Fluids of hard convex molecules Ⅲ. The third virial coefficient

摘要

The method of 2-point measures of molecular geometry is applied to the calculation of the third virial coefficients of fluids of hard convex molecules. For multicomponent fluids, existing semiempirical (SE) theories propose an expression in terms of the 1-point measures volume V(i), surface S(i), and integral mean curvature M(i) of the components i = A, B, C. The method of 2-point measures does not introduce these quantities explicitly. In the limit of C either much smaller or much larger than A and B, an expansion in the ratio of dimensions is obtained, in which the leading terms are expressible in terms of the V(i), S(i), and M(i). For C small, the three leading terms are of this form; the first two agree with the SE equations. For C large, only the leading order is expressible in terms of the 1-point measures; it agrees with the SE equations. The third virial coefficient is calculated numerically for prolate and oblate spheroids using the method of 2-point measures. The infinite set of measures is truncated at the lowest possible level required to yield exact results for hard spheres: all measures involving the curvature asymmetry are neglected. Results are compared with existing exact values obtained by Monte Carlo integration, and with the predictions of the SE theories.