Impedance Spectra and Surface Coverages Simulated Directly from the Electrochemical Reaction Mechanism: A Nonlinear State Space Approach

Current voltage curves and electrochemical impedance spectra (EIS) are crucial for investigating the performance and the electrochemical limitations of electrochemical cells. Therefore, we developed an approach which allows the direct simulation of such data based on microkinetic modeling. This approach allows us to assess the influence of various input parameters on the EIS and on the current–voltage curves and, hence, the overall performance of electrochemical cells. We develop our approach for the oxygen evolution reaction (OER) taking place at the semiconductor–electrolyte interface. At this interface, the microkinetic equations, that is, electrochemical reactions, for the multiple steps in OER are formulated and the resulting set of equations are modeled in a state-space form. As an input to the state-space model, we use the theoretical reaction rates calculated using density functional theory and Gerischer theory for semiconductors. Then, the electrochemical data are simulated as a function of applied potential. Next to the theory and the model development, a case study on the hematite–electrolyte interface which is a typical interface in photoelectrochemical cells is presented. Current voltage curves and EIS data for the hematite interface are simulated from the electrochemical model. The data are compared to experimental measurements. Apart from the current density and the EIS, the model can simulate the coverage of intermediate species as a function of applied potential which is highly demanded for identifying the limiting processes at the interface, but not available from experimental studies. This approach is generic and can be used for other electrochemical interfaces, such as present in fuel cells, electrolysers, or batteries.