Fundamentals of Latex Film Formation: Processes and Properties (Springer Laboratory) 9048128447, 9789048128440

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Springer Laboratory

Springer Laboratory Manuals in Polymer Science

Editor Prof. Harald Pasch Chair of Polymer Characterization Department of Chemistry and Polymer Science University of Stellenbosch Private Bag X1 7602 Matieland South Africa e-mail: [email protected]

Editorial Board PD Dr. Ingo Alig Deutsches Kunststoff-Institut Abt. Physik Schloßgartenstr. 6 64289 Darmstadt Germany e-mail: [email protected] Prof. Josef Janca Université de La Rochelle Pole Sciences et Technologie Avenue Michel Crépeau 17042 La Rochelle Cedex 01 France e-mail: [email protected] Prof. W.-M. Kulicke Inst. f. Technische u. Makromol. Chemie Universität Hamburg Bundesstr. 45 20146 Hamburg Germany e-mail: [email protected]

For other titles published in this series, go to www.springer.com/series/3721

Prof. Harald Pasch Deutsches Kunststoff-Institut Abt. Analytik Schloßgartenstr. 6 64289 Darmstadt Germany e-mail: [email protected]

Joseph L. Keddie • Alexander F. Routh

Fundamentals of Latex Film Formation Processes and Properties

Joseph L. Keddie Department of Physics & Surrey Materials Institute University of Surrey Guildford UK

Alexander F. Routh Department of Chemical Engineering and Biotechnology & BP Institute University of Cambridge Cambridge UK

Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands In association with Canopus Academic Publishing Limited, 15 Nelson Parade, Bedminster, Bristol, BS3 4HY, UK

www.springer.com and www.canopusbooks.com

ISBN 978-90-481-2844-0 e-ISBN 978-90-481-2845-7 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009940449 © Canopus Academic Publishing Limited 2010 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

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Springer is part of Springer Science+Business Media (www.springer.com)

Preface

This book has emerged out of our long-time research interests on the topic of latex film formation. Over the years we have built up a repertoire of slides used in conference presentations, short courses and tutorials on the topic. The story presented in this book has thereby taken shape as it has been told and re-told to a mix of academic and industrial audiences. The book presents a wide body of work accumulated by the polymer colloids community over the past five decades, but the selection of examples has been flavoured by our particular experimental interests and development of mathematical models. We intend the book to be a starting point for academic and industrial scientists beginning research on latex film formation. The emphasis is on fundamental mechanisms, however, and not on applications nor on specific effects of formulations. We hope that the book consolidates the understanding that has been achieved to-date in the literature in a more comprehensive way than is possible in a review article. We trust that the reader will appreciate the fascination of the topic. We are very grateful to the many students and post-docs whom we have had the privilege of supervising, and from whom we have learned much about latex film formation. Several of them have provided artwork for this book, as is noted in the figure captions. Post-docs, in a rough chronological order of their time at the University of Surrey, include Jacky Mallégol, Jean-Philippe Gorce, Chun-Hong Lei, Diana Andrei, Yong Zhao, Elisabetta Canetta, and Carolina de las Heras Alarcón. Post-docs at Cambridge include Venkata Gundabala, Grace Yow and Milan Patel. PhD students and visitors in Surrey, who have studied latex film formation, are Katerina Tzitzinou, Elisabetta Ciampi, Juan Salamanca, Peter Doughty, Nicki Kessel, Philippe Vandervorst, Tao Wang, Tecla Weerakkody, Alexander König, Argyrios Georgiadis, and André Utgenannt. A special mention goes to Tao Wang who contributed to the writing of Chapter 7. Students at Sheffield and Cambridge are Wai Peng Lee and Venkata Gundabala and at Cambridge are Richard Trueman and Merlin Etzold. Athene Donald and Richard Jones first introduced JLK to the topic of latex film formation and provided guidance in his early studies. Paul Meredith and Ruth Cameron were his first academic collaborators in studies of film formation at the Cavendish Lab in Cambridge. The Soft Matter Group members at Surrey, includ-

vi

Preface

ing Peter McDonald, Richard Sear, and Alan Dalton, and formerly Michele Sferrazza and Paul Glover, have shared their expertise related to experimental techniques and polymer colloids. AFR is immensely grateful to Bill Russel and Brian Vincent for providing an education in colloid science and to Bill Russel for the introduction to film formation. We have both learned much from our industrial collaborators and benefited from their insight. They include Panos Sakellariou, David Taylor, Peter Palasz, Olivier Dupont, Keltoum Ouzineb, Peter Mills, Guru Satguru, Jürgen Scheerder, Derek Illsley, Martin Murray, Simon Emmett, Philip Beharrell, John Jennings, Tom Annable, Steve Yeates, Ad Overbeek, Malcolm Chainey, Ann-Charlotte Hellgren, Peter Weisenborn, Ismo Pietari, Tuija Heijen, Andrew Howe and Stuart Lascelles among others. Martin Murray, Bob Groves and Peter Mills have each provided particular help in the research for this book. For over a decade, we have enjoyed the camaraderie and scientific excellence of the UK Polymer Colloid Forum meetings. We have had the privilege of useful discussions with some of the world leaders in polymer colloids including Mitch Winnik, Mohamed El-Aasser, and Pete Lovell. Both of us have benefited from taking part in the European Commission Framework 6 project, NAPOLEON. We have gained much from our academic collaborators including the “film formation team” of Yves Holl, Diethelm Johannsmann, Catherine Gauthier, Laurent Chazeau, Jörg Adams, and Anders Larsson. We have had helpful input from other academics in the project, including Txema Asua, Costantino Creton, Mariaje Barandiaran, Maria Paulis, Elodie Bourgeat-Lami, Tim McKenna, and Katharina Landfester, Christopher Plummer, and Richard Guy, among others. Industrial partners in the NAPOLEON project include Simon Dennington, Bas Lohmeijer, Wolf-Dieter Hergeth, Rob Adolph, and Dirk Mestach. These lists are not exhaustive. We apologise for any omissions. This book would not be possible without the co-operation of numerous authors and journals in providing permission to reprint materials here. We are grateful for their generosity. The staff in the George Edwards Library at the University of Surrey were very helpful in helping to track down a few obscure references. We thank our valiant referee who offered us encouragement in the writing process combined with insightful comments and many highly apt recommendations. We appreciate the support of our publishers at Canopus Academic Publishing (Robin Rees and Tom Spicer) in not losing patience with us and waiting more than three years for the manuscript. On a personal note, JLK was given encouragement in writing this book by his grandmother, Jean DiMatteo, who did not live to see its completion. JLK has received moral support from many people throughout the years of writing this book and throughout his career, especially from Adam Towner and from his parents, Linda and Dave. AFR would not have been able to write this book without the support of Ruth. Joseph L. Keddie, Guildford Alexander F. Routh, Cambridge

Contents

1

AN INTRODUCTION TO LATEX AND THE PRINCIPLES OF COLLOIDAL STABILITY.......................................................................... 1 1.1 What is Latex? ..................................................................................... 1 1.2 Latex Synthesis and Uses..................................................................... 2 1.3 Historical Context and Economic Importance ..................................... 8 1.4 Overview of the Film Formation Process .......................................... 10 1.5 Environmental Legislation ................................................................. 15 1.6 Relevant Colloid Science ................................................................... 17 1.6.1 Interaction Potentials ........................................................... 17 1.6.2 Fluid Motion........................................................................ 22 References ..................................................................................................... 24

2

ESTABLISHED AND EMERGING TECHNIQUES OF STUDYING LATEX FILM FORMATION.................................................................... 27 2.1 Techniques to Study Latex in the Presence of Water (Wet and Damp Films)................................................................................ 28 2.1.1 Physical Probes of Drying ................................................... 29 2.1.2 Specialist Electron Microscopies......................................... 36 2.1.3 Scattering Techniques ......................................................... 42 2.1.4 Profiling Water and Particles with Spectroscopies.............. 52 2.1.5 Probe Techniques for the Aqueous Environment ................ 58 2.2 Techniques to Study Particle Packing and Deformation in Dry Films ....................................................................................... 61 2.2.1 Scanning Probe Microscopies ............................................. 61 2.2.2 Scanning Near-Field Optical Microscopy (SNOM) and Shear Force Microscopy ............................................... 70 2.2.3 Electron Microscopies ......................................................... 71 2.3 Techniques to Study Film Crosslinking ............................................. 73 2.3.1 Ultrasonic Reflection and QCM .......................................... 73 2.3.2 Spectroscopic Techniques ................................................... 73

Contents

viii

Techniques to Study Interdiffusion and Coalescence ........................ 74 2.4.1 Small Angle Neutron Scattering (SANS) ............................ 75 2.4.2 Fluorescence Resonance Energy Transfer (FRET) ............. 76 2.4.3 Transmission Spectrophotometry ........................................ 83 2.5 Concluding Remarks.......................................................................... 83 References ..................................................................................................... 83 2.4

3

DRYING OF LATEX FILMS.................................................................... 95 3.1 Humidity and Evaporation ................................................................. 95 3.1.1 Background ......................................................................... 95 3.2 Evaporation Rate from Pure Water .................................................... 96 3.3 Evaporation Rate from Latex Dispersions ......................................... 98 3.4 Vertical Drying Profiles ................................................................... 99 3.4.1 Scaling Argument.............................................................. 101 3.4.2 Governing Equations ......................................................... 102 3.4.3 Experimental Studies......................................................... 104 3.4.4 Consequence of Inhomogeneous Vertical Drying: Skin Formation .................................................................. 107 3.5 Horizontal Packing and Drying Fronts............................................. 107 3.5.1 Model for Horizontal Drying Fronts ................................. 110 3.5.2 Lapping Time and Open Time........................................... 111 3.6 Colloidal Stability ............................................................................ 114 3.7 Film Cracking .................................................................................. 116 3.7.1 Do the Cracks Follow the Drying Front or Propagate Quickly Over the Entire Film? .......................................... 116 3.7.2 What Sets the Crack Spacing?........................................... 117 References ................................................................................................... 117

4

PARTICLE DEFORMATION................................................................. 121 4.1 Introduction...................................................................................... 121 4.2 Driving Forces for Particle Deformation ......................................... 122 4.2.1 Wet Sintering..................................................................... 123 4.2.2 Dry Sintering ..................................................................... 123 4.2.3 Capillary Deformation....................................................... 124 4.2.4 Capillary Rings.................................................................. 126 4.2.5 Sheetz Deformation ........................................................... 126 4.3 Particle Deformations ...................................................................... 127 4.3.1 Hertz Theory – Elastic Spheres with an Applied Load ..................................................................... 127 4.3.2 JKR Theory – Elastic Spheres with an Applied Load and Surface Tension ................................... 127 4.3.3 Frenkel Theory – Viscous Spheres with Surface Tension .............................................................................. 128 4.3.4 Viscoelastic Particles......................................................... 130

Contents

ix

The Problem with Particle–Particle Approach ................................. 130 4.4.1 Routh and Russel Film Deformation Model...................... 130 4.5 Deformation Maps ........................................................................... 133 4.5.1 Wet Sintering..................................................................... 133 4.5.2 Capillary Deformation....................................................... 133 4.5.3 Dry Sintering ..................................................................... 133 4.5.4 Receding Water Front........................................................ 133 4.5.5 Use of the Deformation Maps ........................................... 134 4.6 Dimensional Argument for Figure 4.6 ............................................. 135 4.6.1 Wet Sintering..................................................................... 135 4.6.2 Capillary Deformation....................................................... 135 4.6.3 Dry Sintering ..................................................................... 136 4.6.4 Sheetz Deformation ........................................................... 136 4.7 Effect of Temperature ...................................................................... 137 4.8 Effect of Particle Size....................................................................... 139 4.9 Experimental Evidence for Deformation Mechanisms .................... 140 4.9.1 Inferring Deformation Mechanisms from Water Distributions ...................................................................... 140 4.9.2 Determination of Deformation Mechanisms Using an MFFT Bar and Optical Techniques .............................. 143 4.9.3 Microscopy of Particle Deformation ................................. 143 4.9.4 Scattering Techniques ....................................................... 146 4.9.5 Detection of Skin Formation ............................................. 146 References ................................................................................................... 146 4.4

5

MOLECULAR DIFFUSION ACROSS PARTICLE BOUNDARIES .......................................................................................... 151 5.1 Essential Polymer Physics................................................................ 153 5.1.1 Interface Width at Polymer-Polymer Interfaces ................ 153 5.1.2 Polymer Reptation ............................................................. 154 5.2 Development of Mechanical Strength and Toughness ..................... 158 5.2.1 Dependence on the Density of Chains Crossing the Interface....................................................................... 162 5.2.2 Dependence on Interdiffusion Distance, Λ........................ 162 5.3 Factors that Influence Diffusivity .................................................... 164 5.3.1 Molecular Weight and Chain Branching ........................... 164 5.3.2 Temperature Dependence .................................................. 165 5.3.3 Influence of Hard Particles ................................................ 168 5.3.4 Latex Particle Size............................................................. 172 5.3.5 Particle Structure and Hydrophilic Membranes................. 172 5.4 Faster Diffusion with Coalescing Aids ............................................ 174 5.5 Simultaneous Crosslinking and Diffusion: Competing Effects .............................................................................................. 175 References ................................................................................................... 179

x

Contents

6

SURFACTANT DISTRIBUTION IN LATEX FILMS.......................... 185 6.1 Introduction...................................................................................... 185 6.1.1 Where Can Surfactant Go in a Dried Film?....................... 186 6.1.2 Effect of Non-Uniform Surfactant Distributions ............... 188 6.1.3 Mechanisms of Surfactant Transport................................. 191 6.2 Adsorption Isotherms ....................................................................... 192 6.3 Modelling of Surfactant Distribution during the Drying Stage........ 194 6.4 Effect of Surfactant’s Vertical Distribution on Film Topography ... 199 6.5 Experimental Evidence for Surfactant Locations............................. 201 6.5.1 Interfaces with Air and Substrates..................................... 201 6.5.2 Surfactant in the Bulk of the Film ..................................... 202 6.5.3 Depth Profiling and Mapping ............................................ 202 6.6 Reactive Surfactants......................................................................... 204 6.6.1 Reactive Surfactant Chemistry .......................................... 205 6.6.2 Effect of Surfmers on Film Properties............................... 205 6.7 Summary .......................................................................................... 207 References ................................................................................................... 207

7

NANOCOMPOSITE LATEX FILMS AND CONTROL OF THEIR PROPERTIES.............................................................................. 213 7.1 Introduction...................................................................................... 213 7.1.1 Properties of Nanocomposites ........................................... 214 7.1.2 Applications of Colloidal Nanocomposites ....................... 216 7.2 Types of Hybrid Particles................................................................. 217 7.2.1 Polymer-Polymer Hybrid Particles.................................... 217 7.2.2 Inorganic and Polymer Nanocomposite Particles.............. 219 7.2.3 ‘Self-Assembly’ of Nanocomposite Particles by Precipitation or Flocculation of Pre-Formed Nanoparticles..................................................................... 223 7.3 Colloidal Particle Deposition and Assembly Methods..................... 225 7.3.1 Deposition Methods........................................................... 227 7.3.2 Vertical Deposition............................................................ 229 7.3.3 Surface Pattern-Assisted Deposition ................................. 230 7.3.4 Long-Range Order from Self-Assembled CoreShell Particles .................................................................... 232 7.4 Colloidal Nanocomposites from Particle Blends ............................. 233 7.4.1 Advantages of Particle Blends........................................... 233 7.4.2 Dispersion of Nanoparticles .............................................. 233 7.4.3 Long-Range Order in Particle Blends ............................... 235 7.5 Three Lessons about the Properties of Waterborne Nanocomposite Films ...................................................................... 238 7.5.1 Lesson One ........................................................................ 238 7.5.2 Lesson Two ....................................................................... 244 7.5.3 Lesson Three ..................................................................... 245 References ................................................................................................... 249

Contents

8

xi

FUTURE DIRECTIONS AND CHALLENGES .................................... 261 8.1 Film Formation from Anisotropic Particles ..................................... 261 8.2 Assembly of Particles over Large Length Scales ............................. 263 8.3 Technique Development .................................................................. 265 8.4 Nanocomposite Structure and Property Correlations ....................... 265 8.5 Interdiffusion of Polymers in Multiphase Particles.......................... 267 8.6 Templating Film Topography .......................................................... 268 8.7 Resolving the Film Formation Dilemma.......................................... 269 References ................................................................................................... 272

APPENDICES

A Derivation of Creeping Flow and the Result for Low Reynolds Number Flow Around a Sphere............................................... 275 A.1 Derivation of Creeping Flow ........................................................... 275 A.2 Scaling of the Navier-Stokes Equation ............................................ 276 A.3 Stokes Flow...................................................................................... 277 A.4 Sedimentation................................................................................... 277

B GARField Profiling Techniques and Experimental Parameters ................................................................................................. 279 References ................................................................................................... 281

C Terminology of Humidity and an Expression for Evaporation Rate....................................................................................... 283 C.1 Humidity .......................................................................................... 283 C.2 Relative Humidity ............................................................................ 283 C.3 Dry Bulb Temperature ..................................................................... 284 C.4 Wet Bulb Temperature..................................................................... 284 C.5 Specific Volume............................................................................... 284 C.6 Enthalpy of Air................................................................................. 285 C.7 Psychrometric Chart......................................................................... 285 C.8 Dew Point......................................................................................... 286 C.9 Relating Humidity to Partial Pressure .............................................. 286 Example 1.................................................................................................... 286 Example 2.................................................................................................... 287 Example 3.................................................................................................... 288 Example 4.................................................................................................... 290 Example 5.................................................................................................... 291 C.10 Evaporation Rate.............................................................................. 292 References ................................................................................................... 294

xii

Contents

D Fracture Mechanics: Terminology and Tests ......................................... 295 D.1 Fracture Toughness, KIC ................................................................... 295 D.2 Plastic Zone Size at the Crack Tip, ry .............................................. 297 D.3 Critical Energy Release Rate, Gc ..................................................... 298 D.4 Fracture Strength.............................................................................. 298 D.5 Fracture Energy................................................................................ 299 References ................................................................................................... 299

INDEX................................................................................................................ 301

Symbols

Generic symbols used throughout this book

Symbol

Eɺ H R P T Tg

η µ φ φm

SI units -1

Meaning

ms m m N m-2 K K N s m-2 N s m-2 – –

Evaporation rate (units of velocity) Film thickness (wet) Particle radius Pressure Temperature Glass Transition Temperature Dispersion viscosity Solvent viscosity Particle volume fraction Close packed volume fraction

Nm = J m2 s-1 Nm = J m m Nm = J – A2 s4 kg-1 m-3 m V

Hamaker Constant Stokes-Einstein Diffusion coefficient Thermal energy Particle radius Spacing between particle centers Interaction potential Permittivity Permittivity of free space Debye length Electrostatic potential on particle surface

Chapter 1 A D0 kT R r U

ε ε0 κ−1 Ψ

xiv

Symbols

Chapter 2 A0, Asp B dI D0 Dapp dp db ep Ed Ep f g2(t) G G' G'' hunit Hdry I I0 IB KP KB L L', L'' m n np Q q

Rf Rg s t tD t0 Tf w Y z

α β γ λ λmin ν θ ∆σf τΑ

m T ( or V s m-2) m m2 s-1 m2 s-1 m m m Nm = J N m-2 s-1 – T m-1 (V s m-3) N m-2 m m – – – – – m N m-2 – – – m-1 – m2 m m s-1 s s s s N m-2 m – – s-1 T-1 m m – – N m-2 s

Tapping amplitudes for AFM Magnetic field strength Interpenetration distance Stokes-Einstein diffusion coefficient for a particle Apparent molecular self-diffusion coefficient Path length for light through sample Beam thickness Average spacing between particles Energy dissipation in tapping mode AFM Storage modulus (obtained from DWS) frequency Correlation function for light scattering Gradient in the magnetic field Shear moduli (storage and loss) Height of fcc/hcp unit cell Average thickness of dry film Intensity of radiation Intensity of incident radiation Background scattering intensity Porod constant Constant of proportionality Length of beam Longitudinal moduli Ratio of refractive indices Refractive index Refractive index of particle Scattering wave vector Quality factor for AFM cantilever Mean-squared displacement Förster radius Radius of gyration (particle or molecule) Speckle rate time Fluorescence decay time Initial time Transmitted fraction of radiation Interfacial width between two phases Young’s modulus (of beam) Void radius Constant of proportionality (for DWS) Exponent in stretched exponential Magnetogyric ratio Wavelength of radiation Wavelength of minimum transmitted radiation Poissons ratio Scattering angle Change in film stress Auto-correlation time

Symbols

ϕ ω

xv

– s-1

Angle of deflection of beam Angular frequency

m2 s-1 m s-1 m m m s-1 m-2 – m m N m-2 N m-2 – – s s m – – N m-1

Diffusion coefficient Evaporation rate (units of velocity) Film thickness (wet) Film thickness (dry) Mass transfer coefficient Permeability of particle bed Sedimentation Coefficient Capillary length Boundary layer thickness Pressure Characteristic pressure Dimensionless capillary pressure Peclet number Time for evaporation Time for diffusion Vertical distance Compressibility Particle volume fraction Surface tension

m N m-2 N N m-2 m – – N m-1 N m-1 N m-1 N s m-2 –

Radius of contact between two particles Young’s modulus Force pushing particles together Shear modulus Approach of particle centers Strain along particle centers Strain Water – air interfacial tension Polymer – water interfacial tension Polymer – air interfacial tension Polymer low shear viscosity Dimensionless group comparing polymer relaxation time to evaporation time Dimensionless group controlling particle deformation Poison’s ratio Dimensionless stress at top of film Angle of contact between sintering spheres

Chapter 3 D E H Hdry km kp K(φ) L Lb P P* Pcap Pe tevap tdiff y Z(φ)

φ γ

Chapter 4 a0 E F G

δ εR ε γwa γpw γpa η0

G

λ ν

σt θ

– – – –

xvi

Symbols

Chapter 5 aT b C1, C2 Db Ea Gc KIC M Me N

Λ σf Σ τe τR τd τXL wI

χ

– m -, K m-2 s-1 J mol-1 J m-2 = N m-1 N m-3/2 – – – m N m-2 m-2 s s s s m –

Time-temperature superposition shift factor Kuhn length for polymer segment WLF equation factors Fickian diffusion coefficient Activation energy Critical energy release rate Fracture toughness Polymer molecular weight Entanglement molecular weight Degree of polymerisation Interpenetration distance Failure stress Density of polymer chains crossing interface Rouse entanglement time Rouse relaxation time Reputation time Time for cross linking reaction Interfacial width for interdiffusion Flory Huggins interaction parameter

mol m-3 mol m-3 m2 s-1 m2 s-1 s-1 mol m-2 mol m-2 – –

Critical concentration in Langmuir isotherm Surfactant concentration in solution Particle diffusion coefficient Surfactant diffusion coefficient Reaction rate constants for surfactant adsorption and desorption Adsorbed amount in Langmuir isotherm Maximum adsorbed amount Particle Peclet number Surfactant Peclet number

m m N m-2 N m-2

Filler diameter Critical length of inclusion Fracture strength Interfacial shear strength

Chapter 6

Α Cs Dp Ds k, k'

Γ Γ∞ Pep Pes

Chapter 7 D Lc

σf τ

Symbols

xvii

Appendix A Fdrag G P P∗

∆ρ ρ U U*

N m s-2 N m-2 N m-2 N m-2 kg m-3 m s-1 m s-1

Drag force Acceleration due to gravity Pressure Characteristic pressure Difference in density Fluid density Velocity Characteristic velocity

s-1 m s-1 T-1 T m-1 – – – s s s s s s

Pulse bandwidth Pixel resolution in a profile Magnetogyric ratio Magnetic field gradient Number of echoes in a train Number of points acquired in an echo Numbers of scans Time interval between points in an echo Time duration of an RF excitation pulse Pulse gap (delay time between RF pulses) Repetition delay time (before sequence repeats) Spin-lattice relaxation time Spin-spin relaxation time

kg/kg kg mol-1 N m-2 N m-2 J mol-1 K-1 m3

Humidity Molar mass Partial pressure of water Pressure Gas constant Volume

Appendix B ∆Ω ∆y

γ Gy

Ν Nacq NS

τD tpd

τ τR T1 T2

Appendix C

Η Mw Pw P R V

xviii

Symbols

Appendix D a

∆ E Gc h, b K1 KIC P ry

Σ WB Y

m m N m-2 J m-2 = N m-1 m N m-3/2 N m-3/2 N m N m-2 J –

Crack length Thickness of sample Elastic (Young’s) modulus Energy release rate Specimen dimensions Stress intensity factor Fracture toughness (critical KI) Applied load Radius of crack tip Applied stress Fracture energy Geometric factor

Chapter 1

1 An Introduction to Latex and the Principles of Colloidal Stability

1.1

What is Latex?

Latex is an example of a colloidal dispersion. It consists of polymeric particles, which are usually a few hundred nanometres in diameter, dispersed in water. The particles typically comprise about 50 percent by weight of the dispersion. Depending on the particular application, there will also be a complex mixture of pigments, surfactants, plasticising aids and rheological modifiers. The whole dispersion is colloidally stable, meaning that it can sit on a shelf for years and remain dispersed, without sedimentation of particles making ‘sludge’ at the bottom. In this book, the word ‘latex’ will be used as shorthand for a wet dispersion. Sometimes, however, latex is used as an adjective, as in ‘latex film’. The plural of ‘latex’ is ‘latices’, not to be confused with ‘lattices’! (An alternative is to say ‘latexes’, but ‘latices’ will be used through this book.) Although colloids have been used since ancient times in Egypt and Greece, colloidal dispersions have been studied scientifically only since the nineteenth century when Thomas Graham first coined the term ‘colloid’. It is derived from the Greek work coll, meaning ‘glue’. A major advance in colloid science was made by Robert Brown, who observed pollen particles ‘dancing’ randomly when dispersed in a fluid. This phenomenon is now termed Brownian motion and is a defining characteristic of a colloidal dispersion. The effect is the result of an imbalance of forces between the colloidal particles and the surrounding molecules of the solvent, and it provides evidence for the existence of molecules. A dispersion in which Brownian motion is present is described as colloidal. An alternative definition, from the International Union of Pure and Applied Chemistry (IUPAC), is that colloidal particles have at least one dimension between 1 nm and 1 µm (IUPAC 2009).

2

1 An Introduction to Latex and the Principles of Colloidal Stability

Fig. 1.1 An emulsion polymerisation reactor. The structure spans an entire building and covers two floors. The top of the reactor houses the stirring motor. (Photographs courtesy of AkzoNobel)

1.2

Latex Synthesis and Uses

Industrially and in the laboratory, latex is most often made by a reaction called ‘emulsion polymerisation’. The process can be scaled up to large quantities, such as is demonstrated by the large reactors in Fig. 1.1. The scale of the structure, which spans two storeys, is indicated by the top two photographs. The top of the reactor and the stirring motor are shown in the bottom photo. The emulsion polymerisation process and newer developments, such as miniemulsion polymerisation, are described in numerous sources elsewhere (Lovell and El-Aasser 1997). A discussion of the polymerisation process is beyond our scope here. Latex may be synthesised from a range of monomers, the typical ones being acrylates (methyl methacrylate, butyl acrylate, ethylhexyl acrylate), styrene, vinyl acetate and butadiene. Copolymers are used extensively. The molar ratio of the monomers in the copolymer determines its glass transition temperature (Tg), the point at which a solid polymer changes into a liquid-like polymer, because long

1.2 Latex Synthesis and Uses

3

range motion of the molecule’s backbone is enabled. A polymer’s viscosity falls sub-exponentially as the temperature increases above the Tg. As we shall see in our discussions in Chapter 5, the temperature at which a latex film is formed should be greater than the (co)polymer’s Tg. Anyone who coats a house with a modern, waterborne paint uses latex to their benefit. The largest household use of latex is for architectural or decorative paints, which typically comprise acrylic or styrene-acrylic copolymers. Most readers will be familiar with commercial latex paints, such as those shown in Fig. 1.2.

Fig. 1.2 Latex paint is marketed in the UK and other countries under the trade name of Dulux, as seen in this advertising material, showing a well-recognised mascot. (Photographs courtesy of AkzoNobel)

4

1 An Introduction to Latex and the Principles of Colloidal Stability

Table 1.1 Typical formulations for gloss, silk and matte paints.

Component

Function

Polymer particles (latex)

Acts as a binder for the pigment Pigment to create opacity Prevents bubble formation during use Adjusts viscosity Stabilizes the pigment in the water phase Lowers the film formation temperature and increases the interdiffusion rate Inexpensive filler, typically minerals such as calcium carbonate Carrier for the wet paint

Titanium dioxide Defoamer Thickener Pigment dispersant

Coalescent

Extender Water

Gloss Paint (Schuler et al. 2000) (wt.%)

Silk Paint Matte Paint (Murray (Murray 2009) (wt.%) 2009) (wt.%)

26.5

20

15

23.0

16

10

0.15 12.0 1.0 2.35

35.0

3 (total for all four)

3 (total for all four)

2

32

59

40

Household paints and varnishes are usually applied over relatively small areas and allowed to dry. Viscosity control is particularly important for paints. Under a low shear rate, such as when coated vertically on a wall, the paint should not flow or drip: the viscosity should be high. When applied with a brush at a higher shear rate, the viscosity should be low to allow even spreading. Hence, rheology modifiers are a key ingredient of commercial paints. Shear thinning behaviour, meaning that the viscosity decreases as the shear rate increases, is desirable to ensure good spreading with a brush or applicator. Film thicknesses for household paints are typically one hundred micrometers. Typical formulations for three types of commercial emulsion (i.e., latex) paint are shown in Table 1.1, and other recipes are found in literature (Heldmann et al. 1999). Gloss paints are highly reflective of light, matte paints are poorly reflective, and silk paints have an intermediate reflectivity. You might be surprised to see that the latex polymer makes up less than 30% by weight in the paint formulations. Note the presence of rheology modifiers and defoamers. Wetting agents are also often added to ensure full coverage of hydrophobic surfaces. Extenders, which are inexpensive minerals used as fillers, are added to matte paints to ‘extend’ how far the more expensive polymers can go. Extenders introduce light scattering and so are not added to gloss paints. Increasingly, latex is being used as a binder in industrial coatings (applied in factory production) and various types of protective coatings for automobiles, aircraft, ships, appliances and more. The demands on industrial and protective coatings are high and go beyond improving the appearance of an object. The coatings need to provide resistance against corrosion, abrasion, wear, fire and chemical attack.

1.2 Latex Synthesis and Uses

5

Beyond paints and coatings, the uses for latex include pressure-sensitive adhesives, sealants, carpet backings, construction additives (such as in cements and mortars), paper coatings, inks, and latex gloves and condoms. Each will be considered briefly here. Pressure-sensitive adhesives (PSAs) are permanently tacky at room temperature, and provide permanent and nearly instant adhesion to almost any surface. They are well-known in their application as tapes and sticky labels. Pressuresensitive adhesives have many specific applications in the household (Fig. 1.3) and in cars (Fig. 1.4). They typically have a glass transition temperature that is around –50oC, and hence are made from monomers such as butyl acrylate or 2ethyl hexyl acrylate to reduce the copolymer’s Tg. Industrially, films are deposited onto long rolls of substrate material running at high speeds through industrial coaters. Most often the ‘transfer coating’ process is used for labels. A sandwich structure, as in Fig. 1.5a, is made. The latex is spread on a ‘release liner’ with a low-surface-energy surface, such as a silicone polymer, and then film-formed. The rate of drying is increased by drawing the film on the backing layer through a long oven or by blowing hot air across it. The dry film thickness for applications is typically 20 µm. Next, a ‘face material’ (or facestock) is pressed into contact with the latex adhesive surface. The air surface of the facestock is decorated appropriately for the adhesive’s application. To use the adhesive, it is peeled off from the release liner and then pressed onto the surface of choice, such as a beer bottle. The final film should be uniform and not have defects, such as pinholes or surface ripples.

Fig. 1.3 Uses of pressure-sensitive adhesives in the home. (Image reproduced with permission of Cytec Specialty Chemicals)

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1 An Introduction to Latex and the Principles of Colloidal Stability

Fig. 1.4 Uses of pressure-sensitive adhesives in a car. (Image reproduced with permission of Cytec Specialty Chemicals)

In a typical industrial coater, as in Fig. 1.5b, a steel roll is rotated through a reservoir of wet latex, picking it up as it rotates. The backing layer is then drawn at high speed across the rotating wet roll to deposit a thick film. The excess latex in the film is skimmed off by passing a grooved bar (called a ‘Meyer rod’) across it. Another process, called ‘gravure’, uses a roll that has grooves engraved in it. When the gravure roll is passed through a reservoir of latex, its grooves pick up some of the latex. The roll is then pressed in contact with a backing layer onto which it leaves a wet film. Higher coating speeds are obtained with the gravure process compared to most other processes. Depending on the process, coating speeds can range from 100 to over 1000 meters per minute. Textiles and carpet backings are often made from acrylic polymers. The coating provides durability to the material surface as well as a resistance to a number of solvents (Campos et al. 2006). Construction materials often have hydrophobic polymer latices added to them. These reduce the water permeability of the final material and will lead to a life extension from reduced corrosion (Stancato et al. 2005). Paper coatings use latex as a binder to enable the incorporation of clays and inorganic fillers. Latex coatings on paper are cheaper than wood pulp and also allow greater penetration of ink during the printing process (Zang and Aspler 1995, Alturaif et al. 1995). Inks for printing on paper and card may use latex as a binder for the pigment or dye particles (Hutton and Parker 2008). There is growing interest in water-based inks to replace solvent-based materials. In inkjet printing, colloidal dispersions are used in inks (Calvert 2001), and the use of latex particles has been demonstrated in an inkjet printer (Wong et al. 1988).

1.2 Latex Synthesis and Uses

7

(a)

(b)

Fig. 1.5 Industrial coating of pressure-sensitive adhesive films. a In the transfer process, the latex adhesive 3 is deposited onto a silicone release coating 2 on a release liner 1. Then the face material 4 is laminated onto the adhesive surface. Image courtesy of Cytec Specialty Chemicals. b An industrial coater. (Photograph used with permission of Cytec Specialty Chemicals)

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1 An Introduction to Latex and the Principles of Colloidal Stability

Fig. 1.6 Latex gloves are being made by dipping moulds into a natural latex dispersion and withdrawing. (Photograph used with the kind permission of Innovative Gloves Co. Ltd, Songkhla, Thailand)

Latex gloves are made by dipping a hand-shaped, ceramic mould into a latex dispersion and drying, such as shown in Fig. 1.6. Condoms are manufactured similarly – but of course with a different mould.

1.3

Historical Context and Economic Importance

There is a natural form of latex that is derived from a tree (Hevea brasiliensis), which – as its Latin name implies – originated in Brazil (Fig. 1.7). Plantations were developed in several Asian countries to support the growing rubber industry in the twentieth century. Natural latex is essentially cis-isoprene emulsified by a protein. During World War II, the supply of this latex from Malaysia was disrupted, and the resulting shortages spurred the development of synthetic latex made via emulsion polymerisation. The first commercially available latex was introduced by the Glidden Company in 1948. Consequently, a large synthetic latex industry grew through the remainder of the century. A second important factor is that some persons have an allergy to the protein in natural latex; about one in 10 persons show sensitisation (Turjanmaa et al. 1996, Liss et al. 1997). This drawback of natural latex has encouraged the growth of the synthetic latex market as an alternative, especially for applications in gloves.

1.3 Historical Context and Economic Importance

9

Fig. 1.7 The white dripping liquid is the sap of the Hevea Brasiliensis tree, which provides the natural form of latex. It is being collected in a bowl at the bottom of the tree for later use in the manufacture of natural rubber objects. (iStockPhoto)

The market for emulsion polymers is large and growing, with worldwide sales in 2007 of 17.9 billion US dollars. The vast range of industries that use polymeric coatings makes the economic influence of the coatings industries particularly immense. For example, the paper industry creates 91 million tonnes of paper in the EU annually, using coatings to provide a brilliant white shine. The annual market for paper coatings in the EU is 800 million Euros (Urban and Takamura 2002). Adhesives and sealants are used in more than 100 end-use product markets, and they had a demand of four million tonnes in the European region in 2008. A growth of 2.5% is predicted between 2008 and 2011. Of the entire European market for adhesives, valued at 11.3 billion Euros (15.8 billion US dollars), a share of 37 % was held by water-based adhesives, which are made from latex (von Dungen 2009). The water-based sector is growing at the expense of other manufacturing processes that emit organic solvents. In 2008, there were 135 billion latex gloves manufactured and the growth rate is around 10% per annum (Tan 2008). In response to the allergic reaction of some people to natural latex, the US market for nitrile latex gloves increased from 18.6% in 2006 to 26.8% in 2007, with the market share of natural rubber falling from 48% to 41% (Tan 2008). The biggest exporter of rubber gloves is Malaysia. In 2007, the total number of exported pairs of gloves was 41.7 billion pairs with a sale value of 5.9 billion Malaysian dollars (1.72 billion US dollars). This corresponds to approximately one percent of the Malaysian GDP (Department of Statistics 2008). For textiles, the annual consumption in 2001 was 160,000 dry

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1 An Introduction to Latex and the Principles of Colloidal Stability

tonnes of polymer, and for carpet backings it was 500,000 dry tonnes of latex in 1999 (Urban and Takamura 2002). Latex is most associated with water-based paints used to paint the inside and outside of buildings and houses, referred to as ‘architectural paints’. It is predicted that – as a result of tough environmental legislation – 88% of all architectural paints sold in Europe in the year 2011 will be water-based, using latex polymers as their binder. Globally, 73% of the market share of architectural paints is predicted to be water-based in that same year. The production of all architectural paints is predicted to reach 21 million metric tonnes in 2011 and to have a value of 47 billion US dollars. Despite a harsh economic climate, an annual global growth rate of nearly 4% is predicted for 2006–2011 (European Coatings Journal 2008).

1.4

Overview of the Film Formation Process

The process of transforming a stable dispersion of colloidal polymer particles into a continuous film is called ‘latex film formation’. It involves many steps that span from a dilute through to a concentrated dispersion, into a packed array of particles, and eventually into a continuous polymer film. From a modelling perspective (and for drawing cartoons!), it is conventional to split the process into three sequential steps (drying, particle deformation, and diffusion). But, as will be discussed in later chapters, the steps can overlap in time. There is a large literature examining the mechanism of film formation with many excellent reviews and commentaries (Steward et al. 2000, Winnik 1997, Dobler and Holl 1996, Winnik 1997b, Keddie 1997). Crucially, the film formation process, sketched in Fig. 1.8, has a pronounced influence on the final film properties. A recurring theme in this book is how the process and properties are interrelated. When a stable dispersion (state 1) is deposited on a surface and subject to evaporation, the particles consolidate into some form of close packing (state 2). The latex dispersion typically does not dry in a uniform manner across the film. As Fig. 1.9 illustrates, the edges often dry first. In this illustration, light scattering by the particles in water makes the wet regions turbid. There is a possibility of colloidal crystallisation (i.e. the formation of an ordered array of particles) if the drying is slow enough. More likely, the particles will collect in the form of a random close-packing with a volume fraction in the region of 0.64 for mono-sized particles (Russel 1990, Routh and Russel 1998, 2001). This means that the spherical particles occupy 64% of the space and the remainder is occupied by water. An image of an array of particles in close packing is shown in Fig. 1.10a. Here, the individual particles make the topography appear like a mountain range with the peak-to-valley distance corresponding to the particle radius. The drying step is considered in detail in Chapter 3.

1.4 Overview of the Film Formation Process

11

Polymer-in-water dispersion State 1 State 1

Close-packing of particles State 2 1. Water loss 100 nm

T> MFFT 3. Interdiffusion and coalescence

2. Deformation of particles Optical Clarity

T > Tg Dodecahedral structure (honey-comb) State 3

Homogenous Film State 4

Fig. 1.8 Schematic of the process of film formation: a colloidal dispersion’s transition into a continuous polymer film. (Drawing courtesy of Jacky Mallégol, University of Surrey)

0 min.

40 min.

90 min.

Fig. 1.9 Drying of 200 nm polystyrene particles in water. The particles pack and consolidate at the edge, and these packed particle fronts propagate laterally across the film toward the centre. (Photographs courtesy of Wai Peng Lee)

When the particles come into close contact, they will deform from their spherical shape to fill the void space around them. As the individual particles are deformed, they can remain as distinct objects (state 3 in Fig. 1.8). With the loss of the interparticle voids, the particle layer becomes optically transparent, because light is no longer scattered by heterogeneities in the refractive index. The onset of transparency is sometimes used to define the point of film formation.

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1 An Introduction to Latex and the Principles of Colloidal Stability

(a)

(b)

Fig. 1.10 a AFM topographical image of a latex film surface in a three dimensional view. The film was cast at room temperature, and since the polymer’s glass transition temperature is about 20 °C, the particles do not flatten much. Scan area is 1 µm x 1 µm. b When viewed from above, the high degree of order in the particle packing in a hexagonal array can be seen. (Images courtesy of J. Mallégol, University of Surrey)

An atomic force microscope (AFM) image of deformed particles is shown in Fig. 1.11a. The particles are no longer spherical, and only small voids are seen at the particle boundaries. There are numerous possible driving forces for the particle deformation, which are discussed at length in Chapter 4 (Brown 1956, Henson et al. 1953, Vanderhoff et al. 1966, Sheetz 1965, Routh and Russel 1999, Dobler and Holl 1996). The resistance to deformation comes from the particles themselves, and hence the temperature, relative to the glass transition temperature, is a crucial parameter in determining the extent of particle deformation. If mono-sized particles are packed into a face-centred cubic array, each particle (in the bulk of the film) will be in direct contact with twelve nearest neighbours. When the contact regions between the particles flatten, the particles will each create a twelve-sided geometric figure called a ‘rhombic dodecahedron’, drawn in Fig. 1.11b. In a face-centred cubic crystal, each particle has six neighbours

1.4 Overview of the Film Formation Process

13

hexagonally arranged around it in the (111) plane (Fig. 1.11a). If a thick film of deformed particles is sliced along a (111) plane, the particle cross-sections will be hexagonal. The array will take on an appearance similar to natural honeycomb (Fig. 1.11c), such as is shown schematically in State 3 in Fig. 1.8.

(a)

(b)

(c)

Fig. 1.11 a Example of flattening at particle/particle boundaries. Particle identity is still retained. Size of AFM image is 1.5 µm along each side. Image courtesy of A. Tzitzinou (University of Surrey). b Two different views of a rhombic dodecahedron. There are six rhomboids on the vertical faces. There are six square faces, three each on the top and bottom. c A cross-section slice of the dodecahedral structure in a film shows a hexagonal array, which is reminiscent of natural honeycomb. (iStockPhoto)

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1 An Introduction to Latex and the Principles of Colloidal Stability

If the particles are too hard, then they will not be able to deform. The film will be cloudy and cracked, as seen in Fig. 1.12a. It will be brittle and possibly powdery. The polymer can be softened by heating to temperatures above its Tg. Then, the film will be less brittle and will achieve optical transparency (Fig. 1.12b). The lowest temperature at which optical transparency may be achieved is referred to as the ‘minimum film formation temperature’ or MFFT. It is an important characteristic of latex formulation because it determines the conditions under which the latex can be successfully applied. If hard particles are blended with softer particles, film formation may still occur (Fig. 1.12c). The softer particles will create the film, and the harder particles will be dispersed throughout it.

(a)

(b)

(c)

Fig. 1.12 a Latex Tg ≈ 80°C; Film cast at room temperature; Film is opaque and has regular cracking patterns. b Latex Tg ≈ 80°C; Film formation at 150°C for 10 min.; Film is cracked but is now translucent, but note the haziness. c A blend of latex particles with Tg ≈80°C (as in (a) and (b)) and Tg ≈ –50°C; Film formation at room temperature (21°C). Film is smooth and transparent. (Photographs courtesy of Tao Wang, University of Surrey)

When the particles are deformed, their surfaces come into close contact over large areas. At temperatures above the polymer’s Tg, the molecular chains within the particles will move across the boundaries between particles. This diffusion blurs the boundaries between individual particles and leads to a continuous film with increased mechanical strength (State 4 in Fig. 1.8). The process by which long polymer chains diffuse in a molten material is called ‘reptation’. It has been shown that full mechanical strength is obtained once reptation has progressed by the distance comparable to the polymer’s radius of gyration (Prager and Tirrell 1981, Richard and Maquet 1992). The diffusion process is considered in detail in Chapter 5.

1.5 Environmental Legislation

15

While the different stages all occur sequentially for a local region of film, they may all be occurring simultaneously in a whole film. For example, a film may have regions that are still fluid (in State 1) and a further region that is fully dry and interdiffused (State 4) with transitions between these two extremes (States 2 and 3). Experimentally, drying fronts may be observed passing laterally across films thus indicating a number of states (Routh et al. 2001). The physical reasons for drying fronts and the consequences of non-uniform drying are explored in Chapter 3.

1.5

Environmental Legislation

In the past, polymers have been deposited from solution in organic solvents for coatings applications as well as in various industrial processes. Small organic molecules that vaporise and are emitted into the atmosphere are called ‘volatile organic compounds’ or VOCs. There are both environmental and health and safety driving forces to reduce VOC levels in coatings and other products. Environmentally, it has found that some VOCs damage the ozone layer, whereas others may contribute to the ‘greenhouse gases’ linked to global warming. Organic solvents that have historically been used in coatings produce toxic oxidants that are damaging to the atmosphere (Wicks et al. 1992). In workplaces that use solventborne products, the odour may be unpleasant and long-term exposure to solvents has raised health concerns for workers, especially professional painters (Bockelmann et al. 2002, 2003, 2004, Steinhauer et al. 2001, Morrow and Steinhauer 1995). Consumers increasingly prefer household products that do not emit VOCs. Governments have responded by introducing regulations and pollution prevention programmes (DeVito 1999). In Europe, the relevant legislation is the EU Directive 2004/42/EC, and it has been implemented into British law with The Volatile Organic Compounds in Paints, Varnishes and Vehicle Refinishing Products Regulations 2005. For the purposes of the EU Directive, a VOC is classified as an organic compound having a boiling point lower than or equal to 250°C at an atmospheric pressure of 101.3 kPa. The specific limits on VOC level depends on the application. The law comes fully into force in 2010, although the VOC limits were reduced in 2007. For instance, for matt indoor paint, the VOC limit for a water-based paint was 75 g per litre in 2007 but it will fall to 30 g per litre in 2010. Most coating manufacturers are striving to reduce their VOC levels below the limits, not only to comply with the legislation, but also to achieve a competitive advantage with the inevitable tightening of future legislation and to satisfy consumer demands. Having a low VOC content can make a product more attractive to consumers and so add to its value (Dennington 2007). Many countries have introduced special labelling schemes to identify ‘environmentally sound’ products. Workers in the manufacturing industries (such as in automotive finishing) are protected by laws that set ‘occupational exposure limits’ to restricted chemicals (Jotischky 2000). These laws influence how chemicals are used in the workplace.

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1 An Introduction to Latex and the Principles of Colloidal Stability

A key driver in the growth of the latex market has been the transformation of solvent-cast polymer processing to waterborne processes. A few decades ago, it was commonplace to use household paints that were solvent-based. Brushes were cleaned with mineral spirits or turpentine. Now, most architectural coatings use latex formulations, with only some types of varnish being solvent-based. Yet, even latex formulations can contain a significant level of VOCs. Various small molecules are employed to plasticise (i.e., soften) the polymer in the latex particles, enabling film formation to occur at room temperature or even lower. After the complete evaporation of the VOC, the polymer reverts to its hard, unplasticised state leaving a high Tg polymer film. It is a major challenge to produce hard latex coatings without VOC emission, and hence there is a continued need for the study of latex film formation. This need adds a sense of urgency to scientific work and has partly inspired the writing of this book. These environmental and economic issues might also explain the growth of interest in latex film formation in scientific literature. Fig. 1.13 gives an historical perspective. Before 1990, there were only a handful of publications with a focus on latex film formation. During the 1990s, there was a steady rise in the number of publications each year, reaching a peak of 53 in the year 2000. Through the first decade of the twenty-first century, the numbers have fluctuated around an average of 41 per year.

Fig. 1.13 Number of publications, by year, on the topic of ‘latex film formation’ according to a keyword search on the ISI Web of KnowledgeSM database.

1.6 Relevant Colloid Science

1.6

17

Relevant Colloid Science

The physics of colloidal dispersions has received extensive experimental and theoretical attention for hundreds of years. Here, we review the theories that are directly relevant to latex. Interested readers may find additional information in the many text books on colloid science (Hunter 2001, Russel et al. 1989).

1.6.1 Interaction Potentials The stability of a colloidal dispersion, or the ability of particles to remain as discrete objects, was first studied systematically by Schulz and Hardy (Hardy 1900), who examined the effect of electrolyte. A comprehensive theory, that is still used extensively today, was derived in the 1940s independently by Derjaguin and Landau in Russia and by Vervey and Overbeek in The Netherlands. It is now known as the ‘DLVO theory’ after the four scientists. Colloidal stability may be understood by determining the energy of interaction between two isolated particles. There are a number of separate constituent energies and the DLVO theory assumes that they are additive. The two most important interactions are the van der Waals attraction and an electrostatic repulsion. In addition, depletion interactions are relevant to latex dispersions. Each of these interaction energies will now be discussed individually.

1.6.1.1 Van der Waals Attraction The electron clouds in the constituent atoms and molecules in a colloidal particle fluctuate as a result of quantum effects. For an instantaneous moment when there is a fluctuation, there will be an asymmetry of the electric charge, which produces a dipole moment. Even non-polar, uncharged atoms and molecules are subject to this effect. The ‘instantaneous dipole’, as it is sometimes called, will create an electric field, which will then act upon the neighbouring molecules. The electric field shifts the electron distributions in the neighbours and thereby polarises them. The strength of their dipole is determined by their electron polarisability. These neighbouring dipoles will interact with the instantaneous dipole, leading to an attraction. It is somewhat surprising – but true – that all molecules (including neutral, nonpolar molecules, such as the noble gases) feel a van der Waals attraction to others. Van der Waals attraction explains why gases condense into the liquid state as the thermal energy decreases. The van der Waals attraction between two molecules is small, but when summed up over two macroscopic bodies, the energy can be considerable. The energy of interaction between two molecules is assumed to scale inversely with the separation distance, r, to the sixth power. Upon summing up all the pair

18

1 An Introduction to Latex and the Principles of Colloidal Stability

interactions, the van der Waals attraction between two equal-sized spheres of radius R with a centre-to-centre separation r is found to be U vdw = −

AR 12 ( r − 2 R )

(1.1)

where A is called the ‘Hamaker constant’ and is an experimentally determined quantity that depends on the dielectric constant and molecular densities of the interacting particles and their dispersing medium. The negative sign indicates that the interaction is attractive. The van der Waals attraction is divergent, meaning that the attraction approaches infinity at close contact (i.e. when r approaches 2R). Because of this, all colloidal dispersions are inherently unstable. The lowest energy state is one where all the particles are fused into a giant structure with minimum surface area. Therefore, colloidal dispersions can only be kinetically stable, meaning that the rate of aggregation, towards the lowest energy state, is slow. The usual way to stabilise a colloidal dispersion is to use an electrostatic repulsion between particles.

1.6.1.2 Electrostatic Repulsion Between Particles Charged groups on the particle surfaces will repel other charges of the same sign, and hence two particles with like charges experience a net repulsion. The magnitude of this repulsion is dependent on the charge, or potential, on the particle surfaces and the medium they are interacting in. Using the same notation as in Eq. (1.1), the electrostatic interaction energy between two like particles is given by

U elec = 2πεε 0 Rψ 2 exp ( −κ ( r − 2 R ) )

(1.2)

where ε and ε0 are the permittivity of the medium and free space, respectively, ψ is the potential on the particle surfaces, and κ is the inverse of the Debye length. The expression will be positive, reminding us that it is repulsive. The Debye length, κ–1, is a measure of the range of distances over which the electrostatic charges are significant. It is a function of the electrolyte concentration because charged ions in solution will screen the effect of electrostatics and hence reduce the repulsion between two charged particles. For a 1 mM solution of sodium chloride in water, the Debye length is 9.6 nm, whereas for a 100 mM NaCl solution, the Debye length reduces to 0.96 nm. The average separation between particles in solution is surprisingly small. For spherical particles at a volume fraction, φ, of 0.024, the average separation between particle surfaces is equal to the particle diameter. As φ increases, the average separation drops. For φ = 0.5, the separation between particle surfaces is reduced to 9% of the particle radius. For illustration purposes, a 50% by volume dispersion of 100 nm diameter particles has an average separation between

1.6 Relevant Colloid Science

19

particles of only 4.5 nm. Comparing this to the magnitude of the Debye length, it may be deduced that if the particles are dispersed in 1 mM NaCl, the particle electrostatic potentials will overlap to a considerable effect. This example shows that the particles are experiencing an electrostatic repulsion from their neighbours. The effect is seen in the dilute case of φ = 0.024 and becomes enhanced as the volume fraction is increased and the average particle spacing decreases.

1.6.1.3 DLVO Theory The concept behind DLVO theory is that the constituent interaction potentials are additive. The original theory considered the sum of van der Waals attractions and electrostatic repulsions. A typical result is shown in Fig. 1.14 where the divergent van der Waals potential dominates at small separations. Because the electrostatic repulsion typically acts over a longer range than the van der Waals attraction, the total potential contains a repulsive part. If the maximum in this potential has a significant value, in comparison to the thermal energy, then the dispersion is kinetically stable. The addition of electrolyte causes the range of the electrostatic repulsion to diminish and become overpowered by the van der Waals attraction. After a long enough time, the kinetic stability will be lost, and the dispersion will become unstable. The presence of electrolyte reduces the total interaction potential as illustrated in Fig. 1.15. It is apparent from this illustration why the addition of salt to a charge-stabilised colloidal dispersion will induce aggregation of particles.

Interaction energy

Total potential from addition of components: Dispersion stability is determined by the magnitude of the maximum

Electrostatic repulsion. Range is determined by the Debye length which is a function of the electrolyte concentration

Particle Separation Van der Waals attraction. Infinite attraction at contact means all colloidal dispersions are thermodynamically unstable

Fig. 1.14 The component potentials of electrostatic repulsion and van der Waals attraction combine to give an overall interaction potential. The maximum in the total potential determines whether the dispersion remains stable or aggregates.

20

1 An Introduction to Latex and the Principles of Colloidal Stability

Total interaction potential

Increasing electrolyte concentration

Separation

Fig. 1.15 Effect of increasing external electrolyte concentration. The van der Waals attraction remains unaltered but the electrostatic repulsion is diminished. The resulting total potential displays a diminishing maximum and hence the dispersion is destabilised.

1.6.1.4 Depletion Interactions It is often observed that a stable colloidal dispersion, in the presence of a nonadsorbing polymer, will experience aggregation1. The reason for this is the depletion interaction, and its physical basis is sketched in Fig. 1.16. The nonadsorbing polymer in the dispersing medium (water in the case of latex) will take on the shape of an expanded random coil, if the medium is a good solvent. The coil has a characteristic size given by its radius of gyration, Rg. As two colloidal particles approach each other, the separation between them becomes less than the size of the random coil, which is excluded from this overlap region. Hence, there is a concentration difference between the bulk solution and the overlap region. The result is an osmotic pressure on the outside region of the particles that is larger than the osmotic pressure in the overlap region. This pressure imbalance provides a force to push the particles together, causing them to aggregate. An alternative way to view the same phenomena is to consider the entropy of the polymer chains in the non-adsorbing polymer. If two particles, as a result of their random thermal motion, approach each other, the exclusion regions will 1

In the colloid science literature, coagulation commonly refers to an irreversible aggregation, and flocculation refers to a weak reversible aggregation. Here, aggregation is used to refer to joining together of particles.

1.6 Relevant Colloid Science

21

overlap. Consequently, the total volume available to polymer chains will increase. The greater available volume increases the entropy of the polymer chains and reduces the Gibbs’ free energy of the overall system. Consequently, there is an attraction between particles whose range extends over the size of the added polymer chain. Its magnitude depends on the polymer concentration.

Overlap Region: The two exclusion regions overlap

R r

Rg

Exclusion zone: Polymer chains are excluded from approaching to a distance less than the radius of gyration

Polymer chain: Size is set by molecular weight and interaction between the polymer and solvent

Energy of interaction is equal to the osmotic pressure of the dispersion, Π, multiplied by the volume of the overlap region, Voverlap. Udep = -Π Voverlap For an ideal solution the osmotic pressure is simply related to the number concentration of polymer chains, Π = n kT. The overlap region is determined from geometry as

Voverlap

  4π  3r 1 − = 3   Rg  4 R1 + R  

  1  r +  16   R g   R1 + R   

       

3

    Rg 3   R 3 1 + R     

Fig. 1.16 Depletion interactions. The exclusion of free polymer chains from the region between two colloidal particles results in an attractive potential between them.

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1 An Introduction to Latex and the Principles of Colloidal Stability

1.6.2 Fluid Motion The motion of colloidal particles in a fluid was derived analytically by Stokes, and the resulting flow pattern is known as ‘Stokes flow’. The effect of particles on dispersion viscosity was also derived analytically, this time by Einstein in 1905. He also built on the work of Brown by deriving the diffusion coefficient of colloidal particles in a dilute dispersion, a result now known as the ‘StokesEinstein diffusion coefficient’. The flow of a Newtonian fluid around colloidal particles satisfies the NavierStokes equation for momentum and mass conservation. Because of the small size of colloidal particles, it is possible to greatly simplify the governing equations to reach the so-called ‘creeping flow limit’, where fluid inertia is ignored. The derivation of creeping flow is presented in Appendix A, wherein the solution to the flow is shown in Fig. A.1. For creeping flow past a sphere, the solution is referred to as ‘Stokes flow’. It tells us that the drag force acting on a sphere of radius R that is travelling in a continuous medium of viscosity µ with a velocity of U is given by 6πµRU. The drag coefficient of the particle is 6πµR.

1.6.2.1 Diffusion Any colloidal particle is being continually subjected to fluid molecules colliding with it. Because of the random nature of the molecule collisions, the average displacement for a colloidal particle in one dimension is zero, although the distribution of sampled positions increases with time. The random motion of the particle is analysed as a diffusional process. In general, a diffusion coefficient is given by the thermal energy, kT, which arises from the momentum of the fluid molecules, divided by the drag coefficient, which describes the damping of the particle motion. Here, k is the Boltzmann constant (1.38 x 10–23 J K–1) and T is the absolute temperature in Kelvin. Following on from the expression for the Stokes drag, the Stokes-Einstein diffusion coefficient is written as D0 =

kT 6πµ R

(1.3)

Equation (1.3) tells us that the diffusivity of a particle will be higher if its radius is smaller. On the other hand, a thickener that raises the viscosity will reduce the diffusion coefficient. In Chapter 3, we shall see how particle diffusion is important to take into account in the drying process.

1.6 Relevant Colloid Science

23

1.6.2.2 Low Shear Viscosity of Colloidal Dispersions Adding colloidal particles to a fluid will increase the viscosity of the dispersion, η. That is, η is a function of the volume fraction of the colloidal particles, φ. In the dilute regime (φ < 0.1), the dispersion viscosity can be predicted from the fluid viscosity, µ, and the flow around an isolated particle. The result of the calculation is a series expression in volume fraction where the higher order terms can be safely neglected:

 

 

η = µ  1 + φ + O (φ 2 )  5 2

(1.4)

At higher particle concentrations, when φ reaches a value corresponding to particle close packing, the dispersion forms a solid, and the viscosity diverges. Accordingly, for higher volume fractions (φ > 0.1), particle interactions must be taken into account. In this regime, it is common to use the Krieger-Dougherty expression

 φm    φm − φ 

2

η = µ

(1.5)

where φm is the volume fraction of particles at which the viscosity diverges. It takes a value of about 0.64 for random close-packing of particles and 0.74 for a face-centred cubic colloidal crystal (Russel et al. 1989). A graphical representation of how the dispersion viscosity varies with particle volume fraction is shown in Fig. 1.17. This viscosity dependence differs strongly from what is seen for a solution of polymers dissolved in a solvent. In this latter case, the viscosity does not diverge until it approaches a polymer fraction of 1. The use of a bimodal distribution of particle sizes, i.e., a blend of large and small particles, enables a higher value of φm to be achieved.

η µ

1

η = µ (1 + 2.5φ )

φm

φ

Fig. 1.17 Effect of volume fraction on dispersion viscosity. At low volume fractions a linearisation applies and the viscosity diverges at a volume fraction of φm.

24

1 An Introduction to Latex and the Principles of Colloidal Stability

References Alturaif H., Unertl W.N., Lepoutre P. (1995) Effect of pigmentation on the surface-chemistry and surface free-energy of paper coating binders. J Adhes Sci Techn 9(7): 801-811 Bockelmann I., Darius S., McGauran N., Robra B.P., Peter B., Pfister E.A. (2002) The psychological effects of exposure to mixed organic solvents on car painters. Disability and Rehabilitation 24: 455-461 Bockelmann I., Lindner H., Peters B., Pfister E.A. (2003) Influence of long term occupational exposure to solvents on colour vision. Ophthalmologe 100: 133141 Bockelmann I., Pfister E.A., Peters B., Duchstein S. (2004) Psychological effects of occupational exposure to organic solvent mixtures on printers. Disability and Rehabilitation 26: 798-807 Brown G.L. (1956) Formation of films from polymer dispersions. J Polym Sci 22:423-434. Calvert P. (2001) Inkjet printing for materials and devices. Chem Mater 13: 32993305. Campos G., Reyes Y., Soto N., Aremas J., Vasquez F. (2006) Development of new carpet backings based on composite particles. J Reinforced Plast Composites 25(18): 1897-1901 Dennington S. (2007) personal communication Department of Statistics (2008), Monthly Trade Statistics, Malaysia. DeVito S.C. (1999) Present and future regulatory trends of the United States Environmental Protection Agency. Prog Organ Coat 35: 55-61 Dobler F. and Holl Y. (1996) Mechanisms of Latex Film Formation, TRIP 4(5): 145-151 European Coatings Journal (2008) Global demand for architectural paint to rise. Issue 4 Hardy W.B. (1900) A preliminary investigation of the conditions which determine the stability of irreversible hydrosols, Proc Royal Soc 66: 110-125 Heldmann C., Cabrera R.I., Momper B., Kuropka R. and Zimmerschied K. (1999) Influence of non-ionic emulsifiers on the properties of vinyl acetate/VeoVa10 and vinyl acetate/ethylene emulsions and paints Progress in Organic Coatings 35: 69-77. Henson W.A., Taber D.A. and Bradford E.B. (1953) Mechanism of film formation of latex paint. Indust Engin Chem, 45(4): 735-739 Hunter R.J. (2001) Foundations of Colloid Science, Oxford University Press, 2nd Edition Hutton B.H., Parker I.H. (2008) Immediate consolidation behaviour of aqueous pigment coatings applied to porous substrates. Chemical Engineering Science 63: 3348-3357 IUPAC (2002) http://goldbook.iupac.org/C01172.html

References

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Jotischky H. (2000) Coatings, regulations and the environment revisited. Surf. Coatings Intern. Pt. B: Coatings Trans 84: 11-20 Keddie J.L. (1997) Film formation of latex. Mat Sci Eng R: Reports R21(3): 101169 Liss G.M., Sussman G.L., Deal K., Brown S., Cividino M., Siu S., Beezhold D.H., Smith G., Swanson M.C., Yunginger J., Douglas A., Holness D.L., Lebert P., Keith P., Wasserman S., Turianmaa (1997) Latex allergy: epidemiological study of 1351 hospital workers. Occupational and Environmental Medicine 54: 335-342. Lovell P.A., El-Aasser M.S. (1997) Emulsion Polymerisation and Emulsion Polymers, John Wiley and Sons Ltd. Morrow L.A. and Steinhauer S.R. (1995) Alterations in heart-rate and pupillary response in persons with organic-solvent exposure. Biological Psychiatry 37: 721-730 Murray M. (2009) Personal communication. Prager S. and Tirrell M. (1981) The healing process at polymer-polymer interfaces. J Chem Phys 75(10): 5194-5198 Richard J. and Maquet J. (1992) Dynamic micro-mechanical investigations into particle/particle interfaces in latex films. Polymer 33(19): 4164-4173 Routh A.F. and Russel W.B. (1998) Horizontal drying fronts during solvent evaporation from latex films. AIChE J 44 (9): 2088-2098. Routh A.F. and Russel W.B. (1999) A process model for latex film formation: limiting regimes for individual driving forces. Langmuir 15: 7762-7773 Routh A.F. and Russel W.B. (2001) Deformation Mechanisms During Latex Film Formation: Experimental Evidence. Ind & Engin Chem Res 40(20): 4302-4308 Routh A.F., Russel W.B., Tang J. and El-Aasser M.S. (2001) A process model for latex film formation: Optical drying fronts. J Coatings Techn 73 (916): 41-48 Russel W.B., Schowalter W.R. and Saville D.A. (1989) Colloidal Dispersions, Cambridge University Press Russel W.B. (1990) On the dynamics of the disorder-order transition. Phase Transitions, 21: 127-137 Schuler B., Baumstarck R., Kirsch S., Pfau A., Sandor M., Zosel A. (2000) Structure and properties of multiphase particles and their impact on the performance of architectural coatings. Prog. Organ. Coatings 40: 139-150. Sheetz D.P. (1965) Formation of films by drying of latex. J Appl Polym Sci, 9:3759-3773 Stancato A.C., Burke A.K. and Beraldo A.L. (2005) Mechanism of a vegetable waste composite with a polymer-modified cement (VWCPMC), Cement and Concrete Composites, 27(5): 599-603 Steinhauer S.R., Morrow L.A., Condray R., Scott A.J. (2001) Respiratory sinus arrhythmia in persons with organic solvent exposure: Comparisons with anxiety patients and controls. Archives of Environmental Health 56: 175-181 Steward P.A., Hearn J. and Wilkinson M.C. (2000) An overview of polymer latex film formation and properties. Adv Coll Interf Sci 86(3):195-267

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Tan, A. (2008) It’s sunny days ahead for nitrile gloves, Rubber Asia November/December 139-140. Turjanmaa K., Alenius H., Makinen-Kiljunen S., Reunala T., Palosuo T. (1996) Natural rubber latex allergy. Allergy 51: 593-602. Urban D. and Takamura K. editors (2002) Polymer Dispersions and Their Industrial Applications, Wiley-V.C.H Vanderhoff J.W., Tarkowski H.L., Jenkins M.C., Bradford E.B. (1966) Theoretical consideration of the interfacial forces involved in the coalescence of latex particles. J Macromol Chem 1(2):361-397 Von Dungen M. (2009) Adhesives and sealants: the European market. European Coatings Journal Issue 6: 12-15. Wicks Z.W., Jones F.N., Peppas S.P. (1992) Organic coatings: Science and technology. John Wiley & Sons, Chichester, p. 259 Winnik M.A. (1997) The formation and properties of latex films. Chapter 14 in Emulsion Polymerisation and Emulsion Polymers, Edited by P.A. Lovell and M.S. El-Aasser, John Wiley and Sons Winnik M.A. (1997b) Latex Film Formation. Curr Opin Coll Interf Sci 2(2): 192199 Wong R., Hair M.L., Croucher M.D. (1988) Sterically stabilised polymer colloids and their use as ink-jet inks. Journal of Imaging Technology 14(5): 129-131 Zang Y.H. and Aspler J.S. (1995) The influence of coating structure on the ink receptivity and print gloss of model clay coatings. TAPPI Journal 78(1): 147154

Chapter 2

2 Established and Emerging Techniques of Studying Latex Film Formation

The study of the processes of latex film formation presents many challenges to the experimentalist. Each stage of film formation has specific requirements for any analytical technique. In the drying stage, there is a need to measure water concentration at various positions laterally and through the depth of a wet film. Latex in the wet state precludes the use of techniques that require the sample to be held in a high vacuum, such as Auger spectroscopy or secondary ion mass spectrometry. Electron microscopy conventionally has a high vacuum in the sample chamber, and so it cannot be used in the standard way. The particles are undergoing constant Brownian motion during the drying stage, and any useful analytical technique must not perturb the particles while it probes them. The ideal probe of particle motion will provide information on short time scales, but a technique that can determine spatial profiles of particle concentration is equally valuable. The drying process itself is discussed in Chapter 3. In the particle deformation stage, water may still be present, and so there are similar restrictions on the techniques. As the particles typically have a diameter less than 300 nanometres, any imaging technique requires high resolution. There is a need to know the particle structure through a film and not only at the interface with air or substrate. Many microscopies, such as scanning probe techniques, may be readily applied to the air interface. Information about the bulk of a film is obtained after cutting cross-sections. There is always a concern that artefacts are being introduced when preparing film cross-sections. Chapter 4 considers the particle deformation mechanisms in detail. Finally, in the interdiffusion stage, the needs are rather different. Here, the molecular level is of greatest interest. Techniques are required to probe noninvasively the individual molecules and the interfaces between particles. The physical aspects of the interdiffusion stage are presented in Chapter 5. This chapter will highlight techniques that are particularly well suited for examining latex film formation. Those techniques that study the polymer film itself

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2 Established and Emerging Techniques of Studying Latex Film Formation

– rather than its processing – are not emphasised. Details of how the techniques work may be found in the many cited sources. The emphasis here will be on the basic principles of operation and on what the techniques can reveal. An historical review of the techniques for studying film formation has been given elsewhere (Keddie 1997) and will not be repeated here. Those techniques that can probe latex in the presence of water (either liquid or solid) are considered separately from those that analyse mainly, or exclusively, the dry film. Through this chapter and the ones that follow, there will be a need to distinguish the plane of a film from the direction normal to it. In microscopy experiments, a cross-sectional slice of a film is sometimes examined. The meanings of these terms are clarified in Fig. 2.1.

Normal to film Cross-sectional slice Plane of film

substrate Fig. 2.1 Illustration of the meaning of the direction normal to the film plane, which is also called the ‘vertical direction’. The direction in the plane of the film is called the ‘horizontal direction’. A cross-sectional slice is taken in a plane perpendicular to the plane of the film.

2.1 Techniques to Study Latex in the Presence of Water (Wet and Damp Films) The challenge of ‘watching paint dry’ has attracted the application of numerous sophisticated techniques. To interrogate latex that contains liquid water (or ice), a probe must be used that does not perturb the material or the particle motion. The probe may be in the form of electromagnetic waves (visible light, X-rays, radio waves), ultrasound waves, or particles (electrons and neutrons). There is an additional technique that uses neither waves nor particles, but instead it uses the substrate as a probe of the mechanical state of the film. This technique, sometimes referred to as ‘beam-bending’, will also be considered here. Yet another approach is to impose an electric field across a film and to determine its electrical conductivity over time while drying.

2.1 Techniques to Study Latex in the Presence of Water (Wet and Damp Films)

29

2.1.1 Physical Probes of Drying We will first consider those techniques that probe the physical state of wet films in some way. These are all rather innovative and developed especially for latex film studies. Optical probes will be considered separately.

2.1.1.1 MFFT Bar Conceptually, the minimum film formation temperature (MFFT) bar is one of the simplest techniques. Because of its simplicity, it is also one of the more common approaches to the study of film formation. First proposed by Protzman and Brown (1960), the MFFT bar consists of a large platen that has a temperature gradient along its length. A film is cast on a substrate that is put in contact with the platen such that one end of the film is held at a temperature that is 20°C or so higher than the other end. The atmosphere above the film should be controlled. At low temperatures, below the dew point, a dry atmosphere is required to prevent the condensation of water (Eckersley and Rudin 1993). The method is defined by international standards (ASTM D2354-98 and ISO 2115:1996). An example of the apparatus may be seen in Fig. 2.2. As its name implies, the MFFT bar finds the lowest temperature at which a latex will form a film. The MFFT can be defined by one of three transitions in the film. There is, however, some ambiguity in the physical meaning of these definitions. 1. Cloudy-clear transition. This is essentially an indicator of the extent of particle deformation. At temperatures below the MFFT, particles are packed into an array, but they are not sufficiently deformed to be able to close up the void space between them. Therefore, light is scattered from the dry film, and it appears turbid. At temperatures above the MFFT, the voids between particles have closed sufficiently to prevent light scattering, and the film appears transparent. The transition point is usually determined visually by the user and is used to determine MFFT. 2. Crack point. This transition is determined visually as the point where cracks are no longer observed in a dry latex film. When there is no interdiffusion between particles in a latex film, it will be brittle. Zosel and Ley (1993) showed that a brittle-to-ductile transition in a latex film is associated with polymer interdiffusion. Hence, the crack point essentially determines the lowest temperature where there is diffusion of polymer molecules across the particle interfaces. 3. Knife point. This transition corresponds to the minimum temperature at which the film can resist mechanical shearing (Lee and Routh 2006). The ASTM standard does not specify a single definition, but merely states that the film’s ‘discontinuity as evidenced by whitening or cracking or both’ should be recorded. The ASTM standard says that the precision of the measurement has not

30

2 Established and Emerging Techniques of Studying Latex Film Formation

been experimentally obtained but that ±2 ºC can be expected. Protzman and Brown (1960) found that the MFFT is invariant with respect to the thickness of the wet film and to the solids content of the latex. The use of the MFFT bar requires a few words of caution. The ASTM standard states that ‘approximately one to two hours are required for the film to dry’ but it does not specify a precise time for observation. This is a serious omission, which could lead to a lack of reproducibility, because film formation is a dynamic process. Particles can be slowly deformed under the action of surface energy over long periods of time, so that their optical properties change (Keddie et al. 1996, Lee and Routh 2006). It is understandable why Sperry et al. (1994) found that the cloudy-clear MFFT moved to lower temperatures over time. A second note of caution concerns the interpretation of the cloudy-clear point. It is sometimes thought that it corresponds to ‘good coalescence’ in a latex film, which implies that all voids are eliminated and that there is extensive interdiffusion between particles. In fact, electron microscopy of clear films has found that they do, in fact, contain interparticle voids (Keddie et al. 1995). Standard theories of optical transmission show us that optical clarity is a function of both the size and the number of air voids in a film (van Tent and te Nijenhuis 2000). When very small particles are used in a latex, the size of the interparticle voids will be reduced proportionally. This suggests that films made from nanoparticles (with a radius of only tens of nm) could appear optically transparent even when there is not much particle deformation. Simulations by van Tent and te Nijenhuis (2000), shown in Fig. 2.3, offer great insight in this respect. If particles are deformed such that the void volume fraction is only 0.03, larger particles (with a radius of 400 nm) will naturally have larger voids compared to smaller particles (radius of 50 nm). In the visible range of wavelengths, the film from larger particles will appear turbid, whereas the film cast from the smaller particles will appear transparent. To counter-act this problem, it has been proposed that – when comparing MFFT for latices with different particle sizes – the ratio of the wavelength of the light to the particle size should be kept constant (van Tent and Nijenhuis 2000). A third note of caution concerns the subjective nature of the measurement of the transitions. In many laboratories, the same person is usually asked to make the MFFT measurements to ensure consistency. Two different observers are likely to define ‘optically clear’ or ‘not cracked’ in slightly different ways, leading to a systematic shift in their MFFT readings. Multiple measurements should be made and averaged to minimise errors. It is little wonder that MFFT has been called ‘an ill-defined concept’ (Dobler et al. 1992). Nevertheless, its measurement offers a simple and fast check on the ability of a latex to form a film.

2.1 Techniques to Study Latex in the Presence of Water (Wet and Damp Films)

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Fig. 2.2 Photograph of an MFFT bar showing two cast films. The cloudy-clear transition point is indicated. (Photograph courtesy of P. Sperry and reproduced with permission from Sperry et al. (1995); copyright 1995 American Chemical Society)

Fig. 2.3 Simulations of optical transmission under the assumption of a void volume fraction of 0.03 and with varying particle sizes, as indicated. The human eye is sensitive to wavelengths in the range from 390 to 770 nm. (Reprinted from van Tent and te Nijenhuis (2000) with permission from Elsevier)

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2 Established and Emerging Techniques of Studying Latex Film Formation

2.1.1.2 Film Scratching (Thin Film Analyser) A specially designed instrument, named the thin film analyser by its inventors (Bahra et al. 1992), provides a direct but invasive way of monitoring changes in the rheology of films during the drying process. A wet film is spread on a temperature-controlled platen set at a single value. A mechanical probe is scanned back and forth in straight trajectories across the film surface (in the film plane), moving to a new position after each stroke. The probe is held by an arm that is joined to an angular displacement potentiometer. The amount of displacement can be calibrated against known imposed forces. What the technique measures depends largely on whether a spherical (ball) or needle probe is used. A spherical or hemispherical probe will mainly impose a shear stress on the film and hence a measure of the drag force is related to viscosity. A drying film will have a complex dynamic modulus, but for Newtonian oils it has been shown that the drag force on a hemispherical probe is linearly related to the viscosity. When the particles in a colloidal dispersion hit the gel point, associated with their close-packing, the instrument is sensitive to the sharp rise in viscosity (Bahra et al. 1992). A needle probe, on the other hand, is capable of scratching films and is thereby sensitive to the hardening and stiffening of a film associated with its crosslinking. The marks left on a surface by a moving needle are a complex function of hardness, friction and tear resistance (Schallamach 1952).

2.1.1.3 Gravimetry One of the simplest ways to study the drying of latex films is to record the mass as a function of time. The solids fraction, φ, can then be followed through the film formation process. A standard laboratory balance is often used for large-area films, and there has been a report of the use of a sorption balance for small droplets, up to 20 mg in mass (Erkselius et al. 2007). Of course, no direct information is obtained about the distribution of water within the film from its mass. Gravimetry is therefore most effective when combined with other techniques such as optical microscopy and photography (Winnik and Feng 1996), IR spectroscopy (Guigner et al. 2001), and magnetic resonance profiling (Mallégol et al. 2006). Narita et al. (2005) have compared their data to a model of drying to determine the importance of osmotic pressure. Erkselius et al. (2007) have pointed out the effects of evaporative cooling on the rate of water evaporation from latex films.

2.1.1.4 Beam Bending (or Optical Cantilever) Technique When two materials are coupled together in parallel in a bi-layer bar, and one of the materials changes dimensions more than the other, the bar will curve. One of the materials will be pulled in tension while the other is placed in compression. A

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33

common example is when there is a mismatch in thermal expansivities in a bimetallic strip. For many years, a cantilever technique operating on this principle was used to measure stress in paint and coatings (Corcoran 1969, Perera and Van den Eynde 1981). But, it was not employed as an in situ probe of film formation itself. Petersen et al. (1999) provided the first major report of the optical lever (beam bending) technique applied to the study of latex film formation. The basic principle is that stress transfer from the film along the length of the beam will cause curvature. If the film is pulling inward (in tension), then the beam will curve upwards (with a concave curvature). If, however, the film is pushing outward against the substrate (in compression), then the beam will curve downward (with a convex curvature). In the experiment of Petersen et al. (1999), a film is cast on a thin strip of metal or other stiff material with a known elastic modulus. The strip is clamped in a fixed position at one end, and the other end is free. Light from a laser source is reflected off a mirror placed on the free end in order to monitor the displacement of the strip. The movement of the reflected light beam is sensed with a quadrant detector, which is sensitive to lateral movement of the light. Fig. 2.4 shows the experimental set-up. The technique requires that the Young’s modulus, Y, of the beam is known. A beam with a length of L will be deflected from a straight position by an angle, ϕ (in radians). For a beam of thickness db, the change in the stress of the film, ∆σf, is given by the Stoney equation:

 Ydb 2  ∆σ f =  ϕ  6 H L  dry  

(2.1)

where Hdry represents the average thickness of the dry film. Petersen et al. (1999) pointed out several caveats in using the beam-bending method. 1. The technique measures the ‘integral stress’ (force per unit width) and not the local stress. 2. It is not sensitive to vertical stress or hydrostatic pressures – just the lateral stresses. 3. The zero position of stress cannot be determined, as there is no way of reaching a stress-free state when the measurement has started (about a minute after film casting). Instead, the zero point is defined as the starting point of data collection. 4. It must be assumed that there is no slip at the interface with the substrate – a sensible assumption for soft films with good adhesion. They also noted that the loss of mass from water evaporation makes the external torque on the beam change over time. The relative contribution of the film weight scales with L2, so shorter beams result in reduced error. In the experiments

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2 Established and Emerging Techniques of Studying Latex Film Formation

of Petersen et al., the effect of film weight on ϕ is 0.0007°, which is not large in comparison to the total deflection of about 0.1°. The beam-bending technique has also been used to investigate the causes of cracking in latex films (Tirumkudulu and Russel 2005) and to determine the role of capillarity in generating film stress during drying (Tirumkudulu and Russel 2004). An interesting extension of the technique is to map the stress distribution in a latex film in two dimensions in its plane by measuring the deformation when it is cast on a thin membrane. This type of experiment was originally demonstrated successfully by biophysicists as a means of examining the stresses generated by stationary living cells (Schwarz et al. 2002). In the approach used by von der Ehe and Johannsmann (2007), the back of the membrane has a mirrored surface. Stress in a latex film induces distortions in the membrane, which are apparent when the image of a grid is reflected off the back of it. The data analysis assumes that the lateral tension in the membrane is the source of the deformation. The vertical displacement of the membrane is related to the local stress in the plane of the film. Variations of stress across a film can be mapped, and the stress development leading up to cracking events can be followed in time. Laser beam Quadrant detector

ϕ

Mirror Latex film

ϕ

Clamp Flexible beam

Fig. 2.4 Experimental set-up for a beam-bending experiment.

2.1.1.5 Ultrasonic Reflection Acoustic waves are influenced by both polymer structure and molecular relaxation. The reflection of shear waves at ultrasonic frequencies (MHz range) is a well established way of measuring the complex shear modulus (real and imaginary components: G' and G") of a wide variety of materials. Alig et al. (1997) developed a fully automated set-up with digital signal analysis that enabled time dependent studies. They showed the evolution of the shear moduli during the film formation of an acrylic latex film. The technique is highly sensitive to the transition between liquid and solid. The shear modulus of the liquid is close to zero, but

2.1 Techniques to Study Latex in the Presence of Water (Wet and Damp Films)

35

it rises sharply when the particles pack together to make a more solid-like material. There is also sensitivity to water loss in the later stages of drying. A further improvement was made by the same group when they devised a method and instrument to measure the complex longitudinal modulus (L' and L") simultaneously with G' and G" over time during film formation (Lellinger et al. 2002). In an isotropic medium, these two moduli are related mathematically to the Young’s modulus, the compression modulus, and Poisson’s ratio, ν. For instance, ν can be calculated from this relation:

ν=

L' −G' 2 L '− G '

(2.2)

Hence, a complete mechanical characterisation of a film, albeit at ultrasonic (MHz) frequencies, can be obtained. In the experimental set-up described by Lellinger et al. (2002), films are cast on the end of a glass rod. A LiNbO3 transducer is attached to the other end, as shown in Fig. 2.5. The transducer is used both to transmit and to receive ultrasonic waves. This single transducer generated longitudinal waves of 8 MHz and shear waves of 5 MHz. These two types of waves travel at different velocities in the glass rod and then reflect from the film interface. The longitudinal wave arrives back at the transducer in a shorter time than taken by the shear wave. Their differing velocities thereby allow separation of the longitudinal and shear properties. The acoustic reflectivity depends on the complex dynamic shear impedance. In turn, the shear impedance is a function of G' and G". There is an analogous relationship between the longitudinal impedance and L' and L". In a wet latex film, the compression modulus is sensitive to the fraction of solids in water, as the two components have differing values. At the gel point, the film can support a shear stress, and G' rises sharply from zero. On the other hand, L' is approximately equal to the compression modulus and so it goes through a more gradual transition, rising steadily with water loss.

Fig. 2.5 Experimental set-up of an ultrasonic reflection experiment in which both longitudinal and shear waves are generated and detected. (Reprinted from Lellinger et al. (2002); copyright Wiley-VCH Verlag GmbH & Co. KGaA; reproduced with permission)

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2 Established and Emerging Techniques of Studying Latex Film Formation

2.1.1.6 Electrical Conductivity Measurements of the electric conductivity of wet films are conceptually simple and just require a sample cell in which electrical contact may be made by inserting metallic wires into the wet film. In this design, a conductivity meter must be sensitive enough to measure values on the order of µS/cm (Bouchama et al. 2002). Another approach is to attach electrodes to a substrate and then spread the film across them. Electrical impedance can be recorded over time starting from the deposition of a wet film. One difficulty with this method is that film cracking leads to a sharp rise in the electrical resistivity of the film and interferes with the measurement (Mulvihill et al. 1997). In the later stages of drying an emulsion, a biliquid foam structure can develop in which the particles (soft droplets) are deformed to fill space with a thin water layer separating them. There is an established relationship between the conductivity of a biliquid foam and its water content, as derived by Lemlich (1978). It may be used to determine whether it is consistent with the proposed foam structure. Hence, information on the deformation of droplets (or soft particles) may be extracted from an experiment. Conductivity measurements are particularly effective in determining whether particle boundaries exist in a film that has dried to a state of optical clarity. A drawback is that the measurement provides an average reading for the entire film. In the methods used to date, there is no information as a function of depth or lateral position. Conductivity measurements are most informative when coupled with simultaneous visual observation using optical microscopy or measurements of water content via gravimetry to aid analysis (Bouchama et al. 2002). This combined analysis has been demonstrated for oil-in-water emulsions, but is less well developed for the study of latex films.

2.1.2 Specialist Electron Microscopies A conventional scanning electron microscope requires specimens that are electrically conductive, in order to avoid negative charge build-up on the surface. A high vacuum is required in the sample chamber and along the path down the microscope column from the source of electrons. These two restrictions make the study of wet latex films impossible within a conventional electron microscope. One way around the problem is to operate at very low temperatures in a cryogenic electron microscope so that the water is frozen (ideally in a glassy state). Another approach is to use environmental scanning electron microscopy (ESEM), which enables a low water vapour pressure in the sample chamber and thereby allows the analysis of wet samples. More recently, environmental microscopes have been adapted to allow scanning transmission electron microscopy (STEM) of wet films. Each of these three will be discussed here.

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2.1.2.1 Cryogenic Scanning Electron Microscopy Ma et al. (2005) have shown that wet latex films may be successfully quenched to cryogenic temperatures so that the water solidifies. Latex particles in water are immobilised – being literally frozen in place. The specimen can then be fractured and loaded into a scanning electron microscope and examined while being maintained at this temperature. Cryogenic microscopy has provided the first direct visualisations of the three-dimensional distribution of latex particles during film drying. The technique is highly effective, and stunning cryo-images are presented in Chapter 3. Yet even so, Ma et al. (2005) outlined numerous artefacts of which the microscopist must be aware. (An artefact is a feature that is created during the analysis and that is not present in the original specimen.) 1. Freezing. For best results, ice formation must be avoided, because the volume change associated with the freezing phase transition disrupts the local structure. Instead, through superfast cooling, at least 105 ºC per second, glassy water can be formed. High pressure is useful here, as it has proven much less disruptive to film structure in comparison to plunge freezing. 2. Freeze-fracture. It is important to remember when viewing cryogenic SEM images of film cross-sections that the surface has been created by fracture. During the fracture process, particles can be elongated and plastically deformed. Surface roughness is the result of the fracture process and not necessarily indicative of material structure. 3. Sublimation. Often in the frozen specimen, ice covers the material of interest. Sublimation of ice on the surface enables underlying latex particles to be observed. Furthermore, etching a small amount of the surrounding ice increases the contrast with the particles. If the sublimation proceeds too far, however, the particles are fully exposed and can rearrange their relative positions. 4. Cryo-transfer. After a specimen is frozen, it must be transferred to the cold stage of the electron microscope. If a frozen latex film is not protected in a dry atmosphere, such as the vapour of liquid nitrogen, or in vacuum, it is subject to the formation of ice crystals from condensed atmospheric moisture. 5. Imaging. The electron beam may damage the specimen. Latex particles may change shape, melt, and even move position under high electron doses. To minimise these effects, low beam current and electron voltages are often used. Furthermore, residual water vapour within the high vacuum microscope chamber should be avoided, such as by using cold traps, to prevent condensation on the surface (Sheehan et al. 1993)

2.1.2.2 Environmental Scanning Electron Microscopy (ESEM) As indicated in the previous section, there are many potential artefacts in cryogenic electron microscopy. An alternative approach, ESEM, permits the observation of hydrated substances, including colloidal films, at temperatures above the

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2 Established and Emerging Techniques of Studying Latex Film Formation

freezing point of water. ESEM has undoubtedly yielded many new insights into the film formation process. Its primary attraction over cryogenic SEM is that sample preparation is minimal. A film can be cast, placed into the microscope chamber, and examined within a few minutes (Donald 2003). An image of a partially wet latex film can be obtained (Fig. 2.6) at the point where particles have packed together but where water still surrounds them. Under the right conditions, latex particle aggregation can be observed at the surface of water (Donald et al. 2000). Many of the key insights leading to the development of ESEM were made by Danilatos (1998). In particular, he developed the use of a microscope column (along which the electron beam travels) with a differential pressure along it. Pressure-limiting apertures maintain the pressure gradient that varies typically from 10–7 Torr around the electron source (the gun filament) up to about 10 Torr in the specimen chamber (Fig. 2.7). In a conventional electron microscope, by comparison, the specimen chamber is maintained at a high vacuum along the whole length of the microscope column. A variety of gases may fill the sample chamber in an environmental electron microscope (Fletcher et al. 1997), but for wet latex films, water vapour is the obvious choice. In addition to the pressure gradient along the microscope column, there are two other key requirements for ESEM, as explained by Donald et al. (2000). One requirement is that there must not be too much scattering of electrons from the gas in the chamber as they pass from the sample surface to the detector. The scattering may be reduced by keeping the distance between sample surface and the detector short, and by keeping the gas pressure in the sample low. A second – advantageous – requirement is that the detector must operate in a gaseous environment rather than a vacuum. The secondary and backscattered electrons emitted from the sample collide with the chamber’s gas molecules to create daughter electrons and positive ions. Because of this cascade process, many more electrons are detected than are originally emitted from the sample. A positively biased environmental (gaseous) detector is used in environmental microscopes to detect the amplified signal. An added benefit of having a low-pressure gas in the specimen chamber is that the positive ions are drawn to the sample surface where they neutralise the negative charge that builds from bombardment by the electron beam (Donald et al. 2000). In conventional microscopy, a thin layer of a conducting material, such as gold or carbon, is deposited on the sample surface to create a path for electron charge transport. Without a conductive coating, fine surface features in an environmental electron microscope will not be hidden or covered up. Furthermore, the sample will not need to be exposed to the vacuum, and hence dried, as is required for the deposition of metallic coatings by thermal evaporation or sputtering.

2.1 Techniques to Study Latex in the Presence of Water (Wet and Damp Films)

39

Fig. 2.6 ESEM image of a latex film in its partially dry state. The water appears as the light grey areas. The dark grey spots are the particles that are emerging from the wet surface. The scale bar is 2 µm. (Image courtesy of Paul Meredith, University of Cambridge)

Fig. 2.7 A diagram of an environmental scanning electron microscope (ESEM) showing the pressure decrease along the electron beam path. (Reprinted from Keddie et al. 1995; copyright 1995 American Chemical Society)

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2 Established and Emerging Techniques of Studying Latex Film Formation

To reduce electron scattering and thus to obtain a quality image in the environmental microscope, the pressure must typically be about 6 Torr (or 6 Torr/760 Torr ≈ 0.008 of an atmosphere). At this pressure, water will boil at room temperature. Considering the temperature dependence of the vapour pressure of water (Fig. 2.8), it is apparent that thermodynamics will favour the condensed state at a pressure of 6 Torr when the temperature is held at 6ºC or below. Hence, there is a range of pressure and temperature combinations under which evaporation is prevented and a latex, or any other sample, can be kept wet but not frozen in ice. The sample is loaded into the specimen chamber at ambient pressure, and a careful pump-down procedure is required to prevent sample drying (Cameron and Donald 1994). One challenge in ESEM is the prevention of electron beam damage to the sample. As the electron beam is rastered back and forth across a surface, it dwells for a longer time at the start of a line. Along the edges of a scanned region, where the amount of irradiation is greater, visible changes may be made to the sample, such as melting or particle rearrangement. When electrons interact with water in the chamber, free radicals are created through the process of radiolysis. These free radicals react with polymers, such as in a latex, and thereby alter the chemical composition (Donald 2000). When polymer surfaces are coated with water, the beam damage is even worse than when water is only in the gaseous state (Kitching and Donald 1998).

Water condenses

Water evaporates

Fig. 2.8 Water vapour pressure as a function of temperature. At higher vapour pressures and lower temperatures in the ESEM chamber, water will condense, and imaging of wet samples is possible.

2.1 Techniques to Study Latex in the Presence of Water (Wet and Damp Films)

41

2.1.2.3 Wet STEM Clearly, ESEM is a powerful tool for the visualisation of colloidal processes, including the drying of films. As explained in the previous section, in ESEM an electron beam is rastered across a surface and an image is created from the secondary and backscattered electrons. A variation on the technique uses a rastered electron beam that is transmitted through a thin wet film, as is illustrated schematically in Fig. 2.9. Called ‘wet STEM’, this technique was pioneered by Bogner et al. (2005), who demonstrated its utility for colloids dispersed in water. In their first report of the technique, they pointed out its main advantages. Wet STEM shares the attractions of ESEM in that it is suitable for wet samples without the need for staining, coating or destructive sample preparation. A clear benefit of wet STEM is that it provides information about the entire volume (i.e., depth) of the wet sample and not just what emerges at the surface. In comparison to TEM, wet STEM yields greater contrast in an image, as a result of the lower voltages leading to a greater number of electron-sample interactions. Using microscopes with a field emission electron source, the resolution can be as low as 1 nm at a voltage of 20 kV, and a resolution of 5 nm was achieved in the study of gold nanoparticles. Somewhat surprisingly, when the sample volumes are sufficiently small, such as in the µm-sized holes of a carbon grid, the images are not affected by particle drift or diffusion. To prepare a sample, a droplet of the colloidal dispersion of interest is placed on a grid used for transmission electron microscopy. Surface tension ensures that the liquid is self-supporting, so that the electron beam can pass through the dispersion layer and to the detector, provided that the layer is sufficiently thin (Bogner et al. 2005). The sample is loaded into the specimen chamber at ambient pressure, and a careful pump-down procedure is required to prevent sample drying, sample freezing, or unwanted condensation (Cameron and Donald 1994). As in the case for ESEM, the specimen chamber must be evacuated without drying the sample. Then, the pressure and temperature of the aqueous sample must be carefully maintained to either induce slow evaporation of water or to maintain a constant volume of water in the sample. The liquid state of water can be maintained at 2°C and a water vapour pressure of 5.3 Torr. Decreasing the pressure or increasing the temperature controls the evaporation of the sample and enables particles the deformation and the film forming process to take place (Arnold et al. 2009). Bogner et al. (2005) used ‘annular dark-field conditions’ in which two semiannular solid-state detectors are used to collect the scattered beam but not the transmitted one. This approach achieves better contrast than the use of the transmitted beam in the bright field. The contrast in the image is influenced by the distance between the sample and the detector, and it can be optimised through systematic variation. An optimum distance was found at 7 mm.

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2 Established and Emerging Techniques of Studying Latex Film Formation

Fig. 2.9 The arrangement used for wet scanning transmission electron microscopy. A Peltier stage a controls the temperature. The incident beam i is transmitted through a thin, wet layer w supported on a stand b within an environmental chamber. A backscattered-electron detector c is positioned under the sample. (Reprinted from Bogner et al. (2005) with permission from Elsevier)

2.1.3 Scattering Techniques The scattering of waves of particles (electrons or neutrons) or electromagnetic radiation (e.g. visible light and X-rays) offers an ideal non-invasive method to probe latex in its wet state.

2.1.3.1 Small Angle Neutron Scattering (SANS) and Small Angle X-Ray Scattering (SAXS) The scattering of neutrons and X-rays gives information on the radial structure of latex particles (and hence its surfactant layer and membrane state) and on the spatial correlation between particles. That is, scattering can tell us whether the particles are spaced at equal distances. It also can tell us whether particles are arranged on an ordered lattice or randomly distributed in space. As a consequence

2.1 Techniques to Study Latex in the Presence of Water (Wet and Damp Films)

43

of the power of these scattering techniques, they have often been used in the study of colloids (Ballauff 2001). The scattering of both X-rays and neutrons uses a common approach. A beam of known intensity, I, and a wavelength, λ, is transmitted into the sample. The scattered radiation is detected at a scattering angle θ with respect to the transmitted beam, as is shown in Fig. 2.10. In a typical experiment, measurements of the intensity of the scattered radiation are made over a range of λ or – more often – over a range of θ. The latter is straightforward when using position-sensitive detectors. In this way, the intensity of the scattered beam is measured as a function of the wavevector, Q:

Q=

4π

θ  sin  λ 2

(2.3)

and data are usually presented as a spectrum of I(Q). Depending on the system, the scattering spectrum is interpreted in terms of an appropriate model. Q is inversely related to the size of the feature that is probed. Hence, to study the relatively large distances associated with colloids – such as particle spacings and diameters – low values of Q must be obtained. Radiation scattered at low θ are thus the most useful, leading to the suitability of small angle – rather than wide – neutron and Xray scattering (SANS and SAXS). The first conclusive demonstration of how SANS can interrogate particle deformation in wet colloidal specimens was given by Crowley et al. (1992).

I

λ latex

θ

I(0) I(Q)

Fig. 2.10 Geometry of the arrangement for a small-angle neutron or small angle X-ray scattering experiment.

As an example of experimental details for SANS, at the neutron source at the National Institute of Standards and Technology in Gaithersburg, Maryland (USA), Kim et al. (2000) used a neutron beam of λ = 20 Å scattered over a range of θ to provide Q from 0.004 Å–1 to 0.039 Å–1. As a second example, Belaroui et al. (2003) obtained even lower values of Q, from 0.0015 Å–1 to 0.034 Å–1, on the D11 and D22 diffractometers at the Institute Laue Langevin in Grenoble, France, using two wavelengths of λ = 6 Å and λ = 10 Å. SANS has provided evidence for surfactant desorption from colloidal polymer particles in partially dried films (Belaroui et al. 2003). To achieve contrast

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2 Established and Emerging Techniques of Studying Latex Film Formation

between the phases, selective deuterium labelling is used. (The scattering density of deuterium differs strongly from hydrogen, and so it is an ideal label.) In the experiments of Belaroui et al. (2003), the continuous serum phase contained 20% D2O with the rest being H2O. Hence, the neutron scattering density of the particles and the serum was matched, so that the dispersion was not expected to scatter neutrons. When the surfactant (sodium dodecyl sulphate) was labelled with deuterium, it had contrast with the particles and the serum, so that desorption could be followed with SANS. There are relatively few examples of the use of X-ray scattering to study latex drying and particle packing. In the past, when Kratky cameras were used, the range of Q was not sufficient to study larger distances in real space. With a modified camera, Dingenouts and Ballauff (1998, 1999) obtained Q in the range from 0.03 to 4 nm–1 for use in studying the ordering of non-deformable particles in dried latex films. Comparing two latices, they were able to relate greater ordering of packed particles to a narrower polydispersity of particle sizes (Dingenouts and Ballauff 1999). X-ray reflection measurements from a concentrated dispersion of colloidal silica particles in water have probed the particle ordering near the interface with air (Madsen et al. 2001). In this case, X-rays were reflected from the wet surface, and the specular beam was detected. (A specular beam reflects from the surface at the same angle as the incident beam strikes it.) To date, this type of experiment has not been reported for latex films.

2.1.3.2 Photo Correlation Spectroscopy, Diffusing Wave Spectroscopy, and Speckle Interferometry Light scattering is a common technique for measuring particle size distributions in dilute dispersions. In a latex dispersion, the particles are undergoing constant random movement referred to as ‘Brownian motion’. As solvent molecules collide from all sides of a colloidal particle, there is a slight imbalance of momentum transfer, so that the particle is pushed a short distance in a certain direction. Over longer times, the particle is seen to follow a random path. The self-diffusion coefficient for a Brownian particle, D0, is defined for an ensemble of particles through the mean of the square of the distance travelled, , in a given time, t, as:

D0 =

r2 6t

(2.4)

A well-known equation, derived from the work of Stokes and Einstein (SE) and presented already in Section 1.6.2.1, shows us how the rate of self-diffusion for a spherical particle of radius, R, is affected by the viscosity, µ, of the continuous phase (e.g., the latex serum):

2.1 Techniques to Study Latex in the Presence of Water (Wet and Damp Films)

D0 =

kT 6πµ R

45

(2.5)

where the product of the Boltzmann constant, k, and the absolute temperature, T, is a measure of the thermal energy. The SE equation (2.5) applies in the dilute limit where particle motion is not affected by interaction with neighbours. We see in (2.5) that measurements of D0, such as by observing the paths of diffusing latex particles with a microscope, provides a measure of R, provided that the dispersion is dilute, the viscosity of the continuous phase is known, and temperature is kept constant during the measurement. The same equation tells us that measurements of D0 for a particle of known size can tell us the viscosity of the continuous medium. In this way, a colloidal particle may be used as a probe of µ in its local region. Equation (2.5) can be generalised to consider a viscoelastic medium, rather than a simple viscous liquid, so that the complex dynamic modulus can be extracted. This concept forms the basis of a microrheology technique (Waigh 2005) in which colloidal particles are used as local probes of the viscoelasticity of concentrated polymer solutions (Papagiannopoulos et al. 2005) and gels (Djabourov et al. 1995). In the type of dynamic light scattering known as ‘photon correlation spectroscopy’ (PCS), the detector is fixed at a certain angle θ, and the scattered intensity is measured over time, I(t). Because colloidal particles in a fluid diffuse over time, there will be fluctuations in the intensity of the scattered light such that I varies with t. Thus at a t = 0, the scattered intensity I(0) will be slightly different than at a later time t. An autocorrelation function, g2, is a measure of these fluctuations over time (Maret and Wolf 1987):

g 2 (t ) =

I (0) I (t ) I (0) 2

(2.6)

where the < > brackets indicate an ensemble average over time. Fig. 2.11 illustrates the physical meaning of the autocorrelation function and gives a typical example. When g2(t) is found in an experiment on a dilute colloidal dispersion, it follows an exponential dependence on time: g2(t) = g0 exp(–t/τΑ), where τΑ is called the ‘autocorrelation time’. It tells us how long it takes for g2(t) to decay to 1/e of its value at time 0. τA is useful because it is related to the parameter of interest, the Brownian diffusion coefficient, D0. PCS makes use of the autocorrelation function to extract D0 and hence to determine the particle size. There are two reasons why PCS cannot be used in the usual way for the study of latex film formation. First, it applies when the incoming photons are scattered only once. To achieve this condition a short optical path is created by using a dilute dispersion. Concentrated latex dispersions cause multiple light scattering, and PCS is not valid. A second reason stems from the fact that to get good results, g2(t) must be measured over sufficiently long times such that t is about a thousand

46

2 Established and Emerging Techniques of Studying Latex Film Formation

times greater than τA. In the later stages of drying, the latex concentration is high, so that D0 is small and τA is large. A probe of the drying of latex films must be able to study multiple photon scattering and must be relatively fast. The study of multiple scattering is enabled by diffusing wave spectroscopy (DWS). The technique can be made faster by averaging over a series of positions in space at one time rather than averaging over time at one position. The name ‘diffusing wave spectroscopy’ was proposed by Pine et al. (1988) who wrote out g2 for the case of multiple scattering. They considered the case of light transmitted through a sample as well as the case of light backscattered from a sample. Latex films are usually quite turbid, and so the backscattering geometry is more suitable. For this geometry, when the film thickness is relatively large, Pine et al. derived an expression for g2(t) in the limit where the thickness of the scattering slab is far greater than the mean free path of the diffusing photons:  −2π nα g 2 (t ) ∝ exp  1   λ r 2 (t ) 2 

    

(2.7)

Variables are as defined earlier; n represents the refractive index of the medium (e.g., the latex serum) and α ≈ 2 (Pine et al. 1988). Thus, measurements from multiple light scattering give us g2(t) and from that the mean-squared displacement of particles can be found. With a measurement of particle displacement, and applying Eqs. (2.5) and (2.6), information about the other unknown, such as local viscosity, particle size, or the effects of colloidal interactions, is gained. The first two published reports of applying DWS to the drying of waterborne colloidal films did not appear until 17 years after the technique’s invention. In a major advance, Breugem et al. (2005) used the Brownian diffusion of colloidal particles as a probe of the storage modulus, Ep, and the viscosity of the film, η, and how these parameters evolved with ongoing water evaporation. Both transmitted and backscattered light was used. In these experiments, g2(t) was measured experimentally and used to extract . Then, in turn, the Laplace transform was used in the generalised Stokes-Einstein equation to find the Laplace-transformed viscoelastic modulus (containing Ep and η). Near the same time as the work of Breugem et al., a different research group (Narita et al. 2004) employed multispeckle DWS to examine the dynamics of latex particles (both deformable and non-deformable) through the drying process by measuring the characteristic time of relaxation. Their approach was significantly different than that of Breugem et al. They recorded the scattered light using a CCD camera so that each pixel in the image recorded a scattering event in a technique described thoroughly by Viasnoff et al. (2002). They then averaged over an ensemble of positions (represented by each point on the detector) rather than averaging over time. They specifically measured the characteristic time of the α

2.1 Techniques to Study Latex in the Presence of Water (Wet and Damp Films)

47

relaxation, which represents the collective rearrangement of particles in a colloidal gel (i.e., when the particles have packed together). DWS has been combined with MR profiling to provide information on the particle motion in a drying film along with simultaneous information on the distribution of water (König et al. 2008). Fig. 2.12 shows the experimental set-up. A typical autocorrelation function in these experiments, which is presented in Fig. 2.11, was fit to a stretched exponential function of the form:

  t β  g 2 (t ) − 1 = A exp −      τ  

(2.8)

where the exponent β provides qualitative information on the dynamical heterogeneity (coexistence of fast and slow dynamics). A value of the amplitude, A, that is far less than unity provides evidence for the presence of static scatterers. It drops sharply when the particles are elastically coupled together in a solid-like form (König et al. 2008).

I(t)

I(t)

g2(τ')−1

0.50

Time

Time 0.25

0.00

1E-5 1E-4 1E-3 0.01

0.1

τ' [s]

Fig. 2.11 An autocorrelation function (g2(τ)-1)obtained from scattering from a latex film. The light intensity fluctuates over time. On the left side, there is a large overlap of the intensity signal with itself when the time is shifted by a small time, τ. On the right, the time shift is greater, and there is less overlap. The autocorrelation function is related to the amount of overlap at various τ values. Mathematically the autocorrelation function is defined as ∞

g 2 (τ ) =

∫ I (t ) I (t + τ )dt 0

∞

∫I

2

(t ) dt

0

such that g2(0) = 1 and it decays monotonically with τ (equivalent to Eq. (2.6)). (Data courtesy of Alexander König and Diethelm Johannsmann, Clausthal University of Technology)

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2 Established and Emerging Techniques of Studying Latex Film Formation

Fig. 2.12 Experimental set-up for the combined use of GARField NMR profiling and diffusing wave spectroscopy (DWS). The light in the laser beam is spread out and then is scattered from the latex film. A photomultiplier tube detects the signal before the light is passed into an autocorrelator. (Drawing courtesy of Alexander König, Clausthal University of Technology)

Prior to the development of DWS for the study of film formation, a closely related technique known as ‘dynamic speckle interferometry’ was reported (Amalvy et al. 2001). Speckle refers to the pattern of light spots that are seen when reflecting an intense coherent light source on a dynamic surface. Speckle is caused by the interference of dephased coherent light after reflecting from a surface having roughness and heterogeneities in its refractive index. In a system in which there is particulate motion, such as a wet latex film, the speckle pattern will fluctuate over time in a dynamic speckle pattern. In an experiment, a laser is used to create a dynamic speckle pattern on a wet film. A CCD camera is employed to capture 512 successive images of the speckle pattern at short time intervals (e.g., 0.08 s). Each image consists of 512 x 512 pixels. The temporal history of the speckle pattern is then presented in an image made up of a column from each of the 512 successive images. Analysis of the image enables the calculation of a co-occurrence matrix and the moment of inertia of the matrix (Almavy et al. 2001, Faccia et al. 2009). The moments of inertia have been shown to correlate with the amount of water in a latex film. A slowdown of water loss rate in a second stage of drying is observed and is comparable to what is found with gravimetric analysis. There have been recent technique developments to create speckle interferometry images of surfaces to visualise heterogeneities (Faccia et al. 2009). An image is created in which the grey scale indicates the ‘activity’, which is related to the movement of scatterers and hence the extent of drying. Simultaneous monitoring of

2.1 Techniques to Study Latex in the Presence of Water (Wet and Damp Films)

49

zones with differing amounts of water – from fully wet to partially dry – is possible. This non-invasive method is particularly well suited to probe lateral drying fronts and particle packing fronts in latex films (see Fig. 3.9 and Section 3.5). An instrument using speckle analysis has already been commercialised (Brun et al. 2006, 2008). Using a proprietary data processing technique, the instrument provides advanced analysis of the speckle pattern through all stages of drying. The analysis does not find an autocorrelation time, τA, but instead it measures the speckle rate, s, which is the inverse of a characteristic time. As the latex dries, particle motion slows down as a result of particle crowding. This effect is seen in the dependence of D0 on the solids volume fraction, φ. When the particles create a gel, one would expect an abrupt slowing down of particle dynamics and for s to decrease. Experimentally for a latex, s is seen to decrease by up to five orders of magnitude as the characteristic time goes from 0.1 s to 10,000 s. Research is in progress to correlate the speckle rate with the physical state of a latex film and the stages of film formation.

2.1.3.3 Evanescent Dynamic Light Scattering Photon correlation spectroscopy may also be performed by using an evanescent wave rather than through directly transmitted light (Lan et al. 1986). In this experiment, light is brought in through a prism to reflect from the interface with a cell containing a concentrated colloidal dispersion. As the refractive index of the prism is greater than the wet latex film, the light is totally reflected from the interface, and the film is probed with an evanescent wave. Autocorrelation spectra can be obtained and used to study the Brownian motion of latex particles near the interface with the prism. Whereas the first evanescent light scattering experiments (Lan et al. 1986) were performed on latex dispersions in a closed cell, Schmidt et al. (1997) extended the technique to a latex undergoing film formation. They cast a latex film on a prism and brought laser light through the prism to reflect from the interface with the film. Their preliminary work used evanescent dynamic light scattering to observe the slowing down of particle motion brought on by the increase of solids content during drying. As with DWS, the technique measures the autocorrelation function as it evolves with the film state.

2.1.3.4 Ultramicroscopy and Confocal Microscopy The rather obvious obstacle in using optical microscopy to study latex film formation is that standard optical microscopes do not have sufficient resolving power to provide useful information on particles, sometimes with sizes less than 100 nm. The reason for the poor resolution stems from the so-called ‘diffraction limit’ that sets the resolution of optical microscopy at about λ/2 (Pohl and Van den Eynde 1984).

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2 Established and Emerging Techniques of Studying Latex Film Formation

Two different types of optical microscopy have been developed to overcome this limit. One is known as ‘ultramicroscopy’, and it detects the scattered light from moving particles. The other type is usually known as ‘scanning near field optical microscopy’ (SNOM), and it beats the diffraction limit by bringing the light source close to the sample surface. SNOM will be discussed in Section 2.2.4, as it is usually applied to dry films. A rather old technique used for some of the early 20th century studies of Brownian motion, ultramicroscopy has been ‘rediscovered’ and applied to the study of latex film formation (Keslarek and Galembeck 2003). A direct image of sub-λ individual particles dispersed in liquid is not created. Instead, the scattered light from the particles is detected, providing information on particle motion and clustering but not yielding information on the structure of individual particles. Experimentally, observations are carried out in the dark-field of an optical microscope with illumination at 90° from the optical axis. Light is scattered by the particles and collected in the objective lens. The light scattering is seen as flashes of light in the dark field. Ultramicroscopy has the potential to be particularly useful when information is required on particle dynamics. Although most dispersions used for coatings and adhesives have particles that are too small for optical microscopy, fundamental scientific studies use larger particles with success. Confocal laser scanning microscopy (typically with λ = 633 or 488 nm) can be used for relatively large latex particles (R > 200 nm). For instance, the technique has been used to show the formation of planar arrays of large particles (R ≈ 650 nm) in a density matched medium under the application of shear at a constant rate (Derks et al. 2004). The tracking of colloidal particles in video analysis is made much easier when they contain a fluorescent core and a non-fluorescent shell (Dullens et al. 2004). Confocal microscopy of this type of core-shell particle composed of poly(methyl methacrylate) prepared by dispersion polymerisation can provide insight into the latex drying process. A twodimensional radial distribution function, which reveals the long range ordering in the packing in the film plane, has been obtained for the surface of a dried layer (Dullens et al. 2003) and along a glass wall for a wet layer (Dullens et al. 2004).

2.1.3.5 Optical Techniques: Transmission Spectrophotometry and Ellipsometry The experimental arrangement for measurements of optical transmission is straightforward. A latex film is cast on a transparent substrate. A light beam of a known wavelength, λ, and with an intensity of I0 shines on the film perpendicular to the surface. The intensity of the transmitted light, I, is recorded so that the fraction transmitted, Tf, can be determined:

Tf =

I I0

(2.9)

2.1 Techniques to Study Latex in the Presence of Water (Wet and Damp Films)

51

Measurements are made over a range of λ, typically extending from the UV to the near infrared. A similar approach is to relate the optical transmission through a wet latex dispersion directly to the latex particle radius R and particle volume fraction, φ, via:

ln T f = −

32π 4 R3φ d p  m2 − 1   2  λ4 m + 2

2

(2.10)

where dp is the path-length through which the light is transmitted (i.e., sample thickness) and m is the ratio of the refractive index of the polymer to the refractive index of the solvent (e.g., the latex serum) (van Tent and te Nijenhuis 1992b). In turn, some of these parameters can be related to the particle/particle spacing, ep, by the relation:

φ=

πR 3 C1 ( R +

(2.11)

ep 2

)3

where C1 is a geometric constant that depends on the particle arrangement in space. Hence, measurements of Tf over time can be used to deduce particle spacing during the drying process, provided that R and dp are known. It is of particular interest to know how the particle spacing and geometric arrangement evolve as a film dries. This information is provided in the signature of ‘interparticle interference’. It is a fortunate coincidence that wavelengths of visible light cover the relevant range of distances to probe the interparticle distances in concentrated polymer colloids. A minimum in the transmission spectra will arise from interparticle interference at a wavelength of λmin. If the particles with a refractive index of np are arranged into a face-centred cubic (or hexagonal closepacked) unit of height hunit, then λmin is simply hunitnp (van Tent and te Nijenhuis 1992b). Strong differences in the interparticle interference can be observed for latices at temperatures above, below and near their MFFT (van Tent and te Nijenhuis 2000). The interference diminishes at high temperatures where particles deform to fill all available void space. Once the film has almost completely dried, the amount of residual water can be detected using a similar method. For isolated spheres of radius, z, in a continuous medium, Rayleigh theory states that lnTf varies with z6 (van Tent and te Nijenhuis 1992). In the later stages of drying, interparticle pockets of water in a latex film can be adequately modelled as spherical. In this case, the continuous medium is the polymer phase and not the serum phase. Information on void closure can thereby be obtained from measurements of optical transmission. The Clausius-Mossotti equation tells us that the refractive index increases with the density of a substance. For instance, if there is a phase change, the denser phase will have a higher refractive index. Therefore, measurements of refractive index can be used to estimate the volume fraction of air voids in a film. This

52

2 Established and Emerging Techniques of Studying Latex Film Formation

technique is best applied to dry films, when there is less ambiguity in interpretation of the data. Tzitzinou et al. (2000) have shown how measurements of refractive index over time can be performed using ellipsometry. The results were interpreted as the closing of air voids as particles deform to fill space. Ellipsometry uses polarised light that is reflected from a surface at a known angle of incidence. The change in the state of the polarisation is characterised by the amplitude and phase of the components of the light in the plane of the reflection and perpendicular to the plane. Ellipsometry determines the change in the polarisation state upon reflection, and the data analysis is used to extract useful parameters, such as the complex refractive index. Ellipsometry is applicable to all stages of latex film formation, starting from a freshly cast film. The technique is particularly sensitive to the creation of air voids in latex films in which the water level drops below the film surface (Keddie et al. 1995). In modelling ellipsometry data, a rough surface can be imagined to contain air voids. Such a surface can be described as having a refractive index, n, that is midway between the ambient air (n = 1) and the bulk material (for a polymer, n is typically 1.5 – 1.6). Tzitzinou et al. (2000) showed that ellipsometry is sensitive to the flattening of latex surfaces as particles deform and flow.

2.1.4 Profiling Water and Particles with Spectroscopies During the drying of uniform films on large areas, the direction normal to the film is of greatest interest. Several different spectroscopies have been adapted and improved to provide profiles of water and/or polymer content in the vertical direction with sufficient resolution. Techniques of infrared and Raman spectroscopy have been well advanced to provide chemical and structural information as a function of position within dynamic polymer systems (Koenig and Bobiak 2007). Infrared radiation is absorbed by condensed matter at specific frequencies that correspond to the energies of particular molecular vibrations, given by hc/λ, where h is Planck’s constant and c is the speed of light. Each bond and type of vibration has a characteristic frequency. The molecular groups in large molecules can be identified through determination of its IR absorption spectra. In Raman spectroscopy, light of a single wavelength is inelastically scattered from the sample with a shift in frequency (and energy) that is dependent on the particular molecular group.

2.1.4.1 Confocal Raman Microscopy In the confocal arrangement, laser light is focused on a specified depth below the surface to provide local information. The optics is designed so that only light from the focal plane is collected in an image. The focus can be moved stepwise from the substrate interface to the air interface. The technique can be properly quantita-

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53

tive, because the Raman signal is linearly proportional to the concentration for the particular Raman-active species. The technique was first established as a way of providing information on film composition as a function of depth from the surface. It thus provided insight into the transport and distribution of surfactants in latex films in what is sometimes called a ‘post-mortem analysis’, i.e., after drying was completed rather than as it occurred (Belaroui et al. 2000). Belaroui et al. (2001) provided a clear demonstration of the capability of the technique for determining the water distribution in the vertical direction as latex films dried. For water depth profiling, the water peak at 3500 cm–1 can be followed and compared to a peak from the polymer phase to determine the concentration. A resolution in the vertical direction of 25 µm has been reported (Belaroui et al. 2001), which is sufficient for profiling films that are a few hundred µm thick. A potential problem in the technique is fluorescence from chemical impurities or from the substrate. A recent development has been inverse-micro-Raman-spectroscopy, in which a Raman spectrometer is coupled to an inverse microscope (Ludwig et al. 2007). Laser light is brought into the specimen through a transparent plate that serves as the substrate after being focused by an objective lens (Fig. 2.13a). As the light travels through a wet latex film from the bottom, there is a decrease in the Raman signal intensity, which is attributed to the effects of elastic light scattering. The loss in intensity is not a function of the wavenumber (i.e., the frequency shift) but decreases uniformly across the entire spectrum (Fig. 2.13b). Consequently, the ratio of the polymer to water peak intensities can be used to measure the water content. Measurements of water concentration can be made with inverse micro-Raman spectroscopy both laterally in the plane of the film and as a function of the direction normal to the film. A time resolution of about 1 second and an optical resolution of 2–3 µm have been reported. Inverse-micro-Raman spectroscopy can therefore measure the progression of a drying front from the edge of a latex film. It can also determine the ingress of water into a partially dry film in a redispersion experiment in which a wet latex drop is applied to a partially dry film (Ludwig et al. 2007).

2.1.4.2 IR Microscopy In IR microscopy, a focused beam of infrared radiation is transmitted through, or reflected from, a layer. A beam spot size of 50 µm can be achieved. Guigner et al. (2001) obtained water concentrations over distances of several mm. In their experimental set-up, a rather unusual sample configuration was used. A 25 µm thick layer was sandwiched in a cell and evaporation was allowed only from one side, rather than from the ‘face’ of the film. Monitoring the change in intensity of a water absorption band (such as the –OH deformation band at 1645 cm–1) provides a quantitative measure of water content.

54

2 Established and Emerging Techniques of Studying Latex Film Formation

Fig. 2.13 a Experimental set-up for inverse confocal microscopy experiment. The light comes up through the substrate (glass plate) and is focused at a desired lateral position. b Raman spectra obtained at three different positions within a wet latex film. Peaks for the polymer phase and the water phase are both observed. The ratio of the peaks remains the same, regardless of the position, which is what is expected if there is a uniform lateral composition. (Reprinted with permission from Ludwig et al. (2007))

2.1.4.3 NMR Profiling and Imaging At the heart of nuclear magnetic resonance (NMR) techniques, is the fact that spin-½ nuclei behave like tiny bar magnets and will align in a magnetic field in one of two energy states, with the distribution between the states depending on the temperature. If a pulse of electromagnetic radiation with the correct energy (in the radio-frequency region of the spectrum) strikes the nuclei, they can be tipped from the alignment direction. The nuclei precess along the direction of the field, just as a child’s toy top precesses around the direction of gravity, at the frequency of the RF pulse. As they relax from an excited state, the nuclei emit energy in the RF range, which is detected as an NMR signal. NMR techniques rely on the principle that the resonant angular frequency, ω, of a spin-½ nucleus (e.g., 1H or 13C) is proportional to the local magnetic field strength, B0. The two quantities are related through the magnetogyric ratio, γ, as expressed by a simple equation:

ω = γB0.

(2.12)

The value of the magnetogyric ratio, γ, for 1H is given as γ/2π = 42.58 MHz T–1 (Hore 1995). The frequency that satisfies (2.12) corresponds to electromagnetic radiation in the radiofrequency (MHz) range. In NMR spectroscopy, there is a small shift in ω (in parts per million) as a result of atomic nuclei feeling slightly different B0 in different chemical environments because of the shielding effect of electron clouds. Solid state NMR 1H spectroscopy can provide information on the local environment of water in a latex film: whether free in the serum phase, in the

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55

surfactant layer at the particle/water interfaces, or dissolved in a hydrophilic polymer particle, such as poly(vinyl acetate) (Rottstegge et al. 2000). When a system of nuclei is placed in a magnetic field gradient, defined as Gy = dB/dy, then Eq. (2.12) must be modified. The expression for the resonant frequency then becomes

ω(y) = γ(B0 + Gy⋅y)

(2.13)

At each position along the gradient direction, there will be a different ω as illustrated in Fig. 2.14. Hence, the magnetic field gradient encodes spatial position through the resonant frequency. This is the fundamental principle at the heart of magnetic resonance imaging or MRI. Techniques of MRI are commonly employed in hospitals for medical diagnosis and follow up to treatment. In recognition of the medical importance of the technique, the 2003 Nobel Prize in Physiology or Medicine was awarded to Paul Lauterbur and Sir Peter Mansfield for the development of MRI. In MRI scanners, the gradient in the magnetic field is created within a superconducting magnetic using electromagnetic gradient coils. The use of coils enables the gradient to be turned on and off and to be varied in strength. Two-dimensional MR images can be used to find the relative distribution of water laterally in drying latex films (Salamanca et al. 2001), but it lacks sufficient resolution (ca. 25 µm) to provide much information about water in the vertical direction in films thinner than a few hundred µm. Nevertheless, MR imaging has sufficient resolution to yield valuable information on the lateral flow of water in drying latex and emulsion films (Ciampi et al. 2000) and enabled the successful validation of drying models (Salamanca et al. 2001). Furthermore, MRI can identify heterogeneous drying, with a polymeric ‘skin’ layer over a more dilute dispersion, in latex layers that are several mm thick with an in-plane resolution of ca. 60 µm (Rottstegge et al. 2003). Standard MR images can be considered to be a map of the density of the nuclear spin of the particular nuclei, e.g., 1H, and hence are ideal for identifying heterogeneities in water distribution. Images can also be weighted by the spin-spin relaxation time, T2, which is correlated to the local molecular mobility. T2weighted images can be used to identify reduced polymer mobility in the skin layers of drying latex films (Rottstegge et al. 2003).

Stray Field Imaging Techniques To obtain high resolution images, strong and stable field gradients are required. When imaging in a single direction, an attractive approach to achieving such a field gradient is to do the experiment in the fringe or ‘stray’ field of a superconducting magnet. At distances close to the magnet, the strength of the magnetic field decreases with increasing distance, hence providing a stable, large G in a field of high strength. ‘Stray-field imaging’ (StraFI) (Newling and McDonald 1998), as the approach is called, has grown in popularity over the past few

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2 Established and Emerging Techniques of Studying Latex Film Formation

decades. It has been applied to several problems in condensed matter and engineering materials, such as water transport in cements or solvent ingress into polymers (Mitchell et al. 2006). In these applications, information is provided over distances of up to a few mm. The technique is suitable for the determination of concentration profiles in the vertical direction in dispersions and emulsions undergoing sedimentation or creaming (Newling et al. 1996). StraFI is a relatively expensive technique because it requires a superconducting magnet and the associated consumption of costly cryogens. Usually restricted to small sample sizes, the profiling resolution can be detrimentally affected by the meniscus of wet films. Although the resolution of stray field imaging is better than that found in two and three-dimensional imaging techniques, it is not acceptable for layers thinner than a few hundred µm. Furthermore, as explained in the next paragraph, the parallel arrangement of G with respect to the main field Bo is not optimum as it precludes the use of a planar surface coil to create the RF field pulse. Recognising these various limitations of conventional stray-field NMR for the profiling of coatings, Glover et al. (1999) specially designed a magnet for this application. The magnet is called ‘GARField’, which stands for ‘Gradient At Right-angles to the Field’. In imaging the stray field of a high-field, vertical-bore superconducting magnet, the static field with strength Bo is oriented parallel to the magnetic field gradient, Gy, in the vertical direction. Therefore B1 from the RF coil must be parallel to the sample plane. In the GARField geometry, on the other hand, B0 is parallel to the sample plane, so that B1 is perpendicular to it. The sample can thereby be positioned against a surface coil that produces the RF pulse, and greater sensitivity can be achieved. Gy is perpendicular to B0 – thus explaining the name of the technique. In order to image a thin slice in a film or coating, the B0 must be highly uniform in the plane of the film. Hence G must be highly homogeneous. In the GARField design, the gradient in the magnetic field is produced by the introduction of a taper in the pole-pieces on a pair of permanent magnets (made from NdFeB or similar material). The required shape to create the desired gradient field was found analytically using a scalar potential method to solve the Laplace equation (Glover et al. 1999). The design of the GARField magnet is shown in Fig. 2.15. There is a curvature in the field of less than 5 µm over a 5 mm x 5 mm area. In the original design, samples are placed in a permanent magnetic field strength of B0 = 0.7 T, and a magnetic field gradient strength of G = 17.5 T m–1 was achieved. A newer magnet design has pole pieces shaped to provide two different magnetic field gradients (G/Bo = 16.7 m–1 and G/Bo = 33.3 m–1) using a single pair of permanent magnets providing the same static field (Bennet et al. 2003). The design has since been modified to accommodate samples with a greater area. In the GARField design of Erich et al. (2005, 2005b), shaped pole pieces are mounted on an electromagnet system, rather than on a permanent magnet. A constant magnetic field of B0 = 1.4 T and a gradient of Gy of 34 T/m are achieved. The GARField technique is closely related to the NMR MOUSE (Eidmann et al. 1996), which provides one-dimensional depth profiles into a sample by pressing a radiofrequency coil up against a free surface.

2.1 Techniques to Study Latex in the Presence of Water (Wet and Damp Films)

(a)

57

(b)

B

ω γ

Gy

B0

B

y

(c)

ω

y Fig. 2.14 The basic principle of magnetic resonance profiling. a The resonant frequency, ω (also known as the ‘Larmor frequency’) is related to the magnetic field strength through γ. b When a magnetic field gradient, Gy, is applied, the magnetic field varies with position. c The position is thereby encoded in the frequency, as is stated in Eq. (2.13).

(a)

B1

y

Gy

Latex film

Curved pole piece

Curved pole piece

B0

RF coil

Permanent magnets

(b)

Fig. 2.15 a Illustration of the curved pole pieces in a GARField magnet, which create a magnetic field gradient, Gy, in the vertical direction. The latex film rests on a radiofrequency coil in the gradient field between the pole pieces of the magnets. b A photograph of the pole pieces in a supporting frame, viewed from above. (Courtesy of the University of Surrey)

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2 Established and Emerging Techniques of Studying Latex Film Formation

GARField Data Interpretation Experimental details and a discussion of the factors that influence the resolution of GARField profiles are found in Appendix B. Fig. 2.16 relates three different types of vertical water distribution to the resulting GARField profile. In a profile, the NMR signal intensity is plotted as a function of the vertical position (height) within the film. The intensity is proportional to the density of the mobile 1H. The 1 H in glassy polymers is not sufficiently mobile to yield an NMR signal in this experiment. Hence, the profiles are only sensitive to water in a ‘hard’ latex film. A signal is obtained, however, from viscous or rubbery polymers, such as in adhesives and alkyd coatings, which are not crosslinked. The signal is then the sum of contributions from the water and polymer. The water content can be deduced by subtracting out the contribution to the signal from the polymer phase. Drying uniformity in waterborne coatings in the vertical direction has been probed with the GARField magnet. A typical result is presented in Fig. 2.17, where the changes over time of the film thickness and water content are observed. Water profiles can be used to test models of drying (Gorce et al. 2002, Ekanayake et al. 2009) and to surmise the extent and mechanisms of particle deformation (Mallégol et al. 2001). The penetration of water from a latex film into a porous substrate can also be examined (Bennet et al. 2003). Low water content near latex film surfaces has confirmed the process of ‘skin formation’ during drying (Mallégol et al. 2006). Reduced polymer mobility resulting from crosslinking reactions can be followed as a function of depth into waterborne films (Wallin et al. 2000) through measurements of the T2 spin-spin relaxation time as a function of depth in a film. (Measurements T2 are obtained from an exponential fit to multi-echo profiles.) Drying uniformity can be determined simultaneously with studies of crosslinking.

2.1.5 Probe Techniques for the Aqueous Environment A new approach to the study of latex drying, as proposed by Baumgart et al. (2000), is to use a variety of small molecules to probe the aqueous phase and interfacial regions throughout the process. There are three main types of probe: (1) spin probe molecules (with unpaired electrons) for electron paramagnetic resonance (EPR); (2) photochromic dyes for forced Rayleigh scattering (FRS) and (3) donor/acceptor fluorescent dye molecules for non-radiative energy transfer (NRET) experiments. The value of probe molecules is that they are inside the wet film and yield insight into the local environment, which is continuously changing as water content decreases and particles come closer together. Each of these noninvasive approaches will be considered separately, although their impact is potentially greatest when used in parallel.

2.1 Techniques to Study Latex in the Presence of Water (Wet and Damp Films)

59

Fig. 2.16 Interpretation of GARField NMR profiles. The signal is proportional to the density of mobile 1H. The horizontal axis shows the vertical position in the layer. a If the particle distribution is uniform, then the profiles are square. When water evaporates, the thickness decreases and the water concentration decreases. b If there some particle accumulation near the film surface, then the profile slopes downward. c If the particles at the film surface coalesce to create a skin layer with water underneath, then there will be a step in the profile. (It is assumed here that there is a signal from the 1H in the polymer.)

2 Established and Emerging Techniques of Studying Latex Film Formation

Relative signal intensity Relative intensity

60

0.5 0.4

Time

0.3 0.2 0.1 0.0 -50

0

50

100 150 Depth (µm)

200

250

Height (µm)

Fig. 2.17 A series of GARField MR profiles obtained over time from a drying latex film. The top of the film is represented at the greater heights. The signal intensity is proportional to the water concentration. With increasing drying time, each successive profile indicates a lower film thickness and a lower water concentration.

EPR requires the introduction of a spin probe, which is a molecule with an unpaired electron. Nearly spherical molecules are often used, such as TEMPO (2,2,6,6-tetramethylpiperidine-1-oxyl), which has an unpaired electron in its nitrogen atom. In wet latex, probes are introduced easily as small molecules or surfactant probes in the serum phase at concentrations of 1 mmol L–1 or less (Cramer et al. 2002a). The interaction of the probe with its environment is found by sweeping an external magnetic field while continuously irradiating with a fixed microwave frequency, so as to induce transitions of the electron spin (Weil et al. 1994). EPR of drying latex has provided information on the local viscosity in the vicinity of ionic and polar probes as a function of water content. It also measures the mobility of molecular or surfactant probes in the changing local environment within the latex. The orientation and position of surfactants in relation to the particles and serum can also be determined. Micellisation and surfactant aggregation can be followed (Cramer et al. 2002b). FRS is ideal for monitoring slow diffusion processes, ranging between 10–13 and 10–21 m2s–1, and hence is well suited for studying the later stages of latex drying (Veniaminov et al. 2002). The relative hydrophobicity of the dye determines what is probed in an experiment. A hydrophobic dye is sensitive to the polymer and polymer-water interface. A hydrophilic dye can probe the serum phase and surfactant clusters but also can be partitioned in the polymer phase and interfacial regions (Veniaminov et al. 2003). Thus, depending on the probe, it is possible to study topics ranging from the continuity of the serum phase and water loss from various components to the possible break-up of particle boundaries and the onset of coalescence.

2.2 Techniques to Study Particle Packing and Deformation in Dry Films

61

The main concept of FRS is to produce a period structure, or grating, in a material using dye molecules and then to follow the loss of this grating as dye diffusion proceeds (Eichler et al. 1986). Diffraction of light from the grating is sensitive to the spatial modulation of the complex refractive index that is created by the dye molecules. The relaxation of the diffraction over time provides a way to determine the tracer diffusion coefficient of the dye. The spacing of the lines in the grating can be adjusted to measure diffusion over various length scales and hence to characterize the size of heterogeneities (Veniaminov et al. 2002). NRET, known also as FRET (fluorescence resonance energy transfer), is well established as a means of probing the interdiffusion of polymer molecules between latex particles. Its principle of operation will be explained in Section 2.4. In the work of Baumgart et al. (2000), the aim of NRET was to determine if, and to what extent, the hydrophilic interface (or membrane) of latex particles can restrict the transport of tracer molecules. Hence, the tracer molecules can be used to probe the integrity of the particle interfaces. In a typical NRET experiment, one phase contains a donor dye, such as phenanthrene, and the other phase contains an acceptor dye, such as perylene or anthracene. In latex experiments, particles containing donor dyes are blended with particles containing acceptor molecules. The steady-state fluorescent intensity of the acceptor molecules, IA, is affected by their distance from the donor molecules. As their separation decreases, such as when the membranes separating the particles break down, IA increases in a known way. The technique has been used to study the early stages of latex film formation when particles first make contact in a drying film (Turshatov et al. 2008). However, it has primarily been used to study the interdiffusion of polymer chains across particle boundaries in dry films, and it will be considered in detail in Section 2.4.

2.2 Techniques to Study Particle Packing and Deformation in Dry Films Many of the techniques that yield information on the particle distribution in wet films can be extended to the case where particles start packing together and deforming. SANS, SAXS and optical transmission all fall in this category. There are other techniques that cannot, for various reasons, be applied to films in the wet state. These will now be considered.

2.2.1 Scanning Probe Microscopies Scanning probe microscopies consist of several techniques, each with a fundamental strategy in common. An ultra sharp probe tip on the end of the cantilever is brought in close enough proximity with a surface to be able to feel attractive and

62

2 Established and Emerging Techniques of Studying Latex Film Formation

repulsive forces. Examples of cantilevers and tips are shown in Fig. 2.18. The tips can have a radius of curvature as low as 10 nm. The various microscopies can then be classified depending on the type of force that is detected: molecular, electrostatic charge, magnetic, shear, etc. Although there is at least one example of scanning probe microscopy on a wet latex surface (Butt et al. 1994) and numerous examples of microscopy in liquids, it is usually applied to dry latex surfaces or to solid surfaces immersed in liquids. (a)

Tip

(b)

(c)

Cantilever

Fig. 2.18 SEM images of three different AFM cantilevers. a A cantilever with a triangular end and a sharp conical tip that is angled away from the end of the cantilever. Scale bar is 40 µm. b A rectangular cantilever with a conical tip that is normal to the cantilever. Scale bar is 20 µm. c A cantilever with a triangular end and a pyramidal tip. Scale bar is 15 µm. (Images courtesy of Dr. Chun-Hong Lei, University of Surrey)

2.2.1.1 Contact Atomic Force Microscopy (AFM) Just six years after the invention of the atomic force microscope was reported (Binnig et al. 1986), it was used to look at close-packed arrays of latex particles (Wang et al. 1992). In the first mode of AFM to be developed, known as the ‘contact mode’, the tip on the cantilever is brought to the surface where it feels a repulsive force and is deflected. The tip is moved across the surface, usually by the x-y motion of a piezoelectric crystal on which the sample sits. A laser light beam that is reflected from the top side of the cantilever tracks the cantilever deflection in a position-sensitive detector. In the constant force mode of operation, a feedback loop is used to adjust the vertical position of the sample while scanning in order to maintain a constant deflection of the cantilever, and hence a constant force. A record of the movements in the vertical direction is used to build a topographic image of the surface (Wang et al. 1992). When AFM is operated in the constant force mode, a relatively weak cantilever is used to provide good sensitivity. The spring constant, which characterises the stiffness, is as low as 0.02 N/m, and the imparted force is on the order of 10 nN (Butt and Kuropka 1995). In the 1990s, contact AFM provided many fundamental insights into film structure, including the effects of surfactant on particle packing (Juhué and Lang 1994a), the flattening of particles during annealing (Goudy et al. 1995, Goh et al. 1993), the role of capillary forces in particle deformation (Lin and Meier 1995), and the exudation of surfactant (Juhué et al. 1995, Tzitzinou et al. 1999). In these early studies, the radius of the AFM tip was as large as 40 nm and the angle of tip

2.2 Techniques to Study Particle Packing and Deformation in Dry Films

63

as large as 110º (Lin and Meier 1995). Hence, there were physical limitations to the tip being able to sense the bottom of the valleys between convex particles (Butt and Gerharz 1995). Researchers devised methods to measure the tip geometry (Odin et al. 1994) and to compensate for its effects on images through deconvolution methods (Markiewicz and Goh 1995). Now, ultra sharp tips are commercially available, and so tip deconvolution is not always needed. When the patch of the reflected light beam is perpendicular to the direction of the scan, the tip deflection is an indication mainly of surface topography. However, when the light path is in the scan direction, the cantilever deflection has a contribution from variations in friction between the tip and sample. This enables the creation of maps of the friction variations across a latex surface as a means of distinguishing material components (Butt et al. 1994). AFM is an attractive technique because there is no need for sample preparation and it operates in air. As demonstrated in an early study of latex (Butt et al. 1994), contact AFM with a constant force suffers from one limitation: even though the force of the tip acting on the surface is small, it is still sufficient to damage the surface or to scrape away molecular layers of surfactant.

2.2.1.2 Intermittent Contact AFM and Phase Imaging Starting in the mid 1990s, another mode of AFM began to be used to determine latex film structure. Called ‘intermittent contact’ or by the trade name of ‘TappingModeTM’, this mode is potentially less damaging to soft surfaces, such as latex (Sommer et al. 1995, Patel et al. 1996). In intermittent contact AFM, the tip and the cantilever are made from the same material, usually silicon. The cantilever is driven to oscillate near its natural resonant frequency (in the kHz range) by driver electronics. When it is brought into close proximity to a surface, the tip makes intermittent contact at the bottom of the oscillation. Parameters needed to describe the tapping conditions are the ‘free’ amplitude Ao (corresponding to oscillation in air) and the set point amplitude Asp (corresponding to the amplitude when the tip is in contact with the sample surface) (Fig. 2.19a). A freely oscillating cantilever has a resonant frequency f0, at which the tapping amplitude will be at a maximum value of A0(f0). Imaging is performed at a frequency f set slightly lower than f0 such that A0(f) is typically 5% less than the peak value at A0(f0). It is important to note that the AFM tip does exert an average force, Fav, on the sample surface, and this force is sufficient to indent into it. The lower that the set point tapping amplitude Asp is in comparison to A0, the greater is the value of Fav. This important parameter is given in a semi-empirical equation (Yu et al. 2000) as:

Fav =

Asp  1k 1 −  A0 ( f ) β , 2 q  A0 ( f 0 ) 

(2.14)

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2 Established and Emerging Techniques of Studying Latex Film Formation

with the off-resonance parameter β given as

β=

A0 ( f ) , A0 ( f 0 )

(2.15)

and where q is the quality factor of the cantilever. Following from the above statements, β < 1 in all cases. Note the importance of the ratio of Asp to A0 in determining Fav, rather than the individual value of Asp alone. For a particular AFM tip, q is obtained from the ratio of f0 to the full bandwidth at 0.707 of the maximum amplitude, ∆f :

q=

f0 . ∆f

(2.16)

q is a function of the atmosphere around the cantilever. The narrowest resonance is obtained in vacuum, and q is thus higher in vacuum compared to air or a liquid. Fav can be calculated in experiments using Eqs. 2.14, 2.15 and 2.16.

Indentation Depth and Height Artefacts It is, however, important to realise that an AFM tip does indent to a depth of zind into a soft (low Tg) surface (Mallégol et al. 2001). When the tip of an oscillating cantilever with a set point amplitude of Asp is in contact with a soft polymer surface, the distance between the tip and sample, dsp, is always less than Asp. Then, zind is found from the difference between these two values:

zind = Asp – dsp .

(2.17)

This relationship between the three parameters is illustrated in Fig. 2.19b. A chief concern among AFM users is how to determine the ‘true’ structure of a soft surface. In providing topographic images of soft surfaces, the technique is prone to height artefacts that may be misleading to the viewer. For several years, it has been recognised that height images obtained with intermittent contact (also called the ‘tapping mode’) do not necessarily indicate true surface topography (Knoll et al. 2001). For instance, it has been shown that differences in the tip indentation depth into hard and soft phases on a smooth triblock copolymer surface create a false impression of surface topography (Kopp-Marsandon et al. 2000). That is, instead of representing the true surface topography, the image is a map of indentation depths. In a different study of a triblock copolymer, an inversion was observed between which block is considered to have the highest topography. This inversion was explained by specific tip-sample interactions dominating in different set point regimes (Wang et al. 2003). In similar work on

2.2 Techniques to Study Particle Packing and Deformation in Dry Films

65

blends of glassy and rubbery polymers (Raghavan et al. 2000), differences in the stiffness of the two domains caused a reversal in which phase appeared to have a greater height, when the tapping force was high. A second reversal was observed at lower tapping forces and was attributed to a switch over between attractive and repulsive regimes between the tip and sample. This type of artefact in colloidal films has not been well documented or described in the literature in comparison to the amount of attention devoted to diblock polymers and polymer blends. In soft latex films, the apparent roughness and topography is highly sensitive to the tapping force, as adjusted through the set point ratio (Mallégol et al. 2001). 2

(a)

Ao: free amplitude

2

Asp: setpoint amplitude

(b) 2Asp

dsp Soft surface

Asp

zind

Fig. 2.19 a Illustration of an AFM cantilever oscillating in air with a ‘free’ amplitude, Ao and in contact with a surface at a set point amplitude, Asp. b Diagram showing the inter-relationship of Asp, the tip-sample distance (dsp) and the indentation depth (zind). (Reprinted from Lei et al. (2008) with permission from Elsevier)

The choice of AFM parameters affects whether the latex particles in a film appear convex or concave (Lei et al. 2007). Fig. 2.20 shows images of the same latex film surface using two different set point ratios. Tip indentation into the film surface is variable, depending on the position, because the latex particles are surrounded by a surfactant-rich component. In Fig. 2.20a, a relatively high Asp/A0 ratio was used, such that Fav is low (1.3 nN), whereas Fig. 2.20b is the result of a relatively low Asp/A0 ratio, such that Fav is high (4.4 nN). In the height images, it is notable that particles appear to be concave under a low Fav but convex under the higher Fav. These observations stem from how the indentation force varies with depth in the latex particles in comparison to the surfactant-rich component.

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2 Established and Emerging Techniques of Studying Latex Film Formation

(a)

(b)

Fig. 2.20 Topographic images of the same latex film surface. a With a high set point ratio, the particles appear concave in shape. b With a low set point ratio, the particles appear to be convex in shape. (Reprinted from Lei et al. (2008) with permission from Elsevier)

Phase-Contrast Imaging In the intermittent contact mode of operation, a phase image may be obtained simultaneously with the height image. The phase image presents the phase lag, φ, of the photodiode output signal in relation to the driving piezoelectric signal as a function of position within the scan area. Changes in φ reflect variations in the energy dissipation, ED, of the cantilever as its tip moves laterally across a surface. φ is related mathematically to ED as (James et al. 2001, Anczykowski et al. 1999):

 f Asp  qE D + sin φ =  .   f 0 A0  πkAsp A0

(2.18)

During a scan, all of the parameters in Eq. (2.18) except ED are fixed, so the phase image provides a map of ED (Anczykowski et al. 1999). When the tip interacts with a highly viscous region on a surface, or a viscoelastic region in which the viscous component is dominant, more energy will be dissipated, and therefore ED and φ will be greater. When the tip interacts with a viscoelastic region in which the elastic component is dominant, it is however expected that less energy will be dissipated, making φ smaller (Scott and Bhushan 2003). In a phase image, the magnitude of φ at a particular position is represented by the relative shade (i.e., darker or lighter). Two possible scenarios in which topographic and phase-contrast images from the same surface differ are presented in Fig. 2.21. In images obtained from latex films, the topographic and phase-contrast images do indeed show different features (Fig. 2.22).

2.2 Techniques to Study Particle Packing and Deformation in Dry Films

67

The reasons for contrast in phase images have been a subject of frequent investigation (Anczykowski et al. 1999, Scott and Bhushan 2003). Phase contrast has been shown to be independent of variations in the elastic moduli (i.e., stiffness) of polymers (Tamayo and Garcia 1997, Bar et al. 1999) because the energy used in surface deformation is elastically recovered. One exception is when the elastic modulus of a region is low. In this case, the AFM tip will push more deeply into the surface and thus have a greater contact area with the deformed surface. The interaction energy will then be greater (Anczykowski et al. 1999). On the other hand, when the tip interacts with a viscous material, energy is dissipated. There is convincing evidence from experiments and modelling (Scott and Bhushan 2003, Leclère et al. 2002) that the energy dissipation in tip-sample interactions is greater in viscoelastic materials with a high viscosity. Variations in viscosity across a surface therefore lead to contrast in phase images and have indeed been observed over lateral distances of a few nm (Leclère et al. 2002). The contrast in both height and phase images has been found to reverse in regimes where there is either a very low or a very high Asp (Scott and Bhushan 2003, Raghavan et al. 2000). A bistable regime for φ has also been reported (James et al. 2001). The air surface of a latex film is most commonly studied with AFM, but the film can be also delaminated from its substrate to examine this lower interface. Furthermore, cross-sections can be cut in a microtome apparatus that uses an ultra sharp blade to slowly cut a film, usually while keeping the sample at a low temperature to prevent mechanical deformation. An example AFM imaging being applied to a film cross-section is given in Fig. 2.23.

Fig. 2.21 Examples of the difference between topographic and phase-contrast images. a A surface with depressions of different depths and with a uniform composition might not show any features in the phase-contrast image. The shade in the topographic image is proportional to the depth of the depression. b A surface that is smooth but that is chemically heterogeneous might show features in the phase-contrast image. More viscous regions will result in greater energy dissipation when the tip interacts with a surface, and hence there is a phase shift in the image. The chemical heterogeneity will not necessarily be apparent in a topographic image. (The possible effect of greater indentation into viscous regions is neglected here.)

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2 Established and Emerging Techniques of Studying Latex Film Formation

(a)

(b)

(c)

(d)

Fig. 2.22 AFM images (10 µm x 10 µm) of a latex film. a Topographic image showing circular regions with a shallow depression. b Phase-contrast image for the same film surface. There is no evidence for the circular regions. Reprinted from Lei et al. 2008 with permission from Elsevier. c In the AFM images of a latex film with a surfactant layer on its surface, the topographic image shows a flower-like pattern. d Phase-contrast image shows a pattern that corresponds to the topography but additionally shows evidence for surface layers that are not apparent in the topographic image. (Images courtesy of Dr C. Lei, University of Surrey)

Supporting polypropylene sheets

ca. 40 µm latex film AFM cantilever

Fig. 2.23 Photograph showing a view from above while performing AFM imaging of a latex film cross-section. The film is sandwiched between two polypropylene sheets to provide mechanical support. (Photograph courtesy of Dr C. Lei, University of Surrey)

A particular problem in the AFM analysis of latex films is the contamination of the tip. Latex films contain free surfactant and other water-soluble materials (e.g., oligomers and salts) which can adsorb onto the tip. The interaction forces with the surface are modified when the tip is contaminated (Fig. 2.24). Its effective size becomes larger with contamination, and hence the image resolution can be decreased. When imaging hard surfaces or when applying a high force on a cantilever, the sharp tip can become blunted, with a detrimental effect on image quality and resolution.

2.2 Techniques to Study Particle Packing and Deformation in Dry Films

(a)

(b)

69

(c)

contamination

Fig. 2.24 SEM images at high magnification showing AFM tips of various condition. a A conical tip that is sharp and uncontaminated. Scale bar is 375 nm. b A pyramidal tip that has been damaged. This blunted tip will not yield images with a high resolution. Scale bar is 750 nm. c A conical tip after being used to scan a latex film. Contamination, attributed to surfactant, is visible on the surface. Scale bar is 375 nm. (Images courtesy of Dr. Chun-Hong Lei, University of Surrey)

2.2.1.3 Electric Force Microscopy (EFM) and Scanning Electric Potential Microscopy (SEPM) Electric force microscopy, EFM, gives information on the electrostatic charge on a surface as a function of position. It was first developed not only as a way of imaging the charge distribution laterally across a surface, but also as a way to deposit charge in selected areas at the nm length scale (Terris et al. 1990). EFM is a so-called ‘two pass’ technique, in that the creation of an image requires two scans or passes. In the first scan, the topography is determined by non-contact AFM. Then, in the second scan, the cantilever is driven at its resonant frequency while grounded or biased by a DC voltage. The spatial derivative of the capacitive tip-sample electric force leads to a shift in the resonant frequency. Accordingly, the oscillation amplitude decreases and there is a shift in the phase of the oscillation. Images of the electric potential distribution can be created from the deviations of either the amplitude or the phase. It was over a decade from its development before reports of its application to latex films appeared. Keslarek et al. (2002) found variations of 200 mV across the surface of dialysed latex film surface compared to 80 mV variations in as-prepared material. The technique of scanning electric potential microscopy (SEPM) has been used extensively for the study of dry latex films. The technique is similar to other scanning probe microscopies in that a tip in close proximity to the surface is rastered back and forth. In this case, the scanning probe is a Kelvin-bridge electrode, so that SEPM is also known as ‘scanning Kelvin probe force microscopy’ (Nonnenmacher et al. 1991). An SEPM image provides a map of the distribution of electric potential sensed by the tip at a fixed distance from the surface. The tip is coated with Pt and fed with an AC-signal that matches the resonant frequency of the cantilever-tip system. Charges buried up to 100 nm below the surface can be detected, depending on the dielectric constant and charge distribution in the near-surface region. However, there is greater sensitivity to charges at the surface. A charge buried 20 nm below the surface is nine times less effective than a surface charge (Keslarek

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2 Established and Emerging Techniques of Studying Latex Film Formation

et al. 2001). As latex contains many charged species, such as salts and ionic surfactants, it is well suited for the technique. Topography is independent of the charge distribution; the two type of features can be studied independently (Galembeck et al. 2001). Remarkable electrical patterns in dried films have been observed and correlated to the packing of particles into arrays (Santos et al. 2004). Comparing the two related techniques, EFM provides sharper images in comparison to SEPM. But, SEPM provides absolute measurements of surface potential, whereas EFM gives information only on its spatial variation (Keslarek et al. 2002).

2.2.2 Scanning Near-Field Optical Microscopy (SNOM) and Shear Force Microscopy When this technique was first developed, it was called by the descriptive name of ‘optical stethoscopy’. Pohl et al. (1984) pointed out that a doctor’s stethoscope is able to resolve the position of a beating heart by detecting very long sound waves (λ ~100 m), and thus achieving resolution on the order of λ/1000. They drew an analogy to the detection of light waves that are relatively long in comparison to a sub-µm object. The stethoscope achieves this good resolution by having a very narrow aperture at its end and by bringing it very close – relative to λ – to the object being studied, the heart. This approach is used in the SNOM technique on shorter length scales. Light is brought in through a very narrow aperture, and the distance between the aperture and object under study is kept smaller than λ. To increase the resolution, the tip-surface distance must be made shorter, or the radius of the tip must be made smaller. In the first demonstration of the technique (Pohl et al. 1984), a resolution of λ/20 – or 25 nm – was achieved. The optical stethoscopy technique was later called ‘near-field optical scanning’ or NFOS microscopy (Dürig et al. 1986), but today SNOM is the standard name. At the heart of the original SNOM design, is a tiny aperture in a conducting metal screen. The aperture is on the apex of a transparent material that is illuminated from behind. When light is forced through an aperture that is smaller than λ, evanescent wavelets are created that have a wavelength less than the size of the aperture. The wavelets cannot travel through free space but wrap around the aperture to create contours of constant energy. In this way, energy is radiated across the aperture (Dürig et al. 1986). An important further development of SNOM came with the use of a transmissive aperture at the apex of the tapered tip of a metal-coated optical fibre (Betzig et al. 1991). This very small aperture (< 20 nm) was brought in close proximity of the surface (λ/50) to achieve a high resolution (12 nm) corresponding to about λ/43. For an optical fibre tip to be scanned across a surface, while keeping the distance between the tip and sample at a fixed value, there must be a means of regulating the tip vertical position in response to the changing surface topography. A commonly used approach is to detect the shear forces between the near-field tip

2.2 Techniques to Study Particle Packing and Deformation in Dry Films

71

and the sample surface in a technique known as ‘shear-force microscopy’ (Betzig et al. 1992). One of the first demonstrated applications was the imaging of polystyrene latex particles of diameters 230 nm and 19 nm (Betzig et al. 1992). In contrast to conventional scanning probe microscopy, shear-force microscopy uses cantilevers that have a high stiffness (indicated by its spring constant) normal to the surface but a low stiffness in the horizontal plane. When shear-force microscopy and SNOM are combined in use, the tapered optical fibre tip is used as a mechanical probe of surface topography while also being the source of evanescent light for optical image formation. There have been just a few reports of SNOM used for the examination of structure in latex films. The serum solute (including water-soluble polymers and surfactant) in sub-monolayers of latex particles has been observed by SNOM (Teixeira-Neto et al. 2004). Variations in evanescent wave intensity found in SNOM images of latex films have been attributed to minute differences in chemical composition of individual particles (Teixeira-Neto et al. 2003). Image contrast in SNOM analysis arises mainly from differences in the refractive index across a surface. Most polymers and organic materials have roughly similar refractive indices, and so contrast is not strong. One way to improve contrast is through the addition of fluorescent molecules. The emitted light can be detected in reflection or transmission modes.

2.2.3 Electron Microscopies

2.2.3.1 Transmission Electron Microscopy (TEM) As a way of determining the extent of particle deformation and packing, TEM has been employed longer than all other techniques, with reports on the topic emerging in the early 1950s (Dillon et al. 1951, Bradford 1952) when the technique was still new. (The world’s first design of an electron microscope was in 1933 by Ernst Ruska, who shared a Nobel Prize for this work 53 years later.) There has been a gradual evolution in the approach to sample preparation for TEM analysis. In the earliest work (Bradford 1952, Bradford and Vanderhoff 1963), replicas of the latex surface were made. The replicas are usually deposited onto the latex surface from the vapour phase by sputtering or thermal evaporation. Next, the latex film is dissolved in a good solvent for the latex to leave a free-standing representation of the original surface. TEM is then performed on the replicas rather than on the original sample. Replicas in the past were evaporated silicon monoxide or collodion deposited from a solution (Bradford 1952, Bradford and Vanderhoff 1963), but carbon replicas were used in later work. In the earlier work, replicas were only made of the interfaces with air or the substrate. Microscopists had to ensure that the replicas faithfully represented the surfaces without loss of resolution or the introduction of artefacts. In some work,

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2 Established and Emerging Techniques of Studying Latex Film Formation

the silicon monoxide replicas were highly fragile, so that cracks can be seen in the images (Vanderhoff 1970). A more important limitation is that no information about the internal particle structure and arrangement is provided. In the 1990s, there was an important technical development, learned from biologists, which overcame the limitations of previous work. The ‘inside’ of dry latex films was revealed for the first time by freezing the films, fracturing them in a vacuum while maintaining temperatures ranging between –115°C and –140°C. The fracture surface was then replicated for TEM analysis. More durable replicas were created by depositing thin layers of Pt onto the surface of interest, and then supporting the replica from the backside with a thicker layer of deposited carbon (Roulstone et al. 1991, Wang et al. 1992). ‘Freeze-fracture TEM’ (FFTEM), as the technique is called, provided the first experimental evidence that latex particles packed in a cubic array deformed to fill space and created rhombic dodecahedra (Wang et al. 1992). One of their striking images appears in Chapter 4 as Fig. 4.1. Point defects in colloidal crystal films, as also observed at the atomic level in ionic crystals, have been identified using FFTEM (Sosnowski et al. 1994). As an alternative to replication, ultrathin slices of dry films can be cut using a microtome (Distler and Kanig 1980). The slices, which are supported on a fine metallic or carbon grid, are thin enough so that the electron beam can pass through it in TEM analysis. Microtoming on low Tg materials is often carried out at cryogenic temperatures to avoid damage during cutting. To achieve greater image contrast between polymer phases, selective staining is often used. For instance, OsO4 is an effective stain for ester groups (Du Chesne et al. 1997) as is uranyl acetate for acrylics and acrylic acid groups (Joanicot et al. 1993). In a core-shell latex film, RuO4 exposure was used to stain poly(butadiene) and poly(butyl acrylate) in particle cores to create contrast with a poly(methyl methacrylate) shell (Domingues dos Santos et al. 2000). The cellular structure of latex films usually cannot be seen in TEM without the use of stains (Joanicot et al. 1993, Distler and Kanig 1980). An alternative to staining is the use of energy filtering TEM with electron spectroscopic imaging (ESI). To obtain images of surfactants that contain hetero-atoms not found in the continuous polymer matrix, ESI and elemental mapping can be applied to microtomed film slices or on film replicas (Du Chesne et al. 1997).

2.2.3.2 Scanning Electron Microscopy (SEM) Since becoming available commercially in the 1960s, and since reports of its application to latex film formation in the 1970s (El-Aasser and Robertson 1975), SEM has become a relatively routine method for a wide range of applications. Latex film structure and surfactant distribution can readily be visualised, even when the surface is coated with a thin conducting film, such as Au (Eckersley and Rudin 1993). Environmental SEM, which was described in Section 2.1.2.2, is applied to dry films also, as it eliminates the need for an electrically conductive coating and the associated imaging artefacts (Keddie et al. 1996). Microscopes

2.3 Techniques to Study Film Crosslinking

73

with a field emission source of electrons are often used to achieve higher resolution (Ming et al. 1995, Teixeira-Neto et al. 2003). Low voltage SEM reduces polymer beam damage during the analysis. Consequently, there is greater time available for focussing, so that images at higher magnifications can be obtained (Gaillard et al. 2004). Images created from backscattered electrons provide information about the distribution of elements across the surface, because the backscattered energy is proportional to atomic number. Backscattered electron images offer poorer resolution than images produced from secondary electrons, but they are not prone to the effects of charge build-up (Teixeira-Neto et al. 2002).

2.3 Techniques to Study Film Crosslinking A complete study of crosslinking reactions requires both chemical information (to confirm the relevant reactions) and mechanical information (to correlate with crosslink density). The ideal technique would be non-invasive, applicable in a range of atmospheres, and provide data as a function of depth and lateral position in a film.

2.3.1 Ultrasonic Reflection and QCM Ultrasonic reflection techniques, already described here, can provide measurements of the dynamic moduli as they evolve in crosslinking materials, such as epoxy resin (Lellinger et al. 2002). A related technique uses the shear wave generated by a quartz crystal vibrating at its resonant frequency to probe the viscoelastic properties of thin films. This technique, called ‘quartz crystal microbalance’ (QCM) with dissipation, has shown some promise for characterising crosslinking in waterborne alkyd emulsion films (Hellgren et al. 2001). A measurement of the amount of energy dissipated during the shear oscillation indicates the extent of crosslinking. A film with a high crosslink density will be stiffer and dissipate less energy. A limitation of this approach is that it is only applicable to films that have a thickness less than the wavelength of the ultrasound (< 2 µm), but is has the attractions of being non-invasive and applicable in any atmosphere. Recent developments in the applications of QCM have been reviewed (Johannsmann 2008)

2.3.2 Spectroscopic Techniques An enormous body of work in developing photoacoustic (PAS) FTIR spectroscopy and other IR techniques was produced by the team led by Urban (1997). Their work mainly concerns the bonding interactions and distribution of surfac-

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2 Established and Emerging Techniques of Studying Latex Film Formation

tants in dry latex films. According to Belaroui et al. (2000), PAS is not properly quantitative and depth profiling is only possible through analysis of layers of increasing thickness ranging up to 20 µm. In NMR spectroscopy, the lifetime of a transient decay, known as the ‘spinspin relaxation time’, T2, is highly sensitive to motion at the molecular level. The values of T2 have been shown to be correlated to the degree of crosslinking in alkyd coating formulation, falling from a few ms to µs as crosslinking proceeds (Mallégol et al. 2002). In an alkyd film undergoing autoxidative crosslinking, the progression of crosslinking from the top film surface has been determined with GARField NMR profiling (see Section 2.1.4.3). The signal intensity falls as the molecular mobility decreases as the alkyd hardens (Mallégol et al. 2002, Erich et al. 2005). The technique has been used to determine the effect of catalysts (known as ‘driers’) on how the oxidative crosslinking extent varies with depth into the film, as a result of oxygen ingress from the surface (Mallégol et al. 2002, Erich et al. 2006, 2006b). NMR profiling has likewise been used to study how the extent of crosslinking varies with depth into coatings undergoing a photo-initiated chemical reaction (Wallin et al. 2000). Complementary to NMR probes of molecular mobility, and hence viscosity, confocal Raman microscopy detects the chemical state as a function of position. An early report of confocal Raman microscopy to obtain crosslinking profiles in coatings came from Schrof et al. (1999) who studied UV curing and the effect of photostabilisers. More recently, Erich et al. (2005b) have used it to probe crosslinking in alkyd coatings. The disappearance of the double bonds in the alkyd’s fatty acid groups was determined as a function of depth. The front position separating the crosslinked and non-crosslinked regions was well correlated with the fatty acid chemical reaction (Erich et al. 2005b).

2.4 Techniques to Study Interdiffusion and Coalescence Although the interdiffusion of polymer molecules between particles during the last stage of film formation has a profound influence on properties, there are comparatively few techniques to probe this process at the molecular level. Commonly, film properties are evaluated, especially mechanical properties, and the extent of interdiffusion is deduced. Similarly, electron microscopy is used to assess the amount and extent of particle coalescence by visualisation of the particle boundaries. Microscopy will not be discussed further in this chapter, but we will turn our attention to three specialist techniques for diffusion studies. There is a similarity between the techniques of SANS and FRET. In each, molecules in a fraction of the particle are labelled (either with deuterium or with a fluorescent dye), and the ‘smearing’ of the boundaries with the neighbouring particles is detected.

2.4 Techniques to Study Interdiffusion and Coalescence

75

2.4.1 Small Angle Neutron Scattering (SANS) SANS was discussed earlier in Section 2.1.3.1 in the context of film drying. This technique has offered conclusive evidence for the interdiffusion of molecules in the later stage of film formation. In a typical experiment, particles that are labelled with deuterium are blended with normal hydrogenous particles. When the polymer is at temperatures above its Tg, molecules will diffuse across the interface with other particles and the effective size of the particle will be seen to grow. This fact is exploited in SANS experiments. The scattering intensity falls as the radius of gyration, Rg, of a particle increases, according to the relation:  − Q 2 Rg 2  . I (Q ) = I (0) exp   3  

(2.19)

When the logarithm of I(Q) is plotted against Q2, in a representation called a ‘Guinier plot’, the slope of the line can be used to find Rg. A Guinier plot is shown schematically in Fig. 2.25. The radius of the particle is then found from R = 5 Rg . 3

(2.20)

As the molecules diffuse out of the confines of the particle at an initial time t0, the size that each particle occupies will increase. The dependence of Rg on time t is predicted to increase to a greater extent when the apparent molecular diffusion coefficient, Dapp, is higher:

Rg 2 (t ) = Rg 2 (t0 )+ 6 Dapp (t − t0 ) .

(2.21)

Measurements of the evolution of Rg thereby provide a direct means to determine Dapp. This approach, however, requires a measurement of Rg at t0. As interdiffusion occurs, the interfaces between particles can be characterised by an interpenetration distance, dI, or by an interfacial width, wI. The first of these, dI, represents merely the difference between R at a given time and the radius at the initial time, R0. The other measurement, wI, is obtained from an analysis using a modification of the Porod law. Whereas the Porod law describes a two-phase system with sharp boundaries, a modified expression is required when there is a diffuse interface. If a Gaussian profile with a standard deviation wI is invoked to describe the interface between deuterated and non-deuterated particles, then I(Q) is given as:

I (Q) =

KP exp(−Q 2 wI 2 ) + K B I B (Q) . Q4

(2.22)

2 Established and Emerging Techniques of Studying Latex Film Formation

Log (Intensity)

76

•• • • • • •• • • • • Short time •• •• •• • • •• • Longer time • Q2 (Å-2)

Fig. 2.25 A schematic illustration of Guinier plots for deuterium-labelled particles with little interdiffusion (at a short time) and with more interdiffusion (at a longer time).

Here, Kp is the Porod constant. The second term contains the product of the background scattering intensity, IB, and a constant of proportionality, KB. Kim et al. (2000) found that that dI is 1.67 times greater than wI.

2.4.2 Fluorescence Resonance Energy Transfer (FRET) In a major development, Peckan et al. (1988) first reported the use of nonradiative energy transfer (NRET) for the study of latex particle structure. The group of Winnik at the University of Toronto have gone on to apply the technique to answer many questions about interdiffusion in latex films. The technique is now usually called ‘fluorescence resonance energy transfer’ (FRET). The basic principle of FRET is that the fluorescence lifetime of fluorescent donor molecules decreases when they are in close proximity to acceptor molecules. The donor and acceptor molecules are grafted to polymer molecules, and they are initially in separate particles. As is shown in Fig. 2.26, when there is diffusion of molecules from one particle to another, the donor and acceptor pairs come into closer contact. The area under a fluorescent decay curve is proportional to the fraction of mixing between the particles (Wang and Winnik 1993).

2.4.2.1 Rate of Energy Transfer Here we will follow the presentation of Farinha et al. (2000). The rate of fluorescence decay for an isolated donor dye molecule is the reciprocal of its lifetime, 1/τD. If the dipoles of all of the donor and acceptor pairs are separated by a distance, r, then the decay rate will be faster, and is given by the Förster relation as:

2.4 Techniques to Study Interdiffusion and Coalescence

• • • • •• o o oo o o o • o • •• • ••• • oo o o o o o • o • • • o o • • • •• oo o o o o o o • • • • • o • o• • •o o oo o • • o o •o o o o • • • o •• •o o o o o • •o • • •o • • • o• o oo o

77

[Cdonor]

x

•

x

•

o o o • • o • • • o o• o •• • o• • • •o o o•o o • o o • o • o • • o o o• o • o • o • o • o • o

x

x

Fig. 2.26 Schematic illustrations of a boundary between a phase labelled with donor molecules (filled circles) and acceptor molecules (open circles). Initially there is no mixing between the phases (top). As diffusion proceeds, the donor and acceptor molecules cross the boundary (middle) until there is no longer a concentration gradient and mixing is complete (bottom). The donor concentration profiles are sketch on the right side.

W (r ) =

3κ 2 1  RF    2 τD  r 

6

(2.23)

where RF is called the ‘Förster radius’. Its value depends on the particular donor and acceptor pair, but it is typically between 2 and 7 nm. For the commonly used pair of phenanthrene and anthracene, RF has been found to be 2.3 nm (Wang and Winnik 1993). The 3κ2/2 term, which is related to the orientation of donor and acceptor dipoles, is typically close to unity and is often neglected in calculations. In the Förster relations, W varies with r –6, thus showing great sensitivity to small values of r, with RF setting the range of sensitivity. This gives the technique its attractiveness and power. In the case of isolated donor dye molecules, the fluorescence intensity, I, is simply an exponential function of time, t.

 −t   I D (t ) = a1 exp τ D 

(2.24)

where a1 is a constant. Ideally, a plot of the logarithm of I(t) against t (where t usually extends from 0 up to a few hundred ns) will give a straight line with a gradient equal to 1/τD. When donors and acceptor pairs are all homogeneously

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2 Established and Emerging Techniques of Studying Latex Film Formation

separated by r in an infinite volume, the decay of I(t) for the donor is faster as a result of quenching by the acceptor. The equation is modified as

I DA (t ) = exp(−t / τ D ) exp[−W (r )t ]

(2.25)

In this equation, we can see how the fluorescence decay contains information about the donor and acceptor pairs and hence can serve as a measure of very short distances between interdiffusing molecules. In latex systems, there are finite volume effects, and there is not a homogeneous distribution of donors and acceptors but a distribution of r. The donor’s fluorescent decay profile, however, can be fit to a phenomenological expression:

  t  −t   −t   + a2 exp  exp − β  I DA (t ) = a1 exp  τD τ D  τ D  

  

0.5 

,  

(2.26)

where a2 and β are constants (Farinha et al. 2000). The first component in this equation is sometimes attributed to the donors that have not yet mixed with acceptor molecules, whereas the second component is attributed to those that have mixed. Fig. 2.27 shows how the fluorescent decay curves are expected to change when there is interdiffusion across a particle interface.

2.4.2.2 Quantum Efficiency and Fraction of Mixing The quantum efficiency of energy transfer, ΦET, can be related to the fraction of molecular mixing in a system of labelled particles (Farinha et al. 2000). ΦET is defined in terms of the areas under the fluorescence decay curves, A, of a donor in the presence of an acceptor, IDA(t) in comparison to the area under the curve of the donor in isolation, ID(t). Of course, the areas can be obtained by integration over time, such that ∞

Φ ET = 1 −

∫I

∞ DA

(t )dt

= 1−

0 ∞

∫I

D

∫I

DA

(t )dt

0

(t )dt

(2.27)

τD

0

where we see that the donor lifetime, τD, is found by integration of the decay curve. In reality, in latex systems, there is always energy transfer at the start of the experiment (t=0) such that ∞

∫I 0

D (t ) dt

> 1, diffusion is relatively weak, and we expect a non-uniform particle distribution with a layer of close-packed particles accumulating at the top surface. The particles do not move fast enough to stay ahead of the downward-moving surface. If the particles are subject to deformation and coalescence, then a skin layer may form and the evaporation rate will diminish considerably. (This is Case C in Fig. 3.2.) For Pe 1 (Gorce et al. 2002). The results are shown in Fig. 3.6. For a Peclet number of 0.2 the water profile is seen to be flat and the film height decreases uniformly with time. For a Peclet number of 16, the water profile is slanted with a lower water content at the top surface.

Vertical Drying Profiles

105

Fig. 3.6 GARField MR profiles showing the water content as a function of position in films at times through the drying process. The magnetisation is proportional to water content. Series A has a Peclet number of 0.2 (obtained with experimental parameters of H ~ 255 µm, Eɺ ~ 0.2 ×10−8 m/s; D ~ 3.23 x 10–12 m2/s). Notice how the water content is uniform throughout the film. Series B has a Peclet number of 16 (obtained with H ~ 340 µm, Eɺ ~ 15 × 10−8 m/s; D ~ 3.23 x 10–12 m2/s). The water content is higher towards the base of the film, indicating an accumulation of particles near the top surface. (Reproduced with permission from Gorce et al. (2002))

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In follow-on experiments, Pe was systematically varied over a wide range by adjusting film thickness and drying conditions. In systems with Pe >10, the water concentration gradient between the upper packed region and the lower dilute region was found to be proportional to Pe to a power of 0.8 (Ekanayake et al. 2009). A scaling argument predicted a weaker dependence with the gradient being proportional to Pe0.5 (Routh and Zimmerman 2004). The precise reasons for the discrepancy are not clear and deserve further study. Two-dimensional MR images provide further direct evidence for heterogeneous drying in thick (H = 5 mm) latex films (Rottstegge et al. 2003). Flowing air at 60°C ensured a fast evaporation rate, leading to a very high Pe (value not reported). The observation of a more dry layer at the film surface, growing over time, is entirely in agreement with expectations. It was found that the addition of excess non-ionic surfactant resulted in a more uniform water distribution. One explanation for this effect of surfactant is that particle segregation is hindered by the formation of a weak gel in the particle network. The structure of final dried films can be determined by small angle neutron or X-ray scattering (SANS or SAXS), where a long range order is detected with peaks in the structure factor (Ballauff 2001). An example is given by Dingenouts and Ballauff (1999) who used X-rays to show that the packed particles in a partially dried film create an amorphous glass with a particle volume fraction of around 64% and the remaining volume filled with water. SANS has also been used to probe latex particle distributions as a function of time over a four-hour drying period (Belaroui et al. 2003). Liao et al. (2000) report Brownian dynamics simulations to explain segregation of poly(methyl methacrylate) (PMMA) particles in a matrix of polystyrene (PS). The PMMA is seen to clump or aggregate, motivating the interparticle potential for electrostatically stabilised particles to be examined. If the particles are aggregated, they diffuse slower and therefore accumulate at the top interface more readily (i.e., Pe is higher). Indeed, the addition of excess salt to a charge-stabilised latex leads to greater non-uniformity in drying (König et al. 2008). Salt causes a screening of charge effects between particles that will reduce the co-operative diffusion coefficient of the particles. This slowing down of the particle diffusion could explain the particle accumulation at the top of the films with higher salt contents. On the other hand, when the salt content is extremely high, particles will sediment. The top surface then consists of water, and the evaporation rate is fast (Erkselius et al. 2008). A different numerical technique was employed by Reyes and Duda (2005) who used a Monte Carlo simulation to examine the ordering of colloidal hard spheres in thin films about eight particle radii thick. As might be expected, a fast evaporation rate resulted in randomly packed films, and a slow evaporation rate showed ordered colloidal domains.

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107

3.4.4 Consequence of Inhomogeneous Vertical Drying: Skin Formation If particles accumulate at the top surface of the film, and they coalesce to form a continuous polymer film, then a barrier to further evaporation forms and drying becomes extremely slow. This skin formation is a common observation when painting thicker films, because of the greater Peclet number. The coalescence must be by a wet sintering mechanism, because capillary stresses are not operational in a film with a fluid below. (The mechanisms of skin formation are discussed further in Section 4.2.) Therefore, skin formation is only observed for thicker films with soft polymers. Skin formation causes the drying time to extend considerably and is therefore an undesirable consequence of vertical inhomogeneities. Experiments have shown that there is a correlation between particle coalescence and the formation of a skin layer, which slows down water loss (Mallégol et al. 2006). The reason for the slowdown is rather obvious. The transport of water by diffusion through the polymer becomes the rate-limiting step in the water loss process. The prediction of the diffusion coefficient of water through a polymer is a difficult task that is complicated by swelling of the polymer by water. The sorptive capacity of polymers may be predicted from knowledge of the chemical make-up. More hydrophilic groups in a polymer lead to a higher sorptive capacity of water (van Krevelen 1990). For instance, the sorption of a phenyl ring, a non-polar group, is 250 times lower than a hydroxyl group. In a poly(vinyl acetate) latex, as an example, water concentrations of 3–4 wt.% are found (Rottstegge et al. 2003). Diffusivity in a polymer with hydrogen-bonding groups increases with increasing water content. The opposite trend – a strong decrease – is found in less hydrophilic polymers, such as polymethacrylates (van Krevelen 1990). The flux of water through the polymer is a function of the product of solubility and diffusivity, and is low for a polymer that will be used in latex. In applications of latex as a binder in a coating, there is often a need to smooth out with a brush or ‘rework’ a wet layer after its initial application. The time available to rework a latex surface is called the ‘open time’ by industrial scientists (Overbeek et al. 2003). Latex films tend to have a shorter open time in comparison to polymer solutions, because of the strong rise in the dispersion viscosity as the solids content increases. Non-uniform drying will have the effect of concentrating the polymer particles at the top surface. The open time will be even shorter in such a case.

3.5 Horizontal Packing and Drying Fronts A common observation is that latex films do not dry uniformly, but instead have fronts of differing appearance (partially transparent, clear etc.) passing laterally across the film as it dries. Fig. 3.7 shows a picture of a dispersion containing 200 nm

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Evaporation

x A

B

C

Fluid dispersion

Water pressure

Packed particles

P*

Pmax

x Fig. 3.7 Top-view of a drying film displaying horizontal drying fronts. The particles consolidate at the edge of the film and this establishes a horizontal flow. Particles are carried to the edge, propagating the drying front laterally across the film. The region marked ‘A’ is still fluid with a particle volume fraction below close packing. The region marked ‘B’ consists of close packed particles, although still saturated with water. Region ‘C’ is presumed to be dry. Notice the cracks propagating into the film from the edge. On the right-hand side, the pressure of the fluid in the film is sketched as a function of lateral distance, x. The sketch shows a cross-sectional view from the edge of the film. In this case, the pressure generated by flow through the consolidated particles, P*, is less than the maximum capillary pressure, Pmax, and hence the water remains pinned at the edge of the film.

Fig. 3.8 Cryogenic SEM image of particles consolidating in a packing front at the edge of a drying film (left-hand side). The right-hand side shows a dilute dispersion in water, which is now in the form of ice. (Reproduced with permission from Ma et al. (2005))

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109

Fig. 3.9 A schematic diagram showing the two different types of horizontal drying front. The particles consolidate into a close-packed solid near the film’s edge. The boundary with the dilute central region defines the packing front. Further towards the edge, the space between particles becomes devoid of water. The boundary with the wet particle bed is called the ‘drying front’.

polystyrene particles in water, which was cast on a substrate and allowed to dry. The milky white region, marked with an ‘A’, is still fluid, with a volume fraction below the point of close-packing. The region marked ‘B’ is a solid in which the particles have consolidated in a close-packed structure. Continued evaporation from the solidified region leads to a flux of material from the fluid centre towards the consolidated edge, carrying particles towards the edge and propagating the front of close-packed particles across the film. This flow pattern is sketched on the right-hand side of Fig. 3.7. This phenomenon can be visualised in experiments. Fig. 3.8 shows a cryogenic SEM image, from the work of Ma et al. (2005), which displays the accumulation of particles at the edge of a film. Horizontal drying fronts have been described since the 1960s (Hwa 1964), although more as a curiosity than anything else. There are usually at least two different types of front in a latex film. The boundary between a dilute dispersion and the packed particles is called a ‘particle packing front’ or simply the ‘particle front’. In a bed of packed particles, there is a boundary between wet and dry regions, which is called the ‘drying front’. These two fronts are shown schematically in Fig. 3.9. Winnik and Feng (1996) measured the propagation rate for the particle front for a range of blends between hard and soft particles and offered the explanation of continued drying from the consolidated regions of the film as being the driver of the packing front. Parisse and Allain (1997) reported a model based on maintaining a constant shape of a still wet drop of a colloidal dispersion. This model captured the observed drying front behaviour and is similar to the model outlined below, in section 3.5.1. The difference arises in the boundary condition at the drop edge, which is assumed to retain a constant shape in the Parisse and Allain model and is free to take up any shape in the model described below. The underlying physics of evaporation from the consolidated region causing a lateral flow towards the edge is however common between the two models. Deegan et al. (1997) report on drops

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of dilute dispersions containing latex particles or particulate additives, such as coffee. The horizontal drying front results in an accumulation of particles at the edge of the drop and hence the common observation of coffee rings on kitchen worktops! Subsequent work explored and exploited the role of the contact line at the edge of the wet film as determining the patterning of the dry particles (Deegan 2000, Deegan et al. 2000).

3.5.1 Model for Horizontal Drying Fronts As just noted, the experimental observations of fronts passing across a drying film are numerous. The important questions are: why does the front form in the first place? And how can the front’s position be predicted? Routh and Russel modelled the flow in a dispersion of initially dilute dispersions (Routh and Russel 1998, Routh et al. 2001) and subsequent experiments using MR imaging verified the approach (Salamanca et al. 2002). The starting point for the analysis is the lubrication approximation, which assumes that the film is thin, such that vertical variations in pressure and particle volume fraction are small and therefore negligible. The result is a flow based on surface tension, with the film height also reducing because of evaporation. The characteristic horizontal length scale in such a problem, L, is termed the capillary length and represents the distance over which surface tension, γ, can cause a flow in a film that is evaporating at a constant rate Eɺ . The capillary length is given by

 γ  L = H  ɺ   3ηE 

1

4

(3.4)

where η is the viscosity of the colloidal dispersion (not the solvent). Surface tension seeks to reduce corners, so that material will flow away from tight bends. Figure 3.10 shows how such a flow, away from an edge, will lead to a reduction in the film height in the edge region. The evaporation rate is assumed to remain constant across the film surface. In a given time interval, each part of the film will lose the same amount of mass and have the same reduction in thickness. The effect on particle volume fraction is far more significant in the thin regions. (Think of a 1 m thick layer at a volume fraction of 25% losing 1 µm in film height because of water evaporation. The effect on the particle volume fraction will be minimal. Compare that case to the effect on the volume fraction in a film of thickness 2 µm losing 1 µm in thickness because of water evaporation.) Because of the reduced height, the particles near the edge will begin to consolidate and to form a solid region prior to the central region. Continued evaporation from the solidified region induces fluid to flow from the bulk to the edge. Particles are carried to the edge, and the close-packed region propagates laterally across the film. This mechanism is as sketched in Fig. 3.7. When the drying front forms, the

Horizontal Packing and Drying Fronts

111

lateral flow due to evaporation in the close-packed region dominates. The capillary length scale is no longer relevant because the drying front propagates across the entire film. The edge region, over which height variations are locked into the film, is however the size of a few capillary lengths.

3.5.2 Lapping Time and Open Time The time it takes for a latex film to start drying at the edge is referred to as the ‘lapping time’, particularly by industrial scientists. When coating a large area, such as a wall, a painter might stop halfway across it. If the lapping time is too short, then there will be a ‘seam’ at the border between the two halves when the other half is coated (Overbeek et al. 2003). In some of the scientific literature, the time at which water recedes from the edge of a latex film has been called the ‘open time’. A model has been developed to predict this time. As fluid flows through the consolidated region, there is a resulting pressure drop along the packed bed. It is sketched in Fig. 3.7, showing the lowest value of the pressure occurring at the film edge. The pressure at the film edge is termed a capillary pressure. There is a maximum value of pressure that the particle network can support. An estimate for this maximum value is approximated as

Pmax =

10γ R

(3.5)

although the value of 10 is for mathematical convenience, and a range from 2 to 12.9 is used by different groups depending on the assumed particle-packing geometry (White 1982, Dunstan and White 1986, Brown 1956, Holmes et al. 2006).

Surface tension induced flow

Initial state

L Capillary length is the distance that surface tension drives the shape in the time that evaporation takes to reduce the film height

Fig. 3.10 Surface tension causes fluid to flow from a tight corner to a more rounded shape. The shape is changed over a capillary length.

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The pressure drop along the particle bed is controlled by the bed permeability, kp. A less permeable bed will require a greater pressure gradient to achieve the same flow as in a more ‘open’ and permeable bed. For Darcy flow we can write

dP µ = − ux dx kp

(3.6)

where ux is the horizontal fluid velocity in the film, with x representing the lateral direction. From (3.6) the characteristic pressure drop along the particle bed, P*, can be estimated by using the characteristic horizontal length scale, L, from (3.4) and the characteristic horizontal velocity, LEɺ / H . After substituting in L for the distance x, and the characteristic horizontal velocity for ux, one finds

P* =

µEɺ L2 Hk p

(3.7)

Comparing the maximum possible capillary pressure (3.5) with the pressure achievable by flow through the particle network defines a dimensionless group, called the ‘reduced capillary pressure’, Pcap. It is written as Pcap =

Pmax 10γHk p = P* µEɺ RL2

(3.8)

If the pressure drop reaches this maximum value, then water will recede from the edge of the film and the particles will become dry. This point will occur when Pcap is less than around unity. A film with a lower Pcap will display a short open time. Conversely, for the cases with Pcap >>1, the maximum capillary pressure will never be reached by the horizontal flow, and the film will remain wet at the edge of the film until the last stages of evaporation. One can think of the water as being ‘pinned’ at the film edge. In these cases, the film will display a long lapping time. Equation (3.8) teaches us what parameters are important in determining the rate of horizontal drying. Drying from the edges may be avoided with slow evaporation rates, and thick films, since these contribute to a high Pcap. The effect of particle size is not immediately clear. The radius appears on the denominator in (3.8) implying that a small particle size leads to a large Pcap. The complication arises however in that the permeability, kp, is a strong function of particle size, with a small particle radius reducing kp significantly. Hence, reducing the particle size reduces Pcap and exacerbates the development of edge drying. The recession of water from the edge of films was followed experimentally by Salamanca et al. (2001) using MR imaging. Their experimental results are shown in Fig. 3.11. The water in the film gives an NMR signal and appears white in the images at its maximum concentration. The top image shows a film with water throughout as found immediately after casting. After a period of time, the particles

Horizontal Packing and Drying Fronts

113

have collected at the edge. The grey region indicates a lower water concentration, and the boundary between the white and grey region defines the position of the packing front. The existence of a water signal indicates that the particles in the packed region remain wet. At later times still, the water has receded from the edge of the film and no signal is then detected from this dry film. The series of images are consistent with the sketch of the two fronts in Fig. 3.9.

0 hr.

Wet, colloidal dispersion

2.6 mm

3 hr. Particle packing front 6 hr. Drying front 22 mm

Fig. 3.11 A series of NMR images obtained from a slow-drying latex layer after casting (zero hours), after three hours of drying, and after six hours. The grey scale corresponds to water content, with white representing higher water concentration, and black meaning no water. Particle packing fronts (separating a wet particle bed and a dilute region) are seen after three hours, and drying fronts are seen after six hours. (Reprinted from Salamanca et al. (2001); copyright 2001 American Chemical Society)

The time before a drying front recedes from the edge of the film is easily determined, and it corresponds to the lapping time. Salamanca et al. followed this time as a function of the dimensionless capillary pressure Pcap, and their results are reproduced in Fig. 3.12. The upward jump in open time around a Pcap of 10 agrees broadly with theoretical predictions, which are shown for comparison. A further consequence of the horizontal drying is that the pressure drop along the packed region places the particle network into compression. The particles can be deformed and film form under the action of this pressure. The result is a front of optical clarity passing across the film a little behind the packed particle front, where particles first come into close contact (Routh et al. 2001). Visually, one can see a turbid film become partially transparent when the packing front passes, and then become fully transparent when the optical clarity front passes.

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3 Drying of Latex Films

Pcap Fig. 3.12 Open time of a drying latex film plotted as a function of the dimensionless capillary pressure Pcap. The points are experimental measurements, whilst the lines are theoretical fits using the theory outlined in the text. A variety of particle sizes and film thicknesses were used to achieve a range of Pcap values. (Reproduced with permission from Salamanca et al. 2001; copyright 2001 American Chemical Society)

3.6 Colloidal Stability As evaporation proceeds, the concentration of electrolyte in the remaining aqueous phase will increase. A natural expected consequence is a loss of particle stability and an aggregation between particles. Depending on the concentrations involved, the particles may already be arranged in a close-packed form in the fluid phase, and so the induced attraction will merely lead to a small consolidation of the bed. Alternatively, if the loss in stability occurs early in the drying process, bulk aggregates may form and will hinder uniform film formation. An example of the effect of colloidal stability is given by Juhué and Lang (1993). Adding surfactant to latex and achieving a full coverage of the particles, thereby ensuring maximum colloidal stability, resulted in optimum packing of the particles and led to a smooth film. Poorer colloidal stability resulted in the settling of particle flocs and a rougher film. There are two ways that a charge-stabilised dispersion can become unstable during drying. Fig. 3.13 shows a theoretical consideration of how the Debye length, κ–1, changes during the drying process. As outlined in Section 1.6 of Chapter 1, the Debye length is the distance over which electrostatic repulsions operate between particles. As the electrolyte concentration increases, the charges become screened and the Debye length decreases. The maximum in the interparti-

Colloidal Stability

115

cle potential, which imparts stability, is reduced (see Fig. 1.14). If the maximum potential is less than a few kT (say 5), then the thermal energy will enable the aggregation of the particles. The energetic barrier between particles is no longer high enough to oppose the attractive van der Waals forces. wmax = 5kT

Particle Spacing (nm)

40

0.05 M 0.10 M 0.15 M

Time

30

Unstable 20

10

0

Stable

0.5

1.0

1.5

Debye screening length (nm) Fig. 3.13 Evolution of Debye length and average interparticle spacing during drying for 90 nm particles at an initial volume fraction of 0.4 and a critical coagulation concentration of 0.2M NaCl. Aggregation is assumed to occur when the interparticle potential has a maximum repulsion of 5 kT. Here the interparticle spacing refers to the distance between the particle surfaces.

Secondly, as the particles become more concentrated, the average interparticle spacing decreases. One could imagine that if the particles are forced to be closer than the distance corresponding to the maximum in the barrier, then aggregation will occur. The calculations in Fig. 3.13 relate to 180 nm latex particles with a critical coagulation concentration (CCC) of 200 mM NaCl. It can be seen that for initial salt concentrations below 50 mM, the dispersion remains stable through the drying process. It is noticeable that right until the point of particle packing (a particle spacing of 0), the barrier is sufficiently high to prevent aggregation. At higher initial salt concentrations, which bring the dispersion closer to its CCC, it is predicted that the barrier height could become so low that aggregation will start before particle contact has been achieved. In reality, colloidal dispersions are designed to be highly stable, which make it unlikely to be subject to flocculation during drying. However, there have been reports of fast drying that are explained by particle flocculation and sedimentation at high salt contents (Erkselius et al. 2008). It has also been proposed that the presence of salt influences the stability of surfactant layers at particle interfaces in a skin layer. The presence of some particular anions and cations favoured particle coalescence in a skin layer (König et al. (2008).

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3.7 Film Cracking The flow of solvent through the packed-particle region of the film causes a pressure drop. The capillary pressure may result in compression of the film as discussed above. If the particles are too rigid to deform, the film can display cracks, as shown in Fig. 3.7, where the cracks follow a short distance behind the particle front through the film. The idea that capillary pressure is the driving force for cracking is now widely accepted (Dufresne et al. 2003, Dufresne et al. 2006). However, the actual mechanism remains in dispute. There are a number of experimental observations that make film cracking a fascinating area of study.

Crack spacing

Position of crack front

Fig. 3.14 A crack front propagating across a drying film. Notice that the cracks all extend up to a common crack front position. The spacing between the parallel cracks is roughly the same.

3.7.1 Do the Cracks Follow the Drying Front or Propagate Quickly Over the Entire Film? Two possibilities have both been reported. The simplest case consists of cracks following the drying fronts across the film (Lee and Routh 2004). Fig. 3.14 shows a screen grab from a video of 20 nm silica particles drying in a film. The cracks propagate as a front across the film in a stick-slip type motion, where a plot of the position of the crack front against time resembles a staircase. The same observation has been made by Dufresne et al. (2003, 2006). Others, however, report that the crack front progression is much more uniform (White 2006) with a linear front progression. Further complicating the observations, some authors have reported a second case in which the films remain intact until the entire film has consolidated, with failure occurring thereafter (Tirumkudulu and Russel 2005). The most likely

117

explanation for this discrepancy is the capillary pressure generated by the horizontal flow being too small to cause failure. The late-time failure might only be observed in the cases with Pcap >>1. This conjecture, however, awaits experimental verification.

3.7.2 What Sets the Crack Spacing? A common observation is that a film displays a characteristic distance between its parallel cracks (Fig. 3.14). The derivation of a prediction of this crack spacing is the subject of many papers. The most common analytical approach is to apply an energy balance between the elastic energy released (or ‘gained’), when cracking the film and the surface-free energy ‘cost’ of creating new surfaces on either side of the crack. The resultant prediction for crack spacing is determined by the size of material needed to provide enough elastic energy to make cracking energetically favourable (Thouless 1990). The underlying assumption for a latex film is that packed particles constitute an elastic solid. However, this assumption might not be valid in a colloidal film in which a fluid is being transformed into a solid. An alternative explanation was put forward by Lee and Routh (2004) who proposed that the flow of solvent away from the crack can also relieve the capillary pressure. The flow provides an additional relaxation mechanism that sets the crack spacing.

References Barnes G.T. and Gentle I.R. (2005) Interfacial Science, Oxford University Press. Ballauff M .(2001) SAXS. and SANS studies of polymer colloids. Curr Opin Coll Interf Sci 6:132-139 Belaroui F., Cabane B., Dorget M., Grohens Y., Marie P., Holl Y .(2003) Smallangle neutron scattering study of particle coalescence and SDS desorption during film formation from carboxylated acrylic latices. J Coll Interf Sci 262: 409-417 Brown G.L. (1956) Formation of films from polymer dispersions, Journal of Polymer Science, 22: 423-434. Brown L.A., Zukoski C.F. and White L.R. (2002) Consolidation during drying of aggregated suspensions. AIChE J 48 (3) 492-502. Brown L.A. and Zukoski C.F. (2003) Experimental tests of two phase fluid models of drying consolidation. AIChE J,. 49(2) 362-372. Ciampi E. and McDonald P.J. (2003) Skin formation and water distribution in semicrystalline polymer layers cast from solution: A magnetic resonance imaging study, Macromolecules, 36:8398-8405 2003.

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Croll S.G. (1986) Drying of latex paint. Journal of Coatings Technology 58(734): 41-49. Croll S.G. (1987) Heat and mass transfer in latex paints during drying. Journal of Coatings Technology, 59(751): 81-92. Cussler E.L. (1984) Diffusion: mass transfer in fluid systems, Cambridge University Press. Deegan R.D., Bakajin O., Dupont T.F., Huber G., Nagel S.R. and Witten T.A. (1997) Capillary flow as the cause of ring stains from dried liquid drops. Nature, 389: 827-829. Deegan R.D. (2000) Pattern formation in drying drops. Physical Review E,. 61(1): 475-485. Deegan R.D., Bakajin O., Dupont T.F., Huber G., Nagel S.R. and Witten T.A. (2000) Contact line deposits in an evaporating drop. Physical Review E 62(1): 756-765 Dingenouts N. and Ballauff M. (1999) First stage of film formation by latexes investigated by small angle x-ray scattering, Langmuir, 15: 3283-3288. Dufresne E.R., Corwin E.I., Greenblatt N.A., Ashmore J., Wang D.Y., Dinsmore A.D., Cheng J.X., Xie X.S., Hutchinson J.W. and Weitz D.A. (2003) Flow and fracture in drying nanoparticle suspensions, Physical Review Letters, 91(22): 4501-4504. Dufresne E.R., Stark D.J., Greenblatt N.S., Cheng J.X., Hutchinson J.W., Mahadevan L. and Weitz D.A. (2006) Dynamics of fracture in drying suspensions, Langmuir 22(17): 7144-7147 Dunstan D. and White L.R. (1986) A capillary pressure method for measurement of contact angles in powders and porous media. Journal of Colloid and Interface Science, 111(1): 60-64. Ekanayake, P., McDonald P.J., Keddie, J.L. (2009) An experimental test of the scaling prediction for the spatial distribution of water during the drying of colloidal films. European Physical Journal – Special Topics 166: 21-27. Erkselius S., Wadsö L. and Karlsson O.J. (2007) A sorption balance based method to study the initial drying of dispersion droplets, Colloid and Polymer Science 285: 1707-1712. Erkselius S., Wadsö L., Karlsson O.J. (2008) Drying rate variations of latex dispersions due to salt induced skin formation. J Coll Interf Sci 317: 83-95. Gorce, J.-P., McDonald, P.J. and Keddie, J.L. (2002) Vertical water distribution during the drying of polymer films formed from emulsions. Eur Phys J E 8: 421-429. Holmes D.M., Kumar R.V. and Clegg W.J. (2006) Cracking during lateral drying of alumina suspensions, Journal of the American Ceramic Society 89 (6): 19081913. Hwa J.C.H. (1964) Mechanism of film formation from lattices. Phenomenon of flocculation, Journal of Polymer Science: Part A 2(2): 785-796. Juhué D. and Lang J. (1993) Effect of surfactant post added to latex dispersion on film formation: A study by atomic force microscopy. Langmuir 9: 792-796.

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König A.M., Weerakkody, T.G., Keddie, J.L. and Johannsmann, D. (2008) Heterogeneous drying of colloidal polymer films: Dependence on added salt. Langmuir 24: 7580-7589. Lee W.P. and Routh A.F. (2004) Why do drying films crack? Langmuir 20(23): 9885-9888. Liao Q., Chen L., Qu X. and Jin X. (2000) Brownian Dynamics simulation of film formation of mixed polymer latex in the water evaporation stage, Journal of Colloid and Interface Science 227: 84-94. Ma Y., Davis H.T. and Scriven L.E. (2005) Microstructure development in drying latex coatings. Progress in Organic Coatings 52: 46-62. Mallégol J., Bennett G., McDonald P.J., Keddie J. and Dupont O. (2006) Skin development during film formation of waterborne acrylic pressure sensitive adhesives containing tackifying resins. The Journal of Adhesion, 82: 217-238. McNamee C.E., Barnes G.T., Gentle I.R., Peng J.B., Steitz R. and Probert R. (1998) The evaporation resistance of mixed monolayers of octadecanol and cholesterol. Journal of Colloid and Interface Science, 207: 258-263. Reyes Y. and Duda Y. (2005) Modelling of drying in films of colloidal particles. Langmuir 21: 7057-7060. Overbeek, A., Bückmann, F., Martin, E., Steenwinkel, P., Annable T. (2003) New generation decorative paint technology. Progress in Organic Coatings 48: 125– 139. Narita T., Beauvais C., Hebraud P. and Lequeux F. (2004) Dynamics of concentrated colloidal suspensions during drying – aging, rejuvenation and overaging, European Physics Journal E 14: 287-292. Narita T., Hebraud P. and Lequeux F. (2005) Effects of the rate of evaporation and film thickness in nonuniform drying of film-forming concentrated colloidal suspensions. European Physics Journal E 17: 69-76. Parisse F. and Allain C. (1997) Drying of colloidal suspension droplets: Experimental study and profile renormalisation. Langmuir, 13(14): 3598-3602. Rottstegge J., Traub B., Wilhelm M., Landfester K., Heldmann C. and Spiess H.W. (2003) Investigations on the film formation process of latex dispersions by solid state NMR spectroscopy. Macromolecular Chemistry and Physics, 204 (5/6): 787-802. Routh A.F. and Russel W.B. (1998) Horizontal drying fronts during solvent evaporation from latex films. AIChE J 44(9): 2088-2098. Routh A.F., Russel W.B., Tang J. and El-Aasser M.A. (2001) Process model for latex film formation: Optical clarity fronts. Journal of Coatings Technology 73(916): 41-48. Routh A.F. and Zimmerman W.B. (2004) Distribution of particles during solvent evaporation from films, Chemical Engineering Science 59: 2961-2968. Salamanca J.M., Ciampi E., Faux D.A., Glover P.M., McDonald P.J., Routh A.F., Peters A.C.I.A., Satguru R. and Keddie J.L. (2001) Lateral drying in thick films of waterborne colloidal particles. Langmuir 17: 3202-3207. Shimmin R.G., DiMauro A.J. and Braun P.V. (2006) Slow vertical deposition of colloidal crystals: A Langmuir-Blodgett process?, Langmuir 22 6507-6513.

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Thouless M.D. (1990) Crack spacing in brittle films on elastic substrates. Journal of the American Ceramic Society, 73(7): 2144-2146. Tirumkudulu M.S. and Russel W.B. (2005) Cracking in drying latex films. Langmuir, 21(11) 4938-4948 Vanderhoff J.W., Bradford E.B. and Carrington W.K. (1973) The transport of water through latex films, Journal of Polymer Science, part C: Polymer Symposium, 41:155-174 van Krevelen D.W. (1990) Properties of Polymers: Their Correlation with Chemical Structure, Their Numerical Estimation and Prediction from Additive Group Contribution, 3rd edition Elsevier: Amsterdam 569-573. Wallin M., Glover P.M., Hellgren A.C., Keddie J.L. and McDonald P.J. (2000) Depth profiles of polymer mobility during the film formation of a latex dispersion undergoing photoinitiated crosslinking. Macromolecules 33: 8443-8452 White L.R. (1982) Capillary rise in powders. Journal of Colloid and Interface Science, 90(2).536-538 White L.R. (2006) Personal communication. Winnik M.A. and Feng J. (1996) Latex blends: An approach to zero VOC coatings. Journal of Coatings Technology, 68(852):39-50.

Chapter 4

4 Particle Deformation

4.1 Introduction When soft particles come into close packing, they will usually start to deform. The ideal result is a structure without voids – although with the individual particles still distinguishable, prior to interdiffusion. For such a deformation there must be a driving force for compaction, and there will be a mechanical response from the particles to balance it. The primary driving force is essentially a reduction in the surface free energy and hence the surface area. Depending on the controlling mechanism, there are three interfacial areas in a latex film that can be reduced: polymer/air; polymer/water; and water/air. For polymeric materials, the rheological response is complex and is crucially dependent on temperature. It is possible to have an instantaneous elastic response or a time-dependent viscous creep. After the drying stage, the packing of the particles will be into a form of close packing, with the evaporation rate crucial in determining whether colloidal crystallisation can occur (Russel 1990, Russel et al. 1990). If the particles pack into a face-centred cubic structure, then after deformation each particle assumes a rhombic dodecahedral geometrical shape when all void space is filled (as in Fig. 1.10b). A TEM image of a close-packed array of dodecahedra is shown in Fig. 4.1. The deformation of particles enables an opaque, powdery film to be transformed into a clear, crack-free material. While subsequent interparticle polymer diffusion is required to achieve mechanical strength (described in Chapter 5), the deformation step is a necessary precursor. The success or otherwise of this deformation transition is the deciding factor in whether the film is useable as a protective coating. Hence, the deformation step is crucial in achieving film formation, and industrial formulators will go to great lengths to ensure its success. This chapter is split up as follows. Firstly, the different possible driving forces, as have been proposed over the previous 50 years, are outlined. Experimental evidence for each mechanism is presented. The mechanical response of two particles is discussed, ranging from the well-known limit of viscous particles sintering under the

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action of surface tension, through to the response of elastic particles under the influence of a force. Instead of considering two isolated particles, the stress-strain response of a bed comprising many particles is derived for the case of viscoelastic particles under the influence of surface tension and a compressive force. This volume-averaged model then provides the basis for the process conditions under which a deformation mechanism may operate. Finally, experimental observations concerning different deformation mechanisms are outlined.

Fig. 4.1 Particles in an FCC array will deform into rhombic dodecahedra. This image was obtained from transmission electron microscopy of a carbon replica of a fractured latex film. (Reproduced with permission from Wang et al. (1992); copyright 1992 American Chemical Society)

4.2 Driving Forces for Particle Deformation There are a number of possible driving forces for particle deformation. A common theme is the reduction in interfacial area as the particles deform, eliminating the boundaries between particles and the interparticle voids. For a 100 µm thick, the number of particles (with a radius of R = 100 nm) in the film is 10–4/ (4/3 πR3) = 2.4 x 1016. The surface area associated with these particles, prior to their deformation, is 4πR2 x 2.4 x 1016 = 3,000 m2, which is comparable

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123

to a football field or a cricket pitch. For a polymer surface tension of 0.01 N/m,1 the energy reduction associated with particle deformation to reduce their area is therefore 30 J. This simple example considers the air and polymer interface, but various other driving forces are discussed next. Sintering is a word used to describe the reduction of interfacial area in order to reduce the surface free energy of a particulate material. In the literature on latex, sintering is described as being either ‘wet’ or ‘dry’ depending on whether the particles are in the presence or absence of water. These and other mechanisms are sketched in Fig. 4.2 and will be discussed individually.

4.2.1 Wet Sintering In the wet sintering mechanism, the surface tension between the polymer and water phases is the dominant driving force. If the particles are pressed together in water, the interfacial area between them is eliminated, and the interfacial free energy is decreased. (Think of what happens when two oil droplets bump together in a salad dressing.) The surface tension between a latex polymer and the aqueous phase is estimated to be about γpw = 0.015 N/m (Eckersley and Rudin 1990). The wet sintering deformation mechanism was first proposed by Vanderhoff et al. (1966). Experimental evidence to support wet sintering was presented by both Sheetz (1965) and then by Dobler et al. (1992), who held latices under water for a considerable length of time and observed a consolidation. Gradual increases in optical transparency (van Tent and te Nijenhuis 2000) and in refractive index (Keddie et al. 1995, 1996b) have been explained by a wet sintering mechanism.

4.2.2 Dry Sintering This mechanism is analogous to wet sintering, except that the polymer-air surface tension, γpa, causes the deformation. Dry sintering is a common mechanism in other types of particulate materials, such as ceramics made from oxide powders. It was originally proposed by Dillon et al. (1951) and given strong experimental backing by Sperry et al. (1994) who followed the cloudy-clear transition of a film by using a minimum film formation temperature bar. Light is scattered from voids within the film, and hence, as these voids become much smaller than the wavelength of light, the film becomes clear (van Tent and te Nijenhuis 2000). The work of Sperry et al. showed that the position of the transition was similar for two films: 1

All forms of condensed matter have a surface (or interfacial) tension, depending on their surroundings (solid, liquid or vapour.) ‘Surface’ usually refers to an interface with air. It is sometimes more intuitive to think in terms of a surface energy (in units of energy per unit area), rather than a tension (in units of force per distance). Note that 1 N/m = 1 J/m2.

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4 Particle Deformation

one drying normally and another that had been fully dried at a far lower temperature before being placed on the temperature gradient of the bar. Particle deformation occurred in the dry particles at the same rate and temperatures as in particles cast in the wet film. Their result proves that water is not relevant in the deformation around the cloudy-clear transition, at least for these acrylic films. Particles were able to deform in air even when they were fully dry.

1. Wet Sintering (Vanderhoff et al., 1966) polymer/water surface tension

2. Dry Sintering (Dillon et al,1951) polymer/air surface tension

3. Capillary Deformation (Brown,1956) pressure at air-water interface

meniscus

4. Capillary Rings (Lin and Meier,1995) Residual water as pendular rings around particle contacts

pendular rings

5. Sheetz deformation (Sheetz, 1965) Solid polymer layer at surface

Fig. 4.2 Possible mechanisms for particle deformation.

4.2.3 Capillary Deformation At a wet film surface, the water between particles will take up a meniscus, which is a curved interface. The radius of curvature depends on the wetting of the particles (indicated by the water contact angle on the polymer surface.) Such a meniscus is shown in Fig. 4.3 with the curvature of the air-water interface creating a negative pressure in the fluid, called the ‘capillary pressure’. (The pressure is always lower on the concave side of the meniscus.) The capillary pressure is

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125

considered in some detail in Chapter 3 in the discussion of lateral drying (Section 3.5). A key point is that the pressure differential across the meniscus is inversely proportional to its radius of curvature. A more tightly curved water surface will create a greater capillary pressure. The pressure is a direct manifestation of the water-air surface tension, γwa, as a greater tension will require a greater pressure to create a curved surface. The accepted value of γwa is 0.073 N/m.

Fig. 4.3 Cryogenic TEM image of consolidated latex particles demonstrating the curvature of the air-water interface. (The water is presently in the form of ice, but the meniscus from the liquid state has been captured.) Reproduced with permission from Ma et al. (2005).

In a mechanism originally proposed by Brown (Brown 1956), the negative fluid pressure is equivalent to a weight being placed on the top surface of a film, compressing the particles. Particle compression pushes water toward the film surface and thereby reduces the curvature of the meniscus. This reduces the capillary pressure. For this reason, the rate of particle deformation is necessarily set to be concurrent with evaporation. Brown balanced the elastic response of particles (determined by the polymer’s shear modulus, G) with the capillary pressure and came up with a criterion for film formation. For particles of radius R, deformation is predicted to occur when G < 35 γwa/R. Numerous other authors have performed similar analyses, deriving slightly different limits, although the prediction of deformation when G < A γwa/R, where A is some number in the range from 30 to 300, is recurrent (Mason 1973, Eckersley and Rudin 1994). Experimentally, there are examples of latex systems in which water evaporation has been found to occur simultaneously with particle deformation, and it acts as the rate-limiting step, as expected for a capillary deformation mechanism (Keddie et al. 1996b).

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4.2.4 Capillary Rings A complication arises with residual water in latex films. For dry sintering to be operative, there must be a polymer-air interface. Any residual water, present as pendular rings around particle-particle contacts, will rule out the possibility of dry sintering. This argument was put forward strongly by Lin and Meier in a series of papers (1995, 1996). Sperry et al. (1994) argue that residual water will be adsorbed into the latex particles, making their surfaces dry and therefore liable to dry sintering. Regardless of the local physical chemistry, the capillary pressure exerted by pendular rings operates in exactly the same way as the polymer-air surface tension, pulling the contact region outwards and hence deforming the particles. The result is that deformation in a humid atmosphere, with hydrophobic particles, is likely to be due to this moist sintering mechanism, although deformation will proceed in exactly the same fashion as the particles undergoing dry sintering.

4.2.5 Sheetz Deformation Sheetz noted that film formation is often vertically inhomogeneous, with a skin of polymer encasing a fluid dispersion below (Sheetz 1965). Sheetz argued that diffusion of water through the continuous polymer produces a compressive force on the film below. It seems more likely, however, that the polymer skin significantly reduces the evaporation rate. Consequently, particles accumulated at the top surface because of inhomogeneous drying (as discussed in Section 3.4) have considerable time to sinter by a wet sintering mechanism. The vertical inhomogeneity has important implications on the final film morphology, and hence Sheetz deformation is retained as a deformation mechanism in its own right. As will be discussed in Section 4.9, all of the deformation mechanisms may be observed in a latex film. The easiest control parameters are evaporation rate, which sets the time over which drying occurs, and temperature, which sets the viscosity of the polymer (and its time response to shear forces). Irrespective of the driving force for deformation, the sintering of particles is common. The next section describes the different models for sintering of two isolated particles. The limitation of this single pair viewpoint is then examined and methods to generate bulk film models are outlined.

4.3 Particle Deformations

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4.3 Particle Deformations

4.3.1 Hertz Theory – Elastic Spheres with an Applied Load The simplest model for two sintering particles is due to Hertz (1881). In this model, two elastic particles of radius R are pushed together by a force F. The exact elastic solution gives the radius of contact a0 as 2 3 RF (1 − v ) a0 = 4 E

(4.1)

where ν is Poisson’s ratio2 and E is the material’s elastic (Young’s) modulus. The geometry is sketched in Fig. 4.4. A further result from the same analysis is that the particle centres approach each other by a distance δ given by 2 2 9 F (1 −ν ) δ = 2 RE 2

2

3

(4.2)

The Hertz theory has been verified for many systems where there is a considerable applied force. At small applied loads, however, discrepancies have been observed. These are because of surface forces (or surface tension) pulling the particles together and leading to an increase in the contact radius. The first analysis of the effects of surface forces in the Hertz theory was carried out by Johnson, Kendall and Roberts (JKR) (1971).

4.3.2 JKR Theory – Elastic Spheres with an Applied Load and Surface Tension Surface energy will act to pull the contact points between particles outward and hence increase the area of contact. (As with dry sintering, an increased contact area will reduce the surface free energy.) Another way to visualise this mechanism is that by increasing the radius of contact between particles, the area of contact with the external fluid decreases, and hence the energy of the system decreases as well. The increase in contact area is sketched in Fig. 4.4. Johnson, Kendall and Roberts used this energy argument to derive the radius of the area of contact, a, as

The Poisson’s ratio, ν, relates strain in orthogonal directions. If a strain ε is applied in one direction, then a strain of νε is observed in a direction at right angles to the direction of the applied strain. For a non-compressible rubbery polymer, ν is 0.5. 2

128

4 Particle Deformation 2 3 (1 −ν 2 ) R     F + 3πγ R +  3πγ RF +  3πγ R   a =     4E 2  2     3

1

2

   

(4.3)

where γ is the surface tension between the particles and the external fluid. It is interesting to note that if γ is set to zero, then (4.3) reverts to the Hertz solution, (4.1). In addition, the surface tension γ provides an adhesion between the particles that requires a (negative) force to ensure separation.

F

R

a

F

Fig. 4.4 Two elastic spheres compressed by a force F have a radius of contact a0. Dotted line shows how contact area will appear, if surface tension is operating.

An interesting aside is that the approach of Johnson, Kendall and Roberts is a so-called ‘macroscopic’ one, with a surface tension derived from a bulk material property. An alternative, but necessarily analogous, approach is to use surface forces with a van der Waals attraction operating between the particles. This alternative approach is followed by Fogden and White (1990) in deriving both the Hertz and JKR results. The discussion about a surface forces versus macroscopic surface tension approach was taken further in a series of papers by Derjaguin and co-workers (Derjaguin et al. 1975, Muller et al. 1980, Muller et al. 1983) and used by Mazur et al. to explain why the deformation of smaller particles is seen to be essentially instantaneous, and therefore elastic (Mazur et al. 1994, 1997; Jagota et al. 1997). Larger particles in contact are predicted to have an initial elastic deformation followed by a slower viscous flow.

4.3.3 Frenkel Theory – Viscous Spheres with Surface Tension The Hertz and JKR approaches assume that the particles are elastic, to derive the material response. The opposite end of the material spectrum concerns viscous particles. The deformation of viscous particles was considered by Frenkel (1945), who estimated the angle of contact between two identical spheres, θ, under the action of surface tension alone. The result is sketched in Fig. 4.5. The spheres are assumed to remain spherical with the radius at any time, R, related to the original

4.3 Particle Deformations

129

radius, R0 by a mass balance. Equating the change in surface energy, γ dS/dt, where γ is the surface tension and S is the total surface area, to the viscous dissipation, which is estimated as Vηγɺ 2 , where V is the total volume, η is the polymer viscosity, and γɺ is the shear rate, estimated for small areas of contact as d/dt (θ 2/2), results in an expression for the angle of contact as

θ2 =

3γ t . 2 R0η

(4.4)

The geometric analysis is then simple to give the approach of particle centres as R0θ 2/2 and the area of contact between particles as πR02θ 2. There have been numerous variations to Frenkel’s theory (Kuczynski et al. 1970, Pokluda et al. 1997, Rosenzweig and Narkis 1981) although the basic rationale remains as outlined above. Experimental evidence to support Frenkel’s theory was given by Dillon et al. (1951) who measured the angle θ, for Saran latex particles, and observed a linear growth rate for θ 2.

(a) γ R

θ

(b)

Fig. 4.5 a Two viscous spheres of radius R sintering because of surface tension. γ is the surface tension between the polymer and the external phase. The degree of sintering can be characterised by the angle θ. b An AFM image (0.5 µm × 0.5 µm) of soft latex particles shows that the boundaries between them is flat. An angle of contact is identified on the image for two particles. (Image courtesy of Argyrios Georgiadis, University of Surrey)

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4 Particle Deformation

4.3.4 Viscoelastic Particles Many authors comment that polymer particles are necessarily viscoelastic (Greenwood and Johnson 1981, Bellehumeur et al. 1998). Lee and Radok (1960) derive the viscoelastic equivalent of the Hertz problem for two spheres compressed by a force F. In a series of papers, Eckersley and Rudin assumed the radius of the circle of contact between particles to be additive between the elastic and viscous components (1990, 1993, 1994). A capillary deformation mechanism was assumed to be balanced with an elastic material response, and a wet sintering mechanism balanced with a viscous material response. This leads to a viscoelastic prediction for the response of two particles, which was tested by measuring the contact area for a range of acrylic particles.

4.4 The Problem with Particle–Particle Approach While a model for sintering of two particles is relevant on the particle length scale, the measurement that is of interest is not the area of contact between two particles but the local volume fraction in the film. That is, to what extent have the particles deformed to fill all available space? Instead of considering the force between two particles, we are more interested in the local stresses (forces per unit area). This is equivalent to saying that the stress-strain relation for a bed of sintering particles is the quantity of most interest, and it happens to be the most easily measured as well. The constitutive relation for the film is necessarily a volume average of sintering particle pairs, and hence a model for the deformation of viscous or elastic particles subject to surface tension and applied forces is needed. The final relation needs to relate the local volume fraction φ of particles to the applied (capillary) stress and surface tension.

4.4.1 Routh and Russel Film Deformation Model There is considerable debate in the early literature on latex film formation. One topic of debate is how to describe the mechanical response to a force (elastic, viscous or viscoelastic) and whether particle pairs or arrays should be considered. A second topic concerns the dominant mechanism for particle deformation (wet or dry sintering, capillary, etc.). Within recent years, the issues have been resolved with the development of a film deformation model (Routh and Russel 1999, 2001a, 2001b). The model considers viscoelastic particles in a bed. It also brings together a description of the many possible mechanisms to show that each is possible, depending on a few key parameters. A particle deformation model is built to describe the deformation of a particle array. Parameter regimes are then

4.4 The Problem with Particle–Particle Approach

131

identified where each deformation mechanism applies. Here, we follow the arguments in the original papers to derive the parameter map. A dimensional analysis argument is also presented in Section 4.6 to explain how the parameter map may be understood.

4.4.1.1 Particle–Particle Deformation The Routh and Russel model for film deformation starts with a particle sintering approach. A generalised viscoelastic model is used with a stress relaxation modulus G(t) defining the polymer rheology. This function relates the stress experienced by the polymer for given applied strain. The simplest way to determine the stress relaxation modulus is to apply a constant strain to a material and to follow the stress as a function of time. With polymers, a large stress is seen at early times, typically followed by a relaxation to a low value. The constitutive equation is integrated over the volume of two sintering spheres compressed by a force F and surface tension γ (applicable to interfaces with air or water). To perform the integration, the particles are taken to remain spherical, as in the Frenkel approach. The deformation is quantified in terms of a strain along the particle centres εR (analogous to θ 2/2 in the Frenkel approach). To lowest order in strain, the sintering is defined by t

( )

2 F 2γ d + ε R = G (t − t ') ε R2 dt ' 2 dt ' πR0 R0 0

∫

(4.5)

For viscous particles, sintering under surface tension alone, (4.5) yields

εR=γt/2ηR0 which is of the same form as the Frenkel result (4.4). For elastic particles under a compressive force, (4.5) yields εR= (F/πGR02)1/2 which differs from the exact Hertz result (4.2) in the exponent being 1/2 rather than 2/3. (In this comparison, εR is related to δ in (4.2) as δ = R0 εR.) This difference occurs because of the simplifying assumption of the particles remaining spherical.

4.4.1.2 Integration to Film Deformation Once a pair deformation model is obtained, it may be integrated over a suitable volume to obtain the stress-strain relation for the film. Choosing a single particle as the representative volume, the average stress may be expressed as the summation of all moments (Batchelor 1970). Hence, the stress may be related to the forces compressing the particles. The strain along the lines of centres, εR, is related to the overall strain field ε. Hence, for a given strain in the film, we may determine the stress through the relaxation modulus. The simplest strain is onedimensional, and the resulting equation for the film compaction is

132

4 Particle Deformation t

σt +

3νφ m 3νφm dε 2 G (t − t ') dt ' γε = 20 R0 56 dt '

∫

(4.6)

0

This equation relates the stress at the top surface σt and surface tension γ, to the strain in the film ε and material response G(t).

4.4.1.3 Assumption of a Viscoelastic Fluid Taking a particular mechanical response allows (4.6) to be solved and hence the deformation to be predicted as a function of time. The mechanical response chosen is a simple viscoelastic fluid with a single relaxation time

 − G∞' t   G (t ) = G∞' exp   η0 

(4.7)

where G∞' is the high frequency modulus and η0 is the zero shear-rate viscosity. Substituting (4.7) into (4.6) allows derivation of a non-dimensional differential equation governing the compaction of a particle bed as

dσ t dε 7γ  dε  + Gσt + + Gε  = Gλ ε ,  dt dt 5  dt 

(4.8)

where the dimensionless groups controlling the compaction, σ t , G , γ and λ are defined in Table 4.1. The first two terms on the left-hand side relate to the stress applied at the top surface of the film. The third term relates to the surface tension causing the film to compact, and the term on the right-hand side describes the mechanical response.

Table 4.1. Definition of dimensionless groups used to determine film compaction Symbol

Definition

Physical Meaning

σt

28σ t R0 3νφmγ wa

Stress at top surface (σt) divided by capillary stress (γwa/R0)

γ

γ γ wa

Surface tension divided by water-air surface tension

G

G∞' H η Eɺ 0

λ

η 0 R0 Eɺ γ wa H

Evaporation time ( H / Eɺ ) divided by polymer relaxation ' time ( η0 / G∞ ) Time for film to compaction (η0R0/γwa) divided by evaporation time ( H / Eɺ )

4.5 Deformation Maps

133

4.5 Deformation Maps Using (4.8), it is possible to generate parameter maps that determine which deformation mechanism applies in each situation. The final result is shown in Fig. 4.6, where four regimes are seen in the vertical direction on the map.

4.5.1 Wet Sintering In the wet sintering mechanism, the particles remain in water. The deformation must be quick enough so that no capillary pressure is established. Hence ε > t , and σ t = 0 . This condition defines a line in a graph of λ / γ versus G , with wet sintering operating below the line.

4.5.2 Capillary Deformation Here, the deformation is concurrent with evaporation, ε = t , and the capillary pressure must be below the maximum value that can be achieved: σ t < σ max . Choosing representative parameter values, σ max is around 20. Ignoring the effect of wet sintering on particle deformation defines a second line on a graph of λ versus G .

4.5.3 Dry Sintering In dry sintering, the particles are assumed to not undergo significant deformation until the water has evaporated. The condition for dry sintering is that the deformation achieved by the capillary stress as the water evaporates is minimal. Setting the capillary stress at its maximum value, and ensuring small deformation (ε < 0.054) at the end of the evaporation, defines a line above which dry sintering applies.

4.5.4 Receding Water Front In Fig. 4.6, there is a receding water front regime between the capillary deformation and dry sintering regimes. In this intermediate regime, significant deformation of the particles occurs because of capillary deformation, but final compaction of the film occurs by a dry sintering mechanism only after complete water evaporation. Hence, this is an inhomogeneous regime, where a water front passes verti-

134

4 Particle Deformation

cally through the film. Capillary deformation occurs below the meniscus of the water front, and dry sintering occurs in the particles above the front. In experiments on latices at temperatures not far above their Tg, it has been found that air voids between particles are present for a short time before decreasing in size and disappearing entirely (Keddie et al. 1995). Although it was first proposed as an additional stage in the film formation process (II*), the observed phenomenon is an example of a receding water front mechanism.

Dry/moist sintering η R Eɺ λ = 0 0 γ wa H

Receding water front

Capillary deformation Wet Sintering (γpw/γwa=0.2) G=

G∞' H Eɺ η0

Fig. 4.6 Deformation regimes for different values of the key parameters. (Reproduced with permission from Routh and Russel 1999; copyright 1999 American Chemical Society)

4.5.5 Use of the Deformation Maps These three lines (separating four regimes) are shown in Fig. 4.6. The map demonstrates how the dimensionless group λ is crucial in determining the deformation mechanism. For any given experimental conditions, the value of λ may in principle be calculated. An engineer may use the maps to investigate how changing a parameter, such as the evaporation rate, film thickness or particle size, will influence the particle deformation mechanism. Section 4.7 will consider the effect of temperature, which has a pronounced effect because it can change the polymer viscosity by several orders of magnitude. Other parameters, such as the surface tension, may typically be adjusted only in real situations by a factor of two or three. The extent of particle deformation will determine the final film morphology.

4.6 Dimensional Argument for Figure 4.6

135

4.6 Dimensional Argument for Figure 4.6 A way to view Fig. 4.6 is as a process where each possible driving force is sampled sequentially. The condition for wet sintering is that the particles deform faster than evaporation reduces the water level in the vertical direction, thereby keeping the particles wet. For capillary deformation, the stress at the top surface must be less than the maximum level that can be supported by the particle bed. For dry sintering, we insist that the particles are essentially undeformed by the time that the water has completely evaporated. The particle deformation rate must be slow, relative to evaporation rate. These basic concepts may be used to derive simple scaling predictions to aid in the understanding of the deformation maps. The symbols and concepts follow on from Section 4.5.

4.6.1 Wet Sintering In the case where particles are consolidated at close packing in the wet state, they will be deformed because of the polymer-water surface tension, γpw, in a wet sintering mechanism. Equally, evaporation will continue at the same rate. For the particles to remain under water, the film must decrease in height faster than evaporation reduces the water height. The time for film compaction under a wet sintering mechanism may be estimated as η0R0/γpw and the time for evaporation is H / Eɺ . Therefore the requirement for wet sintering is

η0 R0 Eɺ

Hγ pw < 1,

which follows from the evaporation time being greater than the sintering time. Assuming a value of the group γpw/γwa to be 0.2 gives a requirement of λ having a value around 1 at the transition to the wet sintering regime. This is shown mathematically as λ ~O(1) or λ being on the order of 1, in the upper range of the wet sintering regime.

4.6.2 Capillary Deformation If capillary pressure is created at the top surface of a film, the height of the film will decrease at a rate set by the evaporation rate. Therefore, the shear stress in the film is given by the polymer viscosity multiplied by the shear rate set by this vertical deformation, or

η 0 Eɺ

H

.

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4 Particle Deformation

This shear stress will balance the capillary pressure, given approximately by γwa/R0 at equilibrium. Deformation will occur when the capillary pressure is greater than the shear stress. Thus, the condition for capillary deformation becomes

η 0 Eɺ

H

< A γwa/R0

where A is a scaling parameter. Upon rearrangement, this becomes λ Vc, the particles create a continuous path.

Fig. 7.14 Minimum film formation temperatures (MFFT) for films made from hard and soft particles blended in a 1:1 ratio by mass. The soft particles had a Tg of ca. 2 °C, and the hard particles had an average Tg of 116 °C. The surface-average particle size of the two particle types was varied, while the mass ratio was fixed. MFFT increases with an increasing ratio of the surface-average soft particle radius, Rsoft, to the surface-average hard particle radius, Rhard. (Reproduced from Colombini et al. 2004)

238

7 Nanocomposite Latex Films and Control of Their Properties

Colloidal crystals can be created from blends of large and small particles, provided that the size distribution of each population is narrow. There is a direct analogy with ionic crystals that are made up of small cations and large anions. The smaller particles fit into the void space between the large particles in a densely packed array. Each particular crystal type requires a certain size ratio of large:small particles. Table 7.4 lists the required ratios for three different crystal types. Unlike the previous examples, in which the number of small particles was much greater than the number of large particles, these colloidal crystal structures dictate that the number ratio of large:small is 1:1.

Table 7.4 Large:Small Size Ratios Required for Colloidal Crystals Made from Bimodal Blends of Latex Particles Crystal Structure

Salt Analogue

Space Occupied Number of by Small Neighbours Particle Around Each Small Particle

Large:Small Size Ratio

Simple Face-centred cubic Diamond

CsCl NaCl

Cubic Octahedral

8 6

1.37:1 2.41:1

ZnS

Tetrahedral

4

4.45:1

7.5 Three Lessons about the Properties of Waterborne Nanocomposite Films The recent spurt of growth of research on waterborne nanocomposites allows us to learn some lessons for future developments. Our interest here is on how the particle structures and the control of the particle arrangement in film formation provide a means of tailoring film properties.

7.5.1 Lesson One A percolating phase, although a minority in the composition, has a strong influence on the properties of the film. Percolation is defined as the situation in which a minority phase creates a continuous path across the majority phase. It is possible to ‘travel’ from one side of the material to the other without leaving the percolating phase. The lowest concentration of the minority phase at which percolation is achieved is called the ‘percolation threshold’.

7.5 Three Lessons about the Properties of Waterborne Nanocomposite Films

239

7.5.1.1 Percolation of Spherical Particles Computer simulations have found that when equal-sized particles of two types (say A and B) are randomly packed together, the particles in the minority will create a percolating cluster when a fraction of 0.326 of the sites are occupied by the minority particles (Frith and Buscall 1991). This cluster is defined by conditions where there are continuous contacts between the same types of particles across the entire layer. At the point when a rigid percolating network is created, there is a strong change in the mechanical properties. The network acts like a skeleton that raises the elastic modulus of the composite. Chevalier et al. (1999) studied hard particles blended in a matrix created by soft particles (film-forming at room temperature). They showed that percolation of the particles had some effect on the modulus, but the effect was more pronounced after the nanocomposite was heated above the Tg of the hard phase. Interdiffusion between particles fused the particles into a rigid skeleton. By comparison, when contact between the hard particles was prevented by encapsulating the particles with a soft shell, the hard particles had a much smaller effect. A percolation model was able to predict the observed increase in the elastic modulus by about three orders of magnitude (Fig. 7.15), when the volume fraction of hard particles rose above the percolation threshold (Chevalier et al. 1999). The percolation threshold is estimated to be at 0.3 in this system. The hard particles were smaller than the soft particles comprising the continuous matrix, so the percolation threshold is lower than the predictions for the packing of equal-sized particles.

Fig. 7.15 Dynamic shear modulus (real part) of latex films made from blends of hard poly(styrene) (PS) particles and soft poly(n-butyl acrylate) particles, for varying volume fractions of PS. The experimental points are shown with the filled circles. The solid line is the prediction of a phenomenological mechanical model for the percolation assuming a percolation threshold of 0.30. (Reprinted with permission from Chevalier et al. 1999, copyright 1999 American Chemical Society)

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7 Nanocomposite Latex Films and Control of Their Properties

7.5.1.2 Percolation of Rod-Like Particles Fig. 7.16 shows the structure of a film in which the concentration of rod-like nanofillers is below and above the percolation threshold. As a general rule, low percolation thresholds of rod-like fillers require particles that are randomly oriented and are finely dispersed (not agglomerated or bundled). The colloidal route can satisfy both these requirements. Relatively large filler particles, i.e., micrometer-sized carbon black particles, have a percolation threshold of 2 vol.% in blends with a latex (Grunlan et al. 2001). On the other hand, the percolation threshold for the onset of electrical conductivity in a nanocomposite of colloidal poly(vinyl acetate) latex and single-wall carbon nanotubes (SWNTs) has been found to be as low as 0.04 wt% (Regev et al. 2004). The percolation threshold of randomly oriented, needle-like particles is inversely related to their aspect ratio, defined as the ratio of their length over their width. Therefore, because nanotubes have a high aspect ratio, they can achieve a low percolation threshold (Foygel et al. 2005). A small number of longer nanotubes and a weak attraction between the nanotubes both reduce the percolation threshold significantly. However, the flexibility and ‘straightness’ of the nanotubes have only a minor effect (Kyrylyuk and van der Schoot 2008). The percolation of electrical conductivity in nanocomposites of polymers and carbon nanotubes has been reviewed (Bauhofer and Kovacs 2009).

(a)

(b)

Fig. 7.16 Illustrations of rod-like, inorganic particles dispersed in a polymer film. a At concentrations below the percolation threshold, some particles are in contact but there is not a path across the film. b Above the percolation threshold, there a paths in all directions moving across the film.

The 3-D percolating network of a conducting inorganic phase can impart high electrical conductivity, and so measurements of conductivity are a good probe of the structure. A three-dimensional honeycomb network of SWNTs created around PS colloidal particles has an electrical conductivity on the order of 104 Sm–1, but it is insulating below the threshold (Dionigi et al. 2007). A network of a conducting polymer in a colloidal nanocomposite achieved a percolation threshold of 0.011,

7.5 Three Lessons about the Properties of Waterborne Nanocomposite Films

241

which is a factor of 10 lower than in a conventional blend, accompanied by an electrical conductivity that is several orders of magnitude greater (Mezzenga et al. 2003). Elsewhere, a soft colloidal nanocomposite of poly(butyl acrylate) and SWNTs achieved a percolation threshold of only 0.03 wt.% (Wang et al. 2008). These colloidal nanocomposites can serve as electrically conductive adhesives and coatings and find applications in electronic devices and displays.

7.5.1.3 Properties in Percolating Systems Percolation can also be achieved by the film formation of core-shell particles. If the shell is thin, then its volume fraction will be in the minority. When the particles are packed together to create a film, this minority shell phase will be continuous through the material. Even though it is a minority phase, it can be dominant in determining the properties. By comparison, in blends of particles, the minority phase is often isolated. Colloidal methods of nanocomposite processing use building blocks with a high surface area, which result in nanocomposites with an extremely high internal interface area. For instance, the interfacial area between particles with a radius of 125 nm (assuming particle deformation but not coalescence) is greater than 10 m2 for every gram of polymer. A shell material will cover this high interface area and therefore be efficiently dispersed. The presence of a percolating shell network can have a pronounced effect on mechanical properties. An excellent example is provided by films made from particles with a soft, rubbery core and a stiff, glassy shell (Domingues dos Santos and Leibler 2003). The nanocomposite films have a continuous glassy phase. The elastic modulus of the film is much higher than that of the core polymer. When the elastic limit is exceeded, the films show a yield point followed by plastic deformation. The mechanical response of the core-shell films differs remarkably from blends of particles made from the same polymers as in the core and the shells. The volume fraction of the glassy phase in the particle blends was kept the same as in the core-shell material, so that a fair comparison could be made. In the particle blend films, the glassy particles are isolated in the soft matrix. In this case, the films are tacky and flow under a low applied stress. Fig. 7.17 shows schematically the two types of structures and the resulting mechanical properties. We can also consider an example of inorganic-polymer nanocomposite particles. Laponite clay platelets have been used to encapsulate particles with a styrene-acrylate copolymer core. When these particles are assembled onto a nanocomposite, a percolating network of clay platelets is created (Negrete-Herrara et al. 2007) in which the clay platelets are arranged in a three-dimensional honeycomb-like structure. The laponite decorates the boundaries between the deformed particles. This honeycomb network is quite efficient in mechanical reinforcement, giving a 50-fold increase in Young’s modulus in comparison with the polymer alone. There is also a strong increase in the maximum stress before failure and in the toughness. See Fig. 7.18 for a comparison of the stress-strain relationship of

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7 Nanocomposite Latex Films and Control of Their Properties

the nanocomposite and a copolymer film without clay. With the addition of clay, the elastic modulus (indicated by the slope at small strain) increases. More importantly, the nanocomposite can be strained by a similar amount as the copolymer without failure. Thus, the addition of clay increases the area under the stress-strain curve and hence the toughness. To see a pronounced effect on the mechanical properties of a core-shell film, a combination of glassy and rubbery polymers is not necessarily required. There is a recent example of a ‘soft-soft’ nanocomposite. This material is made from particles that have a shell that is capable of crosslinking. When film-formed, percolating elastic, crosslinked network is created. This nanomaterial was specifically designed for adhesives to achieve a softening of the material under moderate strains and a stiffening of the material at high strains (Deplace et al. 2009).

Yield point

Soft core

Glassy shell

Core-shell latex Soft matrix

Glassy particles

Particle blend

Strain Fig. 7.17 A comparison of the deformation of two types of nanocomposite films: core-shell structure versus particular blend structure. The phase shown in black is a glassy polymer, and the grey phase is a rubbery polymer. Both films contain 20% of the hard phase. The core-shell structure is stiffer and is tougher. After its elastic limit is reached, the film yields and deforms plastically. The blend film does not show yielding but instead flows under low stress. (Adapted from Domingues dos Santos and Leibler (2003); copyright 2003; reprinted with permission of John Wiley & Sons, Inc)

7.5.1.4 Properties of Hybrid and Blend Systems Core-shell particles are not the only way to create continuous phases in a film. Hybrid latexes prepared by miniemulsion polymerisation are expected to have the two polymer phases mixed at the molecular level. By comparison, blends of particles tend to have a continuous phase created by the majority phase. Domains of the other phase are expected to be the size of the particles or larger.

7.5 Three Lessons about the Properties of Waterborne Nanocomposite Films

243

Fig. 7.18 Tensile stress-strain curves for loading and unloading of latex films: a poly(styrene-cobutyl acrylate) and b nanocomposite of the same copolymer and Laponite. Film nanostructure is shown in Fig. 7.8. (Reproduced from Negrete-Herrera et al. 2007; copyright Wiley-VCH Verlag GmbH & Co. KGaA; reproduced with permission)

These expectations were met in hybrid latex made from polyurethane and an acrylic copolymer via miniemulsion polymerisation. The two phases were cocontinuous in the film. By comparison, films made from blends of the two particles had larger, more distinct phases (Wang et al. 2005). These differences in structure had an influence on the mechanical properties. The hybrid film had a higher yield stress (the point where the material is plastically deformed), and a larger strain at break in comparison to the film made from blends of particles. This example shows that there can be real advantages from mixing phases at the molecular level to create a co-continuous structure. In blends of hard (glassy) and soft (rubbery) particles, the continuity of the two phases is determined by their particle size ratio and volume fractions, as already pointed out. For instance, in a blend that consists of a 1:1 ratio by volume of the hard and soft phases, the elastic modulus at intermediate temperatures is a function of the particle size (Colombini et al. 2004). In an example, illustrated in Fig. 7.19, when the size of the soft particles is 0.36 times the size of the hard particles, there is good continuity of the soft phase, and the modulus is relatively low, but higher than for the pure soft phase. When the soft particles were larger than the hard particles, they were less continuous, and the hard particles made a greater contribution to increasing the modulus. The modulus can be raised substantially through the addition of a hard phase in a particle blend film, even when the hard phase is in the minority by volume. The smaller the size of the hard particles in comparison to the larger ones, the more effective they are in raising the modulus.

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7 Nanocomposite Latex Films and Control of Their Properties

Fig. 7.19 Storage modulus as a function of temperature for films made from blends of hard (Tg ≈ 120 C and soft (Tg ≈ 20 C particles. Results from two films are compared each with equal amounts by mass of the hard and soft polymer. The data shown with the open squares are from a film in which the radius of the soft particles, Rsoft, is lower than for the hard particles, Rhard. The data shown with the filled circles are from a film in which Rsoft > Rhard, as indicated. In the latter case, the hard particles have more connectivity, and the modulus is higher in the temperature region between the two Tg values. (Data from Colombini et al. 2004)

7.5.2 Lesson Two In nanocomposite particles for coatings, the surface of the particles has a dominant influence on the surface properties of the coating. This is an important lesson when designing particles for particular coatings applications. Inorganic phases are often introduced into coatings to increase scratch resistance. The friction of a coating is set by the material at the surface. Thus, if an inorganic phase is encapsulated inside a particle, it will be buried slightly beneath the outermost surface of the coating. The inorganic material will then make a lower contribution to the film’s hardness. For instance, nanocomposite films have been made from acrylic polymers and silica (SiO2) nanoparticles. High scratch resistance was achieved, because the hard silica particle decorated the latex particle – and hence film – surfaces. The hard particles were therefore at the film surface and not buried. (Tiarks et al. 2007). Blends of inorganic nanoparticles and latex usually have a patchier surface with the inorganic appearing in clusters. In this case, some of the polymer is left exposed and is sensitive to scratching.

7.5 Three Lessons about the Properties of Waterborne Nanocomposite Films

245

Another surface-sensitive characteristic is ‘blocking resistance’. This is defined as the tendency to avoid adhesion between polymer surfaces when they are placed in contact. Blocking (adhesion) results from polymer diffusion across the interface, in a process similar to the crack healing discussed in Chapter 5. Silica (or other inorganic particles) at the surface of particles is believed to prevent interdiffusion of polymers across contacting surfaces (Tiarks et al. 2007). The silica nanoparticles presumably create a physical barrier to diffusion across the film-film interface. Hence, blocking resistance is increased. Nanocomposite particles are now being produced industrially for use as a binder in architectural paints. Inorganic nanoparticles that are homogeneously incorporated into polymer latex particles are being sold under the trade name of Col.9® (Weitenkopf 2009). After film formation, a three-dimensional network of nanoparticles is created. It is reported that the inorganic particles make the binder less tacky – especially at higher temperatures – in comparison to standard thermoplastic binders. Hence, there is less pick-up of dirt. However, the polymer phase prevents the binder from being too brittle, so that cracking and loss of pigment particles (called ‘chalking’) is prevented. Formulated paints using the nanocomposite particles as binders are now being produced and sold. Polymer-polymer nanocomposite latex coatings have similarly been used to achieve blocking resistance. Latex particles that contain a hard polymer and a soft polymer phase have been used. The hard polymer phase creates a rougher surface, does not wet other surfaces, and inhibits interdiffusion. The soft polymer phase enables particle coalescence and film formation. When there is too much of the hard polymer present, film formation is not possible (Schuler et al. 2000). The same sort of argument, regarding the importance of particle surfaces, applies to the wettability of surfaces. Poly(dimethyl siloxane), or PDMS, has been incorporated into acrylic particles to increase the hydrophobicity. The contact angle of water, which is used as a measure of a surface’s hydrophilicity, is determined by the composition of the material near the surface. Hence, the contribution of PDMS is lost if the phase is localised inside of the particle cores. The greatest hydrophobicity has been found when the PDMS is copolymerised with the acrylic polymer such that PDMS is found at the surface of the colloidal particles (Rodriguez et al. 2009).

7.5.3 Lesson Three The interface between a nanofiller and the matrix can have a profound impact on the macroscale properties. In the case of nanocomposites manufactured from blends of particles, Wang et al. (2008) have pointed out that the dispersant for waterborne inorganic nanoparticles, such as a surfactant or a water-soluble polymer, becomes localised at the interface with the matrix. Fig. 7.20 shows the effect schematically. One does not expect to find a ‘clean’ interface between an inorganic nanoparticle and the polymer matrix.

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7 Nanocomposite Latex Films and Control of Their Properties

(a)

MWNT

Water

Dispersant

Latex particles

(b) Film MWNT

Interface without PVP

(c)

Fig. 7.20 a Carbon nanotubes are dispersed in water using hydrophilic polymers. b After film formation, the latex polymer creates a matrix in which the carbon nanotubes (CNT) are dispersed. A ‘clean’ interface between the CNT and the matrix is not possible. c Polymers are adsorbed on the CNTs. In the nanocomposite film, the polymers are isolated at the interface between the CNT and the matrix. (Reprinted with permission from Wang et al. 2008c; copyright 2008 American Chemical Society)

Wang et al. found that the value of the adhesive criterion, tan δ/E', of the poly(butyl acrylate) P(BuA)/MWNT colloidal nanocomposites can be tuned through control of the interface structure. A small molecule (surfactant) or short chain polymer yielded a lower tanδ/E' value compared to high molecular polymer chains at the nanotube-matrix interface, and consequently lower adhesion energy resulted. The adhesion energies of the nanocomposite adhesives can be adjusted by the extent of chain entanglement and molecular friction at the interface between the filler and the matrix. Fundamentally, the performance and fracture mechanism of polymer nanocomposites containing high aspect-ratio fillers (e.g., nanofibres (Callister 2007), carbon nanotubes (Coleman et al. 2006b), and nanoplatelets (Bonderer et al. 2008)) are controlled by the interface strength between the matrix and the filler and by the filler’s aspect ratio. A nanofiller will break during deformation of the nanocomposite only when the stress transferred is larger than its fracture strength. If the transferred stress does not exceed the filler’s fracture strength, the filler will pull out from the matrix. Fig. 7.21 illustrates these two fracture mechanisms. The critical length, Lc,

7.5 Three Lessons about the Properties of Waterborne Nanocomposite Films

247

defined as the minimum length at which the stress transferred to a nanofiller equals its fracture strength, is calculated for fibres and platelets as

Lc =

σfD 2τ

(7.1)

where σf is the filler fracture strength, D the filler diameter, and τ the interfacial strength. The critical length of carbon nanotubes (Coleman et al. 2006b) is calculated as

Lc =

σ f D  Di 2  1 −  2τ  D 2 

(7.2)

with Di being the inner diameter of the nanotubes. The nanofiller will pull out from the matrix when its length LNF is less than Lc, and it will fracture when LNF > Lc. It might be expected that the fracture of most colloidal nanocomposites will occur by nanofiller pull-out, because of the difficulty in achieving a high τ . (a)

(b)

(c)

Fig. 7.21 The failure mechanisms in nanocomposites that contain nanosized fillers. a The interface between the filler particles and the polymer matrix has an important impact on the macroscopic properties. b If the interface is strong, the filler particles will fracture along with the matrix. c With a weaker interface, the filler particles will pull out of the matrix but will not fracture.

For a nanofiller to increase the strength of a nanocomposite, stress must clearly be transferred from the matrix to the filler. Recent work has used covalent bonding of the matrix to the filler to ensure high interfacial strength (Lin et al. 2003). There are various examples showing that an increase in τ leads to increased macroscale strength and toughness. For instance, spherical nanoparticles in PP or PS systems

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7 Nanocomposite Latex Films and Control of Their Properties

(Zhou et al. 2007) are highly effective in toughening the nanocomposite when the testing temperature is above the glass transition temperature (Tg) of the polymer matrix. At the higher temperatures, the polymer can wet the nanofillers and provide good interface adhesion. A second example of interface effects is when a polymer is grafted onto MWNTs to improve miscibility with the matrix. The efficient load transfer from the matrix to the nanotubes increases the mechanical performance (Shi et al. 2007). Yet another example is when a high density of polymer chains grafted on SWNT surfaces leads to more effective interfacial stress transfer and results in a pronounced mechanical reinforcement (Xie et al. 2007). 0.30

1

a Stress/MPa

0.25

Pure PBA -3 Σ=2.5 x10 -3 Σ=3.6 x10 -3 Σ=6.5 x10

2

σc

3

0.20

4

0.15

σm

0.10 0.05 0.00

0

0.30

5

10

15 Strain

1

ba

0.25 Stress/MPa

2

1

4

20

25

N=9 N=90 N=3200 N=14144

2 3 4

0.20

3

30

Σ= 0.170 Σ= 0.157 Σ= 0.026 Σ= 0.010

0.15 0.10 0.05 1

0.00

0

5

10

2

3

15 20 Strain

4

25

30

Fig. 7.22 a Stress-strain relationship in nanocomposite films made from blends of poly(n-butyl acrylate) latex and carbon nanotubes. The estimated density of the adsorbed poly(vinyl pyrrolidone) (PVP) dispersant, Σ (units of chains/nm2) is shown by each curve for a fixed degree of polymerisation, N, for the PVP. Results from a film without nanotubes (just pure poly(butyl acrylate)) is shown for comparison. b Similar data in which the degree of polymerisation of the PVP is varied. Values are shown by each curve. (Reprinted with permission from Wang et al. 2008c, copyright 2008 American Chemical Society)

12341234

References

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It is well established that polymer chain length (N) and density (Σ, number of chains per unit area) at interfaces influence fracture (Creton et al. 1992, Norton et al. 1995, Dai et al. 1996), adhesion (Creton et al. 1994), and friction (Bureau and Léger 2004, Casoli et al. 2001). Experiments by Wang et al. (2008c) systematically investigated the interface control of τ in a soft polymer-nanotube nanocomposite through variation of the chain length and density of the polymers at the interface between the nanotubes and the continuous matrix. The macroscale strength and toughness of the nanocomposites were profoundly affected by Σ and N, as demonstrated in the stress-strain curves in Fig. 7.22. Analysis of these results showed that τ increases with Σ, but then levels off above a critical value. The value of τ (per chain) increases with increasing chain length. The results are explained through an analogy between the force required in the nanotube pull-out process and the friction force of polymer brushes on solid surfaces sliding along a rubber. It is predicted that the monomeric friction coefficient of different polymers could be used to tune the interface strength and consequently to adjust the macroscopic properties of colloidal nanocomposites.

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Chapter 8

8 Future Directions and Challenges

This book has aimed to provide a comprehensive introduction to the main topics relevant to film formation. It is interesting to note some of the topics that were considered as future challenges and new directions in 1997 in a review of latex film formation (Keddie 1997): ● Film formation from latex blends; ● Film formation from core-shell and composite particles; ● Using reactive surfactants. Progress on these topics during the intervening years is easily charted. Developments in the creation of nanocomposite films through latex blends and twophase particles were summarised in Chapter 7. Achievements in the use of reactive surfactants were highlighted in Section 6 of Chapter 6. Despite the vast amount of research over the past decades, unanswered questions about the film formation process remain. Interest in the topic therefore remains strong. In numerous developments, polymer colloids are being used in new applications. Here, we highlight a few exciting future directions in the field of latex film formation.

8.1 Film Formation from Anisotropic Particles So far, we have considered film formation only from spherical particles. Historically, techniques of emulsion and dispersion polymerisation have created particles that are perfect spheres. The surfaces of the particles have a uniform composition with homogeneous chemical functionality and reactivity. Latex particles are usually isotropic. In recent years, techniques of synthesis have been developed to create colloidal particles with controlled anisotropy. Particles that have a degree of anisotropy lend themselves to self-assembly into complex structures (Glotzer and Solomon 2007). One type of anisotropy can be broadly said to be geometric, such

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as having facets, a high aspect ratio, or branching. There have been reports, for instance, of ellipsoidal latex particles with an aspect ratio (defined as the ratio of the long axis to the short axis) as high as 12.8 (Mohraz and Solomon 2005). Some ellipsoidal particles can be seen in Fig. 8.1. When the particles are sedimented, some alignment of the long axes parallel to each other can be found.

Fig. 8.1 Ellipsoidal latex particles made from poly(methyl methacrylate) having an aspect ratio of 5.2. (Reprinted from Mohraz and Solomon (2005), copyright 2005 American Chemical Society)

Another type of anisotropy can be broadly classed as chemical in nature; examples include patchiness in surface coverage or chemical patterning. Spherical particles in which opposite faces have differing polarity or charge are called ‘Janus particles’ (Roh et al. 2005). The name ‘Janus’ is derived from the Roman god who had two faces. In the same way, a Janus particle can have two faces, such as one hydrophilic and one hydrophobic. This type of particle will spontaneously assemble at an oil-water interface (Casagrande et al. 1989). Such activity can be harnessed to create supra-particle assemblies. Janus particles can also have opposite electric charge on their two faces. When the particle diameter is greater than the charge screening length, particle clusters (containing up to 13 particles) are formed in aqueous suspensions (Hong et al. 2006). These new anisotropic particles offer fresh challenges in the field of film formation. Numerous forces, as presented in previous chapters, act upon the particles during the film formation process. Beyond these, attractions and repulsions between opposite sides of the particles will influence the orientation of particles during the packing stage. New types of packing, beyond FCC or BCC, will be

8.2 Assembly of Particles over Large Length Scales

263

found with oblong or asymmetric particles. Some earlier work has used particles with two hemispherical phases to create heterogeneous films (Hagen et al. 1996). The structures shown in Fig. 8.2 indicate that the orientation and ordering of the particles was not controlled. In other experiments, individual latex particles that are partly hydrophilic and partly hydrophobic have been shown to become oriented at interfaces (Pfau et al. 2002). The more hydrophilic face was found to absorb on surfaces that were quite hydrophilic. On less hydrophilic surfaces, the hydrophobic face absorbed. In thicker films, the particles adsorbed with their hydrophobic face along the interface, regardless of the substrate’s hydrophilicity. There is plenty of scope for modelling and further experimentation, especially with the aim of controlling particle orientation in thick films.

(a)

(b)

Fig. 8.2 a Phase separation between polystyrene and poly(butadiene) leads to hemispherical phases within particles, as shown in this TEM image in which one phase is stained. b This particle structure is preserved in the films. Hemispherical structures can be seen in the TEM image. A better control over the particle alignment and orientation will lead to films with unique structure over long length scales. (Reprinted from Hagen et al. 1996; copyright Wiley-VCH Verlag GmbH & Co. KGaA; reproduced with permission)

8.2 Assembly of Particles over Large Length Scales With the growth of applications of polymer colloids moving well beyond traditional coatings and adhesives, and going toward new applications, such as tissue scaffolds and photonic crystals, polymer colloid specialists have much to offer. One of the biggest challenges is to achieve the ordering of particles on a lattice

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over large areas. Quite often, there are packing defects (missing particles or extra particles) that disrupt the order. With a tight control over the particle size distribution, and with the right formulation and drying conditions, however, colloidal crystals covering areas as large as 2.6 cm x 2.6 cm have already been achieved (Wohlleben et al. 2007). Good progress has been made in the creation of photonic crystals using latex technology. Photonic crystals are used in all-optical integrated circuits that rely on the transport of photons rather than electrons, as in a conventional circuit. In a photonic crystal, a range of light frequencies are forbidden to exist within the interior of the crystal, thus creating an optical band gap. Photonic crystals have a periodic modulation of refractive index (or dielectric constant at the frequencies of light) to manipulate the light (Joannopoulos et al. 1997). The requirements for photonic crystals are rather strict. The size of the unit cell for a photonic crystal must be comparable to the wavelength of light. For near-infrared light at 1.5 µm, the unit cell must be about 0.5 µm, which puts the size scale in the colloidal domain. To increase the band gap, the magnitude of the refractive index modulations must be increased by using materials with greater index differences. An inverse opal structure, which is found in some types of photonic crystals, can be created from close-packed, hard colloidal spheres. The empty space around the particles is filled in with a high-refractive index material; later the particles are removed (dissolved or etched away), to leave spherical voids. Polymer particles are effective templates for the creation of inverse opals. The challenges in creating newer photonic crystal structures are even greater. In a ‘double-inverse-opal’ structure, a weakly scattering spherical particle is introduced inside each void within a periodic, inverse opal structure (see Fig. 8.3). This design enables optical switching from a reflector state to a photonic crystal state (Ruhl et al. 2006).

Silica particles Titania honeycomb structure

Fig. 8.3 SEM image of a double inverse opal structure created using latex particles packed into an array. Titania was deposited in the void space between latex particles with a silica core (radius of 60 nm). When the polymer was removed, the silica particles are caged inside of the titania honey-comb structure. (Reprinted from Ruhl et al. 2006; copyright Wiley-VCH Verlag GmbH & Co. KGaA; reproduced with permission)

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265

Periodically structured composites that have unit cells smaller than a particular wavelength of light (e.g., visible or infrared) are known as ‘metamaterials’. It has been proposed that in future, anisotropic colloidal particles (including latex particles) could be self-assembled to create metamaterials (Stebe et al. 2009). One of the most exciting applications of metamaterials is to create cloaking devices to render objects invisible at certain wavelengths of light.

8.3 Technique Development The study of latex film formation has benefited enormously from new experimental techniques. Latex films are often used as a ‘model system’ during technique development. Latex systems were studied early on in the emergence of small angle neutron scattering, fluorescence resonance energy transfer (FRET), and atomic force microscopy, among others. This trend is likely to continue, considering the wide applicability of polymer colloids. Drying processes will continue to be of interest. A particular technique developed recently, inverse-micro-Raman-spectroscopy, offers many attractive features. It can determine water content non-invasively in drying latex films in the vertical as well as the horizontal directions. A spatial resolution of 2 – 3 µm and a time resolution of about 1 s are better than other techniques and make the technique particularly powerful (Ludwig et al. 2007). Along a similar vein, recent innovations in the experiment apparatus for FRET allow measurements of interdiffusion as a function of horizontal position in wet latex films (Haley et al. 2007). The use of two or more complementary techniques simultaneously provides rich information and is welcomed. In a recent example, diffusing wave spectroscopy (DWS) has been employed to measure particle diffusivity during the drying stage while magnetic resonance profiling determined the distribution of water (Kınig et al. 2008). DWS has also been successfully combined with a membranebending apparatus to achieve simultaneous measurements of particle dynamics and stress development during drying (Arnold et al. 2009). FRET measurements have been coupled with optical imaging to correlate the position of the drying and particle packing fronts with the extent of interdiffusion. The amount of molecular mixing between particles can then be known in relation to how much water is present locally and how long it has been since the drying and packing fronts have passed (Haley et al. 2008). There is further scope to use FRET in combination with other non-invasive techniques.

8.4 Nanocomposite Structure and Property Correlations Chapter 7 explained how recent research has drawn upon basic latex technology in the development of a class of nanocomposites. The use of hybrid particles provides control at the nanoscale, whereas the arrangement of particles into colloidal crystal

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arrays offers controlled periodicity and symmetry at the mesoscale. The properties of colloidal nanocomposites are modulated over these length scales. Progress has been made in understanding the properties of latex films containing carbon nanotubes. For instance, electrically conducting networks of carbon nanotubes in a soft latex film have been shown to retain electrical conductivity up to strains of 150% (Dalmas et al. 2005). Other results have proven the key role that internal interfaces between nanotubes and the film matrix can play in determining properties. The sliding friction between carbon nanotubes and a soft latex film can be adjusted with small dispersant molecules. It turn, it has a large impact on the mechanical properties (Wang et al. 2008). Interface design therefore is expected to be a particularly worthwhile pursuit. To date, most of the emphasis has been on making hybrid materials and ordered structures, but there has been far less emphasis on the relationship between the nanoand mesostructure and properties. For colloidal nanocomposites to be developed for demanding applications, greater effort must be made. Nevertheless, greater control of the properties of nanocomposites based on latex films or polymer colloid particles is resulting in new applications. Recent examples include thermoelectric devices (Yu et al. 2008, 2009), scaffolds for cell cultures (Firkowska et al. 2006), biocatalytic coatings with controlled pore structure (Lyngberg et al. 2005), and pressuresensitive adhesives (Deplace et al. 2009, Wang et al. 2009). 6000

100

4

Electrical conductivity, σ (S/m)

4000

2

80

1 0 -1 -2 0.1

3000

60 1 CNT wt%

10

40 2000

Thermopower, S (µV/K)

logσ (S/m)

3

5000

20

1000

σ S 0 0

5

10

15

0 20

CNT wt%

Fig. 8.4 Electrical conductivity (circles) and thermopower (squares) for a nanocomposite of a poly(vinyl acetate) emulsion and carbon nanotubes. The thermoelectric figure of merit for a nanocomposite with 20 wt.% CNTs is up to six times greater than found previously for polymers. (Reproduced with permission from Yu et al. 2008; copyright 2008 American Chemical Society)

8.5 Interdiffusion of Polymers in Multiphase Particles

267

In thermoelectric applications, in which temperature differentials are used to generate electrical currents, nanocomposites of latex and carbon nanotubes offer a desirable combination of low thermal conductivity (0.34 W/mK) coupled with high electrical conductivity (4800 S/m) (Yu et al. 2008). Fig. 8.4 reports some of the promising results. In adhesive applications, core-shell latex particles have been used to create a three-dimensional crosslinked network. The shells of the particles were crosslinked together, and the particle cores remained viscous, resulting in the desired nonlinear elasticity (Deplace et al. 2009). In other work, the addition of clay-encapsulated hybrid particles at low concentrations in a soft latex film has increased its adhesion energy through an effect on the balance of viscoelastic properties. The adhesion energy is 70% greater in the nanocomposite compared to a reference latex film. Nanostructured particles are required, as the effect is not as pronounced if the polymer particles and laponite are added separately, as demonstrated in Fig. 8.5 (Wang et al. 2009).

Fig. 8.5 A comparison of the probe-tack stress-strain curves for an acrylic adhesive containing supracolloidal particles with a laponite clay shell (right) and a blend of the corresponding polymer particles and laponite. (Reprinted from Wang et al. 2009, http:// dx.doi.org/ 10.1039/B904740A; reproduced by permission of The Royal Society of Chemistry)

8.5 Interdiffusion of Polymers in Multiphase Particles The use of hybrid particles has the advantage of avoiding the depletion-induced phase separation that is inherent in the use of large and small (or hard and soft) particle blends. In the case of hybrid particles consisting of hard inorganic and soft polymer phases, the topic of interparticle diffusion has been neglected both experimentally and theoretically. Conceptually, the strength development should

268

8 Future Directions and Challenges

be invariant to the presence of a hard component in the centre of each particle. A guess of reptation over the distance of the polymer’s radius of gyration to achieve full mechanical strength seems reasonable. This result however remains pure speculation and requires verification. In addition, the effect of the hard component will become more dominant as its volume fraction is increased. At higher loadings, it might significantly hinder the interdiffusion. This effect implies that there has to be an optimal hard component loading, as a trade-off between achieving high film hardness while also being able to achieve film formation.

8.6 Templating Film Topography The film height profile is a complex function of the drying process. As outlined in Chapter 3, the flows in drying films can be induced by horizontal drying fronts pulling fluid towards the film edge, and surfactant-induced flows driving fluid towards regions of lower surfactant concentration, typically the centre. The result of the two flows in competition with each other allows a range of film profiles to be created. A ridge around the film, a few mm from the edge, is evidence of the

Evaporation occurs uniformly from film surface

Flow instability caused by surfactant at interface Surfactant – desorbed from compacting particles Flow from region of high surfactant concentration Fluid region

Solid region

Flow from fluid to replace evaporated water in solid region

Fig. 8.6 The three different flows associated with a drying film. Flow from the bulk to the edge replaces solvent lost due to evaporation. Desorption of surfactant from coalescing particles can cause a flow from the edge to the bulk and free surfactant in the bulk can cause flow instabilities and film patterning.

8.7 Resolving the Film Formation Dilemma

269

balance of the two flows. The surfactant-induced flow can also result in instabilities such as reported by Gundabala et al. (2008). The different flows are sketched in Fig. 8.6 and, depending on the relative magnitude of each, different profiles will be obtained. The use of these three types of flow to template desired film topography will require careful control over the initial film profile and the drying conditions. Yet, the possibility remains of creating surface structures with controlled undulations in the micrometer size range. An elegant manipulation of film topography has been achieved recently by a technique called ‘evaporative lithography’ (Harris et al. 2007). This technique uses a mask – essentially a plate with a pattern of holes – to cause evaporation to occur faster only in certain regions across a film surface. Flows are created in the underlying film because of non-uniformities in particle concentration. Particles are carried with the flow and hence accumulate in the fast-evaporating regions, which are consequently higher when drying is complete. There are a number of parameters that allow control over the extent of particle transport. These include the initial particle volume fraction, the distance between the mask and the film, and the dimensions of the mask’s patterns. Although evaporative lithography has been demonstrated in a latex film, there is the scope for extending the application of the technique. Coupling the use of masks with the creation of surfactant-induced topography, as seen by Gundabala et al. (2008), will allow control over film profiles over two discrete length scales.

8.7 Resolving the Film Formation Dilemma Through this book, there has been discussion on the dilemma faced when trying to create a hard coating via latex film formation. One option is to employ a hard (high Tg) polymer and to achieve film formation at room temperature through the use of plasticising additives or coalescent. But, this method is not favourable because of its VOC emission. A second option is to use a hard polymer and then carry out the film formation at temperatures well above the polymer’s Tg. This method poses the risk of film cracking as capillary pressure develops in the weak particle network (Tirumkudulu and Russel 2005, Lee and Routh 2004). At elevated temperatures, particles will become sufficiently deformable to undergo film formation by wet sintering or capillary deformation. Cracking, such as is seen in Fig. 8.7, will be avoided (Lee and Routh 2006). However, the film formation of industrial coatings through the use of ovens is an energy-intensive process that adds to the ‘carbon footprint’ of coatings. The future of the coatings industry, along with many others, is green. There is a need to find ways to resolve the film formation dilemma. The environmental drive to reduce VOC levels will continue. There is a continuing need to find ways to soften latex particles to enable film formation, without sacrificing the hardness level of the final coating. A possible method to solve the problem is the use of polymers that are plasticised by water. The

270

8 Future Directions and Challenges

softened latex will film-form in the presence of water, but the polymer will then harden as the water evaporates. A drawback is that such polymers will also be hydrophilic and subject to water uptake in use as a coating. A second method is the blending of hard and soft particles, as discussed in Chapter 7. The soft particles create a continuous film whereas the hard particles increase the elastic modulus and the hardness. Crosslinking of a soft polymer after film formation is yet another way to achieve a hard film (Taylor and Winnik 2004) when filmforming at room temperature. A newly reported way to reduce the use of coalescent (and hence the VOC content) in a latex blend, is to use a low-molecular weight (oligomeric) copolymer latex to reduce the glass transition temperature of the same copolymer with a highmolecular weight (Tomba et al. 2008). The oligomers, which have a lower glass transition temperature, can diffuse readily into the high-molecular weight particles and soften them. The rates of coalescence and diffusion can then be enhanced without the introduction of a ‘foreign’ molecule. The high molecular weight component provides the necessary mechanical strength.

Fig. 8.7 Example of a film cast on glass substrates from acrylic latex with a glass transition temperature of approximately 40°C. When cast at room temperature, an opaque, cracked film results. (Photograph courtesy of A. Georgiadis, University of Surrey)

8.7 Resolving the Film Formation Dilemma

271

A recently proposed method for reducing the use of coalescent, called ‘Designed DiffusionTM’ and developed at the Rohm and Haas Company, relies on blends of two types of polymer particles (Fu et al. 2009). A hard polymer (Tg greater than room temperature) is the majority phase, and a soft (low Tg) polymer is blended to achieve percolation. The key idea of the technology is to select a coalescent that will partition within the hard polymer when the latex blend is in the wet state. The softened particles will be able to undergo particle deformation and coalescence. However, during the film formation process, the solubility of the coalescent switches so that it partitions primarily in the soft phase. The hardness of the high-Tg polymer then returns. The evaporation of the coalescent from the low-Tg polymer phase is fast, so that desirable properties of film hardness, such as blocking resistance and low dirt pick-up, develop quickly. Fig. 8.8 illustrates the process. The rate of property development is significantly faster than when a coalescent is added to hard latex. Furthermore, the concentration of VOCs in a Designed DiffusionTM formulation has been reported to be 30% lower than in a conventional formulation with similar final film properties.

Fig. 8.8 a In the wet latex, the coalescent molecules (identified with x are mainly partitioned in the high Tg polymer particles. b The plasticized ‘hard’ particles are able to be deformed during film formation. c When all water has left the film, the coalescent molecules are transferred into the low Tg polymer phase. d The coalescent molecules can diffuse quickly through the soft polymer phase and evaporate from the film.

272

8 Future Directions and Challenges

As described so far, the technology sounds somewhat mysterious. There are three key requirements for the hard and soft polymer phases that yield the ‘designed’ results. Each requirement stems from a scientific concept, as will be explained. 1. The Tg of the softer polymer should preferably be less than – 5ºC. Not only does this ensure rapid coalescence, but this requirement ensures a high free volume within the polymer. The diffusion of the coalescent through the polymer, and hence the rate at which it leaves the film during film formation, increases as the free volume increases (Vrentas et al. 1985). A more ‘open’ polymer allows faster transport of the VOCs. 2. To ensure there is a pathway for the coalescent to escape from the soft polymer phase, there should be percolation of the soft particles. Yet, the volume fraction of the soft polymer phase should be as low as possible so that the properties of the hard polymer phase are dominant and not compromised. The percolation threshold of the soft phase can be lowered by using a smaller particle size in comparison to the hard particles. 3. The soft polymer phase should ideally be more hydrophilic than the hard polymer phase. This requirement ensures that the coalescent partitions mainly in the hard polymer phase when the latex is in the wet state. When the water evaporates from the soft polymer phase, the partitioning is shifted such that the coalescent is more soluble in this phase. The Rohm and Haas Company has reported that several types of polymers can be successfully used as the soft polymer phase, including acrylic and styreneacrylic copolymers and polyurethane dispersions (Fu et al. 2009). The use of standard coalescent, such as n-methylpyrrolidone and TexanolTM (Eastman Chemical Company), has been demonstrated. This approach presents an exciting way to resolve the film formation dilemma. Future research might find other ways.

References Arnold C. et al. (2009) Mapping the route from wet to dry. European Coatings Journal 11: 28-32 Casagrande C., Fabre P., Raphael E., Veyssie M. (1989) Janus beads – Realisation and behaviour at water oil interfaces. Europhys Lett 9: 252-255 Dalmas F., Chazeau L., Gauthier C., Masenelli-Varlot, K., Dendievel R., Cavaillé J.Y., Forró L. (2005) Multiwalled Carbon Nanotube/Polymer Nanocomposites: Processing and Properties. J Polym Science Part B Polym Phys 43: 1186-1197 Deplace F., Rabjohns M.A., Yamaguchi T., Foster A.B., Carelli C., Lei C.-H., Ouzineb K., Keddie J.L., Lovell P.A., Creton C. (2009) Deformation and adhesion of a soft-soft nanocomposite designed with structured polymer colloid particles. Soft Matter 5: 1440-1447.

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Firkowska I., Olek M., Pazos-Peréz N., Rojas-Chapana, J., and Giersig M. (2006) Highly Ordered MWNT-Based Matrixes: Topography at the Nanoscale Conceived for Tissue Engineering. Langmuir 22: 5427-5434 Fu Z., Hejl A., and Swartz A. (2009) Designed diffusion technology: A paradigm shift in film formation. European Coatings Journal Issue 6: 26-33 Glotzer S.C. and Solomon, M.J. (2007) Anistropy of building blocks and their assembly into complex structures. Nature Materials 6: 557-562. Gundabala V.R., Lei C.-H., Ouzineb K., Dupont O., Keddie J.L., and Routh A.F. (2008) Lateral surface non-uniformities in drying latex films. AIChE J 54(12): 3092-3105 Hagen R., Salmen L., Karlsson O., Wesslen B. (1996) Viscoelastic properties and film morphology of heterogeneous styrene-butadiene latexes. J Appl Polym Sci 62: 1067-1078 Haley J.C., Liu Y., Winnik M.A., Demmer D., Haslett T., Lau W. (2007) Tracking polymer diffusion in a wet latex film with fluorescence resonance energy transfer. Rev Sci Instrum 78: 084101 Haley J.C., Liu Y., Winnik M.A., Lau W. (2008) The onset of polymer diffusion in a drying acrylate latex: how water initially retards coalescence but ultimately enhances diffusion. J Coat Technol Res 5(2): 157-168 Harris D.J., Hu H., Conrad J.C., Lewis J.A. (2007) Patterning colloidal films via evaporative lithography. Physical Review Letters 98: 148301. Hong L., Cacciuto A., Luijten E., Granick S. (2006) Clusters of charged Janus spheres. Nano Letters 6: 2510-2514.s Joannopoulos J.D., Villeneuve P.R., Fan S. (1997) Photonic crystals: putting a new twist on light. Nature 386: 143-149 Keddie J.L. (1997) Film formation of latex. Mat Sci Eng R: Reports R21(3): 101169 König A.M., Weerakkody T.G., Keddie J.L., Johannsmann D. (2008) Heterogeneous drying of colloidal polymer films: Dependence on added salt. Langmuir 24: 7580–7589 Lee W.P., Routh A.F. (2004) Why do drying films crack? Langmuir 20: 98859888 Lee W.P., Routh A.F. (2006) Temperature dependence of crack spacing in drying latex films. Ind. & Eng. Chem. Res. 45: 6996-7001 Lyngberg O.K., Solheid C., Charaniya, S., Ma, Y., Thiagarajan V., Scriven L.E., Flickinger M.C. (2005) Permeability and reactivity of Thermotoga maritime in latex bimodal blend coatings at 80 °C: a model high temperature biocatalytic ccoating. Extremophiles 9: 197-207. Ludwig I., Schabel W., Kind M., Castaing J.-C., Ferlin P. (2007) Drying and film formation of industrial waterborne latices. AIChE J 53: 549-560 Mohraz A. and Solomon M.J. (2005) Direct visualisation of colloidal rod assembly by confocal microscopy. Langmuir 21: 5298-5306 Pfau A., Sander R., Kirsch S. (2002) Orientational ordering of structured polymeric nanoparticles at interfaces. Langmuir 18: 2880-2887

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Roh K.-H., Martin D.C., Lahann J. (2005) Biphasic Janus particles with nanoscale anisotropy. Nature Materials 4: 759-763 Ruhl T., Spahn P., Hermann C., Jamois C., Hess O. (2006) Double-inverse-opal photonic crystals: The route to photonic bandgap switching. Adv Funct Mat 16: 885-890 Stebe K.J., Lewandowski E., Ghosh M. (2009) Oriented assembly of metamaterials. Science 325(5937) 159-60. Taylor J.W., Winnik M.A. (2004) Functional latex and thermoset latex films. JCT Research 1(3): 163-190 Tomba J.P., Ye X., Oh J., Lau W., Winnik M.A. (2008) Polymer blend latex films: Miscibility and polymer diffusion studied by energy transfer. Polymer 49: 2055-2064 Tirumkudulu M.S., Russel W.B. (2005) Cracking in drying latex films. Langmuir 21: 4938-4948 Vrentas J.S., Duda J.L., Ling H.C., Hou A.C. (1985) Free-volume theories for self-diffusion in polymer–solvent system. II Predictive capabilities. J Polym Sci, Polym Phys Ed 23: 289–304 Wang T., Dalton A.B., Keddie J.L. (2008) Importance of molecular friction in a soft polymer-nanotube nanocomposite. Macromolecules 41: 7656 – 7661 Wang T., Colver P.J., Bon. S.A.F., and Keddie J.L. (2009) Soft Polymer and Nano-Clay Supracolloidal Particles in Adhesives: Synergistic Effects on Mechanical Properties. Soft Matter, 5: 3842-3849 Wohlleben W., Bartels F.W., Altmann S., Leyrer R.J. (2007) Mechano-optical octave- tunable elastic colloidal crystals made from core-shell polymer beads with self-assembly techniques. Langmuir 23: 2961-2969 Yu, C., Kim Y.S., Kim D., Grunlan J.C. (2008) Thermoelectric behaviour of segregated-network polymer nanocomposites. Nano Letters 8: 4428-4432. Yu, C., Kim Y.S., Kim D., Grunlan J.C. (2009) Thermoelectric behaviour of segregated-network polymer nanocomposites. Nano Letters 9: 1283-1283.

A

Appendix A Derivation of Creeping Flow and the Result for Low Reynolds Number Flow Around a Sphere

A.1 Derivation of Creeping Flow The Navier Stokes equation is

  ∂u + u • ∇u  = −∇p + µ∇ 2u   ∂t

ρ

(A.1)

where u is the vector of fluid velocities, p is the fluid pressure, µ is the fluid viscosity and ρ is the fluid density. The left-hand side of Eq. (A.1) represents the inertia of the system, or the acceleration of the fluid. On the right-hand side, the pressure gradient represents a force acting on the fluid because of a non-uniform pressure, while the viscous term represents a shear stress on the fluid opposing any motion that is occurring. The volume of liquid is conserved, and this condition is stated as ∇•u = 0

(A.2)

Equation (A.1) is a vector equation, comprising three separate equations. Together with (A.2), the Navier Stokes equation comprises four simultaneous equations for the four unknown variables in the system, which are the three components of the velocity (u) and the fluid pressure (p). The physical problem under consideration will dictate the natural coordinate system to use for the equations. For instance, when considering flow past a spherical particle, it is conventional to use spherical coordinates with the origin at the centre of the particle. Fig. A.1 uses spherical coordinates for such a case.

276

Appendix A: Derivation of Creeping Flow and the Result for Low Reynolds Number Flow

A.2 Scaling of the Navier-Stokes Equation The Navier-Stokes equations are non-linear, and no complete analytical solution exists. For complex flows, it is common to resort to numerical integration. In certain circumstances, however, it is possible to make analytic progress. The case of flows in colloidal systems is one such example, where the smallness of the colloidal particles and the slowness of the flows results in the non-linear terms in (A.1) becoming negligibly small. This condition is derived below with the result that the inertial terms in colloidal flows (left-hand side of (A.1)) are irrelevant. The relative magnitude of the different terms in (A.1) may be estimated by scaling them. The characteristic length scale is the particle radius R. The characteristic velocity is taken as u*. Hence, the characteristic time is expressed as R/u*. The

∂u

∂t

term in Eq. A.1 may be written as

u * ∂u R / u * ∂t where the overbars indicate dimensionless quantities that have a magnitude between zero and one. Performing the same analysis on each term in (A.1) results in a scaled equation:

ρu *2  ∂ u

µu * P*  ∇p + 2 ∇ 2 u + u • ∇u  = −  R  ∂t R R 

(A.3)

It is conventional to divide through by the viscous term and to choose the characteristic pressure to be µu*/R. The result is

ρu * R  ∂u  + u • ∇ u  = − ∇p + ∇ 2 u  µ  ∂t 

(A.4)

where the dimensionless group

ρu * R µ is called the ‘Reynolds number’. It is a measure of the relative magnitude of the inertial terms in relation to the viscous terms. For a 1 µm particle in water (µ = 10–3 Pa s) with a characteristic velocity of 1 µm/s, the Reynolds number is 10–6. Because this is so tiny, the inertial terms on the left-hand side of (A.4) may be

A.3 Stokes Flow

277

safely ignored. In dimensionless terms, the governing equations – in the low Reynolds number limit – become

− ∇p + ∇ 2 u = 0

(A.5)

∇•u = 0

(A.6)

Equation (A.5) tells us that the flow is independent of time. The viscous drag, ∇ 2 u balances the applied pressure gradient ∇p . The condition described by these equations is called ‘creeping flow’, because the equations apply for very low velocities. The equations may be solved analytically for flow around a colloidal particle. This solution is called ‘Stokes flow’.

A.3 Stokes Flow For creeping flow around a spherical particle, an analytic solution is available, if the flow at a great distance from the particle is at a uniform velocity in a single direction, as shown in Fig. A.1. The boundary condition assumes no flow ( u = 0 ) at the particle surface. From the derived flow pattern, the shear stress on a colloidal particle may be calculated. Integration of the stress over the particle surface gives the drag force Fdrag on a particle. Physically, this is the force that resists flow of a particle through a fluid and that arises from the fluid’s viscosity. For a particle of radius R in a uniform flow of velocity U, the drag is given by

Fdrag = 6πµUR

(A.7)

In this limit, the drag resistance experienced by a colloidal particle moving in a viscous fluid is proportional to its size.

A.4 Sedimentation Particles will settle if their density is greater than that of the solvent surrounding them. If the particles are less dense than the solvent, they rise in a process called ‘creaming’. Thus, the direction of particle motion (up or down) depends on whether the difference in density between the particles and solvent (∆ρ) is positive or negative. Sedimentation and creaming are the result of the gravitational force associated with the acceleration due to gravity, g. The gravitational force acting on a single particle is given by Fgrav = 4/3 π R3 ∆ρ g. In this expression, a force is obtained by multiplying g by the difference in mass between a particle and the fluid it occupies. At equilibrium, this gravitational force exactly balances the

278

Appendix A: Derivation of Creeping Flow and the Result for Low Reynolds Number Flow

Stokes drag force (A.7). Setting the two forces equal, the sedimentation velocity is then found to be U sed =

2 ∆ρ R 2 g 9 µ

(A.8)

The strong dependence of Used on R provides a means to separate particles by size. Larger particles sediment to the bottom of a container faster than smaller ones. Similarly, mono-sized particles may be separated by their density differences. Stable colloidal particles, such as in a latex, resist sedimentation and creaming.

U∞

r

Fdrag = 6 π µ U R

R

θ

Stokes Flow Solution

 3R R 2  Cosθ + U r = U ∞ 1 − 2r 2 r 2    3R R 3   Sinθ + U θ = U ∞  − 1 + 4r 4r 3   P = P0 −

3R 2 µU ∞ Cosθ 2r 2 R

Fig. A.1 Flow of a Newtonian fluid past a sphere in the limit of low Reynolds number results in Stokes flow and a drag on the sphere that is linear in the flow velocity.

Appendix B

Appendix B GARField Profiling Techniques and Experimental Parameters

In an MR profiling experiment, the pulses of RF radiation are used to rotate the magnetisation of the aligned nuclear spins. An excitation pulse that lasts for a sufficient time to rotate the magnetisation, from the longitudinal axis into the transverse plane, is referred to as a 90° pulse. In the GARField design, the time duration of a 90° pulse is about tpd = 1 µs (Glover et al. 1999). A 180° pulse logically lasts twice as long as a 90° pulse, and it inverts the direction of the magnetisation along the longitudinal axis. An excitation pulse of RF radiation is followed by an RF pulse sequence that is used to create a series of echoes by refocusing the nuclear spins that are out of synchronisation. In GARField profiling, NMR signals are obtained using a quadrature spin-echo sequence (McDonald and Newling 1998, Mitchell et al. 2006), which is described as: (90°x – τ – (90°y – τ – echo – τ)N – τR) . After the first excitation pulse, there are pulses to create N echoes separated in time by 2τ, where τ is called the ‘pulse gap’. There is repetition delay time of τR before the sequence is repeated again for NS times to enable many averages. In a typical experiment, N = 32 and τ = 95.0 µs (Mallégol et al. 2006). In order to enable the nuclei to relax fully before repeating an acquisition, τR should be chosen so that it is at least five times greater than the spin-lattice relaxation time, T1, of the sample. The same RF coil that is used to create the RF pulse is used to detect the echo signal. As the time between RF pulses is 2τ, and as the pulse itself requires a short amount of time, then the time to acquire the echo signal is slightly less than 2τ. The echo is recorded as a fixed number of points (or acquisitions), Nacq, acquired at regular intervals in time, called the ‘dwell time’, tD. As explained, these two parameters must be chosen so that NacqtD < 2τ.

280

Appendix B: GARField Profiling Techniques and Experimental Parameters

Echoes are acquired as a signal varying in time. A Fourier transform of an echo takes the signal from the time domain to the frequency domain, so that the frequency can be correlated with spatial position through Eq. (2.13). To obtain a GARField profile, each of the N echoes in a train is Fourier-transformed and then summed for each of the NS scans. Profiles are normalised by an elastomer standard to correct for sensitivity decline over film thickness. It is helpful to note that when the spacing in time between the measured points in an echo is tD seconds, then the total range in the frequency domain after a Fourier transform will be 1/tD Hz. This range of frequency converts to the length range that can be viewed in a profile, which will contain Nacq points spaced evenly apart. The thickness of a wet latex film determines the minimum field-of-view (FOV) that is required. The quality of the data increases with an increase in the signal intensity over the background noise level, or the so-called ‘signal-to-noise ratio’ (SNR). Almost always, there is a desire to reduce the resolution (i.e., distance between points in a profile, ∆y), to obtain information on non-uniformities at short length scales. The resolution may be adjusted through the spacing of points in the profile in the frequency domain (1/NacqtD). If the echo train decays quickly in time, as caused by a short T2 relaxation time, then this time sets the resolution rather than the echo acquisition time (NacqtD). The mathematical relationships presented in Table B.1 show how these profile characteristics are determined. For instance, in GARField profiles when Nacq = 256, tD = 0.4 µs (Glover et al. 1999), the pixel resolution is

∆y =

1 = 6.7 µ m (42.58 ⋅10 HzT )(17T / m)(0.4 ⋅10−6 s)(512) 6

−1

It is apparent that a stronger gradient, Gy, will decrease the resolution, ∆y, but the field of view will likewise be decreased. Also, increasing NacqtD will improve the resolution but require longer pulse gaps and hence longer total profiling times, possibly prohibiting the study of fast drying. Taking more scans, NS, will increase the signal-to-noise ratio, but at the expense of more time per profile.

References

281

Table B.1. Interrelationship between NMR Profile Characteristics and Experimental Parameters (McDonald and Newling 1998, Mitchell et al. 2006) Parameter

Relevant Meaning

Equation

Field-of-view, FOV

Thickness of excited volume; Maximum film thickness that can be analysed

FOV =

Relaxation-limited resolution, ∆y

Distance between data points in a profile in more solid-like samples

∆y =

Recording-windowlimited resolution, ∆y

Distance between data points in a profile

∆y =

Signal-to-noise ratio, SNR

Indicates the extent to which the signal is above the noise level and hence the data quality

SNR ∝

∆Ω 1 ∝ γG y γG y t pd

2

γG yT2 2π 2π = γG y t acq γG y t D ⋅ N acq

NS ∆y

∆Ω = pulse bandwidth; tpd = time duration of RF pulse; τ = pulse gap or delay time between RF pulses; tD = dwell time between acquisitions of an echo; Nacq = number of acquisitions in a single echo; tacq = tDNacq = acquisition time; NS = the number of scans (i.e., repetitions of the pulse programme)

References Glover P.M., Aptaker P.S., Bowler J.R., Ciampi E., McDonald P.J. (1999) A novel high-gradient permanent magnet for the profiling of planar films and coatings. J Magn Reson 139: 90-97 Mallégol J., Bennett G., Dupont O., McDonald PJ, Keddie JL (2006) Skin development during the film formation of waterborne acrylic pressure-sensitive adhesives containing tackifying resin. J Adhesion 82: 217-238 McDonald P.J. and Newling B. (1998) Stray field magnetic resonance imaging. Rep Prog Phys 61: 1441-1493 Mitchell J., Blümler P., McDonald P.J. (2006) Spatially resolved nuclear magnetic resonance studies of planar samples. Progr Nucl Magn Reson Spectrosc 48: 161-181

Appendix C

Appendix C Terminology of Humidity and an Expression for Evaporation Rate

The first part of this appendix defines a number of terms relating to humidity. Our experience from numerous undergraduate lectures is that the definitions are difficult to understand upon first reading, but illustration with relevant examples makes them clear. The definitions of relevant terms are given immediately below in Sections C.1 through C.9, and this is followed by a number of worked examples.

C.1 Humidity Consider the atmosphere you are in. The air is at a certain average temperature, and it has some water dissolved in it, making it somewhat moist. The amount of water dissolved in a sample of air, called the ‘humidity’, is given the symbol H and is measured in the SI units of kg of water per kg of dry air. For example, the air in a vessel may have a mass of 100 kg, and it may contain 1 kg of moisture, making the total mass 101 kg. The humidity in this example is H = 1/100 = 0.01 kg water per kg of dry air (or 0.01 kg/kg).

C.2 Relative Humidity The air will be able to support only a certain maximum amount of water. At loadings above this level, the air will be saturated and liquid water will condense from the gas phase. The maximum amount of water that can be supported is a function of temperature and pressure. For instance, warmer air can hold more

284

Appendix C: Terminology of Humidity and an Expression for Evaporation Rate

moisture. A common outcome of this is dew forming on grass in the early morning. At the lowest temperature of the day, the atmosphere cannot hold as much moisture as it could when warm. As a result, water condenses. The ratio of the air’s humidity to the maximum possible humidity at the same pressure and temperature is called the ‘relative humidity’ and is given the symbol H0. As an example, at 25oC and at a pressure P of one standard atmosphere (1.02 x 105 Pa), the saturation humidity is 0.02 kg of water per kg of dry air. For the case considered in Section C.1 with a humidity of 0.01 kg/kg, the relative humidity will be H0 = 0.01/0.02 = 0.5 or 50%. Relative humidity is conventionally expressed as a percentage.

C.3 Dry Bulb Temperature The temperature of a sample of air is termed the dry bulb temperature. It is measured by placing a thermometer into the air sample while ensuring that no liquid water is on the thermometer, i.e., the ‘bulb’ is dry. The significance of dry bulb temperature, and the reason to define what seems like such a mundane quantity, will be clear after defining the counterpart called the ‘wet bulb temperature’.

C.4 Wet Bulb Temperature When liquid water is in contact with water in the air at a pressure less than the vapour pressure of the liquid, there will be evaporation. The process requires energy to overcome the latent heat of evaporation of water, Λl. Hence, during evaporation, there is a heat flux from the air into the liquid water. The result is that liquid water is at a lower temperature than the air in contact with it. The temperature of the water is called the ‘wet bulb temperature’. It is measured with a ‘wet bulb’ by either placing a thermometer into liquid water or by covering it with a wet cloth. The wet bulb temperature is determined by how fast the water evaporates, and so it is a function of the dry bulb temperature and the relative humidity.

C.5 Specific Volume Air is a compressible gas that will change its volume, V, with a dry bulb temperature, T, as described by the well-known ideal gas equation, PV = nRT, where n represents the number of moles of the gas, and R is the gas constant equal to 8.314 J mol–1 K–1. The specific volume of air is measured in the SI units of m3 per kg of dry air at the specified pressure, P. Humid air will have a higher specific volume than dry air at the same temperature, because of the volume contribution of the water vapour.

C.6 Enthalpy of Air

285

C.6 Enthalpy of Air As water evaporates, the latent heat of the water requires a large energy input from the air to achieve the phase change. This is the equivalent to stating that the enthalpy of air increases with humidity. The enthalpy of air should not be confused with the enthalpy of vaporisation, because the former depends on how much water is in the air and is not a function of the water itself. The magnitude of this enthalpy allows for the design of heating duties in industrial dryers and for the estimates of the time needed to allow for drying.

C.7 Psychrometric Chart The quantities defined in the previous sections can all be found on a psychrometric chart, an example of which is given in Fig. C.1. The horizontal axis is the dry bulb temperature, measured in Celsius. The vertical axis, on the right-hand side of the chart, presents the humidity H in units of kJ/kg. Note that the axis is labelled on its left-hand side. With the dry bulb temperature and humidity specified, every other variable may be determined from the chart. The relative humidity runs diagonally on the chart on lines with a slight curvature and with a positive slope; higher values are on the upper left side. As an example, the 40% relative humidity line is labelled. The specific volume is presented as straight lines running diagonally from the upper left to the lower right. The values are identified above the lines. The line of specific volume of 0.875 m3 per kg of dry air is shown in Fig. C.1 as an example. The wet bulb temperature is shown on the curved left hand axis that corresponds to the 100% relative humidity line. The lines run from left to right with a downward slope. The labels for the temperature are written on the lines. The line corresponding to a wet bulb temperature of 20°C is identified in the example. Lines of constant enthalpy of air are also shown on the psychrometric chart. They are presented as the solid lines running nearly parallel to the lines of constant wet bulb temperature. The values are labelled on the vertical axis on the righthand side of the chart and on the diagonal axis on the left-hand side. The line of 40 kJ/kg dry air is identified in Figure C.1. The use of the chart is given in the following example. At a dry bulb temperature of 30°C, and with a humidity of H = 0.02 kg/kg, the chart tells us that the relative humidity is about 75%. The wet bulb temperature is approximately 26°C, showing that evaporative cooling has reduced the water temperature by 4°C. The specific volume of the air is 0.885 m3/kg. Finally, the enthalpy of air for this example is 80 kJ/kg.

286

Appendix C: Terminology of Humidity and an Expression for Evaporation Rate

C.8 Dew Point If a sample of humid air is cooled, at some point liquid water will condense. The temperature at which liquid water first appears is called the ‘dew point’. Because the cooling of an air sample is a constant humidity operation, the dew point can be found by moving horizontally on the psychrometric chart (along a line of constant H) to the 100% relative humidity line and then reading off the temperature. The dry bulb and wet bulb temperatures are identical at 100% relative humidity.

C.9 Relating Humidity to Partial Pressure Recall that humidity is defined as the mass of water per mass of dry air. Another way of describing the water vapour content is to use the water’s partial pressure. In an air sample at total pressure P, the partial pressure of water, Pw leaves a pressure P-Pw remaining for the dry air. Assuming an ideal gas relation, the number of moles of water in the sample is n = PwV/RT using the symbols defined in Section C.5. With 18 being the molar mass of water, 18 Pw V/RT follows as the mass of water in the air. Assuming that the dry air consists of nitrogen gas, its mass is given by 29 (P-Pw)V/RT. Hence, the humidity is related to the partial pressure of water by

H=

18Pw 29 ( P − Pw )

(C.1)

This equation may be inverted to give the partial pressure of water as 29 H Pw 29 18 = H ~ P 1 + 29 H 18 18

(C.2)

where the last approximation is valid if 29H/18 2h, Gc is then calculated as (Kanninen 1973):

K IC =

3∆2 Eh3 12a 2 α c 2

(D.3)

where αc is a correction factor. The geometry presented in Fig. D.2 is for the symmetric base in which the same polymer is on either side of the interface and has the same beam dimensions on both sides. The equation must be modified when applied to the interface between different polymers (with different elastic moduli and dimensions) in an asymmetric DCB test. The calculation of KIC for various other test geometries is presented elsewhere (Williams 1978).

D.2 Plastic Zone Size at the Crack Tip, ry

297

P a

h Healed interface

b Side view

Fig. D.1 Double cantilever beam geometry used to measure fracture toughness in plane strain, KIC.

a ∆

h Healed interface Fig. D.2 A symmetric double cantilever beam test geometry used to measure the fracture toughness KI at a healed interface by driving a wedge at a constant velocity.

D.2 Plastic Zone Size at the Crack Tip, ry The fracture mechanics equation presented in the previous section applies to brittle fracture, which means that failure is by crack propagation. If the stress on a polymer exceeds its yield stress, σy, then there is plastic deformation. Beyond the yield stress, deformation is not fully reversible when the load is removed. Below the yield stress, deformation is elastic and the material returns to its original dimensions after the load is removed. When there is plastic deformation in the zone of maximum stress at the crack tip, the crack tip will become rounded out or blunted. Plastic deformation at the crack tip leads to ductile failure. The likelihood of ductile failure may be assessed by estimating the radius at the crack tip, ry, using this expression:

ry =

1 K c2 2π σ y2

(D.4)

298

Appendix D: Fracture Mechanics: Terminology and Tests

For a plate thickness of h, brittle fracture will occur when ry < h/4. When the ry > h/4, there will be blunting of the crack tip and a transition to ductile failure. Glassy polymers might be expected to undergo brittle fracture, but experiments on poly(styrene) (Tg ≈100 °C) at room temperature have found evidence for deformation at the crack tip (Schnell et al. 1998). In latex films with a glass transition temperature far below the temperature of testing, brittle fracture is clearly not expected.

D.3 Critical Energy Release Rate, Gc The energy release rate is defined as the amount of energy that is released per unit area as a crack grows. The critical energy release rate required to initiate crack growth, Gc is an additional parameter measured in fracture mechanics experiments. The units for Gc are rather intuitive and easy to understand, as they are given in terms of energy per unit area (J m–2 in SI units). Thus, one can think of Gc as the energy required per unit area of crack for stable crack growth. At equilibrium, this energy will equal the energy released in the fracture process. Gc can be found from KIC (or KIIC as appropriate, depending on the experiment) through the elastic modulus, E, of the specimen (Williams 1977, 1978) as

Gc =

2 K IC E

(D.5)

Young’s modulus E, (in units of force per unit area), is determined by the slope of the linear relation between stress and strain in the elastic region. Combining (1) and (D.5) shows that

σ 2 Gc =  2E 

 2 2Y a  

(D.6)

In fracture mechanics experiments, a crack at an interface can be driven by a wedge travelling along an interface at a constant slow velocity. Low velocities, where there is slow, stable crack growth, are used.

D.4 Fracture Strength In a related experiment, called the ‘notched beam test’, a wedge with a 45° angle is cut out of a specimen, as shown in Fig. D.3a. The specimens are strained at a constant rate until they fracture, and the stress at the point of fracture, σf, is recorded. In studies of latex film strength, a common approach is to test specimens under a tensile load (Kim et al. 1994). The specimens are strained at a constant rate. The maximum stress that can be applied before fracture of the specimen is recorded as

D.5 Plastic Zone Size at the Crack Tip, ry

299

the fracture strength, σT. The test is illustrated in Fig. D.3, and an example of how to find σT from a stress-strain curve is also given.

D.5 Fracture Energy Another way to analyse the stress-strain data is to find the total energy required for a specimen to break, which is called the ‘fracture energy’, WB (Zosel and Ley 1993). It can be expressed in units of energy per unit volume (J/m3), which is equivalent the units of stress (N/m2 = Pa). It can be calculated from the area under a stress-strain curve, as shown in Figure D.3c. WB is a function not only of the elastic modulus (indicated by the slope of the linear region at low strain), but is also affected by plastic deformation or flow of the specimen. (b)

(c)

σT Stress (Pa)

(a)

45°

σf

σ= 0

σ = σT

Fracture

WB

Strain

εf

Fig. D.3 a An illustration of the notched beam test geometry. b An illustration of the deformation of a tensile specimen until failure at a stress of σT. c An example of a stress-strain curve for a brittle specimen, showing the meaning of σT and WB.

References Kanninen M.F. (1973) Augmented double cantilever beam model for studying crack propagation and arrest. Int. J Fract. 9: 83-92 Kim K.D., Sperling L.H., Klein A., Hammouda B. (1994) Reptation time, temperature, and cosurfactant effects on the molecular interdiffusion rate during polystyrene latex film formation. Macromolecules 27: 6841-6850 Schnell R., Stamm M., Creton C. (1998) Direct correlation between interfacial width and adhesion in glassy polymers. Macromolecules 31: 2284-2292 Williams, J.G. (1977) Fracture mechanics of polymers. Polym. Engin. Sci. 17: 144-149

300

Fracture Mechanics: Terminology and Tests

Williams J.G. (1978) Applications of linear fracture mechanics. Failure in Polymers. Springer-Verlag, Berlin.. Advances in Polymer Science Series. Vol 27, 67-120 Zozel A, Ley G. (1993) Influence of crosslinking on structure, mechanical properties and strength of latex films. Macromolecules 26: 2222-2227

Index

acomustic waves 34 acrylates 2 acrylic acid groups 174 acrylic copolymers 3 adhesion, effect of surfactants 190 adhesion energy 159 adsorption isotherms 192–3 AFM see atomic force microscopy aggregation, definition of 20 alkyd film 74 anisotropic particles 259–61 anisotropy 259 anthracene 77, 81 Arrhenius equation 166 aspect ratio 240, 246 atomic force microscopy 62–8, 144 cantilever 62, 68 experimental parameters 65 height artefacts 64 indentation depth 64 intermittent contact 63 microtomed cross-sections 67 particle deformation 67 phase imaging 66 contrast in 67 set point ratio 65 TappingModeTM 63 tip 69 contamination 68

atom transfer radical polymerization 220 autocorrelation 45 autohesion 151 barrier resistance effect of surfmers 206 in nanocomposites 216 beam bending 32–34 blocking 159, 169, 216, 245 boundary layer 96 Bragg’s law 232 brittle fracture 293 brittleness 215 Brown, Robert 1 Brownian dynamics simulations of drying 106 Brownian motion 1, 44 applications of 50 Brown mechanism 125 capillary deformation 124–5, 135 experimental evidence 142 capillary length 110, 111 capillary pressure 111–3, 124, 230 effect on cracking 116 capillary waves 157 carbon nanotube 221, 234, 246, 263 carboxylic acid groups 173 carpet backings 6

302

chain branching 164–5 entanglement 159 length 249 pull-out 158 scission 159 chalking 245 chemical patterning 231 Clausius-Mossotti equation 51 clay exfoliation 221 intercalation 221 close packing, random 10, 23, 100 cloudy-clear transition 29, 143 coalescent reduction 268 coalescing aid 174–5 effect on Tg 175 selection of 175 coffee rings 110 Col.9® 245 colloidal crystal 23, 232 classification 238 growth 231 colloidal stability, effect on drying 114 colloid dispersion 1 colloid science 17–23 complex longitudinal modulus 35 confocal microscopy 49–50 laser scanning 50 confocal Raman microscopy 52, 74 construction materials 6 convection of surfactant 194 core-shell particle see particle crack healing 152, 294 cracking 116–7 in nanocomposites 235 relaxation mechanism 117 crack point 29 crack spacing 117 creaming 275 creeping flow 22, 273 critical coagulation concentration 115 critical energy release rate 295–6

Index

critical micelle concentration 191 critical stress intensity factor 293 critical volume fraction 234 crosslinking 58, 73–4, 175 autoxidative 74 control parameter 179 molecular weight effects 178 two-pack 175 two-pack in one pot 175 cryogenic electron microscopy see electron microscopy currant-bun particle 221 dangling chains 178 Darcy flow 112 Darcy’s law 104 Debye length 18, 114 deformation map 133–4, 139 depletion interactions 17, 20 Designed DiffusionTM 269 desorption of surfactant 199 deuterium 44 dew point 283 dialysed latex 189 diffraction limit 49 diffusing wave spectroscopy 46, 263 diffusion 10, 151 activation energy for 166 competition with crosslinking 175 effect of chain branching 164 effect of coalescing aids 174 effect of membranes 173 effect of molecular weight 164–5 effect of particle size 172 effect of reduced mobility 171 effect of temperature 165 in gel 177 near Tg 167 of core shell particles 172 particle shell effects 164 scaling prediction 165 scaling relations 157 shift factor 168 surfactant 195 tortuosity effects 169

Index

diffusion coefficient 22, 153, 166 dirt pick-up 189, 245 DLVO theory 17, 19 double cantilever beam 294 drag coefficient 22 dry bulb temperature 282 drying 10, 95–117 effect of Peclet number 104, 106 effect of salt 106, 115 effect of surfactant 114 horizontal 107–114 factors that affect 112 fronts 108, 109 MRI of 113 importance of 95 particle distribution during 99 three-stage process 98 two-stage process 98 vertical 99–107 factors affecting 102 drying fronts 15 dry sintering see sintering dwell time in MR profiling 277 dynamic speckle 48 elastic particles 127 elastic spheres 128 electrical conductivity 36, 216 electrical impedance 36 electric force microscopy 69–70 electron beam damage 40 electron microscopy 36–42 cryogenic scanning 37, 104, 108 cryogenic transmission 125 dark field 41 environmental, pump down 41 environmental scanning 36, 37–40, 145 design 39 scanning 36, 72–3 backscattering electron images 73 scanning transmission 36 transmission 41, 71–2 freeze-fracture 72 staining 72

303

wet STEM 41–2 electron paramagnetic resonance 60 electron scattering 40 electrostatic repulsion 17, 18–19 ellipsometry 50, 52, 143 emulsion polymerisation 2 emulsion polymers, market for 9 encapsulated particle 221 entanglement molecular weight 155, 160, 178 enthalpy of air 283 environmental (gaseous) detector 38 environmental legislation 15–16 environmental scanning electron microscopy see electron microscopy EU Directive 2004/42/EC 15 evanescent wave 49 evaporation effects on 97 rate 96, 296 evaporative cooling 32, 96 evaporative lithography 267 face-centred cubic 225 Fickian diffusion 153 filler particles 168, 171 effect on diffusion 81, 170 film formation mechanical probe 32 stages of 10, 11 film formation paradox 174 film scratching 32 film topography 267 flame retardancy 214 flammability 214 flocculation, definition of 20 flow, particle in Newtonian fluid 276 flow instabilities 266 fluorescence decay curves 80, 81 fluorescence resonance energy transfer 61, 76 simulations 79 forced Rayleigh scattering 58, 59 Forster radius 77

304

Forster relation 76 fraction of mixing after interdiffusion 79 fracture energy 159, 296 effect of diffusion 160 time dependence 162 fracture strength 159, 296 fracture toughness 159, 293–4 free radicals 40 Frenkel theory 128 FTIR spectroscopy 73 further gradual coalescence 151 GARField 56–58, 277–9 experimental design 57 experimental profiles 105 gel point 35 glass transition temperature, definition of 2 gloss, effect of surfactant 188 Graham, Thomas 1 gravimetry 32 Guinier plot 75 Halpin-Tsai equations 214 Hamaker constant 18 Hertz theory 127 hetero-flocculation 223–4 homogeneous particles 213–4 honeycomb 13 horizontal drying see drying humidity 281–92 definition of 95, 281 relative, definition of 281–2 hybrid 213, 224 types of 217–25 hydrophobicity 245 ideal gas equation 282 industrial coater 6 infrared microscopy 53, 146 infrared spectroscopy 52 inisurfs 205, 207 inks 6 inorganic nanocomposite particles 219 inorganic nanoparticles 245 Institute Laue Langevin 43

Index

interaction potentials 17 interdiffusion 152 effects on 80 techniques to study 74 interdiffusion distance 162 interfacial chain density 162 interfacial strength 247 interfacial width 75, 152 interparticle interference 51 interpenetration distance 75, 157 interphase 215 interstitial space between latex particles 169 inverse micro-Raman spectroscopy 53, 263 iridescence 232 Janus particles 260 Johnson, Kendall and Roberts 127 Kelvin probe force microscopy 69–70 knife point 29 Krieger-Dougherty expression 23 Langmuir isotherm 193 laponite 264 laponite clay 228 lapping time 111 latex blends 213 definition of 1 dialysed 189 gloves 8 market for 9 natural 8 sensitisation 8 latex film formation 10 publications on 16 latex foam structures 173 light scattering 44, 83 dynamic 45 in nanocomposites 234 magnetic resonance imaging 55 magnetic resonance profiling and particle deformation 140 magnetogyric ration 54 Marangoni flows 199, 202

Index

Marangoni instabilities 200 mass transfer coefficient 97 mass transfer resistance 98 melt compression 232 membrane bending 34 membranes 172–3 meniscus 124, 125, 230 MFFT see minimum film formation temperature micelle 191 microrheology 45 miniemulsion polymerisation 217 minimum film formation temperature and particle size ratio 236 definition of 14 effect of particle size 30 effect of surfactant 191 interpretation 30 MFFT bar 29–31, 139, 143 for studying deformation 138 standard for 29 time effects 30 modern art 189 moist sintering see sintering molecular mobility 171 molecular weight 165 Monte Carlo simulation of drying 106 MRI see magnetic resonance imaging multispeckle 46 nanocomposites 213–49 classification 213 conductivity 216 cracking in 235 failure mechanism 247 in paints 216 light scattering in 234 properties 214 silica 227 soft-soft 242 stiffness of 214 toughness of 215 viscoelasticity 215

305

nanoparticle dispersion 233–4 encapsulated 222 hybrid 224 Navier-Stokes equation 22, 273–5 Newtonian fluid 22 NMR see nuclear magnetic resonance non-adsorbing polymer 20 non-radiative energy transfer 58, 61 nuclear magnetic resonance 54 MOUSE 56 spectroscopy 74, 202 occupational exposure limits 15 oligomers 268 opal structure 232 double-inverse 262 inverse 262 open time 107, 111 optical cantilever see beam bending optical clarity front 113 optical stethoscopy 70 optical transmission 143 optical transparency 14 packing, face-centered cubic 12 paints, formulation of 4 paper coatings 6 parameter map 131 partial pressure 296 particle core-shell 218–10, 226 film formation 227, 264 half moon 218 lobed 218 occluded structures 218 particle assembly 225, 261 particle blends advantages of 233 film formation 234 hard-soft 243 particle compressibility 102 particle deformation 10, 12 atomic force microscopy 144 driving forces 121, 122 effect of particle size 139

306

effect of temperature 137–9 MFFT bar 143 scaling argument 135 particle deposition methods 230 particle interfacial area 122 particle packing 12, 260 effect of surfactant 191 front 109 size ratio effects 235–6 particle spacing 51 patterned substrate 231 peak-to-valley height 144, 145 Peclet number 101, 195 effect on drying 104, 106 peel strength 190 pendular rings 126 percolation 238–42 effect on properties 241 model 239 of rods 240 thresholds 239 phase separation 234 in particles 261 phenanthrene 77, 81 photoacoustic spectroscopy 73 photon correlation spectroscopy 45 photonic crystals 262 Pickering emulsion polymerisation 222 plane strain 293 plane stress 293 plasticisation 16, 81 by surfactant 187 plasticisers 174 plastic zone 295 Plateau borders 146 Poisson’s ratio 127 poly-condensation 217 poly(dimethyl siloxane) 245 Porod law 75–6 pressure-limiting apertures 38 pressure sensitive adhesives 190 application of 5 psychrometric chart 283 pulse gap in MR profiling 279

Index

quadrature spin-echo sequence 277 quality factor 64 quantum efficiency of energy transfer 78 quartz crystal microbalance 73 radiolysis 40 radius of gyration 157, 170, 172 compared to diffusion distance 170 Raman spectroscopy 52 surfactant analysis 202 random coil 172 raspberry particles 222 Rayleigh theory 51 reactive surfactant 205 refractive index 143 measurement of 52 replicas, transmission electron microscopy 71 reptation 14, 152, 154 reptation time 156 Reynolds number 274 rheology modifiers 4 rhombic dodecahedron 13, 122 root mean square displacement of chains 156 Rouse entanglement time 156 Rouse relaxation time 156 Routh and Russel film deformation model 130 Rutherford backscattering spectrometry, surfactant analysis 202 saturated vapour pressure 296 scanning electric potential microscopy 69–70 scanning electron microscopy see electron microscopy scanning near-field optical microscopy 50, 70–1 scanning transmission electron microscopy see electron microscopy scattering angle 43 scattering techniques 42–52

Index

scratch resistance 216 secondary ion mass spectrometry 201, 204 sedimentation 275 sedimentation coefficient 102 sedimentation velocity 276 seeded emulsion polymerisation 219 shear force microscopy 70–1 shear modulus 158 Sheetz deformation 126, 136 silica nanocomposites 227 nanoparticles 244 particles 169, 172 sintering dry 123–4, 136 theory 129 moist 126 wet 123, 135 skin formation 58, 107, 141, 146 experimental evidence 142 study of 59 skin layer 55, 115, 146 small-angle neutron scattering 42–4, 145 parameters for 43 surfactant analysis 202 to study interdiffusion 75 small-angle X-ray scattering 42–4 sodium dodecyl sulphate 187 soft-soft nanocomposites 242 sorptive capacity 107 specific volume 282 speckle commercial instrument 49 interferometry 48 spectrophotometry 83 specular reflection 188 spin-casting 228 spin-spin relaxation time 55, 58, 74 star polymer 165 steric stabilisation 234 stick-slip 116

307

Stokes-Einstein diffusion coefficient 22, 44, 101 Stokes flow 22, 275 stray-field imaging 55 strength 214 stress relaxation modulus 131 styrene-acrylic copolymers 3 surface patterns 230 surface roughness 144 surfactant 185–207 anionic 185 cationic 185 classification of 185 convection of 194 desorption 187, 199 exudation 187 cause of 192 effect of surfmers 206 effect of Tg 199 fate of 186–7 gloss effect 188 non-ionic 185 plasticisation by 187 segregation 198 solubility in polymer 187 surfactant-free emulsion polymerisation 185 surfactant-induced flow 267 surfmer 205–7 temperature, effect on particle deformation 137–9 templates for drying 231 tensile strength 160 TexanolTM 174 textile backings 6 thermal conductivity 216 thermoelectric applications 263–4 thin film analyser 146 time-temperature superposition 167 tortuosity 169, 172 toughness 215 transmission electron microscopy see electron microscopy transmission spectrophotometry 50 transport coefficient 104

308

transurfs 205, 207 tube model 155 turbidity 83 ultramicroscopy 50 ultrasonic reflection 34–35, 73 van der Waals attraction 17, 128 van der Waals forces 115 varnishes, formulation of 4 vertical deposition 228–9 vertical drying profiles see drying viscoelastic particles 122, 130 viscosity dependence on volume fraction 23 measurement of 32 viscous flow of particles 128 VOC see volatile organic compounds volatile organic compounds 15, 138

Index

water adsorption 190 diffusion coefficient of vapour 96 distribution profiles 141 surface tension 125 water whitening 191 wavevector 43 wet bulb temperature 282 wet sintering see sintering wet STEM see electron microscopy wetting 152, 157 Williams-Landel-Ferry equation 167 Winnik, M.A., 76 X-ray photoelectron spectroscopy 201 X-ray scattering 44 Young’s modulus 241