Percus-Yevick approximation for fluids with spontaneous partial order: Results for a separable model.

Abstract

Recently we have applied the Percus-Yevick approximation to nematic fluids with partial spontaneous order using a diagrammatic implementation of a Ward identity. In this paper we apply the method to study the isotropic-nematic phase transition of a separable model, where the interparticle potential independently depends on the spatial separation and the relative orientation of the particles. This approach allows us to study the transition directly without other approximations besides the Percus-Yevick closure itself. Previous works of the integral equation method on phase transitions were based on the stability criterion or coexistence condition derived from a truncated density functional expansion. By calculating the correlation functions of the isotropic phase and applying the stability criterion, we find that within the Percus-Yevick approximation there are no numerical solutions indicating an isotropic-nematic phase transition, in agreement with the work by Perera and co-workers [Mol. Phys. 60, 77 (1987); J. Chem. Phys. 89, 6941 (1988)]. With this approach, however, we can determine the orientationally dependent probability density \ensuremath{\rho} self-consistently and we find the orientationally partially ordered nematic phase within the Percus-Yevick approximation. With a general qualitative analysis, we show that the stability limit within the Percus-Yevick approximation is highly unstable numerically, which may explain why no numerical solutions reaching the stability limit have been found in previous works for either isotropic-nematic or nematic-smectic phase transitions. We also show analytically that the stability criterion can be derived from the Ward identity. \textcopyright{} 1996 The American Physical Society.