Journal of Statistical Physics

, Volume 22, Issue 6, pp 709–742 | Cite as

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

  • Boris Barboy
  • William M. Gelbart


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 quantityy. Instead of\({{y_\alpha \equiv \rho _\alpha } \mathord{\left/ {\vphantom {{y_\alpha \equiv \rho _\alpha } {\left( {1 - \sum\nolimits_{\gamma = 1}^v {\upsilon _{0\gamma } \rho _\gamma } } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {1 - \sum\nolimits_{\gamma = 1}^v {\upsilon _{0\gamma } \rho _\gamma } } \right)}}\), whereΝ andρ γ are the particle volume and number density of theγth species in theΝ-component mixture, we define\({{y_\alpha \equiv \rho _\alpha } \mathord{\left/ {\vphantom {{y_\alpha \equiv \rho _\alpha } {\left( {1 - \sum\nolimits_{\gamma = 1}^v {\psi _\gamma ^\alpha \rho _\gamma } } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {1 - \sum\nolimits_{\gamma = 1}^v {\psi _\gamma ^\alpha \rho _\gamma } } \right)}}\), where theψ γ α are determined by optimizing the convergence of the series expressing thermodynamic functions in powers of the yα. This procedure provides in particular a good description of nonadditive binary mixtures of hard spheres withσ22 = 0 andσ12 = (1/2)σ11(1 +δ) (δ ≠ 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 topure fluids ofattracting hard spheres. Critical point properties of the pure fluid are determined via this equivalence, using oury-expansion description of the nonadditivemixture. Finally, we present the results ofy-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-nematic liquid crystal phase transition with those obtained earlier by virial expansions and Padé approximants. Finally, generalization to continuously allowed orientations is discussed.

Key words

y-Expansion hard-core particles nonadditive pair potential Widom-Rowlinson correspondence isotropic-nematic liquid crystal phase transition 


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Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • Boris Barboy
    • 1
  • William M. Gelbart
    • 1
    • 2
  1. 1.Department of ChemistryUniversity of CaliforniaLos Angeles
  2. 2.Camille and Henry Dreyfus Foundation Teacher-ScholarUSA

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