THE ISOTROPIC-NEMATIC TRANSITION FOR THE HARD GAUSSIAN OVERLAP FLUID - TESTING THE DECOUPLING APPROXIMATION

The isotropic-nematic phase transition in a fluid of moderately long m olecules interacting via a hard Gaussian overlap potential is studied using the decoupling approximation and computer simulation. Molecules of length-to-breadth ratios equal to 3 and 5, thought to set the relev ant range of molecular elongations in real nematic liquid crystals, ar e considered. The results of the theory (pressure, order parameter, an d location of the phase transition) and of several of its extensions, are compared with those from computer simulation, and their relative a ccuracy assessed. We first study the standard decoupling approximation , a resummed Onsager virial expansion where only the (exact) second vi rial coefficient, B-2, is retained, and consider two different mapping s to perform the resummation: a fluid of equivalent hard spheres and t he isotropic phase of the hard Gaussian overlap fluid. Whereas the for mer mapping predicts a phase transition already in qualitative agreeme nt with simulation, the mapping to the isotropic phase predicts a tran sition in closer agreement with the simulation result, shifting the lo cation of the transition to lower pressures. However, the transition i s overestimated in both cases, which seems to indicate a poor represen tation of angular correlations. In order to incorporate higher-order c orrelations, an approximate method is proposed to evaluate the B-3 and B-4 virial coefficients in the nematic phase numerically. This new in formation allows us to address two points: (i) the convergence of the virial series for short molecules, and (ii) the performance of extende d decoupling approximation theories, incorporating the third and the f ourth virial coefficients. As expected, inclusion of the high-order vi rial coefficients improves the results of the corresponding truncated virial expansion for the largest elongation considered, and provides q uantitative agreement with the simulations, indicating a fast converge nce of the virial series. The standard decoupling approximation provid es results of similar accuracy. Also, the extended decoupling approxim ation including B-3 improves these results, though the extension to B- 4 degrades the coexistence data slightly, which might indicate that th e latter misrepresents to some extent the importance of angular correl ations. In contrast, for molecules with a length-to-breadth ratio of 3 , the truncated virial expansion is still inaccurate, whereas the exte nded decoupling approximation theories perform better, providing almos t quantitative agreement with the simulations. As a result of our find ings, we conclude that in order to improve the standard decoupling app roximation for fluids of short molecules, it is essential to resum the virial series using knowledge of the B-3 virial coefficient and also the B-4 coefficient for the shortest molecules forming nematic phases. (C) 1997 American Institute of Physics.