The statistical thermodynamics of polydisperse systems of particles is investigated. A Gibbs–Duhem relation is obtained and the equilibrium conditions relevant to a two-phase system are derived. Systems of hard spheres, and hard spheres with Kac tails, are treated as illustrative examples with analytic results given in the context of scaled-particle (Percus–Yevick) theory as well as the polydisperse generalization of the thermodynamic approximation of Mansoori et al. An exact treatment of the analogous one-dimensional systems is also given. Quantitative results using a Schultz distribution of diameters are presented. A model of interpenetrable particles introduced previously by one of us—the permeable-sphere model—is also considered. Its thermodynamics and pair distribution functions are shown to be exactly obtainable in the context of the Percus–Yevick approximation. For this model, polydispersivity in both particle size and particle impenetrability is considered analytically. The pair potential for this model is discontinuous at the interparticle diameter; generalization of the model for which the pair potential is continuous is also introduced as a model of an effective polymer–polymer potential.

No abstract

The method described in the preceding paper [J. J. Salacuse, A. R. Denton, and P. A. Egelstatf, preceding paper, Phys. Rev. E 53, 2382(1996] for computing the static structure factor S (Q) of a bulk Quid is used to analyze molecular dynamics computer simulation data for a model krypton fluid whose atoms interact via a truncated Aziz pair potential. Simulations have been carried out for two system sizes of %=706 and 2048 particles and two thermodynamic states, described by a common reduced temperature T*= 1.51 and reduced densities p* =0.25 and 0.4. Results presented include the X-particle radial distribution function g~(r) and the bulk static structure factor S(Q). In addition we calculate the direct correlation function c (r) from the full S(Q). In comparison with corresponding predictions of the modified hypernetted chain theory, the results are generally in excellent agreement at all r and Q, to within random statistical errors in the simulation data.

The concept of a random system of particles is introduced and a probabilistic description of these types of systems is given. In addition the relationship of random systems to polydisperse systems is explored. The random systems approach to polydisperse systems is a particle as opposed to a continuum type theory and yields a number of results concerning the particle structure of polydisperse systems as well as a statistical mechanical description of polydisperse systems. As an illustration, the thermodynamic properties of a polydisperse system of hard rods are obtained from first principles. Phase equilibrium in polydisperse systems is considered in the context of the random systems approach. A set of equilibrium conditions are derived and shown to be equivalent to conditions previously given.

No abstract