Breath Figures : Mechanisms of Multi-scale Patterning and Strategies for Fabrication and Applications of Microstructured Functional Porous Surfaces [1st ed.] 9783030511357, 9783030511364

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Juan Rodríguez-Hernández Edward Bormashenko

Breath Figures

Mechanisms of Multi-Scale Patterning and Strategies for Fabrication and Applications of Microstructured Functional Porous Surfaces

Breath Figures

Juan Rodríguez-­Hernández  • Edward Bormashenko

Breath Figures Mechanisms of Multi-Scale Patterning and Strategies for Fabrication and Applications of Microstructured Functional Porous Surfaces

Juan Rodríguez-Hernández Institute of Polymer Science & Technology Madrid, Spain

Edward Bormashenko Ariel University, Engineering Faculty, Chemical Engineering Department Ariel, Israel

ISBN 978-3-030-51135-7    ISBN 978-3-030-51136-4 (eBook) https://doi.org/10.1007/978-3-030-51136-4 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Contents

1 Introduction to Micropatterned Surfaces����������������������������������������������    1 1.1 Breath Figures: The Historical Survey����������������������������������������������    3 1.2 Aim of this Book������������������������������������������������������������������������������    8 References��������������������������������������������������������������������������������������������������    9 2 Breath-Figures Formation: Physical Aspects����������������������������������������   13 2.1 Introduction��������������������������������������������������������������������������������������   13 2.2 Evaporation of the Solution��������������������������������������������������������������   14 2.2.1 Role of the Solvent����������������������������������������������������������������   14 2.2.2 Role of the Interfacial Properties of Solvent������������������������   17 2.2.3 Interplay of Evaporation of the Solvent and Interfacial Properties of the Polymer Solution: Marangoni Flows and Formation of the Large-Scale Pattern����������������������������   22 2.2.4 Role of the Substrate������������������������������������������������������������   28 2.2.5 Summary of the Parameters Involved in the BFs Formation����������������������������������������������������������������������   28 2.3 Nucleation, Condensation, and Growth of Water Droplets��������������   30 2.4 Mechanisms of Micro-Scaled Ordering in the Breath-­Figures Self-­Assembly������������������������������������������������   35 2.5 Hierarchy of the Temporal and Spatial Scales Inherent for the Breath-­Figures Self-Assembly: Dimensionless Numbers Describing the Process������������������������������������������������������   41 References��������������������������������������������������������������������������������������������������   43 3 Polymers Employed and Role of the Molecular Characteristics on the BFs Formation������������������������������������������������������������������������������   51 3.1 Introduction��������������������������������������������������������������������������������������   51 3.2 Type of Polymers Employed������������������������������������������������������������   52 3.2.1 Standard Commercially Available Polymers������������������������   52 3.2.2 Stimuli-Responsive Polymers ����������������������������������������������   52 3.2.3 Biodegradable Synthetic and Natural Occurring Polymers��������������������������������������������������������������   58 v

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3.2.4 Engineered High Performance Polymers: High Temperature Stability and Chemical Resistance����������   65 3.2.5 Conductive and Semiconductive Polymers��������������������������   70 3.3 Inorganic–Organic Hybrid Microporous Materials��������������������������   74 3.4 Other Polymers Employed for the Preparation of BFs ��������������������   80 3.5 Macromolecular Characteristics of the Polymers Employed in BFs������������������������������������������������������������������������������   80 3.5.1 Role of the Functional Groups in the Polymer Chain and the Polymer Molecular Weight��������������������������������������   80 3.5.2 Composition and Topology of the Polymer��������������������������   84 References��������������������������������������������������������������������������������������������������  103 4 Methodologies Involved in Manufacturing Self-Assembled Breath-­Figures Patterns: Drop-Casting and Spinand Dip-Coating – Characterization of Microporous Surfaces����������  111 4.1 Introduction��������������������������������������������������������������������������������������  111 4.2 Methods Exploited for Manufacturing Breath-Figures Patterns������  112 4.2.1 Drop-Casting������������������������������������������������������������������������  112 4.2.2 Spin-Coating ������������������������������������������������������������������������  119 4.2.3 Dip-Coating��������������������������������������������������������������������������  122 4.2.4 The Emulsion Technique������������������������������������������������������  124 4.3 Formation of Mono- and Multilayered Microporous Surfaces��������  124 4.4 Methods Used for Characterization of Breath-Figures Patterns ������  129 4.4.1 Optical Microscopy of the Patterns��������������������������������������  129 4.4.2 SEM Microscopy������������������������������������������������������������������  130 4.4.3 AFM Study of the Topography ��������������������������������������������  130 4.4.4 TEM Study of the Breath-Figures Patterns��������������������������  131 4.4.5 X-Ray Photoelectron Spectroscopy (XPS) of the Breath-­Figures Samples����������������������������������������������  131 4.4.6 X-Ray Diffraction (XRD) Analysis of the Breath-­Figures-­­Inspired Structures����������������������������  132 4.4.7 Thermogravimetric Analysis (TGA), Differential Scanning Calorimetry (DSC), and Differential Thermal Analysis (DTA) of the Structures Obtained with the Breath-Figures Self-­Assembly��������������������������������  132 4.4.8 Raman and FTIR Spectroscopy of the Samples Prepared with the Breath-Figures Self-Assembly��������������������������������  133 4.4.9 Nuclear Magnetic Resonance (NMR) of Polymers Used for the Breath-Figures Self-Assembly����������������������������������  134 4.4.10 Mass Spectrometry Methods for the Characterization of Breath-Figures Samples����������������������������������������������������  134 4.4.11 Contact Angle Characterization of the Breath-Figures-­Inspired Topographies ����������������������  135 4.4.12 Quantitative Characterization of Ordering Inherent for Patterns Resulting from the Breath-Figures Self-Assembly����������������������������������������������  141 References��������������������������������������������������������������������������������������������������  144

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5 Introducing Chemical Functionalities to Microporous Surfaces: Strategies��������������������������������������������������������������������������������������������������  149 5.1 General Considerations��������������������������������������������������������������������  149 5.2 Strategies Based on the Use of Functional Polymers/Nanoparticles��������������������������������������������������������������������  150 5.2.1 Homopolymers and Copolymers������������������������������������������  151 5.2.2 Functionalized Amphiphilic Polymers����������������������������������  152 5.2.3 Blends of Polymers ��������������������������������������������������������������  154 5.2.4 Inorganic Compounds and Polymers: Hybrid Structures������������������������������������������������������������������  156 5.3 Strategies Based on the Post-modification of the Pores��������������������  159 5.4 Strategies for the Functionalization of Both/Either Inside and/or Outside of the Pores����������������������������  162 5.5 Plasma Treatment of Polymer Surfaces Arising from the Breath-Figures Self-Assembly ������������������������������������������  164 References��������������������������������������������������������������������������������������������������  165 6 Hierarchically Ordered Microporous Surfaces������������������������������������  169 6.1 Introduction��������������������������������������������������������������������������������������  169 6.2 Hierarchically Structured Porous Films Obtained by Self-Assembly of Block Copolymers������������������������������������������  170 6.3 Hierarchically Ordered Microporous Surfaces Combining BFs and Nanoparticles������������������������������������������������������������������������������  175 6.4 Multiscale Ordered Surface by Demixing from Polymer Blend Solutions��������������������������������������������������������������������������������  178 6.5 Formation of Hierarchically Ordered BFs on Patterned Substrates������������������������������������������������������������������������������������������  181 6.6 Combining Photolithography with BFs��������������������������������������������  183 6.7 Combining Electrospinning/Electrospraying with BFs��������������������  184 References��������������������������������������������������������������������������������������������������  186 7 From Planar Surfaces to 3D Porous Interfaces������������������������������������  189 7.1 Introduction��������������������������������������������������������������������������������������  189 7.2 Honeycomb Structures Formed Nonplanar Substrates ��������������������  190 7.3 Ordered Structures Obtained by Template Organization of Water Droplets������������������������������������������������������������������������������  199 7.4 Hot-Embossed Microporous Films ��������������������������������������������������  200 7.5 Honeycomb-Structured Surfaces in 3D Printed Objects������������������  201 References��������������������������������������������������������������������������������������������������  205 8 Applications of the Porous Structures Obtained with the Breath-Figures Self-Assembly��������������������������������������������������  207 8.1 Introduction��������������������������������������������������������������������������������������  207 8.2 Manufacturing of the Surfaces with Controlled Wettability ������������  208 8.3 Optical Applications of the Films Prepared with the Breath-Figures Self-Assembly��������������������������������������������  210

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8.4 Breath-Figures Self-Assembly and Manufacturing of Separation and Ultrafiltration Membranes ����������������������������������  212 8.5 Membranes Prepared with the Breath-Figures Self-­Assembly and Water–Oil Separation ����������������������������������������������������������������  212 8.6 Electronic Applications of the Structures Prepared with the Breath-­Figures Self-Assembly��������������������������������������������  213 8.7 Biomedical Applications of the Surfaces Prepared with the Breath-­Figures Self-Assembly��������������������������������������������  216 8.8 Antimicrobial Porous Surfaces: Suppression of Biofilm Formation������������������������������������������������������������������������  217 8.9 Structures Prepared with the Breath Figures for the Elaboration of Sensors and Catalytic Purposes��������������������  220 References��������������������������������������������������������������������������������������������������  225 Index������������������������������������������������������������������������������������������������������������������  229

Chapter 1

Introduction to Micropatterned Surfaces

Abstract  An interest in micropatterned surfaces has been boosted in last decades owing to their crucial role, in biotechnology, tribology, optical, and microfluidics applications. Manufacturing of micropatterned surfaces is a key factor for industry implementation of biomimetic-inspired effects such as the lotus and shark skin effects. Our book is devoted to one of the most elegant, inexpensive, and flexible methods, enabling manufacturing micro- and nanopatterned porous, polymer interfaces, namely: the breath-figures self-assembly. This experimental technique allows obtaining well-ordered, hierarchical, honeycomb surface patterns. Breakthrough in the application of the breath-figures patterns was achieved when Widawski, François, and Pitois reported manufacturing of polymer films with a self-organized, micro-scaled, honeycomb morphology using the breath-figures condensation process. The reported process is  based on the rapidly evaporated polymer solutions exerted to humidity. The history of research, key experimental and theoretical findings, and the state of art in this rapidly progressing field is covered in this book. Keywords  Micropatterned surfaces · Breath-figures Self-assembly · Hierarchical honeycomb patterns · Polymer solutions · Polymer interfaces · Humidity

An interest to micropatterned surfaces has been boosted in the last decades owing to their crucial role, among others in biotechnology [1], tribology [2], optical [3], and microfluidics [4] applications. Micropatterned surfaces enable the control of lining cells’ position, shape, and function [1], constituting of dry and wet friction [2], design of the surfaces with prescribed optical properties [3], transport, and precise manipulation of micro-volumes of liquids [4]. Manufacturing of micropatterned surfaces is a key factor for industry implementation of biomimetic-inspired effects such as the lotus and shark skin effects, allowing preparing non-wettable interfaces (see Refs. [5, 6] and Fig. 1.1) and surfaces demonstrating low hydrodynamic drag [7]. The lotus effect supplying to surfaces extremal water repellency is illustrated with Fig. 1.1.

© Springer Nature Switzerland AG 2020 J. Rodríguez-Hernández, E. Bormashenko, Breath Figures, https://doi.org/10.1007/978-3-030-51136-4_1

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Fig. 1.1  A 50 μl water droplet deposited on a pigeon feather. The pronounced superhydrophobicity (lotus effect) of the feather is clearly seen

A variety of sophisticated techniques have been implemented for manufacturing micropatterned surfaces, including micro-printing [1], replica molding [3, 8], photolithography, molecular assembly patterning, stencil-assisted patterning, ink-jet technology, and laser-guided writing of patterns [9]. Excellent introduction into experimental techniques involved in manufacturing of micropatterned surfaces is supplied in Ref. [9]. In contrast to these approaches, several methodologies based on the inherent surface characteristics have been developed. These approaches take advantage of the surface instabilities that can be induced either by external fields (electromagnetic, temperature, mechanical stress, etc.) or exist in inherently unstable thin films to produce different micro- and submicrometer surface patterns [10, 11]. As a result, unprecedented patterns that are difficult if not impossible to obtain by traditional patterning techniques have been straightforwardly achieved by instability-­based patterning. A wide myriad of instability-based patterning processes have been reported including those based on structuration driven by surface/interfacial energy (such as dewetting, phase separation of blends and block copolymers, or template-guided structuration), [12–16], field-induced structuration (electrohydrodynamic/thermal gradient-induced surface patterning, elastic instability and surface wrinkling, and reaction–diffusion surface patterns) [17–19], and influence of water on hydrophobic polymer surfaces (including nanobubble assisted nanopatterning, ion-induced polymer nanostructuration and breath-figures self-assembly) [20–23] (Fig. 1.2). Within this context, our book is devoted to one of the most elegant, inexpensive, and flexible methods, enabling manufacturing micro- and nano-patterned porous, polymer interfaces, namely, the breath-figures self-assembly. This experimental technique allows obtaining well-ordered, hierarchical, honeycomb surface patterns. With that, the use of the breath-figures self-assembly today is focused on polymeric

1.1  Breath Figures: The Historical Survey

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Fig. 1.2  Above: illustration of the micro-printing (a), replica molding (b), and photolithography (c) surface patterning methodologies [24]. Below: examples of instability-based surface patterning approaches (d) [25] and water ion-induced nanostructuration (e) [23]. (Reproduced with permission from ref. and Refs. [23–25])

materials (both thermoplastic and thermosetting [20, 26, 27]) or hybrid polymer– inorganic composites [28, 29].

1.1  Breath Figures: The Historical Survey Generally speaking the notion of the “breath figures” refers to the fog that forms when water vapor contacts a cold surface [30]. BF is a commonly observed phenomenon in daily life. One example is the fog that appears on a window when we breathe on it. This is also the origin of the name “breath figure.” Thus, air and water are necessary for breath figures which are according to pre-Socratic philosophers (Thales and Anaximenes) were regarded as “arche” (“stuff” out of which all is made) of all taking on different forms (earth, water, etc.) through rarefaction and condensation. Diogenes Laërtius stated that Thales taught “Water constituted

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(ὑπεστήσατο, ‘stood under’) the principle of all things [31].” Thus, the breath-­ figures condensation is seen as the process exemplifying the “arche” of nature. In the modern era, systematic study of the process of breath-figures water condensation was carried out by Aitken [32, 33], Rayleigh [34, 35], and Baker [36]. J. Aitken in his 1895th paper describes the process as follows: “these well-known figures are generally produced by placing a coin on one side of a piece of glass, and on the other side opposite it another coin or small plate of metal. The coin and the plate are then strongly electrified—the one positively, the other negatively. When the coin is afterwards removed, and the surface of the glass on which it rested is breathed on, there is developed an image of the coin, showing many of the details of the engraving. The image is produced by the condensed moisture being deposited in different-sized patches at different places. This is easily seen by examining the image by means of a microscope, using a low power, and illuminating the image by means of an ordinary mirror, with a large black spot fixed in the centre. At the parts where the image is bright, it will be seen that the moisture is deposited in very small detached patches of nearly equal size. The surface looks as if it were covered with a layer of small plano-convex lenses of quick curvature, with their edges close to each other” [32]. Consider that Aitken emphasized the role of the static electricity in the formation of the breath-figures pattern. A hundred years later, the electrically charged water droplets were used for formation electrically controlled breath-­ figures-­inspired polymer patterns [37–39]. Aitken also described the experiments performed with thoroughly cleaned glass surfaces: “if we pass over this clean surface the point of a blow-pipe flame, using a very small jet, and passing it over the glass with sufficient quickness to prevent the sudden heating breaking it; and if we now breathe on the glass after it is cold, we shall find the track of the flame clearly marked. While most of the surface looks white by the light reflected by the deposited moisture, the track of the flame is quite black; not a ray of light is scattered by it. It looks as if there were no moisture condensed on that part of the plate, as it seems unchanged; but if it is closely examined by means of a lens, it will be seen to be quite wet. But the water is so evenly distributed, that it forms a thin film, in which, with proper lighting and the aid of a lens, a display of interference colours may be seen as the film dries and thins away.” According to modern scientific wording, Aitken discovered that film-wise water condensation took place on the glass surface treated with a blowpipe flame, whereas the dropwise condensation occurred on the non-treated surface of the same glass, and it is noteworthy that the drop- and film-wise pathways of condensation have been exposed to the deep and extended research recently [40–43]. Dropwise and film-wise scenarios of condensation are schematically depicted in Fig.  1.3. The dropwise and film-wise pathways are exemplified with Figs. 1.4 and 1.5, representing the environmental scanning electron microscope (ESEM) images taken under water condensation observed on pigeon’s feathers and metallic surfaces. Obviously only dropwise condensation gives rise to breath-figures patterns. It is noteworthy that the factors switching the dropwise condensation to the film-­ wise one remain obscure to a large extent. However, it is generally agreed that the

1.1  Breath Figures: The Historical Survey

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Fig. 1.3  Dropwise (a) and film-wise (b) scenarios of condensation are depicted schematically

Fig. 1.4  ESEM image of the dropwise condensation of water on pigeon’s feather is depicted. The scale bar is 50 μm

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Fig. 1.5  ESEM images of the film-wise (the upper image) and the dropwise condensation (the lower image) of water vapor on metallic surfaces (for details see Ref. [29])’ . Scale bar is 1 mm

heat transfer events are crucial for this switching, and consequently they are of a primary importance for constituting the breath-figures pattern [40]. Aitken in his seminal paper, published in 1895, also pointed on the role of dust (contaminations) on the formation of the breath-figures pattern [2]. On contrast Rayleigh and Baker emphasized the importance of grease for patterning, which was removed by the blowpipe flame in the experiments, reported by Aitken, thus influencing the resulting breath-figures pattern [4–36]. Baker also addressed the electrical breath-figures, already considered by Aitken [32, 36]. We recognize that in their classical works Aitken, Rayleigh, and Baker indicated that the breath-­figures patterns originate from the complicated interplay of the physical (mass and

1.1  Breath Figures: The Historical Survey

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thermo-transfer) and interfacial events (presence of grease (fat) and solid contaminations on the surface) exerted to water vapor. Half a century later, the interest to the breath-figures formation was revived in a view of study of atmospheric processes and, in particular, the extended study of a dew formation which turned out to be a complicated physical process. The experimental and theoretical study of dew formation has been carried out by Beysens et al. in Refs. [44–46]. Thermodynamic and kinetic aspects of dew formation, which are crucial for understanding of formation of breath-figures inspired polymer patterns will be addressed further in detail.

Fig. 1.6  The scheme of breath-figures process performed with rapidly evaporated polymer solution is depicted

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Breakthrough in the application of the breath-figures patterns was achieved in 1994–1995 when Widawski, François, and Pitois reported manufacturing of polymer films with a self-organized, micro-scaled, honeycomb morphology using the breath-figures condensation process [47, 48]. The reported process was based on the rapidly evaporated polymer solutions exerted to humidity [20, 26, 47–50]. The evaporation of solvent decreased the surface temperature of the solution, thus promoting the dropwise condensation of water vapor. Water droplets “drilled” micro-­ scaled holes and the residual polymer fixed the honeycomb pattern as depicted schematically in Fig.  1.6. The deep understanding of the patterning, involving a variety of physical and chemical events (condensation, nucleation and growth of droplets, capillarity, water/polymer and water/solvent interaction, etc.), turned out to be challenging, and it is not attained until now. The state of art in the field is supplied in the presented book.

1.2  Aim of this Book The aim of this book is to provide a clear and actualized overview of this rapidly expanding research area. For this purpose the book is organized as follows. We will first discuss (Chap. 2) the main physical aspects related to the breath-figures formation that include the mechanism and the parameters involved. Chapter 3 surveys the polymers that have been employed for the breath-figures self-assembly. Chapter 4 will focus on all the methodologies reported to prepare breath figures as well as the characterization methods employed including the order of the patterns, the voronoi entropy, and the wetting of the surfaces. Chapter  5 is devoted to the analysis of the chemical strategies that can be employed to introduce functional groups on the microstructured surfaces. The use of functional polymers/copolymers, the incorporation of functional polymers as additives, or the post-modification (for instance, using plasma treatments) will the thoroughly described in this chapter. Chapter 6 analyzes the alternatives to, based on the breath-figures approach, prepare more sophisticated surfaces. In particular, Chap. 6 describes the combination of different self-assembly processes to produce hierarchical-ordered porous surfaces. Chapter 7 discusses the possiblities to manufacture 2D and nonplanar 3D micro-porous structures with the breath-figures method.  Finally, Chap. 8 will present the most relevant applications in which the porous surfaces prepared by the breath-figures approach have been employed. This will permit their use in optical applications, for the elaboration of membranes, for catalytical purposes, or for biorelated applications, among others.

References

9

References 1. Chen, C.S., M. Mrksich, S. Huang, G.M. Whitesides, and D.E. Ingber. 1998. Micropatterned surfaces for control of cell shape, position, and function. Biotechnology Progress 14: 356–363. 2. Varenberg, M., and S.N. Gorb. 2009. Hexagonal surface micropattern for dry and wet friction. Advanced Materials 21: 483–486. 3. Xia, Y., E. Kim, X. Zhao, J. Rogers, M. Prentiss, and G.M. Whitesides. 1996. Complex optical surfaces formed by replica molding against elastomeric masters. Science 273: 347–349. 4. Stone, H.A., and S.  Kim. 2001. Microfluidics: Basic issues, applications, and challenges. AICHE Journal 47: 1250–1254. 5. Koch, K., B. Bhushan, and W. Barthlott. 2009. Multifunctional surface structures of plants: An inspiration for biomimetics. Progress in Materials Science 54: 137–178. 6. Barthlott, W., and C. Neinhuis. 1997. Purity of the sacred lotus, or escape from contamination in biological surfaces. Planta 202: 1–8. 7. Wen, L., J.  Weaver, and G.  Lauder. 2014. Biomimetic shark skin: Design, fabrication and hydrodynamic function. The Journal of Experimental Biology 217: 1656–1666. 8. Liu, Y., and G. Li. 2012. A new method for producing “Lotus effect” on a biomimetic shark skin. Journal of Colloid and Interface Science 388: 235–242. 9. Falconnet, D., G. Csucs, H. Grandin, and M. Textor. 2006. Surface engineering approaches to micropattern surfaces for cell-based assays. Biomaterials 27: 3044–3063. 10. Rodríguez-Hernández, J. 2015. Wrinkled interfaces: Taking advantage of surface instabilities to pattern polymer surfaces. Progress in Polymer Science 42. 11. Rodríguez-Hernańdez, J., and C.  Drummond. 2015. Polymer surfaces in motion: Unconventional patterning methods. ISBN 9783319174310. 12. Lu, G., W.  Li, J.  Yao, G.  Zhang, B.  Yang, and J.  Shen. 2002. Fabricating ordered two-­ dimensional arrays of polymer rings with submicrometer-sized features on patterned self-­ assembled monolayers by Dewetting. Advanced Materials 14: 1049–1053. 13. Reiter, G. 1992. Dewetting of thin polymer films. Physical Review Letters 68: 75–78. 14. Xie, R., A. Karim, J.F. Douglas, C.C. Han, and R.A. Weiss. 1998. Spinodal Dewetting of thin polymer films. Physical Review Letters 81: 1251–1254. 15. Byun, M., W. Han, B. Li, X. Xin, and Z. Lin. 2013. An unconventional route to hierarchically ordered block copolymers on a gradient patterned surface through controlled evaporative self-­ assembly. Angewandte Chemie International Edition 52: 1122–1127. 16. Fukunaga, K., H.  Elbs, R.  Magerle, and G.  Krausch. 2000. Large-scale alignment of ABC block copolymer microdomains via solvent vapor treatment. Macromolecules 33: 947–953. 17. Schäffer, E., T. Thurn-Albrecht, T. Russell, and U. Steiner. 2000. Electrically induced structure formation and pattern transfer. Nature 403: 874–877. 18. Vandeparre, H., S. Gabriele, F. Brau, C. Gay, P. KK, and P. Damman. 2010. Hierarchical wrinkling patterns. Soft Matter 6: 5751–5756. 19. Guvendiren, M., S. Yang, and J.A. Burdick. 2009. Swelling-induced surface patterns in hydrogels with gradient crosslinking density. Advanced Functional Materials 19: 3038–3045. 20. Muñoz-Bonilla, A., M. Fernández-García, and J. Rodríguez-Hernández. 2014. Towards hierarchically ordered functional porous polymeric surfaces prepared by the breath figures approach. Progress in Polymer Science 39: 510–554. 21. Escalé, P., L. Rubatat, L. Billon, and Journal, M.S.-E.P.; 2012, U. 2012. Recent advances in honeycomb-structured porous polymer films prepared via breath figures. European Polymer Journal 48: 1001–1025. 22. Tarábková, H., and P.  Janda. 2013. Nanobubble assisted nanopatterning utilized for ex situ identification of surface nanobubbles. Journal of Physics. Condensed Matter 25: 184001. 23. Siretanu, I., J.P. Chapel, and C. Drummond. 2011. Water−ions induced nanostructuration of hydrophobic polymer surfaces. ACS Nano 5: 2939–2947.

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1  Introduction to Micropatterned Surfaces

24. Nie, Z., and E.  Kumacheva. 2008. Patterning surfaces with functional polymers. Nature Materials 7: 277–290. 25. Wu, N., and W.B. Russel. 2009. Micro- and nano-patterns created via electrohydrodynamic instabilities. Nano Today 4: 180–192. 26. Bormashenko, E. 2017. Breath-figure self-assembly, a versatile method of manufacturing membranes and porous structures: Physical, chemical and technological aspects. Membranes (Basel) 7: 1–20. 27. Zhang, A., H. Bai, and L. Li. 2015. Breath figure: A nature-inspired preparation method for ordered porous films. Chemical Reviews 115: 9801–9868. 28. Jiang, X., X. Zhou, Y. Zhang, T. Zhang, Z. Guo, and N. Gu. 2010. Interfacial effects of In Situ -synthesized Ag nanoparticles on breath figures. Langmuir 26: 2477–2483. 29. Li, X., L.  Zhang, Y.  Wang, X.  Yang, N.  Zhao, X.  Zhang, and J.  Xu. 2011. A bottom-up approach to fabricate patterned surfaces with asymmetrical TiO2 microparticles trapped in the holes of Honeycomblike polymer film. Journal of the American Chemical Society 133: 3736–3739. 30. Guthrie, W. 1962. The Milesians: Anaximenes. In A history of Greek philosophy. Cambridge University Press, United Kingdom. 31. Laërtius, D.  No Title Available online: https://en.wikisource.org/wiki/ Lives_of_the_Eminent_Philosophers/Book_I. 32. Aitken, J. 1895. Breath figures. Proceedings of the Royal Society of Edinburgh 20: 94–97. 33. ———. 1911. Breath figures. Nature 86: 516–517. 34. Rayleigh, Lord. 1912. Breath figures. Nature 90: 436–438. 35. ———. 1911. Breath figures. Nature 86: 416–417. 36. Baker, T.J. 1922. Breath figures. London, Edinburgh, Dublin Philosophical Magazine and Journal of Science 44: 752–765. 37. Zhai, S., E. Hu, Y. Zhi, and Physicochemical, Q.S.-C. and S.A.; 2015, U. 2015. Fabrication of highly ordered porous superhydrophobic polystyrene films by electric breath figure and surface chemical modification. Colloids and Surfaces A: Physicochemical and Engineering 469: 294–299. 38. Zhai, S., J. Ye, N. Wang, L. Jiang, and Q. Shen. 2014. Fabrication of porous film with controlled pore size and wettability by electric breath figure method. Journal of Materials Chemistry C 2: 7168–7172. 39. Fei, B., D.-L. Lu, and Q. Shen. 2018. Formation of honeycomb polysulfone film with controlled wettability by surfactant-assisted electric breath figure. Journal of Adhesion Science and Technology 32: 1027–1032. 40. Rose, J.W. 2002. Dropwise condensation theory and experiment: A review. Proceedings of the Institution of Mechanical Engineers, Part A Journal of Power and Energy 216: 115–128. 41. Hou, Y., M. Yu, X. Chen, Z. Wang, and S. Yao. 2015. Recurrent Filmwise and dropwise condensation on a beetle mimetic surface. ACS Nano 9: 71–81. 42. Enright, R., N.  Miljkovic, J.L.  Alvarado, K.  Kim, and J.W.  Rose. 2014. Dropwise condensation on micro- and nanostructured surfaces. Nanoscale and Microscale Thermophysical Engineering 18: 223–250. 43. Starostin, A., V. Valtsifer, Z. Barkay, I. Legchenkova, V. Danchuk, and E. Bormashenko. 2018. Drop-wise and film-wise water condensation processes occurring on metallic micro-scaled surfaces. Applied Surface Science 444: 604–609. 44. Beysens, D. 1995. The formation of dew. Atmospheric Research 39: 215–237. 45. ———. 2006. Dew nucleation and growth. Comptes Rendus Physique 7: 1082–1100. 46. Beysens, D., A. Steyer, P. Guenoun, D. Fritter, and C.M. Knobler. 1991. How does dew form? Phase Transitions 31: 219–246. 47. Widawski, G., M. Rawiso, and B. François. 1944. Self-organized honeycomb morphology of star-polymer polystyrene films. Nature 369: 387–389. 48. François, B., O. Pitois, and J. François. 1995. Polymer films with a self-organized honeycomb morphology. Advanced Materials 7: 1041–1044.

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49. Maruyama, N., T.  Koito, J.  Nishida, T.  Sawadaishi, X.  Cieren, K.  Ijiro, O.  Karthaus, and M. Shimomura. 1998. Mesoscopic patterns of molecular aggregates on solid substrates. Thin Solid Films 327–329: 854–856. 50. Bunz, U.H.F. 2006. Breath figures as a dynamic templating method for polymers and nanomaterials. Advanced Materials 18: 973–989.

Chapter 2

Breath-Figures Formation: Physical Aspects

Abstract  Physical aspects of the process of the breath-figures self-assembly are surveyed. The main physical processes involved in the process are: (1) evaporation of the polymer solution; (2) nucleation of water droplets; (3) condensation of water droplets; (4) growth of droplets; (5) evaporation of water; and (6) solidification of polymer giving rise to the eventual microporous pattern. Hierarchy of the temporal and spatial scales inherent for the breath-figures self-assembly is elucidated. Dimensionless numbers describing the process are supplied. Topological aspects of the self-assembly are considered. Crucial role of the solvent, including its interfacial properties, in the process is addressed in detail. Role of the interfacial Marangoni flows in the formation of the large-scale pattern is treated. The physical properties of the substrate influence the eventual pattern. Nucleation, condensation, and growth of water droplets are addressed in detail. Physical mechanisms of micro-scaled ordering in the breath-figures self-assembly are discussed. The role of the capillary attraction is clarified. Keywords  Pattern · Instability · Evaporation · Nucleation · Condensation · Droplets · Marangoni flows · Hierarchy · Capillary attraction

2.1  Introduction Consider formation of breath-figures inspired patterns obtained with rapidly evaporated polymer solutions [1–3]. Main physical processes involved in the process are (1) evaporation of the polymer solution; (2) nucleation of water droplets; (3) condensation of water droplets; (4) growth of droplets; (5) evaporation of water; and (6) solidification of polymer giving rise to the eventual microporous pattern, as depicted schematically in Fig. 1.5. We will address successively these main stages of the breath-figure self-assembly process and try to understand what physical factors are responsible for the formation of the micro-scaled, polymer, honeycomb pattern.

© Springer Nature Switzerland AG 2020 J. Rodríguez-Hernández, E. Bormashenko, Breath Figures, https://doi.org/10.1007/978-3-030-51136-4_2

13

14

2  Breath-Figures Formation: Physical Aspects

2.2  Evaporation of the Solution 2.2.1  Role of the Solvent A variety of solvents were used for manufacturing breath-figures inspired honeycomb patterns [1–3]. The most reported solvents include carbon disulfide, benzene, toluene, chloroform, dichloromethane, 1,2-dichloroethane, and 1,1,2-­trichlorotrifluoroethane [4]. Obviously the ability of the solvent used to dissolve the polymer is expected to be of utmost importance [4, 5]. It is also naturally agreed that a low water miscibility is crucial for creating well-ordered honeycomb patterns [4]. Evaporation of the solvent from the polymer solution is the initial and crucial stage of the breath-figures self-assembly, providing cooling of the solution/vapor interface, which in turn promotes the condensation of water droplets [6, 7]. Thus, low boiling point (high vapor pressure) and low boiling enthalpy are prerequisites to induce a surface cooling able to start water condensation from the environment [6]. The surface cooling due to the rapid evaporation of the solvent was established experimentally in Ref. [6] as 25 °C below room temperature, resulting in an evaporating polymer surface of near 0°. Temperature as low as −13  °C at the surface 5 wt% polystyrene (PS) dissolved in the mixture of chloroform (CHCl3, 7.6 wt%) and dichloromethane (CH2Cl2, 87.4 wt%) has been registered in Ref. [8]. Very similar values of surface cooling (−12 °C) were reported in Ref. [9]. Moreover, it was demonstrated that a broad diversity of the solvents and polymers brought into existence porous micro-scaled patterns typical for breath-figures self-assembly when the solutions have been first pre-cooled [8]. Modeling of evaporative cooling of polymers solutions was performed in Ref. [9]. Thus, the ability of the solvent to cool the surface under evaporation is definitely a decisive factor in an entire process of the breath-figures self-assembly. However, this is not enough to explain the observed results, reported by various groups. Acetone has a boiling point lower than that of chloroform and similar boiling enthalpy, but it does not allow the formation of breath-figures induced patterns [4]. This may be related to high water miscibility of acetone. The authors of Refs. [4, 10] suggested that the formation of honeycomb structures depends on the thermodynamic affinity between polymer and solvent. Tian et al. investigated the behavior of polyphenylene oxide (PPO) in various solvents and concluded that a thin polymer film can be formed on the surface of water droplets only for good solvents [10]. This film decreases the surface tension between the solvent and the water droplets, thus hindering their coalescence. When a poor solvent is used, migration of polymer chains to the water/solution interface is restricted, resulting in coalescence of water droplets and poor regularity of pores or no breath-figures formation [10]. Escalé et al. summarized the demands to the physical properties of solvent, giving rise to well-ordered breath-figures solvents as follows: “the choice of the solvent is driven by the combination of the following features: high vapor pressure, low boiling point, low solubility in water and preferentially higher density than water” [11].

2.2  Evaporation of the Solution

15

Consider closely the list of demands to solvent suggested in Ref. [11]. The role of the density of a solvent in the process deserves a separate discussion. Actually not only solvents which are denser that water (chloroform, dichloromethane, carbon disulfide) gave rise to typical breath-figures patterns but also solution based on benzene [12–15] and tetrahydrofuran, used for electrospinning of polymer fibers, brought into existence honeycomb micro-scaled topographies [16–19]. Both benzene and tetrahydrofuran have a density smaller than that of water (see Table 2.1). Thus, the impact of the density of the solvent on the breath-figures self-assembly seems to be negligible. Indeed, the impact of gravity on an entire process is minor, and the self-assembly is mainly governed by interfacial forces. The interplay between gravity and interfacial processes is described by the so-­ called capillary length lca, given by Eq. 2.1a or the Bond number (known also as the Eötvös number, and abbreviated Bo), supplied by Eq. 2.1b lca =

γ , ∆ρ ρ g

(2.1a)

Table 2.1  Physical parameters of the solvents used for the breath-figures self-assembly

Solvent Density ρ, g/ cm3 Viscosity η, mPa·s Surface tension, mJ γ wv , 2 m Interfacial tension with water, mJ γ sw , 2 m

Carbone disulfide, CS2 1.26 0.35

Benzene Toluene Chloroform Dichloromethane Tetrahydrofuran 0.88 0.87 1.48 1.33 0.89 0.60

0.56

0.64

0.41

0.46

31.6

28.2

27.9

26.5

27.2

26.4

48.1

34.0

36.1

33.5

28.3

–

61

40

65

Boiling point 46 Tb, °C 48.2 Vapor pressure, 25 °C (kPa) 27.5 Enthalpy of vaporization, kJ/Mol 0.22 Solubility in water (25 °C), g/100 ml Dipole mom. 0 D.

80.1

111

13.0

3.79

26.2

58.2

21.6

33.83

38.01

31.3

28.8

32.0

1.8

0.05

0.8

2.0

Misc.

0

1.15

1.15

1.62

1.63

16

2  Breath-Figures Formation: Physical Aspects

Bo =

∆ρ gl 2

γ

(2.1b)

,

where γ and |Δρ| are the surface tension and the modulus of the difference in density of the two phases, respectively [20, 21]. Quite remarkably, for free and sessile droplets, the value of lca is of the order of magnitude of a few mm for all of existing organic and nonorganic liquids; in this case |Δρ|  =  ρ where ρ is the density of a liquid. The value of lca is on the order of magnitude of millimeter even for mercury for which both ρ and γ are large [20, 21]. In the breath-figures self-assembly, we deal with micro-scaled condensed water droplets with characteristic radii r ≈ 1μm g condensed and floating on the polymer solution; hence ∆ρ = ρ w − ρ s ≅ 0.1 3 , cm (see Table 2.1), where ρw and ρs are the densities of water and solution correspondingly. Thus, for floating droplets, the capillary length is larger than that for free and sessile ones (the role of gravity is partially compensated by buoyancy). Obviously, the inequality lca ≫ r takes place, and the role of the gravity in the formation of the pattern is negligible, and the process is driven mainly by interfacial events [20, 21]. Indeed, typical breath-figures patterns were registered for horizontal and vertical substrates. Hence, we conclude that the impact of density of solvent is well-expected to be negligible. In the terms of the dimensionless Bond number (Bo), we say that its value is much smaller than unity and the impact of gravity may be neglected. Now consider the water miscibility of the solvent, suggested to be important for the promotion of the breath-figures process [11]. Water and THF are miscible with each other, and a complete correspondence with expectations Peng et al. reported that polystyrene dissolved in THF and evaporated in the humid atmosphere did not give rise to breath-figures patterns [22]. In contrast Zhao et al. communicated typical breath-figures topographies for random poly(styrene-co-acrylonitrile) dissolved in THF [16]. Moreover, breath-figures patterns were observed under electrospinning of polystyrene dissolved in THF [18, 19]. How this discrepancy may be explained? The simplest possible reasoning explaining formation of breath figures with water miscible solvents sounds as follows: the presence of polymer in solvent may decrease dramatically the water miscibility of the solution, in particular under already mentioned low temperatures due to evaporation of the solvent [6–9]. Now we address the impact of the boiling point on the process. Solvents with a low boiling point, such as carbon disulfide, chloroform, and dichloromethane, promoted formation of breath figs [1–4].; however the solvents possessing relatively high boiling points, such as benzene and toluene [6, 13–15, 22], also gave rise to honeycomb patterns. We have to agree with authors of Ref. [23] that at present, it is difficult to state which criterion is the most important. The use of humid airflow instead of static conditions should make solvent evaporation easier and allow breath-figures films to form even when using solvents with relatively high boiling points. From the applicative point of view, it is important that variation of solvents allowed control of the shape and chemistry of pores. For example, for THF-based

2.2  Evaporation of the Solution

17

solutions, the pores are always non-spherical, and large amounts of hydrophilic homopolymers are enriched in the pores [24]. Moreover, mixing poly(methyl methacrylate) (PMMA) and amphiphilic copolymers containing glucose in THF enabled manufacturing of microspheres instead of honeycomb structures [25]. Thus, the choice of the solvent plays a crucial importance for manufacturing breath-figuresinduced honeycomb patterns and microparticles. For manufacturing well-ordered honeycomb topographies, we recommend the use of carbon disulfide, chloroform, and dichloromethane possessing low boiling points and low water miscibility. Consider that polar (chloroform, dichloromethane, and THF) and nonpolar solvents (carbon disulfide, benzene) promote formation of the breath-figures patterns.

2.2.2  Role of the Interfacial Properties of Solvent We mentioned that an ability of the solvent to cool the polymer solution/vapor interface is crucial for formation of breath-figures patterns. Now we address the role of the interfacial properties of the solvent. Consider water droplet condensed on the polymer solution water interface as depicted in Fig. 2.1a. Generally, two main scenarios of wetting regime are possible depending on the sign of the spreading parameter S, defined according to Eq. 2.2 [19, 21, 24, 26].:

S = γ sv − ( γ wv + γ sw ) ,



(2.2)

where γsv, γwv, and γsw are the surface tensions at the solution/vapor, water saturated with solvent/vapor, and solution saturated with water/water interfaces, respectively. S > 0 means complete wetting, shown in Fig. 2.1b, and S  0 the complete wetting takes place (i.e., the thin film of condensed water is spread on the polymer solution surface, as depicted in Fig. 2.1b [20, 21]. Obviously the formation of breath-figures-inspired patterns is possible when the condition takes place S  0 takes place is depicted. Polymer solution coats water droplet and encapsulates it (see Ref. [32])

ϒSV evaporation

ϒSW polymer solution

20

2  Breath-Figures Formation: Physical Aspects

mJ mJ mJ , γ sw ≅ 36.0 2 , and hence Sˆ ≅ 6 2 > 0 ; for the xylene-based solu2 m m m mJ mJ mJ tions, we have γ sv ≅ 30 2 , γ sw ≅ 38.0 2 , and hence Sˆ ≅ 3 2 > 0 . m m m Thus, in all of the studied cases, we expect that the solution will climb upon water droplets and coat them, and actually this behavior resulting from Eq. 2.4 was observed. Two different experimental techniques illustrating behavior of water droplets, placed on polymer solutions, were reported, named below as techniques A and B, correspondingly:

γ sv ≅ 29

(A) Water droplets were placed on the bulk polymer solution/air interface. Droplets were dripped with a precise micro-dosing syringe from a height of 3–5 mm. (B) Water droplets were deposited on thin polymer solution layers (thickness ≈10 μm), spread on the solid substrates with a brush. Droplets were then placed on the solution layer as it was according to the technique (A). When water droplets were placed on the chlorinated solvent-based polymer solutions/vapor interface, they were coated by polymer solution, which evaporated, thus bringing into existence polymer film with the thickness of ca 20 μm, which prevented evaporation of the water droplet, and the encapsulated water droplet remained stable for 2–3 h. This was observed irrespectively of polymer type, solution concentration, or experimental technique. When the solutions based on the aromatic solvents were studied (also successfully used for the breath figure self-assembly [6]), the experimental findings were different for techniques A and B. When the droplet was placed on the surface of the bulk polymer solution, it immediately sank (the gravity is not negligible for millimetrically scaled droplets, as follows from the discussion of the value of the capillary length lca supplied by Eq. 2.1). When the water drop has been deposited on the surface of the thin polymer solution layers (technique (B), the solid substrate prevented the droplet from sinking; solution got up and eventually coated the drop in a way similar to the above reported scenario inherent for chlorinated solvents. The model describing climbing of polymer solutions upon water droplets was suggested [31]. The model predicted a weak inverse dependence of the velocity of climbing on the solution concentration, which was tested experimentally. The results reported in Ref. [31] posed a reasonable question: water droplets encapsulated by polymer films do not evaporate; so how the eventual pores-built honeycomb breath-figures pattern becomes possible? The plausible explanation was suggested in Ref. [32]. Ma et al. observed with optical microscopy encapsulation of water droplets by polyphenylene oxide (PPO)/chloroform solutions at the first stage of the breath-figures process [32]. At this stage the encapsulation of water droplets is of a primary impor-

2.2  Evaporation of the Solution

21

solvent evaporation surface

water

water

polymer layer solution Droplets are encapsulated by polymer layer

Temperature rises back

water evaporation

water

surface

water

polymer layer solution Water in droplets evaporates to form surface holes

Fig. 2.3  The mechanism of pores formation, assuming the bursting “hypothesis,” suggested in Ref. [32] is depicted

tance, preventing their coalescence [32]. However, at the second stage of the process, polymer film “bursts” providing evaporation of trapped water and resulting in formation of surface holes [32], as depicted Fig.  2.3. The “bursting hypothesis” suggested in Ref. [32] predicts formation of quasi-spherical sub-surficial cavities (see Fig. 2.3), observed by scanning electron microscopy (SEM) and reported in Ref. [33]. The “bursting hypothesis” is also supported by atomic force microscopy (AFM) study of the topography of the surfaces, typical for the breath-figures process. AFM images reported in Ref. [34] demonstrate dentate polymer projections surrounding the pores, which may be interpreted as remnants of the burst polymer film, coating water droplets. Similar SEM images evidencing distinct polymer projections surrounding the pores were reported also in Ref. [34]. Ma et al. also suggested that at the early stage of the breath-figures process, the solvent is evaporated so fast that the temperature of the solution is low enough to prevent the evaporation of water droplets. As a result, the polymer layer encapsulating the droplets is not burst [32], as shown in Fig. 2.3. After this the temperature rises, and water is evaporated. The following scenarios of the pores formation were suggested: (1) pores appeared later than the formation of droplets. (2) The diameters and the distances between adjacent pores remain almost the same over a relatively long time when the pores are moving. The compact packing array of droplets forms before the appearance of surface holes. Additional experimental data justifying the “bursting hypothesis” are required. Consider also that the results reported in Ref. [31] should be taken cum grano salis, due to the fact that the experiments were performed with “large” millimetrically scaled water droplets, for which the Bond number, supplied with Eq. 2.1b, is close to unity and gravity is essential, whereas the droplets responsible for the formation of typical breath-figures patterns are micro-scaled, being much smaller than the capillary length, thus enabling neglecting gravity-related effects.

22

2  Breath-Figures Formation: Physical Aspects

Fig. 2.4 (a) The pattern observed under evaporation of polycarbonate dissolved in dichloromethane (7 wt.%). Typical boundary separating cells formed under rapid evaporation of polymer solutions. (b) AFM image of the boundary, observed for polymethylmethacrylate dissolved in chloroform (10 wt.%). The boundary is built from microscopically scaled pores

2.2.3  I nterplay of Evaporation of the Solvent and Interfacial Properties of the Polymer Solution: Marangoni Flows and Formation of the Large-Scale Pattern The evaporation of the solvent resulting in the rapid cooling of the solution/vapor interface leads also to the formation of the large-scale pattern, observed under the breath-figures self-assembly and depicted in Figs. 2.4 and 2.5. The characteristic

2.2  Evaporation of the Solution

23

Fig. 2.5  The large-scale patterns observed under the dip-coating process with the polystyrene (5 wt.%) dissolved in the mixture of chloroform (10 wt.%) and dichloromethane (85 wt. %) are shown. (a) Scale bar is 100 μm. (b) Scale bar is 20 μm

lateral dimension of the patterns is ca. 10–50  μm [35–42]. The patterns were observed under various experimental techniques, including drop-casting [35, 42], dip-coating [36, 37], and spin-casting [41]. The patterns were reported for a diversity of polymers (see Chap. 4 for a complete analysis of the type of polymers employed), namely, poly(3-hexylthiophene) (P3HT) [35], polystyrene, polycarbonate, polymethylmethacrylate [36, 37, 39, 41], polyacrylonitrile [39], or polydimethylsiloxane [42] and solvents, namely, chlorinated solvents [35–37, 42] and toluene [38, 41], among others. It should be emphasized that both low (chloroform, dichloromethane) and high boiling point (toluene) solvents give rise to large-scale self-­

24

2  Breath-Figures Formation: Physical Aspects

Fig. 2.6  SEM image of typical breath-figures-inspired pattern obtained with polystyrene dissolved in the mixture of chlorinated solvents is shown. Scale bar is 10 μm

assembled patterns, shown in Figs. 2.4 and 2.5. Thus, both honeycomb, small-scale (~1μm), shown in Fig. 2.6, and netlike large-scale (~10 − 50μm) patterns, depicted in Figs. 2.4 and 2.5, appear under evaporation of rapid evaporation of a diversity of polymers dissolved in low and relatively high boiling point solvents. The process of the formation of the large-scale patterns is two-step. The large-­ scale network appears immediately after the onset of evaporation (the exact experimental data, reporting the time of the onset of large-scale pattering, are absent). Afterward water droplets preferably condense on this network, forming pores, as discussed above (see also Ref. [32]) enabling an explicit visualization of the pattern. µm Shadowgraph technique revealed that these pores migrate rapidly ( v ~ 10 − 30 ) s toward the knots of the network, forming large pores, clearly recognized in Fig. 2.5, as shown schematically in Fig.  2.7, and discussed in Ref. [43]. This migration resembles the drainage phenomenon observed in foams, which relates to the Plateau borders effect [43, 44]. It has been suggested that the migration of pores occurs along the Plateau borders formed in the evaporated solution and is due to the capillary pressure gradient formed within the Plateau borders [43]. It was also suggested that the large-scale pores (knots of the large-scale network) represent zero-velocity points, accumulating pores. Thus, formation of knots arises from the topological

2.2  Evaporation of the Solution

25

peculiarities of the tangential velocity field taking place on the surface of evaporated polymer solution [44]. The very important question to be addressed is formulated as follows: how the large-scale network, reported in Refs [35–42] is created? The origin of this network remains unclear; a number of research groups relate their formation to so-called Marangoni flows [35, 38, 41]. Weh et al. discussed the role of “crack patterns” in the formation of the large-scale patterns [38–40]. Consider the origin of the Marangoni flow-inspired instability. The surface tension of polymer solutions depends on both temperature and concentration of polymer γ(T, c) (see Eq. 2.3 and Refs. [19, 20, 28, 29]). This dependence may bring to the existence the surface flow. Indeed, liquid tends to diminish its surface energy; thus the surface stream will start, while bringing hot particles of a liquid to cold areas of a surface. The Marangoni flows may be generated by gradients in either temperature or chemical concentration at an interface. The first of which is called “thermo-capillary,” whereas the second one is the “soluto-capillary” flow. The temperature dependence of the surface tension is well described by the Eötvös equation (Eötvös rule):

γ (VML ) = 2 /3

kˆ ( Tc − T ) ,



(2.5)

where VML is the molar volume of the liquid: VML = MW/ρL, MW, and ρL are the molar mass and the liquid density, respectively, Tc is the critical temperature of a liquid, and kˆ is a constant valid for all liquids. The Eötvös constant has a value of kˆ = 2.1 ⋅ 10 −7 J / mol 2 / 3 K . An abundance of modifications of the Eötvös formula (2.5) has been proposed; however, for practical purposes, the linear dependence of the surface tension could be supposed [45, 46].

(

)

pores

Fig. 2.7  Velocity field observed at the interface of the evaporated polymer solution (Ref. [43]). Pores are accumulated at the zero-velocity lines

zero-velocity lines

26

2  Breath-Figures Formation: Physical Aspects

Now consider the soluto-capillary Marangoni flow. It arises from the concentration dependence of the surface tension (see Eq. 2.3). Note that under evaporation of the solvent, the concentration of polymer grows instantaneously resulting in the change of the surface tension of the solution. Historically the soluto-capillary flow was discovered first by Italian winemaker C. G. M. Marangoni and J. Thomson, and it was called the effect of wine tears [47, 48]. British physicist C. V. Boys argued that the biblical injunction “Look not thou upon the wine when it is red, when it giveth his colour in the cup, when it moveth itself aright.” (Proverbs, 23:31) refers to wine tears [49]. The Marangoni flows are always compensated by viscous stresses [50, 51]. Consider also that thermo- and soluto-capillary flows often co-occur, and this is the case in the process of breath-figures self-assembly. Indeed, both the temperature and concentration of polymer solution are changed markedly in the course of evaporation of the solvent. This makes an accurate mathematical analysis of flows in rapidly evaporated films of polymer solutions extremely challenging [52, 53]. Thus, we restrict ourselves by the qualitative analysis of the problem. The Marangoni surface flows actually close loops, observed in liquid layers exposed to temperatures gradients, as shown in Fig. 2.8. The evaporated horizontal layer of the polymer solution is cooled under evaporation of the solvent (T2 > T1, as shown in Fig. 2.8, where T2 and T1 are the temperatures of the substrate and evaporated polymer solution, respectively). Owing to the thermal expansion, a density gradient will appear along the vertical axis. When heated from below, lighter fluid lies near the bottom of the layer, while heavier fluid is on the top. Consider a hot particle of liquid pulled up by buoyancy. This particle will be spread on the free surface of a liquid by the Marangoni thermo-capillary flow, closing the velocity loop, depicted in Fig. 2.8. The Marangoni dimensionless numbers describing the motion of the liquid are usually introduced:



 ∂γ   ∂γ   ∂c  ∆cd  ∂T  ∆Td   MaT = − ; MaC = −   ˜ ηD ηκ

(2.6)

where MaT and Ma ˜ c are thermal and concentration Marangoni numbers correspondingly, η, D, and κ are the viscosity, diffusion coefficient, and thermal diffusivity of the evaporated polymer layer, respectively, c is the concentration, of the polymer solution, d is the thickness of the polymer later, and ΔT, Δc are the temperature and concentration jumps across the layer correspondingly. For even liquid layers the absolute value of the critical number Ma (excitation threshold) is 80 for both mass and heat transfer from the layer to the gas phase, derived from theoretical stability analysis [38, 54]. Note that the viscosity, diffusion coefficient, and thermal diffusivity of the evaporated polymer layer are temperature and concentration dependent, and these dependencies are usually not well experimentally established. Hence it turns out that even the calculation of Marangoni numbers, given by Eq. 2.6, turns out to be perplexed. Anyway, researchers ascribed large scale (lateral dimension ca 10–50 μm) to the Marangoni instability [38, 41, 55]. Results reported in Ref. [56]

2.2  Evaporation of the Solution

27

shed light on this problem. Heating from below destroyed patterning in evaporated polymer solutions (see model experiments reported in Ref. [56]). It was suggested that temperature gradient-driven Marangoni instability is hardly responsible for the large-scale patterning in rapidly evaporated polymer solutions comprising amorphous polymers and chlorinated solvents. Actually, heating from below destroyed this kind of patterning. Moreover, the eventual pattern did not follow the symmetry of the temperature field when the evaporated layer is heated from below by a point heat source. Thus, it was plausible to relate the patterning to the effects induced by gradients of polymer concentration, i.e., Marangoni concentration instability. Notice that the concentration of the solution exerts a decisive influence on the large cell characteristic dimensions. Cell dimensions grow linearly with the polymer solution concentration for all a diversity of polymers dissolved in chlorinated solvents [57]. It is also possible that the large-scale patterning is due to the instability of the polymer-­rich layer adjacent to the solution/air interface introduced by Nobel Prize winner Pierre-Gilles de Gennes [58, 59]. De Gennes considered solutions of non-glassy polymers where the surface tension of the solvent is smaller than the surface tension of the polymer. In an evaporating film, a “plume,” of solvent-rich fluid, then induces a local depression in surface tension, and the surface forces tend to strengthen the “plume” [58]. This instability should lead to distortions of the free surface and may be optically observable [58]. De Gennes suggested that it should dominate over the classical Benard–Marangoni instability induced by cooling [58]. For glassy polymers de Gennes suggested another mechanism of patterning, namely, when a glassy polymer film is formed by evaporation, the region near the free surface is polymer rich and becomes glassy first [59]. Thus, the near-surface “crust” is formed [59]. De Gennes argued that the “crust” is under mechanical tension and should form some cracks. This may be the source of the roughness observed on the final, dry films, when the solvent vapor pressure is high (and leads to thin crusts) [59]. It should be emphasized that the mechanism of large-scale patterning in the rapidly evaporated polymer solutions remains highly debatable (Fig. 2.8).

Fig. 2.8  Formation of the Benard–Marangoni cells. Liquid is heated from below. Particles constituting the free surface of a liquid are moving tangentially. Zero-velocity points are shown

free surfaceT1

=0 γ(T,c) liquid cell A

T2>T1 cell B

substrate (T2)

28

2  Breath-Figures Formation: Physical Aspects

2.2.4  Role of the Substrate Investigators reported that the observed patterning depends on the substrate involved in the process [4, 24, 36]. In the previous chapter, we already mentioned that Aitken discovered that film-wise water condensation took place on the glass surface treated with a blowpipe flame, whereas the dropwise condensation occurred on the non-­ treated surface of the same glass; thus the breath-figures formation depends crucially on the surface treatment of the surface. Again, in spite of the essential experimental effort, the impact of the substrate on the pattering remains obscure. Ferrari et al. stated that “Analysis of the literature reveals a confusing picture about the effect of the substrate in the formation of breath-figures” [4]. The qualitative explanation suggested in Ref. [4] looks as follows: The role of the substrate lies in a combined effect with the characteristics of the solution. The combined effect of solvent and substrate could affect the nucleation of water droplets. Water adsorbed on the substrate before the deposition of the polymer can be removed after the application of the polymer solution and transported to the surface by the Marangoni convective movements. More hydrophilic substrates are able to bind higher amounts of water, and this can make the formation of water nuclei faster when the solution is able to remove efficiently this water from the substrate surface [4]. In particular, it was reported that the large-scale patterns observed under the fast dip-coating process disappeared on the substrates with the thickness larger than 100 μm [36]. It was suggested that thick substrates, working at a thermal bath, stabilize the process of evaporation of polymer solution [60].

2.2.5  S  ummary of the Parameters Involved in the BFs Formation As has been already stated, the generation of microporous surface patterns by the BFs approach involves the use of a polymer solution in a volatile solvent and the evaporation in a moist atmosphere. As a result, several different experimental factors and others including the type of solvent employed (discussed above) as well as the chemical structure and topology of the polymer play a key role on the final surface structure. This section will briefly present those aspects that need to be taken into account during the preparation of porous films by the BFs approach. Experimental conditions such as the relative humidity, the environmental temperature, and the polymer concentration are few examples of the parameters that significantly influence both the size and the regularity of the pores formed during the water vapor condensation. In order to provide a concise and clear overview of the factors involved and the consequences in terms of pore shape and size as well as surface homogeneity, Table 2.2 summarizes the most significant parameters to be considered in the preparation of porous materials prepared by water vapor condensation. In addition to Tables 2.2 and 2.3 attempts to illustrate with selected examples

2.2  Evaporation of the Solution

29

Table 2.2  Experimental parameters influencing the pore size and distribution Factor Humidity Airflow

Interfacial tension Solution concentration

Influence of the substrate

Solvent

Evaporation rate Pressure

Temperature

Consequences An increase of the relative humidity usually leads to an increase of pore size [2, 3, 7] Higher flow rates decrease the pore size. In spite of the increase of the evaporation rate, the time required for total evaporation decreases, and thus the resulting average of pore sizes decrease as well [4, 6] High interfacial tension stabilizes the water droplets during solvent evaporation [5, 61] Lower polymer concentration leads to higher pore diameters [6, 62]. The average pore sizes follow the eq. PS = k/c (PS, pore size; k, constant; c, concentration) [2, 7, 8, 63, 64]. However, in some particular cases, no variation as a function of the concentration is observed [9, 10] Independently of the surface hydrophilicity, an increase of the wetting of the polymer solution on the substrates enhances the periodicity and the regularity of the holes [4, 10, 11, 65]. The total condensed water drop volume also increased with the increase in surface roughness which is in good agreement with the increase of the number of nucleated droplets [12, 66] Volatility: Higher volatility produces smaller pores. Lower volatility allows longer water condensation, thus causing the pores to enlarge [7, 13, 22, 63] Type of solvent: The compatibility and the interaction between solvent and polymer play a key role on the water condensation process [4, 9–11, 14, 67] Mixtures solvent/water: The addition of water to polymer solution influences the pore sizes [15, 68] or even the morphology [16, 17, 25, 69]. Ethanol/water or acetone/water [18, 70]. Ratio trichloroethylene/dichloromethane from regular to big pores surrounded by small pores [67] Higher evaporation rates of the solvent increase the diameters of the pores and the distance between them [19, 20, 71, 72] A decrease of the pressure can accelerate the evaporation of the solvent in the same way as the accelerating action of the air flowing across the solvent surface [24, 73]. Li et al. [25, 74] used vacuum to form holes ordered arrays on the surface of polymer films, of which size can be varied by changing the vacuum level A decrease in temperature reduces the evaporation rate of the solvent. As a consequence the evaporation time increases leading to bigger water droplets at the surface and, therefore, bigger pore sizes [8, 27, 28, 75]. Moreover, taking advantage of the influence of the environmental temperature and, thus, the convective flow (between the solution surface and interior, etc.), the arrangement of the water droplets can be disturbed sometimes and organize into another packing structure (for instance, forming squares [13, 22])

Reproduced with permission from Ref. [2]

the morphologies obtained for precise experimental conditions. However, it is worth mentioning that in view of the wide myriad of studies dealing with breath figures, Table 2.2 will be limited to the most significant parameters that can be varied including, among others, airflow rate, relative humidity, temperature, concentration, and type of solvent employed.

30

2  Breath-Figures Formation: Physical Aspects

2.3  N  ucleation, Condensation, and Growth of Water Droplets The breath-figures self-assembly necessarily includes nucleation of water droplets. Nucleation is the formation of an embryo or nucleus of a new phase in another phase [78, 79]. Homogeneous and heterogeneous nucleation scenarios should be distinguished. Heterogeneous nucleation takes place in the presence of foreign particles or surfaces, whereas homogeneous nucleation occurs under while and growing small clusters of molecules [80]. If it is thermodynamically favorable for these clusters to grow, they become recognizable droplets of the liquid phase [46, 80]. It should be emphasized that the precise mechanism of nucleation during the breath-­ figures self-assembly remains unclear, due to the fact that nuclei of water droplets are formed in the presence of solvent vapor [81]. The processes of nucleation and condensation have a decisive influence on the formation of the eventual breath-­ figures-­inspired pattern [81]; hence, additional experimental and theoretical efforts are necessary for elucidating the kinetics of nucleation and condensation taking place under the conditions of the breath-figures self-assembly. The simplest approach to the problem of nucleation may be based on the theory of homogeneous condensation [46, 80, 82]. In the classic nucleation theory, the free energy of forming a liquid cluster of radius r containing N atoms or molecules is the sum of two terms:

∆G = − N ∆µ + 4π r 2γ



(2.7)

where Δμ is the jump in the chemical potential under the phase transition (formation of a liquid from vapor) and γ is the surface tension [80, 82]. The number of molecules in the cluster is easily expressed via the concentration of molecules n (the N number density n = , where V is the volume of the cluster): V

4 N = n π r3. 3

(2.8)

Combining Eqs. (2.7) and (2.8) and taking the derivative of the free energy with respect to radius or number and setting it equal to zero provide the values of N or r at the maximum (see Refs. [80, 82]): Nc =



32πγ 3

(

3n 2 ∆µ 3

rc =

2γ , n∆µ

)

(2.9)

,

(2.10)

2.3  Nucleation, Condensation, and Growth of Water Droplets

31

Table 2.3  Illustrative examples of systems: parameters, polymers, conditions employed, and the resulting pore sizes Parameter Humidity

Polymer Polyion complex of polystyrene sulfonate Poly(vinyl butyral)

Polystyrene (PS) Airflow rate

Concentration

Polystyrene Polystyrene/poly(2-­ vinylpyridine) (5/1) (PS/ PVP) Polyion complex of polystyrene sulfonate Polyimide (PI)

Conditions 50–80% RH

Pore size (μm) 0.5–5

Ref. [2, 7]

56.0% RH 75.1% RH (with N2 flow) 97.0% RH 45–90% RH

1.0–1.5 2.5 (1.0–2.0) 2.0–3.0

[3, 76]

2.1–4.7

30–300 m/min 0.3–0.8 L/min

6–0.5 5.0–1.6

[13, 22] [4, 6] [19, 71]

680 mg/L 68 mg/L 1–30 g/L

2.5 10–15 4–0.9

Polymethylene-b-­ polystyrene Poly(phenylene oxide)

1.5–3.0 wt%

6.0–3.0

5–30 g/L

1.8–2

Temperature

Polyimide

20–4 °C

5.2–18

Solvent

Poly(phenylene oxide)

Carbon disulfide Chloroform Trichloroethylene

1.2 1.4 2.9

Polyimide

Dichloromethane Chloroform 1,2-Dichloroethane Chloroform Carbon disulfide Dichloromethane G (glass) WSi (silicon wafer) GWG (silanized glass) GWO (silanized glass treated) GW (glass treated)

0.8 1.3 2.2 0.7–1.1 2.8–3 No pores 0.7–1.1 1.7–1.9 2.1–2.3 3.6–4.1 3.81–4.3

Polystyrene using glass as substrate Substrate

Polystyrene (using chloroform as solvent)

[2, 7] [7, 63] [8, 64] [9, 10] [27, 75] [9, 10, 14, 67] [7, 63] [4, 11] [4, 11]

(continued)

32

2  Breath-Figures Formation: Physical Aspects

Table 2.3 (continued) Parameter Methodology to form the breath figures

Polymer Dip-coating method in conjunction with an evaporative humidifier 0.2 wt % polystyrene

Conditions Dichloromethane

Pore size (μm) Nanoporous polymer film. Pore size of 80 nm

Ref. [77]

Reproduced with permission from Ref. [2]

defining the size of the critical nucleus. The jump in the chemical potential Δμ may be estimated from the Kelvin equation; this yields for the radius of the critical nucleus: 2γ

rc =

nkTln

, Pv Pv0

(2.11)

where Pv is the pressure of the saturated vapor above the surface of a cluster, and Pv0 is the pressure of the saturated vapor above the flat surface (consider the pressure of the saturated vapor above the curved surface is higher than that above the flat surface; this phenomenon is called the Kelvin effect). The rate of formation of nuclei I is dependent on the both thermodynamic and kinetic factors and may be consequently expressed as:





hom  ∆Gmax  I = Zexp  − , kT   hom ∆Gmax =

γ 4π rc2 , 3

(2.12a)

(2.12b)

where Z is the gas kinetic collisions frequency (collisions per cubic meter–second) max is the height of the energy barrier for the homogeneous nucleation [46, and ∅Ghom 1 80, 82]. The dimensions of the rate nucleation are obviously [ I ] = 3 . The calcums lation of the gas kinetic collisions frequency is an extremely perplexed mathematical task; for the details see Refs. [83–85]. It is also possible that nucleation occurs at the polymer solution/vapor interface. In this case the nucleation rate I is modified through the function depending strongly het  ∆Gmax (θY )  on the equilibrium (Young) contact angle θY, namely, I ≈ exp  −  ,  kBT   het where ∅Gmax is the value of the potential barrier to be surmounted for heterogeneous nucleation, T is the temperature, and kB is the Boltzmann constant. The value het for a contact angle hysteresis free substrate is given by: of ∅Gmax

2.3  Nucleation, Condensation, and Growth of Water Droplets



het hom ∆Gmax (θY ) = ∆Gmax

( 2 + cosθY ) (1 − cosθY ) 4

33 2

,



(2.13)

hom is the potential barrier of the homogeneous nucleation supplied by where ∅Gmax Eq. 2.12b (see Ref. [86]). In spite of the fact that nucleation and condensation of water droplets play a decisive role in the breath-figures patterning, there exists a lack of the experimental results shedding light on the problem. Saunders et al. studied the formation of breath figures under drop-casting of poly(ethylene oxide)–b–poly(fluoro-octyl methacrylate) (PEO-b-PFOMA) [87] diblock copolymer films from Freon 1,1,2-­trichlorotrifluoroethane in a humid atmosphere. It was demonstrated that the pores ordering and size distribution depend on the PEO to PFOMA molecular weight ratio [87]. The authors suggested that the primary factor controlling the pore size and size distribution in the case of the PEO-b-PFOMA polymers appears to be the relative water droplet nucleation rates [87]. The difference in pore size therefore was related to the differences in nucleation density, namely, higher nucleation densities provided more diffusion “sinks” to absorb the condensing water and resulted in smaller final droplet size [87]. It is also reasonable to relate the pronounced dependence of the pore sizes on the molecular weight of polymer, reported in Refs. [88–90] to the heterogeneous nucleation occurring on the polymer solution/vapor interface. Indeed, it seems plausible to suggest that the number of “sites” promoting the heterogeneous nucleation of water droplets depends on the molecular weight of polymer (see Fig. 2.9). Much experimental effort is necessary for the elucidation of

water droplets

polymer solution

sites promoting condensation Fig. 2.9  Condensation of water droplets on the surface of evaporated polymer solution. It is plausible to suggest the number of cites, promoting heterogeneous nucleation will depend on the molecular mass of the dissolved polymer [66]

34

2  Breath-Figures Formation: Physical Aspects

the role of the nucleation in the breath-figures self-assembly. The model of evaporative cooling of polymer solutions crucial for understanding the nucleation process has been suggested in Ref. [9]. Now consider the growth of droplets. Beysens et  al. studied the formation of breath-figures patterns formed on cold borosilicate substrates, either pristine or hydrophobized by a solution of octadecyltrichlorosilane [91]. The treatment by octadecyltrichlorosilane enabled control of the apparent contact angle of the cooled solid substrate [91]. The pattern for water on glass was studied by direct observation and light scattering as a function of the contact angle θY, the velocity of vapor volume transfer “flux,” denoted as Φvol, the degree of supersaturation ΔT, and time t. It was established that when θY  =  00, a uniform water layer forms whose thickness grows as t at a constant Φvol and ΔT. For θY = 900, droplets are formed at a constant Φvol and ΔT; the radius of an isolated droplet grows as t0.23, but as a result of coa1escences, the average droplet radius grows as t0.75 [91]. The most important conclusion following from these considerations is well-expectable, namely, the eventual “breath-figures” pattern depends on the apparent contact angle θY, as predicted by Eq.  2.13. The growth process is accompanied by coalescence of droplets, and it turned out to be self-similar; coalescences simply rescaled the distances and left the basic droplet pattern unaltered [92]. The details of the coalescence were addressed in Ref. [76]; the authors showed that the number of coalescences undergone by a given droplet grows logarithmically with time; the total distance traveled by this droplet is proportional to its size [92]. The experiments, reported by Beysens et al., supported the important information about the kinetics of formation of the “breath-­ figures” patterns [91, 92]. However, these experiments were carried out under model conditions in the absence of evaporated polymer solutions, which essentially complicates the physics of the process; hence, novel experimental data shedding light on the kinetics of formation of breath-figures patterns occurring at the polymer solution/vapor interface are necessary. The impact of external parameters (velocity of air, etc.) on the droplet growth was addressed in Ref. [93]. Assume that atmosphere has a velocity v parallel to the substrate. The velocity decreases near the substrate and equals zero on the substrate. The droplet radius and volume V grow according to (Ref. [93]): ˜ 1/ 3



R ∼t ,



V ∼ t,

(2.14a)

˜

(2.14b)

˜

where t is the so-called reduced time given by: ˜



t ∼ v∗ ∆pDt ,



˜  v∗ ∼ v ν kin D  ,  

(2.15a)

1/ 3

(2.15b)

2.4  Mechanisms of Micro-Scaled Ordering in the Breath-Figures Self-Assembly

35

˜

with ν kin being the kinematic viscosity of air, D the mutual diffusion coefficient of water into air, and Δp = pvap – psat the difference in water vapor saturation pressure. When the velocity v is small (quiet air), the boundary layer becomes very thick and Eq. (2.15a) becomes: ˜



t ∼ v∗ ∆pDt.

(2.16)

A complication may arise when the heat of condensation cannot be released into the substrate. In this case, the temperature of the drop increases; its growth is slowed and can even stop. This is especially the case for very fast growths when the air 1 may appear [93]. The velocity is large. Thus the growth exponents lower than lack of the experimental data related on the nucleation and 3growth of droplets under the breath-figures self-assembly carried out with evaporated polymer solutions should be emphasized.

2.4  M  echanisms of Micro-Scaled Ordering in the Breath-­Figures Self-Assembly Now consider the mesoscopic, micro-scaled patterning observed by various groups [1, 2, 6, 23–25, 94]. These mesoscopic patterns are built from well-ordered micro-­ scaled or sub-micro-scaled pores, demonstrating long-range 2D and sometimes 3D ordering [6, 79, 95, 96]. The mechanism of this patterning was discussed in Refs [7, 97]. Govor et al. in Ref. 81 related the mesoscopic ordering to the capillary interaction between droplets, discussed in much detail in Refs [98–101]. Kralchevsky et al. demonstrated that between two particles placed on the liquid/vapor interface, a force acts (which may be either attractive or repulsive) similar to the Coulomb interaction between two endless wires charged with constant linear charge densities [98–101]. The origin of these capillary forces is illustrated by Fig. 2.10; φ1 and φ2 are interfacial angles (the meniscus slope angles) at the contact lines separating particles and liquid. Two different situations should be distinguished, as depicted in Fig. 2.10. In the first (shown in Fig. 2.10a, c, e), the particles (in our case water droplets) are freely floating. The forces acting in this case were called by Kralchevsky et al. the flotation forces [98–101]. The attraction appears because the liquid meniscus changes the gravitational potential energy of the two particles which decreases as they approach each other. Hence, the origin of this force is the particle weight (including the Archimedes force) [98–101]. Thus, it is well expectable that this force is negligible for micro-scaled water droplets, which are characterized by dimensions much smaller than the capillary length (see Eq. 2.1a). Kralchevsky et al. stated that the flotation force disappears for spherical particles with radius smaller

36

A

2  Breath-Figures Formation: Physical Aspects

Flotation forces

Immersion forces

(effect driven by gravity)

(effect driven by wetting) B

-j 2

-j 1

j1

j2

liquid

C

-j 1

D

-

j1

-j 2

liquid E

Flotation forces disappear

F

for R 0,

(2.17a)

2.4  Mechanisms of Micro-Scaled Ordering in the Breath-Figures Self-Assembly

37

and it will be repulsive, when:

sin φ1 sin φ2 < 0.

(2.17b)

In the case of water droplets contacting polymer solutions Eq. 2.17a holds; thus, the immersion forces are attractive and, in principle, may be responsible for the reported ordering. The immersion forces appear not only when particles are supported by solid substrates but also in thin fluid films, as depicted in Fig. 2.10f. This scenario may take place under free-standing breath-figures self-assembly [34]. The theory developed by Kralchevsky et al. predicts the following asymptotic expression for the lateral immersion force acting between two particles (droplets) of radii R, separated by a center-to-center distance L (Refs [1, 10, 11, 94].):

F ≈ γ R 2 K1 ( qL ) ,



(2.18)

where K1(x) is the modified Bessel function of the first order and q is the parameter with the dimensions of m−1 introduced in Refs. [98–101]. It is seen from Eq. 2.28 that the immersion force increases with the increase in the radius of droplets. Thus, it is well-expected that the patterns built from the larger pores should be more ordered; this prediction calls for experimental verification. Thus it is reasonable to suggest that this capillary (immersion) interaction between droplets, condensed at the polymer solution/humid vapor interface, is responsible for the long-range ordering inherent for breath-figures self-assembly. It was already demonstrated by Bragg, Nye, and Lomer (in Refs. [102, 103]) that the capillary interaction of bubbles promotes the assemblage of bubbles, representing the crystal structure of real metals, such as depicted in Fig.  2.11. However, the immersion forces could hardly be responsible for the multilayer ordering, also reported for the breath-figures self-assembly [6].

Fig. 2.11  Self-assembled soap bubbles form the well-ordered 2D crystal lattice (see Refs. 102, 103)

38

2  Breath-Figures Formation: Physical Aspects

Limaye et al. suggested one more mechanism of attraction of droplets, namely, their hydrodynamic attraction [15]. Neighboring droplets embedded in surface dimples can be considered as a typical bistable system that can be driven by the combined action of hydrodynamic interaction and the noise field created by the convection currents hitting the corrugated evaporated surface [15]. Capillary interaction is not the only kind of physical interaction acting between particles placed at the liquid/vapor interface. It was demonstrated by Pieranski that the repulsive electrostatic interactions between floating particles may be no less important than capillary ones [104]. This kind of interaction may be responsible on the non-coalescence of droplets, condensed on the surface of evaporated polymer solution. Pieranski suggested that floating particles (water droplets) were in their case electrically charged [104]. Water droplets appearing in clouds and aerosols are often electrically charged [105, 106]; thus, the hypothesis that water droplets responsible on the breath-figures self-assembly are charged looks at least reasonable. The distribution of the electrostatic charges appearing when colloidal particles (and in our case water droplets floating on polymer solutions) are partially immersed in water is shown in Fig. 2.12. The dipoles associated with such axially symmetric distribution of charges must be vertical [104, 107]. The potential U(L) arising from the electrostatic interaction of colloidal particles is described by the function:



= U (L)

a1 kBT ak T exp ( −κˆ L ) + 2 3B , 3L L

(2.19)

where a1 and a2 are the pre-factors that determine the order of magnitude of the screened Coulomb, diffuse double layer, and the dipole–dipole interaction, respectively; kB is the Boltzmann constant; κˆ is the inverse Debye screening length; and T is the absolute temperature [107–109]. At large enough particle separations ( κˆ L >> 10 ), the dipolar contribution dominates the interaction. A wide range of experiments confirm the dipolar nature of the interactions, showing that the interparticle potential decays as L−3 [108]. Thus, the capillary force Fel due to the electrostatic interaction scales as L−4. External electrical fields exerted on particles (droplets) floating on the liquid surface give rise to additional lateral forces scaling 1 as [109]. This makes possible the external electrical control of the breath-figures L Fig. 2.12  Origin of the repulsive electrostatic force acting between two floating colloidal particles (droplets) according to Refs. [104, 107]

L

- + + -+ --- -- + ++ + + ++

- + + + -+ + - + +++ +

2.4  Mechanisms of Micro-Scaled Ordering in the Breath-Figures Self-Assembly

39

self-assembly [110]. The role of electrical charging of droplets in the breath-figures self-assembly remains obscure; only few studies devoted to the impact of the electric field on the process were reported [111, 112]. The role of the Marangoni thermo-capillary convection in the formation of ordered honeycomb patterns was mentioned in Refs. [7, 112, 113]. The details of the physical mechanism giving rise to the long-range self-assembly of pores, inherent for breath-figures patterning, remain unclear. It is noteworthy that the formation of ordered ensembles of droplets under the drop-casting method occurs in the vicinity of the triple (three-phase) line, as shown in Fig. 2.13. Self-assembly of colloidal particles (not droplets!) taking place in the vicinity of the triple line was studied extensively in Refs. [114, 115]. However, the approach developed in Refs [114, 115]. could hardly be extended to the explanation of the self-assembly of condensed water droplets, due to their coalescence (to be discussed below). It was also demonstrated that some additives such as PEG and dendrons promote the ordering occurring under breath-figures self-assembly [116–118]. The well-­ ordered honeycomb patterns resulting from breath-figures self-assembly evidence non-coalescence or delayed coalescence of sessile water droplets condensed on the polymer solution/vapor interface. This means that a so-called capillary cluster built from micro-scaled water droplets exists on the polymer solution/vapor interface. The physical behavior of non-coalescent capillary clusters, in which capillary interactions prevail or play an essential role have drawn the attention of investigators recently [119–121]. When droplets of the same liquid touch one another, one expects coalescence [21, 122, 123]. On contrast the pronounced non-coalescence is observed under the breath-figures self-assembly process. The mechanism of the non-coalescence observed in capillary clusters remains disputable. We already discussed in Sect. 2.2.2 one of the possible mechanisms, preventing the coalescence, namely, encapsulation of water droplets with thin layers of polymer solutions, followed by their “bursting,” shown in Fig. 2.3 [31–34]. The non-coalescence also may be related to the aforementioned electrostatic repulsion of water droplets [104, 107–109]. Karpitschka et al. showed an alternative mechanism of the non-coalescence [124–

evaporation

condensation

polymer capillary

triple line

substrate

cluster Fig. 2.13  Breath-figures self-assembly taking place under drop-casting is depicted. A droplet of the polymer solution is evaporated in the humid atmosphere. Water droplets are condensed at the polymer solution/vapor interface. A capillary cluster built from water droplets is formed in the vicinity of the triple (three-phase) line

40

2  Breath-Figures Formation: Physical Aspects

126]. It was demonstrated that sessile droplets from different but completely miscible liquids do not always coalesce instantaneously upon contact: the drop bodies remain separated in a temporary state of non-coalescence, connected through a thin liquid bridge [124–126]. Karpitschka et al. suggested that the delay originates from the Marangoni convection [124–126]. Systematic study of the Marangoni convection-­inspired non-coalescence was that undertaken by Dell’Aversana et al. (Refs. [127, 128]), who performed both laboratory experiments and molecular dynamics simulations. In the case of a pair of sessile droplets, a locally hotter region is formed in the center at the top of droplet, as takes place under the coffee-stain effect [129–132]. These surface temperature variations not only give rise to thermo-­ capillary Marangoni convection within the droplets, as depicted Fig. 2.14, but also may drag air surrounding the drops into the space between them. This gas film serves to lubricate the space between the liquid surfaces, preventing them from coming into contact [125, 126]. It is noteworthy that under the breath-figures self-­ assembly, the experimental situation is essentially complicated by the fact that sessile water droplets are located at the rapidly evaporated polymer solution/vapor interface. This may strengthen the thermo-capillary Marangoni flows [131, 132]. However, as it will be demonstrated below, the condensed droplets relatively rapidly come to the thermal equilibrium; thus, a true role of the thermo-capillary Marangoni flows in preventing coalescence remains unclear. Other mechanisms of non-­ coalescence were discussed in Ref. [128]. We conclude that the details of the non-­ coalescence of droplets in capillary clusters remain unclear and call for further experimental and theoretical insights. Nanoparticles also prevent coalescence of droplets and enable the formation of the additional nanoscale in the hierarchical topographies obtained under breath-­ figures self-assembly (see the extended review of the state-of-the-art of use of nanoparticles in breath-figures self-assembly in Ref. [23] and Refs. [133–136]). Saunders et al. demonstrated that the superlattice of monodispersed gold nanocrystals formed under the breath-figures process an ordered structure at the nanometer scale [136]. An interaction between self-organization processes at the nano- and the micrometer length scale, especially through the formation of a water droplets/evap-

hot areas lubricating gas films

Marangoni flow water drop

water drop

Marangoni flow

substrate Fig. 2.14  Scheme of non-coalescence of sessile droplets is depicted (see Refs. [124–128] for details)

2.5  Hierarchy of the Temporal and Spatial Scales Inherent for the Breath-Figures…

41

orating polymer solution interface and droplets’ collective motions was addressed in Ref. [137].

2.5  H  ierarchy of the Temporal and Spatial Scales Inherent for the Breath-Figures Self-Assembly: Dimensionless Numbers Describing the Process We already mentioned that main physical events occur under the breath-figures self-­ assembly on the spatial scales of ca. 10 μm (see Figs. 2.4 and 2.5) and 1.0 μm (see Fig. 2.6). The nanoscaled picture of the process was addressed in Ref. [137], and it needs additional clarification. Now consider the dimensionless numbers describing micro-scaled breath-figures self-assembly, namely, the aforementioned Bond (Bo) (see Eq. 2.1b), capillary (Ca), and Reynolds (Re) numbers: Ca =

ηv ρ vL ; Re = , γ η

(2.20)

where ρ is the density (the densities of water and polymer solutions are very close, so we don’t specify them for the purposes of the crude scaling estimations), η and γ are the viscosity and surface (interfacial) tension of the polymer solution, respectively, v is the characteristic velocity of droplets and pores, and L is the characteristic spatial scale. Assuming for numerical values of physical parameters appearing in Eqs. 2.1b and 2.20: kg J µm ρ ≅ 1.0 × 103 3 ; γ ≅ 25 × 10 −3 2 ;η ≅ 10 −2 − 10 −1 Pa × s; v ≅ 10 − 30 (the s m m viscosity of the solution is taken for the initial stage of the evaporation, and the velocity equals the maximal velocity of pores established experimentally in Ref. [43]); we conclude that inequalities (see also Sect. 2.2.1):

Bo 0

stage 2 spin-up

dω/dt=0

stage 3 spin-off

stage 4 evaporation Fig. 4.8  Main stages of the spin-coating deposition are depicted. ω is the angular velocity of the dip-coating

Ref. [30]. The spin coating can be broken down into several key stages (see Fig. 4.8): fluid dispense spin-up, stable fluid out flow, and finally evaporation dominated drying [5]. At the first stage of the process, solution is allowed to fall on rotating substrates from a microsyringe, and the substrate is accelerated to the desired speed. At the second stage, the substrate is accelerated up to its final, desired, rotation speed. This stage is characterized by intensive fluid expulsion from the substrate surface by the rotational motion. At the third stage, the substrate is spinning at a constant rate and fluid viscous forces dominate fluid thinning behavior. This stage is characterized by gradual fluid thinning. When spin-off stage finishes, the film drying stage begins. At the final stage of the process, the centrifugal outflow stops, and further shrinkage is due to solvent loss. This results in the formation of thin film on the substrate. At the fourth (final) stage, the substrate is spinning at a constant rate and solvent evaporation dominates the coating thinning behavior. Stage 3 (flow controlled) and stage 4 (evaporation controlled) are the two stages that have the most impact on final coating thickness [29]. Clearly, stage 3 and stage 4 describe the two processes that must be occurring simultaneously throughout all times (viscous flow and evaporation). However, at an engineering level, the viscous flow effects dominates early on, while the evaporation processes dominate later.

4.2 Methods Exploited for Manufacturing Breath-Figures Patterns

121

Fluid flow on a flat spinning substrate is one of the most important physical p­ rocesses involved in spin coating. Assume the natural polar coordinates (r, ϑ, z). The constituting equations describing the flow are:





−η

r

d2v = − ρω 2 r dz 2

(4.1)

∂ ( rq ) ∂h =− ∂r ∂t

(4.2)

where η and ρ are the viscosity and density of the solution, respectively, ω is the angular velocity of the spin-coating, v is the radial flow velocity, q = h v z dz is ∫0 ( ) the radial flow per unit length of the circumference, and z = h corresponds to the free liquid surface. Equation 3.1 is the second Newton law, where the Newtonian nature of the liquid is assumed, and Eq. 3.2. is the equation of continuity. Imposing of the boundary  dv  condition of the absence of shear stresses at the free surface, namely,   = 0 ,  dz  z = h the initial condition h(t = 0) = h0 and integration of the system of Eqs. 4.1 and 4.2 ∂h have to supply the profile of the resulting liquid layer. Assuming h ≠ h ( r ) ; = 0 ∂r and integration yields: h=

h0 4h 2 ρω 2 t 1+ 0 3η

(4.3)

For more general solutions, where the dependence h0  =  h0(r0) is taken into account, see Ref. [30]. Sahu et al. also developed the model of thinning of the rotating film under its evaporation and considered the time dependence of the viscosity [30]. Polymer solutions are essentially non-Newtonian liquids [31]. The complications arising from the non-Newtonian rheology of polymer solutions have been also addressed in Ref. [30]. Spin coating has numerous advantages in coating operations, with its biggest advantage being the absence of coupled process variables. Film thickness is easily changed by changing spin speed or switching to a different viscosity polymer solution. Another advantage of spin coating is the ability of the film to get progressively more uniform as it thins, and if the film ever becomes completely uniform during the coating process, it will remain so for the duration of the process. It is low cost and fast operating system [30]. In general, high spinning rates resulted in a more regular porous structure, whereas at low rotating speed, the evaporation rate can be rather low and, thus, favor the coalescence of the water droplets. Besides, the pore size decreases with increasing spinning rate because the faster evaporation entails low time for water droplet growth, while the nucleation of water droplets is preferred.

122

4  Methodologies Involved in Manufacturing Self-Assembled Breath-Figures Patterns…

A very serious disadvantage of spin coating is its lack of material efficiency. Typical spin coating processes utilize only 2–5% of the material dispensed onto the substrate, while the remaining 95–98% is flung off in to the coating bowl and ­disposed [30]. Moreover, in general, the use of spin-coating normally conducts to less ordered patterns as compared with drop-casting or airflow techniques.

4.2.3  Dip-Coating The dip-coating process was also successfully used for manufacturing self-­ assembled patterns under the conditions of breath-figures process [32–34]. The main stages of the dip-coating are: 1 . Immersion: The substrate is immersed in the solution of the coating material. 2. Start-up: The substrate has remained inside the solution for a while and is starting to be pulled. 3. Deposition: The thin layer deposits itself on the substrate while it is pulled up. The withdrawing is carried out at a constant speed to avoid any perturbations. The speed determines the thickness of the coating as it will be shown below. 4. Drainage: Excess liquid will drain from the surface. 5. Evaporation: The solvent evaporates from the liquid, forming the thin layer. For volatile solvents used for the breath-figures self-assembly, evaporation starts already during the deposition and drainage steps [32–35]. Consider the deposition stage. Let us look at an infinite flat plate which is pulled vertically, with a constant speed vp from a bath of liquid with a viscosity η which has a horizontal free surface, and a steady state is established [35, 36]. What is the thickness of the film of liquid adhering to the plate at a large height above the free surface? This is the drag-out problem, which is of a primary importance for industrial coating and painting problems. As it is expected, the physics of the drag-out problem is governed by the Reynolds and capillary numbers, introduced by Eq. 2.20. De Gennes et al. demonstrated that two very different situations are possible, depending on the pulling speed vp, as shown in Fig.  4.9 (see Ref. [21]). These are the “meniscus regime” depicted in Fig. 4.9a and the “film regime” shown in Fig. 4.9b. The critical pulling speed v∗p , at which a switch from the meniscus to film regime occurs, is given by: v∗p =

γ η 9 3 ln

L Lcutoff

θY3 ,

(4.4)

where Lcutoff and L are the cutoff and scale lengths, introduced in Ref. 21. For L v p > v∗p , a meniscus becomes impossible. In water for θY = 0.1 and ln ≅ 20 , Lcutoff mm ∗ v p ≅ 0.2 (see Ref. [37]). s

4.2 Methods Exploited for Manufacturing Breath-Figures Patterns

vp

123

vp qD

b

a

Fig. 4.9  Two regimes occurring when a vertical plate is extracted from a pool of liquid: (a) v p < v∗p ; (b) v p > v∗p , a meniscus is impossible

The thickness of film liquid h adhering to the plate has been established first in the classical work by Landau and Levich [36]. The thickness h results from the interplay of surface tension, gravity and viscosity. Thus, it is reasonable to introduce the characteristic thickness scale d according to (Eq. 3.5 may be also justified with the dimensional arguments): 1/ 2

 η vp  d =   .  ρg 



(4.5)

η vp 350 nm), cross-linked areas were formed. Interestingly, the reaction can be reversed upon exposure to short-wave UV light (