Estimating Reaction Rate Constants from Impedance Spectra: Simulating the Multistep Oxygen Evolution Reaction

TL;DR

This paper presents a method to estimate reaction rate constants for the oxygen evolution reaction from electrochemical impedance spectroscopy data, combining multiple potentials and frequencies with a maximum likelihood estimator for improved accuracy.

Contribution

It introduces a novel approach to extract multistep reaction rate constants from EIS data using a combined multi-potential, multi-frequency estimation framework with stability and initialization strategies.

Findings

Successfully estimates rate constants from simulated data

Shows the necessity of multiple potentials for unique identification

Demonstrates the method's stability with scaling and global optimization

Abstract

The efficiency of water electrolysis in a photoelectrochemical cell is largely limited by the oxygen evolution reaction (OER) at its semiconductor photoanode. Reaction rate constants are key to investigating the slow kinetics of the multistep OER, as they indicate the rate-determining step. While these rate constants are usually calculated based on first-principles simulations, this research aims to estimate them from experimental electrochemical impedance spectroscopy (EIS) data. Starting from a microkinetic model for charge transfer at the semiconductor-electrolyte interface, an expression for the impedance as a function of the rate constants is derived. At lower potentials, the order of this impedance model is reduced, thus eliminating the rate constants corresponding to the last reaction steps. Moreover, it is shown that EIS data from at least two potentials needs to be combined in order to uniquely identify the rate constants of a particular reduced order model. Therefore, this work details a sample maximum likelihood estimator that integrates not only multiple frequencies, but also multiple potentials simultaneously. Measuring multiple periods of the current density and potential signals, allows this frequency domain estimator to take measurement uncertainty into account. In addition, due to the large numerical range of the rate constants, various scaling methods are implemented to achieve numerical stability. To find suitable initial values for the highly nonlinear optimization problem, different global estimation methods are compared. The complete estimation procedure of the rate constants is illustrated on simulated EIS data of a hematite photoanode.