Statistical Thermodynamics Of Surfaces, Interfaces, And Membranes

Samuel Safran

• Publisher: CRC Press
• Year: 2018
• Print ISBN: 9780813340791
• eBook ISBN: 9780429976766
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

Understanding the structural and thermodynamic properties of surfaces, interfaces, and membranes is important for both fundamental and practical reasons. Important applications include coatings, dispersants, encapsulating agents, and biological materials. Soft materials, important in the development of new materials and the basis of many biological systems, cannot be designed using trial and error methods due to the multiplicity of components and parameters. While these systems can sometimes be analyzed in terms of microscopic mixtures, it is often conceptually simpler to regard them as dispersions and to focus on the properties of the internal interfaces found in these systems. The basic physics centers on the properties of quasi-two-dimensional systems embedded in the three-dimensional world, thus exhibiting phenomena that do not exist in bulk materials. This approach is the basis behind the theoretical presentation of Statistical Thermodynamics of Surfaces, Interfaces, and Membranes. The approach adapted allows one to treat the rich diversity of phenomena investigated in the field of soft matter physics (including both colloid/interface science as well as the materials and macromolecular aspects of biological physics) such as interfacial tension, the roughening transition, wetting, interactions between surfaces, membrane elasticity, and self-assembly. Presented as a set of lecture notes, this book is aimed at physicists, physical chemists, biological physicists, chemical engineers, and materials scientists who are interested in the statistical mechanics that underlie the macroscopic, thermodynamic properties of surfaces, interfaces, and membranes. This paperback edition contains all the material published in the original hard-cover edition as well as additional clarifications and explanations.

CHAPTER 1

Mixtures and Interfaces

1.1 INTRODUCTION

In this chapter, we begin with some remarks on the technological and scientific importance of complex materials and interfaces and motivate the study of interface and surface properties. We then review some of the physical and mathematical methods that are used in the subsequent discussions of interface and membrane statistical thermodynamics. Many of these topics are discussed more fully in the references and throughout this chapter. We begin with a review of classical statistical mechanics^1,2,3,4, including a description of fluctuations about equilibrium and of binary mixtures. The mathematical description⁵ of an interface is then presented (using only vector calculus) and the calculation of the area and curvature of an interface with an arbitrary shape is demonstrated. Finally, the chapter is concluded by a brief summary of hydrodynamics⁶.

Figure 1.1 Colloidal particles in solution stabilized by electrostatic repulsion due to surface charges (left) or by steric repulsion of grafted long-chain, polymeric molecules (right).

1.2 COMPLEX MATERIALS AND INTERFACES

Complex materials refer to either composite solids or to fluid dispersions where the individual molecular species are organized into structures with long (tens of Angstroms to microns) length scales (compared with atomic or simple molecular dimensions). These materials^7,8, which include^9,10 solid colloidal dispersions (see Fig. 1.1), polymers^11,12, and self-assembled amphiphiles^13,14,15 such as micelles, vesicles, and microemulsions are important technologically and as generic models for biological systems. Milk, blood, paint, soaps, and detergents are familiar examples where the properties of dispersion, encapsulation, and cleaning are utilized. While the study of single-component systems such as simple fluids or solids focuses on the behavior of the bulk, serious consideration of the multicomponent nature of complex fluids¹⁶ requires an understanding of the interfaces between materials. The unique properties of the dispersion are then often determined by the behavior of the interface. This often leads to considerable simplification in the study and understanding of the system, since instead of analyzing the behavior of a comple...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• Chapter 1 Mixtures and Interfaces
• Chapter 2 Interfacial Tension
• Chapter 3 Fluctuations of Interfaces
• Chapter 4 Wetting of Interfaces
• Chapter 5 Interactions of Rigid Interfaces
• Chapter 6 Flexible Interfaces
• Chapter 7 Colloidal Dispersions
• Chapter 8 Self-Assembling Interfaces
• Index