polymer. In general, the physical and mechanical properties of nanocomposites based on graphene depend on various factors, including those to the components, their interactions, the degree of dispersion/distribution of graphene layers in the polymer matrix, and the processing conditions. The nanocomposites based on graphene show higher mechanical properties because the superior mechanical properties of graphene (Young’s modulus) are relected in nanocomposites. In addition, the graphene nanosheets are more compatible with organic polymers; as a result,

424

GRAPHENE-BASED NANOCOMPOSITES: MECHANICAL, THERMAL, ELECTRICAL

graphene has attracted considerable attention as nanoiller for polymer nanocomposites. However, one of the most fascinating property of graphene is its excellent electrical conductivity, which makes it suitable for the synthesis of conducting nanocomposites. Graphene nanosheets (GNs) have been viewed as an attractive iller for increasing the electrical conductivity of polymers at relatively low GNs content. However, the general electrical performance of nanocomposites based on graphene depends on the manufacturing process, dispersion/distribution of the graphene into polymer matrix, and the intrinsic characteristics of the used graphene such as the morphology and the aspect ratio. For example, Kim et al. [45] have reported that graphene orientation has an effect on the electrical conductivity of the resulted nanocomposites; it was observed that the compression molded polycarbonate and GO-polyester nanocomposites with aligned platelets have an increased percolation threshold that is about twice as high as the annealed samples with randomly oriented platelets [45]. The addition of graphene in an insulating polymer matrix, may greatly improve the electrical conductivity of the composites, that when the content of graphene exceeds the electrical percolation threshold leading to a conductive network in the polymer matrix. The graphene sheets can provide percolated pathways for electron transfer, making the composites electrically conductive. It was reported [68] that when the conductive network became perfectly established the conductivity of the nanocomposites based graphene, while below the percolation network and due to the insuficient content on GNs the nanocomposite is insulation. The literature works have suggested that graphene with high aspect ratio can achieve electrical percolation within the matrix and can form conductive network with a little content, showing a good conductivity [69]. Zhixian et al. [68] investigated that the electrical percolation threshold for graphene–polystyrene nanocomposites was reported for the nanocomposite with heterogeneously dispersed graphene at about 0.52 vol% [68]. Although Hengchong et al. [69] have observed that by increasing the graphene content to 0.5 wt% (into SEBS-g-MAH matrix), the nanocomposite is still electrically insulating, which is due to the absence of an interconnected graphene network in the matrix. In contrast, when the content of graphene was 4 wt%, a notable increase in electrical conductivity was reached. As reported previously, similar to other conductive carbon illers such as carbon black, carbon nanoibers, and expanded graphite, graphene sheets provide percolated pathways for electron transfer that impart electric conductivity to the composites. However, the insulator-to-conductor transition occurs at a signiicantly lower loading by using graphene. However, we have investigated the effect of GNs on the electrical properties of the nanocomposite based on polymer blend (PA6/ABS). Here, the preparation of polymer blend composites PA6/ABS reinforced by GNs using a master batch approach is reported. Results of electrical properties show a percolating threshold between 1 and 2 wt% GNs content. The observed percolation threshold is attributed to the high speciic surface area of the graphene, its high aspect ratio, and its uniform dispersion in the PA6 phase [70]. Thus, the advantage of using GNs charge in the polymer matrix was to improve the polymer blend conductivity with low charge content. The measurement of the electrical conductivity of the nanocomposite blends lets us notice that

FUTURE PERSPECTIVE

425

Electrical conductivity (S/m)

3e-7

3e-7

2e-7

2e-7

1e-7

5e-8

Figure 12.8

0

1

2 GNs content (Wt%)

3

4

Conductivity of nanocomposites of PA6/ABS versus GNs content.

the co-continuity of the GNs-illed immiscible polymer blends is reached. This means that the formed sea island structure was now a co-continuous one (Figure 12.8). 12.5

CONCLUSION

The aim of this chapter was the development of nanocomposites based on graphene and polymer matrix. The study focused on the nanocomposite samples of the extruded polypropylene matrix (PP), polyethylene (HDPE), PVDF, and ABS/PA6 blend and on the PVDF matrix nanocomposite ilms produced by mixtures in solution. The structural, thermal, mechanical, and electrical properties of the manufactured nanocomposites were greatly improved by the addition of small mass fractions of graphene nanosheets ( 1 or n > 1) or negative deviation (� < 1 or n < 1). Although both Equations 15.3 and 15.4 can it the experimental data, they are unable to supply physical insight into the mechanism of different kinds of deviations. A model based on the simultaneous chain motion (double reptation model) predicts the viscosity of blend as [8] 0 1∕2

�0,b =

�0,1 �21

+

0 1∕2

4GN,1 GN,2 �1 �2 G0N,1 ∕�0,1 + G0N,2 ∕�0,2

+ �0,2 �22

(15.5)

where G0N,i is the plateau modulus of ith component. It is important to see that the blend viscosity relies not only on the components’ viscosity but also on their ability to entangle with each other (or equivalently the plateau modulus). Positive deviation can be predicted from Equation 15.5 when G0N,1 ≈ G0N,2 . Double reptation model was originally suggested for a blend of polymers with similar chemical structures (such as LLDPE/HDPE blend), so it is not applicable in homogeneous blends with different chemical structures. In fact, different chemical structures between components indicate possible difference in glass transition temperature and the monomeric friction coeficient. Under such cases, the local environment of a segment of polymer 1 would be different from that in its pure polymer and may also be different from that of polymer 2. Such phenomena is sometimes called dynamic heterogeneity and strongly related to the dynamic asymmetry (ΔTg , deined as the difference between components’ glass transition temperature). The difference in the local environment of different chain segments can be explained by introducing self-concentration [9], which is deined as the concentration of a chain segment in a reference volume. Self-concentration is different from the average concentration of component 1 in blend due to the chain connectivity, which determines the effective chain mobility in blends. Complex mixing rules of zero shear viscosity can be obtained when the double reptation model is combined with the self-concentration model [10]. The appearance of positive, negative, or more complex pattern of mixing rule is ascribed to the difference in the components’ viscosity, the dynamic asymmetry, self-concentration, and temperature [10]. 15.1.1.2 Thermorheological Complexity For pure polymer melt, the dynamic modulus under different temperatures can often be superimposed to obtain master curves. Success of time–temperature superposition (TTS) is also known as thermorheological simplicity. TTS also works well in some miscible blends such

RHEOLOGY AND PROCESSING OF NANOPARTICLE FILLED POLYMER

494 106

109 PEP/hhPP 50/50

10

PS/PCHMA 50/50

SAN/PMMA 40/60 108

103

bTG′, bTG″ (Pa)

104 G″

G″ (104Pa)

bTG′, bTG″ (Pa)

105

1

G′ 102

10−3

106

105

0.1 101 10−4 10−2 100 102 104 ωaT (rad/s) (a)

107

10−1 101 ωaT (rad/s) (b)

G′

G″

104 10−8 10−5 10−2 10−1 ωaT (rad/s) (c)

Figure 15.2 Master curves of dynamic moduli for PEP/hhPP 50/50 blend at reference temperature Tref = 50 ∘ C. From Ref. [11]. Reproduced with permission of Springer (a), PS/PCHMA 50/50 blend at Tref = 180 ∘ C. From Ref. [12]. Reproduced with permission of Elsevier (b), and PMMA/SAN 60/40 blend at Tref = 117 ∘ C. From Ref. [13]. Reproduced with permission of American Chemical Society (c). All compositions are in weight fraction.

as poly(ethylene-alt-propylene) (PEP)/head-to-head polypropylene (hhPP) blend [11], polystyrene (PS)/poly(cyclohexyl methacrylate) (PCHMA) blend [12], and PMMA/SAN blend [13] (Fig. 15.2). The common feature of these blends where TTS works is the weak dynamic asymmetry. The difference in the glass transition temperature of these blends is rather small, 20 K for PMMA/SAN blend [13], 15 K for PS/PCHMA blend [12], and 40 K for PEP/hhPP blend [11]. In contrast, when ΔTg becomes larger, the failure of TTS becomes gradually obvious, and these blends are called thermorheological complex luids. In some blends (see polystyrene (PS)/poly(vinyl methyl ether) (PVME) blend in Figure 15.3a, ΔTg = 125 K), the failure is rather weak and can only be inferred from loss tangent, which owns higher experimental accuracy than dynamic moduli [14]. In other blends (see poly(ethylene oxide) (PEO)/PMMA blend in Figure 15.3b, ΔTg = 185K [15]), the failure is signiicant in dynamic moduli. The failure of TTS can be explained using the stress contributions of polymer blends. The stress of polymer blends can be regarded as a sum of different contributions. In addition to the contribution from two polymer components, the dynamic heterogeneity may also contribute to the stress. It is usually believed that the failure of TTS is ascribed to the different temperature dependence of these contributions, where the contribution due to dynamic heterogeneity is of great importance. A frequently adopted explanation considers the dynamic heterogeneity that is induced by concentration luctuation [16]. In contrast to the self-concentration concept, the concentration luctuation is an intermolecular effect, which results in the change

RHEOLOGY OF POLYMER BLENDS

109

495 10

40

PS/PVME 30/70

PEO/PMMA 20/80 (Tref = 155 °C)

(Tref = 5 °C)

Tan δ

10

8

107

32 174 °C

1 105 G″ Tan δ 10

4

10

3

G′

0.1 102 −8 10 10−6 10−4 10−2 100 102 ωaT (rad/s) (a)

G″/107 (Pa)

G′, G″ (Pa)

155 °C 106

24

137 °C 120 °C

16

8

0 10−4 10−310−210−1 100 101 102 103 ωaT (rad/s) (b)

Figure 15.3 Master curves of PS/PVME 30/70 blend at Tref = 5 ∘ C. From Ref. [14]. Reproduced with permission of American Chemical Society (a) and PEO/PMMA 20/80 blend at Tref = 155 ∘ C. From Ref. [15]. Reproduced with permission of Elsevier (b). All compositions are in weight fraction.

of local environment. The concentration luctuation model predicts that TTS works in miscible polymer blends only under three conditions [13]. The irst case is that TTS works in the dynamic symmetric system, where all the luctuations have the same local dynamics and the extent of luctuations does not affect TTS. The second case is that TTS works at suficient high temperature (T ≫ Tg ), where the differences in the local dynamics vanish as temperature increases. This is ascribed to the change of the temperature dependence of chain (or segmental) relaxation time from Vogel type to Arrhenius type as temperature is raised. The third case is that TTS works when there is strong interaction between two polymers, where the concentration luctuation is suppressed. The correlation length of concentration luctuation decreases as the Flory–Huggins interaction parameter (�) decreases or as the chain length decreases. It implies that TTS can be applicable even for strong dynamically asymmetric blends such as polystyrene (PS)/poly(phenylene oxide) (PPO) blends (ΔTg = 115 K [17]) with � = −0.05. While for blends with weak interaction (such as polyisoprene (PI)/poly(vinyl ethylene) (PVE) blend with � ≈ 0 [17]), TTS works only in blends when the molecular weight of polymer is low enough. 15.1.2

Immiscible Blends

15.1.2.1 Linear Viscoelasticity In contrast to miscible polymer blends, the heterogeneity in immiscible blends is rather high, and their rheological behaviors are strongly related to the phase-separated morphology. Typically, two kinds of morphology can be observed in polymer blends, namely the droplet–matrix morphology and

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496 105 104

PDMS/PIB 10/90 at 20 °C

105

104

102

G′, G″ (Pa)

G′, G″ (Pa)

103

PP/POE 80/20 at 220 °C

101 100

103

102

10−1 10

G′PIB G′PDMS G′blend

−2

10−3

0.1

1 10 ω (rad/s) (a)

G″PIB G″PDMS G″blend 100

G′PP G′POF G′blend

101

100

0.1

1

G″PP G″POF G″blend

100 10 ω (rad/s) (b)

Figure 15.4 Dynamic moduli of PDMS/PIB 10/90 blend (a) and PP/POE 80/20 blend (b). All compositions are in weight fraction. From Ref. [18]. Reproduced with permission of John Wiley and Sons.

co-continuous morphology. For droplet morphology, the minor component is dispersed as spherical droplets in the continuous matrix of major component. A typical dynamic moduli of such blend (polydimethylsiloxane (PDMS)/polyisobutylene (PIB) 10/90) [18] is shown in Figure 15.4a. It is seen that both the storage modulus and the loss modulus of blend are quite close to that of matrix at high-frequency region, which implies that droplets only induce additional hydrodynamic contribution at such frequencies. However, at low-frequency region, a shoulder is seen in storage modulus, which manifests additional relaxation process. It has been shown both experimentally and theoretically that such relaxation is ascribed to the droplet shape relaxation due to the presence of interfacial tension. Therefore, the interfacial contribution to dynamic moduli can be calculated from the shape evolution of droplets and written in a Maxwell-type expression as [19] ′

Ginterface (�) ′

Gs,max

G′′interface (�) f1 �� �2 � 2 = = , ′ 2 2 2 2 � � + f1 � � 2 + f12 Gs,max

(15.6)

with ′

40(p + 1) (p + 1)(2p + 3)� 6Γ 2 2 Kf , K = ⋅ ,f = , 3 2 5R 5(p + 1) − (5p + 2)� 1 (2p + 3)(19p + 16) 5 f2 = (15.7) 2p + 3

Gs,max =

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where p = �d ∕�m is the viscosity ratio between droplet polymer and matrix polymer, � = �m R∕Γ is the characteristic relaxation time of droplet with R the droplet radius and Γ the interfacial tension. The interfacial contribution plus the components’ contribution will give the dynamic moduli of blends. In the simplest case, the components’ contribution can be expressed as the linear addition of the dynamic ′ moduli of two polymers. At low frequency, if the interfacial contribution (G interface ) is signiicantly larger than that of components’ contribution, an obvious enhancement can be observed in the storage modulus (PDMS/PIB blend in Fig. 15.4a). Since ′ Ginterface is proportional to Γ∕R at low-frequency region and in the range 1–100 Pa for typical interfacial tension (1 mN/m) and droplet radius (1 μm), the enhancement in storage modulus of blend might be not so obvious when the matrix G′ is much ′ higher than Ginterface (polypropylene (PP)/poly(ethylene-α-octene) (POE) blend in Fig. 15.4b). A large amount of experiments have shown that the typical shoulder-like transition in storage modulus is quantitatively correlated to the average droplet size of blends. Actually, different theoretical models, including Palierne model [20], Bousmina model [21], and Yu et al.’s model (Eq. 15.6) [19], can be used to describe the dynamic moduli of blends quantitatively. Several methods have been suggested to determine the average droplet size from dynamic moduli using these constitutive models [22], among which direct-itting method and relaxation spectrum method are the most frequently used. When the fraction of minor component increases, the droplet morphology gradually changes into the co-continuous morphology. Similarly, the interfaces still give additional contribution to the elastic modulus, and enhancement in G′ at low frequency is also observed. In contrast to the shoulder-like transition in storage modulus, G′ of blend with co-continuous morphology exhibits a power law dependence on the frequency (Fig. 15.5). It has been demonstrated recently that such behavior can also be quantitatively related to the morphology of blend. Yu et al. [23] suggested to use tricylinders to approximate the co-continuous morphology, and the dynamic moduli can be obtained from the deformation of cylinders in different directions. It is found that only the cylinder along the shear gradient direction and along the vortex direction will contribute to the stress. The storage modulus is expressed as ) ( �sg 3 f2 �2 � 2 �v ′ (15.8) + Ginterface (�) = ΓSV 6 �v 4 �2 � 2 + f 2 1

where SV is the speciic interfacial area of the domains. �sg and �v denote the extent of preferred orientation of different cylinders. For isotropically oriented domains, �sg ≈ �v ≈ 1. The irst term in the parentheses on right hand side of Equation 15.8 exhibits a nonrelaxing characteristic of the cylinder along the shear gradient direction, while the second term looks similar to Equation 15.6 except that it is a 2D relaxation of ellipse in contrast to the 3D relaxation of ellipsoidal in droplet morphology. The components’ contribution in co-continuous blends can be described by Veenstra model [24], which is close to Palierne model without interfacial tension. It implies that the components’ contribution is rarely dependent on the morphology of blends. The speciic interfacial area of co-continuous blend can be determined by itting the complete model with

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498 105

G′ (Pa)

104

103 PS/POE 40/60 at 180 °C Experiments Veenstra model Yu et al. model (lc = 8 μm)

102

Slope 2 1

10 0.01

0.1

1

10

100

Angular frequency (rad/s)

Figure 15.5 Storage modulus of POE/PS 40/60 blend at 180 ∘ C. All compositions are in weight fraction. From Ref. [23]. Reproduced with permission of Elsevier.

experimental data, from which the characteristic length (lc ) can be obtained through ′ ′ ′ ′ ′ SV = 3�a b ∕2lc . a and b = 1 − a are the reduced average radius and length of ′2 cylinder, which can be determined from the volume fraction of cylinders � = 3a − ′3 2a . It is seen in Figure 15.5 that for POE/PS blend, the characteristic length is about 13 μm from the itting result, which is close to the observation from SEM images [23]. In immiscible polymer blend, as the concentration of one component increases, the morphology will change from droplet–matrix type to co-continuous type. Further increase in the concentration will result in phase-inverted morphology. The concentration range that forms co-continuous morphology is of practical importance. Classical methods [25–27] to determine the co-continuous range include the selective extraction using different solvents, image analysis based on the observations by scanning electron microscopy (SEM), or transmission electron microscopy (TEM). However, these methods suffer from complex experimental treatments or analysis and usually require quite a long time. Because of the different characteristics in dynamic moduli of blends with droplet–matrix morphology and co-continuous morphology, some rheological methods have also been suggested to determine the co-continuous range. One simple method utilizes the non-monotonic dependence of storage modulus or complex viscosity on the compositions. Usually, G′ (and � ∗ ) at low frequency will increase as the concentration of dispersed phase increases in blends with droplet morphology (Eq. 15.6). Because the concentration dependence in droplet morphology (Eq. 15.6) is different from that in co-continuous morphology (Eq. 15.8), a local maximum of G′ (and � ∗ ) is expected and the corresponding concentrations are denoted as the boundaries between droplet morphology and co-continuous morphology. An example is shown in Figure 15.6a

RHEOLOGY OF POLYMER BLENDS

499

80

1.4

1.2

60

α

1.0 α and β

G′(0.01 Hz) (Pa)

70

50

0.8

40

β 0.6

30

0.4

20 10

0

20 40 60 80 100 PMMA content (wt%) (a)

0.2

0

20 40 60 80 100 PEO content (wt%) (b)

Figure 15.6 (a) Storage modulus versus composition of PMMA/SMA blend at 0.01 Hz and 220 ∘ C. (b) Power law exponents α and β for PEO/PVED-HFP blend at 150 ∘ C. From Ref. [28]. Reproduced with permission of The Society of Rheology.

for PMMA/styrene–maleic anhydride copolymer (SMA) blend at 220 ∘ C, where the co-continuous morphology forms when PMMA content is between 50% and 70%. This method is also used in POE/PS blend [29]. The other method takes use of the difference in the frequency dependence of G′ and G′′ at low frequency. In contrast to blend with droplet morphology, both phase domains are continuous, self-supporting in co-continuous blend, which resembles the network in a gel. Therefore, either plotting the slope of G′ and G′′ at low frequencies (in log–log scale) or plotting the loss tangent against the composition will generate two cross points satisfying ′ the requirement for critical gel (G ∝ G′′ ∝ �n ). In the example of poly(ethylene oxide) (PEO)/poly(vinylideneluoride-hexaluoropropylene) (PVDF-HFP) blend ′ shown in Figure 15.6b, the power law exponent α and β in G ∝ �α and G′′ ∝ �β decrease as the content of minor composition increases, and the concentration at which α = β denotes the formation of co-continuous morphology [28]. Similarly, the concentration where the loss tangent becomes frequency independent gives the boundaries of co-continuous morphology. 15.1.2.2 Morphology Evolution and Nonlinear Rheology When an immiscible polymer blend is subjected to low ield, the domains will experience various processes such as deformation, breakup, collision and coalescence, and relaxation. Taking shear low, for example, for droplet morphology, the applied shear stress tends to make the droplet shape deviate from sphere, while the interfacial tension tends to minimize the interfacial energy and keep the spherical shape. The capillary

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500

number (Ca), deined as the ratio between shear stress and interfacial tension, Ca = �m �∕(Γ∕R), ̇ is the most important parameter to determine the droplet morphology in immiscible blends. Droplet shape will not deviate from spheres too much when Ca ≪ 1 since the shear stress is not strong enough to overcome surface tension. As Ca increases, droplets will continue to deform into ellipsoids and even iber or sheet morphology until a critical Ca is reached, above which a steady deformation of droplet cannot be obtained and droplet breakup occurs. The critical capillary number (Cac ) depends mainly on the viscosity ratio of blend [30, 31] and is different in shear low and elongational low. As shown in Figure 15.7, Cac in shear low increases greatly when the viscosity ratio becomes much larger or much smaller than 1, which implies that dispersive mixing becomes easy when the viscosity of two components matches. In contrast, Cac in elongation low is much smaller than that in shear low and is less dependent on the viscosity ratio. Droplet breakup can happen not only during deformation, it may also happen under quiescent condition after certain large deformation. The elongated droplet can be decomposed into a series of smaller droplets through Rayleigh instability, which is initiated by thermal luctuation. Fluctuation with a speciic wavelength has the fastest growth rate and dominates the thread breakup (Tomotika theory [32]). If droplet’s viscosity is much higher than that of matrix, the development of luctuation coincides with the retraction of deformed droplet. Then, the breakup of deformed droplet may or may not happen depending on the competition between two processes [33, 34]. Actually, the interfacial tension is the only driving force of the shape relaxation under quiescent condition. Therefore, thread break process [35] and retraction of short iber

4

3

log CaC

2 Shear

1

0

−1 Elongation −2

−4

−2

0 log p

2

4

Figure 15.7 Critical capillary number versus viscosity ratio in simple shear and elongation low. The plots are based on the empirical itting of Grace’s curves [30] by de Bruijn [31].

RHEOLOGY OF POLYMER BLENDS

501

[36] or ellipsoid [37] are often used to determine the interfacial tension between two polymers in melt state. Under shear condition, droplets may collide and coalescence into a bigger one. The coalescence process starts by the approaching of two droplets, which forms a matrix ilm between two droplets. Drainage of matrix luid from the ilm will make the ilm thinner until a critical thickness (hc ) [38] is reached, where the interfacial instability dominates and ilm ruptures. The coalescence of droplets in shear low is a competition between collision and ilm drainage. Under strong shear low, although the collision between droplets can cause a quick drainage of matrix ilm, the rotation of droplet pair in low ield limits the time for ilm drainage. Therefore, probability of coalescence in shear low will decrease as the shear rate increases [39]. Moreover, the ilm drainage time becomes longer for larger droplets. It implies that there exists a critical droplet size above which coalescence could not happen. According to the partially mobile interface (PMI) model, the critical droplet for coalescence is [40] ( Rc,coal =

4 √ hc 3

)2∕5

( −2∕5

p

�m �̇ Γ

)−3∕5 (15.9)

For an immiscible blend subjected to strong shear low, evolution of droplet morphology always happens with deformation, relaxation, possible breakup, and coalescence. Such morphological change can also be observed from rheological response. The transient irst normal stress difference (N1 ) of an immiscible blend with droplet morphology under step shear is shown in Figure 15.8. An overshoot in N1 is obvious as the

30

N1,excess/N1,excess,0

25

5.0 s−1

4.0 s−1

−1

2.0 s−1

1.5 s−1

1.0 s−1

3.0 s

20 15 10 5 0

0

50

100

150

200 Strain

250

300

350

400

Figure 15.8 Transient irst normal stress difference of PIB/PDMS 10/90 blend under different step shear rates. The solid lines are the prediction of Yu–Zhou model. All compositions are in weight fraction. From Ref. [41]. Reproduced with permission of The Society of Rheology.

502

RHEOLOGY AND PROCESSING OF NANOPARTICLE FILLED POLYMER

peak strain increases with the shear rate. Such overshoot in N1 cannot be ascribed to the polymer components whose peak strain is independent of the shear rate. The constitutive model suggested by Yu et al. [41] can describe such transient phenomena quite well, which attributes the overshoot to the breakup of droplets with different droplet size. The peak corresponds to the end of breakup for droplet with volume average radius, while the end of overshoot corresponds to the end of breakup for the largest droplets in the blend. In addition to the transient behaviors, the steady shear behavior is also strongly related to the morphology evolution. As mentioned earlier, the droplets will undergo breakup to decrease droplet size and coalescence to increase droplet size. The breakup is determined by the critical capillary number, which is only dependent on viscosity ratio. For a speciic polymer blend, Cac is a constant and the critical droplet size below which breakup cannot happen is inversely proportional to the shear rate: Rc,breakup = Cac

Γ �m �̇

(15.10)

It is clear that the critical droplet size of breakup and coalescence is not equivalent and depend on the shear rate in different manners. Schematic plot of the critical droplet size against shear rate is shown in Figure 15.9a, where the space is divided into four zones. When the droplet size is larger than Rc,breakup , breakup of droplet will dominates during the shear until the droplet size reaches Rc,breakup (zone B). If the droplet size is smaller than Rc,coal , coalescence will dominate and droplet size increases until it reaches Rc,coal (zone C). In zone D, the droplet size is too small to breakup, and too large to coalescence, only deformation will happen during shear. At high shear rate after the cross of two limiting lines, droplet size can be larger than Rc,breakup and smaller than Rc,coal , which means breakup and coalescence happen simultaneously during shear. The steady droplet size is determined by the dynamic equilibrium between breakup and coalescence. Because the steady droplet size is strongly related to the initial droplet size, it might be possible that different steady droplet sizes can be obtained under the same shear rate if the initial droplet size is different. Moreover, the shear history may have a critical inluence on the morphology and the rheological response. As shown in Figure 15.9b, if a blend is subjected to a step-up shear rate sweep followed by a step-down shear rate sweep, there appears morphological hysteresis at low shear rate regime. Correspondingly, the steady shear viscosity as a function of shear rate also exhibits hysteresis (Figure 15.9c). 15.1.3

Partially Miscible Blends

Unlike the completely miscible or immiscible blends, some blends are miscible only at certain range of temperatures and may undergo phase separation when temperature changes. Two kinds of phase diagrams are often observed, namely lower critical solution temperature (LCST) and upper critical solution temperature (UCST). During phase separation, great change in morphology happens. Because of the additional contribution of morphology to the stress, rheological methods are often used to study

RHEOLOGY OF POLYMER BLENDS

503

Radius Breakup line

B D

Coalescence line

C B+C Shear rate

(a) 103

1250 Breakup line

1/30 1200

1/130 4 10

26

101

5

26

Shear viscosity (Pa.s)

Droplet radius (μm)

2

8 23

9/22

1150

23 9/22

4

1100

5

8

1050

100 1000

Coalescence line

15/16

15/16

10−1

950 10−3 10−2 10−1 100 Shear rate (1/s) (b)

101

10−3

10−2 10−1 100 Shear rate (1/s) (c)

101

Figure 15.9 Critical droplet size versus shear rate with B, C, D standing for breakup, coalescence, and deformation, respectively (a). Steady droplet size (b) and steady shear viscosity (c) are predicted by Yu–Zhou model [41] in a simulated sweep-up and sweep-down experiments. The numbers in (b) and (c) denote the sequence number in the shear rate sweep test.

the liquid–liquid phase separation of polymer blend. It is not limited by the match of refractive index of two polymers, which constrains the use of optical microscopy or light scattering to study phase separation. One of the frequently used rheological methods to infer phase separation is time–temperature superposition. It is based on the assumption that TTS works in one-phase regime and fails in two-phase regime. An example is shown in Figure 15.10a for PMMA/SAN blends, where the start of TTS failure appears between 160 and 170 ∘ C, and the phase separation temperature is assumed to be in

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106 PMMA/SAN 60/40

G′, G″ (Pa)

105

104 1 150 °C 103

160 °C

2

170 °C 180 °C

102 10–4

10–3

10–2

(a)

100 10–1 aTω (rad/s)

102

101

160 8 140 165.8 ± 1.6 °C 6

100 Tan δ

η″/aT (kPa s)

120

80 60 40

4 ω (rad/s) 0.0158 0.0251 0.0389 0.063

175 °C

20

176 °C

0

180 °C

2

185 °C –20 (b)

0

200

400

η′/aT (kPa s)

600

0 (c)

150

160

170

180

Temperature (°C)

Figure 15.10 Time–temperature superposition of PMMA/SAN 60/40 blend at Tref = 150 ∘ C (a), the shifted Cole–Cole plot for blends PMMA/SAN 40/60 at Tref = 160 ∘ C (b), and the loss angle tangent of dynamic frequency sweep under different temperatures for PMMA/SAN 70/30 blend (c). All compositions are in weight fraction. From Ref. [42]. Reproduced with permission of Elsevier.

RHEOLOGY OF POLYMER BLENDS

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such temperature interval [42]. Since TTS may also fail in miscible blends, such method is only meaningful in blends where TTS works in homogeneous regime. Therefore, such method generally works well in dynamically symmetric blends, while in dynamically asymmetric blends, it works only when the phase separation temperature is much higher than the glass transition temperatures of polymers. Apart from the shifting of dynamic moduli to evaluate TTS, some other plotting methods ′ such as shifted Cole–Cole plot (� ′′ ∕aT ∼ � ∕aT with aT the shifting factor) have also been used [42]. The advantage of the shifted Cole–Cole plot is that all the data measured at different temperatures fall into the same semicircle, and the additional relaxation at low frequency can be observed more clearly as the second semicircle ′ (Fig. 15.10b) due to the deinition of � ′′ (= G ∕�). The shifted Cole–Cole plot usually works well for off-critical blends where droplet–matrix morphology forms during phase separation. For critical blends, co-continuous morphology generates according to the spinodal decomposition mechanism. The gel-like method to detect the co-continuous morphology can be used to determine the phase separation temperature (Fig. 15.10c). The above-mentioned methods take advantage of the characteristics of frequency dependency in homogeneous and heterogeneous states. Since the phase separation is a time process, the time-dependent characteristics are also used to judge the phase separation. As shown in Figure 15.11, when a polymer solution (ultrahigh molecular weight polyethylene (UHMWPE)/liquid parafin (LP)) is quenched into two-phase regime, G′ increases with time due to phase separation. As the temperature increases, G′ continuous to grow but with a slower rate. When the temperature increases further, G′ becomes constant over a quite long time, which

105

122 γ0 = 2%, f = 0.1 Hz

121

119

104

118 117 116

103

102

0

100

G′

115

η∗ Temperature

114

200 Time (min)

300

400

Temperature (°C)

G′ (Pa), η∗ (Pa s)

120

113

Figure 15.11 Evolution of storage modulus G′ and complex viscosity �* as a function of time for UHMWPE/LP 25/75 blend in “inverse quenching” with a ixed frequency of 0.1 Hz and strain of 2.0%. All compositions are in weight fraction. From Ref. [43]. Reproduced with permission of Elsevier.

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means both the phase separation and phase dissolution stop due to the vanishing thermodynamic driving force at such temperature. As the temperature increases again, G′ begins to decrease corresponding to the dissolution of phase domains in one-phase regime. Therefore, the temperature at which G′ becomes independent of time is taken as the phase separation temperature. Another frequently used method to determine the phase separation is temperature ramp under a speciic shear low. Usually the starting temperature locates in the one-phase regime, and ramping direction depends on the type of phase diagram, that is, ramping up for LCST-type system [44–46] and ramping down for UCST-type system [47]. A typical dependence of storage modulus on temperatures for two polymer blends is shown in Figure 15.12. For dynamically asymmetric blend (PS/poly(vinyl methyl ether) (PVME), ΔTg = 125 o C [45]), as temperature increases, G′ decreases irst followed by an evident increase and decreases at higher temperature. The upturn in G′ in such blend is ascribed to the concentration luctuation and phase separation. The inlection point in the upturn of G′ is often taken as the phase separation temperature. In contrast, for dynamically symmetric blend (PMMA/SMA, ΔTg = 30 o C), only slight deviation of G′ from the decreasing trend is observed, where the deviation temperature is taken as the phase separation temperature. The difference in the temperature dependence of G′ during temperature ramp lies in that the contribution of concentration luctuation to dynamic moduli is strongly inluenced by the dynamic asymmetry of blends. It should be noticed that the phase separation temperature determined by using frequency sweep, temperature

105

104

G′ (Pa)

PS/PVME ΔTg = 125 °C 103 PMMA/SMA12 ΔTg = 30 °C 102

101 70 80 90 100 110 120 130 180

200

220

240

260

280

Temperature (°C)

Figure 15.12 Isochronal (0.1 rad/s) dynamic temperature ramp of PS/PVME 40/60 blend (under an applied stress amplitude of 100 Pa and a heating rate of 0.1 ∘ C/min) and PMMA/SMA 20/80 blend (under an applied strain amplitude of 2% and a heating rate of 0.5 ∘ C/min). All compositions are in weight fraction. Adapted from Ref. [45].

RHEOLOGY OF POLYMER BLENDS

507

ramp, and time sweep are all affected by the time of experiments. The phase separation temperature determined by the above rheological methods is accurate only when the phase separation is faster than the measurement speed. Otherwise, there must be some retardant effects in the rheological determined phase separation temperature and can be regarded as apparent values. Phase separation temperature speciied using these methods are often regarded as binodal temperature. Actually, all these methods are empirical since no theoretical model can correlate the dynamic moduli with the binodal temperature directly at present. These temperatures can only be regarded as apparent one. In contrast, the spinodal temperature can be determined from the theory of concentration luctuation. Fredrickson and Larson had suggested that the storage modulus and loss modulus by concentration luctuation can be expressed as [48] k T�2 Gcf (�) = B 1920� ′

G′′cf (�)

k T� = B 240�

]}1∕2 { [ 2 R2g2 [ ]−5∕2 1 Rg1 W(T)2 2(� s − �) (15.11) + 3 �N1 (1 − �)N2

]}−1∕2 { [ 2 R2g2 [ ]−1∕2 1 Rg1 W(T) 2(� s − �) + 3 �N1 (1 − �)N2

(15.12)

�02 �01 + �3�kB T (1 − �)3�kB T

(15.13)

with W(T) =

where kB is the Boltzmann constant, � stands for the angular frequency, Rgi means the radius of gyration of species i, � is the volume fraction of polymer 1, Ni is the number of segments of species i, � s is the interaction parameter at the spinodal temperature, � is the interaction parameter at temperature T, and �0i is the monomeric friction coeficient for species i. Both the Flory–Huggins interaction parameter � and the monomeric friction coeficient �0i depend on the temperature. W(T) in Equations 15.11 and 15.12 can be eliminated and one can obtain [49] [

G′′ 2cf (�) ′

Gcf (�)T

]2∕3 =

B C

(

1 1 − Ts T

) (15.14) ′

where � = A + B∕T is used (A and B are constants). It is seen that if Gcf and G′′cf are known, the above equation can be used to extrapolate the spinodal temperature Ts . ′ Actually, Equation 15.14 has been used in some publications with Gcf and G′′cf ′ replaced by the measured G and G′′ [45, 47, 50]. It should be noticed that such replacement works only when the total moduli are dominated by the concentration luctuation. If such requirement is not satisied, great error could be reached. ′ One example is shown in Figure 15.14a with the plot (G′′ 2cf ∕Gcf T)2∕3 ∼ 1∕T. Although a straight line can be drawn and an apparent transition temperature can be determined from the intercept, it is obvious that the part of the straight line lies

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in the two-phase regime of phase diagram, which contracts with the prediction of theory. More accurately, it is necessary to extract the contribution from concentration luctuation. This can be done by subtracting the measured dynamic moduli with that without concentration luctuation, that is, the components’ contribution. The components’ contribution can be predicted by the constitutive equation of miscible blends (such as double-reptation self-concentration model [52, 53]), or it can be obtained by extrapolating the high-frequency data to low frequency using the assumption that the contribution from concentration luctuation only affect the low-frequency data [42]. ′ In fact, only Gcf is taken since the loss modulus is mainly determined by the compo′ nents’ contribution, and the determination of G′′cf would cause large error. Using Gcf to determine the spinodal temperature through Equation 15.11 requires the knowledge of monomeric friction coeficient in Equation 15.13. This can be accomplished by using the relationship between zero shear viscosity and the monomeric friction coeficient [54], and W(T) can be expressed as W(T) =

1 �

�GN1 b21

4�01 (T) ( )2 ( Me1 M01

M1 Me1

1 )3.4 + (1 − �)

�GN2 b22

4�02 (T) ( )2 ( Me2 M02

M2 Me2

)3.4

(15.15)

[G″2 / (G′T)]2/3

Me represents the mean molecular weight between entanglement points, GN is the plateau modulus, and b is the effective step length of the monomer. Therefore, plotting ′ {Gcf (�)∕[(W(T))2 T]}−2∕5 versus 1∕T and the intercept with horizontal axis denoting as the spinodal temperature (Ts ). One example is shown in Figure 15.13b, where the 5 × 104

(a)

4 × 104 3 × 104

One-phase regime

2 × 104 1 × 104

{G′cf / (T[W(t)2}–2/5

0 0.0020

6.0 × 10–5

Tb = 172 °C

Ts = 219.9 °C 0.0021

0.0022 1/T (K–1)

(b)

0.0023

0.0024

Tb = 172 °C

4.0 × 10–5 2.0 × 10–5 0.0 0.0020

Ts = 178.4 °C 0.0021

0.0022 1/T (K–1)

One-phase regime 0.0023

0.0024

Figure 15.13 Determination of the spinodal temperature by plotting ′ ′ {G′′ 2 (�, T)∕[G (�, T)T]}2∕3 versus 1∕T (a) and {Gcf (�)∕[(W(T))2 T]}−2∕5 versus 1∕T (b) for PMMA/SAN 80/20 blends. All compositions are in weight fraction.

EFFECT OF NANOPARTICLES ON THE MORPHOLOGY OF POLYMER BLEND

509

2μm

(a)

(b)

Figure 15.14 TEM images of PP/EVA/silica blends. (a) PP/EVA with 3 wt% hydrophilic silica located in the EVA phase; (b) PP/EVA with 3 wt% hydrophilic silica located at the PP/EVA interfaces. From Ref. [51]. Reproduced with permission of Wiley.

linear extrapolation is used to determine the spinodal temperature. It is critical to see that the part of data used for extrapolation lies in the one-phase regime, which is well consistent with the theory of concentration luctuation.

15.2 EFFECT OF NANOPARTICLES ON THE MORPHOLOGY OF POLYMER BLEND The phase morphology of polymer blends, such as size, shape, and continuity of the components, has attracted considerable attention over the past decades. Generally speaking, polymer blends can be divided into three categories, namely, miscible, partially miscible, and immiscible blends [55]. However, most commercially used polymers are thermodynamically immiscible, and two typical morphologies, that is, sea-island and co-continuous morphology, are usually observed in immiscible polymer blends. In either cases, the morphology of immiscible polymer blends is changing continuously during the melt processing, and the obtained phase morphology is still in a nonequilibrium state, which is prone to coalescence and coarsening. In order to control the phase morphology, various compatibilization methods have been proposed, such as adding or generating block and graft copolymer at the interfaces. However, in both cases, it is not easy to obtain block or graft copolymer in a large scale because of the complex synthetic routes, and the added or as-prepared copolymer tends to form micelles in the bulk rather than stay at the interfaces. Thus, these compatibilization strategies are neither convenient nor economical [56]. A promising alternative way to control the phase morphology of polymer blends is the incorporation of nanoparticles [57]. The addition of nanoparticles, such as clay, silicon dioxide, carbon black, nanotube, and graphene, can not only enhance the macroscopic properties, such as mechanical strength, electrical, and thermal conductivity, but also modify the microstructure of polymer blends. Because of the complexity of ternary nanocomposites, the inluence of nanoparticles on different

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phase morphology also differs. For immiscible polymer blends, nanoparticles can be used as compatibilizers to reine the phase size and stabilize the phase morphology, which is similar to the particle-stabilized oil/water Pickering emulsion [58]. Particles can also increase the drop size of polymer blends depending on the properties of nanoparticles and mixing conditions [59, 60]. In these cases, the distribution of nanoparticles in polymer blends can be a very powerful and eficient method to control the morphology, especially when the nanoparticles are selectively localized in one phase or at the interfaces between components. Thus, the understanding and control of selective distribution of nanoparticles are key factors to tailor the phase morphology of immiscible polymer blends. On the other hand, the introduction of nanoparticles also has a large inluence on the morphology of partially miscible polymer blends. The preferential interaction between the particles and one of the polymer component to the particle surface can alter the phase behavior, changing the phase separation temperature. Once the polymer blend is phase separated, the presence of nanoparticles will increase the bulk viscosity, impeding the phase separation kinetics. In addition, accompanied with the phase separation, there is also the migration of nanoparticles from the bulk to the preferred phase. Subsequently, the selective localization of nanoparticles in either certain phase or the interphases between phase domains will also impact the phase separation kinetics. 15.2.1

Selective Distribution

In overwhelming majority of ternary nanocomposites, the nanoillers are distributed unevenly between different polymer phases [61]. The unequal localization of nanoparticles was mainly attributed to the interactions among nanoparticles and polymer components. It is a balance between the polymer–nanoparticle interaction and the polymer–polymer interaction. Typically, nanoparticles tend to be selectively located within one of the polymer phases, including dispersed and continuous phases, or at the interfaces between polymer components. The typical phase morphology of illed polymer blends is presented in Figure 15.14. When hydrophilic silica was added to the polypropylene (PP)/ethylene-vinyl acetate copolymer (EVA) blend, almost all the silica particles are preferentially distributed within the dispersed phase, which is EVA phase (Fig. 15.14a). Unlike hydrophilic silica, the hydrophobic silica particles are mainly segregated at the interfaces between PP and EVA (Fig. 15.14b), serving as an interfacial barrier between the droplet and matrix [51]. The selective localization of nanoillers was generally determined by two distinct factors: thermodynamic effects and kinetic effects. The thermodynamic effect deals with the afinity of nanoparticles to different polymers, which determines the equilibrium state of dispersion. While the kinetic effect mainly determines the nonequilibrium distribution state of nanoparticles, and it is determined by the timescale of processing and the driving force of nanoparticles to migrate to their favorable state. In most of the research and industry cases, the dispersion of nanoparticles is a non-equilibrium state; thus, it was usually inluenced by the processing procedures, the shape and dimension of nanoparticles, and the polymer–nanoparticle

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interaction. These two factors are very critical to understand, predict, and control the selective localization of nanoparticles. 15.2.1.1 Thermodynamic Effects When nanoparticles are incorporated into the polymer blends, the particles tend to minimize the interfacial energy through migrating to the position with the most afinity. In a thermodynamic view, the distribution of nanoparticles in the equilibrium state can be predicted by the wetting coeficient, �a : [62] �B∕NP − �A∕NP �a = (15.16) �A∕B in which �B∕NP , �A∕NP , �A∕B are the interfacial energies between polymer B and nanoparticles NP, between polymer A and nanoparticles NP, between polymer A and polymer B, respectively. If �a > 1, the nanoparticles will be preferentially located in polymer A; if �a < −1, the nanoillers will be preferentially located in polymer B; and if −1 < �a < 1, the particles will be selectively located at the interfaces between polymer A and polymer B. In principle, if we can get the interfacial energy for polymer–polymer and polymer–nanoparticle interfaces, the localization of nanoparticles can be easily predicted through the wetting coeficient. However, it is often dificult to obtain those interfacial energies directly from experiments, especially for polymer–nanoparticle interface. Usually, researchers estimated them with the aid of some theoretical models [61]. One of frequently used model is Girifalco–Good [61] equation: √ �12 = �1 + �2 − 2 �1 �2

(15.17)

in which �i is the surface tension of component i. However, sometimes Girifalco–Good equation may not give a reasonable prediction especially when the surface tension of two polymer components is pretty close. Alternative models were also suggested to take into account the dispersive and polar part separately, including harmonic mean and geometric mean equation. The harmonic mean equation is ( d d p p ) �1 �2 �1 �2 (15.18) + p �12 = �1 + �2 − 4 p �1d + �2d �1 + �2 The geometric mean equation is also called Owens–Wendt equation [63]: √ √ p p �12 = �1 + �2 − 2 �1d �2d − 2 �1 �2

(15.19)

In both models, the surface tension was expressed as a sum of dispersive (� d ) and polar (� p ) components. In general, the geometric mean equation is more suitable for a pair of low surface energy material and high surface energy material, while the harmonic mean equation is better for a pair of two low surface energy materials [64].

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Two methods are frequently used to infer the solid’s surface tension (�) and its dispersive (� d ) and polar (� p ) components: contact angle measurement and inverse gas chromatography (IGC) [65]. Among them, the contact angle measurement is more widely used because of its accessibility. Speciically, the calculation of surface tension from the contact angle was based on Young’s equation cos � =

�s − �s∕l �l

(15.20)

where � is the contact angle between solid and liquid, �s and �l are the surface tension of solid and liquid separately, and �s∕l is the interfacial energy between solid and liquid, which can be expressed through Owens–Wendt equation [63]. Then the above-mentioned Young’s equation can be written as √ √ p p �l (1 + cos�) = 2 �sd �ld + 2 �s �l p

p

(15.21)

where �sd , �s , �ld , �l are the dispersive and polar components of solid and liquid, respectively. In general, two different liquids, a polar and a nonpolar liquid, with known surface tension were used to measure the contact angle on a solid surface. With the help of Equation 15.21, the surface tension of polymer and nanoparticles and its dispersive and polar components can be readily obtained. Considering that large majority of surface tension data is measured under room temperature, it is often different from the melt surface tension at high temperature. A correction method proposed by Guhhenheim [66] was frequently used to take this temperature effect into account. Such thermodynamic approach described earlier has been widely used for many polymer blends/nanoillers combinations to predict the nanoparticles’ localization. Those predictions and the corresponding observations from electron microscopy are summarized in Table 15.1. Even there are some discrepancies among different models, especially for the simplest Girifalco–Good equation, the selective localization was successfully predicted for various illed polymer blends with various nanoparticles, including spherical particles, such as silica [51, 67–72], carbon black [62, 72], CaCO3 [73], rod-like particles (multi-walled carbon nanotube, MWCNT) [74–80], and sheet-like particles such as graphene [81] and clay [82, 83]. As exhibited in Table 15.1, the selective localization of nanoparticles can be theoretically predicted, and this preferential localization can be well adjusted through changing the afinity between nanoparticles and polymer components. Different approaches were proposed in the previous researches, such as surface modiication of nanoparticles [51, 69, 70, 73, 83] and adding compatibilizers. After altering the surface properties of silica nanoparticles from hydrophobic to hydrophilic, as depicted in Figure 15.15, the localization of silica changes from PP/EVA interfaces to EVA phase. Similar trend was also observed in PP/PS [69] and PP/POE [70] blends. For layered particles such as montmorillonite (MMT), direct surface modiication with different ammonium cations (C15A and C30B) also altered the preferential location of nanoparticles (Table 15.1) [83]. As shown in Figure 15.15, upon the

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TABLE 15.1 Wetting Coeficient Calculated from Different Equations for Different Blends and Fillers, and the Location was Characterized by Electron Microscopy Polymer A Polymer B Filler (NP)

�a,GG a

�a,GM b

�a,HM c

Filler Location

0.66 2.54 −4.06 −3.589 0.072 −2.38 0.309 −3.351 0.175 −2.046 0.54 −0.076 2.611 −0.746 −3.798 0.028 −0.75 −2.90 −0.327

Interface [51] EVA [51] PU [67] PLLA [68] Interface [69] PS [69] PP [70] POE [70] Interface [71] PS [72] Interface [62] Interface [62] PP [73] Interface [73] PBA [73] Interface [74] Interface [75] PA12 [75] Interface and TPS [76] Interface [77] PC [78] PC [79] PS [80] Interfaces [81] Interface and PLA [82] PLA [83] Interface [83] PLA [83]

EVA EVA PLA PS PP PP PP PP PDMS PP PMMA PMMA PP PP PP EMA EMA EMA PCL

PP PP PU PLLA PS PS POE POE PBD PS PP HDPE POE POE PBA PA6/12 PA6 PA12 TPS

Hydrophobic silica −0.32 Hydrophilic silica 12.69 Hydrophilic silica 9.87 Hydrophilic silica 142.87 Hydrophobic silica 0.618 Hydrophilic silica −6.74 Hydrophobic silica −2.307 Hydrophilic silica 10.251 Hydrophobic silica −1 Carbon black −8.334 Carbon black 6.24 Carbon black 20.98 34.36 CaCO3 8.802 CaCO3 -stearic CaCO3 -g-PBA −410 MWCNT 0.915 MWCNT 0.3213 MWCNT −1.86 MWCNT 1.01

0.727 7.68 −5.19 −8.594 −0.108 −4.57 1.086 −8.345 0.184 −1.903 0.52 0.237 −6.769 −3.233 −9.548 −0.018 −0.79 −4.01 −0.164

PET PC PC PP PLLA PLA

PA6 SAN ABS PS EVA PCL

MWCNT MWCNT MWCNT MWCNT Graphene Clay

0.796 0.626 8.86 6.56 3.256 2.295 −3.706 −2.096 −2.75 −0.184 0.1–1.6 0.1–1.6

PLA PLA PLA

NR NR NR

CNa-MMT C15A-MMT C30B-MMT

20.71 21.34 48.8 −4.167 −5.1–16 2.37 0.354 1.41

a Calculated

from Girifalco–Good equation. from geometric mean equation. c Calculated from harmonic mean equation. b Calculated

grafting PS chains to the surface of MWCNT, the location of nanoparticles changes from SAN phase for pristine MWCNT (Fig. 15.15a), to both SAN and PPE phase for MWCNT grafted with short PS chain (Mn = 21 k) (Fig. 15.15b), and inally to PPE phase for longer PS chain (Mn = 73 k, Fig. 15.15c) [84]. It is also found that the grafted polymer chains exhibited stronger inluence on illers’ distribution than coated polymer chains [85]. The incorporation of another component is also a useful strategy to tune the selective localization. Owing to the strong interaction between maleic anhydride-grafted

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(b)

(a)

0.2 μm

(c)

0.2 μm SAN/PPE 40/60-MWCNT-1 Wt%

0.2 μm SAN/PPE 40/60-MWCNT-PS2821-1 Wt%

SAN/PPE 40/60-MWCNT-PS7673-1 Wt%

Figure 15.15 TEM images of SAN/PPE blends illed with 1 wt% of (a) MWCNT, (b) MWCNT-g-PS21k , and (c) MWCNT-g-PS73k . The dark domains are the PPE phase. All compositions are in weight fraction. From Ref. [84]. Reproduced with permission of Elsevier.

polypropylene (PP-g-MAH) and TiO2 nanoparticles, TiO2 nanoparticles began to move from original location (interface and poly(ethylene terephthalate) (PET) phase, Fig. 15.16a) to PP phase (Fig. 15.16b) [86, 87]. In this case, PP-g-MAH is acting as a compatibilizer to increase the afinity between PP phase and nanoparticles. Similar observations were also made in other blends/iller systems like PP/POE/silica [88, 89], PA6/ABS/MWCNT [90], and SAN/PC/MWCNT [91]. Sometimes, other nanoparticles can offer as an eficient way to trap the original nanoparticles to the interfaces, for example, the addition of graphene oxide successfully trapped the carbon nanotubes to the interfaces of PLLA and EVA [92]. Even though those theoretical models could predict the illers’ location in most cases, there still exist some discrepancies [78, 82, 93]. It was revealed that wetting coeficient is not suficient to explain the complex distribution of nanoparticles in ternary nanocomposites. On the one hand, it is dificult to obtain accurate surface

(a)

(b)

2 μm

2 μm

Figure 15.16 TEM images of PET/PP/TiO2 : (a) PET/(PP+PP-MAH)/TiO2 and (b) nanocomposites, the white dispersed domains are PET. From Ref. [86]. Reproduced with permission of Wiley.

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tension value, especially for high temperatures. On the other hand, the interaction between polymer and nanoparticles is very complex. There may be hydrogen bonding, chemical reaction, and ionic interaction. Simply dividing them into dispersive and polar part may not be enough to account for all these interactions. Most importantly, all the analyses of wetting coeficient described earlier are based on the assumption that the thermodynamic equilibrium is attained. However, the compounding and mixing processes only last several minutes, it is often unable to reach the equilibrium state for that short time. Thus, the kinetic effect on the selective localization of nanoparticles such as the processing condition and mixing sequence should also be carefully considered [51, 61, 94]. 15.2.1.2 Kinetics Effects For an immiscible polymer blends, the morphological evolution during the blending occurs in the following steps [95]: (i) minor phase forms sheets or ribbons; (ii) hole formation and growth inside the sheet; (iii) sheet breaks up into iber; and (iv) iber was further broken up into spherical droplets. When one of the phases has a lower melting temperature, it tends to form the matrix at irst; after the second polymer has melted, phase inversion may occur because of the change in viscosity ratio [56]. When nanoparticles were incorporated into the polymer blends during the mixing, the nanoparticles may not reach the thermodynamic state of dispersion and distribution because of the mixing conditions and high viscosity. In this case, mixing sequence, mixing time, shear strength, and melt viscosity become critical kinetic effects in the selective localization, which determines whether the nanoparticles are capable of migrating to the thermodynamically favorable phase. 15.2.1.2.1 Mixing Condition In general, the blending sequence can be classiied into four categories [95]: (i) all together simultaneously; (ii) polymer irst followed by nanoparticles; (iii) premixed with favorable phase following by the other phase; and (iv) premixed with unfavorable phase followed by mixing with favorable phase. Similar with the neat polymer blend, when mixed at the same time, the nanoparticles may be surrounded with the polymer with low melting temperature. Then it is similar to the sequence 3 or 4, the difference is that such pre-absorption is not so evident as the sequence 3 or 4 [75]. Most of the time, the particles were equally distributed into two polymer phases, and selective localization is frequently observed in the thermodynamically favorable phase. However, when nanoparticles were premixed with unfavorable phase, as indicted in sequence 4, the migration of nanoparticles from the unfavorable phase to the favorable phase was usually observed. In some cases, some nanoparticles reside at the interface instead of moving further forward, and this is an eficient way to produce conductive nanocomposites with low percolation value [62, 72, 96–98]. Elias et al. [69] investigated the location of silica nanoparticles in PP/PS with blending sequence 1 and 4, after 5 min of mixing, the nanoparticles are selectively located in PS phase for both cases. Similar observations were also made in many other illed polymer blends, such as PP/EVA/hydrophilic silica [51], HDPE/PA6/MWCNT [99], and PC/SAN/MWCNT [94]. In the previous studies of Gubbels et al. [96, 97], the migration of carbon black (CB) particles in PE/PS blends was observed by electrical conductivity. After

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premixing CB with unfavorable PS phase, PE was added, and then the CB particles began to migrate from PS to PE. Meantime, the electrical resistivity decreased with mixing time, and reached a minimum when the particles were approaching at the interfaces, and then increase again when particles inally reside in the PE phase. The whole migration process lasts only 5 min. Tan et al. [72] conducted similar research for PP/PS/CB blends through varying the blending sequences, as shown in Figure 15.17, when the CB particles were premixed with PS, they stay inside the PS phase after the second mixing, while for other two sequences, signiicant number of particles are segregated near the interfaces, especially when CB was premixed with unfavorable PP phase. It seems 10 min of mixing is not enough for nanoparticles to cross the interfaces. Similar trend is also observed in PP/EVA/silica system [51], after 5 min mixing, some of the hydrophobic silica particles remain in the unfavorable PP phase rather than interfaces between PP and EVA. Those studies seem to indicate that the time required to attain a thermodynamic equilibrium varies in different cases [94]. Thus, if the mixing was stopped at appropriate time, the nanoparticles will remain at the interfaces. This could be a powerful method to tune the location of nanoparticles in polymer blends. In addition, similar to the effect of mixing time, the shear rate could also be a useful method to control the particles’ selective localization. When nanoparticles were preblended with unfavorable phase (sequence 4), the increase in shear rate during the second mixing will promote the collision probability between two polymer components, thus accelerating the migration from unfavorable to favorable phase [94]. Médéric et al. [100] studied the effect of shear rate on the dispersion and distribution of clay particles in PA/PE blends. It was found that clay particles tend to stay at the PA/PE interfaces for low shear rate. However, for the higher shear rate, some of the clay particles could further migrate into the PA phase. Similar effect was also observed in PC/SAN/graphene system [101] and PC/SAN/CNT system [102], where the increase of mixing speed accelerates the migration of graphene sheets from SAN to thermodynamically favorable PC phase. In fact, the enhanced exfoliation or dispersion of the illers under higher shear rate may also contribute to the migration kinetics.

(a)

(b)

(c)

0.5 μm

0.5 μm

0.5 μm

Figure 15.17 TEM images of PP/PS/CB ternary composites with (a) blending sequence 2, (b) blending sequence 3, and (c) blending sequence 4. From Ref. [72]. Reproduced with permission of Wiley.

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15.2.1.2.2 Physical Properties of Polymers and Nanoparticles Unlike low viscosity emulsions, the physical properties of polymers and nanoparticles such as the shear viscosity and geometry of nanoparticles play an important role on the particles’ distribution. The effect of viscosity ratio on the localization of MWCNT in polycaprolactone (PCL)/poly(lactic acid) (PLA) was investigated by Wu et al. [82]. After one-step mixing, the localization of MWCNT occurred in the PCL phase or at the interface for the blend with high melt viscosity ratio (Fig. 15.18b), whereas the MWCNT particles were preferentially distributed in PLA phase for low viscosity ratio (Fig. 15.18a). Even the MWCNT was premixed with PLA phase, the MWCNT particles still resides in the PCL phase for the blend with high viscosity ratio. Similar phenomenon was also found in the research of PMMA/PP/CB ternary nanocomposites [103]. In that system, PMMA with different molecular weight was blended with the same kind of PP. Wetting coeficient predicts that CB particles should be located in the PMMA phase. At comparable viscosities, the dispersion of CB was consistent with the prediction. While further increasing the viscosity of PMMA, the CB was found to be located at the interfaces and even migrated into PP phase for even higher viscosity ratio. It seems that the thermodynamically driven localization would be hindered or suppressed by the component with higher viscosity, and the nanoparticles tend to stay within the less viscous phase. However, a comparative study of PE/PA/clay ternary composites indicated that the clay location would change from the interfaces to the thermodynamic favorable phase (PA phase) when the viscosity ratio (�PA ∕�PE ) was increased from 0.19 to 5.09 [104]. It was suggested that the difference in viscosity ratio would induce a change of hydrodynamic stresses during the mixing, thus leading to this migration behavior [104]. Gubbels et al. [105] proposed that the effect of viscosity ratio on the migration behavior may also be attributed to the subtle change in the thermodynamic interaction.

PLA droplets

PLA droplets Continuous PCL phase

500 nm

2000 nm (a)

Continuous PCL phase

(b)

Figure 15.18 TEM images for the PLA/PCL/MWCNT samples with the viscosity ratio (�PLA ∕�PCL ) of (a) 1 and (b) 16. From Ref. [82]. Reproduced with permission of John Wiley and Sons.

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Even the mechanism of viscosity effect is not clear, it still offers a useful method to control the selective localization behavior. 15.2.1.2.3 Migration Mechanism Even though abundant literature works on the thermodynamics and kinetics of selective location are discussed, the mechanism of the migration is still not well understood. Recently, general migration mechanism inside the immiscible polymer blends was suggested by Elias et al. [51]. Three mechanisms were proposed: diffusion, shear-induced collision between nanoparticles, and particle trapping during the coalescence. The time for a silica particle to diffuse a distance of its radius was estimated to 2 h in PP/EVA blends [51]. However, the migration of silica particles was fulilled in merely 5 min. Thus, the diffusion is nearly negligible for the migration, and the shear-induced collision and particle trapping become the dominant factors. The investigation of migration behavior in PC/SAN/MWCNT by Göldel et al. [94] validates this hypothesis. It was found that the diffusion is also negligible in PC/SAN/MWCNT system, and the shear-induced collision is the dominant factor. Moreover, there is an optimum shear rate for the transfer of MWCNT, as indicated by Göldel et al. [94], above which the contact time will not be enough to inish the transfer, while below it, the collision between particles and blend domains inhibit the transfer process. The migration mechanism also depends on the geometry of the nanoparticles. Göldel et al. [106] introduced a “Slim-Fast Mechanism” (SFM) to describe the transfer mechanism for nanoparticles with different shapes. It was suggested that the velocity of the migration and inal localization depend on the aspect ratio and dimension of the nanoparticles. For nanoparticles with low aspect ratio such as carbon black, the driving force for the particle to move across the interface was decreasing gradually (Fig. 15.19a), and at certain point, it may reach a force balance, stabilizing the particles at the interfaces. While for high aspect ratio nanoparticles such as carbon nanotubes, the driving force remains constant throughout the transfer until the nanoparticles fully migrate into the favorable phase (Fig. 15.19b). Thus, the carbon black would stay at the interfaces or in the favorable phase (blue phase) (Fig. 15.19c), while carbon nanotubes are fully migrated into the favorable phase (Fig. 15.19d). This mechanism can successfully explain the experimental indings on the localization of agglomerated and dispersed carbon black, stacked and exfoliated clays [100], silica nanoparticles [51], nanotubes [94], and graphene [101]. 15.2.1.3 Compatibilization Effect on the Phase Morphology In low-viscosity luid emulsions, the absorption of particles at the interfaces of the droplets offers an effective and eficient way to stabilize the emulsion [58]. It is also the case for the high-viscosity luid emulsions such as immiscible polymer blends. Similar to the block or graft copolymer, the nanoparticles can act as compatibilizers for the blends, reining and stabilizing the phase morphology. 15.2.1.3.1 Effect on Droplet–Matrix Morphology Extensive research during the last decades has revealed that there is a substantial reduction in the domain size of dispersed phase for various immiscible polymer blends illed with different nanoillers,

EFFECT OF NANOPARTICLES ON THE MORPHOLOGY OF POLYMER BLEND

(a)

(b) γ polymer2-CNT

519

γpolymer1-CNT

γpolymer2-sphere > γpolymer1-sphere Decrease of curvature

θ

- Curvature unchanged

θ2 < 90°

Stable localization at the interface is possible

Polymer 2

(c)

- Force is constant

Polymer 1

Polymer 2

θ2 < 90° θ2

Fcurvature Polymer 1

(d)

Figure 15.19 (a) Ideal low aspect ratio particle at the blend interface, the driving force decreasing during the transfer; (b) high aspect ratio particle at the blend interface, the driving force remains unchanged at the end of the transfer; and typical localization state of particle with (c) low aspect ratio and (d) high aspect ratio. The blue phase is the thermodynamically favorable phase. From Ref. [106]. Reproduced with permission of American Chemical Society.

such as clay, nanosilica, MWCNT, and graphene. Ray et al. [107–109] found that the domain size of dispersed phase in both PC/PMMA and PS/PP blends decreased considerably upon the addition of organoclay, and the compatibilization eficiency of clay could be tuned with different organic modiiers [108]. Si et al. [110] investigated the effect of organoclay on the morphology of PS/PMMA, PC/SAN, and PMMA/EVA blends and found that the domain size for all the blends is reduced signiicantly. This compatibilization effect was believed to be caused by the interfacial localization of clay particles. Similar observations were also made in other clay containing polymer blends [111–115]. Regarding silica particles, Kontopoulou et al. [70, 89] showed that the incorporation of silica nanoparticle into PP/EOC 80/20 blend decreased the average domain size of dispersed EOC phase by nearly 40% with 5 wt% of silica particles, whereas this compatibilization effect is highly dependent on the composition of the blend, for PP/EOC 70/30 and 60/40 blend, the reduction in EOC domain size becomes less evident [88]. Elias et al. [69, 116] systematically investigated the effect of hydrophilic and hydrophobic silica particles on the morphology of PP/PS and PP/EVA blends. In addition to the reduction in the domain size, the authors found that the effective interfacial tension was reduced for both silica particles.

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Moreover, the compatibilization effect of rod-like nanoparticles such as MWCNT has also been frequently reported in the literature [80, 82, 117]. As shown in Figure 15.20, considerable reduction of domain size for PS phase is clearly observed for both cases. When MWCNT was premixed with thermodynamically unfavorable PP phase, this compatibilization effect becomes more pronounced. It was ascribed to the fact that some MWCNT particles tend to localize at the interfaces during the migration from PP to PS [80]. In addition, the sheet-like nanoparticles, such as graphene oxide sheet, have also been identiied as an effective compatibilizer for PA/PPO [118] and PVDF/PA6 [119] blends because of its strong interaction with polar polymer components. 15.2.1.3.2 Effect on Co-continuous Morphology Compared with polymer blends with the droplet–matrix morphology, there is a limited literature concerning the effect of nanoparticles on the co-continuous morphology [68, 96, 120–126]. Lee et al. [121] found that the incorporation of small amount of nanosilica into PP/EOC 50/50 blends resulted in iner co-continuous morphology with smaller characteristic length (Fig. 15.21b). However, with up to 5 wt% of nanosilica, the PP phase tends to form the continuous phase with elongated EOC droplet as dispersed phase. It was suggested that such morphology changes are attributed to the change in the dynamics of droplet breakup rather than the increase in the viscosity of PP phase [121]. The addition of nanoparticles is also an effective method to extend the window of co-continuity in immiscible polymer blends. Gubbels et al. [96] found that the critical PE concentration for co-continuous structure was reduced from 40 to 10 wt% with 4 wt% of CB selectively localized in PE phase, and it is ascribed to the enhancement of stability of phase morphology rather than the increase in viscosity [96]. The investigation of PA6/ABS/nanosilica system by Liu et al. [127] revealed that the phase inversion of PA6/ABS system is more likely caused by the increase in viscosity of ABS/nanosilica phase. Filippone et al. [114, 122] studied the impact of different kinds of nanoparticles, including hydrophilic and hydrophobic silica, and organoclay on the phase inversion behavior of HDPE/PEO blend. The remarkable extension of co-continuity was found to occur only when the nanoparticles (organoclay in this case) are located at the interfaces. This interfacial localization slows down the interfacial relaxation dynamics, hinders the shape relaxation processes, and thus preserves the co-continuous structure [114]. In general, the mechanism for the nanoparticles-induced co-continuity is still not very clear. One of the most convincing reason is that nanoparticles increase the viscosity of NP-containing phase and slow down the phase relaxation dynamics [68, 96, 114, 121, 127]. The other mechanism is the formation of nanoparticles’ network in the polymer blends [124, 125]. Wu et al. [125] thought that the nanoparticles-induced co-continuity in ABS/PA6 was attributed to the self-networking behavior of carbon black. Carbon black is preferentially located in PA6 phase, and with the increase in loading, the particles tend to fuse together to form network structure, resulting in the increased continuity of PA6 phase. Similar phenomenon was also observed in PS/PA66/MWCNT [124] and HDPE/PA6/MWCNT [128] systems.

(a)

(b)

30 μm (e)

(c)

30 μm (f)

(d)

30 μm (g)

30 μm (h) 12 (PP/MWNT)/PS (PS/MWNT)/PP

Dn (μm)

10 8 6 4 2

30 μm

30 μm

30 μm

0

0

1

2

3

4

5

MWNT contents (wt%)

Figure 15.20 Morphology of PP/PS (70/30) blends with different contents of MWCNT: (a) neat blend; (b) 1 wt%, (c) 2 wt% and (d) 3 wt% MWCNT was premixed with PP (denoted (PP/MWCNT)/PS); (f) 1 wt%, (g) 2 wt%, and (h) 3 wt% MWCNT was premixed with PS (denoted (PS/MWCNT)/PP); and (e) the measured droplet size for the above blends. From Ref. [80]. Reproduced with permission of Springer.

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522

500 nm (a)

500 nm (b)

500 nm (c)

Figure 15.21 TEM images of (PP/PP-g-MAH 90/10)/EOC 50/50 composites (a) 0 wt% SiO2 ; (b) 1 wt% SiO2 ; (c) 5 wt% SiO2 . The dark domains are the stained POE phase. All compositions are in weight fraction. From Ref. [121]. Reproduced with permission of Elsevier.

15.2.1.3.3 Morphology Stability In order to obtain polymer blend with tailored properties, the stability of phase morphology is required to maintain the performance. In addition to the compatibilizing effect, nanoparticles could also be used to stabilize the phase morphology of polymer blends. Gubbel et al. [96] showed that under lower loading of carbon black, for instance 2 wt%, the co-continuous morphology is maintained but coarsens considerably with annealing time. However, at higher loading, says 5 wt%, the structure is well stabilized. Liu et al. [126] systematically investigated the effect of nanosilica particles on the phase coarsening behavior of co-continuous PA6/ABS blend under high temperature. Upon the addition of nanosilica, the phase coarsening is well suppressed. The coarsening rate before 10 min decreased from 0.149 μm/s for neat blend to 0.007 and 0.003 μm/s for 2 and 6 wt% illed polymer blends, respectively. After 10 min annealing, the coarsening rate also exhibits similar trend, decreasing from 0.01 μm/s for neat blend to almost zero for illed blends. The addition of nanosilica particles can not only compatibilize the polymer blend with iner and smaller phase domains but also stabilize the co-continuous phase morphology. Lee et al. [88, 121] studied the effect of nanosilica particles on the phase stability of PP/EOC blend with both droplet–matrix and co-continuous morphologies. Similar effects were found in both cases. With the introduction of silica particles, the suppressing of phase coarsening occurs in both kinds of morphologies. Similar effect was also found in PS/PLLA/silica ternary nanocomposites [68]. 15.2.1.3.4 Compatibilization Mechanism Over the past decade, the compatibilization effect of nanoparticles has been investigated in numerous experiments, and several mechanisms for the compatibilization were proposed. Fenouillot et al. [61] summarized the possible mechanisms in a recent review, including (i) reduction in interfacial tension between polymers; (ii) suppression of coalescence; (iii) viscosity

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change; (iv) physical network of particles; and (v) the absorption of polymer chains to the nanoparticles. It is well known that one of the major compatibilization effect for conventional compatibilizer is to reduce the interfacial tension and increase the interfacial adhesion between polymers. Ray et al. [108, 109] suggested that the selectively localized organoclay acted as an eficient compatibilizer and reduced the interfacial tension between polymers. With the help of Palierne model, Hong et al. [129] observed a reduction of interfacial tension from 5.76 to 0.14 mN/m when 1 wt% of organoclay was added and located at the interfaces of 10/90 PBT/PE blend. Elias et al. [116] found that the effective interfacial tension between polymers was decreased for both hydrophobic (mainly located at the interface) and hydrophilic (mainly located at the EVA phase) illed PP/EVA blends. It seems that the compatibilization mechanism for the interfacial localized nanoparticles is the reduction of interfacial energy. However, the investigation of Tao et al. [117] in PA12/EA/MWCNT ternary system revealed that the interfacial energy is unaffected upon the interfacial localization of MWCNT, and the compatibilization effect is ascribed to the suppression of coalescence, in other words, the steric hindrance effect [110, 113]. When nanoparticles are mainly dispersed in the dispersed phase or the matrix, the reduction of interfacial tension between polymers becomes less evident. The viscosity of nanoparticles containing phase increases upon the addition of nanoparticles. Then the composition effect from the change of viscosity ratio is responsible for the compatibilization behavior. The segregation of nanoparticles in one phase may change the viscosity ratio and shift the critical capillary number, which may favor the droplet breakup during the melt blending. Liu et al. [89] pointed out that the increase in viscosity of PP is responsible for the reduced EOC droplet size when silica is selectively dispersed in PP phase. However, sometimes the increase in viscosity is not enough to account for the remarkable compatibilization effect. Liu et al. [126] attributed the signiicant compatibilization impact of nanosilica on the co-continuous morphology of PA6/ABS blend to both the increase in viscosity and the formation of network structure. For the iller with high aspect ratio, particle network tends to form under low loading of particles; while for low aspect ratio iller, the particle network is only formed under high loading. Bailly et al. [70] found that considerable reduction in the droplet size occurs until 7 wt% or more nanosilica is added. Another widely accepted compatibilization mechanism is the suppression of coalescence. Nanoparticles may be trapped between droplets and slow down the colliding and coalescence of droplets. Wu et al. [112] showed that the presence of clay in the PBT phase suppressed the coalescence and agglomeration of PE droplets. Furthermore, Kontopoulou et al. [130] suggested that there is an immobilized layer, including clay and bound polymer, around the dispersed phase, imposing steric hindrance to the droplet coalescence. 15.2.2

Phase Separation

For the immiscible polymer blends, the nanoparticles impart a signiicant compatibilization effect on the phase morphology because of its selective localization and interaction with polymer components. When incorporated into partial miscible polymer blends, the phase stability and phase separation kinetics of polymer blends will

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also be altered due to the interactions between polymer components and nanoparticles. 15.2.2.1 Effect on the Phase Diagram For polymer blends with LCST or UCST, the effect of nanoparticles on the phase behavior, especially the phase diagram, has been investigated intensively over the past decade. Lipatov et al. [131] found that the phase separation temperature of LCST system poly(vinyl acetate)/poly(methyl methacrylate) (PVA/PMMA) was increased upon the addition of the silica nanoparticles. However, for chlorinated polyethylene (CPE)/copolymer of ethylene with vinyl acetate (EVA) blends with LCST behavior, the phase diagram was shifted downward for low loading of silica nanoparticles, but upward for higher loading [132]. Two mechanisms were proposed to address the effect of nanoparticles. One reason is that the selective interaction and preferential absorption between particle surface and one of the polymer components are responsible for the enhanced miscibility [132, 133]. The other reason is the change of molecular weight in the bulk because of the selective absorption for low (or high) molecular weight polymer chains [132]. For the UCST PS/PB system, the phase separation temperature, determined from light scattering, was found to increase (reduced miscibility) with the addition of unmodiied silica nanoparticles, while decrease upon the incorporation of surface-modiied silica particles [134]. The effect of silica nanoparticles has also been intensively investigated in other polymer blends with LCST behavior [135–138]. Huang et al. applied rheological method to obtain the phase diagram of PMMA/SAN blend with and without silica nanoparticles. It was found that the coexistence curve (binodal line) was shifted vertically, and the miscible region was expanded for the illed polymer blends because of the selective absorption of PMMA chains to the silica surface [136]. Similarly, for the PS/PVME system [137], the presence of the nanosilica particles was shown to increase the phase separation temperature by 10 ∘ C, and the reason was suggested to be the selectively absorption of PVME chains to the silica surface (Fig. 15.22). In addition to the spherical silica nanoparticles, the incorporation of nanoparticles with larger aspect ratio, such as reduced graphene oxide (rGO), clay, and MWCNT can also enhance the phase stability of partially miscible polymer blends. The phase behavior of PS/PVME/MWCNT [139] and PS/PVME/rGO [140] ternary systems, investigated by Bose et al., revealed that the miscibility region was expanded with the addition of nanoparticles. The absorption of macromolecular chains onto the particle surface was suggested as the probable reason for these systems. With UCST PE/EVA blends, the presence of either unmodiied or organic modiied clay was shown to promote the miscibility between PE and EVA due to the preferential interaction between clay and EVA [141, 142]. Similar trend is also observed in PMMA/SAN/MMT systems [135, 143]. In contrast, Yurekli et al. [144, 145] found that the phase transition temperature of PS/PVME blends was nearly unaffected with 0.04% volume fraction of layered silicate. Moreover, sometimes the compatibilization effect of nanoparticles is dependent on the phase composition of polymer blends. For some compositions, it shows compatibilization effect, while for others it may have no effect or even diminish

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140

Temperature (°C)

130 120 110 100 TRhco 90 80 0.0

0.2

TDSC

TDSC (nano)

Ttur

Ttur (nano)

0.6

0.4

TRhco (nano)

0.8

1.0

ϕPS

Figure 15.22 Phase diagram of the PS/PVME/silica and PS/PVME blends obtained from various methods: rheological measurements, DSC, and turbidity measurements. Lines are only guides for the eyes. Adapted from Ref. [137].

the phase miscibility. Lipatov et al. observed an enhanced phase stability in all blend compositions except when the fraction of PMMA is less than 0.1 [131]. In poly[(α-methyl styrene)-co-(acrylonitrile)]/poly(methyl methacrylate)/rGO (PαMSAN/PMMA/rGO) blends, the compatibilization effect was only found in blend with 15 wt% of PαMSAN [146]. Also for PMMA/SAN blends, the addition of silica nanoparticles causes the binodal temperature to increase for 60/40 PMMA/SAN blend, but considerable decrease for 30/70 PMMA/SAN blend [147]. The spinodal temperature was also found to increase with the introduction of nanoparticles for all the compositions. Such effect is believed to be caused by the composition difference between particle surface (mainly PMMA because of the preferential absorption) and that of polymer matrix, especially for blend with PMMA as minor phase [147]. In a theoretical view, Ginzburg et al. [148] proposed a simple free energy based model to infer the effect of spherical nanoparticles on thermodynamics of polymer blends. With particles preferentially segregated into one of the polymer component, the shift in spinodal line depends on the blend composition, molecular weight of polymer components, and nanoparticle radius. An increase in phase stability was found for illed polymer blends when nanoparticle radius is smaller than the radius of gyration of polymers. Moreover, for nanoparticles with radius larger than the radius of gyration, this model predicts a shift of phase separation temperature toward narrower miscibility window [148]. Furthermore, when nanoparticles exhibit different interactions with polymer components, the effect on the phase behavior was found to be even more complex [149].

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In the thermodynamics part, the impact of nanoparticles on the equilibrium phase behavior of polymer blends depends on particle–polymer interaction, blend composition, and dimensionality of nanoparticles. As discussed in immiscible blend, the phase separation temperature obtained from different experimental methods is often based on a nonequilibrium state, which is inevitably intertwined with kinetics effect. For the optical or light scattering methods, the presence of nanoparticles enhances the light scattering and impairs the transparency, making it dificult to determine phase separation at the same scale. Furthermore, for another widely used rheological method, the characterization of phase separation is based on the change of moduli due to the interface and concentration luctuation. When the bulk moduli of polymer components are relatively high, the extra contribution to moduli from the phase separation must be large enough to be shown in the rheological test. It means the extent of phase separation at so-called phase separation temperature varies in different polymer blends. Moreover, the complicated particle–polymer interaction makes it more dificult to rule out the kinetics effect. Huang et al. [42, 150] applied different methods to infer the phase separation of LCST PMMA/SAN blends with different silica nanoparticles, in which SiO2 −OH particles selectively segregated into PMMA and SiO2 −PS located at the PMMA/SAN interfaces. It was found that, upon the addition of nanoparticles, there is little difference in the phase separation temperature (cloud point) obtained from optical microscopy (Fig. 15.23). For the rheological methods, the obtained phase separation temperature is composition dependent and varies for different types of silica nanoparticles, and phase separation temperature determined from rheological methods is considerably higher than that from optical methods, indicating different kinetics effect for those measurements. The effect of nanoparticles on the phase diagram still needs further investigation. 15.2.2.2 Effect on the Phase Separation Kinetics Nanoparticles can not only modify the phase diagram of polymer blends but also introduce signiicantly inluence on the kinetics of phase separation. Traditionally, there are two types of mechanisms for the phase separation of polymer blends: (i) nucleation and growth (NG) and (ii) spinodal decomposition (SD). The former type is associated with metastability, and the concentration luctuation of the blend has to be large enough to overcome an energy barrier to form nucleus. Then nuclei grow into spherical domains, exhibiting a droplet-matrix morphology for the polymer blend. While for SD type, due to the negligible energy barrier, even small concentration luctuation will result in the phase separation, forming co-continuous morphology at the initial stage. In addition, there is a unique phase separation type, called viscoelastic phase separation, VPS, found in strongly dynamically asymmetric blends, such as polystyrene (PS)/poly(vinyl methyl ether) (PVME) blends with a large difference in glass transition temperature (Tg ). The incorporation of nanoparticles, especially their selective absorption of polymer chains, increases the viscosity of particle favorable phase domains, changes the viscoelastic asymmetry between polymer components, and slows down the phase coalescence during phase separation.

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190 PMMA/SAN Cloud point Isothermal Neat SiO2-OH

Temperature (°C)

180

SiO2-PS

170

Nonisothermal Neat Rheology Neat SiO2-OH

160

SiO2-PS

150 10

20

30

40 50 SAN content (wt%)

60

70

80

Figure 15.23 Phase diagrams of PMMA/SAN, PMMA/SAN/SiO2 -OH, and PMMA/SAN/ SiO2 -PS blends obtained via rheology and optical microscopy. The content of nanoparticles is 3 wt% in the latter two blends. Adapted from Ref. [150].

Xia et al. [138, 151] investigated the effect of hydrophilic and hydrophobic silica nanoparticles on the viscoelastic phase separation (VPS) of PS/PVME blend. For the neat PS/PVME blend, even the fraction of PS is only 10%, there still forms a transient PS network structure in the intermediate stage (Fig. 15.24, ∼1000 s < t < ∼2000 s), which differs from the droplet–matrix morphology for NG type of phase separation with similar compositional ratio. Such network could sustain for a long time until it breaks up into disconnected droplets because of volume shrinking (Fig. 15.24, t > 4140 s). Upon the addition of hydrophilic silica nanoparticles, the time evolution of phase morphology changes greatly. For A2 sample, similar with neat blend, a typical VPS behavior was observed but kept for a longer time than neat blend, indicating a retarded phase separation kinetics. Moreover, with an increased particle loading (A4 sample, Fig. 15.24), instead of co-continuous structure for VPS, a droplet-matrix structure with even slower coarsening rate was observed for this sample, demonstrating a change of mechanism from VPS to NG. However, a typical VPS behavior was found in PS/PVME blends illed even with 8 wt% loading of hydrophobic silica nanoparticles (mainly segregated in PS phase, shown as R8). In general, both types of silica nanoparticles can retard the phase separation kinetics, but their inluence on the VPS behavior differs. This difference was believed to be caused by the different afinity with the polymer components. For hydrophilic nanoparticles, their preferential interaction with PVME chains hinders the dynamics of PVME chains. Thus, the dynamic asymmetry between two polymer phases was reduced, resulting in a network–droplet morphological transition for higher loading

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50 μm

300s

1710s

4140s

Neat

(b) 960 s

4000s

8600 s

50 μm

(c)1000 s

4000s

8400s

50 μm

(d) 990 s

50 μm

A2

A4

8024s

12053 s

R8

Figure 15.24 Morphology evolution of PS/PVME 10/90 neat blend and illed with 2 wt% hydrophilic silica nanoparticles (A2), 4 wt% hydrophilic silica nanoparticles (A4), and 8 wt% hydrophobic silica nanoparticles (R8). Hydrophilic silica nanoparticles are preferentially segregated in PVME phase, while hydrophobic silica nanoparticles are dispersed in PS phase. From Ref. [151]. Reproduced with permission of American Chemical Society.

of nanoparticles (A4, Fig. 15.24) [151]. However, the interaction between PS and hydrophobic silica nanoparticles further enhances the dynamic asymmetry and thus stabilizes the co-continuous morphology in VPS process [151]. The addition of nanoparticles also enhances the morphological stability of polymer blends phase separation via SD or NG. For the spinodal decomposition (SD) process, a typical co-continuous morphology forms at the initial phase separation stage of polymer blend. But this interconnected structure may inally evolve into droplet–matrix morphology because of the instability of co-continuous morphology. As investigated by Bose et al. [139, 140, 152], the co-continuous morphology formed after spinodal decomposition tends to retain for a longer time in PS/PVME blends illed with nanoparticles, such as MWCNT [139], Ag nanoparticles [152], and rGO

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Time (h) 2

12

No NP MST 5 wt% MST 10 wt% P2K 5 wt% P2K 10 wt%

2500 Correlation length (ξ) (nm)

120

48

2000

1500

1000 4

8

12

16

20

Time1/3 (min1/3)

Figure 15.25 The time dependence of domain correlation length � for ilms of PMMA/SAN neat blend and illed with different types of nanoparticles. Both MST and P2K are silica nanoparticles with the former distributed in PMMA and the latter located at the interfaces between PMMA and SAN. From Ref. [153]. Reproduced with permission of American Chemical Society.

[140], than the neat blend. Such phenomenon was attributed to the delayed dynamics of PVME due to the speciic interaction between nanoparticles and PVME. In addition to the morphology change, the presence of nanoparticles also introduces a signiicant inluence on the phase coarsening process during phase separation. As exhibited in Figure 15.25, the time dependence of domain size for co-continuous morphology was considerably decreased upon the addition of silica nanoparticles, and this effect becomes more evident for higher loading of nanoparticles. Moreover, similar to immiscible polymer blends, the most striking hindrance on the phase coalescence was realized when nanoparticles were located at the interfaces between polymer components rather than in one of the polymer phases [153, 154]. For droplet–matrix morphology, the phase coarsening rate could also be suppressed by the nanoparticles. In PMMA/SAN/nanosilica ternary system, the reduction in coarsening rate was observed for blends illed with SiO2 −OH nanoparticles (located in PMMA phase) and more signiicantly in blends with SiO2 −PS nanoparticles (located at the interfaces) [150]. 15.2.2.3 Agglomeration and Self-Assembly of Nanoparticles In the homogeneous region, the nanoparticles are distributed evenly in the polymer blends; however, after the onset of phase separation, the nanoparticles start to migrate to its

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favorable phase, which is similar to the case in immiscible blends as discussed earlier. The agglomeration of nanoparticles could also be used to tune the microstructure and macroscopic properties of polymer blends [139, 140, 146, 155–157]. The migration of nanoparticles during phase separation of polymer blends was studied by Huang et al. [150]. Initially, the silica nanoparticles are distributed randomly throughout the whole blend (Fig. 15.26a). Some of them are segregated in PMMA-rich domains (shown by green circle), and some are dispersed in SAN-rich phases (shown by blue arrow) or located at the interfaces. With the progression of phase separation, more and more nanoparticles tend to segregate at the interfaces (Fig. 15.26b–d). After 60 min of phase separation, almost all the silica nanoparticles reside at the interfaces (Fig. 15.26d and e). Such agglomeration behavior is driven by the thermodynamic interaction between phase domains and nanoparticles. With the development of phase separation, the composition of phase domains begins to deviate from each other, and thus the interaction between phase domains and nanoparticles varies. Then, the nanoparticles tend to migrate to thermodynamically favorable places. Typically, phase separation of polymer blends produces co-continuous morphology with smaller size scale than immiscible polymer blends. In order to stabilize the co-continuous morphology, the agglomeration of nanoparticles was adopted as an eficient stabilizer [157, 158]. For nanoparticles with preference to locate at the interfaces, the agglomerated nanoparticles are able to stabilize the co-continuous structure, maintaining a jammed morphology in the phase-separated blends [158]. In addition, Li et al. [157] showed that when CdSe nanorods and nanospheres were added to

(a)

(b)

200 nm

(d)

(c)

200 nm

200 nm

(e)

500 nm

1 μm

Figure 15.26 TEM images of PMMA/SAN/SiO2 -PS 70/30/3 blend annealed at 172.5 ∘ C for (a) 8 min, (b) 15 min, (c) 30 min, (d) 60 min, and (e) 120 min. All compositions are in weight fraction. From Ref. [150]. Reproduced with permission of American Chemical Society.

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PS/PVME blends, the selective distribution of CdSe nanoparticles in PVME phase can kinetically arrest the co-continuous morphologies due to the particles network structure formed in PVME phase, whereas nanorods were found be to be more eficient than nanospheres because of its larger aspect ratio [157]. Similar with particles illed immiscible polymer blends, the agglomeration of nanoparticles can be used to tailor the conductivity of polymer blends. Bose et al. [139, 140, 146, 155, 156] investigated the phase separation behavior in a series of ternary polymer blend systems, including P(αMSAN)/PMMA/MWCNT, P(αMSAN)/PMMA/rGO, PS/PVME/MWCNT, and PS/PVME/rGO. It was found that phase separation could be used as a tool to turn the illed polymer blends from virtually insulating at room temperature to a highly conductive material. In those systems, the nanoparticles MWCNT or rGO was found to preferentially located in P(αMSAN) or PVME phase. Upon the phase separation, the nanoparticles migrate to the thermodynamically favor phase, constructing a percolation network because of the increased local concentration. This migration of nanoparticles offers a way to achieve low-percolation value for conducting materials, especially when nanoparticles tend to locate at the interfaces. Most nanoparticles that were used in polymer blends can be regarded as “inert,” where the particle shape cannot change and agglomeration happens due to the particle–particle interactions. The other class of nanoparticles can be regarded as “active,” which are generated in situ in polymers upon changing temperature. One example is dibenzylidene sorbitol (DBS), which is a frequently used nucleating agent in polyolein. DBS molecules can strongly interact in the presence of an organic solvent or a polymer melt and form a physical gel through self-assembling into a ibril network with ibril diameter in nanoscale [159]. During self-assembly, both the ibril length and ibril density increase with time. Liu et al. [160] studied the effect of DBS assembly on the phase separation of ultrahigh molecular weight polyethylene (UHMWPE)/liquid parafin (LP) blends, which has a UCST-type phase diagram. It was found that adding a small amount of DBS can increase the phase separation temperature of UHMWPE/LP blend (decrease miscibility) especially when the DBS content reaches the critical gelation concentration. Figure 15.27a shows the coarsening rate of phase-separated domains under different undercoolings. It is seen that when DBS content is lower than 0.05 wt%, the phase separation behavior is almost identical to that of neat blend. When the DBS content is 0.1 wt%, the coarsening rate increases substantially. Such acceleration effect is ascribed to the enhanced concentration luctuation due to the self-assembly of DBS (Fig. 15.27b). 15.3 15.3.1

RHEOLOGY OF NANOPARTICLES FILLED POLYMER BLEND Viscoelasticity of Partially Miscible Systems

As mentioned earlier, nanoparticles can affect the phase behavior of polymer blends due to the speciic interactions among nanoparticles and polymers. Although the effect of nanoparticles on the morphology of polymer blends has been widely studied, its effect on the phase separation of partially miscible polymer blends is not well

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0.05

DBS = 0 wt% DBS = 0.05 wt% DBS = 0.1 wt%

κ (μm/min)

0.04 0.03 0.02 0.01 0.00 0.0

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3.0

3.5

(a) ϕUHMWPE

ϕUHMWPE

Self-assembly of DBS

DBS molecule LP molecule

DBS ibril UHMWPE chain

(b)

Figure 15.27 Coarsening rate of ultrahigh molecular weight polyethylene (UHMWPE)/ liquid parafin (LP) 10/90 blend with different concentrations of dibenzylidene sorbitol (DBS) (a) and the self-assembly-assisted concentration luctuation mechanism (b). All compositions are in weight fraction. From Ref. [160]. Reproduced with permission of American Chemical Society.

understood. One possible reason is that the blends may become opaque after adding nanoparticles even in one-phase regime of phase diagram, which makes the classical optical methods such as turbidity, phase contrast optical microscopy, and small-angle light scattering fail to detect the phase separation. Actually, optical methods are still suitable only in blends with very low fraction of nanoparticles. Therefore, researchers turn to choose rheological methods to study phase separation, which are not affected by the transparency of samples.

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It is well known that nanoparticles would have inluence on the rheological behaviors of polymers, and the inluence could be very different in polymer blends depending on the particle–polymer interactions and the selective locations of nanoparticles. However, such inluence is rather complex and there are only limited quantitative experimental results at present. The corresponding constitutive model is missing as well. In practice, the effects of nanoparticles are not speciically considered when the phase separation is studied via rheology. Those rheological methods to determine the phase separation temperatures in binary polymer blends are adopted and directly applied in nanoparticles illed ternary polymer blends without modiications. As for the binodal temperatures, a frequently used method takes use of the storage modulus (or loss tangent) during temperature ramp. For an LCST-type blend, deviation temperature of G′ from the trend line in one-phase regime is assigned as the rheological phase separation temperature. Such method is also used as nanoparticle illed polymer. One example is shown in Figure 15.28 for PMMA/SAN/silica blends [42]. Both the nanoparticle illed blend and binary blend exhibit monotonic decrease in G′ as the temperature rises. It is clear that the rheological phase separation temperature for ternary blend is slightly higher than that of binary blend, which implies the expansion of miscible region in the presence of nanoparticles. Such method has also been used in other particle illed blends [139, 141]. It should be pointed out that this method is strongly related to the frequency and the ramping rate. Unless an

106 PMMA/SAN/SiO2 60/40/3

G′ (Pa)

105

T = 185.6 °C

104

103

PMMA/SAN 60/40

×5 T = 184 °C

102

101

150

160

170

180

190

200

210

Temperature (°C)

Figure 15.28 Dynamic temperature ramp for blends PMMA/SAN 60/40 and PMMA/ SAN/SiO2 60/40/3. The straight lines denote the apparent linear it with the storage modulus at low temperature. All compositions are in weight fraction. From Ref. [42]. Reproduced with permission of Elsevier.

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extremely low frequency and a very low ramping rate of temperature are adopted, it will give an overestimated rheological phase separation temperature for LCST-type blends. The other method to determine the phase separation temperature utilizes the frequency-dependent dynamic moduli at different temperatures. Similar to binary blends, shifted Cole–Cole plot can be adopted for off-critical blends, where the appearance of the second relaxation circle is regarded as phase separation. As for near-critical blends, the gel-like behavior is used to determine the phase separation temperature. An example is shown in Figure 15.29. These methods can avoid the transient effect in temperature ramp and give phase separation temperatures much lower than those from temperature ramp (Fig. 15.28). However, it is still limited by the frequency range used in the frequency sweep. Since the concentration luctuation and phase domains have greater contribution to dynamic moduli at lower frequencies, it is expected that the phase separation temperature thus determined should be more accurate if the frequency is swept to lower frequency. For near-critical blends, the cross points at low frequencies in tan � versus blend composition may be scattered a little bit, which also implies that it might not exhibit the ideal gel-like behavior. For spinodal temperature, the theory of Fredrickson–Larson–Ajii–Choplin (Eqs. 15.11, 15.12, and 15.14) or its revision (Eqs. 15.11 and 15.15) is also adopted for ′ nanoparticles illed blends. Figure 15.30 shows the plot of {Gcf (�)∕[(W(T))2 T]}−2∕5 versus 1∕T for PMMA/SAN/silica blends [42]. Similar to binary blends, the spinodal temperature is determined by the extrapolation line from the data in

60

10 167.7 ± 1.6 °C

50 ω (rad/s) 0.0158 0.0251 0.0389 0.063 0.100 0.158 0.251 0.389 0.630 1

6

4

2

150

170 160 Temperature (°C) (a)

180

η″/aT (kPa s)

Tan δ

8

40 30

180 °C 183 °C 185 °C

20

186 °C 190 °C

10 0

0

40

80 120 160 200 240 η′/aT (kPa s) (b)

Figure 15.29 The loss angle tangent of dynamic frequency sweep under different temperatures for PMMA/SAN/SiO2 70/30/3 blend (a) and the shifted Cole–Cole plot for PMMA/SAN/SiO2 40/60/3 blend at Tref = 170 ∘ C (b). All compositions are in weight fraction. From Ref. [42]. Reproduced with permission of Elsevier.

RHEOLOGY OF NANOPARTICLES FILLED POLYMER BLEND

{G′cf (ω)(W(T))2T}–2/5 [N m2/(K s2)]–2/5

6 × 1011

PMMA/SAN/SiO2 70/30/3

535

PMMA/SAN/SiO2 60/40/3

4 × 1011

5 × 1011 3 × 1011 4 × 1011 3 × 10

11

Two-phase regime

Two-phase regime

2 × 1011

2 × 1011 1 × 1011 0

11 One-phase 1 × 10 regime

One-phase regime Tb = 167.7 °C

0.0022

Ts = 167.5 °C

0.0023 1/T (1/K)

Ts = 181 °C

0.0024 0.0021 0.0022

Tb = 171.8 °C

0 0.0023 0.0024

1/T (1/K) ′

Figure 15.30 Determination of spinodal temperature by plotting {Gcf (�)∕[(W(T))2 T]}−2∕5 versus 1∕T for blends PMMA/SAN/SiO2 70/30/3 and PMMA/SAN/SiO2 60/40/3. All compositions are in weight fraction. From Ref. [42]. Reproduced with permission from Elsevier.

one-phase regime. It is found that the spinodal temperature for near-critical blend is less affected by the nanoparticles and that for off-critical blends are more affected [42]. It should be noticed that the contribution from nanoparticles to rheology is omitted in both methods to determine the binodal temperature and spinodal temperature, which might cause great errors in some cases. One example is that the rheological phase separation temperature would be greatly affected by the surface properties of nanoparticles, while the cloud temperatures are not really affected in PMMA/SAN/silica blends [150]. Generally, it can be ascribed to the different interactions among particles and polymers due to different particle surface properties. However, such effect is hard to evaluate since the quantitative inluence of nanoparticles with different surface properties on the rheology of nanocomposites is still unclear. 15.3.2

Viscoelasticity of Polymer Blend Nanocomposites

In immiscible blends, nanoparticles can affect the rheology of blends through different mechanisms, which depend on the distribution and dispersion of nanoparticles. If the nanoparticles are selectively located in one component, it will alter the viscoelasticity of that polymer and change the viscoelastic mismatch between two polymers. If the nanoparticles are selectively located on the interface between two polymers, it will behave like a compatibilizer that changes the interfacial rheology. In both cases, the morphological stability will be inluenced. These inluences can also be inferred from the rheological responses of blends.

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15.3.2.1 Linear Viscoelasticity of Particles Filled Polymer Blends When nanoparticles are added into polymer, the state of dispersion determines the rheological properties of the nanocomposites. If nanoparticles are easily agglomerated, there will be a signiicant increase in dynamic moduli (especially storage modulus) at low frequency as the iller content increases. Gel-like behavior can be observed when the iller content exceeds a critical concentration. Figure 15.31 shows the example of linear low-density polyethylene (LLDPE) illed with carbon black (CB). The plateau at low frequency is ascribed to the network formed by particle clusters. In contrast, if nanoparticles can be well dispersed in the polymer matrix, only the overall increase in dynamic moduli over the whole frequency can be observed, which is mainly ascribed to the hydrodynamic effect of particles. A typical system is poly(ethylene-methyl arylate) (EMA) illed with CB as also shown in Figure 15.31. When nanoparticles are added to immiscible blends, its inluence on rheological behavior depends on the selective distribution. For sea-island morphology, when the nanoparticles are dispersed in droplets, the main contribution is the enhancement in the viscosity and dynamic moduli of droplet phase. The direct result is to increase the viscosity ratio, and the increase in the dynamic moduli of NP illed blends is not signiicant as compared to the neat blends. In contrast, when the nanoparticles are distributed in the continuous phase, as the NPs content increases, dual networks will generate, namely the continuous polymer domain and the particle network in that domain. In such case, the dynamic moduli of illed blend will increase greatly in blends with either sea-island morphology or co-continuous morphology. Figure 15.32 shows the storage modulus of LLDPE/EMA/CB blends with blend

106 105

G′ (Pa)

104 102 102

LLDPE LLDPE/CB 4.84% EMA EMA/CB 4.95%

101 100

10–2

10–1

100

101

102

Anguar frequency (rad/s)

Figure 15.31 Storage modulus of LLDPE, LLDPE/CB 4.84 vol% composite, EMA, EMA/CB 4.95 vol% composite at 160 ∘ C.

RHEOLOGY OF NANOPARTICLES FILLED POLYMER BLEND

537

105

G′ (Pa)

104

102

102

LLDPE/EMA 80/20 LLDPE/EMA/CB 80/20/4.87 LLDPE/EMA 60/40 LLDPE/EMA 60/40/4.89

101

100

10–2

10–1

100

101

102

Anguar frequency (rad/s)

Figure 15.32

Storage modulus of LLDPE/EMA/CB composites at 160 ∘ C.

composition 80/20 for droplet morphology and 60/40 for co-continuous morphology. In both cases, the evident increase in G′ as CB content increase is ascribed to the network of nanoparticles. Such phenomenon is also observed in other particle illed polymer blends including PBT/PE/clay [112], PCL/PLA/MWCNT [161], PA6/ABS/clay [162], PLA/PBAT/MWCNT [163], and PS/PVME/silica [151]. Since the contribution of particle network is usually much larger than that from luid–luid interface, it becomes dificult to observe the interfacial contribution in polymer blends as the iller content increases. 15.3.2.2 Coalescence Suppression When nanoparticles are located on the interface between two polymers, it is similar to the particles stabilized Pickering emulsion. Particles can be trapped in the interfacial regime due to the interfacial tension between two luids. Once the particles are in a planar interface, the energy that is required to escape from the interface is [164] E = �R2p Γ(1 ± cos �)

(15.22)

where Rp is the radius of particle, Γ is the interfacial tension between two luids, and � is the contact angle of particle with luid A. The negative sign in bracket denotes the removal of particles into luid A, while the positive sign denotes the removal of particles into luid B. The energy is of the order 103 kB T, where kB is the Boltzmann constant and T denotes the temperature. Such energy is quite large as compared to the thermal energy of Brownian motion, which means that nanoparticles can hardly escape from the interface once it is located in the interface. As in Pickering emulsion, the nanoparticles can act as an eficient compatibilizer to suppress coalescence of droplet under quiescent and shear conditions.

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538

As shown in previous section, rheology, especially linear viscoelastic behavior, is very sensitive to the morphology of polymer blends. Figure 15.33a shows the dynamic moduli of PIB/PDMS pure blend and blend illed with silica before and after different preshear. It is clear that the storage modulus of particle illed blend does not show evident change as compared to the neat blend, which implies high stability of morphology in NP illed blends. The variation of morphology can be seen more clearly from the interfacial contribution (Fig. 15.33b), which is obtained by subtracting the storage modulus of blends with that of components. The interfacial moduli show a typical Maxwellian behavior from which the droplet relaxation time can be obtained [165]. In order to illustrate the coalescence behavior, usually the sample is sheared under high shear rate irst, and then alternating shear to low shear rate, and inally oscillatory shear are applied on the blend. The droplet size information can be inferred from the characteristic relaxation time according to Palierne model [20] �=

Rv �m (19p + 16)((2p + 3) − 2�(p − 1)) Γ 4 10(p + 1) − 2�(5p + 2)

(15.23)

where the droplet relaxation time can be determined either from the interfacial dynamic moduli [165] or from the relaxation spectrum of blend [166, 167]. The increment in droplet size due to coalescence is greatly suppressed by adding more nanoparticles in the blends. Surface properties also affect the coalescence suppression, and smaller agglomerates could be more effective than larger agglomerates.

103

G′ (Pa)

103

102

101

100

10–1

PDMS/PIB 70/30 –1 0.05 s –1 6.00 s PDMS/PIB silica 70/30/1 –1 0.05 s –1 6.00 s

0.1 1 10 100 Angular frequency (red/s) (a)

G′blend – G′components (Pa)

104

102

101

100

PDMS/PIB 70/30 –1 0.05 s –1 6.00 s PDMS/PIB silica 70/30/0.5 –1 0.05 s –1 6.00 s

10–1

0.1 1 10 100 Angular frequency (red/s) (b)

Figure 15.33 (a) Frequency dependence of the storage modulus after different preshear rates for 70/30 PDMS/PIB blends with no iller added (0%) and 1 wt% silica (T = 25 ∘ C, preshearing time was 800 s). (b) Frequency dependence of the interface contribution to the storage modulus, obtained by subtracting the component contribution from the overall response for the unilled 70/30 PDMS/PIB blend and a blend containing 0.5 wt% silica. All compositions are in weight fraction. From Ref. 165]. Reproduced with permission of Springer.

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Moreover, such effect is also related to the geometry of particles. The role of nanoparticles on the coalescence suppression is unlike the classical compatibilizer, but modifying the interfacial mobility according to the interfacial viscoelasticity [166]. 15.3.2.3 Particle Bridging In particle illed polymer blends, when particles are located on the interface between two polymers, they will hinder the coalescence of two droplets due to the steric effect. In some cases, particles can act as a bridge to connect droplets into noncoalescing clusters or a line of droplets (see the schematics in Fig. 15.34c). Figure 15.34a shows the storage modulus of PIB/PDMS (30/70) blends illed with hydrophobic fumed silica particles [168]. The content of 104 103

75 B30: PIB/PDMS 30/70 B30-1: PIB/PDMS 30/70 with 1% silica

70

65 η* (Pa s)

G′ (Pa)

102 101 100 –1

10

PDMS PDMS/1% silica B30 B30 annealed B30-1 B30-1 annealed

60

55

50

10–2

0.01 0.1 1 10 100 1000 Angular frequency (rad/s) (a)

300 s 4500 s 37 900 s 1 10 100 0.01 0.1 Angular frequency (rad/s) (b)

(c)

Figure 15.34 (a) Effect of 1% fumed silica particles on the linear viscoelastic properties of PDMS homopolymer and of PIB/PDMS blends with 30% PIB. From Ref. [168]. Reproduced with permission of Springer. (b) Complex viscosity of PEO/PIB 10/90 blend containing 0.2% silica particle (R = 2.7 μm) during shearing at 200 Pa. From Ref. [169]. Reproduced with permission of Springer. (c) Schematics of bridging particles together glue drops into noncoalescing clusters. From Ref. [169]. Reproduced with permission of Springer. All compositions are in weight fraction.

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nanoparticles is 1 wt%, which is much smaller than the percolation concentration in PDMS matrix. For neat blends, annealing causes a little change in G′ , whereas an evident increase in G′ at low frequency is observed when the particle illed blend is annealed. More importantly, a plateau is seen at low-frequency regime after annealing, which is regarded as a gel-like behavior. Such behavior is also seen in a similar blend PIB/PEO illed with particles in micron size (Fig. 15.34b) [169]. The complex viscosity of particle illed blends was measured at intervals of shear under constant stress 200 Pa. The complex viscosity decreases with time, and the relaxation process of droplet morphology shifts to lower frequency, which is an indicative of coalescence. More evidently, the plateau in complex viscosity at low frequency gradually disappears, and a sharp-thinning behavior is seen at low frequency. It is a typical phenomenon for yield stress luids, which also indicates the formation of certain network. Similar bridging behavior is also observed in polyamide 12 (PA)/ethylene and ethylene–methyl acrylate copolymer (PE-EMA)/CB system [57]. However, the gel-like behavior is not observed in PA/PE-EMA/CB blends probably due to the high melt viscosity of polymers. 15.4

SUMMARY

Nanoparticles have been added to a wide range of polymer blends to control the morphology, rheology, and the mechanical and electrical properties of polymeric materials. It has been found that the interactions among particles and polymer components are decisive factors for the selective distribution of nanoparticles and the agglomeration of nanoparticles. Various methods have been suggested and tested to control these interactions by modifying the surface properties of nanoparticles and changing the geometry (size and shape) of nanoparticles and also the molecular weight of polymers. Selective distribution of nanoparticles in one polymer can alter the viscoelasticity of that component and then change the viscoelastic mismatch of polymer. Selective distribution of nanoparticle on interface has inluence on the interfacial tension between two polymers and interfacial viscoelasticity. Especially, when the concentration of nanoparticle exceeds the percolation concentration in that component, it will turn the luid-like polymer into solid-like polymer. All these inluences on the components’ viscoelasticity and interfacial viscoelasticity will alter the pathway of morphology evolution and the steady morphology. As a result, complete different morphology under steady low can be obtained in the presence of nanoparticle; moreover, certain transient morphology can be kinetically trapped due to the migration of nanoparticles during shear or phase separation. Thus, it offers more opportunities to control the morphology and properties of polymer blends. Rheology also plays an important role in such systems. It helps to understand the effect of nanoparticles on the components’ contribution and interfacial viscoelasticity. In addition, it serves as a sensitive tool to infer the structural change under shear.

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16 RHEOLOGY AS A TOOL FOR STUDYING IN SITU POLYMERIZED CARBON NANOTUBE NANOCOMPOSITES Guo-Hua Hu, Philippe Marchal and Sandrine Hoppe Laboratoire Réactions et Génie des Procédés, Université de Lorraine – CNRS, Nancy, France

Christian Penu Laboratoire Réactions et Génie des Procédés, Université de Lorraine – CNRS, Nancy, France; TOTAL Research and Technology Feluy, Zone Industrielle Feluy, Seneffe, Belgium

16.1

INTRODUCTION

Polymer nanocomposites are multiphase materials in which particles are dispersed in a polymer matrix at a nanometer scale. Particles in the polymer matrix may be of different shapes, for example, spheroids, ibers, and platelets. By nanometer scale, it means that at least one of the dimensions of the particles is smaller than 100 nm or 0.1 μm. Polymer nanocomposites may exhibit distinct properties compared to their micrometer-scale counterparts owing to the much smaller size of the particles, a much larger surface-to-volume ratio, and/or a much closer particle-to-particle distance. However, prior to dispersion in polymer matrices, nanoparticles are rarely in the form of isolated nanometer-scale particles but are aggregates or agglomerates of nanoparticles that are bound together via interactive forces. This is the case of carbon nanotubes (CNTs), for example. Because of their unique structure and high aspect ratio, CNT possesses excellent mechanical, thermal, and electrical properties. For Rheology and Processing of Polymer Nanocomposites, First Edition. Edited by Sabu Thomas, Rene Muller, and Jiji Abraham. © 2016 John Wiley & Sons, Inc. Published 2016 by John Wiley & Sons, Inc.

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RHEOLOGY AS A TOOL FOR STUDYING IN SITU POLYMERIZATION

these reasons, their use as illers for composites and especially polymer composites has triggered a great interest. Several processes have been proposed to prepare such composite materials. The most common ones are melt blending and solution blending [1]. However, they can hardly break down CNT aggregates. A mixing technique based on ultrasound is often used for breaking or dispersing nanoparticles in a solvent. However, it may break not only nanoparticle aggregates but also polymer chains. In order not to break polymer chains, one may ultrasonically disperse CNT in a monomer solution and then initiate the polymerization. In this way, the use of environmentally unfriendly solvents can be avoided. This technique is called in situ polymerization. Several authors used it for producing well-dispersed CNT polymer nanocomposites [2–24]. Their main objectives were to control the dispersion process and the interface between nanotubes and polymer matrices. The interface was either diffused or localized. In an in situ polymerization process, a localized interface can be obtained by a so-called “grafting from” technique. In other words, the polymerization is initiated from the surface of the nanotube or from active species present on its surface. A “grafting to” technique is to graft existing polymer chains onto nanotubes without polymerization. A diffused interface is generally characterized by a polymer sheet called “polymer coating” around the nanotube. In this case, interactions between nanotubes and polymer matrices are no longer covalent but rather of type van der Waals or �–�. There have been no detailed studies on the effects of CNT on the polymerization kinetics during an in situ polymerization process. This work aims at using rheology as a tool to study the effect of the presence of multi-walled carbon nanotubes (MWCNTs) on the kinetics of N-acyllactam activated anionic polymerization of �-caprolactam (AAPCL), on the one hand, and assess the percolation threshold of the resulting in situ polymerized nanocomposite, on the other hand. It shows that rheology can assess not only the effects of MWCNT on the polymerization kinetics but also and indirectly the state of dispersion of MWCNT in the system.

16.2 16.2.1

BASIC PRINCIPLES OF RHEOKINETICS Systemic Rheology: Couette Analogy/Mixer-Type Rheology

16.2.1.1 Introduction Systemic rheology has been developed in order to assess processes involving rheologically complex and evolving media [25]. This methodology makes direct use of a reactor in which products are formulated. The reactor is equipped with an appropriate mixing device, whose characteristics may vary depending on the mixing requirements of the process, the preparation protocols, and the nature of the phases under consideration. In addition, it is equipped with a torque transducer and a rotor tachometer. The whole device is called rheoreactor. It can work in a batch or semibatch mode. According to the circumstances, rheological information extracted can be complete or partial, but is directly related to the fabrication process. It is obtained from torque versus rotor speed data that can be converted to

BASIC PRINCIPLES OF RHEOKINETICS

553

shear stress versus shear rate curves, thanks to a Couette analogy that has been widely used, in particular, to predict the power consumption in stirred reactors containing non-Newtonian luids [26]. This Couette analogy is nothing but a calibration procedure and is explained in detail in the next section. In short, it consists in determining the dimensions of a virtual Couette device (inner cylinder of length L and radius Ri rotating in a concentric outer cylinder of radius Re ), providing the same torque as the real agitated vessel (mixing device), for the same imposed rotational speed of the impeller and the same Newtonian or non-Newtonian sample. The goal is to determine two geometrical factors K� and K�̇ relating, respectively, the torque C to an average shear stress ⟨�⟩ and the rotational speed N to an average shear rate ⟨�⟩, ̇ in such a way that ⟨�⟩ = K� C and ⟨�⟩ ̇ = K�̇ N. ⟨�⟩ and ⟨�⟩ ̇ can be viewed as mean ields of shear stress and shear rate inside the vessel. The height L of the inner cylinder is chosen to be equal to that of the impeller and the radius Re that of the real vessel. The mathematical expression of Ri is obtained by solving the equations of motion for a power-law luid in a steady state, laminar, and isothermal regime. The boundary conditions correspond to the dimensions of the virtual Couette. Once the value of radius Ri is determined via a calibration luid, K� and K�̇ can be obtained. It is then easy to deduce the average viscosity ⟨�⟩ = ⟨�⟩∕⟨�⟩, ̇ for example. The resulting rheograms are in a fairly good agreement with ofline measurements obtained in conventional rheometers when the behavior of samples allows comparisons between both techniques. 16.2.1.2 Couette Analogy and Rheoreactor Concept As described earlier, the Couette analogy is based on the ability to deine an average stress ield and an average velocity ield in a stirred tank where a complex low takes place. Actually, from an experimental point of view, it is found that shear stress versus shear rate curves obtained with a conventional rheometer equipped with a standard geometry are homothetic to torque versus rotational speed ones performed with a mixer-type rheometer equipped with a close-clearance impeller such as an helical ribbon or an anchor (Fig. 16.1). It means that C ∝ � and N ∝ �, ̇ the proportionality factors being K� and K�̇ , respectively, and also C∕N ∝ �. This implies that it is possible to deine overall average quantities of a complex low such as ⟨�⟩, ⟨�⟩, ̇ ⟨�⟩ proportional to the local absolute ones �, �, ̇ �, … determined in a viscometric low, so that K ⟨�⟩ K� C = = � (C∕N) ⟨�⟩ ̇ K�̇ N K�̇ (16.1) As mentioned earlier, the Couette analogy consists of determining the dimensions of a virtual Couette that are equivalent to those in a real stirred tank in terms of torque versus rotational speed relationship (Fig. 16.2). It is achieved by integrating the equation of motion (Eq. 16.2). �̇ ≡ ⟨�⟩ ̇ = K�̇ N,

� ≡ ⟨�⟩ = K� C,

and

� ≡ ⟨�⟩ =

��⃗v ⃗ ⋅ (�⃗vv⃗) − ∇P ⃗ −∇ ⃗ ⋅ � + �⃗g = −∇ �t

(16.2)

RHEOLOGY AS A TOOL FOR STUDYING IN SITU POLYMERIZATION

554

1

0

10

10

η

(Pa)

0

10

–1

10

10

–1

10

–2

10

–3

10

–4

10

–5

10

–6

10

–7

–2

10

–3

10

C

–4

10

(N.m.s) –5

10

–6

10

–4

10

–3

10

10

–2

10

–1

–1

N (tr.s )

10

0

10

1

2

10

10

10

η= η = Kτ (C/N)10–1 Kγ

10

(Pa . s)

–2

10

(N.m)

C/N

101

0

10

τ

(Pa.s)

10–2

10–1

100

101

10

2

10

10

0

τ= τ = KτC –1 (Pa)

–2

3

γ = γ = Kγ N(s–1)

3

–1

γ (s )

Figure 16.1 Experimental evidence of the proportionalities between the torque and the shear stress and between the rotational speed and the shear rate. The luid is a 2 mass% polyacrylamide solution. Rheograms (�, � vs �) ̇ are performed with a 2∘ cone-plate with a diameter of 50 mm. Rheograms (C, C/N vs N) are obtained with a 30-mm-diameter helical ribbon with a pitch of 30 mm in a 34-mm-diameter cylindrical cup. Real system

Virtual analogue

C

C Fluid Same relation C = f(N)

2Ri

Ri

2r*

r

Re

2Re

2Re N

Figure 16.2

N

Couette analogy principle. Adapted from Choplin and Marchal [25].

In the case of a power-law luid (Ostwald–de Waele model), one has (Eq. 16.3): �(�) ̇ =

�(�) ̇ = m�̇ n−1 �̇

(16.3)

where � is the mass density, v⃗ the luid velocity, P the hydrostatic pressure, � the stress tensor, g⃗ the gravitational acceleration, � the viscosity, �̇ the velocity gradient, that is, ⃗ v)t + the absolute value of the shear component �̇ r� of the rate-of-strain tensor �̇ = (∇⃗ ⃗ v, m the consistency index (Pa sn ), and n is the low index (n = 1 for a Newtonian ∇⃗ luid, n < 1 for a shear-thinning luid, and n > 1 for a shear thickening luid). The

BASIC PRINCIPLES OF RHEOKINETICS

555

choice of a power-law luid is not restrictive since the rheological behavior of a luid can always be approximated by a power law over a limited range of shear rate. Solving Equations 16.2 and 16.3 in a laminar steady state regime leads, on the one hand, to the velocity proile (Eq. 16.4): ( )2∕n ( )2∕n Re Ri − 4�N −�̇ r� (r) 4� n r r = K�̇ (r, n) �̇ r� (r, n) = ( = ( )2∕n ( )2∕n ) ⇒ K�̇ = N n Re R − 1 1 − Ri R i

e

(16.4) where Ri and Re are the radii of the inner and outer cylinders, respectively, and N is the rotational velocity of the inner cylinder, on the other hand, to the stress proile (Eq. 16.5): � (r) C 1 = �r� (r) = ⇒ K� = r� = K� (r) (16.5) C 2�Lr2 2�Lr2 where C is the torque transmitted and L is the height of the inner cylinder. The Couette geometry becomes then the virtual analog of the stirred reactor if the same imposed angular velocity generates the same torque (Fig. 16.2). As the torque is fully transmitted from the inner cylinder to the outer cylinder (conservation of angular momentum), the combination of Equations 16.4 and 16.5 leads to C = 2�

| R2i L�r� |r=Ri |

= 2�

| R2e L�r� |r=Re |

( = 2�

R2e Lm

4� N n((Re ∕Ri )2∕n − 1)

)n (16.6)

Equation 16.6 yields the value of the radius of the inner cylinder Ri : Ri = ( 1+

Re 4�N n

(

2�mLR2e C

)1∕n )n∕2

(16.7)

Ri is determined by a calibration procedure carried out using a luid, Newtonian or not, of the known rheological characteristics m and n. When the torque C is measured for a series of imposed values of N, the numerical value of Ri is calculated from Equation 16.7. Inspection of Equation 16.7 shows that Ri is a weak function of the low index n, especially when n is in the range of 0.15–1.0, which corresponds to the majority of non-Newtonian luids (Fig. 16.3). As a consequence, Ri can be considered as a constant for a given vessel–impeller ensemble. Once the value of Ri is determined, it is now important to examine the inluence of the low index n on the variation of the shear rate in the gap through its inluence on K�̇ (r, n) = �∕N ̇ (Eq. 16.4). Figure 16.4 shows the variation of K�̇ (r, n) (Eq. 16.8) as a function of the reduced gap r/Re for given values of N, Re et Ri , in particular for a large gap (Ri /Re = 0.5). From Figure 16.4, there is a narrow region in which the value K�̇ (r, n) is almost independent of n. In other words, the velocity proile depends very little on the

RHEOLOGY AS A TOOL FOR STUDYING IN SITU POLYMERIZATION

556 0.014

Theoretical curve (Eq.7) Experimental data 0.013

Ri 0.012 (m)

0.011

0.01 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 n

Figure 16.3 Inluence of the low index n on the radius Ri of the inner cylinder of the virtual Couette. Experimental data are obtained with the same helical ribbon as in Figure 16.1. 680.0

200.0

Ri / Re = 0.99

Ri / Re = 0.90

2

1.0

1.002

20.0 0.88

r = Re

r * / Re

580.0 0.988 0.99 0.992 0.994 0.996 0.998

r = Ri

r = Re

r = Ri

Kγ =

Kγ =

γ N

γ N

10

r * / Re 0.9

0.92

r / Re

0.94

0.96

0.98

1.0

1.02

r / Re

2

10

Ri / Re = 0.50

n=1 n = 0.8 n = 0.7 n = 0.6

1

0

10

n = 0.4 n = 0.3 n = 0.2 n = 0.15

n = 0.5 –1

–2

10

r = Re

10

r = Ri

Kγ =

γ N

10

r * / Re

–3

10

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

r / Re

Figure 16.4 Inluence of the low index n on the geometrical factor K�̇ (r, n) (Eq. 16.4) as a function of the reduced radius r/Re inside the gap of the virtual Couette. The graphs display, in particular, the position r = r* (Eq. 16.10) where the K�̇ dependence on n is minimal, that is, where K�̇ is quasi-independent of the rheological behavior of the sample.

BASIC PRINCIPLES OF RHEOKINETICS

557

rheological behavior of the samples in this area. More speciically, inspection of Figure 16.4 shows that the zone of smaller variation of K�̇ (r, n) with n coincides with the crossover point, denoted as r*, between the curves corresponding to the extreme values nmin and nmax of the low index. Indeed, by considering the logarithm of K�̇ (r, n) and its irst derivative with respect to the radius, one obtains ] [( ) [( )] ] Re Re 2∕n 2 4� + ln ln[K�̇ (r, n)] = ln − ln − 1 n n r Ri [

2 � ln[K�̇ (r, n)] = − < 0 �r rn

⇒

2 � � ln[K�̇ (r, n)] = 2 > 0 �n �r rn

(16.8) (16.9)

Equation 16.9 shows that the irst partial derivative with respect to the radius r is negative in the whole range of r and n considered here. It means that whatever be the value of n, the slopes of the curves are always negative. In the same time, the second partial derivative with respect to the low index n is always positive. It means that the slopes of the curves increase with increasing n, that is, decrease in the absolute value. Consequently, as one moves to the right of the intersection point r*, the lower limit of the set of curves around r ∗ is necessarily K�̇ (r, nmin ) as its slope is the steepest negative one. Then, all other curves, corresponding necessarily to low index n > nmin , decrease more slowly and remain above, since the slope is an increasing function of n. Therefore, the gap between the curves increases gradually as one moves to the right. On the contrary, by moving to the left of the intersection point r*, the lower limit of the set of curves around r* is K�̇ (r, nmax ) and all other curves above, corresponding necessarily to low indexes n < nmax , increase faster. And once again, the gap gradually increases as one moves to the left. Consequently, the variation of K�̇ (r, n) with n is minimal at the intersection point r*. As a result, the value of r* can be calculated analytically from Equation 16.4 as ′ an intersection point between two curves with the condition that K�̇ (r, n) = K�̇ (r, n ), ′ n and n corresponding to the extreme values of the low index nmin and nmax that are likely to be reached, the order being irrelevant since Equation 16.10 is symmetrical with respect to n and n′ (i.e., n = nmin and n′ = nmax or n’ = nmin and n = nmax ). Then one arrives at [ r ∗=

(

′ )2∕n

−1 ′ n′ (Re ∕Ri × Re (2∕n−2∕n ) × 2∕n n (Re ∕Ri ) − 1

]

1 (2∕n−2∕n′ )

)

(16.10)

As a consequence, the geometrical factors K�̇ (r, n) and K� (r) are determined in r* in such a way that K� (r ∗) = K� = cst1 and K�̇ (r ∗, n) = K�̇ ≈ cst2. Therefore, at the optimum position r*, whatever the luid, Equations 16.4 and 16.5 reduce to linear relations (Eq. 16.11) between the shear stress � and the torque C, between the shear rate �̇ and the rotational speed N, and between the strain � and the angular displacement

RHEOLOGY AS A TOOL FOR STUDYING IN SITU POLYMERIZATION

558

� of the mixing device of the real system: �(r ∗) = |�r� (r ∗)| = K� C ̇ �(r ̇ ∗) = |�̇ r� (r ∗)| = K�̇ N = K�̇ (�∕2�) (16.11)

�(r ∗) = |�r� (r ∗)| = K�̇ (�∕2�)

where �̇ = 2�N is the angular velocity and � is the angular displacement of the impeller. Material functions such as the viscosity, the elastic and viscous moduli, the creep function, and the relaxation function can then be deduced from Equations 16.11, in particular: �=−

�r� |r∗ K C K = � = � (C∕N) �̇ r� |r∗ K�̇ N K�̇

G ∗ = G′ + iG′′ =

(16.12)

K C K �o |r∗ i� e = 2� � o ei� = 2� � (Co ∕�o )ei� �o |r∗ K�̇ �o K�̇

(16.13)

where � = �o ei�t , � = �o ei�t , �o = �o ei(�t+�) , and C = Co ei(�t+�) . Figures 16.5 and 16.6 compare rheograms and mechanical spectra obtained from conventional and mixer-type rheometers. The agreement between both techniques is good. Figure 16.7 shows the geometrical characteristics of the rheoreactors used in Figures 16.5 and 16.6. 16.2.2

A Couette-Type Rheoreactor for the Kinetics of In Situ Polymerization

During the bulk polymerization of a monomer such as �-caprolactam, the viscosity of the polymerizing system increases as the monomer is being converted to the polymer. Thus, the rate with which the viscosity increases as a function of time is an overall 1000

10

η (Pa.s)

η (Pa.s)

100

1

Cone plate Anchor 1 0.01

0.1

10

Parallel plates Helical ribbon 1 –1

γ (s ) (a)

10

100

0.1 0.001

0.01

0.1

1

10

100

1000

γ (s–1) (b)

Figure 16.5 Rheograms performed in standard and mixer-type rheometers at 25 ∘ C. (a) Aqueous solution (2% by weight) of carboxymethyl cellulose and (b) salad dressing. Adapted from Choplin and Marchal.

BASIC PRINCIPLES OF RHEOKINETICS

559

100

100

G’, G” (Pa)

G’, G” (Pa)

10

1

0.1 0.01

10 G' parallel plates G" parallel plates G' helical ribbon G" helical ribbon

G' cone plate G" cone plate G' anchor G" anchor 0.1

1

10

100

0.1 0.01

1000

0.1

1

10

100

1000

ω(rad s1) (b)

1

ω(rad s ) (a)

Figure 16.6 Mechanical spectra performed in standard and mixer-type rheometers at 25 ∘ C. (a) Aqueous solution (2% by weight) of carboxymethyl cellulose and (b) salad dressing.

50 mm

30 mm

47 mm

Anchor

Figure 16.7

5 mm

30 mm

40 mm

50 mm

6 mm

ϕ = 2.0 mm

42 mm

ϕ = 2.7 mm

40 mm

Helical ribbon

Geometrical characteristics of the rheoreactors used in Figures 16.5 and 16.6.

measure of the polymerization kinetics. This approach is called rheokinetics and is complementary to the calorimetric one [25]. In this chapter, it is used for studying the kinetics of AAPCL in the presence of MWCNTs [26]. A Couette-type rheoreactor is speciically designed for measuring the polymerization kinetics calibrated via the Couette analogy described in the above section. It is a modiied rheometer of type Rheometrics RDA3, as shown in Figure 16.8. The inner and outer cylinder diameters of that reactor are 20 and 25 mm, respectively. The procedure used to prepare the polymerization system is described elsewhere [27]. Briely, the MWCNTs are added to and dispersed in the molten monomer at 80 ∘ C under ultrasound. The activator and the catalyst are then added in and the mixture is homogenized under ultrasound for a given period of time. A total of 4 ml of the mixture is taken using a syringe of 5 ml in capacity and is injected into the rheometer reactor. The course of the polymerization is followed up at a deformation of 2% and a frequency of 5 rad/s. Because of edge effects and the cone proile of the inner cylinder of the reactor, the Couette analogy is applied to calibrate its geometry in order to

560

RHEOLOGY AS A TOOL FOR STUDYING IN SITU POLYMERIZATION

Torque measurement

Cover

1° 20

5° 20 25

Rotation

Thermocouple

Figure 16.8 Schematic of a speciically designed Couette-type reactor used in this study. Lengths are in millimeters. From Ref. [28]. Reproduced with permission of John Wiley and Sons.

obtain a consistent rheological behavior. The temperature in the Couette reactor is 180 ∘ C. At a higher temperature, the monomer starts to evaporate, forming bubbles in the polymerizing system that would drastically affect the rheological behavior of the latter.

16.3 RHEOKINETICS OF IN SITU POLYMERIZATION OF CARBON NANOTUBE/MONOMER SYSTEMS 16.3.1

Effects of the Presence of MWCNT on the Polymerization Kinetics

Figure 16.9 shows the change in complex viscosity during the AAPCL in the presence of different amounts of the MWCNT. The polymerization seems to start at a later time as the amount of MWCNT increases. An empirical model of the isothermal kinetics of the AAPCL at 180 ∘ C is reported in the literature [27]. Based on that model, a relationship between the complex viscosity during the AAPCL and the monomer conversion can easily be built up. Figure 16.10 shows that there is no induction period for the AAPCL. The viscosity remains constant in the initial stage of the polymerization till the conversion has reached 15–20%. This behavior is due to the lower limit of the rheometer coupled with the Couette reactor with respect to the viscosity of the system.

RHEOKINETICS OF IN SITU POLYMERIZATION OF CARBON

561

1000000

100000

η (Pa . s)

10000

1000

100 0 wt% 0.25 wt% 0.5 wt% 1 wt% 1.25 wt%

10

1

0.1

0

100

200

300

400

500

t (s)

Figure 16.9 Complex viscosity (�) during the AAPCL at 180 ∘ C with 0.3 wt% activator, 0.3 wt% catalyst, and the varying amount of the MWCNT. 40 W ultrasound power. From Ref. [28]. Reproduced with permission of John Wiley and Sons.

The viscosity starts increasing when the conversion has reached 15% for the polymerizing systems containing no more than 0.5 wt% MWCNT and 20% when the MWCNT content exceeds 1 wt%. The effect of the presence of MWCNT on the viscosity is obvious. Moreover, two distinct behaviors are observed, depending on the MWCNT content. When the latter does not exceed 0.5 wt%, it does not have a noticeable effect on the viscosity. When it is 1.0 wt% or higher, the viscosity increase follows a different and stronger trend. For the polymerizing system without MWCNT, the viscosity as a function of the conversion from about 15% to 40% could be described by a straight line as shown by the bold one in Figure 16.10. By extrapolation, the viscosity of the pure monomer (X = 0) is found to be 7 × 10−4 Pa s. Mathematically, this bold line could be expressed by � = �0 exp(�X) (16.14) where � is the complex viscosity of the polymerizing system, � 0 is that of the pure monomer, � is a constant, and X is the monomer conversion. The value of � for the polymerizing system with 0 wt% MWCNT obtained by a least-square method is 40. This value is valid for polymerizing systems whose MWCNT contents are no more than 0.5 wt%. For those whose MWCNT contents

RHEOLOGY AS A TOOL FOR STUDYING IN SITU POLYMERIZATION

562 10000 1000 100

η (Pa.s)

10 1 0.1

0 wt% 0.25 wt% 0.5 wt% 1 wt% 1.25 wt%

0.01 0.001 0.0001

0

0.1

0.2 0.3 Conversion degree (X)

0.4

0.5

Figure 16.10 Complex viscosity (�) as a function of the monomer conversion during the AAPCL at 180 ∘ C with 0.3 wt% activator, 0.3 wt% catalyst, and 40 W ultrasound power in the presence of different amounts of MWCNT. From Ref. [26]. Reproduced with permission of John Wiley and Sons.

are 1.0 wt% or higher, the viscosity increases with the conversion in a steeper manner and could also be described by Equation 16.14 with a value of 54 for �, as shown by the dashed line in Figure 16.10. Once the conversion exceeds a critical threshold Xc of 50% for polymerizing systems containing no more than 0.5 wt% MWCNT and 30% for those containing 1.0 wt% MWCNT or higher, the evolution of the viscosity as a function of the monomer conversion does not follow the above-mentioned phenomenological model (see Eq. 16.14). It is important to note that this polymerization kinetic model does not take into consideration the crystallization effects that become signiicant when the monomer conversion exceeds Xc . In other words, conversions simulated after Xc are not accurate. The change in the viscosity behavior before and after a critical conversion Xc has also been observed in the literature [29, 30]. For the AAPCL between 130 and 160 ∘ C, the change in the viscosity behavior at Xc is caused by the appearance of solid crystals that act as illers and bring about a viscosity increase. The presence of the MWCNT increases the crystallization rate because they act as nuclei for the crystallization [31]. The appearance of the crystallization phenomenon at Xc is also observed by differential scanning calorimetry [27].

RHEOKINETICS OF IN SITU POLYMERIZATION OF CARBON

563

16.3.2 Effect of the State of Dispersion of Carbon Nanotubes on the Polymerization Kinetics The state of dispersion of the MWCNT in the polymerizing system under investigation depends very much on how they are dispersed initially in the monomer under ultrasound. An increase in the power input and/or the exposure time would lead to better dispersion of the MWCNT in the monomer. As expected, an increase in the ultrasound power results in a decrease in the rate of viscosity increase and consequently a decrease in the rate of polymerization (Fig. 16.11). The literature reported on the conversion as a function of the ultrasound power at 180 ∘ C [27]. Based on it, the viscosity as a function of the conversion for different ultrasound powers could be calculated till the critical conversion Xc . This is shown in Figure 16.12 for 0.5 wt% MWCNT. As can be seen, all the curves are superimposed whatever be the ultrasound power (40, 120, or 200 W). At the irst glace, this result is surprising because the above-mentioned literature shows that an increase in the ultrasound power results in a decrease in the rate of polymerization and consequently in a decrease in the rate of the viscosity increase. On the other hand, an increase in the ultrasound would also promote the dispersion of the MWCNT in the polymerizing system. The trade-off between those two effects explains the fact that the overall effect of the ultrasound power on the viscosity is negligible. 1000000

100000

η (Pa. s)

10000

1000

100

10

40 W 120 W

1

0.1

200 W

0

50

100

150

200

250

300

t (s)

Figure 16.11 Effect of ultrasound power on the complex viscosity (�) change during the AAPCL at 180 ∘ C with 0.3 wt% activator and 0.3 wt% catalyst concentrations in the presence of 0.5 wt% MWCNT. Ultrasound time exposure = 10 s. From Ref. [28]. Reproduced with permission of John Wiley and Sons.

RHEOLOGY AS A TOOL FOR STUDYING IN SITU POLYMERIZATION

564 10000

1000

η (Pa .s)

100

10 40 W 1

120 W 200 W

0.1

0

0.1

0.2 0.3 Conversion degree (X)

0.4

0.5

Figure 16.12 Complex viscosity (�) as a function of the conversion degree during the AAPCL at 180 ∘ C with 0.3 wt% activator and 0.3 wt% catalyst concentrations in the presence of 0.5 wt% MWCNT. Effect of ultrasound power at 10 s exposure time. From Ref. [28]. Reproduced with permission of John Wiley and Sons.

16.3.3

Inhibiting Effect of the MWCNT on the Polymerization Kinetics

Figure 16.13 shows the morphology of the pristine MWCNT used in this study. It is composed of tubes of different sizes. X-ray spectrophotometry shows that it also contains alumina and iron particles resulting from the catalyst used for the synthesis. Mateva et al. showed that the alumina in the pristine MWCNT could act as a catalyst [32]. Keep in mind that the amounts of impurities and amorphous carbon in the MWCNT are very small. Could one make a hypothesis that the inhibiting effect of the MWCNT be attributed to the MWCNT themselves rather than to these impurities and/or amorphous carbon? Might the latter have neutralized a fraction of the activator and/or catalyst used for the AAPCL? If a fraction of the activator reacts with the MWCNT, then the molar mass of the PA6 would increase with increasing MWCNT content. Table 16.1 compares the molar masses measured by GPC with the simulated ones. Considering the fact that that branching reactions or polycondensation reactions could be limited at the beginning of the polymerization, the simulated molar mass is obtained as follows:

Mn = X

[M0 ] M [A] mon

(16.15)

RHEOKINETICS OF IN SITU POLYMERIZATION OF CARBON

565

Figure 16.13 Transmission electron microscopy image of the pristine MWCNT. From Ref. [28]. Reproduced with permission of John Wiley and Sons.

where Mn is the simulated number molar mass; X, the simulated conversion; [M0 ], the initial monomer molar concentration; [A], the initial activator molar concentration; and Mmon , the molar mass of CL. As can be seen, the measured molar masses are in agreement with the simulated ones within the experimental errors. If the MWCNT had reacted with the activator leading to consumption or a smaller reactivity of the latter, the measured average molar masses should have been higher than the theoretical ones. As it is not the case here, such a reaction likely has not taken place in our polymerizing system. According to the literature [33], the reaction between sec-butyl lithium and C60 can form anions. The latter are stabilized by the delocalization of the negative charges on the conjugated fullerene cage. This stabilization is expected to be stronger with perfect CNTs. Indeed, CNTs were functionalized by secondary butyl anion, and the resulting CNTs then acted as an initiator for the polymerization of styrene [34]. Based on the above results, it is possible that the caprolactamate anions of the catalyst for the AAPCL used in this work have reacted with the MWCNT. This reaction could have led to the formation of an ionic complex between the nanotube, the caprolactamate anion, and the sodium cation through a physisorption mechanism at the MWCNT surface. The anionic polymerization could then have been initiated by the MWCNT-CL-Na ionic complex. Champetier et al. [35] proposed a mechanism of the AAPCL with the aid of an intermediary ionic complex. Frunze et al. [36] studied the anionic polymerization mechanism by solution conductimetry. They found that the polymerization proceeded through both free anions and ion pairs and suggested an ion coordinative mechanism based on the alkali lactamolysis proposed by Champetier et al. We believe that when MWCNT is involved, a

566

0.25 0.5 1.25

0

MWCNT (wt%)

0.01 15,000 230,000 240,000 220,000

Complex Viscosity at 180 ∘ C (Pa s) 30 125 160 299 470

Total Polymerization Time (s) 12 56 62 60 30

16,000 72,000 80,000 78,000 49,000

Simulated Conversion% Mn(g/mol)

18,000 77,000 84,000 80,000 27,000

Mn(g/mol)

2 1.9 1.6 1.8 1.7

Measured Polydispersity Index

TABLE 16.1 Measured versus Simulated Number Average Molar Masses of the PA6 Obtained from the AAPCL with 0.3 wt% Activator, 0.3 wt% Catalyst, and Varying Amount of the MWCNT

RHEOLOGICAL PERCOLATION THRESHOLD OF CARBON

567

similar mechanism may be considered. Because of higher stabilization of the negative charge by the nanotube, the MWCNT-CL-Na ionic complex would be more stable than the CL-Na complex. The MWCNT-CL-Na complex would be less reactive than the CL-Na one, which might explain the fact that the polymerization rate decreased with increasing MWCNT content in the polymerizing system. This is also consistent with the fact that the reaction rate decreases with increasing ultrasound power because of better dispersion of the MWCNT in the polymerizing system and therefore a larger contact area among MWCNT, CL, and NaCL. 16.4 RHEOLOGICAL PERCOLATION THRESHOLD OF CARBON NANOTUBE-BASED NANOCOMPOSITES CNT/polymer nanocomposites are generally composed of a polymer matrix and randomly dispersed CNTs. One can theoretically observe several percolation thresholds, depending on the targeted property. Usually electrical and rheological percolation thresholds are observed for CNT/polymer systems [37–50]. Their values generally differ indicating the different nature of the information relayed by the CNT. Rheological properties of CNT/polymer composites in the molten state are important for designing and/or optimizing their preparation and shaping processes such as extrusion and injection molding. It is important to determine the percolation threshold because the rheological behavior of such composites is generally very different before and after the percolation threshold. In this work, mechanical spectroscopy is used to investigate the rheological properties of a CNT/polystyrene nanocomposite. Several methods reported in the literature are employed to determine the percolation threshold. A faster technique based on material relaxation is also employed. The electrical conductivity is measured to determine the electrical percolation threshold. The latter is compared to the percolation threshold found by relaxation and mechanical spectroscopy. This work aims at comparing which of the rheological parameters such as complex viscosity (�*), elastic modulus (G′ ), and loss modulus (G′′ ) would be most eficient at determining the percolation threshold [51]. Effects of physical parameters such as temperature at which the measurement is carried out and sample preparation procedure are also investigated. Moreover, the presence or absence of CNT networks in the polymer matrix is assessed. According to the observed results, the concept of rigidity threshold [52] is put forth for the irst time for CNT/polymer composites. 16.4.1

Experimental Procedures

Rheological measurements are performed on a strain imposed rheometer of type Rheometric Scientiic RDA3 equipped with Couette or parallel plate geometry. The Couette geometry is speciically designed in the laboratory (see Fig. 16.8 for dimensions). Prior to the rheological measurements, MWCNT/polystyrene (PS) pellets are directly added to the Couette geometry that is preheated to a desired temperature. When using the parallel plate geometry, pellets are irst pressed in a circular mold at 180 ∘ C and 25 MPa for 1 min in order to obtain circular plates of 20 mm in diameter

568

RHEOLOGY AS A TOOL FOR STUDYING IN SITU POLYMERIZATION

and 1 mm in thickness. The latter are placed between the preheated parallel plates of the rheometer for testing. Rheological tests are performed in the linear viscoelastic domain at different temperatures and frequencies. The Couette analogy is used to calibrate the Couette geometry in order to obtain consistent results. The electrical measurements are carried out at room temperature with a Keithley electrometer on composite samples that are prepared under the same conditions as those for the parallel plate rheological measurements. Electrical resistivities are determined based on stabilized voltage and current intensity. 16.4.2

Percolation Threshold Observed by Mechanical Spectroscopy

16.4.2.1 Methods Reported in the Literature for the Determination of the Percolation Threshold Table 16.2 shows some of the methods reported in the literature to determine the rheological percolation thresholds from data obtained by mechanical spectroscopy. They are more or less eficient. Furthermore, for a given composite, the value of the percolation threshold may depend on the rheological property under consideration (complex viscosity, elastic modulus, loss modulus, and so on). One of the most used ones consists in comparing the evolution of the complex viscosity as a function of the frequency in the low-frequency range [37–40, 43, 53]. The percolation threshold is shown by a change from a Newtonian behavior before the percolation threshold to a frequency-dependent behavior after the percolation threshold. However, this method, like the other graphic ones in Table 16.2, is subjective. This is mainly because sometimes it is dificult to graphically assess the change in the rheological behavior. Another more “objective” method consists in using a power-law model as shown in Table 16.2 [38]. The power-law model is an adaptation of the percolation theory, which is based on well-deined clusters, to the rheological percolation by assuming that this latter is deined by the percolation of identical CNTs, CNT packages, or CNTs bundles. It can be applied to the evolution of several parameters such as the complex viscosity, elastic modulus, and loss modulus. In this work, both oscillating and relaxation measurements are carried out on the polystyrene/MWCNT composites in order to determine the rheological percolation threshold. They are made in the linear viscoelastic domain in which the elastic modulus G′ and the relaxation function G(t) are independent of the deformation. It is necessary to work in the linear domain to preserve the structure of the composite, namely, the position, orientation, and the state of dispersion of the MWCNT in the polymer matrix. The frequency used in this work ranges from 0.01 to 100 rad/s and the maximum deformation is 10%. The relaxation measurements are carried out in the Couette geometry after an initial step deformation of 10%. 16.4.2.2 “Rheological” Percolation Threshold Determined by Various Methods In the literature, till now, when oscillating and relaxation tests are used, it speaks about “rheological” percolation. We believe that it should be called “rigidity” percolation when it is higher than the corresponding electrical percolation threshold, as will be discussed later. However, the term “rheological” percolation will be used when the literature is referred to.

RHEOLOGICAL PERCOLATION THRESHOLD OF CARBON

569

TABLE 16.2 Methods Employed in the Literature for the Determination of the Percolation Threshold by Mechanical Spectroscopy Criteria

Method

References

Graphic/visual

G′ = f(�) p > pc : a plateau at low frequencies p < pc : G′ decreases with decreasing � G′′ = f(�) Similar to G′ but less obvious �* = f(�) p > pc : a solid-like behavior at low frequencies p < pc : a Newtonian behavior at low frequencies G′ , G′′ = f(%CNT) at low frequencies p > pc : G′ and G′′ signiicantly increase with CNT content p < pc : G′ and G′′ have a behavior similar to a pure polymer G′ = f(G′′ ) p > pc : change of the slope p < pc : same slope as the pure polymer tan � = f(�) p > pc : tan � ≠ f(�) p < pc : tan � = f(�) d�/d� = f(�) p > pc : � signiicantly increases with frequency p < pc : � remains almost constant tan � = f(%CNT) at different � pc = intersection point of different curves van Gurp–Palmen plot � = f(G*) pc = curve change �* = f(G*) p > pc : curve change p < pc : same curve as the pure polymer ′ G′ � (p − pc,G′ )�G �� �* � (p − pc,� )

[37–43, 53–56]

Power law

[37–41, 43, 53–55] [37–40, 43, 55]

[37, 55]

[37, 39]

[39, 40, 42–44, 55]

[56]

[39] [43] [57]

[57] [38]

p,iller concentration; pc , iller concentration at percolation threshold; �, dephasing angle; �, frequency; �, percolation coeficient; and �*, complex viscosity.

Figures 16.14–16.16 show, respectively, the evolution of the complex viscosity and the elastic and loss moduli as a function of the frequency for different CNT contents in the PS matrix. From Figure 16.14, the pure PS matrix exhibits a typical thermoplastic behavior: a Newtonian plateau at low frequencies and a decrease in the complex viscosity �* at high frequencies. The addition of small amounts of MWCNT results in an increase in viscosity. Nevertheless, the rheological behavior remains similar to a typical thermoplastic up to an MWCNT content of around 0.9%. In other words, up to 0.9% MWCNT, the Newtonian plateau is still obvious at low frequencies.

RHEOLOGY AS A TOOL FOR STUDYING IN SITU POLYMERIZATION

570

|η*| (Pa. s)

1.E+05

1.E+04 3% 1.5% 1% 0.9% 0.6% 0% 1.E+03 0.01

0.1

1

10

100

ω (rad/s)

Figure 16.14 Complex viscosity �* as a function of the frequency for different MWCNT contents at 180 ∘ C. The measurements were done with the Couette geometry. From Ref. [51]. Reproduced with permission of John Wiley and Sons.

1.E+05

1.E+04

G’ (Pa)

1.E+03

1.E+02

3% 1.5% 1% 0.9% 0.6% 0%

1.E+01

1.E+00 0.01

0.1

1

10

100

ω (rad/s)

Figure 16.15 Elastic modulus G′ as a function of the frequency for different MWCNT contents at 180 ∘ C. The measurements were done with the Couette geometry. From Ref. [51]. Reproduced with permission of John Wiley and Sons.

RHEOLOGICAL PERCOLATION THRESHOLD OF CARBON

571

1.E+05

1.E+04

G” (Pa)

1.E+03

1.E+02 3% 1.5% 1% 0.9% 0.6% 0%

1.E+01

1.E+00 0.01

0.1

1

10

100

ω (rad/s)

Figure 16.16 Loss modulus G′′ as a function of the frequency for different MWCNT contents at 180 ∘ C. The measurements were done with the Couette geometry. From Ref. [51]. Reproduced with permission of John Wiley and Sons.

When the MWCNT content is 1% or higher, the Newtonian plateau disappears in the frequency range considered here. This phenomenon is characteristic of a transition from a liquid-like behavior to a solid-like one and is considered by many as the “rheological” percolation threshold [37–43, 53–55]. According to this graphical method, the percolation threshold observed in Figure 16.13 is between 0.9% and 1% MWCNT. This graphical method is frequently used to determine the “rheological” percolation threshold and provides a relatively good assessment of the percolation threshold. Nevertheless, the quality of the assessment depends very much on the number of experiments near the percolation threshold and the visual judgment of the analyst. The same experimental results are used to test all the methods listed in Table 16.2. It turns out that they all could allow for easy determination of the percolation threshold. Nevertheless, it could be easiest to do so by following the evolution of tan � as a function of the frequency for different MWNCT concentrations or that of the elastic modulus G′ as a function of the MWNCT concentration for a given frequency. Figures 16.17–16.20 clearly show the percolation phenomena. Tan � is the ratio of the loss modulus over the elastic one. At low frequencies, the pure polymer has a liquid-like behavior with G′′ ≫ G′ and thus a high tan �. At higher frequencies corresponding to shorter relaxation times, it shows a solid-like behavior. With the addition of CNT, the elastic modulus increases till the behavior of tan � at low frequencies becomes similar to the one at high frequencies. From Figure 16.18, the value of G′ at a frequency of 0.039 rad/s is almost multiplied by a factor of 3 when the MWCNT

RHEOLOGY AS A TOOL FOR STUDYING IN SITU POLYMERIZATION

572 40 35

3% 1.5% 1% 0.9% 0.6% 0%

30

tan δ

25 20 15 10 5 0 0.01

1

0.1

10

ω (rad/s)

Figure 16.17 Tan � (= G′′ /G′ ) as a function of the frequency at different MWCNT concentrations at 180 ∘ C. The measurements were done with the Couette geometry. From Ref. [51]. Reproduced with permission of John Wiley and Sons. 500

400

G’ (Pa)

300

200

100

0 0

0.5

1

1.5

2

2.5

3

% CNT

Figure 16.18 Elastic modulus as a function of MWCNT concentration at 180 ∘ C and a frequency of 0.039 rad/s. The measurements were done with the Couette geometry. From Ref. [51]. Reproduced with permission of John Wiley and Sons.

RHEOLOGICAL PERCOLATION THRESHOLD OF CARBON

573

G” (Pa)

1500

1000

500 0

0.5

1

1.5 %CNT

2

2.5

3

Figure 16.19 Loss modulus as a function of MWCNT content at 180 ∘ C and a frequency of 0.039 rad/s. The measurements were done with the Couette geometry. From Ref. [51]. Reproduced with permission of John Wiley and Sons. 1.E+06

700 600 G(t = 80 s)

500

1.E+05

400 300

G(t) (Pa)

200 100

1.E+04

0 0

2

1

3

%CNT

1.E+03

1.E+02

1.E+01 0.01

3% 1.5% 1% 0.9% 0.6% 0% 0.1

1 t(s)

10

100

Figure 16.20 Evolution of the relaxation modulus G(t) after an initial deformation of 10% in the Couette geometry at 180 ∘ C. Inset: Evolution of the elastic modulus 80 s after the initial deformation, G(t = 80 s) as a function of the MWCNT content. From Ref. [51]. Reproduced with permission of John Wiley and Sons.

RHEOLOGY AS A TOOL FOR STUDYING IN SITU POLYMERIZATION

574

content is increased from 0.9% to 1%. The value of 0.039 rad/s is the lowest possible for the frequency below which the measurement accuracy would be jeopardized. At higher frequencies, the CNT effect is more and more diluted by the rigidity of the polymer matrix. It is interesting to note that when G′′ is plotted against frequency, the percolation threshold also becomes obvious. Nevertheless, it seems to be less obvious than G′ for the composite under consideration. Indeed, Figure 16.19 shows that when the MWCNT content is increased from 0.9% to 1%, the value of G′′ is increased by a factor of 1.5 from 600 to 900 MPa. Figure 16.20 shows the evolution of the relaxation function G(t) as the function of time after a strain of 10% in the Couette geometry. The percolation threshold can be estimated by the values of G at the plateau for different MWCNT concentrations, as shown in the inset. The percolation threshold is the same as the one obtained above. This result is consistent with the fact that in the linear viscoelastic domain, complex moduli are related to the relaxation function via Fourier transform. In both cases, the effect of the nanotubes is most effective in the terminal zone (low frequency or long time) corresponding to the liquid-like behavior of the composite. Nevertheless, the relaxation method has the advantage of being much faster than the oscillating one. This advantage can be extremely important when it comes to time-dependent materials such as thermally sensitive ones. 16.4.2.3 Effect of Sample Preparation Procedure on the Percolation Threshold: Compression versus Free Melting Figure 16.21 compares the Couette and parallel geometries in terms of the evolution of the elastic modulus G′ as a function of the MWCNT content at a frequency of 0.039 rad/s. Both curves show the same trend and the corresponding percolation thresholds are also the same. However, it is noted 500

G’ (Pa)

400

300

200

100

Couette // Plates

0 0

0.5

1

1.5

2

2.5

3

%CNT

Figure 16.21 Comparison between the Couette and parallel plate geometries in terms of the evolution of the elastic modulus G′ as a function of the MWCNT content at a frequency of 0.039 rad/s and a strain of 10% at 180 ∘ C. From Ref. [51]. Reproduced with permission of John Wiley and Sons.

RHEOLOGICAL PERCOLATION THRESHOLD OF CARBON

575

that that the difference in the elastic modulus between 0.9% and 1% MWCNT is somewhat higher for the Couette geometry than for the parallel plates. The reasons for this difference remain unclear. Would it be related to experimental errors or sample preparation procedures? The Couette and parallel plates differ in geometry. Moreover, the samples used are subjected to different preparation procedures. In the irst case, the MWCNT/polystyrene composites are charged in the Couette in the form of pellets. They are molten by heat conduction through the inner and outer cylinders of the heated Couette and adopt naturally the shape of disks. For the parallel plate geometry, pellets are irst hot-pressed into a plate mold before being placed between the plates of the rheometer. In the hot-press, MWCNT could be more or less oriented in the low direction. However, the rheological measurements do not allow revealing its effect. 16.4.2.4 Temperature Effect on the Percolation Threshold. The percolation threshold describes a change in the rheological behavior of the MWCNT/PS composite at a critical MWCNT content. This change reveals a certain rigidity of the system induced by the iller. Thus, the percolation phenomenon is expected to be even more obvious if the initial polymer matrix is less viscous. If so, the percolation threshold should increase with decreasing temperature. At lower temperatures, higher amounts of MWCNT should be added to the polymer matrix in order to bring about a difference in the rheological behavior. For example, Pötschke et al. [43] found that the “rheological” percolation threshold of CNT/polycarbonate composites decreased from 5% at 170 ∘ C to 0.5% at 280 ∘ C. From Figure 16.22, the percolation threshold that is obvious between 0.9% and 1% at 180 ∘ C (see Figs 16.18 and 16.19) in terms of G′ and G′′ is still observable at 7000 6000

G’&G” (Pa)

5000 4000 3000 2000 G’ 1000 G” 0

0

0.5

1

1.5

2

% CNT

Figure 16.22 Evolution of the elastic modulus G′ and loss modulus G′′ as a function of the MWCNT content at a frequency of 0.039 rad/s and a strain of 10% at 160 ∘ C in the Couette geometry. From Ref. [51]. Reproduced with permission of John Wiley and Sons.

RHEOLOGY AS A TOOL FOR STUDYING IN SITU POLYMERIZATION

576 7 6

1.5% 1%

5

0.9% 0.6%

4 tan δ

0%

3 2 1 0 0.01

0.1

1

10

ω (rad/s)

Figure 16.23 tan � as a function of the frequency at different MWCNT contents at 160 ∘ C. The measurements were done with the Couette geometry. From Ref. [51]. Reproduced with permission of John Wiley and Sons.

160 ∘ C. Figure 16.23 shows the evolution of tan � as a function of the frequency for different MWCNT contents at 160 ∘ C. The percolation threshold is no longer obvious, contrary to the same materials at 180 ∘ C (Fig. 16.17). 16.4.3

Electrical Percolation Threshold

Figure 16.24 shows the evolution of the electrical conductivity of the MWCNT/PS composite as a function of the MWCNT content. Keep in mind that the samples are prepared under the same conditions as those for the parallel plate rheological measurements. The electrical percolation threshold is somewhere between 0.5% and 0.6% MWCNT, which is signiicantly smaller than the corresponding rheological one (between 0.9% and 1%). Nevertheless, it should be noted that unlike the rheological properties that are measured in the molten state of the polymer, the electrical conductivity is measured at room temperature. When the MWNCT/PS is cooled down from the molten state to the room temperature, the interdistance between MWCNTs is reduced due to the decrease in volume of the PS. 16.4.4 Determination of the Percolation Threshold by Mechanical Spectroscopy Percolation threshold depends on the physical phenomenon of interest. In the case of the MWCNT/PS composite, it depends on the content, the state of dispersion, and

RHEOLOGICAL PERCOLATION THRESHOLD OF CARBON

577

1.E+00 1.E–01 1.E–02 1.E–03 1.E–04

1.E–06

–5

1.E–07

–6

1.E–08

–7 In(σ)

σ (S/cm)

1.E–05

1.E–09 1.E–10

–8 –9

y = 1.9818x – 10.653 R2 = 0.913

–10

1.E–11

–11

1.E–12

0

1

2

3

P–PC

1.E–13 0

1

2

3

4

%CNT

Figure 16.24 Evolution of the electrical conductivity of the MWCNT/polystyrene composite at room temperature as a function of the MWCNT content. Inset: Power law based on weight fraction. From Ref. [51]. Reproduced with permission of John Wiley and Sons.

the orientation of the MWCNT inside the PS matrix. It is therefore essential not to alter the structure of the material during the sample preparation or measurement. For example, when the material is analyzed by mechanical spectroscopy, it should be done in the linear viscoelastic domain. The state of dispersion and the orientation of the MWCNT depend, among other things, on the preparation process. The MWCNT/PS composites used in this work are prepared by an in situ polymerization process with ultrasound-aided dispersion of the MWCNT in the monomer prior to polymerization. This process is known to be able to ensure a relatively good state of dispersion of the MWCNT in the polymer matrix compared with other preparation processes such as melt compounding in which MWCNT is directly mixed with polymers in the molten state. In the latter case, percolation threshold may depend on the type of mixing machine. Lin et al. [45] used two different types of mixers to incorporate MWCNT in a polycarbonate matrix. The percolation threshold of the composites obtained with a special single-screw mixer was lower than that obtained with a special twin-screw mixer (Miniature Batch Mixer). This difference was attributed to a difference in morphology. There were bigger MWCNT aggregates in the former that helped the formation of the nanotube network. The difference in morphology was believed to result from a difference in stress between those two mixers.

578

RHEOLOGY AS A TOOL FOR STUDYING IN SITU POLYMERIZATION

The alignment of the MWCNT is expected to lower the contact between MWCNT, resulting in an increase in the percolation threshold. McNally et al. [39] found a percolation threshold of 7.5% and explained this high value by the alignment of the MWCNT produced by their passage through an extruder die. It is worthy noting that they published other studies using extrusion [37, 43] in which the percolation thresholds were not as high as the value mentioned earlier. Mechanical spectroscopy is a powerful tool for determining the percolation threshold. However, it is not always easy to compare the values of the percolation threshold of a given system obtained by different research groups. This is because even if the composition is the same, the structure of the material (length, diameter, orientation, and spatial distribution of CNT) might not necessarily be so. 16.4.5

Electrical versus Rheological Percolations

Table 16.3 compares the rheological and electrical percolation thresholds reported in the literature. They may be classiied into three categories: (i) PC rheo < PC elec , (ii) PC rheo ∼ PC elec , and (iii) PC rheo > PC elec . The question is why there exist three scenarios. The electrical percolation threshold is reached when a conductive path is formed across the material from one end to the other. Electrical conduction can be described by two mechanisms [38, 40]: direct conduction or electron hopping. In the irst case, conductive illers are in direct contact with each other. In the second case, electrons “jump” from a conductive iller to another one over a small distance of the order of a few nanometers. 16.4.5.1 Case 1: PC rheo < PC elec A rheological percolation threshold smaller than the electrical one implies that when the rheological percolation threshold is reached, the MWCNT are not in direct contact with each other yet or at least no “ininite” cluster is formed. As the MWCNT content increases in the polymer matrix, the average distance between MWCNT decreases. The rheological percolation is reached when the distance between MWCNT reaches a critical threshold. What might this critical distance correspond to? Hu et al. [38] related this distance to twice the gyration radius of the polymer. According to that work, when the distance between two CNTs is less than twice the gyration radius of the polymer in the molten state, they are linked together by a macromolecular coil. This distance depends on temperature as well as the nature and molar mass of the polymer. It may vary from 10 to 100 nm [57]. According to the reptation theory, a polymer chain moves along a tube like a snake. The distance between entanglements depends on the type of the polymer and is of the order of tens of nanometers [58]. The presence of illers, such as MWCNT, would play the same role as entanglements. When the CNT–CNT distance is close to or smaller than the reptation tube diameter of the pure polymer, the movement of the polymer will be hindered. According to the above discussions, the rheological percolation threshold would be reached when the CNT–CNT average distance is between the polymer entanglement distance and twice the radius of gyration, namely, from 10 to 100 nm. This is

579

MWCNT/PE MWCNT/iPP MWCNT/PET SWNT/PEO SWNT/PMMA

MWCNT/PCL

MWCNT/PC MWCNT/ PA6/ABS SWNT/HDPE

NC

2 0.07 7.5 2 0.6 0.09 0.11 (1 rad/s) 0.12 (0.5 rad/s)

0.38–0.5 2–4 1.5 0.6

PC rheo

2 0.09 7.5 1–2 0.9 0.03 0.39

0.5–0.75 2–4 4 0.6

PC elec

10–50 / 1–10 10–50 10–20 / /

10–15 1–10 0.8–2 /

CNT Length (μm)

10–20 / 10–30 10–20 5–15 / 6.9 (bundles)

10–15 5 int. 10–15 ext. / /

CNT Diameter (nm)

TABLE 16.3 Electrical and Rheological Percolation Thresholds for Different Carbon Nanotube/Polymer Composites

2006 2007 2005 2003 2006 2005 2004

2005 2004 2006

Date

[48] [40] [39] [49] [38] [50] [41]

[45] [44] [46] [42]

References

580

RHEOLOGY AS A TOOL FOR STUDYING IN SITU POLYMERIZATION

larger than the critical distance for the electrical percolation threshold. Therefore, PC rheo < PC elec . 16.4.5.2 Case 2: PC rheo > PC elec If the rheological percolation threshold is higher than the electrical one, the CNT–CNT distance is less than a few nanometers. If the electrical conduction proceeds by the direct contact between the CNTs, the rheological percolation threshold can only be reached after the formation of the irst conductive cluster. The difference in these thresholds can be explained in the following manner. The electrical percolation threshold is reached when the irst ininite conductive cluster is formed while the rheological one is not reached until a rigid CNT network is formed. It is suficient to form one conductive “ininite” path or cluster to form a conductive composite. The formation of the irst “ininite” cluster deines the electrical percolation threshold. However, when this threshold is reached, the amount of iller is not yet high enough to signiicantly affect the elasticity/rigidity of the polymer matrix. More CNTs are needed to form a CNT network inside the polymer matrix that signiicantly solidiies the latter. The percolation threshold observed in this case is then rather a “rigid” rheological threshold than a “soft” rheological threshold. Celzard et al. [52] developed the following relationship between the rigid rheological and electrical percolation thresholds: rigid

PC rheo PC elec

=

8 = 1.6 5

(16.16)

This theoretical value is determined by the Kirkwood–Keating model. The irst author studied the vibration modes of long macromolecular chains [59] and second one the crystal elasticity [60]. In our work, this ratio is rigid

PC rheo PC elec

=

0.9 to 1.0 = 1.7 to 1.8 0.5 to 0.6

(16.17)

The fact that this ratio is close to 1.6 implies that the percolation threshold determined by the mechanical spectroscopy or relaxation measurements is a rheological rigidity threshold. rigid Psoft C rheo < PC elec < PC rheo The two theories presented above are not necessarily contradictory. Rather they allow explaining apparently inconsistent results reported in the literature (see Table 16.3). The soft rheological percolation threshold is reached at a CNT concentration at which the distance between CNT is between 10 and 100 nm (Fig. 16.25). The electrical one is reached when more CNTs are added to the polymer matrix till the formation of the irst “ininite” conductive cluster. Finally, the rigid rheological percolation threshold is reached when the CNTs in the matrix are in such an amount that they form a rigid elastic network. Theoretically, these three percolation thresholds should

REFERENCES

581 %CNT Pc_rheology