Dielectric relaxation of electrolyte solutions

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Abstract
The dielectric relaxation theory of electrolytesolutions is formulated in terms of solvent–solvent, ion–ion, and ion–solvent van Hove time correlation functions. General wave vector frequency‐dependent expressions are given for the longitudinal components of the relevant (i.e., polarization–polarization, current–current, current–polarization, polarization–current) time correlation functions and of the susceptibility, dielectric, and conductivity tensors. The Kerr theory relating the distinct and self parts of the van Hove functions is extended to mixtures of molecular fluids and solved explicitly in the k→0 limit for solutions of spherical ions (assuming that the self part of the van Hove functions is given by Fick’s law) immersed in polar solvents. At this level of theory, the van Hove functions, the time correlation functions and the susceptibilities are all found to depend upon coupled ion–solvent motion. However, the dynamical coupling terms are shown to cancel exactly in the final expressions for the conductivity and dielectric constant yielding relatively simple results. Specifically, the conductivity obtained is independent of frequency and is related to the self diffusion constants of the ions by the Nernst–Einstein expression. If a spherical diffusor model is chosen for the solvent, then the frequency‐dependent dielectric constant is given by a Debye‐type formula with a concentration dependent relationship connecting the Debye and self reorientational relaxation times of the solvent.These results are discussed in the context of previous theories and experimental observations. It is shown that, although obviously oversimplified, the present theory does qualitatively predict the correct concentration dependence of the observed relaxation times for a number of salt solutions.