Superhydrophobicity is the tendency of a surface to repel water drops. A surface is qualified as a superhydrophobic surface only if the surface possesses a high apparent contact angle (>150°), low contact angle hysteresis (<10°), low sliding angle (<5°) and high stability of Cassie model state. Efforts have been made to mimic the superhydrophobicity found in nature (for example, lotus leaf), so that artificial superhydrophobic surfaces could be prepared for a variety of applications. Due to their versatile use in many applications, such as water-resistant surfaces, antifogging surfaces, anti-icing surfaces, anticorrosion surfaces etc., many methods have been developed to fabricate them. In this article, the fundamental principles of superhydrophobicity, some of the recent works in the preparation of superhydrophobic surfaces, their potential applications, and the challenges confronted in their new applications are reviewed and discussed.

Superhydrophobic surfaces: a review on fundamentals, applications, and challenges

Preface.List of Contributors.1 Introductory Remarks (Jurn W.P. Schmelzer).References.2 Solid-Liquid and Liquid-Vapor Phase Transitions: Similarities and Differences (Vladimir P. Skripov and Mars Z. Faizullin).2.1 Introduction.2.2 Behavior of the Internal Pressure.2.3 The Boundaries of Stability of a Liquid.2.4 The Surface Energy of the Interfacial Boundary.2.5 Viscosity of a Liquid along the Curves of Equilibrium with Crystalline and Vapor Phases.2.6 Conclusions.References.3 A New Method of Determination of the Coefficients of Emission in Nucleation Theory (Vitali V. Slezov, Jurn W. P. Schmelzer, and Alexander S. Abyzov).3.1 Introduction.3.2 Basic Kinetic Equations.3.3 Ratio of the Coefficients of Absorption and Emission of Particles.3.4 Generalization to Multicomponent Systems.3.5 Generalization to Arbitrary Boundary Conditions.3.6 Initial Conditions for the Cluster Size Distribution Function.3.7 Description of Cluster Ensemble Evolution Along a Given Trajectory.3.8 Conclusions.References.4 Nucleation and Crystallization Kinetics in Silicate Glasses: Theory and Experiment (Vladimir M. Fokin, Nikolay S. Yuritsyn, and Edgar D. Zanotto).4.1 Introduction.4.2 Basic Assumptions and Equations of Classical Nucleation Theory (CNT).4.3 Experimental Methods to Estimate Nucleation Rates.4.4 Interpretation of Experimental Results by Classical Nucleation Theory.4.5 Nucleation Rate Data and CNT: Some Serious Problems.4.6 Crystal Nucleation on Glass Surfaces.4.7 Concluding Remarks.References.5 Boiling-Up Kinetics of Solutions of Cryogenic Liquids (Vladimir G. Baidakov).5.1 Introduction.5.2 Nucleation Kinetics.5.3 Nucleation Thermodynamics.5.4 Experiment.5.5 Comparison between Theory and Experiment.5.6 Conclusions.References.6 Correlated Nucleation and Self-Organized Kinetics of Ferroelectric Domains (Vladimir Ya. Shur).6.1 Introduction.6.2 Domain Structure Evolution during Polarization Reversal.6.3 General Considerations.6.4 Materials and Experimental Conditions.6.5 Slow Classical Domain Growth.6.6 Growth of Isolated Domains.6.7 Loss of Domain Wall Shape Stability.6.8 Fast Domain Growth.6.9 Super fast Domain Growth.6.10 Domain Engineering.6.11 Conclusions.References.7 Nucleation and Growth Kinetics of Nanofilms (Sergey A. Kukushkin and Andrey V. Osipov).7.1 Introduction.7.2 Thermodynamics of Adsorbed Layers.7.3 Growth Modes of Nanofilms.7.4 Nucleation of Relaxed Nanoislands on a Substrate.7.5 Formation and Growth of Space-Separated Nanoislands.7.6 Kinetics of Nanofilm Condensation.7.7 Coarsening of Nanofilms.7.8 Nucleation and Growth of GaN Nanofilms.7.9 Nucleation of Coherent Nanoislands.7.10 Conclusions.References.8 Diamonds by Transport Reactions with Vitreous Carbon and from the Plasma Torch: New and Old Methods of Metastable Diamond Synthesis and Growth (Ivan Gutzow, Snejana Todorova, Lyubomir Kostadinov, Emil Stoyanov, Victoria Guencheva, Gunther Volksch, Helga Dunken, and Christian Russel).8.1 Introduction.8.2 Some History.8.3 Basic Theoretical and Empirical Considerations.8.4 Experimental Part.8.5 Conclusions.References.9 Nucleation in Micellization Processes (Alexander K. Shchekin, Fedor M. Kuni, Alexander P. Grinin, and Anatoly I. Rusanov).9.1 Introduction.9.2 General Aspects of Micellization: the Law of Mass Action and the Work of Aggregation.9.3 General Kinetic Equation of Molecular Aggregation: Irreversible Behavior in Micellar Solutions.9.4 Thermodynamic Characteristics of Micellization Kinetics in the Near-Critical and Micellar Regions of Aggregate Sizes.9.5 Kinetic Equation of Aggregation in the Near-Critical and Micellar Regions of Aggregate Sizes.9.6 Direct and Reverse Fluxes of Molecular Aggregates over the Activation Barrier of Micellization.9.7 Times of Establishment of Quasiequilibrium Concentrations.9.8 Time of Fast Relaxation in Surfactant Solutions.9.9 Time of Slow Relaxationin Surfactant Solutions.9.10 Time of Approach of the Final Micellization Stage.9.11 The Hierarchy of Micellization Times.9.12 Chemical Potential of a Surfactant Monomer in a Micelle and the Aggregation Work in the Droplet Model of Spherical Micelles.9.13 Critical Micelle Concentration and Thermodynamic Characteristics of Micellization.References.10 Nucleation in a Concentration Gradient (Andriy M. Gusak).10.1 Introduction.10.2 Phase Competition under Unlimited Nucleation.10.3 Thermodynamics of Nucleation in Concentration Gradients: Case of Full Metastable Solubility.10.4 Thermodynamics of Nucleation at the Interface: The Case of Limited Metastable Solubility.10.5 Kinetics of Nucleation in a Concentration Gradient.References.11 Is Gibbs' Thermodynamic Theory of Heterogeneous Systems Really Perfect? (Jurn W. P. Schmelzer, Grey Sh. Boltachev, and Vladimir G. Baidakov).11.1 Introduction.11.2 Gibbs' Classical Approach.11.3 A Generalization of Gibbs' Thermodynamic Theory.11.4 Applications: Condensation and Boiling in One-Component Fluids.11.5 Discussion.11.6 Appendix.References.12 Summary and Outlook (Jurn W.P. Schmelzer).References.Index.

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Nucleation theory and applications

We analyze two representative systems containing a three-phase-contact line: a liquid lens at a fluid-fluid interface and a liquid drop in contact with a gas phase residing on a solid substrate. In addition we study a system containing a planar liquid-gas interface in contact with a solid substrate. We discuss to which extent the decomposition of the grand canonical free energy of such systems into volume, surface, and line contributions is unique in spite of the freedom one has in positioning the Gibbs dividing interfaces. Curvatures of interfaces are taken into account. In the case of a lens it is found that the line tension is independent of arbitrary choices of the Gibbs dividing interfaces. In the case of a drop, however, one arrives at two different possible definitions of the line tension. One of them corresponds seamlessly to that applicable to the lens. The line tension defined this way turns out to be independent of choices of the Gibbs dividing interfaces. In the case of the second definition, however, the line tension does depend on the choice of the Gibbs dividing interfaces. We also provide form invariant equations for the equilibrium contact angles which properly transform under notional shifts of dividing interfaces which change the description of the system but leave the density configurations unchanged. It is shown that in order to accomplish this form invariance, additional stiffness coefficients attributed to the contact line must be introduced. The choice of the dividing interfaces influences the actual values of the stiffness coefficients. We show how these coefficients transform as a function of the relative displacements of the dividing interfaces. Our formulation provides a clearly defined scheme to determine line properties from measured dependences of the contact angles on lens or drop volumes. This scheme implies relations different from the modified Neumann or Young equations, which currently are the basis for extracting line tensions from experimental data. These relations show that the experiments do not render the line tension alone but a combination of the line tension, the Tolman length, and the stiffness coefficients of the line. In contrast to previous approaches our scheme works consistently for any choice of the dividing interfaces. It further allows us to compare results obtained by different experimental or theoretical methods, based on different conventions of choosing the dividing interfaces.

Conceptual aspects of line tensions

Sessile liquid drops have a higher vapor pressure than planar liquid surfaces, as quantified by Kelvin's equation. In classical derivations of Young's equation, this fact is often not taken into account. For an open system, a sessile liquid drop is never in thermodynamic equilibrium and will eventually evaporate. Practically, for macroscopic drops the time of evaporation is so long that nonequilibrium effects are negligible. For microscopic drops evaporation cannot be neglected. When a liquid is confined to a closed system, real equilibrium can be established. Experiments on the evaporation of water drops confirm the calculations.

On the derivation of young's equation for sessile drops : Nonequilibrium effects due to evaporation

https://mds.marshall.edu/cgi/viewcontent.cgi?article=1060&context=physics_faculty

Line tension and its influence on droplets and particles at surfaces

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The line tension and the generalized Young equation: the choice of dividing surface

Using the chemical potential of a solid in a dissolved state or the corresponding component of the chemical potential tensor at equilibrium with the solution, a new concept of grand thermodynamic potential for solids has been suggested. This allows generalizing the definition of Gibbs' quantity $\sigma$ (surface work often called the solid-fluid interfacial free energy) at a planar surface as an excess grand thermodynamic potential per unit surface area that (1) does not depend on the dividing surface location and (2) is common for fluids and solids.

Grand potential in thermodynamics of solid bodies and surfaces

Using the chemical potential of a solid in a dissolved state or the corresponding component of the chemical potential tensor at equilibrium with the solution, a new concept of grand thermodynamic potential for solids has been suggested. This allows generalizing the definition of Gibbs’ quantity σ (surface work often called the solid-fluid interfacial free energy) at a planar surface as an excess grand thermodynamic potential per unit surface area that (1) does not depend on the dividing surface location and (2) is common for fluids and solids.

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Grand potential in thermodynamics of solid bodies and surfaces.

Dependence of the condensate chemical potential on droplet size in thermodynamics of heterogeneous nucleation within the gradient DFT

The gradient density functional theory and the Carnahan–Starling model formulated for describing the contribution of hard spheres have been used to calculate the profiles of condensate density in small critical droplets formed via homogeneous nucleation, as well as in stable and critical droplets formed via heterogeneous nucleation on solid charged and neutral condensation cores of molecular sizes. The calculations performed for water and argon at different values of condensate chemical potential have yielded the heights of the activation barriers for homoand heterogeneous nucleation as functions of vapor supersaturation at preset system temperatures. The interaction of condensate molecules with a solid core has been described by the resultant potential of molecular attractive forces. In the case of a charged core, the long-range Coulomb potential of electric forces has additionally been taken into account. Dielectric permittivities have been calculated as known functions of the local density of the fluid and temperature. The radius of the equimolecular droplet surface has been chosen as a variable describing the droplet size. Dependences of the chemical potential of condensate molecules in a droplet on its size have been plotted for water and argon with allowance for the action of capillary, electrostatic, and molecular forces. It has been shown that the role of the molecular force potential in heterogeneous nucleation increases with the size of condensation cores.

D. V. Tatyanenko

Papers

The line tension and the generalized Young equation: the choice of dividing surface

Grand potential in thermodynamics of solid bodies and surfaces

Grand potential in thermodynamics of solid bodies and surfaces.

Dependence of the condensate chemical potential on droplet size in thermodynamics of heterogeneous nucleation within the gradient DFT

Key thermodynamic characteristics of nucleation on charged and neutral cores of molecular sizes in terms of the gradient density functional theory