# Fileset [wang-et-al-2024-accelerated-electrocatalyst-degradation-testing-by-accurate-and-robust-forecasting-of-multidimensional.pdf](https://mdr.nims.go.jp/filesets/340c9c29-12c5-4aa8-bcc6-be51b966b520/download) ## Creator [Miao Wang](https://orcid.org/0000-0001-9483-6877), [Akimitsu Ishii](https://orcid.org/0000-0002-9261-4047), [Ken Sakaushi](https://orcid.org/0000-0003-4797-9087) ## Rights https://creativecommons.org/licenses/by-nc-nd/4.0/[Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/) ## Other metadata [Accelerated Electrocatalyst Degradation Testing by Accurate and Robust Forecasting of Multidimensional Kinetic Model with Bayesian Data-Assimilation](https://mdr.nims.go.jp/datasets/28fcd3fe-4381-4bb8-8cbf-92d759bb24e0) ## Fulltext Accelerated Electrocatalyst Degradation Testing by Accurate and Robust Forecasting of Multidimensional Kinetic Model with Bayesian Data AssimilationAccelerated Electrocatalyst DegradationTesting by Accurate and Robust Forecastingof Multidimensional Kinetic Model withBayesian Data AssimilationMiao Wang, Akimitsu Ishii, and Ken Sakaushi*Cite This: ACS Energy Lett. 2025, 10, 22−29 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: Degradation tests represent a significant bottleneck inelectrochemical technology development, occasionally requiring tensof thousands of hours. Thus, reliable degradation forecasting in a shorttime frame is a game-changer in accelerating the establishment offuture electrochemical devices. Herein, we show a multidimensionalkinetic model for electrocatalyst degradation by quantifying therelationship among potential, current, and time, applicable undervarious conditions. Aiming to predict reliable degradation behaviors inshorter experimental timeframes and inspired by modern weatherforecasting methods, we integrated Bayesian data assimilation with ourmodel to expedite multidimensional parameter optimization. Con-sequently, we achieved accurate and robust forecasting of electro-catalyst lifetime by employing oxygen evolution reaction as arepresentative system: it takes just 300 h to obtain the final lifetimeof close to 1000 h even with environmental noise. This data-driven approach can accelerate our understanding of themicroscopic electrochemical mechanisms and simultaneously directly bridge this understanding to develop next-generationenergy technologies.The accelerated implementation of next-generationelectrochemical technologies is imperative for achiev-ing carbon neutrality.1,2 In particular, various types ofelectrolyzers are crucial for producing a wide spectrum ofessential chemicals without carbon dioxide (CO2) emissions.Although electrolysis is an old technology dating to the 18thcentury,3 modern electrolyzer systems are key in the 21stcentury: in the present time, different cathodic reactions arecombined with oxygen evolution reaction (OER) in anelectrolyzer,4 such as hydrogen evolution reaction in water/seawater splitting toward green hydrogen production,5 CO2reduction reaction for high-value chemical production,6,7 andnitrogen reduction reaction for green ammonia synthesis.8−11As such, electrolyzer technology is indispensable for thesustainable development of human societies in the 21stcentury,4,12−14 which has triggered worldwide intensiveresearch in affordable and sustainable yet high-performanceelectrocatalysts. For device implementation, electrocatalystrobustness is of great importance same as promoting theelectrocatalytic activity to keep high overall energy efficiencyduring the operation time frame typically a decade ormore.5,15,16 To this end, one key relies on improving thedurability of the OER electrode, i.e., the anode lifetime.2,17−19This is increasingly important because of the unclearfundamental understanding of related microscopic reactionmechanisms,20−23 especially for the electrocatalyst degradationprocess.24−26 Moreover, a durability evaluation for OERrequires a long time, typically several thousand hours, andoccasionally tens of thousands of hours.2 Therefore, reliablemethods to forecast anode lifetime in a short time frame areindispensable for accelerating the development of prospectiveelectrolyzers.Here we employ Bayesian data assimilation (DA) to obtainreliable interpretation of microscopic degradation mechanismReceived: October 16, 2024Accepted: November 15, 2024Letterhttp://pubs.acs.org/journal/aelccp© XXXX The Authors. Published byAmerican Chemical Society22https://doi.org/10.1021/acsenergylett.4c02868ACS Energy Lett. 2025, 10, 22−29This article is licensed under CC-BY-NC-ND 4.0Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on December 10, 2024 at 04:30:44 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Miao+Wang"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Akimitsu+Ishii"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Ken+Sakaushi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acsenergylett.4c02868&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?ref=pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?fig=tgr1&ref=pdfhttp://pubs.acs.org/journal/aelccp?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acsenergylett.4c02868?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://http://pubs.acs.org/journal/aelccp?ref=pdfhttps://http://pubs.acs.org/journal/aelccp?ref=pdfhttps://acsopenscience.org/researchers/open-access/https://creativecommons.org/licenses/by-nc-nd/4.0/https://creativecommons.org/licenses/by-nc-nd/4.0/https://creativecommons.org/licenses/by-nc-nd/4.0/https://creativecommons.org/licenses/by-nc-nd/4.0/https://creativecommons.org/licenses/by-nc-nd/4.0/and estimation of model parameters for lifetime forecasting.DA, a data-driven method, features a combination of a well-defined simulation model and dynamic experimental datathrough effective algorithms, such as an ensemble Kalman filteror a four-dimensional variational method.27,28 Consequently,DA has the ability to improve future forecast features andmodeling simultaneously. Typical applications of DA can befound in modern meteorology and oceanography, and we areinspired by successful implementation of DA in these fieldsresulting, for instance, in quite accurate and robust weatherforcasting.29−31 Recently, aiming to see the potential of DA inelectrochemistry, we employed an ensemble Kalman filter/smoother-based DA to understand microscopic mechanisms inelectrochemistry.32 As a result, we revealed a plausiblerelationship between the free energy of activation in the stepof oxygen adsorption and the change of slope in thepolarization curve of the oxygen reduction reaction, whichcould not be discovered by just a kinetic model. Hence, the DAmethod shows significant application potential in clarificationof the electrode process;33 this is a quite different from “blackbox” machine learning, which is somewhat unsatisfactorybecause of the problematic explanation of microscopicmechanisms.34Based on the above considerations, after inspecting possibleinfluences from the electrode−electrolyte interface on theperformance of the OER, in this work, we established apractical theoretical model to forecast the degradation processof the OER electrocatalysts with a DA method based on theelectrocatalyst dissolution process (Figure 1). As shown below,this DA-based method shows superior advantages over existingcomputational methods such as theoretical calculation basedon molecular dynamics, machine learning methods, or typicalfitting, as evidenced by quantitative comparison. Thus, thisapproach provides an alternative approach to drasticallyaccelerate electrochemical degradation testing. The OERdegradation model was built by focusing on dissolution ofelectrocatalysts with an energetic-span-model (ESM)-basedkinetic analysis.35−40 Through this degradation model, weachieved a dynamic forecast of the anode lifetime for the OERby iteratively conducting DAs with continuously updatedexperimental data. A model diagnosis was successfullyconducted according to the DA results, and the key issues ofthe present model were clarified with guidance for futuremodification. The proposed degradation model and thecoupling with data science in this study opens the way todurability exploration in oxygen electrocatalysis, which webelieve will benefit widely practical applications of electro-chemical techniques for renewable energies in the comingdecades.Considering electrochemical processes in the anode−electrolyte interface, we summarized possible effects onelectrocatalyst degradation, including (1) dissolution ofcatalyst, (2) agglomeration, (3) detachment of catalyst, (4)blocking effect by adsorption/(re)deposition, (5) bubbleblocking, (6) passivation, and (7) dissolution of sub-strate.26,41,42 During the above effects, the loss of active site(mainly by dissolution) was noteworthy under strong anodicOER conditions42−44 and thus was highlighted in this study(see more details in the discussion for Figure S1 in theSupporting Information (SI)). We described the OER activityaccording to the ESM-based kinetics35−39 and finally obtainedan equation set to quantify the degradation process towardOER (please refer to part 1 in the SI for details of thedegradation model):E I ck S tI R r t1ln( )( )app00 RWE,1= + +(1)S t k tSxx( )1( 1 )x xmax1 1/(1 )= +++ikjjjjjjikjjjjjy{zzzzzy{zzzzzz (2)where Eapp is the applied potential, α is the coefficient for theinfluence of potential on the intrinsic OER activity, I is theanode current, c is the current from the substrate (here termedsubstrate current), k0 is the pre-exponential factor for OER,S(t) is the active site number changing with time t, R0 is theinitial additional resistance (i.e., the resistance mainly byelectrolyte and substrate), rRWE,1 is the rate of resistance changedue to substrate passivation, k′ is the apparent dissolutioncoefficient (in this work termed dissolution factor), x′ is theapparent reaction order for dissolution, and Smax is the initialnumber of active sites.After formulating the OER electrocatalyst degradation viathe degradation model, we accessed the reliability byexperiments in a three-electrode configuration employingRuOx as the model electrocatalysts (Figure S3 in the SI).RuOx is widely accepted as a representative OER electro-catalyst due to its distinguished activity toward OER,45 andtherefore, it has been commonly employed in academia andFigure 1. Schematic diagram. (a) OER electrocatalyst degradationmechanism in an aqueous system. Here the dissolution of solidcatalyst is considered as the main driving force of degradation. (b)Integration of experimental data and theoretical model throughDA to forecast the anode lifetime in an assimilation−forecasting−diagnosis cycle: model parameters are regulated based on presentexperimental information and the lifetime is forecasted, followedby refreshing experimental data and updating the modelparameters through new assimilation toward improved forecast-ing; finally, highly accurate lifetime forecasting is achieved, withsubsequent model diagnosis for further modification.ACS Energy Letters http://pubs.acs.org/journal/aelccp Letterhttps://doi.org/10.1021/acsenergylett.4c02868ACS Energy Lett. 2025, 10, 22−2923https://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?fig=fig1&ref=pdfhttp://pubs.acs.org/journal/aelccp?ref=pdfhttps://doi.org/10.1021/acsenergylett.4c02868?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asindustry since the 1960s as the benchmark/model electro-catalyst in many studies in a wide pH range.46−48 In our work,we focus on the dissolution process of electrocatalysts uponOER because the dissolution of metallic species is well-knownas the main and common driving force of the intrinsicinstability of metal-oxide-based electrocatalysts.17,25,49,50 Fromthis viewpoint, RuOx is a particularly highly suitable materialfor our proof-of-concept to quantify the degradation process ofOER as the dissolution mechanism of RuOx during OER, i.e.,soluble Ru-species formation under anodic OER conditions,51is well investigated due to the aforementioned features of thismaterial. Therefore, herein, we chose RuOx as the model OERelectrocatalyst to make a model study. A polarization curve wasfirst collected by using RuOx as the electrocatalyst supportedon a Ti substrate for the OER (see more about the synthesis inExperimental Methods), showing a typical “exponential”relationship between the current of the OER and the potential(Figure 2a). To match the current−potential polarization, werewrote eq 1 by ignoring the substrate current (which waspretty small as compared with the current from RuOx; seemore discussion in Figure S4 in the SI) and setting t as 0,leading to the Butler−Volmer framework:52I I e F E E RT0( )/0 0= (3)where I0 is the exchange current density, α0 is the transfercoefficient, F is Faradaic efficiency, E0 is the equilibriumpotential for OER, R is gas constant, and T is the temperature.As a result, it fit well the experimental results (Figure 2a),further indicated by the close-to-unity adjusted R-square(Table S1 in the SI). As shown in the degradation model, itsuggested a strong correlation between the degradation and thechange of the time-dependent active site number (S(t)). Tosolidify this relationship, we used chronopotentiometry toevaluate the electrocatalyst degradation. It was evident thatwith the increase of applied potential (i.e., the degradation ofthe OER electrocatalyst), the active site number was decreased,as indicated by the trend of double-layer charging current inFigure 2b (see more details in Figure S5 in the SI).Following the above results, we applied the model to thedegradation of the OER electrocatalyst monitored bychronopotentiometry. It showed almost overlapped plots ofthe measured and the fitted curves, further proved by the close-to-unity adjusted R-square (Figure 2c, Table S2 in the SI). Thedegradation model suggested a negative logarithmic relation-ship between the applied potential and the active site number;thus, experimentally there was gradual increase of the appliedpotential initially (e.g., until 2 h in Figure 2c) and a subsequentfast growth (e.g., after 2 h in Figure 2c), accompanied by thecontinuous reduction of active site number. Further resultsshowed that our degradation model could not only be appliedto acid but also neutral and alkaline conditions (Figure S6 andTables S3 and S4 in the SI), various electrolyte concentrations(Figure S8 and Tables S11 and S12 in the SI), as well as highertemperatures (Figures S7 and S8c and Tables S5 and S13 inthe SI) and different current densities (Figure S9 and TablesS14−S16 in the SI). As for the electrocatalysts, apart from thebenchmark RuOx, the degradation of other transition-metal-based materials, such as MnOx, NiOx, FeOx, CoOx, and M (amulticomponent electrocatalyst including Mn, Ni, Fe, Zn, andAg, see the synthesis in Experimental Methods), could be wellquantified through our model (Figure 2d, Tables S6−S10 inthe SI).All in all, the satisfying consistency between theoreticaldescription and experimental data for the OER activity anddurability testing revealed the high reliability of ourdegradation model. This result was also consistent with theFigure 2. Verification of the degradation model. (a) Fitting of the polarization curve (1 mV s−1) of the OER by eq 3; electrolyte: 0.5 MH2SO4 at 35 °C. (b) The trend of active site number during the OER durability testing; lines: chronopotentiometry curve with the currentdensity fixed at 300 mA cm−2, and downward lines were from continuing the measurement after pause; spheres: double-layer chargingcurrents at 0.35 V (vs. Hg/Hg2SO4) with a scan rate of 100 mV s−1 after pausing the chronopotentiometry; electrolyte: 0.5 M H2SO4 at 35°C. (c) Fitting of the OER degradation curve (current density fixed at 300 mA cm−2) by the degradation model in 0.5 M H2SO4 at 35 °C and(d) application of the degradation model to other metal oxides (MnOx, NiOx, FeOx, CoOx) and a multicomponent material (including Mn,Ni, Fe, Zn, and Ag species, here noted as M) in 1 M KPi (pH 7) at 35 °C.ACS Energy Letters http://pubs.acs.org/journal/aelccp Letterhttps://doi.org/10.1021/acsenergylett.4c02868ACS Energy Lett. 2025, 10, 22−2924https://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?fig=fig2&ref=pdfhttp://pubs.acs.org/journal/aelccp?ref=pdfhttps://doi.org/10.1021/acsenergylett.4c02868?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asprevious reports about the depletion of electrocatalysts duringdurability testing.26,53After successfully displaying the versatile application of ourmodel in OER electrocatalyst degradation under variousconditions, we combined a data science-based approach, i.e.,the DA, to carry out dynamic lifetime forecasting to shortenthe time frame for degradation evaluation (see more details inExperimental Methods). The experimental data (spheres inFigure 3a) could be roughly divided into two parts: the slowand ultrarapid increases of applied potential. Transition fromthe slow to the ultrarapid indicated a process from sluggishdegradation to collapse. For convenience, we empirically setthe time at 1.91 V (vs. Hg/Hg2SO4), featuring steep changes ofapplied potentials, as the anode lifetimes for the results areshown in Figure 3a. It was evident that as the length ofassimilation window increased from 20% to 80% of the wholeperiod, the forecasted lifetime decreased from 5.54 to 3.18 h,approaching the experimental 3.24 h. A further comparisonwas conducted by monitoring the trend of the forecast error(the forecasted lifetime vs. the experimental lifetime; see moredetails in eq 10 in Experimental Methods). The decrease inthis forecast error from 71% to 2% clearly exhibited animproving forecast ability with updating the degradation data(spheres in Figure 3b). This was further verified by thereducing trend of deviation for the forecasted lifetime(rhombuses in Figure 3b). We further carried out DAs fordegradation processes with other lifetimes to show thecapability of our DA-based method (Figure S10 in the SI).Next, we carried out a model diagnosis (see the details inFigure S11 in the SI). We found that even under thesimplification the degradation model still worked well, and thedissolution factor (k′) was crucial to achieving accurate lifetimeforecasting.To demonstrate the practical applicability of DA, by using ashort assimilation window (34% of the whole period, i.e., 300h), the lifetime (at 2.5 V) was accurately forecasted with asmall error of 4% for the nearly 1000 h durability testing(Figure 3c). For further highlighting the DA in lifetimeforecasting, we carried out simple fittings by using various datalengths for comparison (Figure 3c; Figure S14 and TablesS18−S23 in the SI; see also Experimental Methods). In thecase of using experimental data up to 300 h, the predictionerror by simple fitting was much larger (60%, Figure S15 in theSI) than that of DA (4%). Moreover, the fitting approachrequired experimental data up to approximately the same timeas the lifetime to forecast as accurately as the DA (Figure S15in the SI). Such superior forecast ability by DA to simple fittingdemonstrated better parameter optimization of DA. This couldbe attributed to the Bayesian inference in DA, making it skilledat optimizing model parameters for reliable lifetime forecastingespecially with nonuniform uncertainties (as indicated by thefluctuations of the experimental data in Figure 3c). In addition,even though it is known that several modern computation-based approaches, typically molecular dynamics simulation ormachine learning, enable determining model parameters, thesemethods still suffer from the limitation of short time scale orhigh cost of preparing massive training data sets.54,55Therefore, our approach employing DA is more promisingand practically useful than the existing typical approaches inforecasting the anode lifetime with optimized modelparameters by the OER degradation model (see a detaileddiscussion on pages 26 and 27 and Figure S13 in the SI).Figure 3. DAs for the OER electrocatalyst degradation. (a) Dynamically forecasting the lifetime of the OER anode with various assimilationwindows (from 20% to 80% of the whole experimental period); experimental conditions: 0.5 M H2SO4 at 35 °C under 300 mA cm−2, withRuOx as the electrocatalyst for the OER. (b) Trend of the forecast error (spheres in the plots: the forecasted lifetime vs. the experimentallifetime; see more in eq 10 in Experimental Methods) with various assimilation windows from 20% to 80% of the whole measurement period(noted as tend/tmax, in which tend is the length of assimilation window and tmax is the whole period of experiment), and deviations of theforecasted lifetime (rhombuses in the plots). (c) Lifetime forecasting for long-term durability by DA with 34% of the whole data as well asthe forecasting based on simple fitting by using the same data length; experimental conditions: 0.1 M sodium carbonate (pH 9.2) at 80 °Cunder 100 mA cm−2, with RuOx as the electrocatalyst for the OER.ACS Energy Letters http://pubs.acs.org/journal/aelccp Letterhttps://doi.org/10.1021/acsenergylett.4c02868ACS Energy Lett. 2025, 10, 22−2925https://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsenergylett.4c02868?fig=fig3&ref=pdfhttp://pubs.acs.org/journal/aelccp?ref=pdfhttps://doi.org/10.1021/acsenergylett.4c02868?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asOur method is based on a mechanism with a singledegradation driving force, i.e., the dissolution-driven degrada-tion, leading to some limitations such as the difficulty intreating degradation by other mechanisms (see furtherdiscussions on the limitations of our method on page 26 andin Figure S16 in the SI). Nonetheless, our knowledge-contained model enables satisfying interpretability for thematched anode degradation process (see a detailed discussionin Figure S17 in the SI). In addition, given a comprehensivedegradation model including multiple degradation processes, itis possible to clarify the dominant degradation mechanismbased on the DA method proposed in this study. For example,after determining all the parameters at a time t in a model byDA, we can analyze the partial derivative of the model withrespect to t for each degradation mechanism. As a result, wewill obtain a quantitative evaluation of the influence of eachdegradation mechanism on the overall degradation behavior.By comparing the above results, we can finally confirm that themaximum absolute partial derivative (and much larger thanothers) corresponds to the dominant degradation mechanism.Moreover, this method can identify a dynamic dominantdegradation mechanism that evolves with the degradationprocess because of the inclusion of time. Based on the aboveconsideration and inspired by control function (or controlfactor) and degree of rate control for quantifying the rate-determining step in chemical kinetics,56,57 herein we proposedegree of degradation control, i.e., rd,i(t), to quantify the influenceof degradation mechanisms on stability:r tR tR t( )( )( )iii id,d,d,=| | (4)where Rd,i(t) is the influence on the overall degradation by theith degradation mechanism at time t. We may also extend thisconcept to not only degradation but also upgradation (i.e., thepromotion of electrode performance), which are furtherunified by the term “destabilization” so that degree ofdestabilization control can be nominated. For a detaileddiscussion, including a complete mathematical description,please refer to part 3 and eqs S33−S35 in the SI.In summary, we conducted a quantification of OERelectrocatalyst degradation with a data-driven approach.Based on the energetic-span kinetic framework, we establishedan effective electrocatalyst degradation model for the OER,which was further verified by experimental results with variousconditions and electrocatalysts. The subsequent application ofthis degradation model was iteratively implemented by using aDA method, achieving dynamic lifetime forecasting throughcontinuous updating of degradation data. This approach led torobust and accurate multidimensional parameter optimization,with clear advantages over existing computational methods, asevidenced by quantitative comparison. We launched a modeldiagnosis based on DA to track the key parameters. Thisdiagnosis indicated that even though the degradation modelsimplified both the kinetics of the OER and the process ofactive site loss, it was still accessible to reliable lifetimeforecasting based on the DA method. We believe that theclosed-loop study of this work by a data-driven approach,including theory establishment and verification, application,and model diagnosis, will benefit the understanding of OERelectrocatalyst degradation and accelerate the rational develop-ment of highly efficient electrodes, especially with long-termstabilities, for electrochemistry-based technologies in thecrucial next few decades to achieve carbon neutrality.■ EXPERIMENTAL METHODSChemicals. RuCl3·xH2O (Ru > 40%) was purchased fromTokyo Chemical Industry Co., Ltd. MnCl2·4H2O (99.0%),NiCl2·6H2O (98.0%), FeCl2·4H2O (99.0%), AgNO3 (99.8%),KH2PO4 (>99.5%), KOH (>85%), and ethanol (99.5%) werefrom Wako Fuji Co. Ltd. ZnCl2 (99.95%) was purchased fromAlfa Aesar. CoCl2 6H2O (99.0%) was purchased from HayashiPure Chemical Ind., Ltd. H2SO4 (96.0%) was from KANTOCHEMICAL CO.,INC. Ultrapure water (18.2 MΩ·cm, Milli-QIQ Element, Merck AG, Germany) was used to prepareelectrolytes.Pretreatment of Ti foil. The titanium (Ti) foil (Ti, 99.5%,Nilaco, 0.05 × 5 × 30 mm) was cleaned by ethanol andultrapure water and subsequently etched in an oxalic acidsolution (10%) at 80 °C for 1 h. Finally, the Ti foil was rinsedby ultrapure water and dried in air.Synthesis of RuOx. A precursor solution (0.05 M RuCl3 inethanol) was dropped (2.5 μL) on the pretreated Ti substrate(dropped region 5 × 10 mm) and subsequently annealed at350 °C for 10 min in air. The above process was repeatedanother nine times and finally annealed at 460 °C for 70 min inair.Synthesis of MOx (M = Mn, Ni, Fe, Co). Similar methodswere used for the synthesis of RuOx, apart from that theprecursor was replaced by MnCl2, NiCl2, FeCl2, and CoCl2,respectively.Synthesis of Multicomponent Oxide (M). A silverprecursor solution (0.05 M AgNO3 in ethanol) was dropped(0.5 μL) on the pretreated Ti substrate, followed by droppinga mixture (2.0 μL, totally 0.05 M metal species in ethanol bymixing MnCl2, NiCl2, FeCl2, and ZnCl2) of a molar ratio of1:1:1:0.5 for Mn:Ni:Fe:Zn. After being dried, it was annealedat 350 °C for 10 min in air.58 The above process was repeatedanother nine times, with final annealing at 460 °C for 70 minin air. The obtained catalyst on the Ti substrate was marked asM. The detailed method can be found in the reference.Electrochemical Measurements. A three-electrode con-figuration in a water bath at 35 °C was used, withelectrocatalysts on the pretreated Ti substrate as the workingelectrode; Pt coil as the counter electrode; and Hg/Hg2SO4(saturated K2SO4), Ag/AgCl (3 M NaCl), and Hg/HgO (1 MKOH) as the reference electrode for acid, neutral, and alkalielectrolyte, respectively (see more details in Figure S3 in theSI). Linear sweep voltammetry (LSV) was carried out with ascan rate of 1 mV s−1 if not specified. A chronopotentiometry(CP) method was conducted at fixed current densities for theevaluation of the degradation processes.In the long-term stability testing, 0.1 M sodium carbonate(pH 9.2) was used as the electrolyte at 80 °C in a heatingmantle, with RuOx as the electrocatalyst on a pretreated Tisubstrate for the OER, a Pt coil as the counter electrode, andAg/AgCl (3 M KCl) as the reference electrode. Achronopotentiometry (CP) method was conducted to accessthe degradation process after the aging period.Double-layer charging currents were used to monitor thetrend of active site number during the degradation process by acyclic voltammetry (CV) method. The CV tests were carriedout with a scan rate of 100 mV s−1 in 0.30−0.40 V (vs. Hg/Hg2SO4) after the CP measurement. The half of the differencebetween the current in the anodic scan (Ja) and the current inACS Energy Letters http://pubs.acs.org/journal/aelccp Letterhttps://doi.org/10.1021/acsenergylett.4c02868ACS Energy Lett. 2025, 10, 22−2926https://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsenergylett.4c02868/suppl_file/nz4c02868_si_001.pdfhttp://pubs.acs.org/journal/aelccp?ref=pdfhttps://doi.org/10.1021/acsenergylett.4c02868?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asthe cathodic scan (Jc) at 0.35 V (vs. Hg/Hg2SO4) served as thetypical double-layer charging currents.Data Assimilation (DA). A nonsequential data assimilationmethod minimizing the cost function using tree-structuredParzen estimator (DMC-TPE), was used for the OERdegradation process in this work.28 For the DAs, at time t astate vector xt (0 < t ≤ tend, where tend represents the length ofthe assimilation window) was defined, including the appliedpotential and its first-order derivative with respect to time. Thext is expressed asEEtx ,ddt ttappappT= |ÄÇÅÅÅÅÅÅÅÅÅÅÅÅÉÖÑÑÑÑÑÑÑÑÑÑÑÑ (5)where the superscript T represents for the transposition. In thisstudy, xt could be calculated asM tx x( , )t 0= (6)where M indicates the degradation model and x0 is a vectorconsisting of the parameters of the model to be estimated.Moreover, at time t we defined the observation vector yt,which contained the experimentally collected applied potentialand its first-order derivatives with time. Notably, both xt and ytwere treated as stochastic variables in DA. The cost functionJ(x0) to evaluate the misfit between xt and yt was expressed asJM t y M tx x x B x xx R x y( )12( ) ( )12( ( , ) ) ( ( , ) )b bttt t t0 0 0T 10 00T 10end=+(7)in which x0b is the background vector. B and Rt are thecovariance matrices of the background and observation errors,respectively. When the optimal vector x0a that minimizes J(x0)was obtained, the corresponding state vector xt = M(x0a, t) wasregarded as the optimal forecast. The coefficients in thedegradation model a, k0, and k′ were estimated in the DAs.The parameter x′ was fixed as 0.01 to release the parameter k′during the DAs. In this study, we conducted five DAs in whichthe length of the assimilation window tend was varied in ratiosof 20%, 33%, 50%, 66%, and 80% as compared with the wholeperiod of the experiment, tmax. Because the DMC-TPE methoddepends on random numbers, the estimated parameters foreach tend were evaluated with the mean and standard deviation(SD) obtained from five results of DA using different randomseed. In the DA for tend = 0.2tmax, the first term of eq 7 wasneglected because of the difficulty in determining x0b and B. Inall other DAs, x0b and B were determined based on the meansand SDs of one previous DA result: x0b = [ma, mk0, mk′]T and B= diag[σa, σk0, σk]. Note that in our DAs, x0b and B would notsignificantly affect the estimation results because the first termof J(x0) is sufficiently small compared to the second term. Rtwas defined as Rt = [σt2, σt′2], where σt and σt’ denoteparameters which determine the magnitude of the observa-tional noises in Eapp and dEapp/dt, respectively. By assumingthat the more recent data more strongly reflect an increase inEapp, σt and σt′ are defined as follows:t t0.0002( ) 0.0001t end= + (8)t t0.01( ) 0.005t end= + (9)The forecast error (%) was calculated byforecast errorforecasted lifetime experimental lifetimeexperimental lifetime100= ×(10)For the long-term durability testing, to diminish detrimentaleffects from noises, σt and σt’ are defined as follows:t t( , )(0.001, 0.05), if 150 or 340 360(0.0001, 0.005), otherwiset t =<