International Journal of Hydrogen Energy 32 (2007) 542 – 547 www.elsevier.com/locate/ijhydene
Electrocatalysis of hydrogen evolution reaction on Pt electrode surface-modified by S−2 chemisorption A.C.D. Angelo Electrocatalysis Laboratory, Chemistry Department, Faculty of Ciências, UNESP, P.O. Box 473, 17033-360 Bauru, SP, Brazil Received 9 August 2005; received in revised form 6 June 2006; accepted 6 June 2006 Available online 15 September 2006
Abstract Kinetic studies of hydrogen evolution reaction (HER) at the surface of Pt in alkaline conditions, reported in this paper, show that electrocatalytic activity is enhanced after adsorption of S−2 ions. EIS and steady-state polarization curve data pointed to an undoubted improvement in performance with the Pt–S cathode that was attributed to higher adsorbed hydrogen coverage. Experimental findings suggested an increase in the electronic density of the modified surface sites that may strengthen the interaction between H2 O and the adsorption site and, consequently, accelerates the Volmer step. 䉷 2006 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. Keywords: Platinum surface; Electrocatalysis; Surface modification; HER
1. Introduction
by the wide accepted reaction scheme:
The hydrogen evolution reaction (HER) is certainly one of the most intensively studied electrochemical reactions due to its importance in the field of alternative hydrogen-based energy production [1–3]. The so-called “hydrogen economy” is a real alternative to energy systems that use fossil derivative fuels, either for its beneficial environmental impact or as a substitute for rapidly exhausted fossil fuels [4–10]. HER has been studied on several electrode materials, in the search for more efficient conditions (lower overpotential and more favorable kinetic characteristics) in which produces the hydrogen gas. Furthermore, this reaction has been used in the attempt to build a theory of electrocatalysis over the last few decades [11–14]. Despite these efforts, the theory developed so far cannot be considered concluded and further contributions still are needed. In HER it is known that the global reaction rate is closely related to the energies of adsorption of the water molecule at the surface site (M) and desorption of the intermediate atomic hydrogen formed by electron transfer. This could be explained
H2 O + M + e− M − Hads + HO− ,
E-mail address:
[email protected].
k1
k−1
k2
M − Hads + H2 O + e− M + H2 + HO− , k−2
(1) (2)
also known as Volmer (1) and Heyrovsky (2) steps, from which it follows that the lower the energy required to form M–Hads , the greater will be the electrocatalytic activity of site M. Hence, a strong interaction between H2 O and site M (at the equilibrium potential, where anode and cathode reactions occurs at equal rates) would mean that the energy needed to make the intermediate is lower. On the other hand, a weak interaction between H and M would reduce the energy needed to break the M–H bond and produce the H2 molecule, according to Eq. (2). The water–surface interaction should play a dominant part in the overall reaction, and so it is usually the first reaction above that is found to be the rate-determining step (rds). From this standpoint, it may be assumed that an increase in the H2 O–M interaction force will accelerate the global HER. One way of attaining this condition would be to make M more susceptible to interact with the water molecule, by giving the surface site a suitable electronic configuration.
0360-3199/$ - see front matter 䉷 2006 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2006.06.052
A.C.D. Angelo / International Journal of Hydrogen Energy 32 (2007) 542 – 547
For many years attempts have been made to explain the electrocatalytic properties of certain electrode materials. Horiuti and Polanyi [15] were among the first to try and relate an increase in the M–H bond energy to a decrease in the heat of activation of HER, in the case when the Heyrovsky reaction is the rds. Conway and Bockris [16] plotted log i0 against the strength of the bond of H with various metals, and found that they fell into two distinct groups: (i) s–p metals, whose rate of reaction at = 0 (reaction equilibrium potential) was comparatively low but increased with the M–H bond strength (as predicted by [15]), and (ii) a large group of transition metals, whose rates were higher but fell as the M–H bond strength rose. The latter behavior may be explained readily if we consider that an increase in the M–H bonding energy implies that more energy is needed to break the bond (and cause the desorption of H), so that, if reaction (1) controlled the rate, there would be a slowing down of reaction (2) and, consequently, of the overall reaction. On the other hand, the higher HER rate produced by transition metals could indicate that d-orbital electrons have a significant role in the water-adsorption step, enhancing its rate and leaving the subsequent step (H desorption) to become the rds. The word electrocatalysis, according to Bockris and Khan [17], has only been in use since 1963 [18] and related to the following: i0 = K ·
nF k · T 0∗ · · ai · e−H /RT h
· eS
0∗ /RT
· e−F ·Erev. /RT ,
543
atom interacts with its surroundings mainly through its valence electrons. In other words, the electrocatalytic properties of materials depend on the electron structures of the valence orbitals of surface sites. Surface site modification has been successfully used to change the surface site condition and to investigate its influence on the particular reaction of interest. To investigate the influence of surface conditions on HER, site-blocking species (SBS), which in some cases could be better named sitemodifier species (SMS), have been employed. Such species are able to change the energetics of the surface sites and they are also able to inhibit/promote the hydrogen sorption [29–37]. Among several SMS used to study HER, a notable example is the sulfide ion. S−2 is chemically adsorbed on metallic surfaces and is electrochemically inactive over the whole range of overpotentials of experimental interest for HER in alkaline solution. These characteristics make this ion an appropriate SMS to explore the influence of the surface condition on HER. The aim of this investigation was to study the influence of the surface site condition on the adsorption processes involved in HER in alkaline medium, in particular to establish if a correlation exists between the electronic configuration of the site and the surface performance as cathode for HER. 2. Experimental
(3)
where H 0∗ is the crucial factor, which describes the heat of activation of the slow reaction (rds) at the reversible potential and the other parameters have the usual meaning described in [17]. The smaller H 0 *, the larger will be i0 and, consequently, the reaction rate is higher. In the case of the adsorption of a water molecule, this activation heat may be reduced by altering the electron density of M so as to enhance the interaction between M and H2 O. The relationship between the reaction rate, determined by the exchange current density (i0 ) and the energy of hydrogen adsorption (Hads,H ) in HER has been viewed in terms of the Horiuti and Polanyi theory [15], but a correlation has also been established between i0 and the d-orbital configuration of the metals [19]. If i0 increases with an increase in Hads (for the hydrogen atom), then the Volmer step is the rds, while if i0 is diminished as Hads rises, the Heyrovsky step is the rds. A volcano-shaped curve is obtained when reaction rate is plotted against bond strength [20], which is equally applicable in chemistry and electrochemistry [21]. Trasatti [22–24] confirmed that this type of dependence exists between i0 and the intermediate M–H bond strength. Considering the configuration of the outermost electron layers in the ground states of the metals, it has been qualitatively observed [25–28] that catalytic activity increases as d electrons are added, up to the maximum in the configuration of the Pt, and then falls rapidly as the next s orbital is filled. Subsequent addition of electrons to p and then d orbitals leads to a further rise in the activity. Trasatti [22,23] points out that a metal
Pt (Pine, = 0.24 cm−2 ) disc surface, adequately polished to a mirror finish, were employed as cathodes for HER. The surface modification was accomplished by immersion of the surface in a freshly prepared and de-aerated 10 mmol dm−3 Na2 S·9H2 O (VETEC) solution for 15 min. After extensive rinsing of the electrodes with deionized water (Barnstead; 18.3 M), they were set up for the electrochemical experiments in a three-compartment Pyrex䉸 built electrochemical cell filled with 1.0 mol dm−3 NaOH (Aldrich—99.99%) deaerated electrolytic solution at 22 ◦ C. The electrochemical experiments were carried out with a Potentiostat/Galvanostat (E.G.G.&P.A.R model 283) coupled to a Frequency Response Detector (E.G.G&P.A.R. model 1025), both monitored by a personal computer. All the potentials were referred to the system Hg/HgO/electrolytic solution, which gave −0.932 V as the equilibrium potential for HER. The steady-state data were obtained from chronopotentiometric curves where a predetermined current density, ranging from 0.08 to 300 mA/cm2 , was applied to the working electrode for 600 s and the corresponding mean potential value, measured at the end of that period, was taken as the steady-state value. This experimental procedure has been shown very helpful to obtain reliable steadystate data. The overpotential data were iRs corrected by using the solution resistance (Rs ) value determined from electrochemical impedance spectroscopy (EIS) complex plane plots. The EIS experiments were carried out in the 10 kHz–0.05 Hz frequency range (r.m.s. amplitude = 10 mV), keeping the electrode for 30 min at each potential before starting data acquisition. During the experiments, nitrogen gas was passed over the electrolytic solution to avoid oxygen interference.
544
A.C.D. Angelo / International Journal of Hydrogen Energy 32 (2007) 542 – 547
-0.9
Pt Pt-(S-2)
-0.8
Overpotential / V
-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 -3
-2
-1
0
log i /A cm-2 Fig. 1. Tafel plots for HER on Pt surfaces in 1.0 mol dm−3 NaOH solution at 22 ◦ C.
Table 1 Tafel parameters for HER on the electrode materials indicated, in 1.0 mol dm−3 NaOH solution at 22 ◦ C Electrode
Parameter b (V dec−1 )
Pt Pt–(S−2 )
0.180 0.170
i0 (A cm−2 ) −5
6.15 × 10 1.58 × 10−4
−250 (V) 0.650 0.544
The Tafel slope b = (RT/F ); i0 is the apparent exchange current density and 250 is the overpotential at current density = 250 mA cm−2 .
3. Results and discussion The Pt electrode reached the electrochemical steady state after the third polarization cycle and no other noticeable change was observed in subsequent cycles. Fig. 1 shows the Tafel plots obtained for HER on Pt and surface modified Pt electrodes. S−2 adsorption improved the performance of HER. The Tafel parameters obtained for the investigated electrode materials are displayed in Table 1. Also from Table 1, it is observable that the surface modification produces an improvement of the electrode performance for HER. The best performance of HER on Pt–(S−2 ) could be due to a real electrocatalytic activity through an enhancement of the suitability of the adsorption surface sites. It must be pointed out that an electrocatalytic activity for HER on M–S surfaces (where M symbolizes a transition metal surface site) is frequently reported in the literature [30,34,38,39]. Despite this, such an improvement of HER on M–S surfaces has not been convincingly explained.
In EIS experiments, a markedly depressed semi-circle was observed at lower overpotentials that became less depressed at higher overpotentials (Fig. 2). Other authors have already noticed such phenomenon and, so far, there is no conclusive explanation about the process that originates it [40]. Actually, the depressed semi-circle appeared to be composed of two individual semi-circles merged. With increasing overpotential one of them increasingly predominated, resulting in the nondepressed semi-circle earlier mentioned. The impedance plots were mathematically adjusted by using the complex non-linear least squares (CNLS) method developed by MacDonald [41], assuming a constant phase element (CPE) model, to estimate the faradaic component of the impedance (A = 1/Rct ) and to calculate the double-layer capacitance, Cdl [12,40]. Fig. 3 shows the calculated Cdl values for Pt and Pt–(S−2 ) electrodes plotted against the electrode overpotential. The surface modification seems not to have caused any significant change in the electrode surface area. Both electrode surfaces showed similar variations of the Cdl with the electrode overpotential up to −0.4 V, after which the Cdl for Pt surface continues to increase with the overpotential, while that for Pt–(S−2 ) reaches a rather constant value. Assuming a Volmer–Heyrovsky mechanism, the steady state and impedance data were mathematically adjusted, to calculate the kinetic parameters of the individual electrochemical steps. The corresponding values of the parameters obtained by fitting for both steps are presented in Table 2. The main feature that is observed in the calculated rate constants is that their absolute values reinforce the previous suggestion that S−2 chemisorption improves the electrode performance for HER. In order to check the consistency of the assumed mechanism and the calculated rate constants, the latter were used to mathematically simulate the steady-state and impedance data and the results compared to the experimental data (Fig. 4). There was good agreement between the experimental and fitted values, verifying the suitability of the assumed mechanism and calculated rate constants. The dependence of surface coverage by adsorbed hydrogen (H ) on the overpotential, determined from the rate constants in Table 2 by assuming a Volmer–Heyrovsky mechanism, is displayed in Fig. 5. It is interesting to observe that the modified surface exhibited larger H values than the unmodified one, and the electrode material that retains a higher concentration of adsorbed H should be a better electrocatalyst for HER, since the Volmer step was supposed to be rate determining. It must be pointed out that the EIS study also allowed the calculation of the Cdl for the electrode materials in this study, and no significant difference was observed for that value, between modified and unmodified surfaces. Therefore, no surface area increase has to be taken into account when analyzing the performance of the surface-modified material. It was proved in the experiments that modification of the Pt surface sites with S−2 caused an improvement of their electrocatalytic activity, compared to a pure Pt surface. If the electron structure of Pt itself was already taken to be ideal, given its d-orbital configuration, the surface modification must have enabled some kind of enhancement of that configuration to occur.
A.C.D. Angelo / International Journal of Hydrogen Energy 32 (2007) 542 – 547
545
-2.0 η=-0.468V
η=-0.068V
-200
-1.5
-100 -50
Z" / Ω cm2
Z" / Ω cm2
-150
2
0 (a)
50
100 150 Z' / Ω cm2
0.0
200
0.5
(b)
1.0 1.5 Z' / Ω cm2
2.0
-5
η=-0.068V
-600
η=-0.468
-500
-4
-400 -300
1 0.5
10K
Z" / Ω cm2
Z" / Ω cm2
1.6
0.0
0
-200
10K
-0.5
0.05
10K
316 -1.0
-100
-3 200 -2 10K
-1
0.5
0 0 (c)
100 200 300 400 500 600 Z' / Ω cm2
0
0
1
(d)
2 3 Z' / Ω cm2
4
5
Fig. 2. Representative complex plane impedance plots for HER on Pt, (a) and (b), and Pt–(S−2 ), (c) and (d); surfaces in 1.0 mol dm−3 NaOH solution at 22 ◦ C. (Points = experimental and line = fitted by using CNLS program.)
changes raise the electronegativity of the Pt surface sites, and this could significantly alter the interaction of these sites with molecules of water at the equilibrium potential. Thus:
Pt Pt-(S-2)
Cd.l./ F cm-2
2.0x10-3
1.6x10-3
H2 O Pt.S H2 O H2 O ) = Pt (Gads .S − sol ,
(4a)
H2 O Pt H2 O 2O (Gads ) = H Pt − sol ,
(4b)
H2 O Pt.S H2 O Pt H2 O H2 O (Gads ) − (Gads ) = Pt .S − Pt ,
(4c)
H2 O where Pt .S denotes the chemical potential of the water 2O molecule adsorbed on the modified Pt surface and H is Pt that of water adsorbed on the pure Pt surface. If we assume that the modification of the surface results in a stronger water molecule-surface site interaction, it follows that:
1.2x10-3
8.0x10-4 0.0
-0.2 -0.4 Overpotential / V
-0.6
Fig. 3. Cdl dependence on the electrode overpotential for HER on Pt surfaces in 1.0 mol dm−3 NaOH solution at 22 ◦ C.
It may be suggested that the adsorption of S leads to a significant change in the contributions, through their d-orbitals, of the modified Pt surface sites. On the other hand, the surface
H2 O H2 O Pt .S < Pt .
(5)
From Eq. (4), the change in the free energy of water adsorption H2 O Pt .S H2 O Pt is: (Gads ) − (Gads ) < 0, so that, in thermodynamic terms, water adsorption on the modified Pt surface is favored in comparison with that on the unmodified Pt. Now, Gads = Hads − T · Sads ,
(6)
546
A.C.D. Angelo / International Journal of Hydrogen Energy 32 (2007) 542 – 547
Table 2 Kinetic parameters for HER on the indicated electrode materials in 1.0 mol dm−3 NaOH solution at 22 ◦ C Electrode
Parameter k1 (mol cm2 s−1 ) −10
k2 (mol cm2 s−1 )
−11
4.49 × 10 2.88 × 10−8
Pt Pt–(S−2 )
k−1 (mol cm2 s−1 )
−10
1.03 × 10 4.13 × 10−10
4.08 × 10 3.32 × 10−10
k−2 (mol cm2 s−1 ) −8
1.79 × 10 2.32 × 10−8
1
2
0.31 0.20
0.50 0.40
100
100
10
10
1
1
log i / Acm-2
log A / ohm-1 cm-2
ki symbolizes the rate constant and i represents the transfer coefficient for step i .
0.1 0.01 1E-3
1E-3
1E-4 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 Overpotential / V (a)
1E-4
0.0 (b)
100
100
10
10
1
log i / Acm-2
log A / ohm-1 cm-2
0.1 0.01
0.1 0.01
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 Overpotential / V
1 0.1 0.01 1E-3
1E-3
1E-4 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 Overpotential / V (c)
1E-4 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 Overpotential / V (d)
Fig. 4. Impedance (log A) and steady-state (log i) data dependence on the electrode overpotential for HER on Pt, (a) and (b), and Pt–(S−2 ), (c) and (d), surfaces in 1.0 mol dm−3 NaOH solution at 22 ◦ C. (Points = experimental and line = calculated from the parameters jointed in Table 2.)
1.00
θH
0.75
0.50
0.25
0.00 0.0
-0.1
-0.2
-0.3 -0.4 Overpotential / V
-0.5
-0.6
Fig. 5. Hydrogen coverage dependence on the electrode overpotential, for HER, in 1.0 mol dm−3 NaOH solution at 22 ◦ C: (×) Pt–S−2 , () Pt.
where it should be noted that Sads will not differ much between the modified and unmodified Pt surfaces, given that the process of adsorption is entropically unfavorable, diminishing the system entropy similarly in each case. Therefore, for the adsorption free energy to be favorable, it is necessary that the heat of adsorption (Hads ) of water on the modified surface be lower than on the unmodified, as implied in Eq. (3) earlier cited. A stronger interaction between water and the modified surface reduces this term and so favors the adsorption process relative to that on pure Pt. It must be recalled that the Volmer step in the mechanism of HER involves the adsorption of water molecule to produce the intermediate M–Hads (Eq. (1)). Therefore, we proposed that the surface modification of Pt surface by S−2 adsorption has enhanced the rate of this step by enhancement of the water adsorption on the surface. As a consequence, the surface coverage by hydrogen increased and the overall reaction was favored. 4. Conclusion The electrochemical experiments carried out indicate a real electrocatalytic action exerted by the Pt–S surface sites on
A.C.D. Angelo / International Journal of Hydrogen Energy 32 (2007) 542 – 547
HER in alkaline medium. The results suggest that the enhancement of catalysis after adsorption of S−2 ion should be attributed to the degree of surface coverage by the species M–H (adsorbed H). Acknowledgment The author thanks Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) for financial support. References [1] Mizuno T, Enyo M. Sorption of hydrogen on and in hydrogenabsorbing metals in electrochemical environment. Modern aspects of electrochemistry, vol. 30. New York: Plenum; 1996. p. 415. [2] Viswanathan B. In: Viswanathan B, Sivasanker S, Ramaswamy AV, editors. Catalysis. New Delhi, India: Narosa Publishing House; 2002. p. 390. [3] Losiewicz B, Budniok A, Rowinski E, Lagiewka E, Lasia A. The structure, morphology and electrochemical impedance study of the hydrogen evolution reaction on the modified nickel electrodes. Int J Hydrogen Energy 2004;29(2):145. [4] Crabtree GW, Dresselhaus MS, Buchanan MV. The hydrogen economy. Phys Today 2004;57(12):39. [5] Tseng P, Lee J, Friley P. A hydrogen economy: opportunities and challenges. Energy 2005;30(14):2703. [6] Turner JA. The sustainable hydrogen economy. Geotimes 2005;50(8):7. [7] Goltsov VA, Veziroglu TN, Goltsova LF. Hydrogen civilization of the future—a new conception of the IAHE. Int J Hydrogen Energy 2006;31(2):153. [8] Ohi J. Hydrogen energy cycle: an overview. J Math Res 2005; 20(12):3180. [9] Maack MH, Skulason JB. Implementing the hydrogen economy. J Cleaner Prod 2006;14(1):52. [10] Penner SS. Steps toward the hydrogen economy. Energy 2006;31(1):33. [11] Jaksic MM. Hypo-hyper-d-electronic interactive nature of interionic synergism in catalysis and electrocatalysis for hydrogen reactions. Int J Hydrogen Energy 2001;26(6):559. [12] Bocutti R, Saeki MJ, Florentino AO, Oliveira CLF, Angelo ACD. The hydrogen evolution reaction on co-deposited Ni-hydrogen storage metallic particles in alkaline medium. Int J Hydrogen Energy 2000;25:1051. [13] Albertini LB, Angelo ACD, Gozalez ER. A nickel–molybdenite cathode for hydrogen evolution in alkaline media. J Appl Electrochem 1992;22:888. [14] Jaksic MM. Advances in electrocatalysis for hydrogen evolution in the light of the Brewer–Engel bond theory. J Mol Catalysis 1986;38:161. [15] Horiuti J, Polanyi M. The basis of a theory of proton transfer. Electrolytic dissociation; prototropy; spontaneous ionization; electrolytic evolution of hydrogen; hydrogen-ion catalysis. Acta Physicochim 1935;2:505. [16] Conway BE, Bockris JOM. Electrolytic hydrogen-evolution kinetics and its relation to the electronic and adsorptive properties of the metal. J Chem Phys 1957;26:532. [17] Bockris JOM, Khan SUM. Surface electrochemistry: a molecular level approach. New York: Plenum Press; 1993. [18] Grubb WT. 17th Annual power sources conference, Atlantic City, NJ, 1963. [19] Conway BE, Bockris JO’M. The d-band character of metals and the rate and mechanism of the electrolytic hydrogen-evolution reaction. Nature 1956;178:488.
547
[20] Fahrenfort J, VanReijen LL, Sachter WMH. Decomposition of HCO2 H on metal catalysts. In: de Boer JH, editor. The mechanism of heterogeneous catalysis. Amsterdam: Elsevier; 1960. [21] Wroblowa H, Kuhn AT, Bockris JO’M. Anodic oxidation of ethylene on noble metals and alloys. Parametric and isotopic examination of mechanisms. Trans Faraday Soc 1967;63:1458. [22] Trasatti S. Work function, electronegativity, and electrochemical behavior of metals. II. Potentials of zero charge and electrochemical work functions. J Electroanal Chem 1971;33:351. [23] Trasatti S. Work function, electronegativity, and electrochemical behavior of metals. III. Electrolytic hydrogen evolution in acid solutions. J Electroanal Chem 1972;39:163. [24] Trasatti S. The work function in electrochemistry. In: Tobias CW, Gerischer H, editors. Advances in electrochemistry and electrochemical engineering, vol. 7. New York: Interscience; 1977. p. 213. [25] Kita H. Periodic variation of exchange current density of hydrogen electrode reaction with atomic number and reaction mechanism. J Electrochem Soc 1966;113:1095. [26] Kita H. Electrocatalysis by d- and sp-metals. J Res Inst Catal 1973;21:200. [27] Kita H. Electrocatalysis by d- and sp-metals. In: Bloom H, Gutmann F, editors. Electrochemistry: the past thirty and the next thirty years. New York: Plenum Press; 1977. [28] Kita, H. In: Bard AJ, editor. Encyclopedia of electrochemistry of the elements, vol. 9a, New York: Marcel Dekker, 1982. [29] Burke ML, Madix RJ. Hydrogen on palladium (1 0 0)-sulfur: the effect of sulfur on precursor mediated adsorption and desorption. Surf Sci 1990;237:1. [30] Protopopoff E, Marcus P. Effect of chemisorbed sulfur on the hydrogen adsorption and evolution on metal single-crystal surfaces. J Chim Phys 1991;88:1423. [31] Gomez R, Fernandez-Vega A, Feliu JM, Aldaz A. Hydrogen evolution on platinum single crystal surfaces: effects of irreversibly adsorbed bismuth and antimony on hydrogen adsorption and evolution on platinum (1 0 0). J Phys Chem 1993;97:4769. [32] Jerkiewicz G. Hydrogen sorption at/in electrodes. Progress in Surf Sci 1998;57:137X. [33] Dhanak VR, Shard AG, Cowie BCC, Santoni A. The structures of sulfur on Pd(1 1 1) studied by X-ray standing wavefield absorption and surface EXAFS. Surf Sci 1998;410:321. [34] Paseka I. Sorption of hydrogen and kinetics of hydrogen evolution on amorphous nickel–sulfur(Sx) electrodes. Electrochim Acta 1993;38:2449. [35] Jerkiewicz G, Zolfaghari A. Determination of the energy of the metalunderpotential-deposited hydrogen bond for rhodium electrodes. J Phys Chem 1996;100:8454. [36] Sung Y-E, Chrzanowski W, Zolfaghari A, Jerkiewicz G, Wieckowski A. Structure of chemisorbed sulfur on a Pt(1 1 1) electrode. J Am Chem Soc 1997;119:194. [37] Zolfaghari A, Villiard F, Chayer M, Jerkiewicz G. Hydrogen adsorption on Pt and Rh electrodes and blocking of adsorption sites by chemisorbed sulfur. J Alloys Comp 1997;253–254:481. [38] deGiz MJ, Ferreira M, Tremiliosi-Filho G, Gonzalez ER. Mechanistic study of the hydrogen evolution reaction of nickel–zinc and nickel–sulfur cathodes. J Appl Electrochem 1993;23:641. [39] González ER, Avaca LA, Tremiliosi-Filho G, Machado SAS, Ferreira M. Hydrogen evolution reaction on nickel–sulfur electrodes in alkaline solutions. Int J Hydrogen Energy 1994;19:17. [40] Brug GJ, van der Eeden ALG, Sluyters-Rehbach M, Sluyters JH. The analysis of electrode impedances complicated by the presence of a constant phase element. J Electroanal Chem 1984;176:275. [41] MacDonald JR. Impedance spectroscopy and its use in analyzing the steady-state ac response of solid and liquid electrolytes. In: Impedance spectroscopy. New York: Wiley; 1987.