Calculation of direct correlation function for hard particles using a virial expansion

Abstract

We have calculated the direct correlation function, c(1, 2), via a high-order virial expansion, for systems of hard spheres and spheroids, in both the isotropic and nematic phases. For hard spheres, we find that truncation at sixth order in density gives good agreement with simulation data. Close to freezing, the virial series still appears to converge to the simulation results, but there are significant discrepancies, particularly at very small separations. In the non-overlap region, the virial theory begins to capture the features found from simulation. We also calculate the pair distribution function, g(1, 2), from our estimates of c(1, 2), and find good agreement with simulation data at all densities up to freezing. For hard, prolate spheroids of aspect ratio 3 : 1, we calculate c(1, 2) and g(1, 2) in the isotropic phase, again finding good agreement with simulation data at moderate densities. Finally, we present the result of our calculations on c(1, 2) for 3 : 1 spheroids in the nematic phase.

Keywords:

• Monte Carlo
• virial expansion
• liquid structure
• direct correlation function

Acknowledgements

The authors gratefully acknowledge the UK EPSRC for providing funding for MD and DC, the University of Manchester and the University of Warwick for computer time, and Marcus Bannerman for supplying simulation g(1, 2) functions. Computing facilities were provided by the Warwick University Centre for Scientific Computing.