Theory of dielectric constant of aqueous solutions

Abstract

We apply principles of statistical mechanics to derive simple expressions relating the hydrogen bond thermodynamic properties to the static dielectric constant of aqueous solutions. The approach followed by us was to develop an expression for the dipolar correlations between a centrally fixed molecule of a given type and its neighbors present in the surrounding shells, in terms of bonding probabilities, and combine the resulting expression with the Kirkwood–Frohlich equation. We considered only those neighboring molecules which are a part of the H-bonded cluster containing the central molecule. The bonding probabilities were evaluated by assuming a reaction equilibrium model, in which the formation of clusters between different association sites was represented by a series of chemical reactions. To demonstrate the utility of the theory, we provide comparison of the results for the temperature and composition variation of dielectric constant and H-bond stoichiometry of three model systems, methanol+water, ethanol+water, and acetone+water mixtures, against available experimental/simulation data.