The isotropic–nematic transition for the hard Gaussian overlap fluid: Testing the decoupling approximation

Abstract

The isotropic–nematic phase transition in a fluid of moderately long molecules 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 relevant range of molecular elongations in real nematic liquid crystals, are considered. The results of the theory (pressure, order parameter, and location of the phase transition) and of several of its extensions, are compared with those from computer simulation, and their relative accuracy assessed. We first study the standard decoupling approximation, a resummed Onsager virial expansion where only the (exact) second virial coefficient, B2, is retained, and consider two different mappings to perform the resummation: a fluid of equivalent hard spheres and the isotropic phase of the hard Gaussian overlap fluid. Whereas the former mapping predicts a phase transition already in qualitative agreement with simulation, the mapping to the isotropic phase predicts a transition in closer agreement with the simulation result, shifting the location of the transition to lower pressures. However, the transition is overestimated in both cases, which seems to indicate a poor representation of angular correlations. In order to incorporate higher-order correlations, an approximate method is proposed to evaluate the B3 and B4 virial coefficients in the nematic phase numerically. This new information allows us to address two points: (i) the convergence of the virial series for short molecules, and (ii) the performance of extended decoupling approximation theories, incorporating the third and the fourth virial coefficients. As expected, inclusion of the high-order virial coefficients improves the results of the corresponding truncated virial expansion for the largest elongation considered, and provides quantitative agreement with the simulations, indicating a fast convergence of the virial series. The standard decoupling approximation provides results of similar accuracy. Also, the extended decoupling approximation including B3 improves these results, though the extension to B4 degrades the coexistence data slightly, which might indicate that the latter misrepresents to some extent the importance of angular correlations. In contrast, for molecules with a length-to-breadth ratio of 3, the truncated virial expansion is still inaccurate, whereas the extended decoupling approximation theories perform better, providing almost quantitative agreement with the simulations. As a result of our findings, we conclude that in order to improve the standard decoupling approximation for fluids of short molecules, it is essential to resum the virial series using knowledge of the B3 virial coefficient and also the B4 coefficient for the shortest molecules forming nematic phases.