Hard-particle fluids. II. Generaly-expansion-like descriptions

Abstract

We present a critical discussion of the "y-expansion" approach to the thermodynamics of hard-particle fluids. First we discuss briefly our original formulation for many-component mixtures of anisotropic species, using the usual virial series as a point of departure. Difficulties arising in the case of attractive tails and nonadditive hard-core interactions are exposed. To resolve these problems we suggest a straightforward generalization of the expansion quantity y. Instead of y~ =- p~/(1 - ~=i voyp~), where Voy and p~ are the particle volume and number density of the 7th species in the v-component mixture, we define ya =- p~/(1 ~ ~=~ ~y"p~), where the ~b~" are determined by optimizing the convergence of the series expressing thermodynamic functions in powers of the y~. This procedure provides in particular a good description of nonadditive binary mixtures of hard spheres with a~2 = 0 and a~2 = (1/2)~z~(1 + A) (A # 0, ~> -- 1 is the usual nonadditivity parameter.) We present a generalization of the analysis of Widom and Rowlinson whereby such systems are shown to be equivalent to pure fluids of attracting hard spheres. Critical point properties of the pure fluid are determined via this equivalence, using our y-expansion description of the nonadditive mixture. Finally, we present the results of y-expansion studies of some anisotropic (i.e., orientationally ordered) states of fluids composed of asymmetric hard particles. For the case of rectangular parallelepipeds whose allowed orientations are restricted, we can compare our description of the isotropic-nemati c liquid crystal phase transition with those obtained earlier by virial expansions and Pad6 approximants. Finally, generalization to continuously allowed orientations is discussed.