Statistical Thermodynamics of Surfaces, Interfaces, and Membranes

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This text introduces several theoretical methods applicable to statistical mechanics in materials science. Each section begins with an introduction and concludes with problems and references. Topics covered include mixtures and interfaces, complex materials, and a review of classical statistical mechanics. The discussion extends to phase separation in binary mixtures and the differential geometry of surfaces. Key concepts include hydrodynamics, interfacial tension, and the free energy of surfaces and interfaces, along with surface-active agents and fluctuations of interfaces. The text addresses thermal fluctuations, capillary instabilities, and the roughening transition of solid surfaces. It also explores the wetting of interfaces, equilibrium states, long-range interactions, and the dynamics of wetting. Interactions of rigid interfaces are examined, focusing on molecular interactions, van der Waals forces, and electrostatic interactions. Flexible interfaces are discussed in relation to fluid membranes, curvature elasticity, and their fluctuations. Colloidal dispersions are analyzed, including interactions among particles and the DLVO theory. Finally, the text delves into self-absorbing interfaces, covering micelles, vesicles, microemulsions, and spongelike phases.