Fluid structure around a rod-like molecule and the additivity rule of the partial molar quantities. 1. A hard needle in a hard disk fluid

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 two-dimensional system composed of hard disks of unit diameter and a hard needle of the thickness 0 (thin needle) or 1 (thick needle). The assumption that the additivity rule holds for the needle of arbitrary length (additivity rule in the strong sense (ARS)) gives the same equation of state for the hard disk fluid as the one derived from the scaled particle theory. The density expansion of the chemical potential shows that ARS does not strictly hold in the second order of density, and that the deviation from ARS is significant for the thin needle. The fluid structure around the needle at finite densities was studied by the Monte Carlo technique with the result that: (i) 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). (ii) The end structure shows little dependence on the needle length for a needle longer than 0.5, irrespective of the needle thickness. Especially, the distribution function along the extension line of the core of the needle is practically the same as the distribution function around the hard disk of the diameter equal to the thickness of the needle. (iii) Small oscillatory structure is developed in the trunk structure near the tip of the needle, which reflects the commensurate and incommensurate structure of solvent disks along the needle. ARS holds for the thick needle at each density studied within the statistical error, although ARS slightly underestimates the excess chemical potential of the thin needle. A useful expression for the packing efficiencies of the tip and the trunk part of the needle was derived using ARS for the thick needle.