A statistical mechanical theory of the self-diffusion coefficient of simple ions in electrolyte solutions

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Abstract
A statistical mechanical theory of the self‐diffusion coefficient of ions in solutions of simple electrolytes has been developed. Beginning with a generalized Langevin equation the self‐diffusion coefficients of ions may be evaluated at the zero‐frequency limit of the Laplace transform of the random force correlation function. We assume that the random force acting on the tagged ion may be separated into contributions from the solvent part, due to the surrounding solvent molecules and an ionic part due to all the other ions. Further, we assume that the evolution of the ionic random force is governed by the Smoluchowski operator. With these assumptions and using the Debye–Hückel pair correlation function, the Onsager limiting law may be derived. Numerical calculations using the HNC pair correlation function shows that our theory can describe experimental data of moderately concentrated solutions adequately.

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