Electrodeposition of Zn in acid sulphate solutions: PH effects

Article abstract of DOI:10.1016/j.electacta.2010.12.026

The kinetics of zinc electrodeposition from acid sulphate solution on a platinum electrode was investigated by means of stationary polarization curves, interfacial pH measurement and electrochemical impedance spectroscopy. The effect of pH, namely pH 2, 3 and 4, was analyzed. A significant dependence of Zn electrodeposition with solution pH was verified. The results obtained cannot be predicted by the available models for Zn electrodeposition. A reaction model is then proposed based on the predominant steps as a function of the potential and the electrode surface nature.

Full text of DOI:10.1016/j.electacta.2010.12.026

Electrochimica Acta 56 (2011) 7931–7939
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Electrochimica Acta
journal homepage: www.elsevier.com/locate/electacta
Electrodeposition of Zn in acid sulphate solutions: pH effects
Rycharda C.M. Sallesb, Guilherme C.G. de Oliveirab, Susana L. Díaza,1
,
Oswaldo E. Barciaa,b,1, Oscar R. Mattosa,∗,1
a LNDC - Laboratório de Ensaios Não-Destrutivos, Corrosão e Soldagem, EE/PEMM/COPPE,
Universidade Federal do Rio de Janeiro, UFRJ, Cx. Postal 68505, CEP 21945-970, Rio de Janeiro, RJ, Brazil
b Dep. Físico-Química, IQ/UFRJ, Rio de Janeiro, RJ, Brazil
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 28 July 2010
Received in revised form 6 December 2010
Accepted 8 December 2010
Available online 15 December 2010
The kinetics of zinc electrodeposition from acid sulphate solution on a platinum electrode was inves-
tigated by means of stationary polarization curves, interfacial pH measurement and electrochemical
impedance spectroscopy. The effect of pH, namely pH 2, 3 and 4, was analyzed. A significant dependence
of Zn electrodeposition with solution pH was verified. The results obtained cannot be predicted by the
available models for Zn electrodeposition. A reaction model is then proposed based on the predominant
steps as a function of the potential and the electrode surface nature.
Keywords:
© 2010 Elsevier Ltd. All rights reserved.
Zn electrodeposition
Adsorbed intermediates
Impedance
pH effects
1. Introduction
diluted Zn sulphate solutions. By considering partial dissociation of
Zn sulphate, the authors concluded that their stationary results can
Zinc electrodeposition from different media has been the
subject of numerous investigations. However, despite the great
number of publications on Zn electrodeposition kinetics, this
process is still a matter of discussion, since the agreement
between the experimental data and the available reaction mod-
els is not satisfactory. Different approaches have been associated
with a restricted number of experimental results and, for this
reason, have not been capable to fully predict the kinetic
behaviour of Zn electrodeposition from acid solutions as a function
of pH.
In particular, to explain the multiple steady states and the time
constants observed in the impedance diagrams obtained during Zn
electrodeposition at pH 4.3, not only the adsorbed intermediates
interactions [1,2] but also the nucleation and growth processes that
give rise to surface relaxation [3,4] have been considered. In the first
case, a reaction model proposed by Epelboin et al. [1,2] was based
on the competition between the inhibition of adsorbed H+ and the
autocatalytic discharge of Zn2+ as well as a reversible adsorption of
the anion specific for the electrolyte [1,2]. Later, Zouari and Lapique
[5] tried a simplification of this model to describe their results in
be grossly fitted by a simple two electron transfer. However, they
also recognized that the various physical phenomena involved in
the overall Zn deposition from sulphate medium cannot be ignored.
In the other approach, to characterize the electrode kinetics
as a function of the morphology of Zn deposits, it was suggested
[3,4] that the reactions would occur at specific sites of the elec-
trode surface. Indeed, the inductive feature in the impedance
plots was partially ascribed to the slow formation and removal
of growth kink sites at the electrode surface, which express the
relaxation of the electrode area [3]. However, this consideration
fails in simulating the pH effects on the electrodeposition pro-
cess, especially in what concerns the electrochemical impedance
behaviour.
Trying to overcome the limitations on the pH agreement, in later
works [6–8] it was suggested that the discharge of Zn2+ is inhibited
by the hydrogen adsorption in highly acid sulphate solutions. Zn
electrodeposition was shown to occur when hydrogen evolution is
passivated onto the deposit surface [7]. In this condition, the auto-
catalytic step in the previous model [1,2] was disregarded, being the
strong activation of Zn2+ adsorption with increasing polarization
the main responsible for progressive Zn deposition predominance.
The main restraint to this approach is that it considers a previous
free Zn surface. Ichino et al. [8] also introduced modifications on the
Epelboin et al.’s [3] model to account for the low frequency capac-
itive loop observed at low solution pH. However, they considered
that this feature is partially ascribed to the diffusion of Zn2+ on a
∗
Corresponding author. Tel.: +55 21 2562 8536; fax: +55 21 2290 1544.
E-mail addresses: susana@metalmat.ufrj.br (S.L. Díaz),
omattos@metalmat.ufrj.br (O.R. Mattos).
1
ISE Member.
0013-4686/$ – see front matter © 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.electacta.2010.12.026

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R.C.M. Salles et al. / Electrochimica Acta 56 (2011) 7931–7939
Fig. 2. Steady state cathodic polarization curves of the Pt RDE in both 1 M Na2SO4
(Zn2+-free) (ꢀ) and 1 M ZnSO4·7H2O (᭹) solutions at pH 2.
Fig. 1. Steady state cathodic polarization curves of the Pt RDE in the 1 M ZnSO4·7H2O
solution at pH 2 (ꢀ), 3 (ꢁ) and 4 (ꢀ).
This procedure was carried out to avoid variations on the solution
concentration and pH during the electrochemical measurements.
Cathodic potentiostatic polarization curves and electrochemical
impedance measurements, in both potentiostatic and galvanostatic
modes, were carried out in a conventional three-electrode cell, by
means of a model Asservissement Electronique rotating electrode
device, using a Pt rotating disc electrode (RDE) with 0.2 cm2 as
working electrode. Some experiments were also performed using a
Zn RDE (0.3 cm2). All tests were accomplished at 1000 rpm of elec-
trode rotation speed to assure the absence of mass transport effects.
The counter electrode was a circular Pt grid (300 cm2) and a sat-
urated mercurous sulphate electrode (SSE) (−0.64 V vs SHE) was
used as reference. All the potential values given in this work were
always against SSE. The polarization curves were obtained through
a model PGSTAT30 AUTOLAB electrochemical interface using the
Linear Sweep Polarization Staircase (Stationary Current) method
with 30 mV of potential step. A PG19 OMNIMETRA potentiostat and
a frequency response analyzer SOLARTRON SI1254 coupled with a
PC were used in the impedance measurements. The signals were
filtered by a model VBF-8 KEMO Filter in low-pass mode. In most
of the experiments, the impedance diagrams were obtained in the
frequency interval of 40 kHz to 3 mHz with the amplitude ranging
from 5 to 15 mV, within the linearity range. The polarization curves
were corrected from ohmic drop through the high frequency part
of the electrochemical impedance plots.
For the pH measurements at the electrode/electrolyte inter-
face, a working electrode of the type already proposed was applied
[16,17]. It consisted of a 75 mesh Pt grid (3.5 cm2) held at the end
of a flat-bottomed glass electrode (Orion mod. 8135 BN) using of
a Teflon adaptor. The pH electrode was connected to a pH meter,
thus measuring the pH of the solution retained in the mesh. The
assembled electrode was motionless and the solution was stirred
to guarantee uniform bulk pH, as detailed elsewhere [10]. Under
these conditions, surface pH and current measurements were
recorded simultaneously as the electrode was potentiostatically
polarized.
motionless electrode. Accordingly, the pH effect was not efficiently
addressed.
The model proposed for acid sulphate electrolyte [7] was also
adapted to describe the Zn deposition mechanism in chloride solu-
tion [9], since the deposition mechanism was considered to occur
from Zn2+. By using the same reasoning, a simplified model for a
fixed solution pH was proposed to account for the charge transfer
reactions and the elementary steps of crystal growth.
Although exerting a significant influence on the kinetics of Zn
electrodeposition, the role of simultaneous H+ reduction has gained
little attention and is still poorly understood. Since the interfa-
cial pH changes when the hydrogen reduction occurs, the chemical
equilibrium of the species present in solution is also modified. It was
shown that H+ reduction is inhibited by the presence of Zn2+ ions in
solution [7,10,11]. Van Parys et al. [12] considered that, besides the
deposition of Zn, ZnO is also formed due to a pH shift during Zn elec-
trodeposition from acid sulphate solution. Although not presenting
the corresponding experimental data, the authors stated that a
strong increase on the interfacial pH occurs, giving rise to hydrox-
ilated intermediate species. Other works [13–15] also assume the
same interfacial alkalination effect to describe the nucleation and
growth behaviour during Zn deposition from acid solution.
From the above discussion the elementary steps that take place
during Zn electrodeposition were discretized for the proposition
of reaction models. However, such models still need experimental
validation, particularly with regard to a wide acid pH range. In this
sense, the objective of the present work is to systematically inves-
tigate Zn electrodeposition from acid sulphate solution in a broad
pH range, with special attention to the role of simultaneous H+ dis-
charge. The goal is to provide a deeper insight into the electrode
reaction mechanism, aiming to a more comprehensive model for
Zn electrodeposition.
2. Experimental
The electrolyte used in this work consisted of 1.0 M ZnSO4·7H2O
solution at three different pH values: 2, 3, and 4. Sodium sul-
phate solutions at the same concentration and pH values were also
employed as blank solutions (Zn+2-free). The solutions were pre-
pared from analytic grade chemicals and double distilled water,
without addition of any other substance such as additives, com-
plex agents or supporting electrolyte. The pH adjustment was done
by means of 1.0 M sulphuric acid additions. All experiments were
performed in triplicate, at 25 ◦C and with a large volume of elec-
trolyte (4 l), which was circulated by means of a peristaltic pump.
3. Results
Fig. 1 presents the cathodic polarization curves obtained with Pt
RDE in the 1 M ZnSO4·7H2O solution in three different pH values:
2, 3, and 4. From these curves, two distinct regions can be observed
independently of the pH. In the first one (Part 1), beginning at the
open circuit potential, the curves show a slow variation of current
with cathodic polarization. In this region, the efficiency for metallic
deposition is negligible and the H+ reduction reaction prevails. With
further polarization increase, the current densities show a sudden

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7933
2.3
2.2
2.1
2.0
1.9
(a)
0.002
0.001
0.000
0.0
-0.3
-0.6
-0.9
-1.2
-1.5
-1.8
E vs SSE/V
4.4
4.3
4.2
4.1
4.0
0.0004
0.0002
0.0000
(b)
0.0
-0.3
-0.6
-0.9
-1.2
-1.5
-1.8
E vs SSE/V
Fig. 3. Potential dependency of both interfacial pH (ꢀ) and current (ꢁ) obtained simultaneously in the 1 M ZnSO4·7H2O solution at bulk pH values of: (a) 2 and (b) 4.
raise, which confers an abrupt change in the slope of the curves that
start to vary sharply with cathodic potential (Part 2). High efficient
Zn deposition was detected at this part of the curves for all the pH
values investigated.
With increasing pH, a decrease in current densities at Part 1 of
the curves is verified in Fig. 1. For each pH value, a current max-
imum is also detected in this potential range, which depends on
the solution pH. Indeed, the current maximum is less intense and
shifted to more negative potentials with higher pH, namely −1.20,
−1.26, and −1.34 V for pH 2, 3, and 4, respectively. After the corre-
sponding maximum, all curves present a decrease in current values
before an abrupt increase with polarization. Moreover, Part 2 of
the curves begins at more positive potentials and also positively
shifted with increasing pH. Since high efficient Zn electrodeposi-
tion occurs in this region, this behaviour indicates an activation of
this process with increasing pH. This result is in agreement with
that reported by Epelboin et al. [1,2] for Zn electrodeposition from
sulphate solutions.
Fig. 2 displays the comparative behaviour of cathodic polar-
ization curves obtained in 1.0 M Na2SO4 (Zn2+-free) and 1.0 M
ZnSO4·7H2O solutions at pH 2.0, at the potential range cor-
responding to Part
1 of the curves in Fig. 1. It can be
noted that, for the Zn2+-free solution, the current increases
continuously with cathodic potential. Moreover, for given
a

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Fig. 4. Impedance diagrams obtained in the 1 M ZnSO4·7H2O solution at different pH values: (a) before; (b) during and (c) after the current maximum in the polarization
curves of Fig. 1 (frequencies in Hz).
potential the current values are considerably higher and no
maximum is observed for the Zn2+-free. The same compar-
ative behaviour was observed for all the pH values investi-
gated.
between new adsorbed species and the H+ reduction. After the cur-
rent maxima, diagrams (c), the capacitive loop at lower frequencies
shows a negative polarization resistance (Rp) for the three solution
pH investigated. These results are in conformity with the decrease
in current values, i.e., with the negative slope, namely polarization
resistance, observed in Part 1 of the curves in Fig. 1.
Measurements of the interfacial pH can be used to obtain infor-
mation regarding not only the electrodeposition process itself, but
also the associated interfacial surface chemistry. In this way, Fig. 3
shows the typical potential dependency of both interfacial pH and
current during Zn electrodeposition on a Pt surface from the solu-
tion at pH 2 and 4. For all the pH values investigated, a strong
interface alkalination was observed before the current maximum
at Part I of the curves. This corroborates the idea that hydrogen
evolution prevails in this potential range. With increasing cathodic
polarization, beyond the current maximum, both current and inter-
facial pH drop. At Part 2 of the curves, wherein high efficient Zn
deposition occurs, a less accentuated decrease on the interfacial pH
with increasing potential was verified for all the pH values investi-
gated. No further alkalination was detected in this potential range.
Moreover, no H2 bubbles on the electrode surface were seen dur-
ing Zn electrodeposition. This result is in disagreement with Van
Parys et al. [12] that considered that Zn electrodeposition from acid
sulphate solution occurs by means of a strong interface akalination.
Fig. 4 presents the impedance diagrams obtained in potentio-
static mode at the potential range corresponding to Part 1 of the
polarization curves in Fig. 1. In all diagrams, the capacitive loop at
higher frequencies is associated with the double layer response. For
the three pH values investigated, the diagrams obtained before the
current maxima, diagrams (a), display one capacitive loop in the
low frequency domain, with corresponding characteristic frequen-
cies (the frequency at the maximum) of 0.13, 0.013, and 0.006 Hz
for pH 2, 3 and 4, respectively, in all cases related to the H+ reduc-
tion. With increasing polarization, diagrams (b), at potential values
associated with the current maxima in the curves of Fig. 1, a new
capacitive loop appears at lower frequencies. The large size of
this loop suggests the emergence of a surface competitive process
Representative diagrams obtained in a Zn+2-free solution (1 M
Na2SO4) at pH 2 are shown in Fig. 5. These diagrams were acquired
in potentiostatic mode at the same corresponding potential values
as those for the 1 M ZnSO4·7H2O solution in the same pH value
(Fig. 4). In Fig. 5(a), the diagram shows two capacitive loops (60 and
0.013 Hz) associated respectively with the double layer response
and the H+ reduction as the single cathodic reaction. The similarity
between this diagram and the corresponding one in Fig. 4(a), pH 2,
confirms that the H+ reduction is the major cathodic reaction at this
potential region for the 1 M ZnSO4·7H2O solution. With increasing
potential, however, Fig. 5(b) and (c), the diagrams are qualitatively
the same as the one obtained at lower potential in Fig. 5(a). They
show two capacitive loops: 400 and 0.13 Hz at −1.20 V; and 1500
and 1.3 Hz for −1.40 V; also related respectively to the double layer
response and the H+ reduction process, Given that no competitive
aspect is observed in the Zn2+-free solution, Fig. 5, the results in
Fig. 4 thus reflect the predominance of H+ reduction reaction and
a subsequently competitive effect brought about by an adsorbed
intermediate for Zn electrodeposition.
Fig. 6 presents the impedance diagrams obtained in galvanos-
tatic mode at Part 2 of the polarization curves in Fig. 1 for pH 2,
3 and 4 at three different potential values. For each diagram, the
capacitive loop at high frequencies is related to the charge trans-
fer resistance in parallel with the double layer capacitance. At the
beginning of Part 2, Fig. 6(a–c), the diagrams depict two inductive
loops in the low frequencies domain for all pH values investi-
gated. This behaviour can be associated with Zn2+ reduction as the
main cathodic reaction. With increasing polarization three induc-
tive loops can be seen for pH 2, Fig. 6(d). At even higher polarization,

R.C.M. Salles et al. / Electrochimica Acta 56 (2011) 7931–7939
7935
with increasing pH. The similarity on the behaviour of Part 2 of the
curves for both Pt (Fig. 1) and Zn (Fig. 7) RDE suggests that, at the
beginning of this potential range (current minimum), the Pt RDE is
already covered by a metallic Zn film.
The impedance diagram obtained in galvanostatic mode with
Zn RDE at the marked point (p), which corresponds to the begin-
ning of Part 2 of the polarization curve for pH 2 in Fig. 7, exhibits
two inductive loops in the low frequency domain. This diagram is
comparable to the ones in Fig. 6(a–c), obtained with Pt RDE. This
corroborates the idea of similar surface condition for both Pt and
Zn RDE electrodes in 1 M ZnSO4·7H2O solution at beginning of Part
2 of the respective polarization curves.
4. Discussion
As presented above, independent of the solution pH, two distinct
potential regions in the polarization curves of Fig. 1 were detected
as a function of the cathodic potential. At low polarizations, Part 1,
the efficiency for Zn deposition is very low and the main cathodic
reaction is the H+ reduction on a Pt surface. Only at the end of Part 1,
where the current reaches a minimum, the main cathodic reaction
becomes the Zn2+ reduction. Under this condition, the Pt surface
becomes covered by a metallic Zn film. Subsequently, Zn deposition
occurs with high efficiency on a Zn surface all through the Part 2
of the curves. For simplification and to make easier the discussion,
a reaction model for Zn electrodeposition in acid sulphate solution
on a Pt RDE is proposed as divided into two parts, considering the
two above-mentioned potential regions.
4.1. Part 1
Some aspects related to this potentials region are emphasized
below:
I. Regardless the solution pH, the current maximum at Part 1 of
the polarization curves comes up as a consequence of a competi-
tion between the hydrogen reduction reaction, which prevails
in this potential range, and surface reactions with the partic-
ipation of Zn2+ ions. The absence of current maxima in the
polarization curves obtained in the Zn2+-free solution corrobo-
rates such behaviour.
Fig. 5. Impedance diagrams obtained in the 1 M Na2SO4 (Zn2+-free) solution, pH 2,
at the corresponding potential values of diagrams obtained in 1 M ZnSO4·7H2O, pH
2, in Fig. 4 (frequencies in Hz).
II. In Part 1, there is a current maximum that depends on the pH of
the solution. With increasing pH, the current value associated
with this maximum decreases and is shifted to more negative
potentials.
III. Apart from the bulk solution pH, the interfacial pH increases
up to the current maximum and then starts to decrease. Con-
sequently, the reaction process responsible for the current
decreasing also accounts for the interfacial pH drop up to the
current minimum.
IV. Impedance diagrams taken at the potential range corresponding
to Part 1 of the polarization curves display, besides the capac-
itive loop related to the double layer response, up to two time
constants associated with the formation of two adsorbed inter-
mediates at the electrode surface.
Fig. 6(g), the inductive loop at very low frequencies is replaced by a
capacitive feature that cannot be described by the available models
for Zn electrodeposition [1–8]. For pH 3, Fig. 6(e) and (h), the same
tendency with increasing polarization is observed. However, this
behaviour is slower as a function of the polarization, if compared
to pH 2. Indeed, for pH 2 the capacitive loop is evident in −1.59 V,
whereas, for the same polarization, this feature is not well defined
in pH 3. Moreover, for pH 4, Fig. 6(f) and (i), the diagrams always
exhibit three inductive loops. In view of the trend observed for the
behaviour at pH 2–3, a capacitive loop would also be expected at
higher polarizations.
Fig. 7 displays the cathodic polarization curves obtained with Zn
RDE in 1 M ZnSO4·7H2O solution at pH values of 2, 3 and 4. Similar to
Fig. 1, these curves can be divided in two regions as well. Starting at
the open circuit potential, the curves present a very slow variation
of current with cathodic polarization (Part 1). However, different
from Fig. 1, where the curves were obtained with Pt RDE, no cur-
rent maxima are observed in this potential range for the Zn RDE
electrode (Fig. 7). In addition, no clear pH dependence is observed
in Part 1 of these curves. With further polarization increase, the
curves show the same qualitative behaviour as the corresponding
ones obtained with the Pt RDE (Fig. 1), i.e., a sharp increase of cur-
rent with cathodic potential (Part 2). The pH dependence of Part
2 of the curves in Fig. 7 is also analogous to that verified in Fig. 1,
namely, the curves are shifted towards more positive potentials
To account for these features, the following reaction model can
be considered for Part 1 of the polarization curves in Fig. 1:
K
−1
H+ + e−−→ Hads (ꢀ1 ≡ Hads
)
(1)
(2)
K
−2
H
+ + Hads + e−−→ H2
K
−3
Zn2+ + Hads + H+ + 2e− ꢂ [Zn(I) − H]+ads + H
K
3
(ꢀ2 ≡ [Zn(I) − H]a+ds
)
(3)

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Fig. 6. Impedance diagrams obtained in the 1 M ZnSO4·7H2O solution at different pH values at the indicated potential/current density values (frequencies in Hz).
can be described by the following equation:
K
q
[Zn(I) − H]+ads−→ Zn + H+
(4)
(5)
I
= −K−1[H+](1 − ꢀ1 − ꢀ2) − K−2[H+]ꢀ1 − 2K−3[H+]ꢀ1
+2K3ꢀ2 − 2K−4[OH−]ꢀ2
K
−4
Zn2+ + [Zn(I) − H]a+ds + OH− + 2e−−→ 2Zn + H2O
F
(6)
where ꢀi corresponds to the electrode coverage by the correspond-
ing adsorbed specie i.
Reactions (1) and (2) reflect the H+ reduction with further hydro-
gen evolution on the Pt surface. These steps give an explanation for
the surface alkalination at Part 1 of the curves before the current
maximum, wherein the hydrogen reduction prevails, as shown in
Fig. 3.
With increasing polarization, reaction (3) in the forward direc-
tion becomes significant and, consequently, the [Zn(I) − H]a+ds
intermediate starts to replace Hads at the electrode surface. Indeed,
from this reaction, the formation of [Zn(I) − H]+ads occurs at the
expenses of Hads. Since in this potential region the efficiency for
Zn deposition is very low, the rate of reaction (4) is considered to
be not negligible. This means that the enhancement of ꢀ2 does not
compensate the vanishing of ꢀ1 in terms of current contribution.
As a result, the current starts to decrease with the establishing
of a maximum. The origin of this current maximum is hence a
function of the ꢀ2/ꢀ1 ratio, as will be further discussed in this
work.
As a consequence of reaction (3) in the forward direction,
chemical reaction (4) starts to occur with the decomposition
of [Zn(I) − H]+ads and the formation of H+. This is the reac-
tion that causes the pH decrease from the maximum up to
the current minimum (Fig. 3). At this point, reaction (5) pre-
vails, being responsible for the coverage of the entire surface by
metallic Zn.
Given the above discussion and considering that the Langmuir
isotherm law is valid, wherein ꢀi is a potential and time dependent
parameter, the current associated with the above set of reactions
Fig. 7. Steady state cathodic polarization curves of Zn RDE in the 1 M ZnSO4·7H2O
solution at pH 2 (ꢀ), 3 (ꢁ), 4 (ꢀ) and impedance diagram obtained at marked point
(p) (frequencies in Hz).

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7937
relaxations of Hads and [Zn(I) − H]+ads resulting from the sine per-
turbation of the cathodic potential.
The mass balance leads to:
dꢀ1
ˇ
ˇ
= K−1[H+](1 − ꢀ1 − ꢀ2) − K−2[H+]ꢀ1 − K−3[H+]ꢀ1 + K3ꢀ2 (7)
Before the current maximum, regardless of pH, the impedance
diagrams, Fig. 4(a), show the presence of a capacitive loop at low
frequencies related to the H+ reduction. From the present reaction
dt
dꢀ2
dt
= K−3[H+]ꢀ1 − K3ꢀ2 − K−4[OH−]ꢀ2 − Kqꢀ2
(8)
˜
˜
model, the ꢀ1/E relaxation in Eq. (13) will give rise to a capacitive
At the steady state, ˇdꢀ1/dt = 0 and ˇdꢀ2/dt = 0. Then,
loop if:
−K−1[H+] + K−2[H+] + 2K−3[H+] > 0
−K−1[H+](1 − ꢀ1 − ꢀ2) = − K−2[H+]ꢀ1 − K−3[H+]ꢀ1 + K3ꢀ2
and
(9)
That can also be written as
−2[H+] + 2K−3[H+] > K−1[H+]
(14)
−K−3[H+]ꢀ1 + K3ꢀ2 = − K−4[OH−]ꢀ2 − Kqꢀ2
Replacing Eq. (10) in Eq. (9) results in:
(10)
K
The condition given by Eq. (14) is in accordance with the reac-
tion model proposed for Part 1, once that, at low potentials, the
current is mainly related to K−2. Eq. (14) should be valid for larger
polarizations as well, since the capacitive loop associated with
the ꢀ1/E relaxation is present in the diagrams, Fig. 4(b) and (c).
Indeed, Eq. (14) is also valid after the current maximum up to the
minimum in Part 1 of the polarization curves, in view of the fact
−K−1[H+](1 − ꢀ1 − ꢀ2) = − K−2[H+]ꢀ1 − K−4[OH−]ꢀ2 − Kqꢀ2 (11)
By applying Eqs. (10) and (11) in Eq. (6), the expression for the
steady state current becomes:
˜
˜
I
= −2K−2[H+]ꢀ1 − 5K−4[OH−]ꢀ2 − 3Kqꢀ2
(12)
F
that K prevails in such conditions.The analysis of the capacitive
−3
loop at lower frequencies should comprise the negative polariza-
Since ꢀ1 > > ꢀ2 at the beginning of the polarization curves, from
˜
˜
tion resistance (Rp), verified in Fig. 4(c), in association with ꢀ2/E
relaxation. To justify this behaviour, a very precise mathematical
condition must be established [18–20]. Moreover, the presence
of Rp < 0 in the diagrams of Fig. 4(c) is in agreement with the
current drop due to ␪2, as proposed by the present model for
Part 1.
the open circuit potential up to the current maximum, the only
contribution to the current is given by the term −2K−2[H+]ꢀ1,
that is, by the H+ reduction. From this term, the higher the
pH the lower is the current, as observed from the experimental
results (Fig. 1).
From the current maximum, wherein ꢀ2 appears, the current
turns out to be equivalent to −2K−2[H+]ꢀ1 − 5K−4[OH−]ꢀ2 − 3Kqꢀ2.
This expression comprises the current drop after the current
maximum, also verified in Fig. 1. According to this expres-
sion, the current diminishes with further potential increase since
−5K−4[OH−]ꢀ2 − 3Kqꢀ2 is not able to balance the decrease on the
term −2K−2[H+]ꢀ1. When the current minimum is attained, where
ꢀ2 ꢂ ꢀ1, the current then corresponds to −5K−4[OH−]ꢀ2 − 3Kqꢀ2.
In this condition, it is clear that the polarization corresponding to
the minimum would be lower at higher pH. This fact accounts for
the positive shift of the current minimum experimentally observed
(Fig. 1).
4.2. Part 2
As mentioned before, starting at the current minimum, the
electrode surface is already covered by metallic Zn. Under this con-
dition, the adsorbed species previously formed onto the Pt surface
no longer exists and new intermediates would be formed. This
implies that the reaction mechanism for Part 2 of the curves must
be distinct from that for Part 1. In fact, the reaction model proposed
to Part 1 gives rise to a metallic Zn surface onto the Pt electrode at
the current minimum. Some relevant aspects related to Part 2 of
the curves can be stressed as follows:
As previously discussed, the potential corresponding to the
current maximum observed at Part 1 of the polarization curves
(Fig. 1) is established by the ꢀ2/ꢀ1 ratio. From Eq. (10), it follows
that
I. Starting at the current minimum, the current varies sharply with
cathodic potential. This current minimum, and consequently
Part 2 of the curves, occurs at more positive potentials for higher
pH values. Moreover, for a given potential in this region, the
current increases with increasing pH.
ꢀ2
ꢀ1
K
−3[H+]
=
K3 + K [OH−] + Kq
−4
II. For the three pH values investigated, at the very beginning of
Part 2 of the polarization curves the impedance diagrams show
only two inductive loops, in addition to the capacitive loop
related to the double layer relaxation. With increasing polar-
ization a third inductive loop appears in the low frequency
range. This loop turns into capacitive with further polarization
increase, being this phenomenon highly pH dependent. In fact,
this capacitive loop at high polarizations becomes harder to
observe the higher is the pH.
III. The variation of interfacial pH during Zn electrodeposition in
Part 2 is smaller than in Part 1 (Fig. 3). Therefore, the H+ con-
sumption at the electrode surface is not as important as in
Part 1.
However, since in the current maximum K−4[OH−] is very small,
the above expression reduces to:
ꢀ2
ꢀ1
K
−3[H+]
K3 + Kq
=
Taking this expression into account, a higher pH causes a
decreasing in the ꢀ2/ꢀ1 ratio. This means that a higher polarization
would be required for a proper ꢀ2/ꢀ1 ratio to occur, giving rise to
the current maximum. This fact justifies the shift of current maxi-
mum towards more negative potentials with increasing pH, as seen
in Fig. 1.
From Eq. (6) the faradaic impedance, ZF, can be obtained:
ꢀ
ꢁ ˜
1
ZF
1
Rt
ꢀ1
=
− F −K−1[H+] + K−2[H+] + 2K−3[H+]
According to these facts, the following reaction model is pro-
posed to Part 2 of the polarization curves:
˜
E
ꢀ
ꢁ ˜
K
ꢀ2
−1
−F −K−1[H+] − K3 + 2K−4[OH−]
(13)
Zn2+ + H2O + e− ꢂ [Zn(I) − H2O]+
(ꢀ3 ≡ [Zn(I) − H2O]+
)
ads
(15)
ads
˜
E
K
1
where Rt is the charge transfer resistance, F is the Faraday’s con-
stant, ꢀ1/E and ꢀ2/E represent the respective surface concentration
K
−2
Zn2+ + [Zn(I) − H2O]+ + 2e−−→ [Zn(I) − H2O]+ads + Zn
(16)
˜
˜
˜
˜
ads

7938
R.C.M. Salles et al. / Electrochimica Acta 56 (2011) 7931–7939
−5[H+]ꢀ4 − K−6[H+]ꢀ5 = 0
(27)
(28)
K
−3
K
Zn2+ + [Zn(I) − H2O]a+ds + SO42− + 2e− ꢂ [Zn(I) − OH]+ads + Zn
K
3
By applying Eq. (25) in Eq. (26), it follows
+ HSO−2 (ꢀ4 ≡ [Zn(I) − OH]+
)
(17)
(18)
ads
K−1(1 − ꢀ3 − ꢀ4 − ꢀ5) − K1ꢀ3 = 0
Eqs. (26) and (28) show that, at the steady state, the reactions
K
(15) and (17) are in equilibrium. By applying Eqs. (26)–(28) in Eq.
(21), the stationary current is given by:
−4
Zn2+ + [Zn(I) − OH]a+ds + 2e−−→ [Zn(I) − OH]+ads + Zn
I
K
= − 2K−2ꢀ3 − 2K−4ꢀ4 − 2K−6[H+]ꢀ5
(29)
−5
H
+ + [Zn(I) − OH]a+ds + e− −→ Hads + [Zn(I) − OH]+
ads
F
(ꢀ5
≡
Hads
)
(19)
(20)
According to the interfacial pH measurements that show a small
variation in Part 2 (Fig. 3) irrespective of the bulk pH, ꢀ5 will always
be smaller if compared with ꢀ3 and ꢀ4. Therefore, regardless of
the bulk pH, the partial current term −2K−6[H+]ꢀ5 will always
be smaller if compared with −2K−2ꢀ3 − 2K−4ꢀ4. Thus, the current
given by Eq. (29) is mainly associated with the first two terms. In
this way, the current increases with increasing pH since, according
to reactions (15) and (17), ꢀ3 and ꢀ4 increase with increasing pH.
This is in conformity with the experimental data in Figs. 1 and 7
related to Part 2 of the polarization curves.
K
−6
H
+ + Hads + e−−→ H2
where ꢀi corresponds to the electrode coverage by the correspond-
ing adsorbed specie i.
Reaction (15) shows the formation of the initial adsorbed
intermediate [Zn(I) − H2O]+ on a Zn surface. Subsequently, this
ads
intermediate participates in the formation of metallic Zn through
the autocatalytic reaction (16). The [Zn(I) − H2O]+ also produces
From Eq. (21), the expression for the faradaic impedance, ZF, is
given by:
ads
the [Zn(I) − OH]+ads species via reaction (17), which participates in
an autocatalytic reduction of Zn2+ to metallic Zn in reaction (18).
The two inductive loops in the low frequency range exhibited in
Fig. 6(a)–(c) and 7(p) are related to the relaxation of these species.
Reactions (15)–(18) are primarily responsible for the current
rise in Part 2 and accounts for the higher currents verified with
increasing pH in this potential region. According to the equilibrium
HSO−4 ↔ H+ + SO24−, the higher the pH, the higher is the sulphate
concentration. Thus, the higher the pH, the greater [Zn(I) − OH]a+ds
and, as a consequence, the faster reaction (18) will be.
ꢀ
ꢁ ˜
1
ZF
1
Rt
ꢀ3
=
− F −K−1 − K1 + K−2 + 2K−3[SO2−
]
4
˜
E
ꢀ
ꢁ ˜
ꢀ4
−F −K−1 − 2K3[HSO−] + 2K−4 + K
−5
4
˜
E
ꢀ
ꢁ ˜
ꢀ5
−F −K−1 + K6[H+]
(30)
˜
E
˜
˜
˜
˜
˜
˜
where Rt is the charge transfer resistance and ꢀ3/E, ꢀ4/E, and ꢀ5/E
are the respective relaxations of surface+concentrations of the inter-
mediates [Zn(I) − H2O]+ads, [Zn(I) − OH]ads and Hads, resulting from
the sine perturbation of the cathodic potential.
The formation of Hads is responsible for the emergence of the
inductive loop at lower frequencies. This intermediate is produced
via step (19) and is catalyzed by the species [Zn(I) − OH]+ads. Hence,
the higher the surface concentration of this species, the lower the
cathodic polarization for the Hads formation will be, with the con-
sequent appearance of the third inductive loop, as shown in Fig. 6.
The rate of reaction (20) decreases with increasing pH. There-
fore, the higher the pH, the larger the cathodic polarization in which
To justify the experimental electrochemical impedance results
˜
˜
˜
˜
shown in Fig. 6, the relaxation of both ꢀ3/E and ꢀ4/E should pro-
vide inductive loops in the whole polarization range investigated.
˜
˜
On the other hand, ꢀ5/E relaxation should originate an inductive
loop, which turns into capacitive at high polarizations. In view
of Eq (30), to oblige this to occur, the following assumptions are
K
−6
becomes higher than K−5. Under this condition, the inductive
loop at lower frequency turns into a capacitive one, as will be dis-
cussed later.
˜
˜
required:for ꢀ3/E
Considering that the Langmuir isotherm is valid and that ꢀi is
a potential and time dependent parameter, the current and mass
balance associated with the set of reactions (15)–(20) are given by:
−K − K1 + K + 2K−3[SO2−] < 0 or K + K1 > K + 2K−3[SO2−
]
4
(31)
(32)
−1
−2
−1
−2
4
˜
˜
for ␪4/E
−K1 − 2K3[HSO−] + 2K + K < 0 or K + 2K3[HSO−] > 2K + K
I
−4
−5
−1
−4
−5
= − K−1(1 − ꢀ3 − ꢀ4 − ꢀ5) + K1ꢀ3 − 2K−2ꢀ3 − 2K−3[SO2−]ꢀ3
4
4
4
F
˜
˜
for ꢀ5/E
+2K3[HSO−]ꢀ4 − 2K−4ꢀ4 − K−5[H+]ꢀ4 − K−6[H+]ꢀ5
(21)
−K−1 + K6[H+] < 0 or K6[H+] < K
(33)
4
−1
and
Reaction (15) in the forward direction (K
)
produces
−1
[Zn(I) − H2O]+ads, which gives rise to two other intermediates,
dꢀ3
ˇ
= K−1(1 − ꢀ3 − ꢀ4 − ꢀ5) − K1ꢀ3 − K−3[SO2−]ꢀ3 + K3[HSO−]ꢀ4
4
4
[Zn(I) − OH]+ads and Hads. To satisfy this condition, K has to be
dt
−1
(22)
higher than K over the entire potential range. This fact confirms
−3
that the assumption of Eq (31) is in agreement with the proposed
model for Part 2.
dꢀ4
dt
= K−3[SO2−]ꢀ3 − K3[HSO−]ꢀ4
(23)
(24)
The value of K is not high enough during the whole polar-
ˇ
ˇ
−5
4
4
ization range associated with Part 2 since, according to Fig. 3, the
variation of the interfacial pH is small in this region. Moreover, tak-
dꢀ5
dt
= K−5[H+]ꢀ4 − K−6[H+]ꢀ5
ing into account that K is the rate of the autocatalytic step (18)
−4
for Zn metallic formation, it is reasonable to consider that, based on
the proposed model for Part 2, the condition imposed by Eq. (32) is
valid over this entire potential range.
At the steady state, ˇ dꢀ = ˇ dꢀ = ˇ dꢀ = 0, then Eqs. (22)–(24)
3
dt
4
dt
5
dt
can be written as
−1(1 − ꢀ3 − ꢀ4 − ꢀ5) − K1ꢀ3 = K−3[SO2−]ꢀ3 − K3[HSO−]ꢀ4
−3[SO2−]ꢀ3 − K3[HSO−]ꢀ4 = 0
(25)
(26)
The condition in Eq. (33) involves the term −K−1 + K6[H+], whose
signal depends on the polarization. At the beginning of Part 2, this
term is negative, given that K6[H+] < K−1. In this case, the relaxation
K
4
4
K
4
4

R.C.M. Salles et al. / Electrochimica Acta 56 (2011) 7931–7939
7939
˜
˜
Three adsorbed intermediates onto a metallic Zn surface exist
at Part 2 of the polarization curves. These species are distinct from
those at Part 1, which are adsorbed on the Pt surface.
The proposed reaction model indicates that the relative rate of
formation and the surface concentration of the different interme-
diates depend on the solution pH, electrode potential and surface
nature.
ꢀ5/E will originate an inductive loop. With increasing cathodic
polarization, K increases progressively in such a way that, at
−6
a particular potential, K6[H+] > K−1 > 0. In this circumstance, the
˜
˜
ꢀ5/E relaxation generates a capacitive loop. Thus, the conversion
of the inductive loop at lower frequencies into a capacitive one,
as seen in Fig. 6, is associated with the changing of K6[H+] < K to
−1
K6[H+] > K−1. Taking into account that the H+ concentration favours
the condition K6[H+] > K−1, the higher the pH, the higher should be
the cathodic polarization for this transformation to occur, as dis-
cussed earlier in this article and verified in the experimental plots
in Fig. 6.
Acknowledgements
The authors are grateful to the support given by the Brazilian
agencies: CNPq, FAPERJ, CAPES, FINEP and FUJB.
5. Conclusions
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