The Structure of Simple Fluids

Abstract

In this chapter, we shall discuss the structure of simple fluids through the radial distribution function, which is the central quantity of most statistical mechanical theories of fluids (McQuarrie, 1976; Hansen and McDonald, 1986). Although all the equations and techniques presented here are applicable to polyatomic fluids (Gray and Gubbins, 1984), for simplicity we shall consider only simple fluids, that is, those that interact by way of a spherically-symmetric, angle-independent intermolecular potential. This chapter is meant to be tutorial in nature, and so in section IMPERFECT GASES, we review the virial expansion of imperfect gases and then in section DISTRIBUTION FUNCTIONS AND LIQUIDS, we introduce several of the types of distribution functions that are used to describe the structures of liquids. A central quantity of this section is the radial distribution function. In section THERMODYNAMIC PROPERTIES OF LIQUIDS, we express the thermodynamic properties of a fluid as functionals of the radial distribution function and in section INTEGRAL EQUATIONS FOR THE RADIAL DISTRIBUTION FUNCTION, we discuss several integral equations that give the radial distribution function in terms of the intermolecular potential. Three important quantities that are introduced in this section are the potential of mean force, the direct correlation function and the Ornstein-Zernike equation. Section SOME NUMERICAL RESULTS OF THE FLUID-THEORY INTEGRAL EQUATIONS consists of a brief comparison of the numerical results of the various integral equations to computer simulations for a fluid of hard spheres and a Lennard-Jones fluid.