Double layer relaxation in liquid electrolytes. Part 1.—Theory of the space charge polarization

Abstract

The linearized transport theory of space charge polarization in alternating fields is applied to relaxation of the diffuse double layer in melts and solutions of the salt M^µ+_aX^ν–_µa/ν. The method reveals factors which limit the validity of empirical a.c. network analogues of the layer. In the approximation to which the calculation is taken, there is a single relaxation time which depends on the cell length and the permittivity and transport coefficients of the electrolyte. Formation of the layer causes d.c. polarization in conductivity cells. Its relaxation with frequency is illustrated by the dispersion curves for conductance and capacitance in a parallel network. The series capacitance, to which the parallel capacitance reduces at low frequencies, depends on the ratios of the transport coefficients and contains separate contributions from each ion. It is converted to the low-potential limit of the Gouy capacitance by substitution of the Nernst-Einstein relations. The relaxation time is numerically equal to the product of the series resistance and the series capacitance and does not resolve into separate ionic contributions. The origin and significance of these results is discussed.