The determination of kinetics parameters of the hydrogen evolution on Pd–Ni alloys by ac impedance

International Journal of Hydrogen Energy 25 (2000) 635±641

The determination of kinetics parameters of the hydrogen evolution on Pd±Ni alloys by ac impedance N.V. Krstajic a, S. Burojevic b, Lj.M VracÏar a,* a

Faculty of Technology and Metallurgy, University of Belgrade, Karnegieva 4, 11000, Belgrade, Yugoslavia b Faculty of Chemistry, University of Belgrade, Studentski trg 12±16, 11000, Belgrade, Yugoslavia

Abstract The hydrogen evolution reaction (HER) at a Pd±Ni electrodeposited alloy electrode has been studied by means of ac impedance spectrum measurements and by dc polarization current behavior in 0.5 mol dmÿ3 NaOH solution at 258C. The rate constants of the forward and backward reactions of the corresponding steps were estimated by a nonlinear ®tting method. It has been found that the overall reaction proceeds through a Volmer±Heyrovsky mechanism, with Heyrovsky as the rate determining step. The coverage vs potential relation is discussed comparing the results of ac impedance calculations with the same of potential decay determinations. 7 2000 International Association for Hydrogen Energy. Published by Elsevier Science Ltd. All rights reserved.

1. Introduction A traditional assumption in the electrochemical study of a multi-step reaction is sometimes oversimpli®ed. According to this assumption there is always a rate-determining step (rds) which characterizes the kinetics behavior of the reaction and the other steps prior to the rds which are in quasi-equilibrium, that means, the adsorption isotherm for reaction intermediates should be introduced for the equilibrium. However, when adsorbed intermediates are involved in an overall electrode reaction, e.g. hydrogen evolution reaction (HER), then the state of chemisorbed intermediates expressed through relation of coverage vs overpotential is of much interest in relation to the mechanism of reaction. Some recent publications [1± 11] show how the ac impedance technique could be used to study electrode reactions with one adsorbed intermediate.

* Corresponding author.

The kinetics characteristics of the reaction are examined in terms of numerical simulation of the observed ac behavior through evaluation of the rate constants of each step using treatment brie¯y discussed in the following. The mechanism of the HER in aqueous basic solution involves the proton discharge electrosorption (Volmer reaction, Eq. (1)), electrochemical desorption (Heyrovsky reaction, Eq. (2)) and H recombination (Tafel reaction, Eq. (3)). k1

M ‡ H2 O ‡ e F MHads ‡ OHÿ …rate v1 † kÿ1

k2

MHads ‡ H2 O ‡ e F H2 ‡ M ‡ OHÿ …rate v2 † kÿ2

k3

MHads ‡ MHads F H2 ‡ 2M …rate v3 † kÿ3

…1†

…2†

…3†

where ki and kÿi are the rate constants of the forward and backward reactions.

0360-3199/00/$20.00 7 2000 International Association for Hydrogen Energy. Published by Elsevier Science Ltd. All rights reserved. PII: S 0 3 6 0 - 3 1 9 9 ( 9 9 ) 0 0 0 7 5 - 0

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The reaction rates of the three steps are expressed by   bFZ v1 ˆ k1 …1 ÿ Y† exp ÿ RT   …1 ÿ b†FZ ÿ kÿ1 Y exp RT 0 ˆ k10 …1 ÿ Y† ÿ kÿ1 Y

  bFZ v2 ˆ k2 Y exp ÿ RT   …1 ÿ b†FZ ÿkÿ2 …1 ÿ Y† exp RT

…4a†

…4b†

q dY F dt

…4c†

…5†

 ˆ v1 ÿ v2 ÿ 2v3

…6†

The steady-state opd H coverage, Y, is expressed by setting r1=0, then Yˆ

…9a†

R20 R1 ‡ R0

…9b†

where

r0 ˆ j=F ˆ ÿ…v1 ‡ v2 † r1 ˆ

…8†

0 bF 2 ‰k10 …1 ÿ Y† ‡ kÿ1 Y ‡ k20 YŠ RT

Rp ˆ ÿ

1 F 2t ˆ R0 q ˆ

The charge balance (r0) under the constant dc current density, and the mass balance (r1) are expressed by the following equations



Rp …1 ‡ jotp †

The double layer capacitance (Cdl) is used as a circuit element of the smooth electrodes. The quantities R1, Rp, Cp and tp are given by     1 @ v1 @ v2 ˆF ‡F R1 @E Y @E Y ˆ

0 ˆ k20 Y ÿ kÿ2 …1 ÿ Y†

v3 ˆ k3 Y2 ÿ kÿ3 …1 ÿ Y†2

Zf ˆ R1 ‡

0 0 ÿ…k10 ‡ kÿ1 ‡ k20 † ‡ ‰…k10 ‡ kÿ1 ‡ k20 †2 ‡ 8k10 k3 Š1=2 4k3

…7† In the impedance studies, the HER mechanism is estimated by using the electric circuit of Armstrong and Henderson [12], given in Fig. 1, which contains the ac impedance elements: R1, Rp and Cp. The total impedance is given by

"

@ v1 @Y





@ v2 ‡ @Y E

 # E

0 0 bF 2 …ÿk10 ÿ kÿ1 ‡ k20 †‰k10 …1 ÿ Y† ‡ kÿ1 Y ÿ k20 YŠ 0 † RT…4k3 Y ‡ k20 ‡ k10 ‡ kÿ1

…9c† and "       # 1 F @ v3 @ v2 @ v1 ˆ 2 ‡ ÿ t q @Y E @Y E @Y E ˆ

F 0 …4k3 Y ‡ k20 ‡ k10 ‡ kÿ1 † q

…9d†

and Cp ˆ ÿ

R0 t R21

…9e†

In this paper, we report the results regarding the HER in 0.5 mol dmÿ3 NaOH solution at 258C, on an electrochemically deposited Pd±Ni alloy electrode. Rate constants for HER were estimated from dc current density, charge transfer resistance (R1) and the relaxation elements (Cp and Rp), for a wide overpotential range.

2. Experimental

Fig. 1. Equivalent circuit for single-adsorbate mechanism (Amstrong's electric circuit).

A Pd(mol%63)-Ni(mol%37) electrode was prepared by electrodeposition onto Cu tape from a solution containing: PdCl2
4H2O (15.0 g dmÿ3 calculated on Pd), NiCl2
H2O (20.0 g dmÿ3 calculated on Ni) and NH4Cl (30.0 g dmÿ3), using a procedure described elsewhere [13]. The electrochemical experiments were performed at 258C in a solution of 0.5 mol dmÿ3 NaOH. The

N.V. Krstajic et al. / International Journal of Hydrogen Energy 25 (2000) 635±641

solution was made with spectrograde NaOH (Merck) and deionized water (Fig. 2). A conventional three-compartment glass cell was used. A reversible hydrogen electrode (RHE) in the same solution as that of the working electrode was used as the reference electrode. A platinum gauze, spotwelded onto a platinum wire sealed into a glass tube, was used as a counter electrode. 3. Results and discussion The polarization behavior of a Pd±Ni electrode is

637

found to be signi®cantly dependent on the pretreatment [13]. If the electrode is not previously polarized, then during cathodic hydrogen evolution the current densities are not steady at the respective controlled constant potentials. However, after cathodic prepolarization at Z=ÿ0.300 V (RHE) for 1 h of time it is found that, during polarization measurements, the current densities become reasonably steady at the constant potentials. Steady-state measurements are made, point by point, at 30 s intervals in a descending direction of overpotential, which gives the most reproducible behavior. Experimental points in Fig. 3 represents the Tafel relation after prepolarization with the value of the

Fig. 2. Experimental (circled points) and solid lines calculated from evaluated ki values complex plane diagrams for the HER on a Pd±Ni electrode in 0.5 mol dmÿ3 NaOH solution at 258C, at several overpotentials.

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Tafel slope close to ÿ0.140 V decÿ1 at 258C. The Tafel line, mostly stable after this pretreatment, implies that the oxygen species previously present on the surface are reduced and a certain equilibrium state of absorbed H into the alloy is reached. Fig. 2 shows the complexplane impedance diagrams at various overpotentials, Z on the Pd±Ni electrode. The experimental data are represented by the circled points. The impedance spectra consist of two overlapping semicircles. Fig. 2a shows that the impedance diagrams for a lower value of Z (Z=ÿ0.15 V (RHE)) have some kind of descending ``tail'' at low frequency ends. This kind of behavior is even more signi®cant for smaller values of overpotential, and could be explained in term of several factors: (a) the in¯uence of H2 di€usion on the kinetics, (b) roughness e€ects which lead to some distortion of the ideal shapes of impedance curve or (c) H absorbed in the region near the electrode surface. Since this e€ect is more signi®cant for a lower value of overpotential it seems that H2 di€usion is not the main reason for the ''tail ''. So the better ®t to the ``tail'' for Z R ÿ0.15 V could probably be obtained by including an additional absorption step in the mechanism or by introducing e€ects of roughness. The experimental data are treated through the NLS ®tting to estimate the elements of the Armstrong`s equivalent circuit given in Fig. 1. The values of the impedance parameters which are necessary to calculate the rate constants in the HER mechanism are listed in Table 1. The rate for the HER and the q value are evaluated from dc current density and ®tted parameter values of

Fig. 3. Tafel polarization curve on a Pd±Ni electrode in 0.5 mol dmÿ3 NaOH at 258C. The continuous line was calculated from evaluated ki values.

the Armstrong's equivalent circuit using factorial ®tting. The evaluated values of the rate constants are the following: k1 is 9.2 10ÿ11; kÿ1 is 9.7 10ÿ10, k2 is 8.0 10ÿ12, kÿ2 is 7.2 10ÿ12, k3 is 1.2 10ÿ10 and kÿ3 is 1.2 10ÿ11 (mol cmÿ2 sÿ1), for the apparent surface area of 1 cm2. The potential dependence of the current density obtained from the estimated rate constants is illustrated by a corresponding solid line in Fig. 3. Zÿlog(1/ R1+Rp) points for the experimental results and numerically simulated curve based on Eq. (9) and the same rate constants as those for the curve in Fig. 3 are shown in Fig. 4. Fig. 5. shows the Bode plots for the same experimental data (as shown in the complexplane plot of Fig. 2c) together with the calculated data from evaluated ki values presented with the solid lines. It can be seen that the numerically simulated curve for q = 20 mC cmÿ2 gives a rather good ®t to the experimental data. This implies that only 10% (YH=1 for q = 210 mC cmÿ2) of surface atoms behave as ``active sites'' for the hydrogen evolution. The surface coverage, Y, of adsorbed hydrogen atoms and the pseudocapacitance, Cf, can be calculated as functions of overpotential from the rate constants and q = 20 mC cmÿ2 by Eq. (7), as shown in Fig. 6a and b. The value of Y increases at more negative potentials and reaches its saturation value of 0.82 at higher overpotentials. The reaction rates of the Volmer, Heyrovsky and Tafel processes in the hydrogen evolution mechanism and the resulting total current value are all independently shown in Fig. 7, as calculated from the esti-

Fig. 4. Experimental (points) and simulated (solid line) Z-(1/ R1+Rp) plot for the HER at a Pd±Ni electrode in 0.5 mol dmÿ3 NaOH solution at 258C.

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639

Table 1 The ®tted parameters values of the equivalent circuit for the Pd±Ni electrode in 0.5 mol dmÿ3 NaOH at 258C (RO=2.98 O cm2) ÿZ (V)

R1 (O cm2)

Rp (O cm2)

Cp (mF cmÿ2)

Cdl (mF cmÿ2)

(d) 0.30 (c) 0.28 0.25 (b) 0.20 0.18 (a) 0.15

132 191 329 765 1033 1542

2.90 6.40 20.5 122 234 460

112 116 104 118 116 114

293 172 164 151 142 138

mated ki values, in a wide potential region. In this Figure, all rate values, vi (mol cmÿ2 sÿ1) are shown in terms of current, Fvi (A cmÿ2). From Fig. 7, one can see that the reaction mechanism is a Volmer±Heyrovsky with Heyrovsky as the rate determining step. Simulated Z-log j curve shows the linear dependence with a slope of 0.138 V decÿ1 within the potential range above Z=ÿ0.15 V (RHE). It is interesting to compare pseudocapacitance behavior evaluated from impedance results with the same evaluated from potential decay results [14]. It should be noted that the dependence of the potential decay curve on j is expressed in the shape of the pseudocapacitance curve according to the equation:   dZ aZF ÿC…Z† ˆ j0 exp …10† dt RT Fig. 8 (from ref. [14]) shows C vs Z plot for a Pd±Ni electrode. Higher values of capacitance, re¯ected by

Fig. 5. Bode plots of vZv and phase angle vs logarithm of frequency, obtained on a Pd±Ni electrode in 0.5 mol dmÿ3 NaOH at 258C and Z=ÿ0.28 V (RHE).

Fig. 6. Potential dependence of the calculated values of the surface coverage by adsorbed hydrogen (YH), and the pseudocapacitance (Cf) on a Pd±Ni electrode in 0.5 mol dmÿ3 NaOH solution at 258C.

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N.V. Krstajic et al. / International Journal of Hydrogen Energy 25 (2000) 635±641

Fig. 7. Potential dependence of the current density ( j ) and the reaction rates for the HER (Eq. 4) on a Pd±Ni electrode in 0.5 mol dmÿ3 NaOH at 258C.

the very long time needed for the potential to decay to its reversible value, should be noticed. Unfortunately, there is no clear maximum in C, but

Fig. 8. Capacitance as a function of potential for the HER on a Pd±Ni electrode at 258C in 0.5 mol dmÿ3 NaOH.

integration of C vs Z gives a charge that corresponds to more than one monolayer. Since it is dicult to cover an electrode with a ®lm of H of more than one monolayer, then the possibility of explaining this behavior is in formation of a hydride or absorbed hydrogen in a relatively few atomic layers of an electrode. This possibility is consistent with the observation already referred to [14±16], that cathodically generated H can di€use into electrode. On one hand, the method of preparation of the electrodeposited electrode may introduce a hydride phase through co-deposition of H during the electroplating, but on the other hand pretreatment of the electrode with 1 h of prepolarization at Z=ÿ0.300 V may introduce a hydride, too. A micro-cavity structure of electrodeposited electrode could result in easier di€usion of H into bulk which is manifested (through subsequent desorption) in a very long potential decay, i.e. 10 s (as compared to 0.1±0.2 s required for full coverage of adsorbed H). The desorption of hydrogen during the potential decay results in very high C values around the open circuit potential but di€erent to the values that follow from the impedance measurements. The decay and steady-state results also suggest that some quasi-reversible potential, di€erent than hydrogen reversible potential, is established on previously cathodically polarized electrode and that could be explained as the existance of some new phase as hydride phase. Then, self-discharge during potential decay takes place through two coupled parallel reactions according to the scheme: My H ‡ OHÿ ˆ yM ‡ H2 ‡ e

…11†

H2 O ‡ e ˆ OHÿ ‡ 12 H2

…12†

where H2 evolution reaction itself involves all three steps (Eqs. (1)±(3)] involving adsorbed H as the intermediate either on M or My, as we suggested in the discussion of ac impedance results. In a system when, as in this case, a polarizing current is interrupted, the potential of the electrode will fall with time because of the continuing passage of current across the double-layer causing discharge of the double-layer capacitance and the decomposition of the surface H adsorbed and H absorbed pseudocapacitance. The latter possibility is consistent with our observation [14] that cathodically generated H can di€use into the Pd±Ni electrode. The di€usion of the observed hydrogen from the inner surface of the bulk electrode is a long process and that is why the potential decay curves cover ®ve decades of time, and overall decay takes a very long time, tr20 s. The process which involves di€usion is also indicated in the ac impedance measurements in the poten-

N.V. Krstajic et al. / International Journal of Hydrogen Energy 25 (2000) 635±641

tial range of Z < ÿ0.15 V (RHE) proving that the HER in that range of potential proceeds through mediation of a decomposing hydride or decomposing absorbed hydrogen. From both ac impedance and potential decay, results follow similar double layer capacitance values of ca 180 mF cmÿ2 meaning that the real apparent area factor is about 6. The decay results provide support for the presence of bulk-type hydrogen sorption in the ``near surface'' electrode region, but ac impedance results show that the presence of absorbed H, acts as a ``poison'' for the HER, which is manifested through quite small OPD H capacitance, i.e. through the fact that only 10% of surface is active for HER. A similar conclusion follows from the investigation of HER in a few Ti±Ni alloys [11] where it is found that a Ti±Ni typical hydric alloy is one of the most inactive and a Ti±Ni3 alloy typical eletrocatalytic, is the most active one. Recently, hydrogen di€usivity through the bulk of a Pd±Ni alloy has also been investigated by examining the electrochemical hydrogen discharge characteristics of Pd and Pd±Ni alloys [17±19], where the authors referred that the discharge capacity seemed to be determined by a counterbalance between the high di€usivity of hydrogen in the bulk and the stability of the hydrides.

4. Conclusions The Tafel plot and ac impedance measurements were used to determine the mechanism and the kinetics of HER in 0.5 mol dmÿ3 NaOH solution on a Pd±Ni alloy electrode. The HER proceeds on a surface partially covered by adsorbed H-intermediate. Limiting coverage is attained at Z < ÿ0.15 V (yH 4 0.82). The HER takes place through a Volmer±Heyrovsky mechanism, with Heyrovsky as the rate determining step.

641

The potential decay results suggest the presence of bulk-type hydrogen sorption. The absorbed H probably acts as a ``poison'' for the HER, which is manifested through low OPD H capacitance, i.e., through the fact that only 10% of surface is active for the HER.

References [1] Harrington DA, Conway BE. J Electroanal Chem, Interfacial Electrochem 1987;221:1. [2] Bai L, Harrington DA, Conway BE. Electrochimica Acta 1987;32:1713. [3] Bai L, Conway BE. J Electrochem Soc 1990;138:2897. [4] Chen L, Lasia A. J Electrochem Soc 1991;138:3321. [5] Potvin E, Lasia A, Menard H. J Electrochem Soc 1991;138:900. [6] Ekdunge P, Jutter K, Kreysa G, Kessler T, Ebert M, Lorenz WJ. JElectrochem Soc 1991;138:2660. [7] Chen L, Lasia A. J Electrochem Soc 1993;140:2464. [8] Lasia A, Rami A. J Electroanal Chem Interfacial Electrochem 1990;294:123. [9] Cheong AK, Lasia A, Lessard J. J Electrochem Soc 1993;140:2721. [10] Okido M, Depo JK, Capuano GA. J Electrochem Soc 1993;140:127. [11] Krstajic NV, Grgur BN, Mladanovic NS, Vojnovic MV, Jaksic MM. Electrohim Acta 1997;42:323. [12] Armstrong RD, Henderson M. J Electroanal Chem 1972;39:81. [13] VracÏar Lj, Stojanovic M. J Serb Chem Soc 1996;61:67. [14] VracÏar Lj, Burojevic S, Krstajic N. J Serb Chem Soc 1998;63:201. [15] Conway BE, Angerstein-Kozlowska H, Sottar MA, Tilak BV. J Electrochem Soc 1983;130:1825. [16] VracÏar Lj, Conway BE. J Electroanal Chem 1990;277:253. [17] Yoshihara M, McLelan RB. Acta Metall 1982;30:1605. [18] Sakamoto Y, Kuruma K, Nakitomi Y. J Applied Electrochem 1994;24:38. [19] Sakamoto Y, Chen FL, Muto J, Flanagan TB. Z Phys Chem 1991;173:235.