Virial coefficients of hard, two-dimensional, convex particles up to the eighth order

Abstract

We calculated virial coefficients for hard ellipses, stadia, rectangles, planar lenses and rhombi up to the eighth order employing Mayer-sampling Monte Carlo simulations. We improved and extended available data for ellipses, stadia, and rectangles and provide virial coefficients for planar lenses and rhombi. The influence of the aspect ratio ν on the virial coefficients is discussed, including hard discs as the limit of ellipses, stadia, and planar lenses and hard squares as the limit of rectangles and rhombi with aspect ratio ν → 1 . In two dimensions, both in the limit ν → 0 and ν → ∞ , anisotropic figures approach hard needles. The dependence of reduced virial coefficients B ~ i = B i / B 2 i − 1 on the shape parameter α = B 2 ∗ − 1 , with B 2 ∗ = B 2 / V P and V P the particle area is analysed. The reduced virial coefficients B ~ i ( α ) are approximated as functions of the shape parameter employing third-order polynomials, enabling an interpolation for all aspect ratios ν.