Charge and electrical potential distributions in a nonequilibrium inhomogeneous electrolyte solution. A statistical mechanical approach I. Single binary electrolyte. Theory

A molecular theory of the liquid junction between two different solutions of the same single binary electrolyte is derived from the statistical mechanical theory of linear response to thermal perturbations. The new theory employs a certain salt representation of the electrolyte solution that involves the transport numbers of the ion constituents. In this representation the solution is formally treated as a binary mixture of nonelectrolytes. The theory leads to expressions for the profiles (distributions through the junction) of charge, electrical potential, and number densities of the ion constituents in terms of the transport numbers and static equilibrium correlation functions formulated at the Born-Oppenheimer level. The implications of the new theory for the liquid junction potential (LJP) at this level remain to be developed. A simple approximation reduces the calculation of these profiles to the McMillan-Mayer level where only the ion-ion equilibrium correlation functions are required. The LJP derived at this level depends on the specific interactions between ions through the short-range part of the ion-ion direct correlation functions. If these interactions are absent (point ions) or if their effect mutually cancels (as in the restricted primitive model) we recover the LJP of classical electrochemistry, a result that is not trivially derived from a molecular theory. Calculations are presented to illustrate the predictions of the theory concerning the charge profile.