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Tafel Slope Analyses for Homogeneous Catalytic Reactions catalysts Article Tafel Slope Analyses for Homogeneous Catalytic Reactions Qiushi Yin, Zihao Xu , Tianquan Lian, Djamaladdin G. Musaev, Craig L. Hill and Yurii V. Geletii * Department of Chemistry, Emory University, Atlanta, GA 30322, USA; [email protected] (Q.Y.); [email protected] (Z.X.); [email protected] (T.L.); [email protected] (D.G.M.); [email protected] (C.L.H.) * Correspondence: [email protected] Abstract: Tafel analysis of electrocatalysts is essential in their characterization. This paper analyzes the application of Tafel-like analysis to the four-electron nonelectrochemical oxidation of water by 3+ the stoichiometric homogeneous 1-electron oxidant [Ru(bpy)3] to dioxygen catalyzed by homoge- 10− 10– neous catalysts, [Ru4O4(OH)2(H2O)4(γ-SiW10O36)2] (Ru4POM) and [Co4(H2O)2(PW9O34)2] (Co4POM). These complexes have slow electron exchange rates with electrodes due to the Frumkin effect, which precludes the use of known electrochemical methods to obtain Tafel plots at ionic 3+/2+ strengths lower than 0.5 M. The application of an electron transfer catalyst, [Ru(bpy)3] , in- creases the rates between the Ru4POM and electrode, but a traditional Tafel analysis of such a complex system is precluded due to a lack of appropriate theoretical models for 4-electron pro- cesses. Here, we develop a theoretical framework and experimental procedures for a Tafel-like 3+ analysis of Ru4POM and Co4POM, using a stoichiometric molecular oxidant [Ru(bpy)3] . The dependence of turnover frequency (TOF) as a function of electrochemical solution potential created 3+ 2+ by the [Ru(bpy)3] /[Ru(bpy)3] redox couple (an analog of the Tafel plot) was obtained from kinetics data and interpreted based on the suggested reaction mechanism. Keywords: Tafel; polyoxometalate; water oxidation; stopped-flow; kinetics; catalyst comparison Citation: Yin, Q.; Xu, Z.; Lian, T.; 1. Introduction Musaev, D.G.; Hill, C.L.; Geletii, Y.V. Tafel slope analysis has become increasingly popular in this era of solar fuels research Tafel Slope Analyses for and photoelectrochemistry [1–6]. This study addresses the possibility of constructing Tafel Homogeneous Catalytic Reactions. plots for homogeneous catalytic multielectron redox processes and the usefulness of this Catalysts 2021, 11, 87. https:// approach. The model homogeneous reaction we have chosen for this study is the oxidation doi.org/10.3390/catal11010087 of water in Equation (1). − − ! + Received: 25 December 2020 2 H2O 4 e O2 + 4 H (1) Accepted: 8 January 2021 + − 2 H + 2 e ! H2 (2) Published: 11 January 2021 2 H2O ! O2 + 2H2 (3) Publisher’s Note: MDPI stays neu- Equation (1) is very unfavorable thermodynamically and requires an external source tral with regard to jurisdictional clai- of energy such as electricity or light (e.g., solar). The overall reaction of water splitting, ms in published maps and institutio- Equation (3), includes two half-reactions, water oxidation and reduction, Equations (1) and nal affiliations. (2), respectively, which proceed in spatially separated sites: The reverse reaction in Equation (3) takes place in fuel cells to directly convert chemical energy into electricity. Copyright: © 2021 by the authors. Li- In electrochemistry, the potential applied between the cathode and anode and the censee MDPI, Basel, Switzerland. current is measured. Commonly, the empirically formulated Tafel relation in Equation (4) This article is an open access article is used to compare the electrocatalytic activities: distributed under the terms and con- ditions of the Creative Commons At- η = a + b log(i) (4) tribution (CC BY) license (https:// creativecommons.org/licenses/by/ where η = E − E0 is the difference between the electrode and standard potentials, i is the 4.0/). current density, and b is the Tafel slope. Catalysts 2021, 11, 87. https://doi.org/10.3390/catal11010087 https://www.mdpi.com/journal/catalysts Catalysts 2021, 11, x FOR PEER REVIEW 2 of 11 Catalysts 2021, 11, 87 2 of 11 where η = E − E0 is the difference between the electrode and standard potentials, i is the current density, and b is the Tafel slope. The utility of Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energyThe conversion utility of has Tafel been slopes reported from a [1,2]. microkinetic However, analysis numerous of aqueous simplifications electrocatalysis and as- for sumptionsenergy conversion in the derivation has been of reportedEquation [ 1(4),2]. leads However, to an incomplete numerous simplificationsdescription of the and ac- as- tualsumptions surface kinetics in the derivation and makes of Equationthe applicability (4) leads of to Tafel an incomplete analysis questionable description [2,3,7,8]. of the actual In manysurface cases, kinetics homogeneous and makes systems the applicability are simpler of Tafeland easier analysis experimentallyquestionable [for2,3 understand-,7,8]. In many ingcases, the reaction homogeneous mechanism. systems Therefore, are simpler we anddeveloped easier experimentallya protocol to construct for understanding Tafel-like plotsthe reactionfor homogeneous mechanism. reactions Therefore, and studied we developed the usefulness a protocol of such to construct plots to Tafel-likebetter under- plots standfor homogeneous the reaction mechanism. reactions and In studied addition, the while usefulness extensive of such mechanistic plots to better analyses understand of mo- lecularthe reaction redox systems mechanism. have In been addition, conducted while prev extensiveiously, mechanisticmany aspects analyses still need of to molecular be pre- ciselyredox addressed systems have[9]. Generally been conducted speaking, previously, the Tafel-like many plot aspects is one still among need tomultiple be precisely ap- proachesaddressed that [9 link]. Generally the kinetic speaking, and thermodyna the Tafel-likemic properties plot is one of among such a multiple catalytic approaches system. thatBoth link half the kineticreactions, and Equations thermodynamic (1) and properties (2), are complex of such multielectron a catalytic system. processes cata- lyzed byBoth transition half reactions, metal complexes. Equations Each (1) and one (2), is routinely are complex studied multielectron individually processes [6,10–12]. cat- Stablealyzed homogeneous by transition metalmolecular complexes. catalysts Each are one ideally is routinely suited studied for studies individually of the reaction [6,10–12 ]. mechanismStable homogeneous and the relationship molecular catalystsbetween arereaction ideally kinetics suited forand studies thermodynamics. of the reaction Indeed, mecha- previousnism and studies the relationship on redox betweenand chemical reaction catalysts kinetics in and different thermodynamics. catalytic systems Indeed, have previous al- readystudies provided on redox theoretical and chemical tools catalystsfor mechanis in differenttic analyses catalytic [9]. More systems recently, have already Costentin pro- vided theoretical tools for mechanistic analyses [9]. More recently, Costentin and Savéant and Savéant thoroughly analyzed the applicability of the Tafel equation to the homoge- thoroughly analyzed the applicability of the Tafel equation to the homogeneous molecular neous molecular catalysis of electrochemical CO2 and O2 reduction [13]. In this work, we catalysis of electrochemical CO and O reduction [13]. In this work, we describe a protocol describe a protocol for deriving2 a Tafel-like2 plot based on theoretical and experimental for deriving a Tafel-like plot based on theoretical and experimental grounds to relate the grounds to relate the reaction rate with the solution electrochemical potential for homo- reaction rate with the solution electrochemical3+ potential for homogeneous water oxida- geneous water oxid3+ation by [Ru(bpy)3] , catalyzed by the stable molecular tetraruthe- tion by [Ru(bpy)3] , catalyzed by the stable molecular tetraruthenium polyoxometalate nium polyoxometalate [Ru4O4(OH)2(H2O)4(γ-SiW10O36)2]10−, Ru4POM. This POM was the [Ru O (OH) (H O) (γ-SiW O ) ]10−, Ru POM. This POM was the first fully inorganic first 4fully4 inorganic2 2 4 (carbon-free),10 36 2 thus oxidatively4 robust, water oxidation catalyst (carbon-free), thus oxidatively robust, water oxidation catalyst (WOC), which is also hy- (WOC), which is also hydrolytically stable over a wide pH range (pH 1–9) [14,15]. Detailed drolytically stable over a wide pH range (pH 1–9) [14,15]. Detailed electrochemical studies electrochemical studies of this complex showed that the rates of electron exchange be- of this complex showed that the rates of electron exchange between an electrode and the tween an electrode and the complex is sluggish under typical catalytic turnover conditions complex is sluggish under typical catalytic turnover conditions [14,16]. As a result, neither [14,16]. As a result, neither the Tafel plot nor the exchange current density, i0, can be meas- the Tafel plot nor the exchange current density, i0, can be measured experimentally. At the uredsame experimentally. time, the catalyst At the shows same excellent time, the activity catalyst in shows homogeneous excellent aqueous activity solutionsin homogene- when ous aqueous solutions when stoichiometric oxidants 3+such as Ce(IV) or [Ru(bpy)3]3+ are stoichiometric oxidants such as Ce(IV) or [Ru(bpy)3] are used. The question was posed used.as to The whether question data was collected posed in as homogeneous to whether data multielectron collected in processes homogeneous can be multielectron used to obtain processesa Tafel-like
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