Equation of state of hard disk and 2D convex bodies

Abstract

An improved two-dimensional (2D) equation of state is proposed on the basis of an expression from scaled particle theory. For pure hard disks, the virial coefficients B 3–B 18 are determined and compared with their pseudo-experimental values. The 2D compressibility factor, Z, of pure hard disks is evaluated from the improved equation of state (IEOS) and compared with Z from Henderson's relation and with simulation data. Similarly, the Z values of mixtures of hard disks with diameter ratios σ2/σ1 = 1, 2, 3, 4, 5 and 10 and mole fractions x 1 = 0.5 and 0.25 were compared with the corresponding simulation data. Fair agreement was found in the case of the pure fluid as well as the studied mixtures. The third and fourth virial coefficients of three types of convex figures—hard ellipses, hard spherocylinders and rectangles—were determined from the IEOS and fair agreement with pseudo-experiment was found. The predictive capability of the considered IEOS was investigated for 2D hard prolate spherocylinders and systems of hard ellipses with three values of the aspect ratio, k = a/b, k = 2, 4 and 6 (where a and b denote the semi-axes of an ellipse). The compressibility factor of the 2D spherocylinders compared well with the MC data; in the case of hard ellipses, the description is fair for the isotropic phase.