A study of the lead dioxide electrocrystallization mechanism on glassy carbon electrodes. Part I: Experimental conditions for kinetic control

Materials Chemistry and Physics 125 (2011) 46–54

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A study of the lead dioxide electrocrystallization mechanism on glassy carbon electrodes. Part I: Experimental conditions for kinetic control V. Sáez a , E. Marchante a , M.I. Díez a , M.D. Esclapez b , P. Bonete b , T. Lana-Villarreal b , J. González García a,∗ , J. Mostany c a

Grupo de Nuevos Desarrollos Tecnológicos en Electroquímica: Sonoelectroquímica y Bioelectroquímica, Departamento de Química Física e Instituto Universitario de Electroquímica, Universidad de Alicante, Ap. Correos 99, 03080 Alicante, Spain Grupo de Fotoquímica y Electroquímica de semiconductores, Departamento de Química Física e Instituto Universitario de Electroquímica, Universidad de Alicante. Ap. Correos 99, 03080 Alicante, Spain c Departamento de Química, Universidad Simón Bolivar, Caracas 1080-A, Venezuela b

a r t i c l e

i n f o

Article history: Received 20 April 2010 Received in revised form 17 August 2010 Accepted 18 August 2010 Keywords: Oxide thin films Rotating electrode Cyclic voltammetry Diffusive mass transport Direct optical observation Kinetic control

a b s t r a c t The dependence on chemical and electrochemical variables of lead dioxide electrodeposition on a glassy carbon electrode from Pb(II) aqueous solutions has been studied. Depending on the experimental conditions, the mechanism of lead dioxide electrodeposition may involve kinetic or mass transport control. Both modeling and morphological studies of the nucleation and growth process have been carried out. The analysis of the chronoamperometric curves obtained from potential step experiments required a previous study regarding (i) the experimental solution conditions (pH, Pb(II) concentration), (ii) range of the final step potential to be used, and (iii) the choice of theoretical models used to obtain the kinetic parameters. Direct microscopic observation of the electrode through the initial stages of oxide phase formation has provided independent values of nucleation kinetics parameters (N0 A), growth constants (k), induction time (t0 ) and their dependence on the electrochemical variables. The fitting of the experimental curves using some of these independent values allowed other ones, with more realistic values, to be obtained. Further discussion on the mechanistic details of the lead dioxide electrodeposition is presented. © 2010 Elsevier B.V. All rights reserved.

1. Introduction The importance of lead dioxide as an electrode material [1] keeps active nowadays the interest in its development [2–4], not only for the very familiar lead/acid battery, but also for other electrochemical applications and emerging technologies, aimed at the development of electrochemical power sources [5,6] and waste water treatments [7]. In order to improve the electrochemical properties of this material, research can be found in the literature analyzing the influence of chemical (electrolyte media [8], temperature [9], morphological forms [10,11], electroactive species concentration and nature [12], additives [13]) and/or pure electrochemical operational variables (substrate [14] or deposition current density [15]) on the lead dioxide electrocrystallization. We can find specific literature on the mechanisms of nucleation and growth of lead dioxide, the major part of this work being performed using an inert substrate and acidic media [9,16–21]. The mechanism has been modified from the first version of Fleischmann and Liler

∗ Corresponding author. E-mail address: [email protected] (J. González García). 0254-0584/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2010.08.069

[16] where insoluble oxygen–Pb(IV) intermediates are proposed, through ones involving the presence of several soluble intermediates such as the oxygen–Pb(IV) species proposed by Chang and Johnson [18], and the oxygen–Pb(III) intermediate suggested by Velichenko et al. [19], who afterwards proposed the existence of both oxygen–Pb(III) and oxygen–Pb(IV) soluble intermediates [21]: H2 O → OHads + H+ + e−

(1)

Pb2+ + OHads → Pb(OH)2+

(2)

Pb(OH)2+ + H2 O → Pb(OH)2 2+ + H+ + e−

(3)

Pb(OH)2 2+ → PbO2 + 2H+

(4)

In a later paper, Velichenko et al. [22] established that the limiting step of the PbO2 electrodeposition is determined by factors such as the electrode surface potential and state, the concentration of lead(II) ions in solution and the hydrodynamic conditions of the process, as well as by the overpotential, the rate-determining step at low overpotentials being the second electron transfer reaction (step (3)), and the diffusion of Pb(II) [23] being the controlling process at high overpotentials.

V. Sáez et al. / Materials Chemistry and Physics 125 (2011) 46–54

The nucleation and growth processes play an important role in the properties and behavior of any electrodeposited film. In the literature, two markedly different descriptions for nucleation and growth processes can be found [24]: those where incorporation of ions to the growing nucleus lattice (kinetic control) is the rate-determining step, and those where mass transport from the solution to the growing nucleus (diffusion control) is the rate-determining process. Several theoretical models have been proposed either for diffusion-controlled growth, recently reviewed by Hyde and Compton [25] and kinetic-controlled growth [26]. For this latter type of mechanism, all the theories provide mathematical expressions for chronoamperometric transients for the different types of nucleation (instantaneous and progressive) and growth (two- or three-dimensional) [27–29]. These mathematical expressions present several kinetic parameters which provide quantitative information about the process, not only about the substrate but also about the kinetics of the film growth. A summary of the current density–time (j–t) expressions for kinetically controlled nucleation and growth (i.e. without mass transport effects) has been reported previously [30]. In this work, a preliminary study of the electrodeposition of lead dioxide as a function of Pb(II) concentration at two different pH values has been carried out by means of a voltammetric analysis and a series of potential step (chronoamperometric) experiments, with the results compared to those found in the literature [9,18]. In addition, the kinetics of PbO2 phase formation in Pb(II) solutions with 1 M HNO3 as supporting electrolyte are studied both by direct observation of micrographs and by analysis of chronoamperometric curves, correlating the theoretical analysis of the nucleation process with direct observation of phase formation from which experimental values of the kinetic parameters are obtained. In all cases, we have paid special attention to the early stages of the electrodeposition, during which the process of water discharge plays a relevant role. 2. Experimental section The voltammetric and chronoamperometric curves corresponding to the crystallization and growth of the PbO2 phase were obtained using a VoltaLab electrochemical system with a DEA 332 potentiostat and an IMT 102 electrochemical interface, connected to a PC for data acquisition and control. A glassy carbon rod CV25 (0.07 cm2 electrode area) from Sofacel (Le Carbone-Lorraine) and a glassy carbon disk (EDI6000 rotating disk electrode, Radiometer Copenhagen, diameter 3 mm) were used as working electrodes. The glassy carbon (GC) rod was sheathed by two Teflon cylinders. The first cylinder was fitted thermally whereas the second one was fitted by pressing, providing a tight seal around the GC rod. The counter electrode was a spiral wound platinum wire and the reference electrode a saturated calomel electrode (SCE) (Radiometer, Copenhagen), connected to the electrochemical cell via a Luggin capillary. All potentials in this manuscript were measured and are quoted relative to this reference electrode. It is worth mentioning that the surface state of the working electrode is an important variable to take into account. In fact, it has been observed that the background current depends quantitatively on the pre-treatment, due to the promoting nature of the superficial functional groups [31] towards oxide formation. Thus it is necessary to implement a well-defined routine to obtain reproducible results [32]. Glassy carbon electrodes were polished to mirror finish with decreasing sizes of alumina powder (1, 0.3 and 0.05 ␮m) and rinsed with ultrapure water before each experiment. After each experiment, the lead dioxide deposit was removed with 1:1 H2 O2 /Acetic acid followed by rinsing thoroughly with water. All solutions were prepared using ultrapure water from a Millipore Mill-Q system. Lead(II) nitrate, lead(II) acetate, sodium hydroxide and nitric acid (Merck A.R.) were used in the amounts required to obtain the desired working concentrations. Solutions were degassed and saturated with a stream of Ar prior to the electrochemical experiments to avoid additional reactions caused by the presence of oxygen. A stream of Ar was also maintained over the surface of the electrolyte during the measurements. The micrographs were obtained with an optical inverted microscope (Nikon Epiphot) equipped with a computer-controlled video camera (Hamamatsu CCD camera, model C5405). A standard 3-electrode electrochemical cell with a fused silica window was designed to be used with the microscope. A magnification of 40× objective was regularly employed. The distance between the electrode surface and the silica window was about 6 mm. The electrochemical measurements were performed in a nitrogen-purged electrolyte with a PC-controlled Autolab PGSTAT30.

47

Fig. 1. Cyclic voltammetry (first and second cycles) of a glassy carbon electrode in 0.1 M Pb(NO3 )2 + 1 M HNO3 , scan rate 20 mV s−1 , T = 20 ◦ C. The first cycle is indicated by one arrow and the second one by two arrows.

3. Results and discussion 3.1. Preliminary studies Fig. 1 shows the cyclic voltammograms (first and second cycles) for the GC electrode in 0.1 M Pb(NO3 )2 + 1 M HNO3 , at 20 ◦ C and 20 mV s−1 . The third cycle (not shown) is virtually the same as the second one. In the first cycle, a significant crystallization overpotential (close to 250 mV) is required for the deposition of lead dioxide onto a fresh inert substrate surface during the sweep towards positive potentials. Massive lead dioxide electrodeposition takes place at electrode potentials higher than 1600 mV vs SCE. In the second cycle, after a reverse scan to 400 mV vs SCE, the crystallization overpotential is markedly decreased (the anodic peak potential decreases by more than 150 mV). The cathodic peak in the second cycle presents a lower current density, but a broader shape, indicating that the structure of the lead dioxide deposit is different. Therefore, we can conclude that the substrate surface remains activated for the electrodeposition process, probably due to the presence of non-reduced lead dioxide accumulated during the cathodic stripping peak [8,18,21,33]. From these results, it is evidenced, as previously mentioned, that the initial surface state of the substrate is critical in order to compare different experimental results. The electrocrystallization of lead dioxide involves a pHdependent complex mechanism [8] which requires a detailed study. Fig. 2A presents the chronoamperometric response of a glassy carbon electrode at 20 ◦ C when the potential is shifted from open circuit potential to 1540 mV vs SCE at three different lead(II) nitrate concentrations, 0.01, 0.05 and 0.1 M, in 1 M HNO3 . Under these experimental conditions (pH, lead(II) concentration and step final potentials), the j vs t transients are characterized by several features: after the onset of the potential step, a sharp decrease of the current density occurs until a minimum value j0 is reached, being this time much higher than expected for double layer charging. The current density remains at j0 during an induction time t0 , after which the current density begins to increase until it reaches a steady state value jss . In the literature [34], the induction time is normally related to the time lag of the subcritical cluster distribution to achieve steady state. The steady state current density jss is reached as the massive phase grows with a constant rate, given the necessary overpotential and time scale for the experiment (20 min). At this low pH, a higher Pb(II) concentration causes

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V. Sáez et al. / Materials Chemistry and Physics 125 (2011) 46–54

Fig. 3. Chronoamperometric curves for 0.1 M Pb(NO3 )2 + 1 M HNO3 at a glassy carbon electrode obtained in a standard voltammetric cell for different final step potentials: (a) 1490 mV, (b) 1500 mV, (c) 1510 mV, (d) 1520 mV, (e) 1540 mV and (f) 1560 mV, T = 20 ◦ C.

3.2. Analysis of the process with potential step experiments

Fig. 2. Chronoamperometric curves for PbO2 deposition at a glassy carbon electrode, T = 20 ◦ C. (A) Step final potential of 1540 mV in 1 M HNO3 + (a) 10−2 M, (b) 5 × 10−2 M and (c) 10−1 M Pb(NO3 )2 . (B) Step final potential of 500 mV in 1 M NaOH + (a) 10−2 M, (b) 2.5 × 10−2 M and (c) 5 × 10−2 M Pb(Ac)2 .

a slight decrease of t0 and a proportional increase of the plateau current density jss , which is in agreement with prevailing kinetic control. Fig. 2B presents the chronoamperometric response for a glassy carbon electrode at 20 ◦ C, for a potential step of 500 mV in 1 M NaOH [8] at a similar range (0.01, 0.025 and 0.05 M) of concentrations of lead(II) acetate. In this case, the response obtained is quite different: (i) first of all, the necessary potentials for the electrodeposition process to take place and the time scale for obtaining a fully developed response are significantly lower, (ii) secondly, despite the other operational variables apart of pH being the same, the recorded current densities are higher at basic pH and (iii) finally, the shape of the transient is different: a very short induction time (if any), shorter time scale with a strong peak, followed by a steady state current density, both increasing with the concentration. From these experimental results, we conclude that the lead dioxide electrodeposition rate depends not only on the electrode potential [9] but also on the concentration of lead(II) in the electrolyte and its pH. From the figure it can be deduced that acidic conditions do not favor the electrodeposition process. This is reflected by longer induction times and lower steady state current densities. These results agree with those reported previously in the literature [18]. In the present work, the kinetics and mechanism of PbO2 electrodeposition in acidic media are analyzed, using different models found in the literature. PbO2 formation and growth in less acidic conditions will be studied in the second part of this work.

3.2.1. Analysis of the process using a standard electrochemical cell Fig. 3 shows a typical series of j vs t at different final step potentials. As mentioned previously, three features can be highlighted: a falling current at short times followed by an induction time (t0 ), after which a rising current develops up to a steady state value (jss ) at long times. It is clear that the charge associated with the falling current is too high to be exclusively ascribed to double layer charging. This response has been also observed in other electrochemical systems [35–38], often precluding analysis of transient processes when short induction times are present. Recently, Milchev et al. [39], studying copper electrodeposition, analyzed this current decay in terms of ion and electron transfer electrochemical reactions which take place prior to and simultaneously with the process of nucleus formation and the growth of a new phase. The falling current in lead dioxide electrodeposition can be analyzed in a similar way, along with other possible interpretations. The Supporting Information presents a deeper analysis of this aspect, studying transients in the presence and in the absence of Pb(II). A general conclusion establishes that the assignment of residual currents in the falling current and during the induction time (t0 ) is highly speculative, but, in any case, we can discard a simple adsorption of OH species at monolayer level and consider OHads as an adsorbed product of the H2 O discharge on the electrode surface, regardless of the identity of functional groups produced on the electrode surface. The influence of the hydrodynamic conditions on lead dioxide electrodeposition in acidic media has been widely reported. However, the forced convection conditions have been imposed from the beginning of the voltammetry [19] or the chronoamperometric experiments [18,30], where it can be seen that the onset of the nucleation and growth process is notoriously retarded with the imposition of convective conditions at low overpotentials. This is consistent with the soluble nature of the proposed intermediates: it should be stressed that not only it is necessary that the OHads species coverage is high enough in order that step (2) can take place at a reasonable rate, but also the concentration of this soluble intermediate near the electrode surface should be high enough to allow the electron transfer at the last step (3). If this last electron transfer is slow, the process can be retarded by removing this soluble intermediate by rotating the electrode. However, according to a picture where the first step (1) is relevant at an early

V. Sáez et al. / Materials Chemistry and Physics 125 (2011) 46–54

49

Fig. 4. Chronoamperometric curves for PbO2 deposition in 0.1 M Pb(NO3 )2 + 1 M HNO3 at a glassy carbon electrode for different final step potentials: 1520 mV (A and C) and 1560 mV (B and D), T = 20 ◦ C. Rotation speed: (a) 0 rpm, (b) 200 rpm, (c) 400 rpm, (d) 600 rpm, (e) 800 rpm, (f) 2500 rpm and (g) 5000 rpm.

stage of the lead dioxide electrodeposition, additional experiments were carried out in order to verify the mass transport control on the experimental time scale. Fig. 4 shows different potential steps where convective conditions were imposed in two different stages of the nucleation and growth of the PbO2 deposit. The potential step was initially carried out in static conditions, and either on the rising part of the current transient (Fig. 4A and B) or after the onset of the steady state current at longer times (Fig. 4C and D), rotation of the RDE was imposed at successively higher rotation rates (from 200 to 5000 rpm). Experimental responses at two different final step potentials were recorded: 1520 mV vs SCE (Fig. 4A and C) and 1560 mV vs SCE (Fig. 4B and D). At the initial stages of lead dioxide formation, mainly over the glassy carbon substrate, electrodeposition appears to be under kinetic control, as Levich behavior is not observed, the current being practically independent of the rotation rate. At longer times, when PbO2 is forming at a steady state rate mainly over previously deposited lead dioxide (Fig. 4C and D), growth is favored by enhanced mass transport conditions, but without showing the full Levich behavior typical of mass transport controlled processes. These results are in disagreement with those reported by Chang and Johnson [18] for similar acid and Pb(II) concentrations, where the jss decreases by 10–50% under forced mass transport conditions. The fact that the electrodeposition of lead dioxide is more favored on lead dioxide than on glassy carbon is in agreement with the previous voltammetric results (see above). 3.2.2. Analysis of the process using an electrochemical cell equipped with an optical inverted microscope In order to obtain independent information for the process, chronoamperometric measurements were performed at the same

time that the PbO2 crystal growth was being recorded using a video camera coupled with an optical microscope. Despite the large number of studies on lead dioxide electrodeposition, to our knowledge no direct optical observation studies have been previously reported for this system, even though useful information is provided by this kind of in situ study. Therefore, a series of potential step experiments were carried out in the electrochemical cell, recording simultaneously both micrographs and chronoamperometric curves. The micrographs obtained during the course of the electrodeposition process were analyzed and used to determine by direct observation the nuclei density N and radius R of nuclei as a function of time. Micrographs were taken at selected times along the transients over a wide region of the surface in order to record a representative sample of the electrode surface during lead dioxide electrodeposition. Analyses were performed only for micrographs taken after the induction time period, between the onset of the nucleation and growth process and the beginning of nucleus overlapping, when less than 5% of the total charge of the whole transient has passed. According to Fig. 4A and B, no mass transport limitations are present at this early stage. Micrographs obtained in the final part of the transients showed that the overlapping between crystals was not completely developed as small regions of the glassy carbon substrate were still clearly observed. Fig. 5 show a typical micrograph. Nuclei size dispersion does not necessary follow only from progressive nucleation, as even under an instantaneous nucleation regime, isolated nuclei will grow faster than those with close neighbors, giving rise to size dispersion at long times. However, the recorded movies showed that progressive nucleation of PbO2 occurs under the experimental conditions

50

V. Sáez et al. / Materials Chemistry and Physics 125 (2011) 46–54 Table 1 Kinetic parameters of lead dioxide electrodeposition in 1 M HNO3 obtained from analysis of the micrographs (M) and theoretical analysis of the early stages, assuming progressive nucleation (E). Ef (mV vs SCE)

1520 1540 1560

Fig. 5. Typical micrograph of the glassy carbon electrode at the early stage of the lead dioxide electrodeposition in 0.1 M Pb(NO3 )2 + 1 M HNO3 T = 20 ◦ C.

of this work. For each potential step experiment, the set of micrographs were analyzed to obtain (a) the nuclei number per cm2 (N) vs time relationship and (b) the nucleus base surface (R2 ) vs time relationship for a set of nuclei (ca. 10 nuclei), chosen so as to avoid the presence of any influential close neighbors. Fig. 6 shows N vs time and nucleus radius (R) vs time results for potential step experiments carried out at 1520, 1540 and 1560 mV vs SCE. As shown, the time dependence of N is linear. Therefore a direct evaluation of the nucleation rate constant, N0 A, can be obtained directly from the slope of the N(t) vs t curves of Fig. 6. In addition, the intercept tN=0 on the time axis relates to the induction time t0 as tN=0 = (2 /6)t0 [34]. On the other hand, experimental R(t) vs time profiles were are also linear. The slope of the R(t) curve was independent of the size (and therefore age) of the nucleus, and increased at more positive potential step values. A linear relationship, R(t) = (Mk/)t, has been postulated theoretically for disk [24] and hemisphere-shaped nuclei growth under kinetic control, where the slope allows the determination of the potential-dependent lateral growth constant k (mol cm−2 s−1 ) at fixed concentration. In the case of right circular cone-shaped nuclei, the growth in directions parallel and perpendicular to the substrate is defined by the independent rate constants

t0 (s) M

E

143 ± 2 119 ± 1 50 ± 3

168 ± 2 122 ± 4 64 ± 1

k (mol cm−2 s−1 )

N0 A (cm−2 s−1 )

(4.72 ± 0.01) × 10−8 (5.61 ± 0.02) × 10−8 (9.61 ± 0.01) × 10−8

11,314 ± 10 18,599 ± 10 24,807 ± 10

k and k , so a similar linear R(t) vs time relationship can be assumed. It could be thought that extrapolation of nuclei radius vs time lines to the time axis in Fig. 6B could also give information about the induction time. In fact, the estimated induction times with this last procedure in Fig. 6B are similar to those obtained from Fig. 6A. However, this last procedure is based on information provided by a few nuclei (with different birth times in a progressive nucleation), and therefore this information is less representative in comparison with the information used in Fig. 6A (nuclei numbers normally higher than 50). Induction times can be also estimated from analysis of the early stages of the current transients [40,41]. Table 1 shows the values of the nucleation rate N0 A, lateral growth constant k, and the induction time t0 obtained from the analysis of the micrograph sets, in addition to the t0 obtained from current transient analysis. As mentioned in the description of Fig. 4A and B, the value of the lateral growth constant k is obtained with no limitations of mass transport at this early stage of the process. From micrograph analysis, very low values of N0 A and high values of t0 are obtained if we compare with values found in the literature [42] for other electrodeposition processes. However, N0 A values are in agreement with the long time scale of our experiments (20 min) and with the high crystallization overpotential shown in the voltammetric analysis. The values of t0 obtained from analysis of the current transients are slightly higher than those obtained by direct observation of micrographs. This can be expected due to the fact that a detectable current is only measured once a reasonable number of nuclei have developed. 3.2.3. Analysis of the process by means of theoretical approaches A summary of the j–t expressions for electrodeposition processes under pure kinetic control can be found in a previous work

Fig. 6. (A) Nuclei (N) vs time and (B) nuclei radius (R) vs time profiles at the early stage of the lead dioxide electrodeposition in 0.1 M Pb(NO3 )2 + 1 M HNO3 T = 20 ◦ C. () 1520 mV, () 1540 mV and (䊉) 1560 mV.

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51

Table 2 Kinetic parameters of lead dioxide electrodeposition in 1 M HNO3 derived from analysis of the experimental transients shown in Fig. 7 with pure kinetic control and mixed control theories. Ef (mV vs SCE)

1520 1540 1560

Pure kinetic control theory

Mixed control theory

j0 (mA cm−2 )

t0 (s)

k2 (mol cm−2 s−1 )

k (mol cm−2 s−1 )

0.396 ± 0.003 0.097 ± 0.0004 0.44 ± 0.04

189.1 ± 0.7 119.0 ± 0.5 50 ± 3

(4.56 ± 0.03) × 10−8 (3.95 ± 0.01) × 10−8 (5.4 ± 0.1) × 10−8

4.72 × 10−8 5.61 × 10−8 9.61 × 10−8

[30]. It can be observed that several kinetic parameters, such as the nucleation rate (A), the number of nucleation sites (N0 ) or lateral (k) and perpendicular (outward) (k ) growth rate constants, often appear in the same term, making their estimation by numerical fitting of the corresponding equations to experimental data rather difficult. In this work, the kinetic parameters of PbO2 electrodeposition were determined by means of two distinct models found in the literature. If we consider lead dioxide electrodeposition as a kinetically controlled progressive 3D nucleation process, a j–t behavior described by expression (5) should be observed:





j = j0 + zFk 1 − exp

−M 2 k2 N0 A (t − t0 )3 32



(5)

in which we have included the parameter j0 as a background current density term. Examination of this equation reveals that the constant k can be easily estimated from the value of jss , the current in the steady state attained at long times. Besides, some of these parameters (namely N0 A, t0 and k) have been estimated by direct observation or by analysis of the early stages of the current transient. This information can be used in the fitting of the current density response to the appropriate kinetic expression, decreasing the number of fitting parameters and giving a more realistic estimation of their values. In Fig. 7 we present the experimental data recorded in the electrochemical cell equipped with an optical inverted microscope (dots) and the evaluation of Eq. (5) for two different values of the perpendicular growth constant k : the result of numerical fitting of data to experimental data using the same time range used for the optical analysis (less than 5% of charge passed) (k2 , grey line, see Table 2), and the value obtained from the steady state current observed in Fig. 3, a similar set of experiments at the same overpotentials recorded on a standard voltammetric cell with a wide gap between the electrode and the bottom of the cell (k3 , thin black line, see Table 3). Except for short times, neither of these approaches gives a satisfactory fit for the whole transient. Experimental currents are smaller than predicted from k2 , while k3 predicts lower current values, but in none of the experiments does the current attain a steady state, i.e. it still rises at long times. In this sense, it is important to note that areas of uncovered substrate were observed in the analyzed micrographs. These results can be explained by the conditions imposed by the cell configuration devised to acquire in situ images, where a small gap (a few mm) between the electrode surface and the fused silica window exists. This configuration results in hindered mass transport conditions, as lead(II) from the bulk diffuses across a thin cylindrical section approximately 6 mm

N0 A (cm−2 s−1 )

t0 (s)

11,314 18,599 24,807

143 119 50

N0 A (cm−2 s−1 ) (1.51 ± 0.05) × 105 (1.59 ± 0.01) × 105 (3.63 ± 0.02) × 105

high, a situation opposite to the typical RDE experiment. Therefore, the lead(II) concentration cannot be considered constant over the course of the experiments. In fact, for the experiment carried out at 1560 mV, the charge recorded implies a 50% decrease from the initial Pb(II) concentration present in the region adjacent to the electrode. Small spikes can be observed in the transients at long times. They originate from small bubbles formed at the top of some nuclei, ascribed to oxygen evolution. In fact, the enhancement of the recombination of OHads to give molecular oxygen, a competing reaction to lead dioxide electrodeposition, is favored due to the depletion and shortage of Pb(II) supply adjacent to the electrode surface. As previously discussed when analyzing Fig. 4, it seems feasible that lead dioxide electrodeposition under highly acidic conditions occurs under kinetic control at early stages and low potentials, shifting to mixed control at higher potentials. As a second approach to the analysis of PbO2 electrodeposition current transients in acidic media, we considered the stationary nucleation of independently growing PbO2 crystals under conditions of combined charge transfer and diffusion limitations, following a model suggested by Milchev [34,39], where the initial current decay is ascribed to an electrochemical reaction taking place prior to and simultaneously with nucleus formation. Assuming that this electrochemical reaction is the discharge and adsorption of the resulting species on the electrode surface, an expression for the current density related to this process could be described by the expression: ji = ai exp(−bi t)

(6)

where ai and bi provide information related to the number of adsorbed species, the number of active sites on the electrode surface and the rate constants of the process. This electrochemical reaction takes place on the whole electrode surface, whereas the nucleation and growth of the clusters occurs only on a limited number of active sites. Hence, the total current density can be described by:



j = j0 + ai exp(−bi t) + q[

1 + 2nt − 1]

3

(7)

where q and n are defined for our process as [39]: q=

n=

32MF 4 (Dc)3 3  3jexc

 3˛F 

N0 A exp −

RT



(8)

2 M jexc Q 4F 2 Dc

(9)

Table 3 Kinetic parameters of lead dioxide electrodeposition in 1 M HNO3 derived from analysis of the experimental transients shown in Fig. 3 with pure kinetic control (E: early stages, F: full transient) and mixed control theory. Ef (mV vs SCE)

Pure kinetic control theory j0 (mA cm−2 )

E 1520 1540 1560

0.294 0.383 0.501

Mixed control theory

t0 (s)

330 175 75

k3 (mol cm−2 s−1 )

k (mol cm−2 s−1 )

(2.500 ± 0.009) × 10−8 (3.347 ± 0.006) × 10−8 (3.789 ± 0.009) × 10−8

4.72 × 10−8 5.61 × 10−8 9.61 × 10−8

N0 A (cm−2 s−1 )

t0 (s)

N0 A (cm−2 s−1 )

F 421 ± 1 178.8 ± 0.7 78.9 ± 0.8

11,314 18,599 24,807

421 179 79

(7.85 ± 0.05) × 104 (1.61 ± 0.01) × 105 (1.91 ± 0.02) × 105

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Fig. 7. Chronoamperometric curves for 0.1 M Pb(NO3 )2 + 1 M HNO3 at a glassy carbon electrode obtained in the voltammetric cell equipped with the inverted optical microscope for different final step potentials: (A) 1520 mV, (B) 1540 mV and (C) 1560 mV vs SCE, T = 20 ◦ C. Experimental data (). Pure kinetic control theoretical fit with ) and with value of k taken from the plateau in Fig. 3 ( ). Mixed control theoretical fit ( ). value of k given by the simulation (

Q = exp

 2˛F  RT

 − exp

 −2(1 − ˛)F  RT



(10)

where jexc (Eq. (8)) is the exchange current density and ˛ is the charge transfer coefficient of the process. For the analysis of the experimental transients using Eq. (7), a constant term j0 was included to account for the background current. Several solutions are possible if we use all the parameters (ai , bi , j0 , q, n and t0 ) as fitting variables. To reduce the degrees of freedom of the fitting procedure, ai and bi were estimated using Eq. (6) to fit the initial falling current, and j0 from the steady state current density on the induction period prior to nucleation and growth of the new phase. The equilibrium potential (1326 mV) was obtained either from the open circuit potential measured with a massive deposit formed after a 20-min potential step experiment or from the crossover in the steady state voltammetry. jexc (0.05 mA cm−2 ) and ˛ (0.485) were obtained from a Tafel plot of the same steady state conditions, and D (2.8 × 10−5 cm2 s−1 ) from independent experiments. In this way, regression can be performed leaving only q (containing the N0 A term) and t0 as fitting variables. The thick black line in Fig. 7 shows the results of fitting Eq. (7) to the initial part of experimental transients, and Table 2 compiles the resulting values for t0 and N0 A. The N0 A values obtained from this model are one order of magnitude larger than those obtained by visual analysis of the micrographs. Besides, the introduction of (i) N0 A values obtained in micrographs and (ii) values of q obtained from the regression into Eq. (8) results in diffusion coefficients three times higher than those obtained experimentally. At a constant concentration of the electroactive species, k and k depend on the electrode potential, and t0 and N0 A on both electrode potential and initial surface state. Therefore, the information obtained from the visual analysis should also be useful in the analysis of the transient obtained in a standard electrochemical cell, Fig. 3, provided that reproducible experimental conditions are achieved. Visual comparison between experimental transients recorded at the same potential in Fig. 3 and Fig. 7 evidences close similarities between both responses, and shows that differences between the induction time t0 and the rising part of the transient obtained in both experimental setups diminish as the step potential increases. From these results we can conclude that the surface state influence can be neglected in comparison with the electrode potential influence. Therefore, Eq. (5) was used to analyze the rising part of the transients obtained in the standard cell, without including in the analysis the initial decaying current (Eq. (7)), as the induction times under these experimental conditions are large enough to avoid

overlapping of the initial surface process with the current response related to the nucleation and growth of lead dioxide. As in previous cases, we have used k and N0 A values provided by micrograph analysis and j0 estimated from the induction period of the transients to perform the regression of Eq. (5) on the experimental data with k and t0 as adjustable parameters. The comparisons between the experimental data (dots) and the resulting transients are shown in Fig. 8 (a–c thin lines) and the corresponding regression parameters can be found in Table 3. In this table we have also included the estimation of the induction time t0 , determined by analysis of the early stages of the current transient. Good agreement is obtained, mostly at high potentials, as expected if the influence of the surface state on the nucleation process becomes less important as the electrode potential increases. These results demonstrate the usefulness and validity of the kinetic parameters obtained by direct observation of the electrode process, as the obtained fits are quite satisfactory. However, according to Fig. 4, it is clear that the electrodeposition process on top of a previously formed lead dioxide substrate is under mixed control, as jss increases with rotation rate at long times. In fact the value of this jss reaches an independent value at high rotation rates, so we can estimate the real k value from

Fig. 8. Chronoamperometric curves for 0.1 M Pb(NO3 )2 + 1 M HNO3 at a glassy carbon electrode obtained in a standard voltammetric cell for different final step potentials: (a) 1520 mV, (b) 1540 mV and (c) 1560 mV vs SCE, T = 20 ◦ C. Experimental data (). Pure kinetic control theoretical fit ( ) with k and N0 A parameters taken from micrograph analysis and fitting parameters: k and t0 . Mixed control theoretical fit ( ) with t0 taken from results in Table 3.

V. Sáez et al. / Materials Chemistry and Physics 125 (2011) 46–54

the jss at levels f and g of Fig. 4C and D. The values estimated were 8.996 × 10−8 mol cm−2 s−1 for 1520 mV, 1.041 × 10−7 mol cm−2 s−1 for 1540 mV and 1.182 × 10−7 mol cm−2 s−1 for 1560 mV, which are quite close to those found by optical measurements for the lateral growth constant k (Table 1). For this reason, the combined “charge transfer” and “diffusion limitations” model (Eq. (7)) proposed by Milchev was used to analyzed the transients obtained under unconstrained mass transport conditions. The comparison between the experimental data and the resulting fitted transients (thick black line) is shown in Fig. 8. The corresponding regression parameters can be found in Table 3. For this analysis we have used the induction times provided by the pure kinetic model. Values of N0 A given by the mixed model are again one order of magnitude higher than those provided by the purely kinetic model. It was not possible to fit the initial decreasing part of the transient using Eq. (6) with reasonable parameters. This is in agreement with the fact that the residual currents cannot be related to a simple adsorption of OH species at monolayer level and a more complex process takes place. Although the obtained fits are satisfactory for the initial stages of PbO2 formation and growth, the kinetic parameters obtained are far from the observed values. Moreover, during the early stages of the process where PbO2 is being formed onto vitreous carbon, kinetic control of the process prevails (e.g., Fig. 4A and C), making Milchev’s model inadequate for this situation, as Eq. (7) is valid only for the initial stages of mixed control processes. 4. Conclusions It has been demonstrated that the lead dioxide electrodeposition follows a complex mechanism and depends on several factors such as initial surface state, pH, applied potential, coverage of PbO2 , and convective conditions, some of which can even change in the course of a single experiment. Once the detailed mechanism of the process has been established, then fitting the appropriate equations to the data can be a valid procedure to determine the relevant physicochemical quantities form the experimental results. With this statement, several facts can be stressed:

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the combination of visual analysis of micrographs and numerical fitting has provided more realistic and accurate results. Good fitting in the nuclei formation region has been obtained with the pure kinetic model using two different electrochemical setups. The values of the kinetics parameters (N0 A and t0 ) are consistent with voltammetric profiles with high crystallization overpotentials. (e) In spite of the good fitting between experimental and theoretical curves obtained with the mixed control model at the very beginning of the nucleus formation, the kinetic parameters derived do not present good agreement with the experimental ones and the situation cannot be predicted with accuracy using this combined “charge transfer” and “diffusion limitations” model suggested by Milchev. (f) It could be interesting to direct future research towards the activation of the surface electrode prior to nucleation and growth of the nuclei. On one hand, it would be interesting to identify the surface groups on glassy carbon electrodes and to evaluate their electrocatalytic properties as active sites for the nucleation. On the other hand, it should be useful to develop a reliable procedure to prepare reproducible surfaces to be used as a substrate. Work on this last approach is in progress. Acknowledgments This work has been carried out in the framework of project GV05/104 financed by the Generalitat Valenciana (Spain) and the project MAT2009-14004 financed by the Ministry of Science and Innovation. J.G.-G. and M.D.E.-V. thank Caja de Ahorros del Mediterráneo. J.G.-G., M.D.E. and P.B. thank Generalidad Valenciana for its financial support under projects AORG09/051 and ACOMP09/128. J.G.-G. and E.M. thank Universidad de Alicante for the award of a research initiation grant BII2007-48535854. J.G.-G. and M.I.D. also thank Universidad de Alicante for the award of a research initiation grant BII4770. The authors thank Dr. Mary Thompson for her help with the English edition of the manuscript. Appendix A. Supplementary data

(a) Nucleation is less favored on glassy carbon (inert substrate) than on lead dioxide itself. Once the nucleus is stable, its growth is fast, being faster at more positive potentials. In addition, the growth rate in acidic medium can be slightly increased by electrolyte convection at higher overpotentials, but is does not follow Levich behavior. (b) pH is a chemical variable with a strong influence on the process. On one hand, it influences the induction time, i.e. the initial stages of the nucleation process. From our results, we are not able to distinguish if the effect of pH is determined by the nature of the surface groups on glassy carbon electrodes, or by the chemical species of the Pb(II) involved at different pH values, or both. On the other hand, we observed a drastic modification of the lead dioxide electrodeposition rate when changing from acidic to alkaline solution at lower lead(II) concentrations, a behavior indicative of the effect of pH both in the early stages of the nucleation step on an inert substrate and also on the massive deposition on lead dioxide itself. (c) Lead(II) is not involved in the falling current at the early stage during the potential step experiments in nitric acid medium. Lead dioxide electrodeposition in nitric acid medium seems to be kinetically controlled, while the oxygen evolving reaction, a competitive process, is absent to a considerable extent for high enough lead(II) concentration. At less acidic pH, the process seems to be under mass transport control. (d) Direct observation and the theoretical analysis of the early stages have helped to select appropriate kinetic parameters and

Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.matchemphys.2010.08.069. References [1] H. Hamsah, A.T. Khun, T.H. Randle, in: A.T. Khun (Ed.), The Electrochemistry of Lead, Academic Press, London, 1979, p. 283. [2] I. Sirés, C.T.J. Low, C. Ponce de León, F.C. Walsh, Electrochim. Acta 55 (2010) 2163. [3] R. Amadelli, L. Samiolo, A.B. Velichenko, V.A. Knysh, T.V. Luk’yanenko, F.I. Danilov, Electrochim. Acta 54 (2009) 5239. [4] D. Pech, T. Brousse, D. Bélanger, D. Guay, Electrochim. Acta 54 (2009) 7382. [5] A. Hazza, D. Pletcher, R. Wills, Phys. Chem. Chem. Phys. 6 (2004) 1773. [6] D. Pletcher, R. Wills, Phys. Chem. Chem. Phys. 6 (2004) 1779. [7] V. Sáez, M.D. Esclapez Vicente, A.J. Frías-Ferrer, P. Bonete, J. González-García, Water Res. 43 (2009) 2169. [8] D. Velayutham, M. Noel, Electrochim. Acta 36 (1991) 2031. [9] A.B. Velichenko, R. Amadelli, A. Benedetti, D.V. Girenko, S.V. Kovalyov, F.I. Danilov, J. Electrochem. Soc. 149 (2002) C445. [10] N. Munichandraiah, S. Sathyanarayana, J. Appl. Electrochem. 18 (1988) 314. [11] M.E. Hyde, M.J. Jacobs, R.G. Compton, J. Phys. Chem. B 108 (2004) 6381. [12] S. Abaci, K. Pekmer, T. Hökelek, A. Yildiz, J. Power Sources 88 (2000) 232. [13] T.C. Wen, M.G. Wei, K.L. Lin, J. Electrochem. Soc. 137 (1990) 2700. [14] Ch. Comninellis, E. Plattner, J. Appl. Electrochem. 12 (1982) 399. [15] S.A. Campbell, L.M. Peter, Electrochim. Acta 34 (1989) 943. [16] M. Fleischmann, M. Liler, Trans. Faraday Soc. 54 (1958) 1370. [17] H.A. Laintinen, N.H. Watkins, J. Electrochem. Soc. 123 (1976) 804. [18] H. Chang, D.C. Johnson, J. Electrochem. Soc. 136 (1989) 17. [19] A.B. Velichenko, D.V. Girenko, F.I. Danilov, J. Electroanal. Chem. 405 (1996) 127. [20] J. Gonzalez-García, F. Gallud, J. Iniesta, V. Montiel, A. Aldaz, A. Lasia, J. Electrochem. Soc. 147 (2000) 2969. [21] A.B. Velichenko, E.A. Baranova, D.V. Girenko, R. Amadelli, S.V. Kovalev, F.I. Danilov, Russ. J. Electrochem. 39 (2003) 615.

54

V. Sáez et al. / Materials Chemistry and Physics 125 (2011) 46–54

[22] A.B. Velichenko, T.V. Luk’yanenko, N.V. Nikolenko, R. Amadelli, F.I. Danilov, Russ. J. Electrochem. 43 (2007) 118. [23] A.B. Velichenko, D. Devilliers, J. Fluorine Chem. 128 (2007) 269. [24] R. Greef, R. Peat, L.M. Peter, D. Pletcher, J. Robinson, Southampton Electrochemistry Group, Instrumental Methods in Electrochemistry, Elliserwood, Chichester, 1985. [25] M.E. Hyde, R.G. Compton, J. Electroanal. Chem. 549 (2003) 1. [26] P.J. Sonneveld, W. Visscher, E. Barendrecht, Electrochim. Acta 37 (1992) 1199. [27] M.Y. Abyaneh, Electrochim. Acta 27 (1982) 1329. [28] E. Bosco, S.K. Rangaranjan, J. Electroanal. Chem. 134 (1982) 213. [29] Y.G. Li, A. Lasia, J. Electrochem. Soc. 144 (1997) 1979. [30] J. González-García, F. Gallud, J. Iniesta, V. Montiel, A. Aldaz, A. Lasia, Electroanalysis 13 (2001) 1258. [31] M. Noel, P.N. Anantharaman, Surf. Coat. Technol. 28 (1986) 161. [32] M. Noel, P.N. Anantharaman, Analyst 110 (1985) 1095.

[33] L.M. Peter, Surf. Sci. 101 (1980) 162. [34] A. Milchev, Electrocrystallization, Fundamentals of Nucleation and Growth, Kluwer Academic Publishers, Boston/Dordrecht/London, 2002. [35] M.H. Holzle, V. Zwing, D.M. Kolb, Electrochim. Acta 40 (1995) 1237. [36] L.H. Mendoza-Huizar, J. Robles, M. Palomar-Pardave, J. Electroanal. Chem. 521 (2002) 95. [37] M. Miranda-Hernández, I. González, J. Electrochem. Soc. 151 (2004) C220. [38] G. Gunawardena, G. Hills, I. Montenegro, B.R. Scharifker, J. Electroanal. Chem. 138 (1982) 255. [39] A. Milchev, T. Zapryanova, Electrochim. Acta 51 (2006) 2926. [40] M.Y. Abyaneh, A. Tajali Pour, Trans-IMF 72 (1994) 19. [41] M.Y. Abyaneh, V. Sáez, J. González-García, T.J. Mason, Electrochim. Acta 55 (2010) 3572. [42] M. Hyde, O. Klymenko, R.G. Compton, J. Electroanal. Chem. 534 (2002) 13.