Frequency-Dependent Dielectric Permittivity in Poisson-Nernst-Planck Model

The approaches developed for studying the polarization of molecules and the dynamics of ions in dielectric materials are usually considered separately. The two effects are often believed to take place in different frequency ranges. The low frequency response is usually dominated by ionic migration, whereas the high frequency response is played by molecular polarization. The goal here is to clarify the interplay between free and bound charge densities and their influences on permittivity and impedance profiles by proposing a version of the Poisson-Nernst-Planck (PNP) model that allows to include the effect of a frequency-dependent (and thus not instantaneous) polarizability.