Surface Energy Edited by Mahmood Aliofkhazraei SURFACE ENERGY Edited by Mahmood Aliofkhazraei Surface Energy http://dx.doi.org/10.5772/59354 Edited by Mahmood Aliofkhazraei Contributors Hisham M. Abourayana, Denis Dowling, Meicheng Li, Andrew Titov, Anna Rudawska, Boryan Radoev, Daeyoung Kim, Jeong-Bong(J.-B.) Lee, Homayun Navaz, Calin Jianu, Uros Cvelbar, Harinarayanan Puliyalil, Gregor Filipič, Jesorka, Irep Gözen, Paul Dommersnes, Do Hyun Kim, Jeffrey Streator © The Editor(s) and the Author(s) 2015 The moral rights of the and the author(s) have been asserted. All rights to the book as a whole are reserved by INTECH. The book as a whole (compilation) cannot be reproduced, distributed or used for commercial or non-commercial purposes without INTECH’s written permission. Enquiries concerning the use of the book should be directed to INTECH rights and permissions department (permissions@intechopen.com). Violations are liable to prosecution under the governing Copyright Law. 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The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. First published in Croatia, 2015 by INTECH d.o.o. eBook (PDF) Published by IN TECH d.o.o. Place and year of publication of eBook (PDF): Rijeka, 2019. IntechOpen is the global imprint of IN TECH d.o.o. Printed in Croatia Legal deposit, Croatia: National and University Library in Zagreb Additional hard and PDF copies can be obtained from orders@intechopen.com Surface Energy Edited by Mahmood Aliofkhazraei p. cm. ISBN 978-953-51-2216-6 eBook (PDF) ISBN 978-953-51-6646-7 Selection of our books indexed in the Book Citation Index in Web of Science™ Core Collection (BKCI) Interested in publishing with us? Contact book.department@intechopen.com Numbers displayed above are based on latest data collected. For more information visit www.intechopen.com 3,800+ Open access books available 151 Countries delivered to 12.2% Contributors from top 500 universities Our authors are among the Top 1% most cited scientists 116,000+ International authors and editors 120M+ Downloads We are IntechOpen, the world’s leading publisher of Open Access books Built by scientists, for scientists Meet the editor Dr. Mahmood Aliofkhazraei works in the Corrosion and Surface Engineering Group at the Tarbiat Modares University, Iran. He is the head of Aliofkhazraei research group (www.aliofkhazraei.com). Dr. Aliofkhazraei has received several honors, including the Khwarizmi award and the best young nanotechnologist award of Iran. He is a member of the National Association of Surface Sciences, Iranian Corrosion Association, and National Elite Foundation of Iran. His research focuses on materials science, nanotechnology and its use in surface and corrosion science. Contents Preface XI Section 1 Interfaces 1 Chapter 1 Re-derivation of Young’s Equation, Wenzel Equation, and Cassie-Baxter Equation Based on Energy Minimization 3 Kwangseok Seo, Minyoung Kim and Do Hyun Kim Chapter 2 Capillary Bridges — A Tool for Three-Phase Contact Investigation 23 Boryan P. Radoev, Plamen V. Petkov and Ivan T. Ivanov Chapter 3 Solid-Liquid-Solid Interfaces 55 Jeffrey L. Streator Section 2 Surface Properties 83 Chapter 4 Adhesive Properties of Metals and Metal Alloys 85 Anna Rudawska Chapter 5 Plasma Processing for Tailoring the Surface Properties of Polymers 123 Hisham M. Abourayana and Denis P. Dowling Chapter 6 DFT Investigations on the CVD Growth of Graphene 153 Meicheng Li, Yingfeng Li and Joseph Michel Mbengue Chapter 7 Modern Methods (Without Determining the Contact Angle and Surface Tension) for Estimating the Surface Properties of Materials (Using Video and Computer Technology) 179 A.O. Titov, I.I. Titova, M.O. Titov and O.P. Titov Chapter 8 A General-Purpose Multiphase/Multispecies Model to Predict the Spread, Percutaneous Hazard, and Contact Dynamics for Nonporous and Porous Substrates and Membranes 205 Navaz Homayun, Zand Ali, Gat Amir and Atkinson Theresa Section 3 Surfaces 263 Chapter 9 Micro/Nano Hierarchical Super-Lyophobic Surfaces Against Gallium-Based Liquid Metal Alloy 265 Daeyoung Kim and Jeong-Bong Lee Chapter 10 Effect of Certain Ethylene Oxide Heterogeneous Heterobifunctional Acyclic Oligomers (HEHAO) on Wetting 289 Calin Jianu Chapter 11 Recent Advances in the Methods for Designing Superhydrophobic Surfaces 311 Harinarayanan Puliyalil, Gregor Filipič and Uroš Cvelbar Chapter 12 Lipid Self-Spreading on Solid Substrates 337 Irep Gözen, Paul Dommersnes and Aldo Jesorka X Contents Preface The words “hydro”, “phobic” and “philic” are derived from Greek and they mean water, fear and adoration respectively. These words are being used to define the interaction of wa‐ ter and other materials. As an example, these words are being used in classification of liq‐ uids and solids based on their solubility in water, as well as classification on the solid surfaces regarding to their wettability. A lot of surfaces in the nature have Superhydropho‐ bic and self-cleaning properties. For example the wings of a butterfly, leaves of some plants, including cabbage and Indian Cress, have the mentioned properties. The best example is the LOTUS leaf. The electron microscope pictures of the lotus leaf show some protrusion parts which have a 20-40 μm distance from each other and are being covered with a rough surface with a waxy structure. A numerous studies confirm that this coarsened structure is a combination of mi‐ cro and Nano meter scale which have a low surface energy; and this combination causes a contact angle higher than 150° and a low slide angle and self-cleaning effect. Surfaces with such properties are called “Superhydrophobic”. Some natural examples don’t show this two scaled structure and there are some questions about the necessity of this two scaled struc‐ ture, which are going to be discussed in section 2 from the wettability point of view. Before 1996, there were a few attentions to the superhydrophobic surfaces which were based on the connection of the static contact angle of the water and the geometry of the rough surface. In 1997 two German botanist, Neinhuis and Barthlott, using SEM discovered the two scaled structure of the lotus leaf and investigated its chemical composition. That study was a revo‐ lution, which revealed two important guidelines for researchers who study on superhydro‐ phobic surfaces. First one is the roughening of the surface of materials with low surface energy and the second one is modification and creation of the rough surfaces using low sur‐ face energy materials. So the unusual surface wettability in the nature can be created by con‐ trolling the microstructure of the geometry of the surface and low surface energy. After that discovery (by German scientists) a lot of research and review articles related to the superhy‐ drophobic surfaces were published, explaining the applications of the superhydrophobic surface in the day life. These applications include self-cleaning windscreen of the car, optical equipment, windowpanes ,and anti fog and anti corrosion coatings. This book collects new developments in the science of surface energy. I like to express my gratitude to all of the contributors for their high quality manuscripts. I hope open access format of this book will help all researchers and that they will benefit from this collection. Dr. Mahmood Aliofkhazraei Tarbiat Modares University Iran www.aliofkhazraei.com Section 1 Interfaces Chapter 1 Re-derivation of Young’s Equation, Wenzel Equation, and Cassie-Baxter Equation Based on Energy Minimization Kwangseok Seo, Minyoung Kim and Do Hyun Kim Additional information is available at the end of the chapter http://dx.doi.org/10.5772/61066 Abstract Recently, Young’s equation, the Wenzel equation, and the Cassie-Baxter equation have been widely used with active research on superhydrophobic surfaces. However, experiments showed that the Wenzel equation and the Cassie-Baxter equation were not derived correctly. They should be reviewed on a firm physical ground. In this study, these equations are re-derived from a thermodynamic point of view by em‐ ploying energy minimization and variational approach. The derivations provide a deeper understanding of these equations and the behavior of a contact angle. Also, in applying these equations, the limitations and considerations are discussed. It is ex‐ pected that this study will provide a theoretical basis for the careful use of these equa‐ tions on rough or chemically heterogeneous surfaces. Keywords: Young’s equation, Wenzel equation, Cassie-Baxter equation, contact angle, energy minimization, variational method 1. Introduction The easiest way to determine the wetting property is to drop a liquid drop on the surface. The drop on the surface forms a unique contact angle depending on the wetting property. By measuring the contact angle, it is easy to examine the surface wettability. Young’s equation on the ideal surface, the Wenzel equation on the surface with roughness, and the Cassie-Baxter equation on the surface with chemical heterogeneity have been widely used for the analysis of the contact angle. Although these equations were not derived correctly, they have been used without consideration of the limitations. Application of these equations to surfaces such as a © 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. surface with large contact angle hysteresis that do not meet the conditions for these equations can give errors inherently. In this chapter, Young’s equation, the Wenzel equation, and the Cassie-Baxter equation will be re-derived by energy minimization and variational approach. From analyses of the derivations, properties of a contact angle will be reviewed. Also, the limitations and the considerations will be discussed in applying these equations to various surfaces. We expect that this study will help in the understanding of the nature of the contact angle and its application. 1.1. Young’s equation, Wenzel equation, and Cassie-Baxter equation It is possible to quantify the wettability of a surface by simply measuring the contact angle of a drop resting on a surface. Young’s equation has been used as a basic model. Application of this equation is limited to an ideal surface that is rigid, perfectly flat, insoluble, non-reactive, and chemically homogenous. The surface is assumed to have no contact angle hysteresis. On the surface, a contact angle of liquid drop can be described by the following Young's equation: g g q g + = cos sl so (1) where γ , γ sl , and γ so are liquid/gas surface tension, solid/liquid interfacial energy, and solid/gas surface energy, respectively. The apparent contact angle ( θ ) is an equilibrium contact angle ( θ Y ) . However, since all the real surfaces are not ideal, models were developed to describe the contact angles on the real surfaces. There are two models to describe the contact angle on a real surface, i.e. the Wenzel model and the Cassie-Baxter model. Contrary to the ideal surface, the real surface can have chemical heterogeneity and surface roughness. The Wenzel model considers the rough surface but with chemical homogeneity [1]. The Cassie-Baxter model considers the flat surface but with chemical heterogeneity [2]. In the Wenzel model, the surface roughness r is defined as the ratio of the actual area to the projected area of the surface. The Wenzel equation can be written as: q q = * cos cos Y r (2) where θ * is the apparent contact angle and θ Y is the equilibrium contact angle from Young’s equation on an ideal solid without roughness. In the Cassie-Baxter model, f 1 and f 2 are the area fractions of solid and air under a drop on the substrate. The Cassie-Baxter equation can be written as: q q = - * 1 2 cos cos Y f f (3) Surface Energy 4 where θ * is the apparent contact angle and θ Y is the equilibrium contact angles on the solid. From the Wenzel model, it can be deduced that the surface roughness amplifies the wettability of the original surface. Hydrophilic surface becomes more hydrophilic and hydrophobic surface more hydrophobic. In the Cassie-Baxter model, the area fractions under the drop is important in that the larger the area fraction of air, the higher the contact angle. Although these two models were proposed half a century ago, these equations have been widely used recently with active research on superhydrophobic surface [3-6]. 1.2. The fallacy of the Wenzel model and the Cassie-Baxter model In the Wenzel model and the Cassie-Baxter model, the contact angles were obtained from the non-smooth or chemically heterogeneous state of the surface under the drop. However, Gao and McCarthy demonstrated the fallacy of these models experimentally [7]. They prepared a surface with a hydrophilic spot on a hydrophobic surface, as shown in Fig. 1a. Fig. 1b shows a smooth hydrophobic surface with a superhydrophobic spot. D and d are mean diameters of the drop and the spot. With various diameters of the drops and the spots, advancing and receding contact angles were measured. They proved that the state of internal surface inside the triple line does not affect the contact angles experimentally and the contact angles are determined only by the state of the surface at triple contact line. It means that the previous Wenzel model and Cassie-Baxter model should be revised for rigid physical meaning [7]. Since then, an active discussion on them has been made [8-12]. Also, these models have been derived in a more rigorous way. We have summarized the derivations of these models studied to date in Table 1. All the derivations verify that a contact angle is determined at the triple line regardless of the external fields. Experiments also confirmed these findings [13-15]. Here, we will introduce the derivations by energy minimization using simple mathematics or calculus of variations. Figure 1. Depictions of (a) a hydrophilic spot on a hydrophobic surface and (b) a superhydrophobic spot on a smooth hydrophobic surface. Reprinted with permission from reference [7]. Copyright (2007) American Chemical Society. Re-derivation of Young’s Equation, Wenzel Equation, and Cassie-Baxter Equation Based on Energy Minimization http://dx.doi.org/10.5772/61066 5 Derivation method External field Region to determine a contact angle Reference Homogenization approach N/A At triple line Xu and Wang, 2010 [16] Fundamental calculus N/A At triple line Seo et al ., 2013 [17] Fundamental calculus N/A At triple line Whyman et al , 2008 [18] Variational approach Gravity At triple line Bormashenko, 2009 [19] Variational approach Electric field At triple line Bormashenko, 2012 [20] Table 1. Derivations for the Wenzel model and the Cassie-Baxter model. 2. Derivation with simple mathematics For the derivation of Young’s equation in a rigorous way, the following assumptions will be used. First, the surface is ideal and it has no contact angle hysteresis. Thus, the contact line can freely move around. Second, the drop is in zero gravity and the shape of the drop is always a section of sphere, i.e., spherical cap. As shown in Fig. 2, when the shape of the drop is deformed by spreading or contracting, the solid/liquid interfacial area varies with a contact angle that is a one-to-one function of the interfacial area. By the free movement of the contact line on an ideal surface, the drop can change freely its shape in order to satisfy the minimum energy state of the system. When the drop is at the equilibrium state, there will be no residual force at the contact line. At this point, the contact line and the shape of the drop will be fixed. Figure 2. Formation of the contact angle of a drop on an ideal surface. Reprinted with permission from reference [17]. Copyright (2013) Springer-Verlag. 2.1. Derivation of Young’s equation With a thermodynamic approach, Young’s equation can be derived with simple mathematics. Fig. 3 shows a drop on an ideal surface. The volume of the spherical cap is V = π h 6 (3r 2 + h 2) or Surface Energy 6 V = π R 3 3 (1 − cos θ ) 2 (2 + cos θ ) . The surface area of the cap is A = 2 π R h or A = 2 π R 2 (1 − cos θ ) . The total energy of the system can be written as ( ) ( ) ( ) p g g p g p q g g p q g = - + × = - + - 2 2 2 2 ( sin ) 2 1 cos sl so sl so E r Rh R R (4) Figure 3. Cross-section of the drop on an ideal surface. Reprinted with permission from reference [17]. Copyright (2013) Springer-Verlag. The variation of the energy is written as ( ) ( ) ( ) ( ) p g g q q q q g q q q é ù = × - × + + × - + ë û 2 2 sin sin cos 2 1 cos sin sl so dE R dR R d dR R d (5) The variation of the energy is equal to zero at the equilibrium state ( dE = 0). Dividing both sides by dR is written as ( ) ( ) q q p g g q q q g q q é ù æ ö æ ö = × - × + + × - + = ê ú ç ÷ ç ÷ è ø è ø ë û 2 2 sin sin cos 2 1 cos sin 0 sl so dE d d R R R dR dR dR (6) dE dR = 0 means that there is no energy variation by an infinitesimal change of the shape of the drop. At this point, the shape of the drop satisfies the minimum energy state. Here, in order to induce d θ dR , the constant-volume condition of the drop is used ( dV = 0). The volume of the drop is given by ( ) ( ) p q q = - + 3 2 1 cos 2 cos 3 R V (7) d θ dR can be obtained from the condition of the constant volume. Re-derivation of Young’s Equation, Wenzel Equation, and Cassie-Baxter Equation Based on Energy Minimization http://dx.doi.org/10.5772/61066 7 ( )( ) ( ) q q q q q - + = - + 1 cos 2 cos sin 1 cos d dR R (8) Substituting Eq. (8) into Eq. (6) gives ( ) ( )( ) ( ) ( ) ( )( ) ( ) q q g g q q q q q g q q æ ö æ ö - + ç ÷ - × + - ç ÷ ç ÷ ç ÷ + è ø è ø æ ö - + + × - - = ç ÷ ç ÷ + è ø 2 1 cos 2 cos sin cos 1 cos 1 cos 2 cos 2 1 cos 0 1 cos sl so (9) Rearranging the above equation gives rise to the Young's equation. g g q g + = cos sl so (10) 2.2. Derivation of the Wenzel equation Fig. 4 shows a drop in the Wenzel state. The radius of the drop is a . The radius of the smooth region of the substrate under the drop is b . When b is equal to zero, the substrate becomes a uniform rough surface. The contact line of the drop is assumed to be located on the rough region of the substrate. Figure 4. Schematic of the drop in the Wenzel state. The radius of the drop is a . The smooth region is b . Reprinted with permission from reference [17]. Copyright (2013) Springer-Verlag. From the figure, the total energy of the system can be written as ( ) ( )( ) p g g p g g g = - + - - + 2 2 2 sl so sl so s E b K a b A (11) K is the surface roughness factor. A s is the gas/liquid interfacial area. The variation of the energy is written as ( ) ( )( ) p g g p g g g é ù ù é ù é = - + - - + û ë û ë ë û 2 2 2 d sl so sl so s dE b d K a b d A (12) Surface Energy 8