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Electrochemistry Communications 1 (1999) 379–382

The Tafel–Heyrovsky route in the kinetic mechanism of the hydrogenevolution reaction

M.R. Gennero de Chialvo, A.C. Chialvo *Programa de Electroquımica Aplicada e Ingenierıa Electroquımica (PRELINE), Facultad de Ingenierıa Quımica, Universidad Nacional del Litoral,´ ´ ´ ´ ´

Santiago del Estero 2829, 3000 Santa Fe, Argentina

Received 14 June 1999; received in revised form 10 July 1999; accepted 22 July 1999

Abstract

The examination of the dependence of surface coverage on overpotential for the kinetic mechanism of the hydrogen evolution reaction(HER) through the Volmer–Heyrovsky 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 Tafel–Heyrovsky route, under Frumkin adsorption conditions. q 1999 Elsevier Science S.A.All rights reserved.

Keywords: Hydrogen evolution reaction; Kinetic mechanism; Tafel–Heyrovsky route

1. Introduction

It has been considered that the hydrogen evolution reaction(HER) in alkaline (or acid) solution:

y y2H Oq2e ™H q2OH (1)2 2

is verified through the Volmer (V), Heyrovsky (H) andTafel (T) steps simultaneously [1–3], which allows us todefine three routes (VH, VT, TH) [4]. Nevertheless, Hor-iuti’s 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.

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)-10y3

and , being the equilibrium reaction rate of step ie e ev )v vH V i

* Corresponding author. Fax: q54-342-457-1162; e-mail: [email protected]

[6]. In such a case, unless , the occurrence ofe ev DvT H

reaction:

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:

y yH Oqe qH ™H qOH (3)2 (a) 2

Consequently, part of the molecular hydrogen generatedby 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 Tafel–Heyrov-sky route, which operates in parallel with the Volmer–Hey-rovsky route.

Taking into account previous results [3,6,7], it can beconcluded that u(h))ue only if . Under this condi-e ev )vV H

tion, the HER can be simulated appropriately by the VH routewhen and conversely by the VT route whene e ev 4v v 4H T T

. The kinetic behaviours of VH and VT routes are wellevH

known [8–10] 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 H

HER can be described through the TH route, has not yet beenstudied. It should be borne in mind that when ,e ev svV H

u(h)sue.

M.R. Gennero de Chialvo, A.C. Chialvo / Electrochemistry Communications 1 (1999) 379–382380


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.

2. Theoretical analysis

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]:

2(1yu)e y2lv sv s (4a)qT T e 2(1yu )2ue 2(1yl)v sv s (4b)2yT T eu

ue (1yl)v sv s exp[y(1ya)fh] (4c)qH H eu

(1yu)e ylv sv s exp(afh) (4d)yH H e(1yu )

where:

essexp[u(uyu )] (5)

with u the interaction parameter of the adsorbed hydrogenatoms, and the forward and backward reaction ratesv vqi yi

of 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.

At steady state, the rate of reaction (1) and those of steps(2) and (3) are related by:

2Vsv s2v s2(v yv ); v sv yv (6)H T H T i qi yi

Substituting the expressions of the reaction rate of the cor-responding steps (4a)–(4d) and dividing by :ev H

2V j u (1yl)s s s exp[y(1ya)fh]e o e≥v j uH H

(1yu) (1yu)yl y2ly s exp(afh) s2n sTe e 2¥ ≥(1yu ) (1yu )2u u2(1yl) (1yl)y s s2 s exp[y(1ya)fh]2e e¥ µ≥u u

2(1yu) (1yu)yl y2ly s exp(afh) yn sTe e 2¥ ≥(1yu ) (1yu )2u 2(1yl)y s (7)2e ¥∂u

where , j is the current density and is thee e on sv /v jT T H H

exchange current density of the Heyrovsky step. From Eq.(7), the following implicit function of u can be defined:

2a(u)u qb(u,h)uqc(u,h)s0 (8)

where:

2(1yl) y2ls sa(u)s2n y (9a)2T e e 2≥ ¥u (1yu )

y2l4n sTb(u,h)s e 2(1yu )

yl (1yl)s s exp(yfh)qexp(afh) q (9b)e e≥ ¥(1yu ) u

y2l yl2n s exp(afh)sTc(u,h)sy y (9c)e 2 e(1yu ) (1yu )

and sss[u(h)] is given by Eq. (5).Eqs. (7), (8), (9a), (9b) and (9c) describe completely

the dependence of the current density on overpotential for theTH route.

2.1. Tafelian domains

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.

(a) Considering the case in which nT<1 (nT-10y3),the following limiting implicit function usf(h, u, ue, u) canbe obtained from Eq. (8):

euus (10)e eu q(1yu )s exp(yfh)

The corresponding expression for the dependence j(h) is:

2(1yl)j 2n s [exp(y2fh)y1]Ts (11)o e e 2j [u q(1yu )s exp(yfh)]H

This expression leads to a linear dependence only if(1yue)-10y3. In this case there is a region of low over-potential values where [(1yue)exp(yfh)]<1. From Eq.(10) it follows that (uyue)<1, therefore s(1 and conse-quently the following equation is obtained:

ext ext ojsj exp(y2fh); j s2n j (12)l l T H

In this domain of h, the Tafel slope (bl) is equal to 2.3026RT/2F and can be obtained by extrapolation. Fig. 1 illustratesextj l

the dependences of and u on h, obtained by simulationoln j/j H

of Eqs. (7), (8), (9a), (9b) and (9c) using the followingvalues of the parameters involved: (1yue)s10y3,lsas0.5, us5 and 10y5FnTF103. Solid circles corre-spond to the values, which must be verifiedext oln j /j sln 2nl H T

according to Eq. (12), for lines (a), (b) and (c).(b) When the condition nT)1 is applied, a range of low

overpotentials can be found where the terms that do not con-tain nT can be neglected and therefore the following expres-sion can be obtained from Eqs. (8), (9a), (9b) and (9c):

M.R. Gennero de Chialvo, A.C. Chialvo / Electrochemistry Communications 1 (1999) 379–382 381


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)

; (s) .ext o ext oln j /j ln j /jl H h H

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/

; (s) .o ext oj ln j /jH h H

e 2(1yu ) 2 2s y1 u q2uy1s0 (13)2e≥ ¥u

where the unique valid solution is usue (ss1). In the over-potential range where exp[y(1ya)fh]4exp(afh), thefollowing expression is obtained:

ext ext ojsj exp[y(1ya)fh]; j sj (14)l l H

Lines (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 s0H

to Eq. (14). Another interesting example is illustrated in Fig.2, with lsas0.5, us5, nTs103 and different ue values.

(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:

Uo y2l2j n sH T Ulim ej s ; s sexp(yuu ) (15)e 2(1yu )

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).

2.2. Pseudo-Tafelian domains

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.

Varying ue at nT<1 (nT-10y2) (Fig. 3), pseudo-Tafe-lian domains with RT/2F-blFRT/F can be observed at lowh (-0.2). At intermediate h values (0.2–0.4 V), there areother pseudo-Tafelian domains with 2RT/F-b-3RT/F. Alimiting kinetic current density is defined at high h values forall curves. For higher nT values (10y2-nT-1), the pseudo-Tafelian domains at low h are missing and only those atintermediate h values remain (Fig. 4).

3. Discussion

The TH route involves the re-adsorption of the dissolvedH2 produced by the Heyrovsky step and located on the reac-tion plane. Consequently, the HER cannot be initiated in theabsence of molecular hydrogen through the HT route. In sucha case, an induction period should be verified, where the H(a)

will be necessarily produced by the Volmer step. Then, theHT route will reach the steady state. Therefore, when ev )H

M.R. Gennero de Chialvo, A.C. Chialvo / Electrochemistry Communications 1 (1999) 379–382382


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

ues0.4, (b) 0.7, (c) 0.9, (d) 0.99.

and )0, this route can describe appropriately the reac-e ev vV T

tion kinetics. In this context, the descriptive capability of theTH route for the dependences of current density and surfacecoverage on overpotential was analysed.

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. 1–4. 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.

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

account in the kinetic analysis in order to avoid aprioristicrestrictions in the interpretation of experimental results.

Acknowledgements

The financial support of UNL, CONICET and ANPCYTis gratefully acknowledged.

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