ABSTRACT
This chapter focuses on the technological and scientific importance of complex materials and interfaces and motivates the study of interface and surface properties. It considers an important application of the ideas to the problem of phase separation in binary mixtures. A study of the physics of single surfaces or interfaces begins with the characterization of the shape of the interface. The chapter reviews classical statistical mechanics, includes a description of fluctuations about equilibrium and of binary mixtures. Some worked examples are presented to illustrate the thermodynamics of the nearly ideal gas and the Gaussian probability distribution for fluctuations. A generalization of the harmonic oscillator to a system with many spatial degrees of freedom is called the Gaussian model. The chapter also considers the calculation of the thermal averages and fluctuations of various functions of the position and momenta. In a many-particle system, fluctuations of the density lead to scattering of radiation: light, neutrons, X-rays.
