Dielectric dispersion and dielectric friction in electrolyte solutions. I.

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  • J. Hubbard
    Center for Theoretical Studies, University of Miami, Coral Gables, Florida 33124
  • L. Onsager
    Center for Theoretical Studies, University of Miami, Coral Gables, Florida 33124

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<jats:p>A self-consistent, kinetic theory of ion–solvent interactions is developed within the framework of continuum mechanics. It is shown that the hydrodynamic coupling between viscous momentum transport and dielectric relaxation leads not only to a theory of ion mobility but also to a description of the dielectric properties of electrolyte solutions. The concept of kinetic polarization deficiency is introduced, whereby the static permittivity of a solution is reduced from that of the pure solvent by an amount proportional to the product of solvent dielectric relaxation time and low frequency conductivity of the solution. Furthermore, if the viscous and dielectric relaxation times are assumed to be comparable it is demonstrated that ’’deformation inertia’’ should make a significant contribution to the decrement Δε0. Ion mobility is calculated to first order in a coupling parameter which is inversely proportional to the fourth power of the ion radius, the limiting case of zero ion size is analyzed, and general aspects of ion migration are investigated with the aid of the principle of minimum dissipation. Given that the pure solvent has a dispersion characterized by a single Debye relaxation time τD, it is asserted that the solution will, as a consequence of dielectric friction, possess an infinite number of relaxation times extending from τD down to the longitudinal time τL=τD(ε∞/ε0).</jats:p>

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