New analytical and numerical results on virial coefficients for 2-D hard convex bodies

Abstract

We present new Monte Carlo calculations of the third and fourth virial coefficients for isotropic systems of different two-dimensional hard convex bodies: ellipses, rectangles and spherocylinders for various aspect ratios, and needles. Our results differ significantly from previously published values. The accuracy of our Monte Carlo method is tested by comparison with the exact value of B 3 for unaligned hard needles, which we have obtained analytically. Finally, the validity of some approximate equations of state is investigated.