PERCUS-YEVICK APPROXIMATION FOR FLUIDS WITH SPONTANEOUS PARTIAL ORDER- RESULTS FOR A SEPARABLE MODEL

Recently we have applied the Percus-Yevick approximation to nematic fl uids with partial spontaneous order using a diagrammatic implementatio n of a Ward identity. In this paper we apply the method to study the i sotropic-nematic phase transition of a separable model, where the inte rparticle potential independently depends on the spatial separation an d the relative orientation of the particles. This approach allows us t o study the transition directly without other approximations besides t he Percus-Yevick closure itself. Previous works of the integral equati on method on phase transitions were based on the stability criterion o r coexistence condition derived from a truncated density functional ex pansion. By calculating the correlation functions of the isotropic pha se and applying the stability criterion, we find that within the Percu s-Yevick approximation there are no numerical solutions indicating an isotropic-nematic phase transition, in agreement with the work by Pere ra and co-workers [Mel. Phys. 60, 77 (1987); J. Chem. Phys. 89, 6941 ( 1988)]. With this approach, however, we can determine the orientationa lly dependent probability density rho self-consistently and we find th e orientationally partially ordered nematic phase within the Percus-Ye vick approximation. With a general qualitative analysis, we show that the stability limit within the Percus-Yevick approximation is highly u nstable numerically, which may explain why no numerical solutions reac hing the stability limit have been found in previous works for either isotropic-nematic or nematic-smectic phase transitions. We also show a nalytically that the stability criterion can be derived from the Ward identity.