Homogeneous Molecular Catalysis of Electrochemical Reactions

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Homogeneous Molecular Catalysis of Electrochemical Reactions. Scaling Relations, Intrinsic and Operational Factors Cyrille Costentin, and Jean-Michel Savéant J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b09154 • Publication Date (Web): 04 Nov 2018 Downloaded from http://pubs.acs.org on November 5, 2018

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Journal of the American Chemical Society

Homogeneous Molecular Catalysis of Electrochemical Reactions. Manipulating Intrinsic and Operational Factors for Catalysts’ Improvement Cyrille Costentin*,1,2 and Jean-Michel Savéant*,1 1

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. 2 Present address : Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, Massachusetts 02138, United States. timization. The conditions in which the catalyst candidates are likened should accordingly be precisely defined and understood for insuring a meaningful and equal footing comparison. Concerning both preparative-scale and non-destructive techniques such as cyclic voltammetry, these conditions are the so-called “canonical” conditions. Their definition and analysis are the first of our tasks. The achievement of “canonical” conditions opens the possibility to introduce in rigorous manner the notion of turnover frequency and its relation with the rate of the catalytic reaction. In sake of simplicity, this tutorial exposé will be developed in the framework of the unsophisticated but not trivial catalytic schemes such as the one shown in Scheme 1. Scheme 1

ABSTRACT: Benchmarking and optimization of molecular catalysts of electrochemical reactions have become a central issue in the efforts to match contemporary renewable energy challenges. In view of some confusion in the field, we precisely define the notions and parameters (potentials, overpotentials, turnover frequencies) involved in the accomplishment of these objectives and examine the correlations that may link them, thermodynamically and/ or kinetically to each other (catalytic Tafel plots, scaling relationships, “iron laws”). To develop this tutorial section, we have picked as model catalytic reaction scheme, a moderately complex mechanism, general enough to illustrate the essential issues to be encountered, and sufficiently simple to avoid the algebraic nightmare that a systematic study of all possible pathways would entail. The notion of scaling relation will be the object of a particular attention, having notably in mind the delimitation of their domain of applicability. At this occasion, emphasis will be put on the necessity of clearly separating what is relevant to intrinsic characteristics (through standard quantities) to what deals with the effect of varying the reactant concentrations. It will be also stressed that the occurrence of such scaling relations, otherwise named “iron laws”, is not a general phenomenon but rather concerns families of catalysts. Likewise, the search of a general correlation between the maximal turnover frequency and the equilibrium free energy of the electrochemical reaction appears as irrelevant and misleading. This general analysis will then be illustrated by experimental data obtained witth the O2to-H2O conversion catalyzed by ironIII/II porphyrins in N,N’ dimethylformamide in the presence of a Brönsted acid.

This a one-electron process with two successive chemical steps in the rate determining sequence. In the first one, an adduct is formed reversibly from the active form of the catalyst, Q, and the substrate S. This adduct reacts, in a second step with a cosubstrate. For reductive processes the cosubstrate is in number of cases, a Brönsted acid, HA, that protonates the primary adduct and generates its conjugated base. The protonated adduct then regenerate the starting form of the catalyst, while going to products by a series of fast reactions in which the intermediates, if any, obey the steady state conditions. Transposition to oxidation is straightforward as well as generalization to other types of cosubstrates. This reaction scheme, though quite simple, is sufficiently more complex than the elementary one-electron one-step scheme to retain the essential features that will allow to demonstrate the importance of separating intrinsic factors from reactant concentrations in the analysis of experimental data. These problems and their resolution follow the same lines in the long list of more sophisticated multi-electron- multistep reactions 8 to which the present analysis can be adapted with no major fundamental difficulty albeit with some tedium. The last section is devoted to the illustration of what precedes by experimental data recently acquired in the O2-to-H2O conversion catalyzed by ironIII/II porphyrins in N,N’ dimethylformamide in the presence of a Brönsted acid, to which the mechanism depicted by Scheme 1 has been put forward. 9,10

Introduction Contemporary renewable energy challenges are strong incentive for catalysis of the electrochemical transformation of small molecules. 1,2,3,4,5,6,7 Since these processes face severe kinetic barriers, catalysis is generally required to carry them out at reasonable rates and reasonable electrode potentials. In view of the ever-growing number of molecular catalysts, often transition metal complexes, proposed for these purposes, benchmarking their performances has emerged as an important issue. Based on the understanding of the notions they convey, we will first attempt to clarify the definitions of the various physical quantities (potentials, overpotential, turnover frequency) needed to accomplish this task, with particular attention to the fact that the same word may have been used to name different quantities. Most of these molecular catalysts involve redox couples that undergo fast electron exchange with the electrode, thus obeying the Nernst law and being thermodynamically characterized 0 0 by a standard potential, Ecat . The difference between Ecat and the

potential of the electrode, E is the main thermodynamical factor that drives the reaction. The resulting catalytic current and how it varies with the electrode potential provide a measure of the catalytic efficiency, thus forming the bases of catalysts’ benchmarking and op-

Canonical conditions. Turnover frequency and catalytic Tafel plots (variation with the electrode potential) The turnover frequency is sometimes simply equated, without further ado, to the first order catalytic rate constant obtained at large

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overpotentials. 8,11,In fact, a correct definition has to start from the classical notion of turnover frequency in homogeneous chemistry, namely, the total number of moles transformed into the desired product by one mole of the active forms of the catalyst per unit of time. It ought obviously to be worked out to fit electrochemical conditions. 12 Indeed, concentration profiles depending on the distance to the electrode surface have to be taken into account instead of the space-independence of homogeneously dispersed reactant concentrations. This situation is pictured in figure 1 in the case of the reaction sequence depicted in Scheme 1. All equations corresponding to Scheme 1 are derived in the Supporting Information (SI).

I

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I plateau i  S 1  exp  F ( E  E 0 ) / RT  cat  

0 b b Dcat kcatCsub . with I plateau  FCcat  HA and E1/2  Ecat

In this situation, currently named “canonical”, the S-shaped response is independent of the scan rate and the backward trace is superimposed to the forward trace. The pseudo-first-order rate constant kcat Csub  HA controls not only the magnitude of the catalytic current but also the thickness of the diffusion-reaction layer, which is approximately equal to b





b Dcat / kcat Csub  HA . More exactly, the catalyst profiles vs. the

distance x to the electrode can be expressed as (see SI):

CQ ( x )  (CQ ) x 0 exp  

b  HA / Dcat x  kcatCsub 

Integration along this profile leads to the following expression of the turnover frequency (see SI): TOF 

b kcat Csub  HA

(1)

0 1  exp  F ( E  Ecat ) / RT   

The TOF is thus a function of the electrode potential, which reflects the fact that the whole concentration profile of the active form of the catalyst at the electrode surface is itself a function of the electrode potential: b Ccat





b exp  kcat Csub  HA / Dcat x  0   1  exp  F ( E  Ecat ) / RT    This is illustrated in figure 1b and c, by the difference between the catalyst concentration profiles at the two different potentials taken as examples.

CQ ( x ) 

According to equation (1), the turnover frequency increases when pushing the electrode potential toward negative values, reaching as-

Figure 1. Cyclic voltammetry of a catalytic reaction following the reaction sequence depicted in Scheme1 under canonical conditions. a: resulting S-shaped CV response in red. The blue reversible CV response recalls what happens in the absence of substrate. b, c: concentration profiles through the reaction-diffusion layer (beige) and the diffusion layer (blue) up to the bulk of the solution (light blue). For clarity, the layers’ sizes on the figure do not respect the actual sizes. The concentration’s profiles are shown in two illustrative examples, b: for a potential close to the E1/ 2 , where (CP )x0  0 and

b ymptotically a maximal value: TOFmax  kcat Csub HA . It is amusing that this TOFmax is, fortuitously, the same as the TOF intro-

duced elsewhere without justification as mentioned earlier. A precise establishment of TOF expressions should however been encouraged, particularly when multielectron-multistep catalytic reactions 8 are concerned. In any case, it should be born in mind that the validity of the above analyses and expressions hinges upon the fulfillment of pure kinetic conditions with constant substrate and cosubstrate concentrations. This applies to preparative-scale electrolyses as well as to CV experiments or even other techniques such as rotating disk voltammetry. In the CV case, S-shaped current-potential responses are expected. Application of the equations appropriate to these conditions when peaks are observed instead of plateaus, 13 necessarily lead to erroneous values of the rate constants and thereof of the TOFs as well as to problematic mechanistic conclusions. Techniques to reach canonical behaviors (Foot-of-the-Wave Analysis and/or raising the scan rate) have been described 12 and applied to many systems, under the condition that intermediates obey the steady state approximation. In the CV or preparative scale experiments where TOF is de scribed by equation (1) or equivalently by equation (2):

c: at a potential negative enough for the plateau to be reached. In preparative electrolysis as well as in non-destructive techniques such as cyclic voltammetry (CV), systems of actual interest bring about the achievement of pure kinetic conditions, i.e., the establishment of a steady state resulting from the mutual compensation of diffusion and reaction of each member of the catalyst couple. The catalyst concentration profiles are consequently squeezed within a thin reaction-diffusion layer adjacent to the electrode surface. If at the same time, substrate and cosubstrate are in sufficient excess; their concentrations remain constant across the reaction layer. The concurrent fulfillment of these two conditions results in an S-shaped cyclic voltammetric (CV) response as shown in figure 1a. The equation of the CV is (see SI):


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Journal of the American Chemical Society TOF 

TOFmax

0 Ecat , TOFmax may also change through a change in kcat . There

(2)

0 1  exp  F ( E  Ecat ) / RT   

is no general rule that could predict whether or not the change in 0 kcat is related to the change in Ecat . However, the two changes

the potential E, and the values it may take are imposed or measured by difference with a fixed-potential conventional reference electrode, not depending on concentration of any reactant participating to the catalytic reaction under investigation. “Catalytic Tafel plots” have been originally introduced as logTOF vs. E. plot, taking as reference electrode potential the standard potential of the target reaction, in the aim of expressing how far the catalytic system is from a situation where the target reaction would be fast and reversible. 10, 14 In this case, the electrode potential, E, was replaced by the

may be correlated within a “family” of catalysts as observed in several cases. This is, e.g., the case with transition metal complexes 0 is varied by the introduction of electron-withcatalyst, whose Ecat

0 drawing (or donating) substituents, which moves the Ecat posi-

tively (or negatively) by the influence they exert on the metal through the complex structure. The same substituent that changes 0 Ecat may affect in a parallel manner the thermodynamics and the

0 overpotential and Ecat referred to the standard potential of the

kinetics of the homogeneous reaction sequence that provides catalysis, even though it bears no direct chemical relationship with the initial electron transfer step. In the present case we may consider, in agreement with the values of the reaction orders, that the first step acts as a pre-equilibrium to the second, rate-determining step. The rate constant of the overall rate determining sequence is thus:

0 target reaction, Etarget , leading to an alternative expression of equation (2):

TOF 

b kcat Csub  HA





F  F 0  1  exp  E0  Ecat    exp    RT   RT target

(2’)

b kcat = K1k2 and TOFmax  K1k2Csub  HA

For the reasons evoked earlier, the variations of the pre-equilib-

The comparison between different catalysts of a given reaction can be made in the same manner whatever the fixed-potential electrode to which the electrode potential is referred during all the comparative experiments. In so far the catalyst couple is Nernstian, the catalytic Tafel plot thus defined (figure 2a) is obtained from equation (2)

0 rium formation of the QS adduct may parallel the variations of Ecat

. If this correlation obeys a linear (at least approximately) standard free energy relationship, then: 0 log( K1 )  G10 /  RT ln10  1FEcat /  RT ln10  Cst1

1 is the linear correlation coefficient. The standard free energy of the second step may be expressed, from the standard chemical potentials (the  0 s) as: 0 0 0 G20  QS  QSH  HA  0  A

=RT ln10  pKaQSH  pKaHA/A   

If a linear standard free energy relationship is again at work: log( K2 )   G20 /  RT ln10  -

0   2 FEcat /  RT ln10   pKaHA/A  Cst2

where  2 is another linear correlation coefficient. We next introduce a linear (or close to) activation-driving force relationship that links the rate constant of the rate determining step, k2 , to its driving force (i.e. the opposite of the standard free energy Figure 2. Catalytic Tafel plots correlating the turnover frequency to the electrode potential measures against a fixed potential reference electrode a: plot for a given catalyst characterized by its standard

0 of this reaction, Grds ), which is linearized in the approximate 15 Brönsted manner:

0 potential, Ecat , and at given substrate and cosubstrate concentra-

log(k2 / Z )  G20 / ( RT ln10)

b [HA] .b: for a given cattions, Csub and [HA] , by TOFmax  kcat Csub alyst, effect of changing the concentration of substrate or cosubstrate. c: effect of changing catalyst. d: “iron law” or “scaling relationship” resulting from the superposition of a linear free energy relationships and a linear kinetic/ thermodynamic Brönsted corre-

(Z is the pre-exponential factor for this step) leading to:

0 lation as a function of the descriptor, Ecat .

( C 0 is a normalizing concentration, e.g., 1 M). All Cst’s are constants within a family of catalysts and are independent from reactant concentrations The change of TOFmax within a family of catalysts

b





0 log TOFmax (s1 )   1  2 FEcat /  RT ln10    pKaHA/A  



b  log Csub / C0

One may also change catalyst at given substrate and cosubstrate concentrations, as illustrated in figure 2c. Besides the change in


-

 HA / C0   Cst3

(3)




for a given reaction (i.e. for a given cosubstrate HA), is dictated by equation (3) as represented in figure 2d. This “iron law” may also be named a “scaling relation” by analogy with the terminology used in electrocatalysis, 16 albeit the exact meaning of the notion we used here is somewhat different since it explicitly encompasses both a thermodynamic and kinetic aspect as defined earlier. Along the

their roles are not exactly symmetrical since



Cst in the above equation is independent of concentrations. As shown in the preceding section, there are two thermodynamic parameters that can be changed to modify the TOFmax , namely -

0 and pK HA/A . Albeit their roles are not exactly symmetrical Ecat a 0 since Ecat partially dictates the stability of the key intermediate

another type of catalyst, or, if substituent effects are considered within the same family, by changing the nature of the communication between the substituent and the metal. 17 There are two thermodynamic parameters that can be changed in

0 Ecat

-



netic response. Such scaling relations may be broken (meaning that, for a given reaction and a given substrate concentration, a catalyst will lead to a TOFmax off the correlation line) by simply going to

0 and order to modify the TOFmax , namely Ecat



0 log TOFmax (s1 )   1  2 FEcat /  RT ln10    pKaHA/A      log  pO / p0  HA  / C 0   Cst   2 

0 same lines, Ecat serves as a thermodynamic “descriptor” of the ki-

pKaHA/A

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FeIII+Og2 whereas the HA pKa thermodynamically controls the

second step of the catalytic sequence, they can both viewed as thermodynamic descriptors. Figure 3a represents accordingly the scal ing relation (iron law) for one of the acid and figure 3b show how TOFmax varies with the pKa of the acid.

. Albeit

partially dictates

a

the stability of the key intermediate QS, whereas the HA pKa thermodynamically control the second step of the catalytic sequence, they can both viewed as thermodynamic descriptors.

6 log (

5 4

Catalysis of the O2-to-H2O conversion by ironIIporphyrins A recent study 8,9 of the catalysis of the O2-to-H2O conversion by iron II porphyrins (PFe) in N,N’ dimethylformamide (DMF), in the presence of an acid, HA, may serve as an experimental example illustrating the analysis developed in the preceding section. Indeed, according to this work, in the global reaction,

b

TOFmax 1 s ) pO HA 2

p0





C0

log (

TOFmax 1 s ) pO HA 2

p0





C0

6 5 4

3

3

2

2

1

0 Ecat (V vs. Fc+ /Fc)

pKaHA

1

0 0 2 0 2 4 6 81 0 0 . 30 . 40 . 50 . 6 -

  2H O + 4AO2 + 4e-  4HA   2

, the rate determining sequence, as derived from the reaction orders  1 for both O2 and the acid HA  is as shown in Scheme 2. 9. Scheme 2

  FeII FeIII+ + e-  

0 Ecat

  FeIII+Og FeII + O2   2

K1, (G10 )

(1)

K2 , (G20 ), k2

(2)

FeIII+Og2

 HA  FeIII+Og2H + A-

, the first step of the catalytic reaction acting as a pre-equilibrium (equilibrium constant: K1 , standard free energy: G10 ) toward the second, rate-determining, protonation step (equilibrium constant: K 2 , standard free energy: G20 , rate constant: k2 . The rate constant of the overall rate determining sequence is thus: 1 0 kcat = K1k2 and TOFmax (s )  K1k2  HA pO / p . 2

pO and  HA  are the oxygen partial pressure and the acid con2

centration respectively ( p0 is a normalizing pressure, e.g. 1 bar). Thus, following the analysis reported in the preceding section, from equation (3):

Figure 3. Catalysis of the O2-to-H2O conversion by ironIIporphyrins in DMF. a: scaling relation (iron law) with the strongest acid, [HDMF+] . b: variation of TOFmax with the pKa of the acid in the case of FeTPP. From the data in references 8 and 9.


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Journal of the American Chemical Society of the strongest acid investigated. Equation (4) carries some resemblance with a Brönsted linear free energy relationship that would relate in a very general manner the kinetics of any reaction to its driving force. This seems to be put forward on an intuitive basis with no elements of theoretical justification. In fact, there is no reason for the kinetics to be correlated to the overall driving force of the reaction as it is governed by the driving forces of the rate determining sequence, i.e. steps (1) and (2) in Scheme 2. Moreover, we note that linear free energy relationships between thermodynamic quantities as well as Brönsted relationships between kinetics and thermodynamics involve standard free energies, as such independent from concentrations. A “general correlation” as expressed via equation (4) is in fact meaningless as shown by the experimental results gathered in Table 1 of reference 10 where it appears that the “correlation” coefficient m is not a constant as should be the case with a real correlation ( mHA  16.9, mE  18.5, m pK  5.1, mP  67.6, to which we

The above analysis appears to be at large variance with a recently proposed general approach, 10 which presents scaling relations that are claimed to apply to any set of catalysts of the same target reaction and to apply to any catalyzed reactions. As discussed earlier, we insist, on the contrary, on the fact that such scaling relations only exist within families of catalysts in which through-structure electronic effects affect in a parallel manner the catalyst standard potential on the one hand and the thermodynamic and kinetics of the rate-determining catalytic sequence on the other. Such scaling relations are easy to break: it suffices to go to another family of ligand or to change metal. Even in the same family of catalysts introduction of ligand substituents that exert a through-space effect on the metal are able to break the scaling relation observed with substituents exerting through-structure effects. 17 These phenomena have been observed in the molecular catalysis the CO2-to-CO electrochemical conversion. 18,19,20 Although the mechanisms of these catalytic reactions are more complicated than in the present case, the correlation between the formation of the initial adduct between active catalyst and substrate is of the same type. 21 The role Brönsted acids is however more complex, since it involves both H-bonding and proton transfer. It has nevertheless be analyzed with sufficient rigor to allow meaningful comparison to be drawn (refs 17 and refs therein). Coming back to catalysis of the O2-to-H2O conversion by ironII porphyrins, another source of serious disconsensus is the role played by variations of reactant concentrations in scaling relations. Before going to a detailed analysis of this question, it is worth noting that there is some confusion in the definition of the turnover frequency and its maximal value in references 9 and 10 where the maximal value of TOF, TOFmax is called TOF as the running value

1/ 2

a

O2

can add mH O  0). Closer examination of the derivations in ref. 2 10, shows that equation (4) is not applied exactly as written. There are actually several m coefficients, one for each of the parameters present in the expression of EORR , including reactant concentrations, showing that equation (4) should in fact be replaced by equation (6):





a log TOFmax  log  kcat  HA  pO b  2   jmax



of the turnover frequency. As shown earlier, canonical conditions have as a consequence that (in the present case) TOFmax  kcat pO  HA . It follows that it suffices to replace TOF





ORR

0  Ecat / x j

 log TOFmax / x j

 E mj

j 1



(6) C

by TOFmax when examining the contentions and derivations of ref-

where the m j are the individual coefficients relative to each parameter x j . Concerning more specifically the coefficients m rela-

erence 10. We will also replace E1/2, which has no thermodynamic

tive to concentrations it is easy to see that:

2

value by the standard

0 potential Ecat

, which is what the authors

aj  mj 

have actually in mind. The next step in reference 10, in the framework of the global reaction:

the number of electron exchanged in the global reaction and the  j s the stoichiometric factors in this reaction. Thus, once the reaction orders have been determined experimentally as is the case here  1 for both O2 and HA, the corresponding m j ensue, in a plainly

consists the following “correlation”:

 





(4)

tautological manner.

where m is a correlation coefficient and C a constant. EORR is the

and

0 sides standard quantities  the standard potential, EORR , and the

actants formally involved in the global reaction: 2  - 4   H2 O   A   RT ln10 RT ln10 (5)  pKa  log  4  F 4F  pO  HA   2  

Equation (4) was apparently inspired by the data of figure 1 in ref.





0 10, which plots log TOFmax against EORR  Ecat for the series of

ironII

 EORR  Ecat0 



as expressed by equation (4) is meaningless

simply because the “correlation” coefficient is not constant. Although correct, equation (6) is of little interest since its application is nothing else than a convoluted way of expressing the reaction combined with an intrinsic activation-driving force correlation. As shown in the first part of this section, proper correlations can be obtained by basing the analysis on reaction orders and on thermodynamic and kinetic linear free energy relationships. What precedes does not mean that TOF variations with reactant concentrations are unimportant. They are the way in which mechanisms can be established through the determination of reaction orders. They also contribute together with other factors, such as those

-

pKaHA/A  the bulk concentrations (or partial pressure) of all re-

EORR 



In summary, the notion of a correlation between log TOFmax

equilibrium potential of the above global reaction. It contains, be-

0 EORR

(7)

where the a j s are the reaction orders for reactants or products, n

  2H O + 4AO2 + 4e-  4HA   2 0 log TOFmax  m EORR  Ecat C

RT ln10 j nF

porphyrins (those in the above figure 3) at two concentrations



concerning the cell design and characteristics, to optimizing practical electrolysis performances. 22

Page 6 of 7

thus important to clearly separate the intrinsic molecular characteristics of the catalyst from the effect of reactant concentrations. In this framework, breaking these scale relations to develop better catalysts still belongs in large part to the exciting domain of chemical ingenuity.

Conclusion In front of the large variety of possibilities for improving molecular catalysts of electrochemical reactions, both in terms of potential and turnover frequency, it is tempting to look for the help of rules based on simple thermodynamic parameters. Such rules do exist but ought not to be forced to generality at the risk of becoming unrealistic or simply erroneous. This is the reason that the domain of application of resultant scale relations should be carefully delimited. Besides, it might not be superfluous in view of recent discussions, to recall that scaling relations (viz iron laws) are based on relationships involving standard quantities, (reaction standard free energies, “driving forces”, standard free energies of activation, standard potentials), as such independent of concentrations. It is

SUPPORTING INFORMATION Derivation of the equations corresponding to the mechanism in Scheme 1. AUTHOR INFORMATION Corresponding Authors [email protected], [email protected] The authors declare no competing financial interest.

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