Bond-number distribution of a solute molecule in the hard-sphere fluid

Abstract

The validity of the bond-number (coordination-number) distribution of a molecule in a fluid is studied for a solute molecule interacting with solvent molecules through a square-well potential. The bond number is defined as the number of solvent molecules in the square well. The effect of the strength of the solute-solvent interaction on the chemical potential of a solute molecule is expressed rigorously by a moment generating function of the bond-number distribution of a reference system in which the solute molecule behaves as a hard sphere. A cumulant expansion of the generating function gives an expansion of the chemical potential of the solute molecule around a reference value. The characteristics of the bond-number distribution, and the validity of the statistical mechanical relations are demonstrated for a hard-sphere solvent over a wide density region by Monte Carlo calculations. The average bond number of the reference system increases almost linearly with increasing density, although the variance ...