NEMATIC VIRIAL-COEFFICIENTS OF VERY LONG HARD MOLECULES AND ONSAGER THEORY

The virial coefficients B-2-B-5 of a fluid of hard molecules interacti ng via a hard Gaussian overlap potential have been obtained by Monte C arlo integration. Molecular elongations re ranging from 1 to 10(5) are considered. Virial coefficients are computed as a function of the nem atic order parameter S, using a simple representation for the orientat ional distribution function. The calculations cover the entire order p arameter 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 v irial coefficients in the case S = 0 are seen to vanish in the limit o f infinitely long molecules (k --> infinity), though the asymptotic re gime sets in rather slowly. Similar asymptotic behaviour is observed e ven for relatively high values of S, which implies that, for the Value s where the transition to the nematic is expected to occur and well wi thin the nematic range, the covergence properties of the virial expans ion must be rather insensitive to the nematic order parameter. This re sult may indicate that Onsager theory for the isotropic-nematic transi tion, a virial expansion truncated at second order, is exact in the li mit k --> infinity.