9
Electrochimica Acta, Vol. 42, No. 6, 951-959, pp. 1997 Copyright 0 1997 ElsevierScience Ltd. PIE soo13-4686(%)00272-1 Printed in &at Britain. All rights reserved 0013-4686/97 $17.00 + 0.00 An electrochemical impedance study on the kinetics and mechanism of the hydrogen evolution reaction on nickel molybdenite electrodes E. B. Castro,’ M. J. de Giz,2 E. R. Gonzalez2 and J. R. Vilche’* ‘Institute de Investigaciones Fisicoquimicas Teoricas y Aplicadas (INIFTA), Facultad de Ciencias Exactas, Universidad National de La Plata, Sucursal 4-CC. 16, (1900) La Plata, Argentina 21nstituto de Quimica de Sao Carlos, IQSC/USP, C.P. 780, 13570-970, Sao Carlos-SP, Brasil (Received 7 June 1996) Abstract-Electrodeposited Ni/NiMoSz electrodes have shown good electrocatalytic activity towards the hydrogen evolution reaction as well satisfactory long-term operational performance. The hydrogen evolution reaction on these electrodes, which in previous investigations using steady-state polarizations, cyclic voltammetry and scanning electron microscopy revealed high surface area and a very heterogeneous surface morphology, has been studied by applying electrochemical impedance spectroscopy (EIS). The kinetics and mechanism of the hydrogen evolution reaction (HER) on electrodeposited Ni/NiMoSz electrodes have been investigated in the frequency range 5 mHz ,<f < 10 kHz. A detailed dynamic system analysis is presented taking into account the contributions of Tafel-Volmer-Heyrovsky reaction steps as well as the absorption and diffusion of hydrogen atoms into the electrode material. For comparison results obtained for the HER on electrodeposited Ni electrodes are also discussed. Copyright 0 1997 Elsevier Science Ltd Key woru!s: Hydrogen evolution reaction, hydrogen absorption reaction, electrode kinetics, nickel molibdenite electrodes, electrochemical impedance spectroscopy, hydrogen atoms diffusion. Ar cdl CH G ACH(XJ) ACH(X,W) D f F IF P, NOMENCLATURE Ah(t) Real active area Double layer capacitance Absorbed hydrogen concentration at x=0 i J(x, t) k Steady-state concentration of absorbed Hatx=O Pertubation of absorbed H concen- tration at point x and time t Fourier transform of AC&x, t) Diffusion coefficient of absorbed hydro- gen atoms RS T ZF 2 8 Frequency of potential sinusoidal oscil- lation Faraday constant Faradaic current Steady-state faradaic current Aott) e” Y- *Author to whom correspondence should be addressed. w 951 Perturbation in faradaic current due to p? perturbation Absorbed H flux at point x and time t Formal rate constant of step (i) Reaction rate of step (i) Universal gas constant Solution resistance Temperature Faradaic impedance Total impedance Transfer coefficient related to step (i) Fraction of active surface covered by adsorbed H (Had) Perturbation in 0 due to potential perturbation Steady-state value of 0 Overpotential Maximum surface concentration (mol cm-2) of adsorbed hydrogen Angular frequency

An electrochemical impedance study on the kinetics and mechanism of the hydrogen evolution reaction on nickel molybdenite electrodes

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Electrochimica Acta, Vol. 42, No. 6, 951-959, pp. 1997 Copyright 0 1997 Elsevier Science Ltd.

PIE soo13-4686(%)00272-1 Printed in &at Britain. All rights reserved

0013-4686/97 $17.00 + 0.00

An electrochemical impedance study on the kinetics and mechanism of the hydrogen evolution reaction on nickel molybdenite

electrodes

E. B. Castro,’ M. J. de Giz,2 E. R. Gonzalez2 and J. R. Vilche’*

‘Institute de Investigaciones Fisicoquimicas Teoricas y Aplicadas (INIFTA), Facultad de Ciencias Exactas, Universidad National de La Plata, Sucursal 4-CC. 16, (1900) La Plata, Argentina

21nstituto de Quimica de Sao Carlos, IQSC/USP, C.P. 780, 13570-970, Sao Carlos-SP, Brasil

(Received 7 June 1996)

Abstract-Electrodeposited Ni/NiMoSz electrodes have shown good electrocatalytic activity towards the hydrogen evolution reaction as well satisfactory long-term operational performance. The hydrogen evolution reaction on these electrodes, which in previous investigations using steady-state polarizations, cyclic voltammetry and scanning electron microscopy revealed high surface area and a very heterogeneous surface morphology, has been studied by applying electrochemical impedance spectroscopy (EIS). The kinetics and mechanism of the hydrogen evolution reaction (HER) on electrodeposited Ni/NiMoSz electrodes have been investigated in the frequency range 5 mHz ,<f < 10 kHz. A detailed dynamic system analysis is presented taking into account the contributions of Tafel-Volmer-Heyrovsky reaction steps as well as the absorption and diffusion of hydrogen atoms into the electrode material. For comparison results obtained for the HER on electrodeposited Ni electrodes are also discussed. Copyright 0 1997 Elsevier Science Ltd

Key woru!s: Hydrogen evolution reaction, hydrogen absorption reaction, electrode kinetics, nickel molibdenite electrodes, electrochemical impedance spectroscopy, hydrogen atoms diffusion.

Ar

cdl CH

G

ACH(XJ)

ACH(X,W)

D

f

F IF

P,

NOMENCLATURE Ah(t)

Real active area Double layer capacitance Absorbed hydrogen concentration at x=0

i J(x, t) k

Steady-state concentration of absorbed Hatx=O Pertubation of absorbed H concen- tration at point x and time t Fourier transform of AC&x, t) Diffusion coefficient of absorbed hydro- gen atoms

RS T ZF

2 8 Frequency of potential sinusoidal oscil- lation Faraday constant Faradaic current Steady-state faradaic current

Aott)

e”

Y- *Author to whom correspondence should be addressed. w

951

Perturbation in faradaic current due to p? perturbation

Absorbed H flux at point x and time t Formal rate constant of step (i) Reaction rate of step (i) Universal gas constant Solution resistance Temperature Faradaic impedance Total impedance Transfer coefficient related to step (i) Fraction of active surface covered by adsorbed H (Had) Perturbation in 0 due to potential perturbation Steady-state value of 0 Overpotential Maximum surface concentration (mol cm-2) of adsorbed hydrogen Angular frequency

952 E. B. Castro et al.

1. INTRODUCTION

In a search of electrodes exhibiting high electrocata- lytic activity for the hydrogen evolution reaction (HER) in alkaline media, different electrode materials have been the target of several investigations. These are mainly based on the modification of Ni surfaces by codeposition with other elements to enhance the rate of the HER in comparison to results obtained under similar experimental conditions by using either mild steel or electrodeposited Ni electrodes.

Conway et al. studied the electrochemical behaviour of Ni-Ma-Cd codeposits associating the electrocatalytic effect with an increase in the effective area and changes in the properties of the adsorbed species [l, 21. Gonzalez et al. [3] reported high area Ni-Zn electrodeposits after partial leaching of Zn with KOH (roughness factor x 1130). Ni-Raney type coatings obtained from Ni-Al alloys were investi- gated by Choquette er al. [4] and Gassa et al. [5]. Other studies of the kinetics of the HER on Ni-Zn, Ni-Al and Ni-Mo were carried out by Lasia et al. [6-lo]. Recently, N&Co-Zn alloys with small amounts of Co exhibited good chemical stability and adequate mechanical properties together with high electrochemical activity [ 111.

Electrodeposits of Ni-S were also tested [12] because of the low cost of preparation and good long term performance. Vandeborre er al. [ 131 related the activation by cathodic polarization of Ni--S codeposits, to an increasing amount of H atoms dissolved in the cathode. Nidola and Schira [14] reported that the codeposition of MO& and Ni produces electrode materials that have acceptable operating overpotentials and long-term catalytic activity.

In general it is accepted that the HER, in aqueous electrolytes, proceeds according to either the Volmer- Tafel or the Volmer-Heyrovsky reaction schema. An expression of the impedance transfer function related to these reaction pathways was developed by Harrington and Conway [15], as a particular case of the more general physicochemical treatment derived by Armstrong and Henderson [16] for a two-step reaction involving an adsorbed intermediate, where diffusional contributions of species either in the electrolyte solution or in the electrode material were neglected.

Several studies demonstrated that Ni and some of its alloys have a strong tendency to incorporate adsorbed H-atoms to form hydride (NiH,) species of ill-defined composition [17-191, giving rise to an alternative reaction path for the HER in which the hydrogen absorption reaction (HAR) is taken into account. Therefore, the additional contributions to the faradaic impedance of the system due to the HAR and the corresponding diffusion of H atoms into the electrode material were considered by Lim and Pyun [20] in order to derive an appropriate expression for the theoretical faradaic

impedance to simulate electrochemical impedance spectroscopy (EIS) data of the hydrogen evolution reaction on Pd membranes. Comparative measure- ments carried out on polycrystalline Pt and Ni electrodes and on different amorphous metals to study the kinetics of HER in alkaline solutions allowed to distinguish EIS as a powerful tool to test the reliability of kinetic models based on reaction mechanisms [2 1,221.

In this paper the hydrogen evolution reaction on Ni/NiMo& electrodes was studied by EIS. Exper- imental impedance data were successfully simulated taking into account the Volmer-Heyrovsky-Tafel reaction steps as well as the H atoms absorption process and the diffusion of H atoms into the electrode material. The kinetic constants for the different chemical and electrochemical steps were determined and the diffusion coefficient of H atoms in electrodeposited Ni/NiMoSz was estimated.

2. EXPERIMENTAL

Working electrodes were prepared by mounting mild steel substrates into epoxy resin, leaving an exposed area of 0.5 cm2. Prior to electrodeposition the metal surface was treated with emery paper and cleaned with dilute HCl and acetone. Nickel was deposited first, using a Watts bath. The codeposition of Ni and MO& particles was performed on this surface employing a second bath. The composition of the baths as well as the electrodeposition conditions were the same already detailed in a previous publication [23]. For comparison, an electrodeposited Ni electrode was also used.

The electrolyte solution was 6 M KOH prepared from analytical grade (p.a. Merck) reagent and purified Mill&Q water. Electrochemical measure- ments were carried out under purified Nz gas atmosphere at 25°C in a conventional three-compart- ment glass cell. A high area Pt sheet was used as auxiliary electrode. Potentials were measured and referred to in the text against a Hg/HgO/6M KOH reference electrode.

Steady-state current us potential data were obtained galvanostatically employing a PAR 273A potentiostat. Impedance spectra were recorded in the 5 mHz <f< 10 kHz frequency range, using the Solartron 1255 FRA and PAR 27319 potentiostat integrated with an IBM PS/2-55 computer.

3. RESULTS AND DISCUSSION

For the sake of comparison Fig. 1 shows typical Tafel plots corresponding to Ni/NiMo& and Ni electrodes, where an enhanced electrocatalytic effect is clearly evident in the case of the NijNiMoSz electrode with respect to Ni. This may be due, in principle, to either an increase of the active area or a true electrocatalytic effect or both effects simul- taneously. Voltammetric studies [23] suggested an

Hydrogen evolution reaction 953

1.6

1.4

> \ w 1 1.2

1.0

I . ...**.-a . . .,..--I . ...cnl-

: DNI

. v N1/NiMoS2

o= oe ocP”on :

v : C

on so 0

0 vv+?v v

. 0 VV

vvv VV

VV 09

- 0 v

c . . . . I . . . . . . . 1 . . ..-..I . . . . ..A 10-J 1 o-2 10” 100

log[ I / A cm-* 1

Fig. 1. Tafel plots for the HER on Ni and Ni/NiMoSz electrodes in 6 M KOH.

increase in the effective area of Ni/NiMoSz electrodes as compared with that of Ni, but it was concluded that the better performance of Ni/NiMoS2 electrodes was caused by the incorporation of MO& and not only to an increase in the active area. From the stationary polarization curves presented in Fig. 1, a cathodic Tafel slope, b, = 8 E/i? log Iii, of about b, x -lSOmVdec-’ can be calculated for Ni electrodes, whereas Ni/NiMoSz electrodes do not exhibit a clear single Tafel-type behaviour. It is worth noting that two approximately linear regions

2 0 10 20 50 40

Z(R.)/n 2.0, , , , , , , 1 , -60

_ l.S-

c

2 i.o- v

- 0.5 - ,o

0.0 -

-60

-40 b

-30 p

+ -20

-0.6 0

-3 -2 -1 0 1 2 3 4 6

100 ( f / Hz 1 Fig. 2. Nyquist and Bode diagrams corresponding to the HER on Ni/NiMod electrode, measured at g = -0.05 V.

9’ ’ :~K.t’ -4

e t g -2

N

0

0.6 I I , I , , I

- 0.6 C \ N 0.3 Y

P 0.0

-0.3

0 2 4 6

Z@.)/ n

0

-3 -2 -1 0 1 2 5 4 5

log ( f / Hz ) Fig. 3. Impedance diagrams of the HER on Ni/NiMo& electrode at q = - 0.15 V.

can be defined, at low cathodic overpotentials 6, z - 50 mV dec-’ while at high overpotentials b,~ -2OOmVdec’.

3.1. Impedance data of Ni/NiMoSz electrodes

Nyquist and Bode plots corresponding to the HER on a Ni/NiMoSr electrode are shown in Figs 2-5. Two overlapped and distorted capacitive contributions can be distinguished in the impedance spectra measured at 1~1 < 0.25 V (Figs 24) whereas

f-m/ . 0.4 0.6 1.2 1.6 2.0 2.4

Z(Rd/n

- -24

C E

N --16 g

v T - -12 +

- -0

Y 0 I 1 1 c * 3 0 I I

-2 -2 -1 6 1 2 1 4 6

hl ( f / Hz 1

Fig. 4. Impedance diagrams of the HER on Ni/NiMo& electrode at q = -0.25 V.

954 E. B. Castro et al.

-0.6 C

' -0.4

T z -0.2

0.0 0.0 0.2 0.4 0.6 0.6 1.0 1.2 1.4 1.6

Z(R6) /f'

1 1 0 0

# -0.1 0%6nx

i. 0

,80°

00 88 -

10 WI 0.0

-or&

-16 0.2

C 0.1 -12 .

\ ?

N 8

v 0.0 -6 = \

B 9

-0.1 -4

-0.2 0

-2 -1 0 1 2 3 4 I

log ( f / Hz 1

Fig. 5. Impedance diagrams of the HER on Ni/NiMo& electrode at q = -0.35 V.

at higher cathodic overpotentials the capacative loops seem to be practically undistorted (Fig. 5). Figures 6(a) and 6(b) correspond to expansions of the high frequency region of Nyquist plots presented in Figs 2 and 5, respectively. Figure 6(a) exhibits impedance data at an operational potential close to the equilibrium potential (q = -0.05 V), while those given in Fig. 6(b) were measured at tl = - 0.35 V where HZ bubbles were clearly seen over the electrode surface. The phase angle associated with Fig. 6(a) (after electrolyte resistance subtraction) is f#J z -45”, a value that corresponds to a porous and highly inhomogeneous surface in accordance with SEM micrographs shown in [23]. From the high frequency region of Fig. 6(b) a phase angle of - 90” can be calculated, this value may be indicating that Hz bubbles smooth out the electrode surface blocking the electroactive pores and cavities, so that the electrode behaves like a flat homogeneous surface.

3.1.1. Reaction mechanisms

Results presented in Figs 1-6 for the hydrogen evolution reaction on electrodeposited Ni/NiMoSs can be analysed, in principle, according to the following reaction steps:

Hz0 + M + e- &&t MH,d + OH- (I) Volmer step I

MH,,j + Hz0 + e-+M + Hz + OH- (II) Heyrovsky step

and/or

MH,d + MH,,j --% 2M + Hz (III) Tafel step.

-0.2 - 0 0

5 0

E 5

00

N -0.1 - o.Lnx

oo" S k5

dzm 0.06

0.0 0.1 0.2 0.3

Z(Rdh Fig. 6. Impedance plots corresponding to an expansion of the high frequency region of the Nyquist plots of Fig. 2 (Fig. 6(a)) and Fig. 5 (Fig. 6(b)).

The reverse reactions of steps (II) and (III) were not considered, in agreement with Conway et al. [15]. If the whole electrode process could be represented by equation (I), (II), and/or (III) the impedance response of the system would be identical to the impedance of the equivalent circuit proposed by Armstrong et al. [16], shown in Fig. 7. Therefore, experimental impedance data corresponding to Ni/NiMoSz elec- trodes are compared in Fig. 8 with the theoretical impedance response that is expected for this equivalent circuit, using a non-linear least-squares fit procedure to obtain the theoretical transfer function that best approaches experimental results. As it is evident from Fig. 8(a) the equivalent circuit response

Fig. 7. Equivalent circuit related to the HER according to the Volmer-Heyrovsky-Tafel mechanism.

Hydrogen evolution reaction 955

Z(R*)/n

-0.5

0.0 0.0 0.5 1 .O 1.5 2.0 2.5

2(R.)/n Fig. 8. Comparison between experimental data correspond- ing to Ni/NiMoSz electrode (-) and theoretical data (0) derived from the transfer function related to the equivalent circuit given in Fig. 7.

fails to simulate correctly the experimental data at small TV values, but it seems to be adequate for high cathodic overpotentials (see Fig. 8(b)).

According to Bockris et al. [24] H atoms may be absorbed into the substrate (Has) according to the following reaction:

MHti +M + H.L, (IV) HAR step. 4

Taking into account that absorbed H atoms can diffuse into the electrode material, the HAR step as well as the diffusion of H.b species must be included in order to derive the appropriate faradaic impedance.

The fundamental equations relating charge and mass balances are given by the following IF(t) and g(t) functions:

ZF = -fl7k,(l - 0) - k-,8+&?]

g = r de/dt = kl(l - e) - k_,e - kze

(1)

- 2k3e* - k4e + k4cH(i - e) (2)

where ki = &exp(bir~), TV corresponds to the cathodic overpotential q = (E - E), k; denotes Zq at the reversible potential ZP, bi = -jiF/RT and b-i = (1 - pi)F/RT, CH is the H.b concentration just beneath the surface and Z the maximum surface concentration (mol cmT2) of adsorbed hydrogen.

Steady-state conditions. In this case de/dt = 0 and so

80 = (W + k~)/(k, + k-1 - k2) (3)

C: = [2k3(eo)2 + eyk, + k_, + b + k4) - k,lj

[k-41 - eo)] (4)

where 8’ and C!, correspond to steady-state values. Determination of CH(X, t) profile. Fick’s first and

second laws must be solved

J(x, t) = - D[KH(x, t)/ax]

d&(x, t)/dt = D[~‘CH(X, t)/ax’]

(5)

(6)

3.1.2. Faradaic impedance analysis

Taking into account that Zr = I&, 6), the faradaic impedance & can be calculated from equations (l), (2), (5) and (6) after a Taylor series expansion limited to the first order terms and subsequent Fourier Transform [25]

l/zF = AIF(W

= ($)r4a0 + (%)r9a0 gg C7)

where the term Ae(w)/Aq(w) needs to be evaluated through linearization and Fourier transform of equations (2):

w so,,oco AW) * 3”

ACH(O,O)

A@) ’ (8)

In order to determine ACH(W)/A~Z(O), equation (6) has to be solved with the proper boundary conditions when a small sine-wave potential perturbation is applied to the system. Thus, equation (6) can be expressed in following form [26]:

a&&, t) at = Do,,,“)) (9)

which after Fourier transform yields

joAC(x,w) = .(,,~~~~~~). (10)

It is worth noting that equation (5) can be expressed, following a similar procedure, as

dl(x, w) = -D aAcH(x, w) ax (11)

956 E. B. Castro et al.

Equation (10) admits the solution:

A&(x, w) = A4 exp(x,/‘&$)

H being a 3 x 3 matrix whose elements h,j are the coefficients of the unknowns xj, this means the j variable in equation (i):

+ Nexp(-xm) (12)

in which, under the present circumstances, the - 1 hl.2 0

boundary conditions can be given as: H = 0 kz.2 hz,,

At x-cc, for the semi-infinite diffusion layer, I I 0 h3.2 h,.,

A&(x, o) -+ 0 so that: where

A&(x, w) = N exp( -xm). (13) h1.2 = -F(-k, -k_, + k*)

On the other hand, at x = 0 h2.2 = (-k, - k-, - k2 - k, - k_4CH - 4k@ - r&0)

ArAJ(0, w) = AU&D) h2.3 = k-4(1 - eo)

= - ArD(aACu(O, 0)/8X) (14) hs,2 = _(k4 + k_,e,)

where Ar is the electrode active area and u~v the reaction rate of step (IV).

Therefore, taking into account equations (11) to hj3 = DAr

’ (14) one can derive the expression

On the other hand, Y is the 3 x 1 matrix of the se(w)

et,.4 Mw)

independent terms y,,, related to equation (I):

aurv + i%i Boco (>

ASH@, w)

b(o) - H

=A,.D where

(15) y1.1 = F(k,b,(l - eo) - k_,b_,@ + k&80)

Accordingly, the mathematical relationships given yz,, = -(k&,(1 - eo) - k_,b_,8O - kzb28O) in the set of equations (7), (8) and (15), can be and X is a 3 x 1 matrix whose elements are the rewritten as: unknowns xj,,:

1 A@) _- zf - AW)

(k,b,( 1 - eo) - k-lb_,80 + k&80) i I

.

ASH@)/& =-

1/z X = A@(o)/A@)

The solution of equation (19) is:

Am) +(-k,-k-,+kz)-

1 (16)

X = H-‘Y. (20)

From equation (20), Z,(o) can be derived by giving

rjo $$ = (k&,(1 - eo) - k_,b_ 180 - k26280) numerical values to the constants: D, k,, and r. The value of fl, is supposed to be close to 0.5, whereas 6O

+ (-k, - k-1 - k2 - k4 - km& - 4k3e0) and P, can be calculated from equations (3) and (4) using the experimental values of pF at each rl.

x $-$$ + (k-4(1 - eo)) AC$$) (17)

(k4 + k-G,) $$ - [k&l - eo)] “%y;,O)

=ArD d--

@ A~H@,w)

D k(w) (18)

Thus, equations (16), (17) and (18) constitute a three linear-equations system, with three unknowns: [ l/Zr]; [Ae(o)/Av(w)]; and [ACH(O)/AP~(W)]. The new set of equations (16), (17) and (18) can be expressed, using matrix notation, in the form [26,27]:

3.1.3. The total transfer function impedance

In order to simulate experimental impedance data, an appropriate expression for the total impedance, ZT, must be derived taking into account the contributions of the electrolyte resistance, R,, and that of the double layer capacitance, Cd,. In the case of a flat homogeneous electrode surface the expression for ZT is usually given in the form

ZT = RJ + ZF(1 +jwCd,Z&‘. (21)

High frequency impedance data measured at low overpotentials (]rl] < 0.25 V), are in accordance with a porous surface behaviour (Fig. 6(a)). Nevertheless,

Hx=Y (19) equation (21) is still valid in low frequency range

Hydrogen evolution reaction 951

-1.1

0.0 0 I I 7

Fig. 9. Comparison between experimental results (0) and theoretical impedance data (V) simulated in terms of equation (20), corresponding to the HER on Ni/NiMoSt electrode at q = -0.05 V (a) and q = -0.150 V (b).

(f< 10 Hz) [28,29], so it can be adequately employed to simulate impedance data in the low frequency range. At relatively high cathodic over- potentials, ]q] > 0.25 V, equation (21) results to be valid in the entire frequency range covered in this work. Therefore, taking into account equation (21), Figs 9 and 10 show experimental and simulated Nyquist plots corresponding to the hydrogen evolution reaction on a Ni/NiMo& electrode, at different cathodic overpotentials. Optimum fit par- ameters are assembled in Table 1.

From Figs 9 and 10, a good accordance can be observed between experimental and simulated Nyquist diagrams. System parameters assembled in Table 1 indicate that the HER proceeds according to

-1.0, I g--0.25"

IO nz I

* - -0.35 Y I

Fig. 10. Experimental (0) and simulated (V) impedance data corresponding to the HER on Ni/NiMoh electrode at v = -0.05 V (a) and q = -0.35 V (b).

958 E. B. Castro et al.

a Volmer-Heyrovsky mechanism, the Heyrovsky step being the rate determining step (rds). Values given for Z agree with data reported in the literature for Ni electrodes [30]. The effective electrode area (Ar) was estimated through the relation between the value of Cdl needed to simulate impedance data and that reported for polycrystalline flat Ni elec- trodes, C,+i(Ni) x 80 pF cmm2 [30], Ar = C.ji/Cd/(Ni). The value of the diffusion coefficient of H atoms reported in Table 1, D = 10-i’ cm2s-‘, is similar to those reported for amorphous Ni-base alloys [31].

It is worth noting that as the HAR is a potential-independent chemical process, the rate of Heyrovsky step (II) becomes higher than that of the parallel step (IV) when potential is set more negatively. Accordingly, the reaction pathway related to steps (D-o-(I) dominates the frequency response of the system. Consequently, the equivalent circuit given in Fig. 7 is able to simulate correctly impedance data at relatively high cathodic overpotentials (Fig. 8(b)), while it fails to describe impedance diagrams measured at low rl values (Fig. 8(a)).

On the other hand, the validity of transfer function (21) found support taking into account that according to de Levie (see, for instance, Fig. 1 in [32]) the profile of impedance diagrams for flat and porous electrodes cannot be distinguished at frequencies lower than w < 0.1 (Z?C)-I. This condition is fulfilled in the case of Ni/NiMoSz electrodes at w ,< 10 Hz for the most critical polarization condition r~ = - 0.05 V (exhibiting the larger Ar value). This upper frequency becomes even higher with increasing cathodic polarization as both R and C values diminish. It is worth noting that at the most critical polarization value, the frequency response analysis at w > 7 Hz leads to the conclusion that ZF( jw) approaches the proper charge transfer resistance.

3.2. Impedance data of Ni electrode

Figure 11 shows experimental and simulated impedance data corresponding to the HER on a Ni electrode, measured at r~ = -0.47 V (Fig. 1 l(a), Z = -25 mA) and q = -0.52 V (Fig. 11(b), Z = - 46 mA). Impedance data were fitted in terms of the equivalent circuit of Fig. 7. The constant value of the Tafel slope found in the whole potential range (Fig. 1) can be attributed to the fact that the HER proceeds through the Volmer-Heyrovsky mechanism [33]. A single capacitive contribution in impedance diagrams of Ni electrode indicates Ae(w)/At~(w) = 0, which means that the value of 8 is potential-indepen- dent (either 0 or 1). In this case, the faradaic current may be expressed as:

ZF = 2FkAr (22)

where k = k’ exp(bq) corresponds to the rate con- stant of the rds. The Cdl value determined from the fitting procedure allowed us to calculate, following the procedure described above, a real active area of about 1.5 cm*, which suggests a roughness factor

Fig. 11. Comparison between experimental impedance data corresponding to the HER on Ni electrode (0) and theoretical data (V) fitted in terms of the equivalent circuit given in Fig. 7.

close to 3. Assuming /l = 0.5, k’ may be calcu- lated from equation (22), yielding approximately k’ = ZF[2FAr exp(bq)]- ’ ~25 4 x lo-I2 mol s-l ctn2. This value is smaller than that presented in Table 1 for the rds rate constant of the HER on Ni/NiMoSz electrodes, its magnitude being coincident with that reported for polycrystalline Ni electrodes [33]. Therefore, a real electrocatalytic activity for the HER can be assigned to Ni/NiMoSz electrodes.

CONCLUSIONS

The application of EIS to the analysis of the kinetics and mechanism of HER on electrodeposited Ni/NiMoSz electrodes proved that absorption of hydrogen adatoms takes place as a parallel reaction to the Heyrovsky step. The contribution of hydrogen absorption and subsequent diffusion of Hab to the total faradaic impedance becomes more important as the electrode potential is closer to the equilibrium potential. When 1~1 > 0.25 V, the reaction proceeds according to the Volmer-Heyrovsky mechanism, the Heyrovsky step being the rh.

The comparative study accomplished with an electrodeposited Ni electrode allowed us to conclude that the enhanced electrocatalytic activity of the Ni/NiMoSz electrode may be attributed to both an increased active surface area and to a larger rate constant of the corresponding rds.

ACKNOWLEDGEMENTS

This work was financially supported by the Consejo National de Investigaciones Cientificas y Tecnicas (CONICET), the Comision de Investiga- ciones Cientificas de la Provincia de la Provincia de Buenos Aires (CIC) and the Fundacion Antorchas of

Hydrogen evolution reaction 959

Argentina, and by the Conselho National de Desenvolvimento Cientifico e Technolbgico (CNPq) and the Fundacao de Amparo a Pesquisa do Estado 16* de Sao Paul0 (FAPESP) of Brazil. 17.

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