Fluid structure around a rod-like molecule and the additivity rule of the partial molar quantities

Abstract

Fluid structure around a rod-like molecule and its relation to the additivity rule of the partial molar quantities have been studied for a system composed of hard spheres of unit diameter and a hard needle of thickness 0 (thin needle) or 1 (thick needle). The assumption that the additivity rule holds for a needle of arbitrary length (additivity rule in the strong sense (ARS)) leads to several useful expressions for a chemical potential and the fluid structure. The extended scaled particle theory (XSPT) proposed by Gibbons and Boublík is consistent with the ARS for a short needle, whereas the XSPT result becomes an unphysical one as the needle length increases. According to an analysis of the second-order term in the density expansion of the chemical potential, the ARS gives a reasonable value for a thick needle, while its deviation is significant for the thin needle. The fluid structure around a needle at high densities was studied by the Monte Carlo technique. The fluid structure around the trunk part of the needle (trunk structure) is more distinct than the structure around the tip of the needle (end structure). The end structure did not depend on the needle length for a needle longer than 0·2, irrespective of the needle thickness. Small oscillatory structure is developed in trunk structures near the tip of the needle. The ARS holds for the thick needle, whereas it does not work well for the thin needle. Although these characteristics of the three-dimensional system are the same as those of the two-dimensional system (needle in discs), (i) the trunk structure of the three-dimensional system depends on the needle thickness, and (ii) no needle length dependence of the oscillatory structure in the trunk structure was found.