Statistical distributions in solutions

Statistical correlations are considered for molecules in a liquid perturbed by solute molecules. A new integrodifferential equation is derived for the conditional distribution functions. This describes the changes in the distribution functions in response to small displacements of the solute molecules, which produce the external perturbing field. An explicit solution is derived in the form of a functional series in exp (–u_s)–1, in which u_s is the potential energy in the interaction of the solute molecules with the particles of the medium. The coefficients in the series are dependent on the unperturbed distribution functions for the pure solvent. The solution is used to examine the decay of the perturbations produced by the solute molecules. For the case of strong solvation, the problem reduces to finding the distribution for the particles of a nearly ideal gas in the external field of a solute molecule. The distribution for a hard-spheres model is calculated in the first approximation with respect to the density of the medium. It is found that solute molecules larger than the particles of the medium stabilize the structure of the solvent, whereas ones smaller than the latter tend to break up the structure.I am indebted to F. M. Kuni for advice and assistance in this work.