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Catalysis of Electrochemical Reactions by Surface-Active Sites. Analyzing the Occurrence and Significance of Volcano Plots by Cyclic Voltammetry Cyrille Costentin, and Jean-Michel Savéant ACS Catal., Just Accepted Manuscript • Publication Date (Web): 21 Jun 2017 Downloaded from http://pubs.acs.org on June 21, 2017
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ACS Catalysis
Catalysis of Electrochemical Reactions by Surface-Active Sites. Analyzing the Occurrence and Significance of Volcano Plots by Cyclic Voltammetry Cyrille Costentin* and Jean-Michel Savéant* Université Paris Diderot, Sorbonne Paris Cité, Laboratoire d'Electrochimie Moléculaire, Unité Mixte de Recherche Université - CNRS N° 7591, Bâtiment Lavoisier, 15 rue Jean de Baïf, 75205 Paris Cedex 13, France.
[email protected];
[email protected] ABSTRACT: Cyclic voltammetry (CV) of heterogeneous electrocatalysts offers a convenient means to critically assess the occurrence of “volcano plots” rendered popular by acids’ reduction on metal electrodes. The equations relevant to VolmerHeyrovsky-type reactions shows that the adsorption free energy of the surface-bound intermediate is one of the rate-controlling parameters, which, plotted against the exchange current could lead to a volcano-looking curve if other rate-controlling factors such as the rate-ratio of the two successive electron transfer steps would remain constant upon changing electrocatalyst. This is not necessarily the case in practice, thus blurring the occurrence of volcano plots. Careful recording and analysis of the CV responses should thus be a preferred strategy, leading additionally to catalytic Tafel plots for rational electrocatalysts’ benchmarking. The alternative Volmer-Tafel mechanism gives remarkably rise to Sshaped current-potential responses and to a volcano upon plotting the exchange current against the adsorption standard free energy of the primary intermediate. Again a wealth of kinetic information results from the characteristics of the current-potential responses.
always been eliminated from the data. These question have been fully discussed recently accompanied with the proposal to use nanometric particle of the metal to speed up steady-state diffusion above the levels permitted by rotating disk electrode techniques. 8,9 Such approaches could also be achieved by cyclic voltammetry, using the scan rate to speed up diffusion, scan rate being a parameter easier to manipulate than the size of a ultramicroelectrode or that of a nanoparticle. 10 In this framework, the following discussion is devoted to the application of cyclic voltammetry 10 to the detection and characterization of volcano plots as a possible manifestation of the Sabatier principle. As a grossly qualitative rule of a thumb, the Sabatier principle tells us that either a very strong or a very slight stabilization of the primary intermediate on the reaction pathway is not a good start for the design of an efficient catalytic system. Our goal is, beyond the role of the thermodynamic stabilization of the primary intermediate, to come closer to quantitative characterization of electrocatalytic kinetics and mechanisms by use of cyclic voltammetry so as to entail a rational approach of electrocatalysts’ benchmarking. In this endeavor, many mechanistic, thermodynamic and kinetic factors may come into play besides the thermodynamic stabilization of the primary intermediate. This the reason that we have selected two examples of relatively simple mechanisms to which simplifying assumptions have been associated to serve as tutorial examples for the investigation or reinvestigation of electrocatalytic reactions. Multiplying the number of possible cases, while keeping a reasonable number of governing parameters would have led to an intractable taxonomic nightmare. Therefore, in accordance with their historical importance in the volcano plot approach of electrocatalysis, we consider the two reaction schemes displayed in Schemes 1 and 2, reminiscent of the VolmerHeyrovsky mechanism of proton reduction, shown on the right-hand side, 11,12,13 (P is a catalytically active surface site, A is a substrate, Z a cosubstrate, Q is a surface-bound intermediate and C the product (s)) and of the
Keywords: volcano plots, cyclic voltammetry, electrochemistry, electrocatalysis, hydrogen evolution. The existence of “Volcano plots” is an issue that recurrently attracts attention since a long time in the field of electrocatalysis. It derives from the application of the Sabatier principle 1 to heterogeneous catalysis of electrochemical reactions by surface active sites on metal electrodes. “Electrocatalysis” then implies the electron transfercoupled formation of a transient intermediate adduct between substrate and surface active site. Its further transformation into product regenerates the surface active sites for a new catalytic cycle. Insofar catalysis kinetics is essentially function of the thermodynamic stability of this E10 adduct, there is a tradeoff between the formation and decomposition of the intermediate. The rate of the catalytic reaction is thus expected to go through a maximum − the apex of the volcano− as a function of the E20 thermodynamic parameter measuring the stability of the intermediate. These notions have been developed for the hydrogen evolution (her) 0 EA,Z/C and hydrogen oxidation (hor) reactions 2,3,4 although they are more general in scope. Volcano plots are thus “a valiant attempt to understand catalytic reactions with the aid of a single descriptor”, 5,6 Scheme 1. Volmer-Heyrovsky type reaction scheme “typically the energy of adsorption of a single intermediate. However, the kinetics of complex reactions are not so simple.” 7a This is one of the most serious theoretical criticism of the general occurrence of Volcano plots. 7 From an experimental viewpoint, the scatter of data points is, in most cases, so large that the very existence of a volcano plot for the her, hor and oxygen reduction can be questioned. Another difficulty concerns fast reactions, such as, e.g., the her and hor on platinum electrodes, where the contribution of mass transport has not Scheme 2. Volmer-Tafel type reaction scheme
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values correspond to stable intermediates and vice versa) and several values of the two other parameters. Note that the above equations have been derived assuming a simple Langmuirian adsorption for the keyintermediate Q. Adaptation to other adsorption isotherms could be introduced if necessary. We note the existence of a volcano curve when the exchange current is plotted against the stability of the 0 = E10 + E20 / 2 . The adsorbed intermediate as seen in Figure 1b. It is a direct consequence Scheme 1, with, for the global reaction, EA,Z/C of the Sabatier principle in the case where the two other stability of the catalytic surface-bound intermediate is expressed by the 1 1 iη =0
Volmer-Tafel mechanism of the same reaction, respectively. All symbols used in the text and in the Supporting Information (SI) are defined on top of the latter. The thermodynamics of the first catalytic reaction is defined in
(
)
0 standard free energy of adsorption of Q on the electrode, ∆gad ,Q , expressed in eV when the potentials are expressed in V, with: 0 0 0 0 0 E10 = EA,Z/C − ∆g ad ,Q and E2 = EA,Z/C + ∆g ad ,Q
i
FSk S1CA0 Γ 0
0 0 FSk S1CA Γ
0.8
0.8 0.6
0.6
a
0.4
0.4
b
0.2 0.2
0 We define the overpotential as: η = EA,Z/C − E (E: electrode potential) as a concentration-independent thermodynamic characteristic of the reaction. The CV response expressed as the dimensionless current,
(
0 0 F ∆ g ad ,Q
Fη RT
0 -0.2 -15
-10
-5
0
-0.2
RT ln10 -4
-2
0
2
-0.4 4
)
0 i / FS Γ0kS1CA / C 0 , vs. the dimensionless potential Fη / RT is a Fig. 1. Reaction Scheme 1. a: dimensionless current-potential responses for various values of the intermediate stability constant, 0 0 ∆gad ,Q , of two other parameters, F ∆ g ad function, besides ,Q / ( RT ln10 ) = -3 (blue), -2 (green), -1 (red), 0 (black), 1
( kS 2CZ0 ) / ( kS1CA0 )
(
( kS1CA0 / C0 ) ( RT / Fv)
)
that measure the (magenta), 2 (orange), 3 (cyan). b: resulting volcano plot showing the variation of the dimensionless exchange current with the intermediate competition between the two electrochemical rates and the competition stability constant . In all cases, the two other parameters were taken as: between one of those and the scan rate (v), respectively. k S 1 and k S 2 0 0 kS1CA / C 0 / ( Fv / RT ) =1 and kS 2CZ0 / kS1CA =1 are the standard rate constants of the two electron transfer reactions. Electron transfer kinetics are described using Butler-Volmer like 0 kinetic laws with transfer coefficient equal to 0.5. 14 The concentra- parameters are held constant. For negative values of ∆gad ,Q a preand
(
tions of substrate and cosubstrate, C A0 and CZ0 at the electrode, are assumed to remain constant and equal to the bulk values, either because they are large enough or because the scan rate has been raised so as to render negligible the contribution of diffusive transport of these two species to the kinetics (see SI for a quantitative analysis of
)
(
)(
)
0 wave appears in front of the catalytic rise of the current. As ∆gad ,Q
increases, the pre-wave shifts in the cathodic direction while the catalytic curve moves in the reverse direction, ending up in complete merging of the two waves. The pre-wave appears in what is conventionally called an “underpotential deposition” range of potentials, simply meaning potentials that are less negative than the standard
this issue). C0 is a normalization concentration (e.g. equal to 1 M). Γ 0 0 is the total surface concentration of the free and occupied catalytic potential of the global reaction, EA,Z/C . 15,16. How does this picture surface sites on the electrode surface. As shown in the Supporting Information (SI), the dimensionless CV responses can be expressed as: changes upon varying the two other parameters? Particularly, may these variations affect the very existence of a volcano plot? Figures i F 0 0 = exp η − ∆g ad × / C0 2a,b illustrates the effect of the parameter ( Fv / RT ) / kS1CA ,Q 0 2 RT FS Γ0 k S 1 C A / C0 0 for a given value of ∆g ad ,Q .The catalytic wave does not change ΓQ F 0 0 0 η − ∆g ad ,Q appreciably, while the pre-wave current is proportional to the parame1 − 0 1 + C / CA exp − RT Γ ter, and particularly to the scan rate and its peaks move toward negative potentials upon raising the scan rate as expected for a quasik S 2C Z0 F ΓQ 0 + exp η + ∆g ad ,Q 0 irreversible one-electron surface wave. 17 On the opposite, changing 0 2 RT Γ k S 1C A with:: 0 the parameter kS 2CZ0 / kS1CA may have an important impact on the F ΓQ 0 occurrence of volcano plots. There is indeed no reason that changing η − ∆g ad ,Q × 1 − 0 exp 2 RT Γ 0 0 ΓQ electrocatalyst does not change this parameter and not only ∆gad ,Q . d 0 k S1 CA 0 Figures 2c and 2d provides examples of what are the expected conseΓ = C 0 1 + C exp − F η − ∆g 0 ad ,Q RT 0 Fv quences in terms of volcano plots. It is seen that the apex location is Fη CA d 0 RT RT not necessarily at ∆gad 0 ,Q =0 and depends on the value of the parame F ΓQ k S 2C Z 0 + exp + ∆ g η ad ,Q 0 k C0 0 2 RT Γ ter kS 2CZ0 / kS1CA .There is no reason that, upon changing electro S1 A
(
(
)
(
)
)
(
(
(
)
)
(
(
)
(
)
(
)
when the contribution of diffusion can effectively be neglected, i.e.,
(
)
)
(
)(
)(
)
)
0 catalyst, ∆gad ,Q would the only variable parameter while the standard
when k S 1Γ 0 / C A0 DA Fv / RT → 0 ( DA is the diffusion coefficient rate constant, k S 1 and k S 2 would remain constant in the series. 18 of A). Figure 1 shows various examples of dimensionless CV respons- This is one important factor, among others, that may explain the large 0 data scatter observed around volcano plots in the her, hor and oxygen es as a function of the stability of the intermediate, ∆gad ,Q (negative
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reduction. 7 Another approach to catalyst benchmarking consists in the comparison of the catalytic current potential responses in the potential
0 F ∆g ad k S 2CZ0 ,Q exp 0 0 k C RT 0 Fη CA S1 A i log + log 2 Γ k S1 0 = 0 FS 2 RT ln10 C k S 2C Z0 F ∆g ad ,Q 1+ 0 RT k S 1CA
at the right hand of the catalytic Tafel plot. The existence of this linear asymptote, with the appropriate slope, may be observed experimentally, giving access, though its intercept, to the group of constants in the last term of the above-equation, and from its variation with C A0 (and possibly with C Z0 ), to Γ 0 k S 1 and Γ 0 k S 2 , thus allowing the currentnormalization shown in Figures 1-3. As can be seen in the right hand side of Figure 4, the intercepts follows the same tendency to give volcano plots as discussed previously for the exchange current values ( iη = 0 ), with however the same restrictions, notably that k S 2 / k S1 remains the same in the series of catalytic electrodes under comparison. We now address the same questions for the Volmer-Tafel type mechaFig. 2. Reaction Scheme 1. a, b: Dimensionless current-potential nism depicted in Scheme 2. The thermodynamics of the reaction is characterized by the following relationships: 0 responses for F ∆g ad ,Q / RT ln10 = -2. Effect of the parameter RT 0 0 0 EA ln ( K dim ) = E10 + ∆g ad C = E1 + ,Q 0 0 2F kS1CA / C / ( Fv / RT ) = 1 (black), 3 (green), 10 (red), with two
(
)
0 different normalization of the current. c, d: Volcano plots for Scheme The overpotential is still defined as: η = EA,/C − E . As for the Scheme 0 0 0 0 1, with kS1CA / C / ( Fv / RT ) =1 and kS 2CZ / kS1CA =0.1 1 process, we assume that the diffusive transport of substrate in the solution has been made negligible (see SI). Cases of practical interest (red), 1 (blue), 10 (green). are those where the dimerization reaction is fast enough for the zone where the pre-wave current can be neglected, similarly to the intermediate to be at steady-state. The most distinctive feature of the catalytic Tafel plots advocated for benchmarking molecular catalysts. CV responses in this case is that, unlike reaction scheme 1, they are S19,20,21 Figure 3 shows examples of such plots. It is seen that the CV shaped, thus reaching a plateau, which may be expressed as (see SI):
(
2 1
)
(
)(
i log FSk C 0 Γ 0 S1 A
)
( )
i pl = 2 FSk+0 Γ 0
0
2
0 F ∆g ad ,Q exp RT
(1)
while the whole response obeys the following equation.
-1 -2
γ etdes-dim
-3 -4
F η RT ln10
-5 -2
-1
0
1
i i pl
(
F η − ∆g 0 ad ,Q − exp 2 RT CA0 C0
(
2
Fig. 3. Reaction scheme 1. Catalytic Tafel plots for
( kS1CA0 / C 0 ) / ( Fv / RT ) =1, ( kS 2CZ0 ) / ( kS1CA0 ) = 1. and:
F η − ∆g 0 ad ,Q i C0 0 1 + exp − i pl CA RT
) +
) − 1 = 0
where γ etdes - dim is the parameter (see Figure 4) that measures the competition between the desorption-dimerization and initial electron 0 F ∆gad ,Q / RT ln10 = -3 (blue), -2 (green), -1 (red), 0 (black), 1 transfer steps for the kinetic control of the global reaction. Cases of particular interest are those where one of the two steps prevails over (magenta), 2 (orange), 3 (cyan). des - dim .The conditions to be fulfilled to response tends toward a limiting expression when raising the overpo- the other as defined by γ et observe these limiting behaviors and measure their characteristics are tential, η (see SI): summarized in Figure 4 (see SI for a detailed treatment). That a potential-independent current is reached at high overpotentials simply 0 F ∆g ad results from the fact that the kinetics is then controlled by the potenkS 2CZ0 ,Q exp tial-independent rate of the desorption-dimerization step since the 0 RT i Fη k S1CA electron transfer step has become infinitely fast. = exp 0 0 F ∆g 0 2 RT C k C In both limiting cases, the experimental S-shaped CV curves can be ad ,Q 2 FS Γ0 k S1 A0 1 + S 2 0Z profitably examined by means of a log analysis, revealing a linear C kS1CA RT variation of the log-analysis function with the overpotential, characterized by its slope and its intercept. which results in a linear asymptote:
3
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0 lyst, ∆gad ,Q would be the only variable parameter while the standard
rate constant, k S 1 and k +0 Γ 0 would remain constant in the series.
Fig 5. Reaction scheme 2. Plot of the dimensionless exchange current vs. the dimensionless standard free energy of adsorption of the primary intermediate for C A0 / C 0 = 1 and k +0 Γ 0 / k S 1 = 100 (green), 1 (blue), 0.01 (red). Fig. 4. Reaction scheme 2. Current – potential CV responses in the two limiting cases. In the first case ( γ etdes-dim → 0 dimerization):
(rate determining desorption-
0 i pl − i C0 F ∆g ad ,Q = − Fη + ln − ln A0 C RT RT i
( )
2k+0 Γ 0
2
(
0 exp F ∆g ad ,Q / RT
(2)
) may then be obtained from the plateau
0 current (equation 1) and F ∆g ad ,Q / RT from the intercept of the log
plot (equation 2, as C A0 / C 0 is known), finally leading to the determi-
( )
0 0 0 nation of ∆gad ,Q and k+ Γ
2
.
In the second case ( γ etdes-dim → ∞ (rate-determining initial electron transfer): 0 F ∆g ad 2 ,Q i 2k+0 Γ 0 exp RT CA i pl Fη (3) 2ln + 2ln 0 − 2ln = 0 F ∆g ad C 1 − i RT ,Q k S1Γ 0 exp − i pl RT
( )
( )
) may then be obtained from the plateau 0 current (equation 1) and kS1Γ0 exp ( − F ∆gad ,Q / 2 RT ) from this and 2k+0 Γ 0
2
(
0 exp F ∆g ad ,Q / RT
equation 3, as C A0 / C 0 is known. In both cases, the exchange current (i.e., the current at zero overpotential) may be expressed (see SI) by equation (S1) in the SI. As illustrated in Figure 5, the exchange current variation with the adsorption 0 standard free energy, ∆gad ,Q leads to a volcano plot when the other parameters are held constant as expected from the Sabatier principle. However, as in the Volmer-Heyrovsky case, the apex location is not 0 necessarily at ∆gad ,Q =0 and depends on the value of the parameter
k +0 Γ 0 / k S 1 . Again, there is no reason that, upon changing electrocata-
In summary, we have shown how cyclic voltammetry may be used for evidencing and characterizing volcano plots, taking as illustrative example reactions involving the electron transfer-coupled formation of an intermediate adsorbed on a catalytically-active surface site followed by its electron-coupled conversion into products, regenerating the catalytic site. Although more general, the relationships thus derived may be applied to the reduction of acids on metal electrodes according to the Volmer-Heyrovsky mechanism, which has been the most popular playground for hunting volcano plots. These are expected to come out when plotting exchange currents (currents at zero overpotential) against the adsorption free energy of the reduced proton (or more generally of the intermediate resulting from the initial electron transfer step) on the electrode material. Our analysis indicates that the free energy of adsorption of this intermediate is indeed an important parameter of the overall kinetics of the reaction revealed by the CV responses. However it is not the only kinetic parameter of the reaction. Even if precaution is taken to eliminate the contribution of substrate diffusion, two additional parameters come nevertheless into play. One is the ratio of the two electrochemical rates and the other measures the competition between one of those and the scan rate. The second of these parameters modulates the location of the underpotential deposition wave, but has little influence on the catalytic wave. This is not the case of the rate ratio parameter, whose value strongly affects the catalytic wave. Volcano are clearly identified and characterized as long as this parameter is held constant. This may not be the case in practice upon changing electrocatalyst, thus blurring the occurrence of a volcano plot. The above analysis of CV responses thus enlightens and specifies the reservations already issued regarding the actual relevance of this approach, 7,16 reinforced by the doubts concerning actual experimental observations. 16 Another drawback of the volcano plot approach is that it focuses on a single experimental point, viz. the current at zero overpotential, while using the whole CV response brings about a more complete information that can be analyzed by means of the above-described relationships. This also allows the establishment of heterogeneous catalytic Tafel plots enabling a rational benchmarking of the various electrocatalysts of a given electrochemical reaction. It was also worthwhile analyzing the classical alternative to the Volmer-Heyrovsky mechanism in the electrocatalytic reduction of acids, namely, the Volmer-Tafel mechanism under the same conditions and with the same objectives. The most remarkable feature of the CV analysis of such a reaction pathway is the occurrence of Sshaped current-potential responses, unlike what happens with the Volmer-Heyrovsky mechanism. Volcanos are identified and characterized as long as parameters other than adsorption free energy of the reduced proton are held constant. Again, it may not happen in practice
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upon changing electrocatalyst. The present analysis provides the necessary tools for a lucid re-investigation of acid reduction on metals as well as for the study of any other electrocatalytic processes by means of cyclic voltammetry.
Supporting Information. Derivation of equations.
REFERENCES
1. Sabatier, P., La Catalyse En Chimie Organique, Librairie Polytechnique, Paris et Liège, 1920. 2. Parsons, R. T. Faraday Soc. 1958, 54, 1053-1063. 3. Gerischer, H. Bull. Soc. Chim. Belg. 1958, 67, 506-527. 4. Koper, M. T. M. J. Solid State Electrochem. 2013, 17, 339-344. 5. Nørskov, J. K.; Bligaard, T.; Logadottir, A.; Kitchin, J. R.; Chen, J. G.; Pandelov, S.; Stimming, U. J. Electrochem. Soc. 2005, 152, J23-J26. 6 Medford, A. J.; Vojvodic, A.; Hummelshøj, J. S.; Voss, J.; AbildPedersen, F.; Studt, F.; Bligaard, T.; Nilsson, A.; Nørskov, J. K. J. Catal. 2015, 328, 36-42. 7.(a) Quaino, P.; Juarez, F.; Santos, E.; Schmickler, W. Beilstein J. Nanotechnol. 2014, 5, 846-854. (b) Zeradjanin, A. R.; Grote, J.-P.; Polymeros, G.; Mayrhofer, K. J. J. Electroanalysis 2016, 28, 2256-2269. 8. Chen, S.; Kucernak, A. J. Phys. Chem. B 2004, 108, 13984-13994. 9. Kucernak, A. R.; Zalitis, C. J. Phys. Chem. C 2016, 120, 1072110745. 10. (a) In practice, in electrolyzers or fuel cells, the electrodes at which the reactions of interest take place are not operated under linear scan of the potential. The cyclic voltammetric investigations we are advocating, which include the use of the maximal possible range of scan rates, aim at establishing the intrinsic mechanistic and kinetic characteristics of the reaction of interest to be used in models of actual devices, together with the characteristics of the other electrode and of separators. (b) Other analytical techniques such as potential step chronamperometry, impedance as well as rotating disk voltammetry (RDEV) could be used instead of CV. Speeding up diffusion is equivalently obtained by raising the scan rate in the first case, decreasing the measurement time in the second, raising the frequency in the third and raising the rotation rate in the fourth. For indications of good reasons to use CV rather than the other techniques see reference 10c. It may seem at first sight that the conditions in which RDEV experiments are carried out are closer to those prevailing in generators and electrolyzers than cyclic voltammetric conditions. This is not true. Both techniques operate under microelectrolytic non-destructive conditions as opposed to the macroelectrolytic conditions in generators and electrolyzers in which large amounts of reactants are transformed. Thus, if RDEV were to be chosen as the microelectrolytic technique to be used instead of CV to speed up diffusion, the same intellectual transposition to generators and electrolyzers operating conditions would have to be done. (c) Savéant, J.-M., Elements of Molecular and Biomolecular Electrochemistry: An Electrochemical Approach to Electron Transfer Chemistry; John Wiley & Sons: Hoboken, NJ, 2006. 11. Erdey-Gruz, T.; Volmer, M. Z Phys. Chem A-Chem. Thermodyn. Kinet. Elektrochem. Eigensch.lehre 1930, 150, 203-213. 12. Heyrovský, J., A Recl. Trav. Chim. Pays-Bas 1927, 46, 582-585. 13. Tafel, J. Z. Phys. Chem. 1905, 50, 641-712. 14. (a) Indications for using other kinetic laws or transfer coefficient values different from 0.5 in electron transfer reactions (and also in protoncoupled electron transfer 14b) can be found in 10c. (b) Jackson, M. N.; Surendranath, Y. J. Am. Chem. Soc. 2016, 138, 3228-3234. 15. Waves appearing in the underpotential deposition domain are not necessary related to a catalytic process, as is the one shown in Figure 1. Other pre-waves corresponding to stronger adsorption may well have no catalytic counterpart, precisely because adsorption is too strong. 14 The danger of correlating the kinetics with the strongest adsorption, 5 which in fact is not involved in the catalytic reaction have been emphasized. 14 16. Santos, E.; Hindelang, P.; Quaino, P.; Schulz, E. N.; Soldano, G.; Schmickler, W. ChemPhysChem 2011, 12, 2274-2279. 17. Reference 10c, pp. 44-50.
18. The standard rate constants may be expressed as equal to a preexponential factor × exp(activation standard free energy/RT). The standard activation free energy is not likely to be the same for different metals for both the Heyrovsky and Volmer steps since they involve bond making (MH) / bond breaking (M-H) processes implicating metal active sites. 19 . Costentin, C.; Drouet, S.; Robert, M.; Saveant, J.-M. J. Am. Chem. Soc. 2012, 134, 11235-11242. 20. Artero, V.; Savéant, J.-M. Energy Environ. Sci. 2014, 7, 38083814. 21. Costentin, C.; Robert, M.; Savéant, J.-M. Acc. Chem. Res. 2015, 48, 2996-3006.
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