Supporting Information Linear Free Energy Relationships in the Hydrogen Evolution Reaction: Kinetic Analysis of a Cobaloxime Catalyst

Transcription

1 Supporting Information Linear Free Energy Relationships in the Hydrogen Evolution Reaction: Kinetic Analysis of a Cobaloxime Catalyst Eric S. Rountree, Daniel J. Martin, Brian D. McCarthy, Jillian L. Dempsey* Department of Chemistry, University of North Carolina Chapel Hill, North Carolina , United States * dempseyj@ .unc.edu Table of Contents Page SI 1 Characterization of Anilinium Complexes and Summary of pk a values... S2 References for pk a values Acid characterization and pk a determination SI 2 Determination of Electrochemical Parameters for Simulations... S6 Diffusion coefficient of 1 determined via cyclic voltammetry Standard rate constant determined via trumpet plot SI 3 Reactions of 1 with Aniline... S8 UV-Vis spectrum, cyclic voltammograms, discussion, digital simulations SI 4 Optically Monitoring the Decomposition of 1... S13 UV-Vis spectra, discussion SI 5 Determination of Global Rate Constants from Plateau Currents... S15 Catalytic cyclic voltammograms of 1 with substituted aniliniums Voltammograms recorded at high acid concentration Plateau currents as a function of acid concentration Calculated rate constants as a function of the number of homogeneous and heterogeneous electron transfers Summary of rate constants SI 6 Evaluating k 1 via foot-of-the-wave analysis... S28 Voltammograms and FOWA for all acids k FOWA vs. [HA] plots to obtain k 1 values Discussion of precautions taken to accurately apply FOWA SI 7 Extracting Kinetics Information from Voltammograms Exhibiting Total Catalysis... S34 KT2: Simulation of concentration profiles Extending the KT2 equation to an ECEC' mechanism. Identifying conditions for valid use of KT2 equation (Equation 5) Determining k 1 from total catalysis data SI 8 Oxidation of unreacted 1 2 (H + )... S42 SI 9 Effects of an acid-independent chemical step on FOWA and plateau analysis... S46 References... S49 S1

2 SI 1 Characterization of Anilinium Complexes and Summary of pk a values Table S1. pk a Values in acetonitrile Acid para-substituent pk a pk a ref 4-methoxyanilinium OCH tert-butylanilinium C(CH 3 ) anilinium n/a chloroanilinium Cl trifluoromethoxyanilinium OCF this work 4-(methylbenzoate)anilinium COOCH this work 4-trifluoromethylanilinium CF cyanoanilinium -CN 7 3 Acid characterization and pk a determination 4-trifluoromethoxyanilinium tetrafluoroborate Figure S1. 1 H NMR of 4-trifluoromethoxyanilinium tetrafluoroborate in CD 3 CN. The pk a of 4-trifluoromethoxyanilinium in acetonitrile was determined via spectrophotometric titration. 2 Briefly, 4-trifluoromethoxyanilinium was titrated into a solution of 3-nitroaniline (pk a = 7.68) and the 3-nitroaniline absorbance was monitored by UV-vis absorbance spectroscopy (λ max = 373 nm, ε = 1394 M -1 cm -1 ). Concentrations of 4-trifluoromethoxyanilinium, 4- trifluoromethoxyaniline, and 3-nitroanilinium at each titration point were calculated based on the concentration 3-nitroaniline (determined by UV-vis) and the initial concentrations of all reagents. Linear regression of a plot of ([4-OCF 3 -aniline]/[4-ocf 3 -anilinium])*[3-no 2 -anilium] vs. [3-NO 2 - aniline] was used to determine the pk a of 4-trifluoromethoxyanilinium: 3 log. S2

3 Figure S2. Spectrophotometric titration of mm 3-nitroaniline with 4-trifluoromethoxyanilinium. 4-trifluoromethoxyanilinium is transparent in the region plotted above and does not contribute to the overall signal. Figure S3. The slope of ([4-OCF 3 -aniline]/[4-ocf 3 -anilinium])*[3-no 2 - anilium] versus [3-NO 2 -aniline] (m = ) can be used to determine the pk a for 4-trifluoromethoxyanilinium (pk a = 9.28). S3

4 4-(methylbenzoate)anilinium tetrafluoroborate Figure S4. 1 H NMR of 4-(methylbenzoate)anilinium tetrafluoroborate in CD 3 CN. To determine the pk a of 4-(methylbenzoate)anilinium, a spectrophotometric titration was performed following the same procedure as described for 4-trifluoromethoxyanilinium. Figure S5. Spectrophotometric titration of mm 3-nitroaniline with 4-(methylbenzoate)anilinium. 4-(methylbenzoate)anilinium is transparent in the shown region and does not contribute to the overall signal. S4

5 Figure S6. The slope of ([4-COOCH 3 -aniline]/[4- COOCH 3 - anilinium])*[3-no 2 -anilium] versus [3-NO 2 -aniline] (m = 0.115) can be used to determine the pk a for 4-(methylbenzoate)anilinium (pk a = 8.62). 4-trifluoromethylanilinium tetrafluoroborate Figure S7. 1 H NMR of 4-trifluoromethylanilinium tetrafluoroborate in CD 3 CN. S5

6 SI 2 Determination of Electrochemical Parameters for Simulations Diffusion coefficient of 1 determined via cyclic voltammetry The diffusion coefficient (D) of 1 was determined from a series of cyclic voltammograms recorded at scan rates between 0.01 and 7.5 V/s. Per the Randles-Sevcik equation (Eq. S1), which relates the peak current i p (amperes) of a reversible, diffusion controlled redox process to the scan rate υ, the diffusion coefficient was calculated as 9.22 x 10 6 cm 2 /s. This value differs slightly from the reported value which was determined via electrochemical simulation (D = 8 x 10-6 cm 2 /s) / Eq. S1 n is the number of electrons in the redox process, F is the Faraday constant, T is temperature, and R is the universal gas constant. Figure S8. The peak current of the 1 0/ cathodic wave plotted vs. υ 1/2. The baseline currents of the voltammograms were subtracted from the peak intensities of the 1 0/ reduction ( ). The slope of this line corresponds to. / per the Randles-Sevcik equation and can be used to determine the diffusion coefficient D. S6

7 Standard rate constant k s for heterogeneous electron transfer determined via trumpet plot analysis The peak potentials of the oxidation and reduction waves of 1 were determined for a 0.5 mm solution of 1 in 0.25 M [Bu 4 N][PF 6 ] from CVs recorded at various scan rates υ. The voltammograms were corrected for uncompensated resistance by the procedure outlined in the Supporting Information section of reference 2. A plot of E p E 1/2 vs. log (υ) was then overlaid with a simulated working curve for which D sim = 1 x 10-5 cm 2 /s and k s,sim = 1 cm/s. The x-axes (log (υ)) of the two plots were translated until the E p E 1/2 data overlapped (Figure S9). At the overlap, Λ s,co = Λ s,sim, where Λ s is a dimensionless parameter defined as follows 5 Λ where k s is the standard rate constant, R is the gas constant, T is temperature, F is Faraday s constant, and D is the diffusion constant. At the overlap,, And it follows that,, 1 2 log log From this analysis, a standard rate constant for heterogeneous electron transfer for 1 was estimated (k s,co = cm/s). Figure S9. Trumpet plot of 1 overlaid with the working curve described above. S7

8 SI 3 Reactions of 1 with aniline The aniline bases were shown, both electrochemically (Figures 1, S10) and spectroscopically (Figure S11), to coordinate to 1. Prior to the addition of an aniline base, the Co III/II redox wave is electrochemically irreversible and centered at ~0.2 V vs. Fc + /Fc, consistent with previous reports. 4 After aniline addition, the Co III/II wave shifts cathodically and gains electrochemical reversibility. The location of the Co III/II wave depends on the identity of the aniline added, stronger bases shift the wave to more negative potentials (Figure S9). Unexpectedly, the Co II/I redox is unaffected by aniline addition. We attribute this to a rapid equilibrium between the coordinated and uncoordinated species, with coordination favored for cobaloximes in higher oxidation states. Simulation of the voltammograms (Figure S12) supports this assignment. Co III Equilibrium [Co(dmgBF 2 ) 2 (CH 3 CN) 2 ] + + aniline [Co(dmgBF 2 ) 2 (CH 3 CN)(aniline)] + + CH 3 CN Co II Equilibrium Co(dmgBF 2 ) 2 (CH 3 CN) 2 + aniline Co(dmgBF 2 ) 2 (CH 3 CN)(aniline) + CH 3 CN Co I Equilibrium [Co(dmgBF 2 ) 2 (CH 3 CN)] + aniline [Co(dmgBF 2 ) 2 (aniline)] + CH 3 CN Figure S10. Cyclic voltammograms of 0.38 mm 1 in the absence of added base (black), in the presence of 2 mm 4-methoxyaniline (blue), and in the presence of 5 mm aniline (red). Voltammograms recorded at 100 mv/s in 0.25 M [Bu 4 N][PF 6 ]. S8

9 Figure S11. a) Titration of 0.11 mm 1 with aniline (up to 1 M), monitored via UV-Vis absorption spectroscopy. b) Absorbance at 430 nm corresponding to presumed isosbestic point of 1(CH 3 CN) 2 and 1(aniline) 2. c) absorbance of 1, 1(aniline) 2 and intermediate 1(aniline). Fitting of the dataset in (b) using the equilibrium equations for a singly and doubly bound species allowed for the determination of the spectra of the intermediate (1(aniline) in panel c). A linear combination of each of these three spectra in accordance with the fit in panel b is sufficient to derive each spectrum in panel a. The values for K Co(A) and K Co(A)2 are not reported here as the fit also required the fitting of the absorbance for 1(aniline) at 430 nm. The interdependency of these three parameters prevented an exact value from being determined. Thus the spectrum for 1(aniline) in plot c is qualitative. Figure S12. The same cyclic voltammograms shown in Figure S10 without added base (top), and with 4-methoxyaniline (bottom), along with an overlay of their corresponding digital simulation (blue dashed traces). The parameters used to simulate the data in DigiElch are provided below. S9

10 Parameters for Digital Simulations presented in Figure S12 Scan Rate Cycles R u (Ω) C di (F) Temp. (K) Geometry Area (cm 2 ) 0.1 V/s e Planar 0.07 Diffusion Potential Steps (V) Gauss-Newton Iteration Noise Level (A) Semi-Infinite 1D Grid Expansion Factor Rel. Truncation Error Xmas/SQRT(Dt) Charge Transfer reactions: Local FEM error level: 0.02 Reaction E (V vs. Fc + /Fc) α k S (cm/s) e e [1-A] + + e [1-A] [1-A] + e [1-A] Chemical reactions: Reaction K eq (M -1 ) k f (M -1 s -1 ) k b (s -1 )* A [1-A] x 10 8 * 1 x A 1-A 1 1 x x A [1-A] 3.55 x 10-9 * 1 x x *constants automatically calculated via DigiElch Species Parameters: D (cm 2 /s) Initial Conc. (M) x x x A 9.22 x [1-A] x [1-A] 9.22 x A 1 x or S10

11 Figure S13. Linear sweep voltammograms of varied concentrations of 1 in the presence of 75 mm anilinium. Data shown in Figure 3 in the main text was obtained from these voltammograms. All traces recorded at 100 mv/s. Figure S14. a) Linear sweep voltammograms of varied concentrations of 1 in the presence of 140 mm 4-trifluoromethylanilinium. All traces recorded at 100 mv/s b) Plateau current obtained at V vs. Fc/Fc + from the voltammograms in plot a. S11

12 Figure S15. Comparison of the data from Figure 3 and Figure S14b showing different curvature. S12

13 SI 4 Optically Monitoring the Decomposition of 1 Compound 1 is known to decompose in the presence of moderately strong acids in acetonitrile, 4,6,7 and the phenyl-substituted version of 1 has been reported to degrade to cobaltcontaining nanoparticles in the presence of perchloric acid under reducing conditions. 8 Consequently, the stability of 1 was carefully evaluated under the conditions explored for this work. First, the stability of 1 in acetonitrile electrolyte solution without added acid was monitored by UV-vis spectroscopy over a period of approximately two weeks. Slow loss of the primary absorption peak of 1 was observed (Figure S16), corresponding to a rate of ca. 3 x 10-5 mm/hr assuming the product does not absorb in the same region. Any 1.0 mm solutions of cobaloxime were utilized within three and a half weeks during which less than 1.8% of the sample degraded. Figure S16. Left) UV-vis spectra of 1 (initial concentration of mm) in 0.25 M [Bu 4 N][PF 6 ] CH 3 CN solution over time. Right) Calculated concentration of 1 (assuming that the decomposition products do not absorb at 423 nm) over time. Next, the stability of 1 was studied in acetonitrile electrolyte solutions with added acid. Decomposition was observed for both 4-trifluoromethylanilinium (pk a = 8.03; Figure S17) and 4- cyanoanilinium (pk a = 7; Figure S17) on the timescale of minutes, with decomposition accelerated with the stronger acid 4-cyanoanilinium. In response to these observations, data collection procedures were modified for samples containing these acids. See experimental section for details. S13

14 Figure S17. Left) UV-vis spectra of 1 (initial concentration of 0.2 mm) in 0.25 M [Bu 4 N][PF 6 ] acetonitrile solution with 60 mm 4-trifluoromethylanilinium. Right) Absorbance at 423 nm over time. Figure S18. Left) UV-vis spectra of 1 (initial concentration of 0.2 mm) in 0.25 M [Bu 4 N][PF 6 ] acetonitrile solution with 100 mm p-cyanoanilinium. Right) Absorbance at 423 nm over time. S14

15 SI 5 Determination of Global Rate Constants from Plateau Currents Catalytic cyclic voltammograms of 1 with substituted aniliniums The catalytic voltammograms were recorded for 1 with 8 acids. Each voltammograms was recorded using a freshly pretreated electrode in order to minimize any potential fouling. The acids below are organized by increasing strength. Some of the strongest acids warranted evaluation under lower-substrate concentrations in order to minimize decomposition. Acids of pk a > ca. 11 Figure S19. Cyclic voltammograms of 0.5 mm 1 in the absence and presence of 4-methoxyanilinium titrations. Voltammograms recorded at 100 mv/s in 0.25 M [Bu 4 N][PF 6 ]. S15

16 Figure S20. Cyclic voltammograms of 0.5 mm 1 in the absence and presence of 4-tert-butylanilinium. Voltammograms recorded at 100 mv/s in 0.25 M [Bu 4 N][PF 6 ]. Figure S21. Cyclic voltammograms of 0.5 mm 1 in the absence and presence of anilinium. Voltammograms recorded at 100 mv/s in 0.25 M [Bu 4 N][PF 6 ]. S16

17 Figure S22. Variation of peak current at -1 V vs. Fc + /Fc versus scan rate for voltammograms collected of a solution of 0.5 mm 1 and 75 mm anilinium in 0.25 M [Bu 4 N][PF 6 ]. Acids of pk a = 9.7 and 9.28 Figure S23. Cyclic voltammograms of 0.5 mm 1 in the absence and presence of 4-chloroanilinium. Voltammograms recorded at 100 mv/s in 0.25 M [Bu 4 N][PF 6 ]. S17

18 Acids of pk a < ca. 9 Figure S24. Cyclic voltammograms of 0.5 mm 1 in the absence and presence of 4-trifluoromethoxyanilinium. Voltammograms recorded at 100 mv/s in 0.25 M [Bu 4 N][PF 6 ]. Figure S25. Cyclic voltammograms of 0.5 mm 1 in the absence and presence of 4-(methylbenzoate)anilinium. Voltammograms recorded at 100 mv/s in 0.25 M [Bu 4 N][PF 6 ]. S18

19 Figure S26. Cyclic voltammograms of 0.5 mm 1 in the absence and presence of 4-trifluoromethylanilinium. Voltammograms recorded at 100 mv/s in 0.25 M [Bu 4 N][PF 6 ]. Figure S27. Cyclic voltammograms of 0.5 mm 1 in the absence and presence of 4-cyanoanilinium. Voltammograms recorded at 100 mv/s in 0.25 M [Bu 4 N][PF 6 ]. S19

20 Voltammograms recorded at high acid concentration Voltammograms were recorded at high acid concentrations in order to access plateau currents that are acid concentration and pk a independent. As there is literature precedent for the degradation of 1 in strongly acidic solutions with proton sources such as HBF 4, HCl and HClO 4, these experiments were performed with great caution. We directly evaluated catalyst decomposition for strong acids (SI 4). Relatedly, we found little evidence for catalyst decomposition for weak acids during the course of experiments. In response, to minimize the time frame in which 1 could potentially decompose, 1 was exposed to acid only for relatively brief periods. For these titration experiments involving high acid concentrations, multiple, identical solutions of 1 were used in which a single addition of acid and a single scan were taken, substantially reducing the net exposure time of 1 to acid. Figure S28. Cyclic voltammograms of a 0.5 mm solution of 1 in the presence of varying concentrations of anilinium, as denoted. All voltammograms recorded at 100 mv/s in 0.25 M [Bu 4 N][PF 6 ]. S20

21 Figure S29. Cyclic voltammograms of 1 and varying concentrations of 4-(methylbenzoate)anilinium. Addition of acid stock significantly diluted catalyst concentration. All voltammograms recorded at 100 mv/s in 0.25 M [Bu 4 N][PF 6 ]. S21

22 Figure S30. Cyclic voltammograms of 1 and varying concentrations of 4-(methylbenzoate)anilinium beyond those presented in Figure S29. The return scan was excluded for clarity. Solid acid was added to solution to avoid further catalyst dilution. The final light blue trace was taken 10 minutes after the final acid addition in the attempt to limit significant catalyst degradation. No changes in voltammogram shape (light blue and green) or subsequent catalyst concentration were observed. All voltammograms recorded at 100 mv/s in 0.25 M [Bu 4 N][PF 6 ]. S22

23 Figure S31. Cyclic voltammograms of 1 and varying acid concentrations of 4-trifluoromethylanilinium. Addition of acid stock diluted catalyst concentration. Current plateaus are likely a function of both catalyst dilution and k Ω (see main text for discussion). All voltammograms recorded at 100 mv/s in 0.25 M [Bu 4 N][PF 6 ]. S23

24 Figure S32. Cyclic voltammograms of 1 and varying acid concentrations of 4-trifluoromethylanilinium beyond those presented in Figure S31. The return scan was excluded clarity of presentation. Solid acid was added to solution to avoid further catalyst dilution. Additions of acid resulted in slightly decreased current intensities; however, after 30 seconds of stirring, the same solutions produced slightly higher plateaus. No changes in voltammogram shape (dark blue and purple traces) or subsequent catalyst concentration were observed. All voltammograms recorded at 100 mv/s in 0.25 M [Bu 4 N][PF 6 ]. S24

25 Figure S33. Cyclic voltammograms of 1 and varying acid concentrations of 4-cyanoanilinium (added as a solid). The change in voltammogram shape and slope is indicative of catalyst decomposition over the course of the experiment. All voltammograms recorded at 100 mv/s in 0.25 M [Bu 4 N][PF 6 ]. S25

26 Plateau currents as a function of acid concentration First-order dependence of plateau current on (acid concentration) 1/2 is expected for reactions that are first order in acid. By contrast, first-order dependence of plateau current i pl (or peak current, in the absence of a plateau) on acid concentration is expected for solutions in which the peak current is governed by the diffusion of substrate into the reaction layer. Experimentally, for weak acids, we observe the half-order dependence with a current density dependent upon acid strength (Figure S34). However, for stronger acids, the current density approaches a pk a independent value and is linear with acid concentration (Figure S35). Figure S34. Current density as a function of [HA] 1/2 and [HA] for the four weaker acids, 4- methoxyanilinium, 4-tertbutylanilinium, anilinium, and 4-chloroanilinium. Figure S35. Current density as a function of [HA] 1/2 and [HA] for the four stronger acids, 4-trifluoromethoxyanilinium, 4-(methylbenzoate)anilinium, 4-trilfluoromethylanilinium, and 4-cyanoanilinium. Note that the current [HA] 1/2 plot does not intercept the origin. S26

27 Calculated rate constants as a function of the number of homogeneous and heterogeneous electron transfers For an ECEC' reaction in which both electron transfers occur at the electrode (heterogeneous), the following equation 9 describes the plateau current as a function of rate constant and substrate concentration: i 2FAC C For a system in which there exists both one homogeneous and one heterogeneous electron transfer, the equation below describes the plateau current: i FAC 2 C Rearranging these two equations, we obtain: and i 4DC F A C i 2DC F A C respectively. Only a factor of two separates these two equations, suggesting that if the system is incorrectly assumed to contain two heterogeneous electron transfers, then will be underestimated by a factor of two. Summary of rate constants Table S2. Table of calculated rate constants as determined by FOWA (k 1 ), plateau analysis (k 2 ), and the maximum plateau current (k Ω ). Acid Identity pk a (CH 3 CN) (M -1 s -1 ) (M -1 s -1 ) (s -1 ) 4-methoxyanilinium x tert-butylanilinium x anilinium x chloroanilinium x trifluoromethoxyanilinium x ~125 4-(methylbenzoate)anilinium x * - 4-trifluoromethylanilinium x * ~125 4-cyanoanilinium x * ~125 *Indicates k 2 values extrapolated from data points in the higher pk a regime. S27

28 SI 6 Evaluating k 1 via foot-of-the-wave analysis Foot-of-the-wave analysis To perform foot-of-the-wave analysis on the catalytic voltammograms, the potential axis was converted to exp /. The current is then plotted as the ratio of the catalytic current (i c ) divided by peak current (i p ) of the Co II/I reduction wave. The equation derived for FOWA of an ECEC' mechanism 10 (Eq. S2) is divided by the Randles-Sevcik Equation (Eq. S3) to obtain the i c /i p relationship (Eq. S4). The linear portion at the foot of the wave can be fit with a straight line to obtain the slope (m) which is represented by Eq. S5. Solving Eq. S5 for k FOWA yields Eq. S6, which is used to obtain the observed rate k FOWA from the FOW analysis exp / / Eq. S2 Eq. S3. exp / Eq. S4 Inserting numerical values for constants; R = J mol -1 K -1, T = 298 K, F = 96,485 C mol -1 y = m x exp 38.9 / The slope of the line (m) obtained from FOWA for an ECEC' mechanism is:. Eq. S5 Solving for k FOWA :. Eq. S6 In this work, n = 1 because the n in this equation is imparted from the Randles-Sevcik equation (Eq. S3) and corresponds in our analysis to the height of the Co II/I redox wave. υ = 0.1 V/s for all FOWA datasets and thus 2.27 S28

29 As is shown in SI 3, when aniline bases are present in solution, the Co III/II (1 0/+ ) redox wave shifts to a position that overlaps the ferrocene/ferrocenium couple. Because FOWA results are significantly impacted by any deviations in applied potential, each wave must be referenced to an internal standard already present in solution. It has been our general practice first to scan cathodically in our catalytic measurements and scan through the ferrocene reference on the reverse trace. However, as seen in Figure S33, this made referencing to ferrocene very difficult as catalysis produces the aniline base, which coordinates to 1 and shifts the Co III/II (1 0/+ ) wave to overlap the ferrocene wave. For improved accuracy, we scanned through the ferrocene wave first in our voltammetric measurements to minimize the interference arising from the production of aniline. Results for each anilinium are shown below in Figures S34 and S35. Voltammograms of two samples, 4-methoxyanilinium, and 4-tertbutylanilinium, suggest a small amount of aniline is available to bind cobaloxime prior to catalysis, inhibiting precise referencing and the result of this can be seen in the rate constant vs. concentration data shown below. Figure S36. Cyclic voltammogram of 0.5 mm 1 with 28 mm anilinium. After scanning through the catalytic wave, referencing to ferrocene becomes difficult; as can be seen here, the Co III/II wave, with aniline bound, overlaps with the ferrocene wave and prevents precise referencing. S29

30 Figure S37. FOWA of the four weaker acids, 4-methoxyanilinium, 4-tertbutylanilinium, anilinium, and 4- chloroanilinium. Plots, from left to right for each acid are the original catalytic waves (left), conversion to the FOWA axis, exp /, (center), and the resulting rate constant vs. acid concentration plot (right). S30

31 Figure S38. FOWA of the four stronger acids, 4-trifluoromethoxyanilinium, 4-methylbenzoateanilinium, 4- trilfluoromethylanilinium, and 4-cyanoanilinium. Plots, from left to right for each acid are the original catalytic waves (left), conversion to the FOW axis, exp /, (center), and the resulting rate constant vs. acid concentration plot (right). Foot-of-the-wave Analysis in the total catalysis regime To ensure that FOWA is applicable under KT2 conditions, simulation of a KT2 voltammogram was performed and the simulated voltammogram was evaluated by FOWA. It was shown that FOWA does give an accurate result, even in the case of total catalysis. S31

32 Figure S39. a) Simulation of a KT2 voltammogram utilizing the EC mechanism. Parameters for the simulation are outlined in the tables below. The blue portion of the trace represents the section that was fit to a line on the FOW plot. b) Conversion of the voltammogram to the FOW axis, exp. The blue line represents the linear fit of the foot and has a slope of , which, per the equation, results in a of 9.29 x 10 6 M -1 s -1. The simulated value was 1 x 10 7 M -1 s -1. Parameters for Digital Simulations presented in Figure S36 Scan Rate R u (Ω) C di (F) Temp. (K) Geometry Area (cm 2 ) 0.1 V/s Planar 1 Diffusion Potential Steps (V) Gauss-Newton Iteration Noise Level (A) Semi-Infinite 1D Grid Expansion Factor Rel. Truncation Error Xmas/SQRT(Dt) Charge Transfer reactions: Local FEM error level: 0.02 Reaction E (V vs. Fc + /Fc) α k S (cm/s) P + e Q Chemical reactions: Reaction k f (M -1 s -1 ) Q + A P + Prod 1 x 10 7 S32

33 Species Parameters: D (cm 2 /s) Initial Conc. (M) P 1 x Q 1 x A 1 x S33

34 SI 7 Extracting Kinetics Information from Voltammograms in the Total Catalysis Zone KT2: Simulation of concentration profiles Figure S40. This figure illustrates the kinetic, thermodynamic, and concentration factors that give rise to the KT2 voltammogram. The cyclic voltammogram in the center was generated using the EC' mechanism with a bulk concentration for the catalyst [P] of M and for the substrate [A], a concentration of M. The rate constant for the homogeneous reaction is k e = 1x 10 8 M -1 s -1 and the scan rate is 100 mv/s. The surrounding plots show the concentration of the catalyst P, substrate A and reduced catalyst Q as a function of the distance from the electrode for each of the marked points on the cyclic voltammogram. At point 1, the scan has not begun, so the concentration is the same as bulk for each species. Points 5 and 7 both are both at the E 0' of the catalyst (as such [P] = [Q] at distance = 0). In all of the plots, it can be seen that the concentrations of P and Q are defined by the Nernst Equation at the surface of the electrode (distance = 0 cm). As the voltammogram is scanned between points 2 and 4, the substrate at the surface of the electrode is consumed before the concentration of active catalyst (Q) reaches a value visually different from point 0. Points 5 7 illustrate that once the potential is in a range that significantly alters the concentrations of P and Q from their bulk values, no substrate is available near the electrode. The depletion of substrate continues to grow over the course of the scan, leading to a Nernstian redox wave for the catalyst. Restated, the catalyst is reduced (and reoxidized) and has no substrate in the reaction layer to react with. At point 8, we can see that once Q is completely re-oxidized, either at the electrode during the anodic scan or via reaction with A, the substrate diffuses back towards the electrode surface. S34

35 Extending the KT2 Equation to an ECEC' mechanism. In our efforts to extend the equation defining peak position for an EC' reaction exhibiting total catalysis (Equation 4, S7) to a two electron, two proton system, we empirically determined that the peak position is well described by Equation 5 (S8) for scenarios in which the second electron transfer is much easier than the first and k 2 is infinitely faster than k 1 (see below). Equation 5 (S8) differs from Equation 4 (S7) in the catalyst concentration; the concentration of catalyst is multiplied by a factor of 2 for the ECEC' reaction. This can be understood by realizing that each active catalyst consumes two equivalents of substrate. Simulated results presented in Figure S41 show a comparison of an EC' reaction, an EC' reaction with twice the concentration of catalyst, and an ECEC' reaction in which the second electron transfer is much easier than the first. As illustrated below, we have determined that Equation 5 (S8) can be more widely applied to scenarios beyond those in which the second electron transfer is much easier than the first and k 2 is infinitely faster than k 1 (see below) Eq. S Eq. S8 Figure S41. Voltammograms for an EC' reaction with [P] = M (top), an EC' reaction with [P] = M (middle), and an ECEC reaction with [P] = M (bottom) under conditions in which catalysis conforms to Zone KT2. The peak location of the middle and bottom voltammograms are identical. Other significant simulation parameters: [A] = M, scan rate = 100 mv/s, and all diffusion coefficients = 1x10-5 cm 2 /s. The rate constants for chemical steps were 1x10 9 M -1 s -1. Simulations performed in DigiElch. S35

36 Identifying conditions for valid use of KT2 equation (Equation 5) To determine the region in which the empirically determined KT2 equation (Equation 5, S8) is valid, voltammograms were simulated over the range of excess factors ( / ) from 1 to 56 using a grid of k 1 and k 2 values each ranging from 10 to 1 x M -1 s -1. The simplified two electron, two substrate, mechanism shown here was used for these simulations: The simulations were performed with a diffusion coefficient for P of D P = 8x10-6 cm 2 /s and for A of D A = 1.25x10-5 cm 2 /s. It was assumed the second electron transfer was much significantly easier than the first (E P/Q = 0 V, and E PA/QA = 0.3 V). The script for generating grids of peak potential values was prepared in-house with MATLAB (The Mathworks, Inc.) using a higher order Crank-Nicolson finite differences method. 12,13 To confirm the accuracy of this method, results were checked against simulations with identical parameters using the commercial DigiElch package. Scripts are provided as a separate supplementary file. An example of one of these grids is shown here in Figure S39. Figure S42. The peak potential value is plotted against the log of k 1 and k 2. This particular dataset was obtained for concentrations [P] = M and [A] = 0.002, with a scan rate of 100 mv/s. S36

37 To simplify the analysis of this data, we examined the 2D cross sections where either k 1 = 1 x M -1 s -1 or k 2 = 1 x M -1 s -1, seen in Figure S40. Figure S43. (Right) Cross sections from Figure S39 where k 1 = 1 x M -1 s -1 (black) and k 2 = 1 x M -1 s -1 (blue). The dashed lines represent the values determined from Equation 5 (S8) for identical conditions. The dashed red lines represent what we have assigned as our hard (k = 1x10 5 M -1 s -1 ) and soft (k = 1x10 7 M -1 s -1 ) boundaries for use of Equation 5. (Left) The voltammograms at each of the points marked A, B, and C. From Figure S40, we have assigned boundaries for use of the KT2 equations; our hard boundary is defined by the region in which Equation 5 and the simulation results are within half a log unit of one another (k 1 and k 2 > 1 x 10 5 M -1 s -1 ) and our soft boundary is defined by the region in which Equation 5 and the simulation results are indistinguishable from one another (k 1 and k 2 > 1 x 10 7 M -1 s -1 ). The voltammograms shown for points A, B, and C highlight that 1) for small values of k 1 (point A), a reversible wave is obtained, as the catalyst does not interact with the substrate fast enough to affect change, 2) for small values of k 2 (point B), the response is identical to that expected for an ECE reaction, whereby the peak current is proportional to two times the catalyst concentration and no redox wave is observed at E P/Q, and 3) at or above our boundaries (point C), a total catalysis response is obtained, whereby the peak current is proportional to the substrate concentration and reduction of P to Q can be seen at E P/Q. As noted above, Equation 5 (S8) was determined based on two assumptions: 1) the second electron transfer is much easier than the first (E P/Q < E PA/QA ) and 2) the second chemical step is much faster than the first (k 2 >> k 1 ). Simulations were performed to quantify these conditions. Simulations were initially performed under conditions which Equation 5 (S8) is valid: the simulated peak potential matched the value determined from Equation 5 (S8). A series of voltammograms were then simulated in which value of k 2 and the potential of the second electron transfer (E PA/QA ) were altered (n.b. neither parameter is a factor in Equation 5). From these data, the difference between the peak potential obtained from the digital simulation and S37

38 the peak potential determined from Eq. 5 (E(sim) E(Eq.5)) was determined as a function of both the ratio of the rate constants (k 2 /k 1 ) and the difference between the potentials for the two electron transfer reactions (E PA/QA E P/Q ) (Figure S41 S43). From these data, we determined specific conditions in which Equation 5 accurately predicts the peak potential, defined by log Figure S44. Plot of the peak potential difference between the simulated value and the value predicted from Equation 5 (colormap, green represents no deviation) as a function of the difference in potential between the first and second electron transfer (horizontal axis) and the logarithm of ratio of k 2 and k 1 (vertical axis). The black line represents the equation log At values below 2.7, the simulated peak potentials no longer match the predicted potential from Equation 5. For this simulation, k 1 = 1 x 10 8 M -1 s -1, E 1 = 0 V, υ= 0.1 V/s, and k 2 and E 2 were varied according to the axis. Figure S45. Plot of the peak potential difference between the simulated value and the value predicted from Equation 5 (colormap, green represents no deviation) as a function of the difference in potential between the first and second electron transfer (horizontal axis) and the logarithm of ratio of k 2 and k 1 (vertical axis). The black line represents the equation log At values below 2.7, the simulated peak potentials no longer match the predicted potential from Equation 5. For this simulation, k 1 = 1 x 10 9 M -1 s -1, E 1 = 0 V, υ = 0.1 V/s, and k 2 and E 2 were varied according to the axis. S38

39 Figure S46. Plot of the peak potential difference between the simulated value and the value predicted from Equation 5 (colormap, green represents no deviation) as a function of the difference in potential between the first and second electron transfer (horizontal axis) and the logarithm of ratio of k 2 and k 1 (vertical axis). The black line represents the equation log At values below 2.7, the simulated peak potentials no longer match the predicted potential from Equation 5. For this simulation, k 1 = 1 x 10 8 M -1 s -1, E 1 = 0 V, υ= 0.2 V/s, and k 2 and E 2 were varied according to the axis. Determining k 1 from total catalysis data ln 2 Equation 5 (replotted above) can be rearranged to accommodate multiple experimental variables. In order to consider a series of voltammograms in which the substrate concentration ( ) is varied, the equation can be rearranged to produce Equation S9. / /. Eq. S9 As such, k can be determined by plotting the function of the catalytic peak potential against the inverse of substrate concentration. By a similar argument, a series of voltammograms in which the scan rate is varied can be analyzed by the Equation S10. / /. Eq. S10 Finally, for a series of voltammograms in which the concentration of catalyst is varied, data can be analyzed by Equation S11. / /. Eq. S11 S39

40 In this case, k can be determined by plotting the function of the catalytic peak potential against the square of the catalyst concentration. Examples of data analyzed through these methods is shown below. Figure S47. Peak potentials as a function of acid concentration were used to determine k 1. From voltammograms recorded at 0.5 mm 1, 100 mv with p-cyanoanilinium. Figure S48. Peak potentials as a function of scan rate were used to determine k 1. From voltammograms recorded at 0.5 mm 1 with 0.5 mm p- cyanoanilinium. S40

41 Figure S49. Peak potentials as a function of catalyst concentration were used to determine k 1. From voltammograms recorded at 5 mm p- cyanoanilinium, 100 mv/s. S41

42 SI 8 Oxidation of unreacted 1 2 (H + ) For solutions containing 1 and a weaker acid (pk a > 9.5), a broad oxidation wave is observed on the anodic scan at potentials positive of the anodic feature of the reversible 1 0/ wave recorded in the absence of acid (See SI 3 and SI 5). This feature is most pronounced at low acid concentrations. We assign this feature to the oxidation of unreacted 1 2 (H + ). Because the rate constant k global is on the order of 3.39 x 10 1 to 1.76 x 10 3 M -1 s -1 for acids in this range, turnover is expected to be slow with respect to the timescale of the experiment when low concentrations of acid are employed (ca mm, depending on k global ). As scan rate is increased, this feature becomes more pronounced and shifts to more positive potentials (Figure S50 S51). Figure S50. Cyclic voltammograms of a solution containing 1 (black trace) and 4- chloroanilinium, as denoted. Voltammograms were taken at (increasing): 100, 150, 200, 300, 400, 500, 600, and 700 mv/s. All voltammograms recorded in 0.25 M [Bu 4 N][PF 6 ]. The peak potential and intensity of this feature were also found to be dependent on the concentration of base in solution (Figure S48). Upon the addition of aniline (or substituted derivative), the peak location of the oxidation shifts cathodically. We attribute this kinetic shift to a coupled proton transfer reaction, where oxidation of 1 2 (H + ) is coupled to the removal of the appended proton by local base. At higher concentrations of base, the peak shifts to negative potentials, as expected for an electrochemical EC mechanism and a concerted proton transferelectron transfer process ((EC) concerted ). 14 S42

43 Figure S51. The black trace is a portion of the cyclic voltammogram of a solution containing only 1, and reflects the oxidation of 1 -/0. Sets of colored circles identify the peaks of the oxidation at 100, 150, 200, 300, 400, 500, 600, and 700 mv/s in solutions containing acid and varying amounts of base, as noted. The complete voltammograms from which these data were collected follow in Figures S52 - S55. All voltammograms were recorded in a solution of 0.5 mm 1 and 1.0 mm 4-chloroanilinium with 0.25 M [Bu 4 N][PF 6 ] electrolyte. Figure S52. Black trace is of a solution containing 1.0 mm 1. Red traces are catalytic voltammograms of the same solution with added 1.0 mm 4- chloroanilinium and no additional base. Voltammograms were recorded at 100, 150, 200, 300, 400, 500, 600, and 700 mv/s, respectively. The peak potential and current of the oxidation (approx mv/s) are independently identified in Figure S51. All voltammograms recorded in a 0.25 mm [Bu 4 N][PF 6 ] CH 3 CN solution. S43

44 Figure S53. Black trace is of a solution containing 1.0 mm 1. Green traces are catalytic voltammograms of the same solution with added 1.0 mm 4- chloroanilinium and 1.0 mm 4-chloroaniline. Voltammograms were recorded at 100, 150, 200, 300, 400, 500, 600, and 700 mv/s, respectively. The peak potential and current of the oxidation (approx mv/s) are independently identified in Figure S51. All voltammograms recorded in a 0.25 mm [Bu 4 N][PF 6 ] CH 3 CN solution. Figure S54. Black trace is of a solution containing 1.0 mm 1. Blue traces are catalytic voltammograms of the same solution with added 1.0 mm 4- chloroanilinium and 2.0 mm 4-chloroaniline. Voltammograms were recorded at 100, 150, 200, 300, 400, 500, 600, and 700 mv/s, respectively. The peak potential and current of the oxidation (approx mv/s) are independently identified in Figure S51. All voltammograms recorded in a 0.25 mm [Bu 4 N][PF 6 ] CH 3 CN solution. S44

45 Figure S55. Black trace is of a solution containing 1.0 mm 1. Purple traces are catalytic voltammograms of the same solution with added 1.0 mm 4- chloroanilinium and 2.0 mm 4-chloroaniline. Voltammograms were recorded at 100, 150, 200, 300, 400, 500, 600, and 700 mv/s, respectively. The peak potential and current of the oxidation (approx mv/s) are independently identified in Figure S51. All voltammograms recorded in a 0.25 mm [Bu 4 N][PF 6 ] CH 3 CN solution. S45

46 SI 9 Effects of an acid-independent chemical step on FOWA and plateau analysis In order to determine the effects of an acid independent step (described by k Ω ) on FOWA and current plateau analysis, we carried out a series of digital simulations. Simulations were based on the rate constants determined for 4-trifluoromethylanilinium, the strongest acid for which both FOWA and plateau current analysis were performed. This allowed us to assess the worst case scenario in which k Ω could influence the plateau current analysis. General Parameters for Simulation Scan Rate Cycles Ru(Ohm) CdI(F) Temp. (K) Geometry Area (cm 2 ) 0.1 V/s Planar Diffusion Potential Steps (V) Gauss-Newton Iteration Noise Level (A) Semi-Infinite 1D Grid Expansion Factor Rel. Truncation Error Xmas/SQRT(Dt) Charge Transfer Reactions Local FEM error level: 0.02 Reaction E (V) α k s (cm/s) e e Charge Transfer Reactions Reaction K eq k f k b * HA A 1x10 4 1x10 7 M -1 s -1 1x10 M -1 s -13 HA A - 5x10 3 M -1 s -1 0 H s -1 for data in Figure S50, as denoted in legend for Figures S49 and S51 0 *constants automatically calculated via DigiElch rate constants used are representative of those determined for 4-trifluoromethylanilinium, the strongest acid for which both FOWA and plateau current analysis were performed. S46

47 Species D (cm 2 /s) C 0 (M) 8x x x x x HA 1x10-5 As described in legend for Figures S49 and S50, 5 M for Figure S51 A 1x H 2 1x The impact of k Ω on plateau analysis Figure S56. Simulated catalytic voltammograms of 0.5 mm 1 in solution with 2.5, 5.0, 10.0, 15.0, and 20.0 mm acid concentrations for k Ω = 125 s -1. Inset: Current maxima at each acid concentration for three sets of simulations: (black) when k Ω = 125 s -1, (red) when k Ω = 300 s -1, and (green) when k Ω = 100,000 s -1. The speed of the acidindependent step minimally impacts the current maxima and subsequent calculation of k 2(global). For weaker acids, for which the rate k 2(global) rate constants are smaller, an even more minimal impact of k Ω is anticipated. S47

48 Effects of excess [HA] on plateau currents Figure S57. Simulated catalytic voltammograms of a solution of 0.5 mm 1 and varying acid concentrations (as noted). The maximum plateau current i c MAX does not change with an increase in acid concentration and is limited exclusively by k Ω. Effects of k Ω on plateau currents and FOWA Figure S58. Simulated catalytic voltammograms of 0.5 mm 1 with excess acid. In the presence of excess acid, the plateau current maximum is controlled exclusively by the acid-independent step, k Ω. Further, the foot-of-the-wave is not affected by k Ω. S48

49 References (1) Kaljurand, I.; Kütt, A.; Sooväli, L.; Rodima, T.; Mäemets, V.; Leito, I.; Koppel, I. A. J. Org. Chem. 2005, 70, (2) McCarthy, B. D.; Martin, D. J.; Rountree, E. S.; Ullman, A. C.; Dempsey, J. L. Inorg. Chem. 2014, 53, (3) Appel, A. M.; Lee, S.; Franz, J. A.; DuBois, D. L.; Rakowski DuBois, M.; Twamley, B. Organometallics 2009, 28, (4) Hu, X.; Brunschwig, B. S.; Peters, J. C. J. Am. Chem. Soc. 2007, 129, (5) Savéant, J.-M. Elements of Molecular and Biomolecular Electrochemistry; John Wiley & Sons, Inc.: Hoboken, (6) Baffert, C.; Artero, V.; Fontecave, M. Inorg. Chem. 2007, 46, (7) Hu, X.; Cossairt, B. M.; Brunschwig, B. S.; Lewis, N. S.; Peters, J. C. Chem. Commun. 2005, 1, (8) Anxolabéhère-Mallart, E.; Costentin, C.; Fournier, M.; Robert, M. J. Phys. Chem. C 2014, 118, (9) Rountree, E. S.; McCarthy, B. D.; Eisenhart, T. T.; Dempsey, J. L. Inorg. Chem. 2014, 53, (10) Costentin, C.; Savéant, J.-M. ChemElectroChem 2014, 1, (11) Costentin, C.; Drouet, S.; Robert, M.; Savéant, J.-M. J. Am. Chem. Soc. 2012, 134, (12) Liu, J.; Pope, G. A.; Seperhrnoori, K. Appl. Math. Model. 1995, 19, (13) Crank, J. In The Mathematics of Diffusion; Oxford University Press: Bristol, England, 1975; pp (14) McCarthy, B. D.; Donley, C. L.; Dempsey, J. L. Chem. Sci. 2015, 6, S49