## 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.

## Keywords

Hard Sphere Radial Distribution Function Intermolecular Potential Simple Fluid Virial Expansion## Preview

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## References

- Barker, J.A., and Henderson, D., 1967, Perturbation Theory and Equation of State for Fluid. II. A Successful Theory of Liquids, J. Chem. Phys., 47:4714.ADSCrossRefGoogle Scholar
- Barker, J.A., and Henderson, 1976, What is a “liquid”? Understanding the states of matter, Rev. Hod. Phys., 48:587.MathSciNetADSGoogle Scholar
- Carnahan, N.F. and Starling, K.E., 1969, Equation of state for nonattracting rigid spheres, J. Chem. Phys., 51:635.ADSCrossRefGoogle Scholar
- Carnahan, N.F. and Starling, K.E., 1970, Thermodynamic properties of a rigid-sphere fluid, J. Chem. Phys., 53:600.ADSCrossRefGoogle Scholar
- Gray, C.G. and Gubbins, K.E., 1984, “Theory of Molecular Liquids”, Clarendon Press, Cambridge.Google Scholar
- Hansen, J.P. and McDonald, I.R., 1986, “Theory of Simple Fluids”, Academic Press, New York.Google Scholar
- Hansen, J.P. and Verlet, L., 1969, Phase transitions of the Lennard-Jones system, Phys. Rev., 184:151.ADSCrossRefGoogle Scholar
- Helfand, E., 1961, Theory of the molecular friction constant, Phys. Fluids. 4:681.MathSciNetADSCrossRefGoogle Scholar
- Hill, T.L., 1956, “Statistical Mechanics”, McGraw-Hill, New York.MATHGoogle Scholar
- Levesque, D., 1966, Study of the Percus-Yevick, hypernetted chain, and Born-Green equations for classical fluids, Physica, 32:1985.Google Scholar
- Mandel, F., Bearman, F.J. and Bearman, M.Y., 1970, Numerical solutions of the Percus-Yevick equation for the Lennard-Jones (6–12) and hard-sphere potentials, J. Chem. Phys., 52:3315.ADSCrossRefGoogle Scholar
- McQuarrie, D.A., 1976, “Statistical Mechanics”, Harper and Row, New York.Google Scholar
- Robinson, R.A., and Stokes, R.H., 1965, “Electrolyte Solutions”, 2nd Ed., Butterworths, London.Google Scholar
- Thiele, E., 1963, Equation of state for hard spheres, J. Chem. Phys., 39:474.ADSCrossRefGoogle Scholar
- Throop, G.J., and Bearman, R.J., 1965, Numerical Solution of the Percus-Yevick Equation for the Hard-Sphere Potentials, J. Chem. Phys., 42:2408.Google Scholar
- Verlet, L. and Devesque, D., 1967, Theory of classical fluids, Physics, 36:254.Google Scholar
- Weeks, J.D., Chandler, D., and Andersen, H.C., 1971, Role of repulsive forces in determining the equilibrium structure of simple liquids, J. Chem. Phys., 54:5237.ADSCrossRefGoogle Scholar
- Werthein, M.S., 1963, Exact solution of the Percus-Yevick integral equation for hard spheres, Phys. Rev. Letters, 10:321.ADSCrossRefGoogle Scholar