On the kinetics of the hydrogen evolution reaction on nickel in alkaline solution

Journal of Electroanalytical Chemistry 512 (2001) 16 – 26 www.elsevier.com/locate/jelechem

On the kinetics of the hydrogen evolution reaction on nickel in alkaline solution Part I. The mechanism N. Krstajic´, M. Popovic´, B. Grgur, M. Vojnovic´, D. S& epa * Department of Physical Chemistry and Electrochemistry, Faculty of Technology and Metallurgy, Uni6ersity of Belgrade, Karnegije6a 4, P.O. Box 3503, 11000 Belgrade, Yugosla6ia Received 18 September 2000; received in revised form 19 March 2001; accepted 27 May 2001

Abstract The mechanism and kinetics of the hydrogen evolution reaction (her) were studied in 1.0 mol dm − 3 NaOH at 393.0 K. It was found that a combination of classical steady-state voltammetry and impedance spectroscopy can help to elucidate dilemmas concerning the role of the Heyrovsky and Tafel steps in the mechanism of this reaction. Thus, within the potential region − 0.95 \ E\ −1.1 V (SHE) (curvilinear part of the polarization curve) the mechanism of the her is a consecutive combination of the Volmer step, followed dominantly by a rate controlling Tafel step, while the contribution of the parallel Heyrovsky step is negligible. At potentials E B (approximately − 1.2 V) a Tafel line with a slope of −0.121 V dec − 1 is obtained, with almost full coverage by Hads (qH “1). In this potential region the mechanism of the her is a consecutive combination of a Volmer step, followed by a Heyrovsky step, while the contribution of the Tafel step is negligible. The comparison of the calculated partial rate constants for these two steps shows that the rate of the her is controlled by the Heyrovsky step. © 2001 Published by Elsevier Science B.V. Keywords: Hydrogen evolution reaction; Nickel electrode; Alkaline solution; Spectroscopy of electrochemical impedance; Mechanism; NLS fitting; Rate constants

1. Introduction The hydrogen evolution reaction (her) is one of the most frequently studied electrochemical reactions because it takes place through a limited number of reaction steps with only one reaction intermediate involved. There are also numerous investigations of the kinetics of this reaction on nickel in alkaline solutions where the common feature of a unique Tafel slope close to−120 mV dec − 1 has been observed at overpotentials more than a few hundred mV negative to the equilibrium potential of the her [1 – 17], which was not established at a Ni electrode. Previous concepts of the mechanism

* Corresponding author. Tel.: + 381-11-3370-460; fax: + 381-113370-387. E-mail address: [email protected] (D. S& epa).

of the her have been made, based on the assumption that, in electrochemical studies of multi-step reactions, there is a rate-determining step (rds) which characterizes the kinetic behavior of the overall reaction. Consequently, the other reaction steps prior to or after the rds are usually regarded as being in quasi-equilibrium. Also, adsorption isotherm analyses for the only reaction intermediate of the her are based on the same quasi-equilibrium approximation. On the basis of the above-mentioned value of the Tafel slope for the her, obtained from steady-state polarization measurements, the Volmer step was proposed as rate determining [13], without further conclusions being drawn about the involvement of the Tafel and Heyrovsky steps in the mechanism of the her. In spite of this, the most frequently cited mechanism for the her at nickel in alkaline solutions is the Volmer – Tafel route [17].

0022-0728/01/$ - see front matter © 2001 Published by Elsevier Science B.V. PII: S 0 0 2 2 - 0 7 2 8 ( 0 1 ) 0 0 5 9 0 - 3

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The determination of the coverage by the reaction intermediate Hads versus the negative potential is another important feature of the kinetics of the her needed for the better understanding of the mechanism. However, the only reasonable experimental information concerning details on the potential dependence of the coverage by adsorbed hydrogen for the her has been obtained for underpotential-deposited (upd) H at noble metals [18–20], using the cyclic voltammetry technique which provides results of high sensitivity and accuracy. Similar information on Ni in alkaline solutions has not been available to date. However, in recent years, considerable progress has been made in studies of absorbed surface species at appreciable current densities by opencircuit potential decay [21– 23] and impedance spectroscopy [24–30] methods. Extensive kinetic studies of the her by impedance spectroscopy have introduced new numerical simulation techniques of the observed complex-plane diagrams, which have opened up the possibilities of evaluation of rate constants for all steps, as discussed in Ref. [31], based on fundamental analysis by Armstrong and Henderson [32]. Recently, Diard et al. [33] analyzed the her thoroughly on Ni in alkaline solution by impedance spectroscopy and concluded that the appearance of the inductive component in the low frequency range in impedance diagrams was in good agreement to the corresponding theoretical diagrams for the Volmer– Heyrovsky mechanism. Kreysa et al. [17] have analyzed the different types of kinetic behavior of the her at polycrystalline and amorphous nickel electrodes and, using experimental steadystate polarization curves for the her recorded at different temperatures, they have calculated values of rate constants for three basic steps by a non-linear fitting procedure. They also observed a ‘limiting current’ for the her at high current densities (close to 1 A cm − 2). Within the Volmer– Tafel mechanism they assumed that this limiting current is caused by the Tafel step as the rds due to the relatively slow surface diffusion of Hads atoms as the controlling factor both in releasing molecular hydrogen from the electrode surface and in the rate of the overall reaction. It is important to point out that there is still no common agreement on the mechanism of the her in alkaline solutions. Therefore, further investigations of the her are needed. We found a combination of classical steady-state voltammetry and impedance spectroscopy to be a source of valuable experimental information on the kinetics of the her which can help to elucidate dilemmas concerning the role of the Heyrovsky and Tafel steps in the mechanism of this reaction at nickel in alkaline solution.

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2. Experimental

2.1. Cell and chemicals A conventional three-compartment cell was used. The working electrode (WE) compartment was separated by fritted glass discs from the other two compartments. The WE compartment was jacketed and thermostated during measurements at 20.0 °C using an ultrathermostat. All measurements were performed in 1.0 mol dm − 3 solution of NaOH (Spectrograde, Merck), prepared in deionized water. The WE compartment was saturated with purified hydrogen at standard pressure during measurements.

2.2. Electrodes Polycrystalline nickel wire (ESPI, USA, diameter 1 mm, purity 99.995%) of 1 cm2 exposed surface area was used as the WE. To avoid problems connected with roughness when impedance data are interpreted, the electrode was highly polished with alumina prior to use. The counter electrode was a platinum sheet of 5 cm2 geometric area. The reference electrode was the Hg HgO electrode in 1.0 mol dm − 3 NaOH, held at a constant temperature of 25 °C. All potentials are referred to the standard hydrogen electrode scale (SHE). The calculated value of the equilibrium potential of the her in 1.0 mol dm − 3 solution of NaOH (pH 14.17) at 20.0 °C is − 0.824 V.

2.3. Pretreatment of the WE Before measurements the WE was first oxidized for 5 s at 0.578 V and then reduced for 1 h at − 1.42 V. After such pretreatment, when the WE was held at any constant potential within the range − 0.95 to −1.42 V, a steady-state current density was recorded. When measurements were made in the more negative or the more positive potential direction, no significant hysteresis on the polarization curve was observed. Therefore, steadystate measurements following positive changes of the potential were performed.

2.4. Measurements Tafel lines were recorded using potentiostatic steadystate voltammetry, point by point at 60 s intervals, in the range of potential from −1.42 to − 0.95 V, using a PAR 273 potentiostat, with good reproducibility of measurement. In an additional experiment, the region of potential was extended down to approximately − 1.8 V, when extremely high current densities (approximately 2 A cm − 2) with the character of a limiting current den-

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sity were recorded. However, at the WE held at these extreme conditions, a hysteresis in the polarization curve was observed, when it was recorded in the positive and negative potential directions. Whenever the potential of the WE approached approximately −1.4 V (or when current densities were close to, or above approximately 0.1 A cm − 2) it was found that the uncompensated solution resistance was significant. Therefore, the IR drop was determined systematically in all measurements, using ac impedance methods. All data presented in this article are corrected for the IR drop. Simultaneously with the Tafel lines, electrochemical impedance spectra of the WE at selected constant potentials were determined, using a PAR 273 potentiostat, together with a PAR 5301 lock-in-amplifier, controlled through a GPBI PC2A interface. The fast Fourier transformation (FFT) technique was used to obtain the

Fig. 1. Tafel polarization curve for the her on a Ni electrode in 1.0 mol dm − 3 NaOH at 20 °C. Marked potentials: a = − 1.196 V; b = −1.290 V; c = −1.362 V; d = − 1.418 V. Insert: polarization curve in the extended region of potential.

Fig. 2. Impedance spectrum in the complex plane for the her on Ni in 1.0 mol dm − 3 NaOH at 20 °C at constant potential within the curvilinear part of the polarization curve in Fig. 1.

real (Z%) and imaginary (Z¦) components of the WE impedance at each frequency used. So, both impedance spectra in the complex plane and the corresponding Bode diagrams were obtained in the frequency range from 50 mHz to 100 kHz, at the following constant potentials of the WE: − 1.015, − 1.196, −1.290, − 1.362 and − 1.418 V. In all measurements above 5 Hz, ten frequency points per decade were taken.

3. Results A typical polarization curve for the her in the region of potential from −0.95 to − 1.42 V is presented in Fig. 1. A Tafel line, characterized by a slope of − 121 mV dec − 1 is observed within the region of potential from approximately − 1.2 to − 1.4 V. A transfer coefficient h= 0.48 and an exchange current density jo = 1.1× 10 − 6 A cm − 2 characterize the kinetics of the her in this potential region. In all experiments the equilibrium potential for the her at a nickel electrode was not established. Current densities lower than approximately 10 − 4 A cm − 2 had an oscillating character, and therefore, any steady-state data at potentials higher than approximately −0.95 V could not be recorded. The insert of Fig. 1 presents the polarization curve for the her in the extended region of potential, i.e. from approximately −0.95 to − 1.8 V. At current densities higher than approximately 1 A cm − 2, a limiting current is observed similar to that found by other authors [17].We found that the limiting current density is independent of temperature indicating that it is a result of the her approaching an activationless reaction, which will be discussed more thoroughly in Part II. Within a potential region of approximately −0.95 to − 1.2 V a curvilinear part of the polarization curve is obtained. The electrochemical impedance spectrum in the complex plane recorded in this region of potential, as presented in Fig. 2 for E= − 1.015 V, clearly indicates a charge transfer controlled process at the WE. Hence, any speculations on the nature of this curvilinear part of the polarization curve, such as a limiting current of various Faradaic processes different from the her [34,35] are strongly suspect. It was reasonably assumed that, in the potential region where the Tafel line is obtained, the kinetics of the her on the WE are charge transfer controlled. Therefore, it was expected that the electrochemical impedance spectroscopy (EIS) method would provide data consistent with the steady-state measurements. Four values of electrode potentials (indicated by the arrows in Fig. 1) were selected to cover the entire Tafel region and impedance spectra of the WE in the complex plane were determined and are presented in Fig. 3. In Fig. 4 are presented Bode diagrams corresponding to

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Fig. 3. Impedance spectra in the complex plane for the her on Ni in 1.0 mol dm − 3 NaOH at 20 °C, at four constant indicated potentials within the Tafel region of the polarization curve in Fig. 1. Circled points are experimental data and solid lines are calculated using the NLS fitting procedure.

the spectrum at −1.196 V in Fig. 3. The circled points in Figs. 3 and 4 are experimental data and lines are obtained by the NLS fitting procedure [36] described later. The impedance data were interpreted using the equivalent electric circuit of Armstrong and Henderson [32], given in Fig. 5, where R is the charge transfer resistance for the electrode reaction at the WE, Cdl the double layer capacitance of the WE, Rp is basically related to the mass transfer resistance of the adsorbed intermediate Hads, usually called the pseudo-resistance, and Cp is the pseudo-capacitance of the WE. For the Armstrong equivalent electric circuit the Faradaic impedance, Zf is defined as follows: Zf = R +

Rp 1+j…~p

(1)

where … is the frequency and ~p =RpCp is a time constant related to the relaxation rate of the WE when its potential is changed. Data presented in Figs. 3 and 4 are interpreted by NLS fitting procedure [36] to determine the elements of the Armstrong equivalent circuit of the WE, given in Fig. 5. The values of all parameters obtained by this procedure are presented in Table 1. The ohmic resistance of the solution was RV =0.78 V cm2. Now, using data from Table 1, it was possible to calculate the functions Z% – Z¦, log Z −log … and b– log … and to compare them to the corresponding experimental spectra. As is evident from Figs. 3 and 4, fitting is satisfactory. The values of the parameters in Table 1 are then used to interpret the kinetics of the her. At any of the

Fig. 4. Bode plots for the her on Ni in 1.0 mol dm − 3 NaOH at 20 °C and E = −1.196 V. The continuous lines are calculated by the NLS fitting procedure using a value for q of 80 mF cm − 2.

Fig. 5. Armstrong and Henderson equivalent electric circuit of the WE. RV is the ohmic resistance (uncompensated resistance) of the solution, R is the charge transfer resistance, Cdl, the double layer capacitance, Rp, the pseudo-resistance and Cp, pseudo-capacitance.

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Table 1 Parameters of the Armstrong equivalent circuit for the her at Ni in 1.0 mol dm−3 NaOH at 20.0 °C, taken at constant potentials within the linear part of the polarization curve in Fig. 1 −E/V (SHE)

R /V cm2 Rp/V cm2 Cp/mF cm−2 Cdl/mF cm−2

1.196 1.290 1.362 1.418

34.34 5.39 1.49 0.52

6.93 0.146 0.01 –

1370 1245 1878 4287

178 169 164 146

two lines of 1.19. However, when the Temkin adsorption isotherm is taken into account under the same conditions a separation value of 1.86 is required [25]. Hence, based on the above-mentioned experimental evidence and Conway’s theoretical analysis, Langmuirian adsorption of H is assumed in this study of the her at Ni in alkaline solution.

4. Discussion selected constant potentials the sum R +Rp presents the total Faradaic resistance of the WE. Hence, its reciprocal is directly related to the Faradaic current density at the potential considered. Since the her is charge transfer controlled within the entire region of potential considered, a plot of E versus log(R +Rp) − 1 should be linear and its slope equal to the Tafel slope, b. Fig. 6 shows that data obtained by EIS give a linear relationship for E versus log(R +Rp) − 1 with the slope equal to bEIS = − 0.116 mV dec − 1, which is close to the experimental value of the Tafel slope obtained by potentiostatic steady-state voltammetry (PSV): bPSV = − 121 mV dec − 1. The insert of Fig. 6 shows that the experimental E versus log j and the simulated E versus log(R +Rp) − 1 plots (curves 1 and 2 in Fig. 6) are two parallel lines separated at the abscissa by the value of 1.19. Conway and coworkers [25] have shown that at sufficiently high E when [H is almost constant and for Langmuirian adsorption, the theoretical separation between the above parallel plots is equal to log(iF/RT). With i= 0.5 and T= 293 K, log(iF/RT) = 1.29, which is close to the experimentally observed separation between the

4.1. Analysis of the PSV data Generally, the mechanism of the her in aqueous alkaline solutions is treated as a combination of three basic steps, two electrochemical and one chemical which are presented in Table 2, together with the corresponding theoretical rate laws. In these rate laws only surface concentrations of the intermediate Hads and the corresponding free adsorption sites at the WE are given as coverages, or surface concentration fractions, [H and 1 − [H, respectively. If it is assumed that any particular combination of the basic steps from Table 2 is operable in the her, then for equilibrium: 6V = 6H = 6T = 0

(2)

When Eq. (2) is applied to the equilibrium of any of the steps in Table 2, it follows that only four of six rate constants are independent parameters, since two of them are always defined by the others. For example, from the equilibrium of the V and H steps it follows that k %-H = (k %Vk %H)/k %-V and analogously for the V and T steps: k-T = (k %V2kT)/k %V2.

Fig. 6. Linear E – log(R + Rp) − 1 relationship for the her on Ni in 1.0 mol dm − 3 NaOH solution at 20 °C, obtained from data taken from the impedance spectra in Fig. 3. Insert: experimental (circled points) and simulated (solid lines) Tafel plot (curve 1) and E – log(R +Rp) − 1 plot (curve 2) for the her on Ni in 1.0 mol dm − 3 NaOH solution at 20 °C.

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Table 2 Stoichiometric equations and rate laws for three basic steps of the her Name of the step

Abbreviation

Stoichiometric equation

Theoretical rate law

Volmer Heyrovsky Tafel

V H T

M+H2O+e− =MHads+OH− MHads+H2O+e− =M+H2+OH− 2MHads =2M+H2

6V =k %V(1−[H)−k %-V[H 6H =k %H[H−k %-H(1−[H) 6T =kT[ 2H−k-T(1−[H)2

Note: electrochemical rate constants (in mol cm−2 s−1) k %(i i = 9 V, 9H), are defined as follows: k%V =kV exp(−iVFE/RT); k %-V =k-V exp[(1− iV)FE/RT] and k %H = kH exp(−iHFE/RT); k %-H =k−H exp[(1−iH)FE/RT] where ki (i= 9 V, 9 H) are chemical rate constants (in 0 mol cm−2 s−1) which are defined as follows: kV = k 0Vc(H2O); k-V =k 0-Vc(OH−) and kH =k 0Hc(H2O); k−H =k−H c(OH−)p(H2)/p°, where k 0i (i = 9V, 9H), are partial standard chemical rate constants (in cm s−1). The standard state is defined as follows: c°(OH−) =10−3 mol cm−3, c°(H2O)=5.56×10−2 mol cm−3, [H = 1/2 and p(H2)= p°.

In the region of potential where the kinetics of the her are charge transfer controlled, an unknown combination of steps from Table 2 is responsible for the steady state. Therefore, the steady-state kinetics of the her at constant current density are characterized by the conditions of the charge balance (with rates in mol cm − 2 s − 1): r0 = j/F= − (6V + 6H)

(3)

and the mass balance with respect to the intermediate Hads: r1 = q/[F(d[H/dt)E ]= 6V −6H −26T

(4)

which have to be satisfied at any constant potential. When a particular value of the mass balance, i.e. r1 = 0 is set, the steady-state coverage of occupied adsorption sites at the WE can be calculated, assuming that the Langmuir adsorption isotherm is operable. If the rate constants for the H and T steps in the backward direction (k%− H and k − T) are neglected at the equilibrium potential of the her, the steady-state coverage of the intermediate Hads is the following function of the electrochemical rate constants of the V and H steps and the partial standard chemical rate constants of T step: [H =

− (k %V + k %-V +k %H) + (k %V +k %-V +k %H) +8k %VkT 4kT (5) 2

The presence of the electrochemical rate constants in Eq. (5) clearly indicates the rather complex dependence of [H on the electrode potential.

4.2. Analysis of EIS data Theoretically, six variables, i.e. four independent chemical rate constants of the three basic steps and two symmetry factors of the electrochemical steps (iV and iH) describe any mechanism of the her for the WE and solution used. However, it can be reasonably assumed for elementary electrode reactions that iV =iH = 0.5. With this assumption the problem is reduced to four independent variables. Hence, to calculate the values of

the chemical rate constants for the basic steps of the her, four independent equations which describe their kinetics at the WE are required. For any charge transfer controlled elementary electrode reaction, the reciprocal of the charge transfer resistance is represented by the Tafel slope: (R ) − 1 = F(#6/#E). Considering the three basic steps of the her separately, only the electrochemical steps (V and H) are characterized by definite Tafel slopes. Hence, at constant coverage of Hads: (R ) − 1 = F[(#6V/#E)UH + (#6H/#E)UH] =(i/F 2/RT)[k %V(1−[H)− k %-V[H + k %H[H] (6) Generally, it is reasonable to assume that more than one of the basic steps is involved in the mechanism of the her, which means that the value of the experimental Tafel slope is determined by the reciprocal of the Faradaic resistance (i.e. the sum of charge transfer and pseudo-resistances), (R + Rp) − 1, where the pseudo-resistance is presented by: Rp = − [R0/(R + R0)]

(7)

and the parameter R0 is defined as follows: (R0) − 1 = [(F 2~p)/q][(#6V/#[H)E + (#6H/#[H)E ]

(8)

with the time constant ~p equal to: 1 ~− p = (F/q)[2(#6T/#[H)E + (#6H/#[H)E − (#6V/#[H)E ] (9)

where q is the charge of the WE which is equivalent to [H “ 1. When the rate laws from Table 2 are used and properly introduced to Eqs. (8) and (9), another two equations relating the four independent rate constants and coverage to parameters R0 and ~p are obtained: 1 R− 0

=

iF 2(k %H − k %V − k %-V)[k %V(1−[H)+ k %-V[H − k %H[H] RT(4kT[H + k %H + k %V + k %-V) (10)

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Table 3 Values of the chemical rate constants calculated (in mol cm−2 s−1) and partial standard chemical rate constants (in cm s−1) for individual steps of the her on Ni in 1.0 mol dm−3 NaOH at 20.0 °C kV 7.8×10−17 k 0V 1.4×10−15

k−V 1.5×10−1 0 k−V 1.5×102

kH 3.2×10−19 k 0H 5.8×10−18

k−H 3.7×10−6 0 k−H 3.7×10−3

and 1 ~− P = (F/q)(4kT[Hk %H +k %V +k %-V)

(11)

Hence, Eqs. (3), (4), (6) and (7) are four independent equations which describe the kinetics of the her at the WE and contain implicitly full information on its mechanism. Experimental data obtained by the PSV and EIS methods are taken to fit Eqs. (3), (4), (6) and (7). The method of factorial fitting and minimizing residuals (S) of the sum of each experimental datum (either PSV or EIS) was used, in accordance with the equation [36]. S=

1 N %{[( ji, exp − ji, th)ji, exp]2 N 1 + [(R , exp −R , th)/R , th] 2

+ [(Rp, exp − Rp, th)/Rp, th] }

kT 1.3×10−9 k 0T 1.3×10−9

available for adsorption of the intermediate Hads is approximately one-third of the total sites.

4.4. Thermodynamics of single V and H steps Starting from the stoichiometric equations for the V and H steps, given in Table 2, the following equations can be written for their equilibrium electrode potentials, i.e. for the V step: Ee,1 =

 !    RT F

ln

The corresponding values of chemical rate constants and partial standard chemical rate constants (the standard state was defined in the footnote to Table 2) for the V, H and T steps were calculated and are presented in Table 3.

4.3. Dependence of [H – E Using values of the rate constants from Table 3 and Eq. (4) it is possible to calculate the dependence of [H on the potential of the WE (between the theoretically calculated equilibrium potential of the her, Ee(her) = − 0.824 V and −1.40 V) which is presented in Fig. 7. At potentials close to Ee(her) calculated values of [H are rather low, while at potentials of approximately 0.2 V negative to Ee(her) the nickel electrode is almost fully covered by Hads. It should be noted, that in the region of potential where the Tafel line is recorded, i.e. EB − 1.2 V, the kinetics of the her are characterized by [H “1 It is interesting that the theoretically calculated value of the maximum charge of the WE (i.e. corresponding to [H “1), obtained in the above-mentioned procedure of fitting the experimental data, is close to 80 mC cm − 2, which is approximately one-third of the hypothetical charge required to cover each surface atom of nickel by Hads, which was calculated for the (111) plane of Ni [37] to be 250 mC cm − 2. Hence, the number of sites at the surface of the nickel electrode in 1.0 mol dm − 3 NaOH

Ee,2 =

       RT F

− ln

ln

 

"

k 0V c(H2O) (1−[H) + ln + ln − 0 k -V c(OH) [H (13)

and for the H step: 2

(12)

k−T 7.8×10−12 0 k−T 7.8×10−12



k %H c(H O) p° c O OH+ ln 0 2 k %-H c (H2O) pH2 cOH-

1− [H [H

(14)

with the standard state defined in the footnote to Table 2. From Eqs. (13) and (14) and using data from Table 3 the standard equilibrium electrode potentials [E O i = 0 (RT/F) ln(k 0i /k − ), for i =V, H] for each of these two i steps are calculated as follows: for the V step: E O V = − 0.99 V and for the H step: EO = − 0.86 V H

Fig. 7. Potential dependence of the calculated surface coverage by adsorbed hydrogen ([H) at a Ni electrode in 1.0 mol dm − 3 NaOH solution at 20 °C with the her occurring simultaneously.

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Table 4 Equilibrium potentials for V and H steps at various coverages by Hads at Ni in 1.0 mol dm−3 NaOH at 293 K, with the her occurring simultaneously −E (her)/V (SHE) qH (Fig. 7, or Eq. (5)) −Ee,V/V (SHE) −Ee,H/V (SHE)

0.824 0.07 0.92 0.93

0.90 0.50 0.99 0.86

0.95 0.76 1.02 0.83

1.10 0.98 1.09 0.76

1.20 0.99 1.11 0.74

1.40 0.99(6) 1.13 0.72

Table 5 Sequence of rates of V, H and T steps at characteristic potentials of the her at Ni in 1.0 mol dm−3 NaOH at 20.0 °C. −E/ V (SHE)

0.824 0.95 1.40

qH

j/A cm−2

0.07 0.76 0.99(6)

Sequence of rates

V

H

T

8×10−6 1.3×10−4 3.3×10−2

2.7×10−8 3.5×10−6 3.4×10−2

6.2×10−7 7.2×10−5 1.2×10−4

Two significant figures for these potentials are compatible with the accuracy of corresponding values of the calculated partial standard chemical rate constants. The equilibrium electrode potentials of the V and H steps are identically affected by the pH: (#Ee, i /#pH)c(H2O), p(H2), [ H = −2.303(RT/F) (i = V, H)

(15)

However, the partial pressure of hydrogen affects the equilibrium electrode potential of the H step only: [#Ee,H/#log p(H2)]c(H2O), c(OH−), [ = − 2.303(RT/F) H

= ( + /−)2.303(RT/F)

established at the Ni electrode in the system studied. The same conclusion holds down to potentials of the Ni electrode close to − 1.0 V. However, data in Table 4 concerning the potential region of the experimental polarization curve for the her (− 0.95\ E\Ee,V) should be considered approximate, because thermodynamic calculations of equilibrium potentials of the V and H steps are applied for values of [H which characterize not equilibrium but the steady state of the her.

4.5. Kinetics of the single V and H steps at [H = constant

(16)

Finally, coverage by Hads affects the equilibrium electrode potential of both the V and H steps, but in an inverse manner: [#Ee, i /#log(1 −[H)/[H]c(H2O), c(OH−), p(H

6V\6T\6H 6V\6T\6H (6V :vH)\vT

2)

(17)

where sign ‘+ ’ holds for i= V, and sign ‘− ’ for i= H. The equilibrium potential of the V step, i.e. the step which initiates any mechanism of the her, is essentially determined by coverage with Hads at the electrode (affected when the her has occurred), providing that the composition of the system is kept constant. Table 4 presents the calculated equilibrium potentials of the V step (for the H step also) for several selected values of the coverage by Hads at characteristic potentials of the her within the region of potential Ee(her) \E \ − 1.40 V for the her. Analyzing data from Table 4 it follows that, in the equilibrium state of the her Ee(her) \Ee,V, which means that within the potential region Ee(her) \E \ Ee,V, the V step cannot spontaneously initiate the mechanism of the her. This is consistent with the experimental observation that the equilibrium potential of the her was not

Previous analysis of PSV and EIS data of the polarization curve for the her in the system studied, results in the values of the partial standard rate constants for the V, H and T steps. So it is possible from the corresponding rate laws to calculate the rates of these steps at various coverages by Hads in the system studied. For the V step: jV = k 0VF(1− [H)c(H2O) exp(− iVFE/RT) −k 0-VF[HcOH− exp(− i-VFE/RT)

(18)

for the H step: jH = k 0HF[Hc(H2O) exp( − iH FE/RT)

(19)

and for the T step: jT = k 0TF[ 2H

(20)

For three selected potentials of the WE (i.e. the equilibrium potential of the her, and the initial and final potentials of the experimental polarization curve) the coverages by Hads were calculated from Eq. (5) and then the current densities for each step from Eqs. (18)–(20) were calculated and are presented in Table 5, together with the corresponding sequences of rates of the three basic steps at each potential.

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It follows from Table 5 that, within the entire region of potential considered, 6V \6T but the ratio of the rates of the H and T steps is changed. Two characteristic ratios of rates of the V, H and T steps are presented in Table 5 for limiting values of the experimental range of potential −0.95\E \ −1.4 V but without any information on the ranges of potential where they are dominant. Equal rates of the H and T steps are followed from rate laws (19) and (20), introducing the critical electrode potential Ecr(H= T), i.e. the particular negative potential where jH =jT, which is the following function of coverage by Hads: Ecr(H=T) = − (RT/iF)[ln k 0T/(k 0HcH2O) +ln [H)]

(21)

Hence, it is the potential region Ee(her) \E \Ecr (H =T) where the ratio 6T \6H is operable and the sequence of steps 6V \6T \6H dominates. Using Eq. (21) and data available (assuming i =0.5) the limiting value (for [H = 1) of this critical electrode potential equal to Ex (H=T) = − 1.1(2) V is calculated. However, in the entire region of potential −0.95 \E\ − 1.2 V where the curvilinear part of the polarization curve at Fig. 1 is observed, coverages by Hads are rather high, so values of Ex (H =T) are close to the limiting value of −1.1(2) V, as is seen from data in Table 6. Table 6 Values of the critical electrode potential in the region of the curvilinear part of the polarization curve for the her (Fig. 1) −E/V (SHE) qH −Ecr (H=T)/V (SHE)

0.95 0.76 1.1(1)

1.10 0.98 1.1(2)

1.20 0.99 1.1(2)

Fig. 8. (a) Potential dependence of the theoretically calculated individual rates for the V, H and T steps occurring simultaneously with the her on Ni in 1.0 mol dm − 3 NaOH solution at 20 °C, within the potential region Ee(her)\ E\ − 1.4 V. (b) Theoretical polarization curve, obtained by summing individual curves in (a) is represented by the full line. Experimental data for the her on Ni in 1.0 mol dm − 3 NaOH solution at 20 °C are presented by circled points, in the potential region −0.95 \E\ −1.4 V.

Another characteristic sequence of steps given in Table 5, i.e. (6V : 6H)\ 6T, is presented only for the final value of the potential of the experimental region where the kinetics of the her are studied. Information on the initial potential when this sequence of steps is operable is obtained indirectly when rate laws (18) and (19) are equated. However, instead of a common electrode potential for jV = jH, a critical co6erage by Hads is defined, which is independent of the electrode potential: [H, cr = k 0V/(k 0V + k 0H)

(22)

Thus, when the coverage of the electrode by Hads reaches the value of [H,cr the condition 6V =6H is fulfilled. When data from Table 3 are introduced to Eq. (22) [H,cr = 0.99(6) is obtained. Now, from Fig. 7 and Eq. (5) it can be estimated that [H,cr is reached at an electrode potential close to − 1.2 V. Hence, the sequence of rates (6V = 6H)\ 6T is operable in the potential region − 1.2\E\ −1.4 V. Prior analysis of the kinetics of the her within the experimental potential region 0.95\ E\ − 1.4 V indicates a third region of potential: − 1.1\ E\ −1.2 V, where the sequence of rates of the V, H and T steps is different from the two presented in Table 5. However, since Ecr(H=T) : − 1.1 V when 6H : 6T and at E= −1.2 V, 6H : 6V, obviously in this range of potential, the rate of the electrochemical H step is increased relative to the rate of the T step, but the rate of the V step remains the highest. So in this region of potential, the following sequence of steps is operable 6V\(6H\ 6T).

4.6. Kinetics of the V, H and T steps occurring with [H dependent on potential As shown above the kinetics of the her in the system studied are related to coverage by Hads which is dependent on the potential in accordance with Eq. (5). When Eq. (5) is introduced to the rate laws (18–20) it is possible to calculate the theoretical cathodic polarization curve for each of the V, H and T steps within the potential region Ee(her)\E \ −1.4 V. These theoretical polarization curves are shown in Fig. 8a in the common E–6 diagram. These lines present simulations of the kinetics for each step, assuming that each step occurred separately within the region of potential considered during the occurrence of the her at the electrode. The most interesting is the polarization curve for the chemical T step which is evidently potential dependent down to potentials of approximately −1.0 V which is a direct consequence of the potential dependence of [H. However, at potentials where the condition [H “ 1 is approached, the rate of the T step turns out to be independent of potential. When the theoretical polarization curves for the three steps in Fig. 8a are summed, they give the integral theoretical polarization curve for the her, which is

N. Krstajic´ et al. / Journal of Electroanalytical Chemistry 512 (2001) 16–26

presented in Fig. 8b by the full line with the overall rate recalculated to show the current density ( j= F(6)). The circles in Fig. 8b are experimental data for the polarization curve presented in Fig. 1. Excellent fitting of the experimental polarization curve for the her at Ni in 1.0 mol dm − 3 NaOH by the theoretically calculated integral polarization curve is evident.

4.7. Mechanism of the her On the basis of the full experimental and calculated data the following information concerning the kinetics of the her at nickel in 1.0 mol dm − 3 NaOH at 20.0 °C, can be summarized: “ the equilibrium potential of the her was not established at the electrode; “ within the potential region Ee(her) \E \ (approximately −0.95 V) no reliable current densities could be recorded; “ within the entire region of potential, i.e. − 0.95\ E \(approximately −1.4 V) the kinetics of the her are charge transfer controlled; “ within the potential region −0.95 \ E \ (approximately − 1.2 V) a curvilinear steady-state E versus log j line is recorded; “ at potentials EB (approximately −1.2 V), a Tafel line with a slope of − 0.121 V dec − 1 close to the theoretical value of − 0.116 V dec − 1 is recorded. On the basis of the calculated values of the partial standard rate constants for the V, H and T steps, additional information on the kinetics of the her is obtained: “ the dependence of the coverage by Hads on potential (Fig. 8) indicates a high value of [H within the entire region of potential −0.95 \E \ −1.4 V, with almost full coverage at E B −1.2 V, where the Tafel line is recorded; “ characteristic calculated sequences of rates for the three basic steps in the mechanism of the her are dependent on the range of potential:6T \6H within Ee(her)\ E\ approximately −1.1 V;6H \6T within approximately −1.1 V \E \ approximately − 1.2 V; and(6V :6H)\ 6T within approximately − 1.2 V \ E; “ when the function [H =f(E) was introduced into the rate laws of the V, H and T steps, the corresponding polarization curves were obtained, which by simple addition correctly fitted the experimental polarization curve for the her in the potential region studied. On the basis of all this information, a proposal for the mechanism of the her at a Ni electrode in 1.0 mol dm − 3 NaOH solution is almost straightforward. Generally, the mechanism of the her is considered as the consecutive combination of the V step with parallel H and T steps. Calculated sequences of rates of these

25

three steps in various regions of potential indicate the corresponding mechanism of the her. Thus, within the potential region − 0.95\ E \approximately − 1.1 V the mechanism of the her is a consecutive combination of the V step (occurring close to its equilibrium potential), followed dominantly by the T step, while the contribution of the parallel H step is negligible. Hence the T step controls the rate of the her in this region of potential. Coverages by adsorbed intermediate Hads in this region of potential are relatively high ([H \ approximately 0.8) which is consistent with kinetically significant rates of the T step. The occurrence of the T step requires two adjacent adsorption sites occupied by Hads which is satisfied at high coverage by Hads. The experimental steady-state E–log j relationship for her is curvilinear in this region of potential as a result of the effect of coverage by Hads on the rate of the T step.

4.8. Analysis of the mechanism of the her at EB − 1.2 V The catalytic role of the electrode surface is changed in this region of potential. Now, in accordance with the mechanism of the her, both the V and H steps occur at a single adsorption site. This indicates an increased catalytic efficiency of adsorption sites for the her, compared to the region of potential E\ − 1.1 V when two adjacent adsorption sites were involved in the T step as the final step of the her. As was mentioned above, at practically full coverage of the electrode only approximately one-third of the available sites at the surface of the Ni electrode are occupied by Hads which means that catalytic sites are highly efficient, as is proved by rather high experimental current densities for the her recorded in this region of potential. Conventional analyses of kinetic parameters for the three basic steps of the her in formal kinetics, indicate that the slope of the Tafel line for the her close to − 2.30RT/iF at [H “ 1 is characteristic of the H step as rate controlling. The comparison of the calculated partial standard rate constants for these two steps (Table 3) shows: k 0H  k 0V, indicating also that the rate of the her in this region of potential should be controlled by the H step. This can be additionally proved as follows. If it is assumed that in the potential region EB −1.2 V, the experimentally recorded current densities are determined by the rate of H step, then: 6H = k 0Hc(H2O)[H exp(− iFE/RT)=jexp/2F

(23)

Under these conditions, taking [H : 1, and introducing to Eq. (23) data from the experimental polarization curve in Fig. 1: jexp = 1.3× 10 − 2 A cm − 2 at E= −1.30 V, and assuming i= 0.5 for the H step, it is then possible to calculate from the experimental data the partial standard rate constant for the H step, which is

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N. Krstajic´ et al. / Journal of Electroanalytical Chemistry 512 (2001) 16–26

equal to: k 0H(exp)= 8.0 ×10 − 18 cm s − 1. Fine agreement of this value and the same constant from Table 3, k 0H (exp)=5.8×10 − 18 cm s − 1, proves that the H step really controls the kinetics of the her within the potential region EB −1.2 V, although its rate is equal to the rate of the V step.

4.9. Analysis of the mechanism of the her within − 0.95 \E\ − 1.1 V As has already been mentioned in this region of potential, consecutive combination of the V and T steps with the T step as rate determining, was proposed for the mechanism of the her. As is seen from Fig. 4, coverage by Hads in this region of potential is rather high, i.e. at − 1.0 V, [H =0.95. So, it is reasonable to assume that under these conditions the rate of the T step is practically independent of coverage by Hads. In accordance with the above mechanism, the experimental rate of the her should be equal to the rate of the T step: 6exp =jE /2F = 6T =kT[ 2T

(24)

Now, using Eq. (24) it is possible to calculate the chemical rate constant of the T step, using experimental evidence only, i.e. the current density of the her at E= − 1.0 V taken from the polarization curve in Fig. 1 ( jE = 2.54× 10 − 3 A cm − 2), and [H =0.95. So kT = 1.2× 10 − 9 mol cm − 2 s − 1 is obtained which is close to the corresponding value 1.3×10 − 9 mol cm − 2 s − 1 from Table 3, which is additional support for a correctly proposed mechanism of the her.

4.10. Comment on the equilibrium potential of the her As noted above, in the system studied, the equilibrium potential of the her was not established. Also, within the region of potential Ee(her) BE B − 0.95 V any reliable E–log j relationship for the her could not be found experimentally. A rather low value of the calculated coverage by Hads at the equilibrium potential of the her ([H :0.07), also affects the equilibrium potential of the V step so that Ee(her)\ Ee,V (see Table 4). This means that spontaneous initiation of the her mechanism by the V step at Ee(her) is not thermodynamically probable as was observed experimentally. This is consistent also with the lack of empirical data on the underpotential deposition of hydrogen at nickel in basic solutions.

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