Nematic virial coefficients of very long hard molecules and Onsager theory

Abstract

The virial coefficients B 2-B 5 of a fluid of hard molecules interacting via a hard Gaussian overlap potential have been obtained by Monte Carlo integration. Molecular elongations Kranging from 1 to 105 are considered. Virial coefficients are computed as a function of the nematic order parameter S, using a simple representation for the orientational distribution function. The calculations cover the entire order parameter range and include the limiting cases S = 0 (randomly oriented molecules) and S = 1 (completely parallel molecular arrangements). In analogy with results from previous studies for spherocylinders, the virial coefficients in the case S = 0 are seen to vanish in the limit of infinitely long molecules (K → ∞), though the asymptotic regime sets in rather slowly. Similar asymptotic behaviour is observed even for relatively high values of S, which implies that, for the values where the transition to the nematic is expected to occur and well within the nematic range, the covergence properties of the virial expansion must be rather insensitive to the nematic order parameter. This result may indicate that Onsager theory for the isotropic-nematic transition, a virial expansion truncated at second order, is exact in the limit K → ∞.