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 processes. 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 conditions 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 catalyzed 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 provided 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 can plot. be used This studyto obtain addresses a Tafel-like that questionplot. This and study aims addresses to focus on that the question adaptation and of aimsan analog to focus of on traditional the adaptation Tafel plots of an to analog the four-electron of traditional water Tafel oxidation plots to processthe four-electron specific to waterhomogeneous oxidation species.process specific to homogeneous species.

2.2. Results Results and and Discussion Discussion 2.1.2.1. Theoretical Theoretical Considerations Considerations Here,Here, we we assume assume that that water water oxidation oxidation in in homogeneous homogeneous conditions conditions proceeds proceeds through through fourfour fast fast Nernstian Nernstian reversible reversible electron electron transfertransfer stepssteps followedfollowed byby the the irreversible irreversible O O2 forma-2 for- mationtion step, step, Equations Equations (5–8), (5–8), where where C0C0 isis thethe restingresting oxidation state state of of the the catalyst, catalyst, C, C, and and C1–C4C1–C4 are are the the one- one- to to four-electro four-electronn oxidized oxidized forms forms of of the the catalyst. catalyst.

oo C0C0− − e ⇄ C1 E E 1 (5)(5)

C1 − e ⇄ C2 Eoo2 (6) C1 − e C2 E 2 (6) C2 − e ⇄ C3 Eoo3 (7) C2 − e C3 E 3 (7)

C3 − e ⇄ C4 Eoo4 (8) C3 − e C4 E 4 (8)

2 ⟶ 2 + o C4C4 ++ 22 HH2OO → C0C0 ++ OO2 + 4 H ko (9)(9) If the Ifequilibria the equilibria are fast, are fast,then then an applied an applied and and electrochemical electrochemical solution solution potential, potential, E, E, is is linkedlinked via via the the Nernst Nernst equation, equation, Equation Equation (10): (10):

o o o E − E 1 = (RT/F) × ln([C1]/[C0]), E − E 2 = (RT/F) × ln([C2]/[C1]), E − E 3 = (RT/F) × ln([C3]/[C2]), o (10) E − E 4 = (RT/F) × ln([C4]/[C3]),

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where R is the universal gas constant, T is the temperature, and F is the Faraday constant. The concentration of the catalyst in oxidation state i = 0 − 4 is described by a distribution function, Equation (11):

i o 1 o 2 o αi = [Ci]/[Ct] × [exp(F(iE − ∑0 Ei )/RT)]/[1 + exp[F(E − ∑0 Ej )/RT] + exp[F(2E − ∑0 Ej )RT] 3 o 4 o (11) + exp[F(3E − ∑0 Ej )/RT] + exp[(4E − ∑0 Ej )/RT],

where [Ct] = total concentration of the catalyst. If a stoichiometric oxidant is used as a sacriﬁcial electron acceptor, the Nernst law gives the applied potential equal to the solution potential. Here, we consider the case 3+ 2+ when [Ru(bpy)3] , Ru3, is an oxidant (Ru2 represents [Ru(bpy)3] ). The electrochemical solution potential, E, created by this oxidant is:

E = E0 + 0.059 × log ([Ru3]/[Ru2]) = E0 + 0.059 × log ([Ru3]/([Ru3]o − 0 10 0 10 (12) [Ru2]+[Ru2]o)),

0 where E 0 = 1.26 V (SHE) is the standard reduction potential of the Ru3/Ru2 couple, and [Ru3]o and [Ru2]o are the initial concentrations of Ru3 and Ru2, respectively. If the rate limiting step is Equation (9), then the reaction rate (current) is:

−d[Ru3]/dt = 4ko[C4] = TOFapp × [Ct] (13)

and the apparent turnover frequency (TOFapp) with respect to Ru3 consumption is:

TOFapp = 4α4 ko (14)

Here, ko is the rate constant for the oxidation of water. The value of the distribution factor, α4 is time-dependent and can be determined from Equations (10) and (11), and TOFapp is a kinetic parameter. The full equation linking TOFapp and apparent potential is complex, but can be simpliﬁed if ko is known and [Ru2]o = 0, Equation (15):

0 log10(TOFapp) ≈ log10(4ko) + E 0 + 0.059 × log10 ([Ru3]/([Ru3]o − [Ru3])) − 4E (15)

At high applied potentials, [C4] ≈ [Ct] and TOFapp reaches a plateau with the value 4ko. This value is the maximum turnover frequency (TOF) achievable by a given catalyst. This is an intrinsic property of a catalyst and its associated turnover activity. However, TOF0 of a certain catalytic system can be achieved at different potentials, ETOF. As a result, the catalytic activity of two systems cannot be compared by a single number such as TOF0. Two parameters, TOF0 and ETOF, are required to describe the catalytic activity. The slope of the Tafel-like plot at moderate potentials is a complex dependence of the catalyst reduction potentials and the Ru3 concentration. In our homogeneous catalytic system, Ru3 is used as a stoichiometric electron acceptor. Ru3 can also be generated in situ in a photoinduced 2− reaction of Ru2 with persulfate, S2O8 , or electrochemically.

2.2. Homogeneous Electrochemical Reactions in the Presense of an Electron Transfer Catalyst As the electron transfer from Ru4POM to the electrode is slow, we attempted to accelerate the overall reaction with the addition of an electron transfer catalyst. The stability of Ru3 is well documented to increase at lower pH. Therefore, the cyclic voltammetry (CV) was recorded at a slightly lower pH of 7.2. The CV of Ru3/Ru2 has an almost ideal shape with an anodic-cathodic peak separation of 69 mV and a ratio of anodic and cathodic current close to 1; E1/2 = 1.26 V (versus SHE) in 80 mM sodium phosphate buffer at pH 7.2. The addition of 15 µM of Ru4POM to 1.0 mM Ru2 results in a slight increase in anodic current (Figure1), indicating that the reaction between Ru3 and Ru4POM takes place. At higher concentration, Ru4POM forms an insoluble adduct with Ru2, which does not allow CV measurements over a broad range of catalyst concentrations. A foot of the wave analysis cannot be applied, as no catalytic current is CatalystsCatalysts 20212021, 11, 11, x, 87FOR PEER REVIEW 4 of4 of11 11 Catalysts 2021, 11, x FOR PEER REVIEW 4 of 11

system [17]. The CV simulation with the SIM4YOU software package using the heteroge- systemseen [17]. in this The system CV simulation [17]. The with CV simulationthe SIM4YOU with software the SIM4YOU package software using the package heteroge- using neous electron transfer reaction rate constant 0.065 cm s−1 (measured −in1 0.1 M H2SO4) [18] neousthe electron heterogeneous transfer electron reaction transfer rate constant reaction 0.065 rate cm constant s−1 (measured 0.065 cm in s 0.1(measured M H2SO4) in [18] 0.1 M for Ru3 and a glassy carbon electrode (surface area is 0.0668 cm2) is in good 2agreement for HRu32SO and4)[ 18a ]glassy for Ru3 carbon and aelectrode glassy carbon (surface electrode area is (surface 0.0668 cm area2) is is in 0.0668 good cm agreement) is in good with the experiment under the assumption of irreversible oxidation of Ru3 at the electrode withagreement the experiment with theunder experiment the assumption under of the irreversible assumption oxidation of irreversible of Ru3 at oxidation the electrode of Ru3 at a potential of 1840 mV vs. SHE (Figure 1). The simulation results in the presence of at aat potential the electrode of 1840 at amV potential vs. SHE of (Figure 1840 mV 1). vs.The SHE simulation (Figure 1results). The simulationin the presence results of in Ru4POM is also in reasonable agreement with the experiment when the reaction mecha- Ru4thePOM presence is also ofin Rureasonable4POM is agreement also in reasonable with the agreementexperiment with when the the experiment reaction mecha- when the nism and rate constants described below are applied. Clearly, simple cyclic voltammo- nismreaction and rate mechanism constants and described rate constants below describedare applied. below Clearly, are applied. simple Clearly,cyclic voltammo- simple cyclic grams do not provide much information on Ru4POM redox potentials. gramsvoltammograms do not provide do much not provide information much on information Ru4POM redox on Ru potentials.4POM redox potentials.

FigureFigure 1. 1.CyclicCyclic voltammograms voltammograms of of1.0 1.0 mM mM [Ru(bpy) [Ru(bpy)3]Cl2]Cl in 80in mM 80 mM sodium sodium phosphate phosphate at pH at 7.2 pH 7.2 Figure 1. Cyclic voltammograms of 1.0 mM [Ru(bpy)3]Cl2 3in 802 mM sodium phosphate at pH 7.2 (red) and in the presence of 15 μµM Ru4POM (blue); the simulated curves are dotted lines. Scan (red)(red) and and in the in thepresence presence of 15 of μ 15M RuM 4RuPOM4POM (blue);(blue); the thesimulated simulated curves curves are aredotted dotted lines. lines. Scan Scan rate, rate, 100 mV/s; potential versus SHE. rate,100 100 mV/s; mV/s; potentialpotential versusversusSHE. SHE. 2.3.2.3. Linear Linear Sweep Sweep Voltammetry Voltammetry 2.3. Linear Sweep Voltammetry LinearLinear sweep sweep voltammetry voltammetry (LSV) (LSV) at atvery very low low scan scan rate rate with with vigorous vigorous stirring stirring of of the the Linear sweep voltammetry (LSV) at very low scan rate with vigorous stirring of the solutionsolution is iscommonly commonly used used to obtain to obtain the thedepen dependencedence of the of potential the potential as a function as a function of the of solution is commonly used to obtain the dependence of the potential as a function of the logarithmthe logarithm of the of current the current (Tafel (Tafel equation). equation). The experimental The experimental LSV curves LSV curves are shown are shown in in logarithm of the current (Tafel equation). The experimental LSV curves are shown in FigureFigure 2a.2a. We We then then plotted plotted the the applied applied potential potential (in (in the the range range 900–1200 900–1200 mV) mV) as as a a function function Figure 2a. We then plotted the applied potential (in the range 900–1200 mV) as a function ofof the the current current normalized normalized per per concentration concentration of of added added [Ru [Ru4POM4POM] (an] (an analog analog of of TOF) TOF) in in of the current normalized per concentration of added [Ru4POM] (an analog of TOF) in FigureFigure 2b.2b. Figure 2b.

(a) (b) (a) (b) Figure 2. (a) Linear sweep voltammograms with stirring at a scan rate 3.0 mV/s of 1.0 mM FigureFigure 2. (a) 2. Linear(a) Linear sweep sweepvoltammograms voltammograms with stirring with at stirring a scan atrate a scan3.0 mV/s rate of 3.0 1.0 mV/s mM of 1.0 mM [Ru(bpy)3]Cl2 in 80 mM sodium phosphate at pH 7.2. [Ru4POM]: 0 (black), 5 (red), 10 (blue), and [Ru(bpy)[Ru(bpy)3]Cl23 in]Cl 802 inmM 80 sodium mM sodium phosphate phosphate at pH 7.2. at pH [Ru 7.2.4POM [Ru]: 04 POM(black),]: 05 (black),(red), 10 5 (blue), (red), and 10 (blue), 15 μM (green and orange); (b) Tafel plot in the range of potentials between 900 and 1200 mV. 15 μandM (green 15 µM and (green orange); and orange);(b) Tafel ( bplot) Tafel in the plot range in the of range potentials of potentials between between 900 and 900 1200 and mV. 1200 mV. The “Tafel slope” in the range of potentials between 900 and 1200 mV is ~120 mV/dec- TheThe “Tafel “Tafel slope” slope” in inthe the range range of ofpotentia potentialsls between between 900 900 and and 1200 1200 mV is ~120 mV/dec- mV/decade ade(Figure (Figure2) for 2) threefor three different differentRu POMRu4POMconcentrations. concentrations. Based Based on the on formal the formal interpretation interpre- of ade (Figure 2) for three different Ru4 4POM concentrations. Based on the formal interpretation of the Tafel equation, this slope is consistent with α = 0.5 and a one-electron process. tationthe of Tafel the equation,Tafel equation, this slope this isslope consistent is consistent with α with= 0.5 α and = 0.5 a one-electronand a one-electron process. process. However,

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as the theory of such measurements is not yet developed for a homogeneous WOC system, the meaning of this slope value is unclear.

2.4. Tafel Plot from Kinetic Curves in Homogeneous Systems The kinetics of water oxidation by Ru3 can be followed either by measuring oxygen formation or by the consumption/formation of Ru3/Ru2. The consumption of Ru3 can be followed by a decrease in absorbance at 670–680 nm (ε = 420 M−1cm−1)[14]. The reaction is fast and requires a stopped-flow instrument to collect high-quality kinetics data. The experimental details were described in our previous publications [14,19]. Both Ru2 and Ru4POM slightly absorb light at 680 nm, which must and can be taken into account for quantitative analysis of raw experimental data. Here for simplicity, a kinetic curve of [Ru3] consumption versus time is the decrease in absorbance at 680 nm. At a given time t, the reaction rate can be approximated as d[Ru3]/dt ≈ ([Ru3](t − ∆t) − [Ru3]t + ∆t))/2∆t and TOFap = (d[Ru3]/dt)/[Ct] can be quantified ([Ct] is the total concentration of Ru4POM). We make the reasonable assumption, based on our earlier studies, that the reaction mechanism is Equations (5)–(9). If reversible reactions are in equilibrium and [Ct] << [Ru3], then the electrochemical solution potential at time t can be calculated from the Nernst equation 0 0 E = E 0 + 0.059 × log10(([Ru3]t/([Ru3]0 − [Ru3]t)), where E 0 = 1.26 V is the standard reduction potential of the [Ru3]/[Ru2] couple, and [Ru3]0 is the initial concentration of Ru3. As Ru3/Ru2 and Ru4POM have large and opposite charges, their reduction potentials and the rates of their intermolecular reactions are ionic-strength-dependent. In order to keep pH constant, the use of buffered solutions is required. However, even low concentrations of sodium phosphate buffer (e.g., 25 mM) create a high ionic strength (µ ~ 75 mM). Therefore, in this work, we use the experimentally determined value of the reduction potential for the Ru2/Ru3 couple as the reference point in all calculations (e.g., 1.06 V versus 3.0 M NaCl Ag/AgCl reference electrode). We define TOF as (d[Ru3]/dt)/[Ct]. This procedure converts a single kinetic curve to the dependence of TOF on applied potentials. The self-decomposition of Ru3 is relatively slow at pH 7.0–8.0, and the O2 yield approaches 80% of the theoretical value at [Ru4POM] > 5 µM. Therefore, the kinetics 3+ of [Ru(bpy)3] consumption can be considered as the kinetics of water oxidation. The beginning of kinetic curves (up to 15% conversion) has the highest Ru3/Ru2 ratio, which quickly changes with time and makes the rate measurements problematic. The typical kinetic curves and the corresponding Tafel-like plots are shown on Figure3 . The initial rates are commonly used to study the reaction kinetics. In this work, we did not use this approach, due to two major problems. First, if Ru2 is not added in the reaction mixture, the rate quickly changes at very low conversions, creating uncertainty in the definition of the initial rate. Secondly, in the early stage, small experimental uncertainties in Ru2 concentration will lead to significant errors in [Ru3]/[Ru2] ratio. The experimental log10(TOF) dependence on the electrochemical solution potential is weakly dependent on catalyst concentration and is not linear. In order to interpret the data, we build a kinetic model of homogeneous processes, performed the fitting of kinetics curves, and then simulated the Tafel plot. It appeared that the simulated Tafel plots are weakly dependent on parameters obtained from fitting. Therefore, we had to narrow the ranges of variable parameters using additional sets of experimental data. In this respect, differential pulse voltammetry could be helpful to estimate the oxidation potentials of Ru4POM. Catalysts 2021, 11, x FOR PEER REVIEW 5 of 11

However, as the theory of such measurements is not yet developed for a homogeneous WOC system, the meaning of this slope value is unclear.

2.4. Tafel Plot from Kinetic Curves in Homogeneous Systems The kinetics of water oxidation by Ru3 can be followed either by measuring oxygen formation or by the consumption/formation of Ru3/Ru2. The consumption of Ru3 can be followed by a decrease in absorbance at 670–680 nm (ε = 420 M−1cm−1) [14]. The reaction is fast and requires a stopped-flow instrument to collect high-quality kinetics data. The experimental details were described in our previous publications [14,19]. Both Ru2 and Ru4POM slightly absorb light at 680 nm, which must and can be taken into account for quantitative analysis of raw experimental data. Here for simplicity, a kinetic curve of [Ru3] consumption versus time is the decrease in absorbance at 680 nm. At a given time t, the reaction rate can be approximated as d[Ru3]/dt ≈ ([Ru3](t − Δt) − [Ru3]t + Δt))/2Δt and TOFap = (d[Ru3]/dt)/[Ct] can be quantified ([Ct] is the total concentration of Ru4POM). We make the reasonable assumption, based on our earlier studies, that the reaction mechanism is Equations (5)–(9). If reversible reactions are in equilibrium and [Ct] << [Ru3], then the electrochemical solution potential at time t can be calculated from the Nernst equation E = E’0 + 0.059×log10(([Ru3]t/([Ru3]0 − [Ru3]t)), where E’0 = 1.26 V is the standard reduction potential of the [Ru3]/[Ru2] couple, and [Ru3]0 is the initial concentration of Ru3. As Ru3/Ru2 and Ru4POM have large and opposite charges, their reduction potentials and the rates of their intermolecular reactions are ionic-strength-dependent. In order to keep pH constant, the use of buffered solutions is required. However, even low concentrations of sodium phosphate buffer (e.g., 25 mM) create a high ionic strength (μ ~ 75 mM). There- fore, in this work, we use the experimentally determined value of the reduction potential for the Ru2/Ru3 couple as the reference point in all calculations (e.g., 1.06 V versus 3.0 M NaCl Ag/AgCl reference electrode). We define TOF as (d[Ru3]/dt)/[Ct]. This procedure converts a single kinetic curve to the dependence of TOF on applied potentials. The self-decomposition of Ru3 is relatively slow at pH 7.0–8.0, and the O2 yield approaches 80% of the theoretical value at [Ru4POM] > 5 μM. Therefore, the kinetics of [Ru(bpy)3]3+ consumption can be considered as the kinetics of water oxidation. The beginning of kinetic curves (up to 15% conversion) has the highest Ru3/Ru2 ratio, which quickly changes with time and makes the rate measurements problematic. The typical kinetic curves and the corresponding Tafel-like plots are shown on Figure 3. The initial rates are commonly used to study the reaction kinetics. In this work, we did not use this approach, due to two major problems. First, if Ru2 is not added in the reaction Catalysts 2021, 11, mixture,x FOR PEER the REVIEW rate quickly changes at very low conversions, creating uncertainty in the def- 6 of 11 Catalysts 2021, 11, 87 6 of 11 inition of the initial rate. Secondly, in the early stage, small experimental uncertainties in Ru2 concentration will lead to significant errors in [Ru3]/[Ru2] ratio. line is calculated using Equation (15). The black line is generated by Copasi software with the same parameters as in (a).

The experimental log10(TOF) dependence on the electrochemical solution potential is weakly dependent on catalyst concentration and is not linear. In order to interpret the data, we build a kinetic model of homogeneous processes, performed the fitting of kinetics curves, and then simulated the Tafel plot. It appeared that the simulated Tafel plots are weakly dependent on parameters obtained from fitting. Therefore, we had to narrow the ranges of variable parameters using additional sets of experimental data. In this respect, differential pulse voltammetry could be helpful to estimate the oxidation potentials of Ru4POM. (a) (b)

2.5. Differential3+ Pulse3 3+ Voltammetry Figure 3. (Figurea) The kinetics3. (a) The of kinetics [Ru(bpy) of 3[Ru(bpy)] consumption] consumption measured measured at 670 nm. at 670 Sodium nm. Sodium borate borate buffer buffer (25 mM) at pH 8.0, (25 mM) at3+ pH 8.0, 0.85Differential mM [Ru(bpy) pulse3]3+, Ru voltammetry4POM—0 (orange), (DPV) 2.5 has (blue), two 5.0 features: (red), and The 10 μeffectM of the charging 0.85 mM [Ru(bpy)3] , Ru4POM—0 (orange), 2.5 (blue), 5.0 (red), and 10 µM (green). The fitting using Copasi software to (green). The fitting using Copasi software to the mechanism in Equations (15)–(21) is in solid lines the mechanism in Equationscurrent (15)–(21) can is be in solidminimized lines [20 and]; (b )only turnover faradaic frequency current (TOF) is extracted. and potential This are technique calculated asis well [20]; (b) turnover frequency (TOF) and potential are calculated as described in the text. The brown described in the text. The brownsuited line for is electrochemical calculated using Equation examination (15). The of Ru black4POM line,is which generated has bya low Copasi rate software constant with of elec- the same parameters as in (atron). transfer to electrode; however, like other electroanalytic techniques, DPV requires the use of a high electrolyte concentrations. Indeed, the DPV peaks significantly increase with an increase in NaNO3 electrolyte concentration in 80 mM sodium borate buffer at pH 8.0 2.5. Differential Pulse Voltammetry and also shift to lower potentials (Figure 4). The first peak becomes visible at 0.5 M NaNO3 at ~0.65Differential V and shifts pulse to a voltammetrylower potential (DPV) at 0.75 has M twoNaNO features:3. The width The effect of the of peak the is charging around 90current mV, which can be is minimized consistent and with only the faradaic one-elec currenttron transfer is extracted. process This (theoretical technique value is well 90 mV).suited The for second electrochemical peak has a examination width of about of Ru45 4mVPOM and, which thus is has very a lowlikely rate a two-electron constant of process.electron At transfer low ionic to electrode; strength, however, the potential like otherof the electroanalytic second peak is techniques, in the range DPV of 1.0–1.1 requires V vs.the Ag/AgCl. use of a high electrolyte concentrations. Indeed, the DPV peaks significantly increase withWe an increaseconsidered in NaNOstudying3 electrolyte the kinetics concentration of water oxidation in 80 mMat elevated sodium concentrations borate buffer of at electrolytepH 8.0 and in also order shift to to have lower the potentials similar conditio (Figurens4). to The those first used peak in becomes electrochemical visible atstudies. 0.5 M However,NaNO3 at the ~0.65 rate V of and water shifts oxidation to a lower by potential Ru3 decreases at 0.75 Mwith NaNO an increase3. The width in electrolyte of the peak con- is centrationaround 90 mV,due whichto ionic is strength consistent effects, with the bu one-electront the rate of transferRu3 self-decomposition process (theoretical remains value unchanged90 mV). The and second becomes peak hasthe apredominant width of about kinetic 45 mV event. and thus As issuch, very the likely redox a two-electron potentials measuredprocess. At by low DPV ionic could strength, be extrapolated the potential to of lo thew ionic second strength peak is to in estimate the range the of 1.0–1.1possible V vs. Ag/AgCl. range of Ru4POM potentials.

Figure 4. Differential pulse voltammetry curves of 1.0 mM Ru4POM in 80 mM sodium borate buffer Figure 4. Differential pulse voltammetry curves of 1.0 mM Ru4POM in 80 mM sodium borate bufferat pH 8.0at pH at varying8.0 at varying concentrations concentrations of NaNO of 3NaNO: 0.15 M3: 0.15 (blue), M (blue), 0.25 M 0.25 (red), M 0.5 (red), M (green), 0.5 M (green), and 0.75 M and(black). 0.75 DifferentialM (black). Differential pulse voltammetry pulse voltam (DPV)metry parameters: (DPV) parameters: V (mV/s) =V 20, (mV/s) sample = 20, width sample (ms) = 17, widthpulse amplitude(ms) = 17, pulse (mV) amplitude = 50, pulse (m widthV) = (ms)50, pulse = 50, width pulse period(ms) = 50, (ms) pulse = 200, period quiet (ms) time = (s) 200, = 2.quiet time (s) = 2. We considered studying the kinetics of water oxidation at elevated concentrations of 2.6.electrolyte Kinetic Model in order of toHomogeneous have the similar Water conditionsOxidation by to [Ru(bpy) those used3]3+ inCatalyzed electrochemical by Ru4POM studies. However, the rate of water oxidation by Ru3 decreases with an increase in electrolyte Having information on the range of redox potentials of Ru4POM and making mini- malconcentration assumptions, due the to ionicmechanism strength in effects, Equations but the(16)–(22 rate of) is Ru3 proposed: self-decomposition remains unchanged and becomes the predominant kinetic event. As such, the redox potentials

Catalysts 2021, 11, x FOR PEER REVIEW 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 energy conversion has been reported [1,2]. However, numerous simplifications and assumptions in the derivation of Equation (4) leads to an incomplete description of the actual surface kinetics and makes the applicability of Tafel analysis questionable [2,3,7,8]. In many cases, homogeneous systems are simpler and easier experimentally for understanding the reaction mechanism. Therefore, we developed a protocol to construct Tafel-like plots for homogeneous reactions and studied the usefulness of such plots to better understand the reaction mechanism. In addition, while extensive mechanistic analyses of molecular redox systems have been conducted previously, many aspects still need to be precisely addressed [9]. Generally speaking, the Tafel-like plot is one among multiple approaches that link the kinetic and thermodynamic properties of such a catalytic system. Both half reactions, Equations (1) and (2), are complex multielectron processes catalyzed by transition metal complexes. Each one is routinely studied individually [6,10–12]. Stable homogeneous molecular catalysts are ideally suited for studies of the reaction mechanism and the relationship between reaction kinetics and thermodynamics. Indeed, previous studies on redox and chemical catalysts in different catalytic systems have already provided theoretical tools for mechanistic analyses [9]. More recently, Costentin and Savéant thoroughly analyzed the applicability of the Tafel equation to the homogeneous molecular catalysis of electrochemical CO2 and O2 reduction [13]. In this work, we describe a protocol for deriving a Tafel-like plot based on theoretical and experimental grounds to relate the reaction rate with the solution electrochemical potential for homogeneous water oxidation by [Ru(bpy)3]3+, catalyzed by the stable molecular tetraruthenium polyoxometalate [Ru4O4(OH)2(H2O)4(γ-SiW10O36)2]10−, Ru4POM. This POM was the first fully inorganic (carbon-free), thus oxidatively robust, water oxidation catalyst (WOC), which is also hydrolytically stable over a wide pH range (pH 1–9) [14,15]. Detailed electrochemical studies of this complex showed that the rates of electron exchange between an electrode and the complex is sluggish under typical catalytic turnover conditions [14,16]. As a result, neither the Tafel plot nor the exchange current density, i0, can be measured experimentally. At the same time, the catalyst shows excellent activity in homogeneous aqueous solutions when stoichiometric oxidants such as Ce(IV) or [Ru(bpy)3]3+ are used. The question was posed as to whether data collected in homogeneous multielectron processes can be used to obtain a Tafel-like plot. This study addresses that question and Catalysts 2021, 11, 87 7 of 11 aims to focus on the adaptation of an analog of traditional Tafel plots to the four-electron water oxidation process specific to homogeneous species.

2. Results and Discussion measured by DPV could be extrapolated to low ionic strength to estimate the possible 2.1. Theoretical Considerations range of Ru4POM potentials.

Here, we assume that water oxidation in homogeneous conditions proceeds through 3+ 2.6. Kinetic Model of Homogeneous Water Oxidation by [Ru(bpy)3] Catalyzed by Ru4POM four fast Nernstian reversible electron transfer steps followed by the irreversible O2 formation step, Equations (5–8), where C0Having is the informationresting oxidation on the state range of ofthe redox catalyst, potentials C, and of Ru4POM and making minimal C1–C4 are the one- to four-electroassumptions,n oxidized forms the mechanism of the catalyst. in Equations (16)–(22) is proposed:

o 10 −1 −1 9 C0C0 + Ru3 − e ⇄ C1 + Ru2 E 1 k1 = 1 × 10 ; k−1 = 10 M s (5);K1 = 1 × 10 ; ∆E1 = −0.61V (16) 10 5 −1 −1 4 C1 + Ru3 C2 + Ru2 k2C1= − 1 e× ⇄10 C2; k − E2 o=2 (4.6 ± 8) × 10 M s ;K2 = 2.2(6)× 10 ; ∆E2 = −0.26 V (17) 10 5 −1 −1 4 C2 + Ru3 C3 + Ru2 kC23 = − 1 e× ⇄10 C3 ; k − 3E=o3 (5.4 ± 9) × 10 M s ;K3 = 1.8 (7)× 10 ; ∆E3 = −0.26 V (18) 7 8 −1 −1 C3 + Ru3 C4 + Ru2 kC34 =− (1.5e ⇄± C40.8) × E10o4 ; k−4 = (8.0 ± 4) × 10 M s (8);K4 = 0.2; ∆E4 = 0.10 V (19) −1 C4 + 2 H2O ⟶ C0 + O2 + 4 H+ C4k→o C0 + O2 k0 = 18(9)± 2 s (20) −1 If the equilibria are fast, then an applied and electrochemicalRu3 → Rux solution potential,kd = 0.0023 E, is± 0.0005 s (21) linked via the Nernst equation, Equation (10): 5 −1 −1 10 Ru3 + Rux → 10 Ru2 + Pr kdd > 1 × 10 M s (22) The latter two reactions are added to describe the rate and stoichiometry of the Ru3 self-decomposition reaction in the absence of a catalyst. The values were determined from the fitting of five kinetic curves and assuming the rate law for Equation (21) as d[Ru3]/dt = −kdd[Ru3][Rux]. It appeared that the overall reaction rate and O2 yield are 5 −1 −1 independent of kdd, if kdd > 1 × 10 M s . We assumed that the very thermodynamically favorable reactions between two reactants with opposite charges proceed with the diffusion- controlled rate constants 1 × 1010 M−1s−1. The optical density at 670 nm was calculated as A(670) = 420 × [Ru3] + 20 × [Ru2]). The results of the fitting are strongly dependent on dioxygen yield over the reaction time. Therefore, we used an additional set of experimental data. The dioxygen yield at 20 ± 2 s was measured to be 41, 60, and 85 µM in the presence of 2.5, 5.0, and 10 µM Ru4POM, respectively. The calculated values of O2 were the same as the experimental ones within a 5% range. For each concentration of Ru4POM, two kinetic curves with different reaction times were used. The results of the fitting are given in Figure3 and the values of the parameters are given in Equations (16)–(22). The values of the variable parameters are highlighted in italics. The standard deviations are generated by the fitting software. As expected, the values of rate constants extracted by fitting have a large error range due to the low number of experimental curves used in fitting. The increase in the numbers of curves requires much longer computing time and results in only a slight decrease in accuracy of the extracted parameters. As the focus of this work is not the study of the explicit reaction mechanism, we did not fit a large set of experimental curves. It is important to note that the Tafel-like plot cannot be used to confirm a specific kinetic model. However, it can provide additional information about the activity of a catalytic system.

2.7. Comparison of Different Homogeneous Catalytic Systems Using Tafel-Like Plots

First, we used the kinetic data on O2 evolution in water oxidation by Ce(IV) under acidic conditions catalyzed by Ru4POM [15]. The experiment was performed in unbuffered 1.1 mM Ce(IV) solution. The estimated pH was 2.5. The standard redox potential of the Ce(IV)/Ce(III) couple was taken to be 1.5 V [21–23]. The value of the overpotential was calculated as a difference between the Nernstian electrochemical solution potential (E = 1.5 + 0.059 × log([Ce(IV)]/[Ce(III)])) and the standard oxidation potential of water (E = 1.24 −0.059 × pH). We digitized the data in Figure S10 from Ref. [15] and obtained the Tafel plot in Figure5 (blue circles). Based on our kinetic model, we simulated the dependence of TOF for O2 formation as a function of overpotential at pH 8.0 (Figure5 red circles). As expected, both sets of data form almost a straight line with a slope of 67 mV per decade, which describes the catalytic activity of Ru4POM over a wide range of conditions. Catalysts 2021, 11, 87 8 of 11 Catalysts 2021, 11, x FOR PEER REVIEW 8 of 11

Figure 5. Tafel-like plots for water oxidation catalyzed by soluble Ru POM and Co4POM (com- Figure 5. Tafel-like plots for water oxidation catalyzed by soluble Ru4POM4 and Co4POM (com- Catalysts 2021, 11, x FOR PEER REVIEWpletely homogeneous catalysts) derived using the described methodology compared to heterogenized9 of 11 pletely homogeneous catalysts) derived using the described methodology compared to heterogen- izedPOM POM Tafel Tafel plots plots measured measured via via electrochemistry. electrochemistry. Conditions Conditions for forCo Co4POM4POMsystem: system: 80 80 mM mM sodium so- o diumborate borate buffer buffer at pH at 8.0, pH 0.34 8.0, mM0.34 Ru3,mM Ru3, 2.5 (light 2.5 (light blue), blue), 5 (green), 5 (green), 10 (yellow) 10 (yellow)µM Co μM4POM Co4POM, 24 ,C. 24 o C. As the current in these electrochemical experiments can be directly converted to TOF Finally, we collected stopped-ﬂow data for another well-established homogeneous (four electrons per turnover), we10– can then compare the Tafel plots of the heterogenized WOC,Finally, [Co4 (Hwe2 O)collected2(PW9O stopped-flow34)2] (Co4POM data)[ for24 ],another in 80 mMwell-established sodium borate homogeneous buffer at pH Co4POM to those of the homogeneous Co4POM (Figure 5). We note that these samples WOC,8.0 under [Co4(H conditions2O)2(PW9 similarO34)2]10– to(Co those4POM for) [24],Ru4POM in 80. mM The datasodium were borate processed buffer in at the pH same 8.0 have similar electroactive surface areas as measured by capacitive current. The differences underway asconditions described similar above, to where those thefor Ru TOF4POM for O. The2 formation data were is processed equal to 1/4 in the of thesame TOF way for in exchange current density must therefore be a result of counterion effects. In this case, asRu3 described consumption, above, andwhere plotted the TOF in Figure for O62. formation The Co4POM is equalis more to 1/4 active of the than TOFRu 4forPOM Ru3at as they follow the expected trend of lower Lewis acidity, giving rise to higher catalytic consumption,overpotentials and lower plotted than in 0.44 Figure V, while 6. The it isCo lower4POM at is overpotentials more active than higher Ru than4POM 0.44 at over- V. The currents, we can generally attribute the observed trend to their Lewis acid–base chemistry. potentialsdifferences lower in Tafel than slopes 0.44 V, indicate while thatit is thelower rate-determining at overpotentials steps higher and/or than the 0.44 correspond- V. The differencesing WOC reactionin Tafel slopes mechanism indicate are that different the rate-determining in these two systems. steps and/or the corresponding WOC reaction mechanism are different in these two systems. In order to understand how the reaction parameters in Equations (15)–(21) affect the Tafel slope, we simulated the Tafel slope using Copasi and then observed the effects of changing each of the parameters within a range of 104–106 from the fitted values of Ru4POM. We have found that if the equilibrium of the reaction in Equation (19) is shifted to the left side (corresponding to the condition that the first oxidation potential is very high), then the Tafel slope becomes 30 mV/decade. This leads us to believe that the first oxidation potential of Co4POM is higher and the step depicted in Equation (19) becomes rate-determining instead. Here, it is worth mentioning that experimental slopes in Figure 3 are slightly higher than the theoretical 30 and 60 mV/decade. The TOF was also calculated based on the rate of Ru3 consumption, which includes the Ru3 self-decomposition side reaction that we deemed negligible for our analysis.

2.8. Tafel Slope for Heterogeneous Co4POM Complex

FigureOne 6. ofTafel the reasons plot of heterogenized for performingCo 4aPOM Tafel-likeon glassy analysis carbon on electrodesthe homogeneous with different catalysts coun- Figure 6. Tafel plot of heterogenized Co4POM on glassy carbon electrodes with different counteri- ons.isterions. to Conditions: make Conditions: comparisons 1 mV/s 1iR mV/s compensated to the iR analogous compensated chronoamperometry he chronoamperometryterogeneous in catalysts 0.1 M pH in 0.1 where8 sodium M pH accessible. 8borate sodium buffer Vari- borate 4 andousbuffer 0.1 different M and KNO 0.1 3counter-cation electrolyte M KNO3 electrolyte solution. variants Reference solution. of Co electrode, ReferencePOM were Ag/AgCl electrode, heterogenized (1.0 Ag/AgCl M KCl); via (1.0counter a M5 wt% KCl); electrode, Nafion counter graphite.mixtureelectrode, and graphite. drop-casted onto a glassy carbon electrode in order to measure their Tafel behavior. These Tafel plots are shown in Figure 6. They all exhibit similar Tafel slopes of 3.about Materials In80 ordermV/decade, and to Methods understand which is how greater the than reaction the 60 parameters mV/decade in Equationsobserved for (15)–(21) amorphous affect the Tafel slope, we simulated the Tafel slope using Copasi and then observed the effects cobaltAll oxides. common This synthetic suggests chemicals either awere differ reagentent WOC grade mechanism and purchased or different through cobalt-cen- commer- of changing each of the parameters within a range of 104–106 from the fitted values of cialtered sources active such species as Sigma-Aldrich are involved in and with VWR the twoand types used ofwithout cobalt-containing further purification. WOCs. None- Syn- theless,Ru4POM it is. Welikely have that found all these that variants if the equilibrium of Co4POM of thehave reaction the same in Equationrate-determining (19) is shifted step thesis of Ru4POM and Co4POM was performed following exact literature procedures and givento the their left similar side (corresponding Tafel slopes. to the condition that the first oxidation potential is very recrystallized from aqueous solution [14,24]. Synthesis of the [Ru(bpy)3]3+ source, high), then the Tafel slope becomes 30 mV/decade. This leads us to believe that the first [Ru(bpy)3](ClO4)3, was obtained by oxidizing [Ru(bpy)3]Cl2 using PbO2 in 0.5M H2SO4 and precipitating by addition of HClO4 [25]. The product was then dried and stored in a refrigerator (4 °C). Stopped-flow UV-Vis spectroscopy was performed on a Hi-Tech KinetAsyst Stopped Flow SF-61SX2 instrument equipped with a diode array detector operating between wave- lengths ranging from 400 to 700 nm. One of the feeding syringes was filled with a solution of [Ru(bpy)3]3+ and the second with a freshly prepared buffer solution containing the catalyst. The consumption of [Ru(bpy)3]3+ was followed by a decrease in absorbance at 670 nm (ε670 = 4.2 × 102 M–1 cm–1) with an optical path length of 10 mm. The data were acquired and treated using KinetAsystTM 3.0 software. Consequent analysis of the resulting kinetic data were performed using Excel and the Copasi software package [20]. Electrochemical analyses were carried out using standard three-electrode measurements on a Pine Research Instrument WaveDriver 20 bipotentiostat and a BAS CV-50W potentiostat. All potentials were measured using glassy carbon electrodes against 1 M KCl Ag/AgCl reference electrodes (+0.235 V vs. NHE) purchased from CH Instruments. The counter electrodes were either a platinum wire or a graphite rod. Electrochemical cells were either cylindrical or conical electrochemical glassware or three-necked round-bottom flasks. All electrochemical measurements were done with the reference and working electrodes in proximity and clear from obstructions that would hinder contact with the reaction solution.

Catalysts 2021, 11, 87 9 of 11

oxidation potential of Co4POM is higher and the step depicted in Equation (19) becomes rate-determining instead. Here, it is worth mentioning that experimental slopes in Figure3 are slightly higher than the theoretical 30 and 60 mV/decade. The TOF was also calculated based on the rate of Ru3 consumption, which includes the Ru3 self-decomposition side reaction that we deemed negligible for our analysis.

2.8. Tafel Slope for Heterogeneous Co4POM Complex One of the reasons for performing a Tafel-like analysis on the homogeneous catalysts is to make comparisons to the analogous heterogeneous catalysts where accessible. Various different counter-cation variants of Co4POM were heterogenized via a 5 wt% Naﬁon mixture and drop-casted onto a glassy carbon electrode in order to measure their Tafel behavior. These Tafel plots are shown in Figure6. They all exhibit similar Tafel slopes of about 80 mV/decade, which is greater than the 60 mV/decade observed for amorphous cobalt oxides. This suggests either a different WOC mechanism or different cobalt-centered active species are involved in with the two types of cobalt-containing WOCs. Nonetheless, it is likely that all these variants of Co4POM have the same rate-determining step given their similar Tafel slopes. As the current in these electrochemical experiments can be directly converted to TOF (four electrons per turnover), we can then compare the Tafel plots of the heterogenized Co4POM to those of the homogeneous Co4POM (Figure5). We note that these samples have similar electroactive surface areas as measured by capacitive current. The differences in exchange current density must therefore be a result of counterion effects. In this case, as they follow the expected trend of lower Lewis acidity, giving rise to higher catalytic currents, we can generally attribute the observed trend to their Lewis acid–base chemistry.

3. Materials and Methods All common synthetic chemicals were reagent grade and purchased through com- mercial sources such as Sigma-Aldrich and VWR and used without further purification. Synthesis of Ru4POM and Co4POM was performed following exact literature procedures 3+ and recrystallized from aqueous solution [14,24]. Synthesis of the [Ru(bpy)3] source, [Ru(bpy)3](ClO4)3, was obtained by oxidizing [Ru(bpy)3]Cl2 using PbO2 in 0.5M H2SO4 and precipitating by addition of HClO4 [25]. The product was then dried and stored in a refrigerator (4 ◦C). Stopped-flow UV-Vis spectroscopy was performed on a Hi-Tech KinetAsyst Stopped Flow SF-61SX2 instrument equipped with a diode array detector operating between wave- lengths ranging from 400 to 700 nm. One of the feeding syringes was filled with a solution 3+ of [Ru(bpy)3] and the second with a freshly prepared buffer solution containing the 3+ catalyst. The consumption of [Ru(bpy)3] was followed by a decrease in absorbance at 2 –1 –1 670 nm (ε670 = 4.2 × 10 M cm ) with an optical path length of 10 mm. The data were acquired and treated using KinetAsystTM 3.0 software. Consequent analysis of the resulting kinetic data were performed using Excel and the Copasi software package [20]. Electrochemical analyses were carried out using standard three-electrode measurements on a Pine Research Instrument WaveDriver 20 bipotentiostat and a BAS CV-50W potentiostat. All potentials were measured using glassy carbon electrodes against 1 M KCl Ag/AgCl reference electrodes (+0.235 V vs. NHE) purchased from CH Instruments. The counter electrodes were either a platinum wire or a graphite rod. Electrochemical cells were either cylindrical or conical electrochemical glassware or three-necked round-bottom flasks. All electrochemical measurements were done with the reference and working electrodes in proximity and clear from obstructions that would hinder contact with the reaction solution.

4. Conclusions We describe a protocol to obtain Tafel-like plots for two different homogeneous catalytic systems based on kinetic and thermodynamic data. These plots visualize the Catalysts 2021, 11, 87 10 of 11

activity of different catalysts under different solution overpotential conditions and allow for the ready comparison of their activity with each other, as well as with heterogeneous catalysts whose Tafel plots can be obtained using a traditional electrochemical setup. The resulting Tafel slopes indicate that the reaction mechanisms in water oxidation catalyzed by Ru4POM and Co4POM are likely different with distinct rate-determining steps. This establishes a template with which molecularly discrete homogeneous WOCs can be directly compared to each other, regardless of the oxidant used, and addresses one of the biggest issues in WOC development: that of how to compare the catalytic reactivity of homogeneous and heterogeneous systems. In the future, we hope to expand upon this work and show further utilization of these protocols to elucidate the reaction mechanisms of other WOC systems.

Author Contributions: Conceptualization, Q.Y. and Y.V.G.; methodology, Y.V.G.; formal analysis, Q.Y. and Y.V.G.; investigation, Q.Y., Z.X. and Y.V.G.; writing—original draft preparation, Q.Y. and Y.V.G.; writing—review and editing, T.L., D.G.M. and C.L.H.; visualization, Q.Y. and Y.V.G.; funding acquisition, T.L., D.G.M. and C.L.H. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Solar Photochemistry Program, Award Number DE-FG02-07ER15906. Data Availability Statement: Data is contained within the article. Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

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