Debye–Falkenhagen dynamics of electric double layer in presence of electrode heterogeneities

A phenomenological theory of electric double layer (EDL) polarization of an electrode (in the absence and presence of electroactive species) is obtained using the Debye–Falkenhagen equation for the potential. The influence of surface heterogeneities on the compact layer causes the distribution in relaxation time, resulting in constant phase element (CPE) response. This contribution of the compact layer is included through the current balance boundary constraint at the outer Helmholtz plane. The results for the impedance and the capacitance are obtained in terms Debye screening length and dynamic polarization length which is dependent on the surface heterogeneity parameter. At frequencies less than the characteristic compact layer relaxation frequency, the EDL is controlled by the compact layer dynamics and shows CPE response. The intermediate frequencies show the emergence of pseudo-Gerischer and pseudo-Warburg like behavior for systems with lower concentration and lower diffusion coefficients of ions. EDL behaves like a resistor at larger frequencies. Theoretical results capture various observations in the experimental capacitance dispersion data.