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Identifying and Breaking Scaling Relations in Molecular Catalysis of Electrochemical Reactions Michael L. Pegis,* Catherine F. Wise, Brian Koronkiewicz, and James M. Mayer* Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States S Supporting Information *
confined in the reaction diffusion layer is reduced (for reductive catalysis), and turnover is limited by chemical rather than electrochemical steps.3−5 The effective overpotential for a molecular catalyst (ηeff) is therefore defined as the difference between Erxn and the reduction potential that initiates catalysis (E1/2, eq 1).6−9
ABSTRACT: Improving molecular catalysis for important electrochemical proton-coupled electron transfer (PCET) reactions, such as the interconversions of H+/H2, O2/H2O, CO2/CO, and N2/NH3, is an ongoing challenge. Synthetic modifications to the molecular catalysts are valuable but often show trade-offs between turnover frequency (TOF) and the effective overpotential required to initiate catalysis (ηeff). Herein, we derive a new approach for improving efficiencieshigher TOF at lower ηeffby changing the concentrations and properties of the reactants and products, rather than by modifying the catalyst. The dependence of TOF on ηeff is shown to be quite different upon changing, for instance, the pKa of the acid HA versus the concentration or partial pressure of a reactant or product. Using the electrochemical reduction of dioxygen catalyzed by iron porphyrins in DMF as an example, decreasing [HA] 10-fold lowers ηeff by 59 mV and decreases the TOF by a factor of 10. Alternatively, a 10fold decrease in Ka(HA) also lowers ηeff by 59 mV but only decreases the TOF by a factor of 2. This approach has been used to improve a catalytic TOF by 104 vs the previously reported scaling relationship developed via synthetic modifications to the catalyst. The analysis has the potential to predict improved efficiency and product selectivity of any molecular PCET catalyst, based on its mechanism and rate law.
ηeff = Erxn − E1/2
(1)
A longstanding challenge in molecular PCET catalysis is to increase the TOF without compensating changes in the E1/2 (and thus the ηeff). Significant progress has been made with catalyst designs, such as the incorporation of outer coordination sphere proton relays10,11 and electrostatic groups.12 Still, tradeoffs between TOF and ηeff“scaling relations”are the norm and have recently been reported for proton,13−15 dioxygen,6 and carbon dioxide16 reductions. For example, we observed that log(TOF) for the oxygen reduction reaction (ORR) in DMF scales linearly with ηeff when the iron porphyrin (Fe(P)) catalyst or acid concentration is varied (Figure 1).6 Computa-
fficient catalysis for complex multielectron/multiproton reactions is a critical challenge in energy science. These reactions include H+/H2 and O2/H2O interconversions and the reductions of CO2 and N2. Catalysts for these interconversions are evaluated with respect to their turnover frequency (TOF), turnover number, selectivity, and overpotential (η). Efficient catalyst systems have high TOFs at low η, at close to the thermodynamic (equilibrium) potential for the reaction under the experimental conditions (Erxn). Achieving high efficiencies in proton-coupled electron transfer (PCET) catalysis has been quite difficult. Molecular catalysts are of increasing interest due to their potential for more precise structural control and more detailed mechanistic understanding than traditional heterogeneous electrocatalysts. For a heterogeneous electrocatalyst, higher TOFs are obtained at higher η’s (cf. Tafel plots).1 The TOF for an ideal molecular catalyst, however, reaches a plateau at applied potentials beyond the E1/2 of the catalyst.2 This maximum TOF (TOFmax3) occurs when essentially all of the active catalyst
E
© 2017 American Chemical Society
Figure 1. Scaling of log(TOF) with ηeff for the ORR in DMF catalyzed by substituted Fe(P)’s.6 The ηeff was independently varied with catalyst E1/2 and with [HA] (= [H-DMF+]).
tional studies showed that these relations originate from the correlation of multiple catalyst properties with the catalyst E1/2. These properties include the Keq for initial O2 binding and the pKa of the protonated superoxide intermediate (P)FeIIIO2H•+, which is formed in the rate-determining step.6,17 Figure 1 and other TOF vs ηeff plots for molecular catalysts are thus Received: May 31, 2017 Published: July 19, 2017 11000
DOI: 10.1021/jacs.7b05642 J. Am. Chem. Soc. 2017, 139, 11000−11003
Communication
Journal of the American Chemical Society ⎧ ⎪ ° − E1/2 − log(kcat[HA]a PO2 b) = m⎨EORR ⎪ ⎩
somewhat analogous to volcano plots for heterogeneous materials.18 The goal of higher catalytic efficiency is represented by the arrow pointing off the scaling line, toward higher TOF and lower ηeff. Herein, we derive the relationship between the TOF and ηeff from the catalytic rate law and Nernst equation, using the ORR as an example. Adjusting each of the experimental variables ([HA], PO2, pKa, [H2O]) results in a unique scaling relationship. This provides a novel approach to tune catalytic systems toward high TOFs at lower ηeff, which we have used to exceed the scaling relationship in Figure 1 by 4 orders of magnitude in TOF. The analysis is general to homogeneous catalysis of any PCET process. It provides an intuitive basis for improving the efficiency of catalysis by targeting half reaction components other than the catalyst. While the requirements of a complete device may constrain some of the parameter space explored here, knowledge of the scaling relations is critical to understand, compare, and optimize the catalytic aspects of efficiency. For the ORR in nonaqueous solvents (eq 2), the equilibrium potential EORR is given by the Nernst equation (eq 3), O2 + 4HA + 4e− ⇌ 2H 2O + 4A−
° − EORR = EORR
⎛ [H O]2 ⎞ 2.303RT 2 ⎟ log⎜⎜ + 4⎟ nF P [H ] ⎠ ⎝ O2
⎫ ⎛ [H O]2 [A−]4 ⎞ ⎪ ⎟⎟ + (0.0592 V)pK a ⎬ + C (0.0148 V) log⎜⎜ 2 4 ⎪ ⎝ PO2[HA] ⎠ ⎭ (8)
We aim to describe how changes to the catalyst or reaction conditions affect the correlation slope m, the relationship between TOF and ηeff. The general expression (eq 8) simplifies greatly when only one concentration or parameter (x) is varied while holding all other parameters (A) constant (eq 9). ⎛ ∂ log TOF ⎞ (∂ log TOF/∂x) A ⎟⎟ = mx = ⎜⎜ ∂ η ∂ η ∂ / x ( eff )A ⎝ ⎠ eff
The key result is that the correlation coefficients mx are dif ferent for each parameter of the catalytic system. In other words, the TOF will respond differently to changes in ηeff accomplished varying different parameters (e.g., changing [HA] vs PO2). The derived correlation coefficients can be validated by comparison to experimental values, as shown below. We first consider the effect of varying the [HA] or PO2 for the ORR. Evaluating eq 9 with respect to [HA] or PO2, keeping all other parameters constant, yields the correlation coefficients mHA and mO2 in eqs 10 and 11,
(2)
(3)
where E°ORR is the standard potential and PO2 is the O2 partial pressure above the solution. For the case of catalysis with weak acids (as is common for molecular catalysts in organic solvents), eq 3 can be expanded to include the ratio of weak acid to conjugate base concentrations ([HA]/[A−]) and the pKa of the acid in that solvent. Derivations involving fully dissociated acids are in the Supporting Information (SI). Combining eqs 1 and 4 gives the ηeff as a function of the reaction conditions (eq 5). ⎛ [H O]2 [A−]4 ⎞ ° − (0.0148 V) log⎜ P2 [HA]4 ⎟ EORR = EORR ⎝ O2 ⎠ − (0.0592 V)pK a ⎛ [H O]2 [A−]4 ⎞ ° ηeff = EORR − E1/2 − (0.0148 V) log⎜ P2 [HA]4 ⎟ ⎝ O2 ⎠ − (0.0592 V)pK a (5)
Scaling relationships such as Figure 1 relate log(TOF) and ηeff. The TOF5 is given by the rate law for the catalytic reaction, as shown in general for the ORR in eq 6. The log(TOF)/ηeff scaling relation is often linear, defined by a correlation coefficient or slope m (eq 7). (6)
log(TOF) = m(ηeff ) + C
(7)
mHA = a /0.0592 dec/V = 16.9a dec/V
(10)
mO2 = b/0.0148 dec/V = 67.6b dec/V
(11)
(see derivation in the SI; dec = decade in TOF). The a and b in these equations are the reaction orders in [HA] and PO2, respectively (eq 6). The different numerical values result from the different stoichiometries of HA and O2 with respect to the electrons transferred in the ORR, 1:1 for HA:e− vs 1:4 for O2:e−. Experimentally, we have found that ORR catalysis by iron tetraphenylporphyrin (Fe(TPP)) is first-order in both [HA] and in PO2 (a = b = 1 in eq 6).6,19 Thus, a factor of 10 increase in [HA] results in a 10-fold increase in the TOF (Figure S10). This also gives a 59.2 mV increase in the ηeff, per eq 5. The predicted slope mHA is therefore 16.9 decades in TOF per volt shift in ηeff [(0.0592 V/dec)−1], and we measured 18.5 dec/V (Figure 1). In contrast, a 10-fold increase in the O2 pressure causes a 10 times increase in the TOF but only a 15 mV shift in ηeff and therefore an improvement of 44 mV from the scaling relation in Figure 1. This example shows the power of the analysis in eq 8: the relationship between the TOF and ηeff responds dif ferently to dif ferent changes in the reaction conditions. The concentration of reaction products usually does not affect the TOF, providing another method to decouple TOF from ηeff. In this case, changing [A−] or [H2O] by an order of magnitude does not affect the TOF (mA− = mH2O = 0) but will shift the ηeff by ±0.0592 and ±0.0296 V, respectively (eq 4). ORR catalysis by Fe(TPP)OTf was unaffected by the [H2O], confirming that mH2O = 0 (Figures S11−S13). In general, changing the [H2O] in organic solvents has only a small effect on ηeff (59.2 mV for [H2O] = 10 mM vs 1 M), so it is not a major concern if studies of O2 and CO2 reduction in organic solvents have not taken this shift into account.
(4)
TOF = kcat[HA]a PO2 b
(9)
Combining the expressions for the TOF (eq 6) and the ηeff (eq 5) yields the general scaling relation involving the parameters of the catalytic system that appear in eq 4: pKa, [HA], [A−], [H2O], PO2, and E1/2 of the catalyst (eq 8). 11001
DOI: 10.1021/jacs.7b05642 J. Am. Chem. Soc. 2017, 139, 11000−11003
Communication
Journal of the American Chemical Society
The striking feature is the diversity of the correlation coefficients, reflecting the variety of effects predicted or measured for a single catalyst or within a series of similar catalysts. The table also shows why a single scaling relationship appears in Figure 1 when both E1/2 and [HA] were varied: coincidentally, the correlation coefficients mE1/2 and mHA are very close, as illustrated by the black and red lines in Figure 2. Inspired by the prediction of a very shallow dependence of TOF on the pKa of the acid used, we measured the TOFs of the Fe(TPP)-catalyzed ORR with p-toluenesulfonic acid, trifluoroacetic acid, and salicylic acid (pKas in DMF = 2.5, 6.0, and 8.2, all weaker than H-DMF+ (pKa = 0)21,22). ORR TOFs were measured using foot-of-the-wave (FOW) analysis under conditions of equimolar amounts (100 mM) of water, acid, and conjugate base, and the selectivity and mechanism were found not to change with acid (see SI). Changing from HDMF+ to buffered salicylic acid decreased ηeff by 333 mV but only decreased the TOF by 1.7 orders of magnitude.23 The measured Δlog(TOF)/Δηeff of 5.1 dec/V is in excellent agreement with the predicted coefficient mpKa = 5.1 in Table 1. ORR catalysis by Fe(TPP) in buffered salicylic acid is 4 orders of magnitude faster than expected from the prior scaling relationship based on changing the catalyst structure (mE1/2) or the concentration of dissolved acid (mHA; arrow in Figure 2). These predictions and observations are for catalysis with ratedetermining protonation. If the catalyst TOF is independent of the acid pKa, then α = 0 in eqs 12 and 13 above and mpKa = 0 decade of TOF/V in ηeff. Such a switch to zero slope is evident in Figure 3 in the paper by Dempsey et al.,24 since changes in pKa imply changes in ηeff (eq 5). The analysis presented here is general and readily adapted to any multielectron/multiproton catalysis.25 This approach may be particularly valuable for electrochemical CO2 and N2 reductions, predicting (for example) substantial improvements under higher substrate pressure when unfavorable CO2 or N2 binding occurs in or prior to the rate limiting step. The prediction is not simply the typical higher TOF at higher pressure, but rather an increase in TOF relative to the change in overpotential. For an N2 reduction process that is first-order in N2 and H+, for instance, a 10-fold increase in TOF could be achieved by increasing either PN2 or [HA], but the increases the overpotential would be only 10 mV for PN2 vs 59 mV for [HA]. The diversity of effects of the different parameters of the catalytic system in Table 1 contrast with the traditional use of a single “activity descriptor” in heterogeneous catalysis and electrocatalysis. This descriptor is solely a feature of the catalyst, typically a thermochemical property such as the bond strength between the surface and a reaction intermediate like H or OH. The analysis developed here shows that it is insuf ficient to consider only the catalyst. The performance of a catalytic system, specifically the TOF as a function of overpotential, depends on all components of the catalytic system. The analysis presented here should be valuable for heterogeneous electrocatalysts as well. Consider, for instance, an electrocatalytic process in which protonation by HA is the rate-determining step at a specific applied potential. Increasing the concentration of HA would increase the TOF at that potential, but this would be at a cost in overpotential because the equilibrium potential also shifts with [HA]. In contrast, increasing the concentrations of both buffer components, keeping the [HA]/[A−] ratio constant, would increase the TOF
The acid pKa affects the TOF when protonation is a preequilibrium or rate-determining step. For ORR/Fe(P) catalysis, protonation is rate limiting. The correlation coefficient mpKa can only be estimated using the Brønsted Law for proton transfer rate constants kHA, that log(kHA) varies as a fraction of the change in the pKa (eq 12).20 Combining eqs 8 and 12 yields the expression for mpKa (eq 13). Δ log(kHA ) = −α(ΔpK a) mpKa = =
(
∂ log TOF ∂ηeff
α 0.0592
)=
(12)
(∂ log TOF / ∂pK a)A (∂ηeff / ∂pK a) A
dec/V
(13)
The Brønsted coefficient α is often assumed to be 0.5; in this case α ≅ 0.3 from theory and experiment (ref 6 and Figure S15). A decrease in acid strength of 1 pKa unit decreases ηeff by 59.2 mV but reduces the TOF by only a factor of 10α, or 3.1 for α = 0.5 and only 2 for α = 0.3. These changes in TOF are much smaller than the same changes induced from [HA] or PO2 described above because proton transfer is rate limiting. The examples above describe the changes in TOF and ηeff for a single catalyst upon changes in the concentrations and properties of the reactants and products. Our previous ORR study showed a more traditional scaling relationship relating log(TOF) with a catalyst property (E1/2) over a series of catalysts, which had a slope of 18.5 dec/V (0.054 V/dec, Figure 1).6 The conclusions about the iron porphyrin-catalyzed ORR reactions are summarized in Table 1 and the lines in Figure 2. Table 1. Correlation Coefficients for the Fe(P)-Catalyzed ORR parameter varied
corr coeff (decade of TOF/V in ηeff)
[HA]a
catalyst E1/2b
acid pKac
PO2a
16.9
18.5
5.1
67.6
mHA and mPO2 predicted from the first-order behavior of the TOF on [HA] and PO2. bmE1/2 from experimental variation of catalyst E1/2. cmpKa predicted using α = 0.3 from theory and experiments with H-DMF+ and a series of catalysts. a
Figure 2. Scaling relations for Fe(P) ORR catalysis predicted (lines) and measured (points) upon changing the acid concentration (black), partial pressure of O2 (green), pKa of the acid (purple) and E1/2 of the catalyst (some data from ref 6). The intersection point is Fe(TPP) with 100 mM H-DMF+ under 1 atm O2. 11002
DOI: 10.1021/jacs.7b05642 J. Am. Chem. Soc. 2017, 139, 11000−11003
Communication
Journal of the American Chemical Society
B.K. is supported by a Graduate Research Fellowship from the National Science Foundation.
without any change in the equilibrium potential or overpotential. Changes in selectivity depending on catalysis conditions should also be predictable from related scaling relationship coefficients derived from the rate laws for the competing paths. This could be applied to changes in selectivity between different products from the same reactant, as in CO2 reduction, or to optimize the selectivity between different reactions, such as how to encourage the electrochemical reduction of N2 to NH3 over H+ to H2. For O2 reduction, Nocera and co-workers have reported a roughly linear correlation between ηeff and H2O vs H2O2 selectivity for a diverse set of ORR catalysts, including our own.9 The %H2O2 increases as ηeff is decreased via changes to the solvent, proton source, or catalyst. However, the analysis here suggests that changes to ORR selectivity will in general depend on how the ηef f is varied, via changes in catalyst E1/2, [HA], or the pKa of HA. For example, we observed only a small increase in %H2O2 from 2 to 6% for Fe(TPP) catalysis with different acids (Figures S17−19), while the correlation reported by Nocera would predict an increase from 0 to ∼21% for this 333 mV decrease in ηeff. Current work in our laboratory is exploring the prediction of diverse selectivity based-scaling relations and their mechanistic implications for the ORR. In summary, we derive here the theoretical basis for linear free energy relationships between turnover frequency and effective overpotential in molecular catalysis of PCET reactions. The slopes of these scaling relationships vary substantially depending on the parameter that is varied: the acid concentration, acid pKa, substrate pressure, or catalyst E1/2. This analysis therefore predicts how to improve a catalytic system toward high TOFs at lower overpotentials. As an example, weaker acids yielded a catalytic system 4 orders of magnitude more efficient than expected from the previous scaling relationship. Understanding and exploiting the TOF:ηeff scaling relationships present new opportunities to compare and optimize catalytic systems under different conditions.
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(1) Tafel, J. Z. Phys. Chem. 1905, 50, 641. (2) Saveant, J. M. Chem. Rev. 2008, 108, 2348. (3) Costentin, C.; Drouet, S.; Robert, M.; Savéant, J.-M. J. Am. Chem. Soc. 2012, 134 (27), 11235. (4) Artero, V.; Saveant, J.-M. Energy Environ. Sci. 2014, 7, 3808. (5) The TOF of a homogeneous reaction is the number of moles of product produced per unit time per mole of catalyst. For molecular electrochemical catalysis, the TOF is defined relative to the amount of catalyst in the reaction diffusion layer, following Savéant.2−4 This TOF (TOFmax/2) can be measured with CV; see refs 3 and 4. (6) Pegis, M. L.; McKeown, B. A.; Kumar, N.; Lang, K.; Wasylenko, D. J.; Zhang, X. P.; Raugei, S.; Mayer, J. M. ACS Cent. Sci. 2016, 2, 850. (7) More precisely, the effective overpotential is the difference between the equilibrium potential (Erxn) and the catalytic half-wave potential (Ecat/2) in the absence of side phenomena. Often, as found for the ORR case discussed here, Ecat/2 is essentially equal to the catalyst reduction potential E1/2 (here, the Fe(III/II) potential). For other cases, see the SI. (8) Rountree, E. S.; McCarthy, B. D.; Eisenhart, T. T.; Dempsey, J. L. Inorg. Chem. 2014, 53, 9983. (9) Passard, G.; Ullman, A. M.; Brodsky, C. N.; Nocera, D. G. J. Am. Chem. Soc. 2016, 138, 2925. (10) Helm, M. L.; Stewart, M. P.; Bullock, R. M.; DuBois, M. R.; DuBois, D. L. Science 2011, 333, 863. (11) Costentin, C.; Drouet, S.; Robert, M.; Savéant, J.-M. Science 2012, 338, 90. (12) Azcarate, I.; Costentin, C.; Robert, M.; Savéant, J.-M. J. Am. Chem. Soc. 2016, 138, 16639. (13) Raugei, S.; Helm, M. L.; Hammes-Schiffer, S.; Appel, A. M.; O’Hagan, M.; Wiedner, E. S.; Bullock, R. M. Inorg. Chem. 2016, 55, 445. (14) Dutta, A.; Ginovska, B.; Raugei, S.; Roberts, J. A. S.; Shaw, W. J. J. Chem. Soc., Dalton Trans. 2016, 45, 9786. (15) Cardenas, A. J. P.; Ginovska, B.; Kumar, N.; Hou, J.; Raugei, S.; Helm, M. L.; Appel, A. M.; Bullock, R. M.; O’Hagan, M. Angew. Chem., Int. Ed. 2016, 55, 13509. (16) Azcarate, I.; Costentin, C.; Robert, M.; Savéant, J.-M. J. Phys. Chem. C 2016, 120, 28951. (17) Baran, J. D.; Grönbeck, H.; Hellman, A. J. Am. Chem. Soc. 2014, 136, 1320. (18) Parsons, R. Trans. Faraday Soc. 1958, 54, 1053. (19) Wasylenko, D. J.; Rodriguez, C.; Pegis, M. L.; Mayer, J. M. J. Am. Chem. Soc. 2014, 136, 12544. (20) Brönsted, J.; Pedersen, K. Z. Phys. Chem. 1924, 108, 185. (21) Pegis, M. L.; Roberts, J. A. S.; Wasylenko, D. J.; Mader, E. A.; Appel, A. M.; Mayer, J. M. Inorg. Chem. 2015, 54 (24), 11883. (22) Fourmond, V.; Jacques, P. A.; Fontecave, M.; Artero, V. Inorg. Chem. 2010, 49, 10338. (23) The pKa shift on changing from DMF-H+ to buffered salicylic acid should cause a decrease in ηeff of 0.0592 × 8.2 V = 0.485 V, but changing the acid also caused a compensating E1/2 shift of −0.152 V. (24) Elgrishi, N.; Kurtz, D. A.; Dempsey, J. L. J. Am. Chem. Soc. 2017, 139 (1), 239. (25) Costentin, C.; Savéant, J.-M. ChemElectroChem 2014, 1, 1226.
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b05642. Mathematical derivations and experimental data, including Figures S1−S19 (PDF)
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REFERENCES
AUTHOR INFORMATION
Corresponding Authors
*
[email protected] *
[email protected] ORCID
Michael L. Pegis: 0000-0001-6686-1717 James M. Mayer: 0000-0002-3943-5250 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research was supported as part of the Center for Molecular Electrocatalysis, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, and has been tremendously stimulated by interactions among the members of the Center. 11003
DOI: 10.1021/jacs.7b05642 J. Am. Chem. Soc. 2017, 139, 11000−11003
