Integration of Charge-Carrier Dynamics and Electrochemical Modeling in a Unified Microkinetic Model for the Oxygen Evolution Reaction in Water Splitting
Authors: van den Boorn Bart F. H. , van Berkel Matthijs , Bieberle-Hütter Anja 
Published: February 2024

Water-splitting in a photo-electrochemical cell is a promising method for the sustainable production of hydrogen. However, these cells are not yet able to achieve the efficiencies required for commercial use. The reaction that generates oxygen at the photo-anode, the oxygen evolution reaction (OER), is commonly regarded as the performance limiting reaction. Modeling of the OER can provide several opportunities [1,2]: (1) to identify and verify the prominent reaction mechanism by comparison to experimental electrochemical data, (2) to determine variables that are difficult to obtain from experiments, such as the surface coverage of the intermediate OER reaction species at the semiconductor-electrolyte interface, and (3) to rapidly explore new semiconductor materials for increased oxygen evolution.
Previously in our group, a time-dependent non-linear microkinetic model of the OER has been developed. [3,4] This model consists of two parts: (1) A microkinetic model of the reaction kinetics at the semiconductor-electrolyte interface. The model equations describe the time-evolution of the current density and the intermediate species under applied potential. (2) A simplified description of the charge-carrier transport dynamics at the surface of an iron oxide (hematite) semiconductor. This model is able to simulate the steady-state behavior, such as current-voltage curves. However, the dynamic behavior and the simulation of electrochemical impedance spectra are not possible with the current model.
Therefore, in this work a more detailed description of the charge-carrier dynamics is developed and implemented. While in the earlier model [3, 4] the two charge-carriers, electrons and holes, were simulated only at the surface of the semiconductor, in this work, also processes in the bulk of the semiconductor are included, through addition of a space-dependency of the charge-carriers in the semiconductor. The advantage is that we can fully include drift-diffusion effects, charge transfer at the interface, electron-hole pair generation, and the recombination processes at the interface and in the bulk of the semiconductor. The resulting partial differential equations are connected to the state-space system of the reaction kinetics through semi-discretization in the spatial dimension.
In addition, we will present a global sensitivity analysis to characterize the influence of the model input parameters, such as free energies and reaction rates, on the output, i.e. current density. [5] This analysis, using Sobol's method, presents the influence of each parameter on the uncertainty of the model output, the current density, at different potentials. [6] As a result, this analysis can indicate exactly which parameters to research to decrease the output uncertainty most effectively.
This work presents for the first time an integration of the spatial charge-carrier dynamics and the electrochemical model of the OER into one combined model. As such, we can investigate the limiting processes in both components simultaneously, while the sensitivity analysis allows us to probe these limiting processes under a wide range of conditions, such as varying illumination levels and temperatures. The combined model, in conjunction with global sensitivity analysis, will be used to accurately determine the surface coverages of the OER, which can be validated by comparison with experimental data, e.g., from ATR-FTIR measurements. [7] Additionally, by implementing different materials, in addition to iron oxide, we aim to identify the most promising catalyst for OER.
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Figure 1: Framework of the microkinetic model with two components: (1) the electrochemical model with the OER reaction mechanism, and (2) the charge-carrier dynamics with drift-diffusion, charge transfer and recombination processes. The results of the global sensitivity analysis of the electrochemical model are represented by the sensitivity indices (SOER), which express the influence of each of the input parameters on the output, i.e., the current density, as a percentage.

Figure 1