Modular theory for EIS response of electron transfer coupled with electric double layer on rough and heterogeneous electrode

The dynamic phenomenological coupling of charge transfer kinetics with electric double layer (EDL) dynamics on a rough and heterogeneous electrode is a theoretically challenging problem. Here, we solve this complex problem using a modular theoretical approach for the electrochemical impedance spectroscopic (EIS) technique, also transcends the limitations of equivalent circuit model. Theory based on modular approach allow us to analyse the EIS response for multi phenomena over seven decades of frequency. Qualitatively EIS response can be classified in three frequency regimes: (i) ω>ωH, largely controlled by ohmic and EDL dynamics, (ii) ωH≥ω≥ωCH, coupling between EDL and electron transfer, and extent of coupling depends on applied potential and (iii) ω<ωCH, usually controlled by solvent kinetics. The frequency ωH is characteristic EDL formation frequency or inverse time for the closest approach of an ion to the electrode surface, which is also a prerequisite for an electron transfer step. The characteristic (low) frequency ωCH in aqueous system represents the onset of sluggish water splitting kinetics. The intermediate frequency response is dynamically influenced by the morphological complexities of electrode surface which is usually characterized through the finite fractal roughness. Our work highlights that the enhanced viscosity of the medium results in (i) lowering of ωH caused by increase in the electrolyte resistance, (ii) lowering of diffusion coefficient. Similarly, the temperature has significant influence on the ωH. Finally, this modular approach captures the experimental responses obtained through variation in externally applied potential, viscosity of the medium, temperature and the electroactive area.