Coupling covariance matrix adaptation with continuum modeling for determination of kinetic parameters associated with electrochemical CO2 reduction

Abstract

•Characterization methods for CO2R catalysts that neglect mass transfer are inaccurate•CMA-ES coupled with continuum modeling rigorously parameterizes literature CO2R data•Fit parameters are broadly distributed, suggesting differences in catalyst structure•Presented method is applicable to any electrochemical system affected by mass transfer Electrochemical synthesis processes (e.g., the electrochemical reduction of carbon dioxide [CO2R]) possess immense potential to electrify the manufacturing of chemicals and fuels. Key to rationalizing and optimizing the performance of these systems is the characterization of electrocatalysts. However, the extraction of intrinsic kinetic behavior from experimental data is convoluted by poor mass transfer of synthesis reagents. Hence, common methods of benchmarking catalysts result in the misreporting of intrinsic behavior. To address this issue, the methodology presented here employs advanced optimization strategies informed by continuum modeling to deconvolute non-kinetic effects and rigorously benchmark catalysts for CO2R. The developed method is broadly applicable to any electrochemical system where mass transfer is relevant, such as ammonia synthesis or organic electrosynthesis, making it a powerful tool in the development of electrocatalysts for electrochemical synthesis. In electrocatalysis, the rate of a reaction as a function of applied potential is governed by the Tafel equation, which depends on two parameters: the Tafel slope and the exchange current density (i0). However, current methods to determine these parameters involve subjective removal of data due to the convoluted effects of mass transfer and competitive surface or bulk reactions, resulting in unquantifiable uncertainty. To overcome this challenge, we couple covariance matrix adaptation with a continuum model of CO2 reduction (CO2R) that explicitly deconvolutes non-kinetic effects to extract kinetic parameters associated with 26 literature datasets of CO2R over Ag and Sn catalysts. The fitted kinetic parameters do not converge to a unique set of values, and the Tafel slope and i0 possess an apparent correlation, which we suggest is a consequence of variations in catalyst preparation methods. This work facilitates rigorous benchmarking of electrocatalysts in systems where mass transfer is relevant. In electrocatalysis, the rate of a reaction as a function of applied potential is governed by the Tafel equation, which depends on two parameters: the Tafel slope and the exchange current density (i0). However, current methods to determine these parameters involve subjective removal of data due to the convoluted effects of mass transfer and competitive surface or bulk reactions, resulting in unquantifiable uncertainty. To overcome this challenge, we couple covariance matrix adaptation with a continuum model of CO2 reduction (CO2R) that explicitly deconvolutes non-kinetic effects to extract kinetic parameters associated with 26 literature datasets of CO2R over Ag and Sn catalysts. The fitted kinetic parameters do not converge to a unique set of values, and the Tafel slope and i0 possess an apparent correlation, which we suggest is a consequence of variations in catalyst preparation methods. This work facilitates rigorous benchmarking of electrocatalysts in systems where mass transfer is relevant. Electrochemical reduction of carbon dioxide (CO2) emitted from point sources (e.g., cement production, separation from natural gas, iron and aluminum ore smelting, and fermentation of sugars) using electricity from renewable resources (e.g., wind and solar) offers a means for recapturing its carbon content. Moreover, if the CO2 can be taken from the atmosphere and converted electrochemically to chemicals and fuels, one could envision a closed carbon cycle.1Blanco D.E. Modestino M.A. Organic Electrosynthesis for Sustainable Chemical Manufacturing.J. Trends Chem. 2019; 1: 8-10Abstract Full Text Full Text PDF Scopus (4) Google Scholar,2De Luna P. Hahn C. Higgins D. Jaffer S.A. Jaramillo T.F. Sargent E.H. What Would It Take for Renewably Powered Electrosynthesis to Displace Petrochemical Processes?.Science. 2019; 364eaav3506Crossref PubMed Scopus (921) Google Scholar,3Bui J.C. Lees E.W. Pant L.M. Zenyuk I.V. Bell A.T. Weber A.Z. Continuum modeling of porous electrodes for electrochemical synthesis.Chem. Rev. 2022; 122: 11022-11084Crossref PubMed Scopus (13) Google Scholar,4Levi P. Vass T. Mandova H. Gouy A. Chemicals—Analysis. International Energy Agency, 2018Google Scholar In order to produce desired products with high rates and selectivity, it is important to understand how to design electrochemical cells that enable achievement of these objectives.5Goldman M. Lees E.W. Prieto P.L. Mowbray B.A.W. Weekes D.M. Reyes A. Li T. Salvatore D.A. Smith W.A. Berlinguette C.P. Electrochemical Reactors.in: Carbon Dioxide Electrochemistry: Homogeneous and Heterogeneous Catalysis. The Royal Society of Chemistry, 2021: 408-432Google Scholar,6Bui J.C. Kim C. King A.J. Romiluyi O. Kusoglu A. Weber A.Z. Bell A.T. Engineering Catalyst–Electrolyte Microenvironments to Optimize the Activity and Selectivity for the Electrochemical Reduction of CO2 on Cu and Ag.Acc. Chem. Res. 2022; 55: 484-494Crossref PubMed Scopus (27) Google Scholar,7Garg S. Li M. Weber A.Z. Ge L. Li L. Rudolph V. Wang G. Rufford T.E. Advances and challenges in electrochemical CO2 reduction processes: An engineering and design perspective looking beyond new catalyst materials.J. Mater. Chem. A. 2020; 8: 1511-1544Crossref Google Scholar,8Nitopi S. Bertheussen E. Scott S.B. Liu X. Engstfeld A.K. Horch S. Seger B. Stephens I.E.L. Chan K. Hahn C. et al.Progress and Perspectives of Electrochemical CO2 Reduction on in Aqueous Electrolyte.Chem. Rev. 2019; 119: 7610-7672Crossref PubMed Scopus (0) Google Scholar A key element in pursuit of this goal is accurate representation of individual product formation rates and their dependence on reactant concentration, pH, and cathode potential. For the design and simulation of electrochemical processes, the current density (ij) for producing product j is most commonly represented by the Butler-Volmer equation (Equation 1) or the simpler Tafel equation (Equation 2), which is based on the assumption that the reaction is irreversible at large overpotentials. In this work we only consider the Tafel equation for the cathodic direction.ij=i0,j(−exp(−αc,jFRTηj)+exp(αa,jFRTηj))(Equation 1) ij=−i0,jexp(−αc,jFRTηj)(Equation 2) Here R is the ideal gas constant, F is Faraday’s constant, ηj is the overpotential or driving force for the electrochemical reaction j, T is the absolute temperature, αc,j is the transfer coefficient, and i0,j is the exchange current density. In Equation 2, there are two important parameters, the transfer coefficient (αc,j) that describes the sensitivity of the product current density to changes in the overpotential (i.e., the electrochemical driving force) and the exchange current density (i0,j), which is the pre-factor for the exponential term.9Newman J. Thomas-Alyea K.E. Electrochemical Systems.Third Edition. John Wiley and Sons, Inc., 2004Google Scholar It is important to note that the exchange current density contains explicit concentration dependences on the reactants and products of a given reaction, as derived in Note S1. Many studies of electrochemical synthesis report the Tafel slope, which is directly related to the transfer coefficient and defined as the overpotential required to obtain a 10-fold increase in product current density.9Newman J. Thomas-Alyea K.E. Electrochemical Systems.Third Edition. John Wiley and Sons, Inc., 2004Google Scholar,10Limaye A.M. Zeng J.S. Willard A.P. Manthiram K. Bayesian Data Analysis Reveals No Preference for Cardinal Tafel Slopes in CO2 Reduction Electrocatalysis.Nat. Commun. 2021; 12703Crossref PubMed Scopus (31) Google ScholarTafelslope=−ln(10)RTαc,jF=−59.125[mVdec−1]αc,jforT=298K(Equation 3) For multi-step kinetics, the Tafel slope, or related transfer coefficient αc,j, has been used to infer which elementary step is rate-limiting in the formation of a particular reaction product.11Shinagawa T. Garcia-Esparza A.T. Takanabe K. Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion.Sci. Rep. 2015; 513801Crossref PubMed Scopus (1595) Google Scholar,12Dunwell M. Luc W. Yan Y. Jiao F. Xu B. Understanding Surface-Mediated Electrochemical Reactions: CO2 Reduction and beyond.ACS Catal. 2018; 8: 8121-8129Crossref Scopus (139) Google Scholar,13Bockris J.O. Nagy Z. Symmetry Factor and Transfer Coefficient: A Source of Confusion in Electrode Kinetics.J. Chem. Educ. 1973; 50: 839-843Crossref Scopus (83) Google Scholar A commonly used method to calculate Tafel slopes involves a least-squares regression on the linear portion of the logarithm of the measured current density vs. cathode potential (i.e., the kinetic region of the polarization curve). This approach involves manual exclusion of data that lie in the mass-transport-limited regime (Figure 1, top).10Limaye A.M. Zeng J.S. Willard A.P. Manthiram K. Bayesian Data Analysis Reveals No Preference for Cardinal Tafel Slopes in CO2 Reduction Electrocatalysis.Nat. Commun. 2021; 12703Crossref PubMed Scopus (31) Google Scholar For electrochemical CO2 reduction (CO2R), the mass-transport-limited regime occurs at potentials for which the predicted rate of CO2 consumption by electrochemical and homogeneous chemical reactions becomes greater than the rate of CO2 transport to the surface. Mass-transport limitations in CO2R are caused primarily by the low solubility and diffusion coefficient of CO2 in the aqueous electrolyte.14Weng L.C. Bell A.T. Weber A.Z. Modeling gas-diffusion electrodes for CO2 reduction.Phys. Chem. Chem. Phys. 2018; 20: 16973-16984Crossref PubMed Google Scholar,15Clark E.L. Resasco J. Landers A. Lin J. Chung L.T. Walton A. Hahn C. Jaramillo T.F. Bell A.T. Standards and Protocols for Data Acquisition and Reporting for Studies of the Electrochemical Reduction of Carbon Dioxide.ACS Catal. 2018; 8: 6560-6570Crossref Scopus (189) Google Scholar Because the regimes of kinetic control and the onset of mass-transfer control are defined arbitrarily, this method of identifying the regime of kinetic control is prone to human error and leads to a reduction in the number of data points available for analysis. It is also notable that in electrochemical synthesis the product must be quantified at every applied potential through time-consuming steady-state measurements. The need for product quantification contrasts with water electrolysis for which catalytic behavior can be measured rapidly at thousands of points via linear-sweep voltammetry. Because data in electrochemical synthesis must be collected by steady-state chronopotentiometry or chronoamperometry to generate sufficient product for quantification, rapid current-voltage sweeps are impractical if one wants to determine the partial current densities for each product. In other words, the steady-state nature of electrochemical synthesis, in which multiple products are formed, limits the number of available data points for each product. Prior work has sought to address these concerns and provide rigorous methods for determining kinetic parameters.10Limaye A.M. Zeng J.S. Willard A.P. Manthiram K. Bayesian Data Analysis Reveals No Preference for Cardinal Tafel Slopes in CO2 Reduction Electrocatalysis.Nat. Commun. 2021; 12703Crossref PubMed Scopus (31) Google Scholar,16Agbo P. Danilovic N. An Algorithm for the Extraction of Tafel Slopes.J. Phys. Chem. C. 2019; 123: 30252-30264Crossref Scopus (11) Google Scholar,17Khadke P. Tichter T. Boettcher T. Muench F. Ensinger W. Roth C. A simple and effective method for the accurate extraction of kinetic parameters using differential Tafel plots.Sci. Rep. 2021; 118974Crossref PubMed Scopus (11) Google Scholar Recently, Limaye et al. have attempted to address the challenge of data insufficiency in Tafel analysis for electrochemical CO2R by using a Bayesian learning algorithm,10Limaye A.M. Zeng J.S. Willard A.P. Manthiram K. Bayesian Data Analysis Reveals No Preference for Cardinal Tafel Slopes in CO2 Reduction Electrocatalysis.Nat. Commun. 2021; 12703Crossref PubMed Scopus (31) Google Scholar in which current-voltage data are fit to a representation of the intrinsic reaction rate given by the Tafel equation together with the effects of mass transfer. Using such a model enabled fitting of all experimental data without the need to arbitrarily define the Tafel region, even for limited datasets (5–20 data points). Furthermore, the Bayesian learning model used in this work provided a distribution of potential Tafel slopes and a defined uncertainty threshold. This approach revealed the human errors involved in fitting Tafel slopes reported in the literature. A limitation of this work is that the physical model employed did not account for the coupling of mass transfer effects with competing electrochemical and homogeneous buffer reactions that consume reactants and change local pH,18Rabinowitz J.A. Kanan M.W. The future of low-temperature carbon dioxide electrolysis depends on solving one basic problem.Nat. Commun. 2020; 115231Crossref Scopus (179) Google Scholar,19Zhang Z. Melo L. Jansonius R.P. Habibzadeh F. Grant E.R. Berlinguette C.P. pH Matters When Reducing CO2 in an Electrochemical Flow Cell.ACS Energy Lett. 2020; 5: 3101-3107Crossref Scopus (81) Google Scholar,20Liu X. Schlexer P. Xiao J. Ji Y. Wang L. Sandberg R.B. Tang M. Brown K.S. Peng H. Ringe S. et al.pH effects on the electrochemical reduction of CO(2) towards C2 products on stepped copper.Nat. Commun. 2019; 1032Google Scholar as well as the complex dependences of the intrinsic kinetics on species activities,6Bui J.C. Kim C. King A.J. Romiluyi O. Kusoglu A. Weber A.Z. Bell A.T. Engineering Catalyst–Electrolyte Microenvironments to Optimize the Activity and Selectivity for the Electrochemical Reduction of CO2 on Cu and Ag.Acc. Chem. Res. 2022; 55: 484-494Crossref PubMed Scopus (27) Google Scholar,19Zhang Z. Melo L. Jansonius R.P. Habibzadeh F. Grant E.R. Berlinguette C.P. pH Matters When Reducing CO2 in an Electrochemical Flow Cell.ACS Energy Lett. 2020; 5: 3101-3107Crossref Scopus (81) Google Scholar,21Hashiba H. Weng L.C. Chen Y. Sato H.K. Yotsuhashi S. Xiang C. Weber A.Z. Effects of electrolyte buffer capacity on surface reactant species and the reaction rate of CO2 in Electrochemical CO2 reduction.J. Phys. Chem. C. 2018; 122: 3719-3726Crossref Scopus (7) Google Scholar,22Yang K. Kas R. Smith W.A. In situ Infrared Spectroscopy Reveals Persistent Alkalinity near Electrode Surfaces during CO2 Electroreduction.J. Am. Chem. Soc. 2019; 141: 15891-15900Crossref PubMed Scopus (137) Google Scholar preventing the approach from capturing complex curvature in the CO2R polarization curve at higher applied potentials or deconvoluting contributions due to various surface reactions. In this work, we present a one-dimensional (1D), reaction-transport model of CO2R to CO and H2 over an Ag catalyst, as well as CO2R to HCOO−, CO, and H2 over an Sn catalyst, that is then used in combination with covariance matrix adaptation evolutionary strategy (CMA-ES), an advanced data analysis tool, to fit the Tafel parameters (i.e., αc and i0) for a variety of Ag and Sn catalysts. This approach provides a rigorous means for identifying the parameters required for continuum simulations without the need for subjective human intervention while accounting for mass transfer, which the sensitivity analysis performed in this study elucidates is key to accurately determining kinetic parameters. Application of this approach to 18 datasets for CO2R to CO on Ag, as well as 8 datasets for CO2R to CO and HCOO− on Sn, in similar experimental setups reveals that the fitted rate parameters are broadly distributed, probably due to differences in catalyst morphology (i.e., distribution of surface facets and roughness) that we propose could be a result of variations in catalyst preparation across various studies. The methodology reported here provides a rigorous approach for determining the Tafel parameters associated with product partial current density vs. cathodic potential curves obtained for electrochemical processes that produce multiple products. This finding is particularly important for systems in which the formation of one product influences the rate of formation of other products through the effects of mass transfer and bulk reactions. To assess the impact of mass transport and bulk reactions on observed partial current densities, a sensitivity analysis was carried out. By this means, the sensitivity of the product partial current densities to changes in the kinetic parameters (αi,c and ii,0) is determined (Note S2). This procedure enables an assessment of the degree of sensitivity between the outputs and input parameters in the model (i.e., how much an output parameter changes when an input parameter is changed). When an output is positively sensitive to an input, an increase in the input results in an increase in the output; when an output is negatively sensitive to an input, an increase in the input results in a decrease in the output. The sensitivity analysis revealed that the CO partial current density is highly negatively sensitive to mass transfer (i.e., LBL) due to low availability of CO2 in the aqueous electrolyte; however, the H2 partial current density is less sensitive to mass-transfer effects because of the high availability of solvent water, which was assumed to be the proton source for H2 evolution reaction (HER) (Figures S3–S5). We also observed that the CO partial current density was positively sensitive to i0,CO and αCO, but more interestingly, negatively sensitive to the HER kinetics (i0,H2 and αH2) (Figure S3). As the HER current increases, the pH rises due to concomitant generation of OH−, and the generated OH− anions consume reactant CO2 via homogeneous buffer reactions thereby reducing the CO evolution reaction (COER) partial current. Continuum simulations were then used to assess the accuracy of the traditional Tafel analysis (see supplemental information section effect of mass transport on apparent kinetic parameters and Note S3) for simulated polarization curves where mass transport or competitive reactions were relevant. Figures 2A and 2B depict the results of performing traditional Tafel analysis to extract the kinetic parameters from CO polarization curves generated by the simulation, all of which possess a constant CO Tafel slope but different values of the mass-transport boundary layer (BL) thickness, LBL, (Figure 2A) or i0,H2(Figure 2B). In other words, these plots possess a constant value of the intrinsic kinetic parameters of COER (i0,CO and αc,CO), but the value of LBL is changed from 0.5× to 1.5× its base value (Figure 2A), and the value of i0,H2 is changed from 1× to 100× its base value (Figure 2B). As can easily be seen, even though the CO Tafel slope should be identical for all plotted polarization curves, the apparent Tafel slope as measured by a traditional approach is different for every curve, revealing the extent to which mass transport affects the apparent Tafel slope. Key to this sensitivity analysis is recognizing that concentration gradients in CO2 and pH within the BL are quite severe (Figure S6), particularly at high potentials, meaning that the concentration in the bulk is not the same as the concentration at the reaction plane, and that the large gradients in reactant activity within the BL necessitate the simulation of mass transport to determine activities accurately at the reaction plane. Therefore, the continuum model is necessary to deconvolute the effects of mass transport from the intrinsic kinetics of the surface reactions. Intriguingly, when the apparent CO Tafel slope (Figure 2C) and i0,CO (Figure S7) are plotted against LBL, they approach their intrinsic values as LBL approaches zero. In other words, in the limit of no mass-transport losses of CO2, traditional Tafel fitting is sufficient and accurate. This finding suggests traditional assessment of Tafel slopes could be done using data that are minimally affected by mass transfer. Porous electrodes, which have BL thicknesses approaching the nanometer length scale, have also been suggested for determining the intrinsic kinetics of electrochemical reactions.3Bui J.C. Lees E.W. Pant L.M. Zenyuk I.V. Bell A.T. Weber A.Z. Continuum modeling of porous electrodes for electrochemical synthesis.Chem. Rev. 2022; 122: 11022-11084Crossref PubMed Scopus (13) Google Scholar,23Higgins D. Hahn C. Xiang C. Jaramillo T.F. Weber A.Z. Gas-Diffusion Electrodes for Carbon Dioxide Reduction: A New Paradigm.ACS Energy Lett. 2019; 4: 317-324Crossref Scopus (322) Google Scholar However, the chemistry and morphology of such electrodes were found to impact observed kinetics in non-trivial ways due to the possibility of overlapping BLs, along with the complex multiphase (gas, liquid, and sometimes solid-electrolyte phases) transport occurring in the porous medium.3Bui J.C. Lees E.W. Pant L.M. Zenyuk I.V. Bell A.T. Weber A.Z. Continuum modeling of porous electrodes for electrochemical synthesis.Chem. Rev. 2022; 122: 11022-11084Crossref PubMed Scopus (13) Google Scholar Rotating disk24Vos R.E. Koper M.T.M. The Effect of Temperature on the Cation-Promoted Electrochemical CO2 Reduction on Gold.ChemElectroChem. 2022; 9: 1-11Crossref Scopus (4) Google Scholar or rotating cylinder25Jang J. Rüscher M. Winzely M. Morales-Guio C.G. Gastight rotating cylinder electrode: Toward decoupling mass transport and intrinsic kinetics in electrocatalysis.AIChE J. 2022; 68e17605Crossref Scopus (10) Google Scholar,26Richard D. Tom M. Jang J. Yun S. Christofides P.D. Morales-Guio C. Quantifying Transport and Reaction Electrocatalytic Processes in a Gastight Rotating Cylinder Electrode Reactor via Integration of Computational Fluid Dynamics Modeling and Experiments.SSRN Electron. J. 2022; 440141698Google Scholar electrode systems can also aid in deconvoluting the effects of mass transfer. However, the use of these techniques does not eliminate completely mass transfer at high cathode potentials and current densities. Hence, modeling of mass transport and the kinetics of bulk reactions occurring in an aqueous BL will always be necessary for determination of Tafel parameters. In addition to hydrodynamics, the presence of bulk reactions occurring in the thin BL can impact the apparent Tafel slopes. Figures 2B and S3 illustrate the effect of the HER current density on apparent CO kinetics, demonstrating that at high current densities for HER, the apparent CO kinetic parameters can be quite inaccurate. Importantly, this competition for reactant CO2 is indirect and is a result of the consumption of CO2 by HER-generated OH− anions to form HCO3− and CO32− anions in the BL, as opposed to direct electrochemical consumption. Indeed, many catalysts experience direct electrochemical competition for reactant CO2. For instance, formate (HCOO−) forms competitively with CO on Cu,8Nitopi S. Bertheussen E. Scott S.B. Liu X. Engstfeld A.K. Horch S. Seger B. Stephens I.E.L. Chan K. Hahn C. et al.Progress and Perspectives of Electrochemical CO2 Reduction on in Aqueous Electrolyte.Chem. Rev. 2019; 119: 7610-7672Crossref PubMed Scopus (0) Google Scholar Pd,27Nguyen D.L.T. Nguyen T.M. Lee S.Y. Kim J. Kim S.Y. Le Q.V. Varma R.S. Hwang Y.J. Electrochemical conversion of CO2 to value-added chemicals over bimetallic Pd-based nanostructures: Recent progress and emerging trends.Environ. Res. 2022; 211113116Crossref Scopus (2) Google Scholar Sn,28Ge H. Gu Z. Han P. Shen H. Al-Enizi A.M. Zhang L. Zheng G. Mesoporous tin oxide for electrocatalytic CO2 reduction.J. Colloid Interface Sci. 2018; 531: 564-569Crossref PubMed Scopus (38) Google Scholar,29Liu G. Li Z. Shi J. Sun K. Ji Y. Wang Z. Qiu Y. Liu Y. Wang Z. Hu P.A. Black reduced porous SnO2 nanosheets for CO2 electroreduction with high formate selectivity and low overpotential.Appl. Catal. B. 2020; 260118134Crossref Scopus (92) Google Scholar,30Daiyan R. Lovell E.C. Bedford N.M. Saputera W.H. Wu K.H. Lim S. Horlyck J. Ng Y.H. Lu X. Amal R. Modulating Activity through Defect Engineering of Tin Oxides for Electrochemical CO2 Reduction.Adv. Sci. (Weinh). 2019; 61900678PubMed Google Scholar and Ag,31Thevenon A. Rosas-Hernández A. Fontani Herreros A.M. Agapie T. Peters J.C. Dramatic HER Suppression on Ag Electrodes via Molecular Films for Highly Selective CO2 to CO Reduction.ACS Catal. 2021; 11: 4530-4537Crossref Scopus (34) Google Scholar and such direct competition for CO2 impacts the apparent Tafel slopes for these products. As shown in Figure 2D, the occurrence of competing HCOO− formation dramatically increases the apparent CO Tafel slope beyond its intrinsic value. For the largest i0,HCOO− tested, corresponding to roughly equal co-generation of CO and HCOO−, as has been observed on Cu8Nitopi S. Bertheussen E. Scott S.B. Liu X. Engstfeld A.K. Horch S. Seger B. Stephens I.E.L. Chan K. Hahn C. et al.Progress and Perspectives of Electrochemical CO2 Reduction on in Aqueous Electrolyte.Chem. Rev. 2019; 119: 7610-7672Crossref PubMed Scopus (0) Google Scholar and Pd,27Nguyen D.L.T. Nguyen T.M. Lee S.Y. Kim J. Kim S.Y. Le Q.V. Varma R.S. Hwang Y.J. Electrochemical conversion of CO2 to value-added chemicals over bimetallic Pd-based nanostructures: Recent progress and emerging trends.Environ. Res. 2022; 211113116Crossref Scopus (2) Google Scholar the apparent CO Tafel slope is nearly 50 mV dec−1 larger than the reference value employed in the model (93.55 mV dec−1). i0,CO,αHCOO−, and i0,HCOO− exhibit similar inaccuracies (Note S3). The transfer coefficient quantifies how much of the applied potential driving force goes to driving the rate of a given electrochemical reaction. In electrochemical synthesis systems, the applied potential driving force drives a suite of competitive surface reactions and overcomes losses attributable to low rates of mass transfer (i.e., Nernstian losses). Thus, taking kinetic parameters directly from measured polarization data typically leads to an overestimation of the Tafel slope (and, hence, an underestimation of the transfer coefficient due to their inverse proportionality) by neglecting the potential losses associated with mass transport and competitive surface reactions. As mass transfer improves, and in the limit of a single surface reaction, the intrinsic kinetics can be measured experimentally. However, the presence of competing electrochemical reactions and poor mass transfer is the norm in electrochemical synthesis, rather than the exception. These results underscore the need for physiochemical models that enable the determination of intrinsic Tafel parameters for individual reaction kinetics unaffected by the effects of mass transport, bulk reactions occurring the mass-transfer BL, or competing surface reactions. Recent work has attempted to delineate more accurately the kinetically controlled and mass-transport controlled regimes in polarization data by employing a technique known as differential Tafel analysis, in which Tafel slopes and/or their derivatives are plotted as a function of potential.32Corva M. Blanc N. Bondue C.J. Tschulik K. Differential Tafel Analysis: A Quick and Robust Tool to Inspect and Benchmark Charge Transfer in Electrocatalysis.ACS Catal. 2022; 12: 13805-13812Crossref PubMed Scopus (1) Google Scholar,33van der Heijden O. Park S. Eggebeen J.J.J. Koper M.T.M. Non-Kinetic Effects Convolute Activity and Tafel Analysis for the Alkaline Oxygen Evolution Reaction on NiFeOOH Electrocatalysts.Angew. Chem. Int. Ed. Engl. 2023; 62e202216477Crossref PubMed Scopus (4) Google Scholar However, differential Tafel analysis requires substantial data collection and is quite challenging for electrochemical synthesis application, for which product quantification as a function of potential, particularly liquid-phase products, limits data availability. Even if data insufficiency were not a concern, differential Tafel analyses would not be able to fully deconvolute the contributions to partial current density from mass transport and kinetics due to the significant impact of mass transfer in these CO2R reactions at nearly all relevant applied potentials (Note S4). This is especially true for minority products such as HCOO− on Ag, for which there are no regions in which differential Tafel analysis can identify kinetic control. By accounting for mass transfer effects directly in the mathematical model, the method reported here enables direct simulation of the various competing phenomena and, correspondingly, the extraction of kinetically relevant Tafel parameters for multiple surface reactions simultaneously for CO2R. We first established that our model and coupled CMA-ES approach for fitting Tafel parameters is capable of simultaneously fitting the parameters for CO and H2 formation for different sets of data taken from the literature with high accuracy and quantified uncertainty without human intervention (see supplemental information section CMA-ES continuum modeling fit of experimental Ag data for plots of all H2 and CO polarization curves and the corresponding fitted Tafel parameter values). Next, we sought to determine whether the fitted Tafel slopes and transfer coefficients converged to a set of unifying values. Bockris and co-workers derived what they refer to as cardinal values for the transfer coefficient of αc= 0.5, 1.0, 1.5, etc.13Bockris J.O. Nagy Z. Symmetry Factor and Transfer Coefficient: A Source of Confusion in Electrode Kinetics.J. Chem. Educ. 1973; 50: 839-843Crossref Scopus (83) Google Scholar This can be done starting with Equation S62 and assuming integer values for s and q, a ν of 1, and a symmetry factor of the rate-determinin