Beyond Tafel Analysis for Electrochemical CO2 Reduction



The development and characterization of active and selective catalysts is critical for the simulation and optimization of electrochemical synthesis of chemicals and fuels using renewable energy. The rate of electrochemical generation of a specific product as a function of electrode potential can be described by a Tafel equation, which depends on two parameters: the Tafel slope (or the related transfer coefficient) and the exchange current density. However, common methods for calculating Tafel slopes are subjective and limited by data insufficiency resulting from challenges associated with product quantification, and, as shown here, the effects of mass transport, bulk reaction occurring in the mass-transfer boundary layer, and the occurrence of competitive surface reactions. Errors in the Tafel slope extracted from experimental data can also lead to errors in the exchange current density estimation. To address these issues, we present a technique that leverages statistical learning methods informed by physics-based modeling to calculate kinetic parameters (the transfer coefficient and exchange current density) with quantified uncertainty. The method is applied to 21 sets of data for the electrochemical reduction of CO2 to CO and H2 on Ag catalysts acquired under similar experimental conditions. We find that fitted values for the transfer coefficient and exchange current density do not converge to a unique set of values, and that there is an apparent correlation of these parameters; however, the most probable value of the exchange coefficient for CO and H2 formation correspond reasonably well with the DFT-predicted values of this parameter. While the system explored is relatively simple, the techniques developed can be used to evaluate the transfer coefficient and exchange current density for many other electrochemical processes.


Supplementary material

Supporting Information for Beyond Tafel Analysis for Electrochemical CO2 Reduction
Detailed Description of Modeled Physics, Table of Parameters Employed in Model, Derivation of Concentration Dependent Tafel Kinetics Employed in Model, Supplementary Fitting Methods, Sensitivity Analysis, Sensitivity of Polarization Curves to Kinetic Parameters and Boundary Layer Thickness, Effect of Mass Transport on Apparent Kinetic Parameters, Definition of traditional Tafel analysis, Relationship between αc,k and Tafel slope, Effect of Competing Reactions on Apparent Kinetic Parameters, Initial Guess for Kinetic Fitting, Attempted Fits with Gradient Descent Method (fmincon), CMAES Fit of Experimental Data, Impact of Simultaneous Data Fitting in Varied Electrolyte Concentration, Additional Kinetic Parameter Distributions, Relationships between Parameters