The Tafel–Heyrovsky route in the kinetic mechanism of the hydrogen evolution reaction

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<ul><li><p>1388-2481/99/$ - see front matter q 1999 Elsevier Science S.A. All rights reserved.PII S1388- 2481 (99 )00078 -8</p><p>Tuesday Aug 31 12:44 PM StyleTag -- Journal: ELECOM (Electrochemistry Communications) Article: 88</p><p>www.elsevier.nl/locate/elecom</p><p>Electrochemistry Communications 1 (1999) 379382</p><p>The TafelHeyrovsky route in the kinetic mechanism of the hydrogenevolution reaction</p><p>M.R. Gennero de Chialvo, A.C. Chialvo *Programa de Electroqumica Aplicada e Ingeniera Electroqumica (PRELINE), Facultad de Ingeniera Qumica, Universidad Nacional del Litoral, </p><p>Santiago del Estero 2829, 3000 Santa Fe, Argentina</p><p>Received 14 June 1999; received in revised form 10 July 1999; accepted 22 July 1999</p><p>Abstract</p><p>The examination of the dependence of surface coverage on overpotential for the kinetic mechanism of the hydrogen evolution reaction(HER) through the VolmerHeyrovsky route shows that, under certain conditions, the Tafel re-adsorption can be produced. On this basis,the HER could be described with the contribution of Tafel and Heyrovsky elementary steps. The present communication derives and analysesthe kinetic mechanism of the HER for the TafelHeyrovsky route, under Frumkin adsorption conditions. q 1999 Elsevier Science S.A.All rights reserved.</p><p>Keywords: Hydrogen evolution reaction; Kinetic mechanism; TafelHeyrovsky route</p><p>1. Introduction</p><p>It has been considered that the hydrogen evolution reaction(HER) in alkaline (or acid) solution:</p><p>y y2H Oq2e H q2OH (1)2 2is verified through the Volmer (V), Heyrovsky (H) andTafel (T) steps simultaneously [13], which allows us todefine three routes (VH, VT, TH) [4]. Nevertheless, Hor-iutis equation [5] establishes that, as there is a unique reac-tion intermediate, only two routes are independent anddescribe completely the kinetics of reaction (1), unless cer-tain kinetic approximations are done, such as neglecting theH2 re-adsorption in the Tafel step.</p><p>From the three elementary steps involved in the HER, onlythe electrochemical ones will take place unfailingly in theproposed direction. The corresponding direction of the Tafelstep will be based on the behaviour of the surface coverageof the adsorbed hydrogen (u) on overpotential (h). Whenu(h))ue (equilibrium surface coverage), the Tafel step willtake place in the proposed direction, but when u(h)-ue thereaction will be reversed. This last type of dependence canoccur for example for the VH route when (1yue)-10y3and , being the equilibrium reaction rate of step ie e ev )v vH V i</p><p>* Corresponding author. Fax: q54-342-457-1162; e-mail: achialvo@fiqus.unl.edu.ar</p><p>[6]. In such a case, unless , the occurrence ofe ev DvT Hreaction:H H qH (2)2 (a) (a)should be considered. This situation was found in the exper-imental results obtained for the HER on Ni in alkalinesolution[7]. Under these conditions, reaction (1) can be describedby reaction (2) followed by the discharge of water (or pro-ton) through the Heyrovsky step:</p><p>y yH Oqe qH H qOH (3)2 (a) 2Consequently, part of the molecular hydrogen generated</p><p>by this step and present in the reaction plane is re-adsorbedthrough the Tafel step, regenerating H(a). The sequenceformed by reactions (2) and (3) defines the TafelHeyrov-sky route, which operates in parallel with the VolmerHey-rovsky route.</p><p>Taking into account previous results [3,6,7], it can beconcluded that u(h))ue only if . Under this condi-e ev )vV Htion, the HER can be simulated appropriately by the VH routewhen and conversely by the VT route whene e ev 4v v 4H T T</p><p>. The kinetic behaviours of VH and VT routes are wellevHknown [810] and were recently re-examined for the caseof a Frumkin-type adsorption [6]. But the case in whichu(h)-ue, that is , where the kinetic behaviour of thee ev -vV HHER can be described through the TH route, has not yet beenstudied. It should be borne in mind that when ,e ev svV Hu(h)sue.</p></li><li><p>M.R. Gennero de Chialvo, A.C. Chialvo / Electrochemistry Communications 1 (1999) 379382380</p><p>Tuesday Aug 31 12:44 PM StyleTag -- Journal: ELECOM (Electrochemistry Communications) Article: 88</p><p>The present work analyses the kinetic mechanism of theHER for the TH route, when the adsorbed intermediate fol-lows the Frumkin isotherm, without kinetic approximations.</p><p>2. Theoretical analysis</p><p>As the elementary steps of the TH route are reactions (2)and (3), the corresponding expressions for the reaction ratewith a Frumkin-type adsorption are [6,10]:</p><p>2(1yu)e y2lv sv s (4a)qT T e 2(1yu )</p><p>2ue 2(1yl)v sv s (4b)2yT T eu</p><p>ue (1yl)v sv s exp[y(1ya)fh] (4c)qH H eu</p><p>(1yu)e ylv sv s exp(afh) (4d)yH H e(1yu )</p><p>where:essexp[u(uyu )] (5)</p><p>with u the interaction parameter of the adsorbed hydrogenatoms, and the forward and backward reaction ratesv vqi yiof step i (isT, H), respectively, and fsF/RT (38.92039Vy1 at 298.16 K). Furthermore, a and l are the reaction andadsorption symmetry factors respectively, and they are con-sidered equal for all elementary steps.</p><p>At steady state, the rate of reaction (1) and those of steps(2) and (3) are related by:</p><p>2Vsv s2v s2(v yv ); v sv yv (6)H T H T i qi yiSubstituting the expressions of the reaction rate of the cor-responding steps (4a)(4d) and dividing by :ev H2V j u (1yl)s s s exp[y(1ya)fh]</p><p>e o ev j uH H(1yu) (1yu)yl y2ly s exp(afh) s2n sTe e 2 (1yu ) (1yu )</p><p>2u u2(1yl) (1yl)y s s2 s exp[y(1ya)fh]2e e u u2(1yu) (1yu)yl y2ly s exp(afh) yn sTe e 2 (1yu ) (1yu )</p><p>2u 2(1yl)y s (7)2e uwhere , j is the current density and is thee e on sv /v jT T H Hexchange current density of the Heyrovsky step. From Eq.(7), the following implicit function of u can be defined:</p><p>2a(u)u qb(u,h)uqc(u,h)s0 (8)</p><p>where:</p><p>2(1yl) y2ls sa(u)s2n y (9a)2T e e 2 u (1yu )</p><p>y2l4n sTb(u,h)se 2(1yu )</p><p>yl (1yl)s s exp(yfh)qexp(afh) q (9b)e e (1yu ) u</p><p>y2l yl2n s exp(afh)sTc(u,h)sy y (9c)e 2 e(1yu ) (1yu )</p><p>and sss[u(h)] is given by Eq. (5).Eqs. (7), (8), (9a), (9b) and (9c) describe completely</p><p>the dependence of the current density on overpotential for theTH route.</p><p>2.1. Tafelian domains</p><p>The existence of overpotential domains with a lineardependence of the logarithm of j on h, as in the cases of theVH and VT routes, is not straightforward. Nevertheless, asin the other routes [6], for certain ranges of nT and ue values,a linear variation can be obtained.</p><p>(a) Considering the case in which nT</p></li><li><p>M.R. Gennero de Chialvo, A.C. Chialvo / Electrochemistry Communications 1 (1999) 379382 381</p><p>Tuesday Aug 31 12:44 PM StyleTag -- Journal: ELECOM (Electrochemistry Communications) Article: 88</p><p>Fig. 1. Dependence of ln j/ and u on h. (1yue)s10y3; asls0.5; us5;ojH(a) nTs10y5, (b) 10y4, (c) 10y3, (d) 10y1, (e) 10, (f) 103; (d)</p><p>; (s) .ext o ext oln j /j ln j /jl H h H</p><p>Fig. 2. Dependence of ln j/ and u on h. nTs103; asls0.5; us5; (a)ojHues10y3, (b) 0.1, (c) 0.2, (d) 0.4, (e) 0.7, (f) 0.9, (g) 0.999; (h) ln jlim/</p><p>; (s) .o ext oj ln j /jH h H</p><p>e 2(1yu ) 2 2s y1 u q2uy1s0 (13)2e uwhere the unique valid solution is usue (ss1). In the over-potential range where exp[y(1ya)fh]4exp(afh), thefollowing expression is obtained:</p><p>ext ext ojsj exp[y(1ya)fh]; j sj (14)l l HLines (e) and (f) in Fig. 1 show this behaviour, which ischaracterised by a Tafel slope (bl) equal to 2.3026RT/(1ya)F. Open circles correspond to , accordingoln j/j s0Hto Eq. (14). Another interesting example is illustrated in Fig.2, with lsas0.5, us5, nTs103 and different ue values.</p><p>(c) When the overpotential is high enough, it can be ver-ified from Eq. (8) that the surface coverage tends to zero.This behaviour leads to a limiting current density of kineticorigin, which is described by the following equation:</p><p>Uo y2l2j n sH T Ulim ej s ; s sexp(yuu ) (15)e 2(1yu )</p><p>which implies an infinite Tafel slope (bhs). Consequently,the TH route at sufficiently high h values always defines alimiting kinetic current density, independent of the behaviourin the low h region. Open squares in Fig. 2 illustrate thevalues of jlim/ corresponding to lines (a), (b), (c) andoj H(d).</p><p>2.2. Pseudo-Tafelian domains</p><p>The ln j versus h relationships with a slight curvature aredefined as pseudo-Tafelian dependences [3,6]. The extrap-olation at hs0 of the linear regressions of such curves isarbitrary and therefore cannot be related to the kinetic para-meters of the elementary reaction steps.</p><p>Varying ue at nT</p></li><li><p>M.R. Gennero de Chialvo, A.C. Chialvo / Electrochemistry Communications 1 (1999) 379382382</p><p>Tuesday Aug 31 12:44 PM StyleTag -- Journal: ELECOM (Electrochemistry Communications) Article: 88</p><p>Fig. 3. Dependence of ln j/ and u on h. nTs10y3; asls0.5; us5; (a)ojH(1yue)s10y4, (b) 10y3, (c) 10y2, (d) 0.05, (e) 0.1. Fig. 4. Dependence of ln j/ and u on h. nTs0.1; asls0.5; us5; (a)ojH</p><p>ues0.4, (b) 0.7, (c) 0.9, (d) 0.99.</p><p>and )0, this route can describe appropriately the reac-e ev vV Ttion kinetics. In this context, the descriptive capability of theTH route for the dependences of current density and surfacecoverage on overpotential was analysed.</p><p>The results obtained show ln j versus h dependences rathersimilar to those evaluated before by the VT route [6]. Theslopes of the Tafelian domains, which are not observed unlessu(h)(ue, take only the values RT/2F or RT/(1ya)F and,as in the cases of VH and VT routes analysed previously [6],do not depend on parameter l. Opposite behaviour was foundfor the dependence of the surface coverage on overpotential.The TH route shows a monotonically decreasing u(h)dependence, always reaching a null surface coverage at suf-ficiently high h values. However, when u becomes dependenton potential, pseudo-Tafelian domains can arise, as shown inFigs. 14. The corresponding apparent slopes b, obtained byfitting a reasonable overpotential region, are approximatelycomprised in the range RT/2F-b-RT/F for low h and2RT/F-b-3RT/F for intermediate h values.</p><p>Finally, the present results show that the Tafel step cantake place in the backward direction during the hydrogenevolution reaction and consequently it should be taken into</p><p>account in the kinetic analysis in order to avoid aprioristicrestrictions in the interpretation of experimental results.</p><p>Acknowledgements</p><p>The financial support of UNL, CONICET and ANPCYTis gratefully acknowledged.</p><p>References</p><p>[1] D.A. Harrington, B.E. Conway, Electrochim. Acta 32 (1987) 1703.[2] L. Bai, J. Electroanal. Chem. 355 (1993) 37.[3] M.R. Gennero de Chialvo, A.C. Chialvo, J. Electroanal. Chem. 415</p><p>(1996) 97.[4] P.C. Milner, J. Electrochem. Soc. 111 (1964) 228.[5] J. Horuiti, J. Res. Inst. Catal., Hokkaido Univ. 5 (1957) 1.[6] M.R. Gennero de Chialvo, A.C. Chialvo, Electrochim. Acta 44 (1998)</p><p>841.[7] M.R. Gennero de Chialvo, A.C. Chialvo, J. Electroanal. Chem. 448</p><p>(1998) 87.[8] B.E. Conway, M. Salomon, Electrochim. Acta 9 (1964) 1599.[9] A. Lasia, Current Top. Electrochem. 2 (1993) 239.</p><p>[10] M. Enyo, J. Res. Inst. Catal., Hokkaido Univ. 25 (1977) 17.</p></li></ul>

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