AJ Appleby

C Costentin

FJ Recio

H Gerischer

J Rossmeisl

JK Nørskov

JM Zagal

Marc T. M. Koper

MTM Koper

OA Petrii

R Parsons

S Trasatti

W Schmickler

English

Crossref

ORIGINAL PAPERActivity volcanoes for the electrocatalysis of homolyticand heterolytic hydrogen evolutionMarc T. M. Koper1Received: 30 July 2015 /Revised: 6 September 2015 /Accepted: 8 September 2015 /Published online: 7 October 2015# The Author(s) 2015. This article is published with open access at Springerlink.comAbstract This paper derives a simple kinetic model for theelectrochemical current generated by a heterolytic model forhydrogen evolution, as it would apply to the reaction takingplace on molecular catalysts, and compares the activity trendsto the classical Volmer-Heyrovsky-Tafel models. It is demon-strated that in the heterolytic mechanism, pH plays a crucialrole in optimizing the overall activity.IntroductionThis contribution to the special issue for José Zagal’s 65thbirthday combines two prominent aspects of José’s work:electrocatalysis on molecular complexes, and volcano activitycorrelations [1]. My aim in this paper is to take the canonicalexample of hydrogen evolution and introduce a new pathwayinto the classic models considered decades ago by Parsons andGerischer [2, 3], in order to derive new volcano correlationsbetween activity and system parameters. The reason for doingso is that classic models for the electrochemical hydrogen evo-lution reaction (HER) on metal electrodes do not always applyto molecular catalysts. In models for the HER on solid elec-trodes, the formation of the hydrogen molecule often follows ahomolytic pathway, assuming the recombination of two iden-tical hydrogen adatoms (Tafel reaction). In molecularelectrocatalysis and enzyme catalysis, hydrogen molecule for-mation typically follows a heterolytic pathway, combining a(negatively charged) hydride and a proton. Costentin et al.have recently published a diagnostic strategy for distinguishinghomolytic from heterolytic pathways in molecularelectrocatalysis, showing the importance of reaction rate con-stants and acid concentration [4]. In this paper, I will map thereactivity for heterolytic hydrogen evolution onto two descrip-tors: the bond strength of the hydride intermediate bound to thecatalyst, and the solution pH (or the pKa of the AH/A− protondonor), as opposed to the Parsons-Gerischer model, whichapplies to homolytic hydrogen evolution, and which has onlythe hydrogen-catalyst bond strength as descriptor. The currentmodel is an extension of a recently developed theoreticalframework for multiple proton-coupled electron transfer(PCET) highlighting the role of pH in electrocatalytic mecha-nisms which feature (negatively) charged intermediates [5, 6].Model and resultsHomolytic pathwayThe model is based on a well-known model for hydrogenevolution introduced more than 50 years ago by Parsons [2]and Gerischer [3]. The model explains the so-called “volcanoactivity plot” in electrocatalysis [7–12]. Parsons’ model as-sumes the usual three reactions for the mechanism of hydro-gen evolution:Hþ þ M þ e‐ ⇆M−Hads ð1ÞHþ þ M−Hads þ e‐ ⇆ H2 þ M ð2Þ2 M−Hads ⇆ H2 þ 2 M ð3ÞDedicated to Prof. José H. Zagal on the occasion of his 65th birthday andin recognition of his seminal contributions to electrocatalysis.* Marc T. M. Koperm.koper@chem.leidenuniv.nl1 Leiden Institute of Chemistry, Leiden University, PO Box 9502,2300 RA Leiden, The NetherlandsJ Solid State Electrochem (2016) 20:895–899DOI 10.1007/s10008-015-3036-ztermed Volmer, Heyrovsky, and Tafel reactions, respectively.M-Hads is the adsorbed hydrogen intermediate. On a metalsurface, the adsorbed hydrogen is to be considered as un-charged, as confirmed by DFTcalculations [13, 14]. The ratesfor these reactions are expressed as a function of the electrodepotential ESHE (referenced with respect to the standard hydro-gen electrode (SHE)), the concentration of protons [H+], thecoverage of the adsorbed hydrogen θH, and the bond strengthof M-Hads surface bond, ΔGH (to be understood as a freeenergy):v1 ¼ k01 Hþ½  1−θHð Þexp−αFESHE−βΔGHRT ð4Þv−1 ¼ k0−1θHexp1−αð ÞFESHE þ 1−βð ÞΔGHRT ð5Þv2 ¼ k02 Hþ½ θHexp−αFESHE þ 1−βð ÞΔGHRT ð6Þv−2 ¼ k0−2pH2 1−θHð Þexp1−αð ÞESHE−βΔGHRT ð7Þv3 ¼ k03θ2Hexp2 1−βð ÞΔGHRT ð8Þv−3 ¼ k0−3 1−θHð Þ2pH2exp−2βΔGHRT ð9ÞThe equilibrium potentials for reactions 1 and 2 have beenincorporated into the forward and back rate constants k10, k− 10 ,k20 and k− 20 ; F, R, and T have their usual meaning. The modelassumes a Butler-Volmer-type kinetics for the electrochemicalsteps, with α the corresponding transfer coefficient (that wewill simply assume to be a constant equal to 0.5). Variations inthe binding energy of hydrogen impact on the rate constantthrough the Brønsted-Evans-Polanyi (BEP) coefficient β [2,12, 15].Expressions for the total current density can be calculatedfor the case of a Volmer-Heyrovksy VH mechanism (i.e., re-actions 1 and 2) and Volmer-Tafel VT mechanism (i.e., reac-tions 1 and 3). In the steady-state appromixation, assumingthat the back reaction to reaction 2 can be neglected, the VHexpression for the current density is as follows:j ¼ −2Fk02 Hþ½ exp −αFESHE þ 1−βð ÞΔGHRT 1þ k0−1k01 Hþ½  expFESHE þΔGHRT þ k02k01expΔGHRT  ð10Þ(The term [H+] multiplying k2o was erroneously missingfrom the expression in ref. [12]). In the pre-equilibriumapproximation, the following expression can be derived forthe VT mechanism:j ¼ −2Fk03exp 1−βð ÞΔGHRT 1þ k0−1k01 Hþ½  expFESHEþΔGHRT 0@1A2ð11ÞAt this point, it is useful to introduce the potential versusthe reversible hydrogen electrode, ERHE, accounting for thefact that the activity for hydrogen evolution, at least on solidelectrocatalysts, is usually measured versus this potential, totake into account the fact that in a real electrochemical device,the second electrode is ideally a fully reversible electrode atwhich proton and electron transfer always take place concert-edly. The RHE is in fact the equilibrium potential of the HE atthe pH of the working solution:ESHE ¼ ERHE−0:059pH ¼ ERHE− RT ln10F pH ¼ ERHE þRTFln Hþ½ ð12ÞInserting this into Eqs.10 and 11 gives for theVHmechanism:j ¼ −2Fk02 Hþ½ 1−αexp −αFERHE þ 1−βð ÞΔGHRT 1þ k0−1k01expFERHE þΔGHRT þ k02k01expΔGHRT  ð13Þand for the VT mechanism:j ¼ −2Fk03exp 1−βð ÞΔGHRT 1þ k0−1k01exp FERHEþΔGHRT 0@1A2ð14ÞNote that in the expression for the VT mechanism (Eq.14),pH (or [H+]) is now no longer a parameter. In Eq. 13, pH stillplays a role because the Heyrovsky reaction, which involvesproton transfer, is considered out-of-equilibrium.Both expressions predict a volcano-type plot for the currentas a function of the binding energy of hydrogenΔGH, as shownin Fig. 1. As shown in a previous paper, the slope of a Tafel plot(i.e., ln|j| vs. E) yields the transfer coefficient α; and the slope ofa volcano plot (i.e., ln|j| vs. ΔGH) yields the Brønsted-Evans-Polanyi coefficient β [12]. It is important to mention two keyassumptions made in generating Fig. 1: (1) the rate-determiningstep is independent on ΔGH, whereas in reality, the rate-determining step may actually differ on either leg of the volca-no; (2) ΔGH is a constant independent of coverage.Heterolytic pathwayIn molecular electrocatalysis, concerted proton-coupled path-ways such as the Volmer and the Heyrovsky reactions (1) and(2) are typically replaced by reactions generating a negativelycharged hydride intermediate and its subsequent heterolytic896 J Solid State Electrochem (2016) 20:895–899recombination with a proton. In such mechanisms, proton andelectron transfer do not take place concertedly in every reac-tion step. To illustrate this, the following heterolytic pathwayfor hydrogen evolution should be considered, in which thereaction generating the hydride is written as consisting oftwo elementary steps, taken into account the molecular char-acter of the catalyst “M”:MN þ e─ ⇄MN−1 ð15ÞMN−1 þ Hþ þ e─ ⇄MN−1─H↔MN−H─ ð16ÞHþ þ MN─H─⇄MN þ H2 ð17ÞThe first step expresses the fact the (metal in the) molecularcatalyst changes oxidation state before it will bind the hydro-gen in the second reaction. Following Costentin et al. [4], thehydrogen bound to the molecular catalyst can be in (or is asuperposition of) two “resonant” states: hydrogen and hy-dride. In contrast to hydrogen on metal surfaces, the hydridestate is more typical for molecular catalysts, and we will con-sider the hydride state for the remainder of the paper. If anelectrocatalyst follows this heterolytic mechanism, this hassignificant consequences for the pH dependence of the cur-rent. To demonstrate this, consider that the catalyst MN is in afilm on an inert electrode surface, and there is good and fastelectronic contact between the electrode and the catalyst film.The reaction rates are again expressed as a function of theelectrode potential ESHE or ERHE, the concentration of protons[H+], the fraction of MN-1 catalyst in the hydride state θH, andthe bond strength of the MN─H─ bond, ΔGH (to be under-stood as a free energy). We will consider the final step (reac-tion 17) to be rate-determining and hence neglect its backreaction, and therefore, we must consider that in a solutionof high pH, the forward reaction 17 still takes place througha reaction with water, i.e.,:Hþ þ MN─H─→MN þ H2 ð18ÞH2O þ MN─H─→MN þ H2 þ OH─ ð19ÞWe obtain an expression for the current by making asteady-state approximation for θH:j ¼ −2F k3a10−pH þ k3b exp1−βð ÞΔGHRT 1þ 1CN−11K2expF ERHE−E02 þΔGHRT þ k3a10−pH þ k3bCN−1k02 10−pH 1−α expαF ERHE−E02 þ βΔGHRT  ð20Þwhere the labels 1, 2, 3a, and 3b correspond to reactions equa-tions 15, 16, 18, and 19, resp., with K2=k20/k− 20 , and we haveconsidered that reaction 15 is in equilibrium such that:CN−1 ¼ C0N 1þ expF ESHE−E01 RT  	−1¼ C0N 1þ 10−pHexpF ERHE−E01 RT  	−1ð21Þwhere CN0 is the initial concentration of MN in the film so thatCN=CN0 −CN−1, CN−1 being the concentration of MN−1 in thefilm.It can be verified numerically that for certain values of theparameters, Eq. 20 yields a volcano-shaped curve as functionof pH, confirming our previous result that PCET reactions inwhich decoupled proton-electron transfer takes place may ex-hibit an optimal pH when activity is considered on the “rele-vant” RHE potential scale [5],[6]. Figure 2 shows a typicalvolcano curve for the activity of the reaction as a function ofΔGH / kJ mol-1ln|j/a.u.|VHVTFig. 1 Activity volcanoes predicted by Eqs. 13 and 14 for the Volmer-Heyrovsky (VH) mechanism and Volmer-Tafel (VT) mechanism. Currentin arbitrary units. Most constants in Eqs. 13 and 14 were set equal to 1.The plot for the VH mechanism is drawn for the limit k2o→0J Solid State Electrochem (2016) 20:895–899 897pH, for a given fixed value ofΔGH. In the limit that the thirdterm in the denominator is large compared to the second, onederives the following expression for the optimal pH:Hþ½ top≈α1−α1B; pHtop≈logB−logα1−αð22Þwhere B=expF ERHE−E01ð ÞRT . Since the model now dependson two parameters, i.e., the catalyst property ΔGH and theelectrolyte property pH, we plot in Fig. 3 a two-dimensionalactivity plot to illustrate that the ideal catalyst now optimizesfor both properties. It can be seen from this plot that for verynegative ΔGH, the activity vs pH dependence changes shapethough it in fact still displays a maximum, albeit for unrealisticvalues of pH. I do not want to dwell on the detailed shape ofthe surface shown in Fig. 3 as it may be the result of specificand perhaps not very realistic assumptions (under certain con-ditions) made in the model and in the steady-state approxima-tion to obtain Eq. 20.In volcano-type activity correlations in molecular catalysts,as considered in numerous papers by Zagal [1, 11, 16], it iscustomary to consider the redox potential of the MN/MN−1redox couple as a descriptor, E10, rather than the bond strengthΔGH. It is expected that there is a relation between the redoxpotential and its ability to stabilize the hydride, i.e., betweenE10 and ΔGH. Since it is assumed that the reduced state of theredox couple binds the hydride, a more positive redoxpotential (i.e., more stable reduced state) should yield a stron-ger binding of the hydride. One may postulate assume a sim-ple linear equation such as:E01 Hð Þ ¼ E001 −γFΔGH or ΔGH ¼E01 Hð Þ−E001γFð23Þto describe this relationship.In the above model, it was tacitly assumed that the HERtakes place in an aqueous electrolyte in which the pH is ameasurable and adjustable parameter. In non-aqueous electro-lytes, it is rather the concentration of the acid that is varied,together with its pKa, i.e., its ability to donate protons. Thisyields a corresponding equation for [H+] to be used in theabove equations. Also, a second proton donor, such as thewater in reaction 19, may not exist in non-aqueous solvents.As a final comment, let me emphasize that the activity plotsshown in Fig. 2 and 3 were obtained by evaluating the currentas a function of pH at a fixed potential on the RHE scale. Inmy view, this is a more sensible reference potential, as it au-tomatically corrects for the pH dependence of the equilibriumpotential of the overall PCET reaction, and hence, rates arecompared at the same thermodynamic driving force. Activityplots using the SHE as the electrode potential reference do notpredict volcano relationships, as explained in detail in ref. [6].ConclusionsIn this paper, I have considered a simple model for theelectrocatalytic hydrogen evolution reaction which in-cludes a heterolytic H-H bond making step and derivedan expression for the activity of the reaction as a func-tion of the ability to stabilize the hydride intermediatepHln |j/a.u.|Fig. 2 Activity volcano for the heterolytic pathway as predicted byEq. 20 for the current (in a.u.) vs. pH. k3a=1, k3a=0.001, expF ERHE−E01ð ÞRT =105, ΔGH=0, K2=1, CN0=1, expF ERHE−E02ð ÞRT = 1, 1k02expαF ERHE−E02ð ÞRT =103, α=0.5ln |j/a.u.|Fig. 3 Two-dimensional activity plot for the heterolytic pathway aspredicted by Eq. 21. Parameters as in Fig. 2, β=0.5898 J Solid State Electrochem (2016) 20:895–899and the proton-donating capability of the electrolyte (i.e.,pH or pKa of the acid). The model generates a two-dimensional activity volcano, with an optimal hydridebinding energy (similar to the existing models for hydro-gen evolution) and with an optimal pH so that the acidityof the electrolyte solution (or equivalently the proton-donating capability of the acid) matches the proton-accepting capability of the catalyst active intermediate.The model highlights that the acid/base character (orgenerally, the charged nature) of the catalytic intermedi-ates featuring in so many pathways relevant to molecularcatalysts is what makes these pathways so sensitive toelectrolyte pH, and what often distinguishes them frompathways on heterogeneous catalysts [5].Open Access This article is distributed under the terms of the CreativeCommons At t r ibut ion 4 .0 In te rna t ional License (h t tp : / /creativecommons.org/licenses/by/4.0/), which permits unrestricted use,distribution, and reproduction in any medium, provided you give appro-priate credit to the original author(s) and the source, provide a link to theCreative Commons license, and indicate if changes were made.References1. Zagal JM, Gulppi M, Isaacs M, Cardenas-Jiron G, Aguirre MJ(1998) Electrochim Acta 44:13492. Parsons R (1958) Trans Faraday Soc 34:10533. Gerischer H (1958) Bull Soc Chim Belg 67:5064. Costentin C, Didri H, Savéant JM (2014) J Am Chem Soc 136:137275. Koper MTM (2013) Chem Sci 4:27106. Koper MTM (2015), Top Catal, in press7. Nørskov JK, Bligaard T, Logadottir A, Kitchin JR, Chen JG,Pandelov S, Stimming U (2005) J Electrochem Soc 152:J238. Schmickler W, Trasatti S (2006) J Electrochem Soc 153:L319. Trasatti S (1977) J Electroanal Chem 39:16310. Petrii OA, Tsirlina GA (1994) Electrochim Acta 39:173911. Appleby AJ, Zagal JH (2011) J Solid State Electrochem 15:181112. Koper MTM (2013) J Solid State Electrochem 17:33913. Koper MTM, van Santen RA (1999) J Electroanal Chem 472:12614. Rossmeisl J, Nørskov JK, Taylor CD, Janik MJ, Neurock M (2006)J Phys Chem B 110:2183315. Nørskov JK, Bligaard T, Hvolbaek B, Abild-Petersen F,Chorkendorff I, Christensen CH (2008) Chem Soc Rev 37:216316. Recio FJ, Canete P, Tasca F, Linares-Flores C, Zagal JH (2013)Electrochem Comm 30:34J Solid State Electrochem (2016) 20:895–899 899

Journal of Solid State Electrochemistry

Activity volcanoes for the electrocatalysis of homolytic and heterolytic hydrogen evolution

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Activity volcanoes for the electrocatalysis of homolytic and heterolytic hydrogen evolution

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