Dielectric dispersion and dielectric friction in electrolyte solutions. II

Abstract

Presented herein is a thorough investigation of the consequences of coupling ion migration to dielectric relaxation in the solvent. A self-consistent continuum model is developed from both local (stress tensor) and global (dissipation function) considerations. The friction coefficient of a moving ion is computed in terms of the dimensionless coupling parameter where e is the ion charge, η is the solvent viscosity, ε0 and ε∞ are the low and high frequency dielectric constants of the solvent, respectively, τD is the Debye dielectric relaxation time of the pure solvent, and R is the ionic radius. For small ions the computed frictional drag is practically independent of ion radius, provided some degree of hydrodynamic slip is allowed at the ion surface. The effect of ion migration on the dielectric relaxation time of the solution is analyzed in detail. It is shown that the Debye–Falkenhagen effect should lead to an increase in the observed relaxation time, while the kinetic ion–solvent coupling introduces one or more relaxation times, all less than the Debye time of the pure solvent.