Shape integrals for polar convex molecules

Abstract

The contributions of electrostatic forces to the second virial coefficient and thermodynamic functions of convex molecule fluids can be determined using the perturbation approach. Particular terms in the perturbation expansion are given by multi-fold integrals; these integrals can be expressed after factorization as a product of two parts–simple integrals in terms of variable distance and (at least) three-fold integrals in angular coordinates. The latter integrals (denoted as J integrals) characterize the effect of the shape of molecular cores on the electrostatic interactions. Within this paper, values of several J integrals were calculated for hard spherocylinders of different reduced lengths (or diameter) with six types of embedded electrostatic interactions: dipole–dipole, quadrupole–quadrupole, dipole–quadrupole, dipole–induced dipole, quadrupole–induced dipole and quadrupole–induced quadrupole. The different J integrals were determined as functions of shapes for (like and unlike) pairs of hard convex bodies and expressed in the form of rational functions. The theoretical predictions of the second virial coefficient are compared with the pseudo-experimental values determined in our laboratory; comparison indicates sufficiency of the suggested method to evaluate thermodynamic properties of polar compounds.