Theory of space-charge polarization for determining ionic constants of electrolytic solutions

A theoretical expression of the complex dielectric constant attributed to space-charge polarization has been derived under an electric field calculated using Poisson's equation considering the effects of bound charges on ions. The frequency dependence of the complex dielectric constant of chlorobenzene solutions doped with tetrabutylammonium tetraphenylborate (TBATPB) has been analyzed using the theoretical expression, and the impact of the bound charges on the complex dielectric constant has been clarified quantitatively in comparison with a theory that does not consider the effect of the bound charges. The Stokes radius of TBA+(=TPB-) determined by the present theory shows a good agreement with that determined by conductometry in the past; hence, the present theory should be applicable to the direct determination of the mobility of ion species in an electrolytic solution without the need to measure ionic limiting equivalent conductance and transport number.