The Gerischer finite length impedance: A case of unequal diffusion coefficients

This work is devoted to the theoretical study of the impedance response associated with coupled homogeneous first-order chemical reaction in diffusion layer and reversible heterogeneous electrochemical reaction (CE mechanism). For the first time, the exact analytical expression for the Gerischer finite length impedance is obtained for different diffusion coefficients of the species involved in the homogeneous first-order chemical reaction. In a general case, the Gerischer finite length impedance has two capacitive loops, one associated with the diffusion of the inactive species and the other with the homogeneous chemical reaction. The effect of the diffusion coefficients difference is observed at low frequencies. At high frequencies, the impedance behavior is determined by the diffusion coefficient of the active species. At low chemical reaction rate constants, the classic behavior of the Gerischer impedance is observed in the complex plane. The position of the zero-frequency point in the Nyquist plot is determined by the thickness of the kinetic (reaction) layer. The obtained results can be applied for a better understanding of reaction-diffusion impedance, especially during analysis of the parameters extracted from low frequency range of impedance.