Growth of passive layers on nickel during their voltammetric anodic dissolution in a weakly acid medium

Article abstract of DOI:10.1016/j.electacta.2006.05.051

Quartz crystal microbalance in combination with voltammetry has been used for studying the electrochemical oxidation behaviour of a nickel deposit in a weakly acid medium. The instantaneous mass/charge ratio (Fdm/dQ) analysis allows to obtain the fraction of charge consumed in the passivation process, and, that way, the experimental kinetic equation of the passive layer growth. This experimental law has been fitted to the theoretical equation derived from the point defect model theory under voltammetric conditions.

Full text of DOI:10.1016/j.electacta.2006.05.051

Electrochimica Acta 52 (2006) 658–664
Growth of passive layers on nickel during their voltammetric anodic
dissolution in a weakly acid medium
1
∗,1
Joan Gregori, Jose Juan Garc ´ı a-Jare n˜ o , D. Gim e´ nez-Romero, Francisco Vicente
Department of Physical Chemistry, University of Valencia, C/Dr. Moliner 50, 46100 Burjassot, Spain
Received 27 March 2006; received in revised form 30 May 2006; accepted 31 May 2006
Available online 10 July 2006
Abstract
Quartz crystal microbalance in combination with voltammetry has been used for studying the electrochemical oxidation behaviour of a nickel
deposit in a weakly acid medium. The instantaneous mass/charge ratio (Fdm/dQ) analysis allows to obtain the fraction of charge consumed in
the passivation process, and, that way, the experimental kinetic equation of the passive layer growth. This experimental law has been fitted to the
theoretical equation derived from the point defect model theory under voltammetric conditions.
©
2006 Elsevier Ltd. All rights reserved.
Keywords: EQCM; Instantaneous mass charge analysis; Point defect model
1
. Introduction
point defect model (PDM) theory [17–19] as follows:
ꢀ
k
1
χ
−
Nickel is a very important element from a technological
m + V −→ MM + vm + χe
(1)
(2)
(3)
M
point of view. It takes part in many alloys thus increasing their
corrosion resistance [1–3]. This is because nickel has been
the subject of many researches related with dissolution and
passivation mechanisms in acid and basic medium by means
of different electrochemical techniques [4–12]. However, sev-
eral points are yet unclear because of the strong tendency for
self-passivation of nickel and, that way, the process of active
dissolution, passive layer formation and chemical dissolution
cannot be well separated in the obtained experimental results.
This tendency should prove more pronounced in weakly acid
or alkaline media [10–12] and is drastically affected to a great
extent by the anions [13] and other experimental conditions
6,7]. Passive layers on nickel have a great importance because
of their use in rechargeable alkaline batteries [14], cathodes
in fuel cells [15] and electrocatalysts for oxygen evolution
16].
When a passive layer completely covers all the electrode
surface, the processes which take place at the metal/passive
layer/solution interfaces can be schematized, according to the
k3
χꢀ
MM−→ M (aq) + VM + (δ − χ)e−
δ+
ꢀ ꢁ
k2
χ
m−→ MM +
V
2− + vm + χe−
O
2
k4
+
V
2− + H2O−→ OO + 2H
(4)
(5)
O
k5
χ
MOχ/2 + χH −→ M + 2 H2O + (δ − χ)e−
+
δ+
k6
χ+
m−→ M + vm + χe−
(6)
(7)
i
χ+ k7
M
i
−→ Mδ+(aq) + (δ − χ)e−
[
where the symbols are defined as follows: m (metal atom),
χ+
Mi (metal cation interstitial), OO (oxygen anion in anion site),
M (aq) (metal cation in solution), vm (vacancy in metal phase),
[
ꢀ
δ
ꢀ
χ
2−
MM (metal cation in cation site), VM (cation vacancy) and VO
anion vacancy). In the case of nickel χ = 2 and δ = 2. Eqs. (1)
(
and (2) are responsible for metal electrodissolution, whereas
Eqs. (3) and (4) are responsible for metal passivation (passive
film growth) when the electrode surface is fully covered by a
passive film [18,19]. Processes (1), (3) and (6) take place at the
metal/film interface, whereas processes (2), (4), (5), and (7) take
∗
Corresponding author.
E-mail address: Francisco.Vicente@uv.es (F. Vicente).
ISE members.
1
0
013-4686/$ – see front matter © 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.electacta.2006.05.051

J. Gregori et al. / Electrochimica Acta 52 (2006) 658–664
659
place at the passive film/solution interface. The global process,
which leads to the passive film growth can be schematized as
follows:
electrode. A platinum grid was used as an auxiliary elec-
trode. Solutions were prepared from Na2SO4 (Sigma, reagent
grade), H3BO3 (R.P. Normapur, reagent grade), NH4Cl (Pan-
reac, reagent grade), with double deionised water (MilliQ).
For EQCM experiments the working electrodes (supplied
by Matel–Fordahl) were made from a quartz sheet embedded
between two pieces of gold connected to a resonance circuit.
The resonance frequency of the quartz at air was 6 MHz. One
of the pieces of gold serves as an electrical surface in con-
+
−
(
2/χ)m + H2O → [(2/χ)MM + OO] + 2H + 2e
(8)
For example, in the case of the formation of nickel hydroxide,
Eq. (8) can be written the following way:
+
−
Ni + 2H2O → [Ni + 2OHOH] + 2H + 2e
(9)
Ni
2
tact with the electrolyte. The electrical area was 0.234 cm and
or, for the formation of nickel oxide:
2
the effective mass area was 0.196 cm . The microbalance was
+
−
Ni + H2O → [Ni + OO] + 2H + 2e
(10)
Ni
an UPR15/RT0100 (UPR of the CNRS). The resonance fre-
quency of quartz was measured with a Fluke PM6685. The
current in the auxiliary electrode was measured with a Keith-
ley PM2000 multimeter. The potential was applied with a 263A
EG&G PAR Potentiostat. The whole system was controlled by a
GPIB board. The EQCM was calibrated by means of a galvano-
static Cu deposition [40]. The experimental Sauerbrey constant
In the first case (Eq. (9)) the passive layer contains water
molecules and interacts almost with two water molecules at
the passive film/solution interface, whereas in the second one
(
Eq. (10)) only one water molecule interacts at the passive
film/solution interface.
In the case of passive layers on nickel, metal interstitials do
not play a significant role, and consequently Eqs. (6) and (7)
can be disregarded [18,19]. Eq. (5) represents the chemical dis-
solution of the passive layer. A steady-state for film growth is
reached when the rate of two non-conservative processes, Eqs.
7
−1
was 9.50 × 10 Hz g
.
Nickel electrodeposits on the microbalance electrodes were
obtained by means of a potentiostatic method in a 0.245 M
K2SO4 (Probus, reagent grade), 0.005 M H2SO4 (Merk, reagent
grade) and 0.001 M NiSO4·6H2O (Scharlau, reagent grade)
solution prepared with double deionised water (MilliQ). In
this case, pH 2.7 and the temperature cell was T = 298 K. The
reference electrode used in the electrodeposition process was
an SSE electrode (Saturate Sulphate Electrode). A potential
E = −1450 mV (versus SSE) was applied for 5 min. This pro-
cess was repeated several times at the same potential, and finally,
the calculated mass density for the nickel deposit on the elec-
(
5) and (8), are equal [19].
In recent years the use of the mass/charge ratio in the analy-
sis of the electrochemical quartz crystal microbalance (EQCM)
experimental results has proved very useful in the field of film
modified electrodes [20–29] and metal electrodissolution pro-
cesses [30–33], when the relation between the changes in the
resonance frequency of quartz and mass changes on the elec-
trode surface follows the Sauerbrey equation [34]. Instantaneous
mass charge/ratio (Fdm/dQ function) [31] is defined as
−
2
trode surface was about 23.7 ␮g cm . From this value and the
nickel density value, the nickel deposit thickness can be esti-
mated, δ = 0.027 ␮m. This thickness is small enough and then
no non-ideal contributions are expected and Sauerbrey equation
applies [34,40]. The surface of nickel deposits obtained by this
procedure shows a well homogeneous aspect when observed by
SEM.
ꢂ
dm
dQ
MWi
ni
F
=
γi ± contribution of mass changes due to
(11)
i
uncharged species
where MWi is the molecular mass of i species, which inter-
changes ni electrons, γi the charge ratio due to the i process
and F is the Faraday constant.
The voltammetric sweep was carried out in the [−500,
500] mV (versus Ag/AgCl/KCl (sat.)) potential interval at
20 mV/s. The electrolyte was bubbled for 5 min with Ar (Air
Liquide) so as to remove the dissolved oxygen before the elec-
trochemical experiment, and all the measurements were made
under inert atmosphere and at constant and controlled tempera-
ture T = 298 K.
The applicability of Fdm/dQ analysis according to Eq. (11)
is based on the assumption that all electrogenerated films are
perfectly rigid, and therefore all changes of the resonant fre-
quency are due to mass changes of the films. For thin films
(thickness δ < 0.1 ␮m) Sauerbrey equation [34] can be used
without limitation coming from viscoelastic properties of the
film [41,42] or other non-ideal contributions, which could
cause frequency shifts, like roughness [43]. In all cases films
were thin enough (less than 0.1 ␮m) and then no non-ideal
contributions are expected and Sauerbrey equation becomes
applicable.
Recent works of Landolt and co-workers used EQCM mea-
surements in the study of passivation as well as passive state of
valve metals [35–37]. In these works, an interesting procedure is
developed for obtaining the passive film growth fraction, that is
to say, the charge fraction used in the passive film growth [35].
Instantaneous mass/charge analysis proved useful in the char-
acterization of the passive layer growth of Ni(OH)2 generated at
constant potential in a weakly acid sulphate medium [38]. This
work is focused on the study of the usefulness of Fdm/dQ func-
tion during the active/passive transition observed on the anodic
scan of cyclic voltammograms [39].
2
. Experimental procedure
All the experiments were carried out in a typical three
electrodes cell under these conditions: 0.32 M H3BO3, 0.26 M
NH4Cl, 1.33 M Na2SO4, pH 5.1 and T = 298 K. The poten-
tial was measured versus the Ag/AgCl/KCl (sat.) reference
Fortheimpedancemeasurementsthepotentialwascontrolled
by means of a 273A EG&G PAR Potentiostat–Galvanostat and

6
60
J. Gregori et al. / Electrochimica Acta 52 (2006) 658–664
the impedance spectra was recorded with the help of a 5210
EG&G PAR Lock-in Amplifier. The working electrodes were
made from a nickel sheet (99.9%, Johnson&Matthey). The
2
geometrical area was 0.25 cm . The impedance spectra were
recorded at different stabilization potentials, E0, in the [−0.125,
0
] V potential range (versus Ag/AgCl/KCl (sat.)). The stabiliza-
tion potential E0 (versus Ag/AgCl/KCl (sat.)) was applied for
min before recording the impedance spectrum. The impedance
5
4
−2
measurements were carried out from 10 to 5 × 10 Hz fre-
quency range and the amplitude of the harmonic potential per-
turbation was 5 mV r.m.s. The impedance measurements from
1
0 kHz to 5 Hz were performed in a single-sine type of experi-
ment, and from 5 Hz to 50 mHz in a multi-sine type experiment.
The fitting of the experimental impedance data to the proposed
equivalent circuit was carried out by means of a non-linear
least squares procedure based on the Marquardt algorithm for
function optimisation [44,45]. According to Boukamp [46], fol-
lowing the idea of “measurement models” of Agarval et al.
Fig. 1. Voltammogram (solid line) and mass variations during the voltammetric
cyle for a nickel deposit. [−500, 500] mV, scan rate 20 mV/s, 0.32 M H3BO3,
[
47], the condition sufficient for immittance data to be valid and
0.26 M NH4Cl, 1.33 M Na2SO4, pH 5.1, T = 298 K.
KKT (Kramers Kronig transformation) transformable is their
compliance with any passive equivalent circuit used as a mea-
surement model. The equivalent circuit used for this purpose
is nothing more than a number of adjustable real parameters,
which do not have any direct physical meaning. The measure-
ment model involves as many R and C elements as needed to
get a close enough fit of relevant linear function to experimental
data. No restriction is imposed on signs of Ri and Ci param-
eters, except that their products, or time constants τi = RiCi,
should be real and positive numbers [46–48]. In this case, two
parallel R#C combinations are sufficient for obtaining a very
good fitting of the measured impedance spectra. The addition
of more time constants does not appreciably improve the fit-
ting. Two time constants can be well defined in the obtained
impedance results [47]. This shows the compliance of the mea-
sured impedance spectra with the constraints of the linear system
theory [48].
potentiostatic transient [38], since Eq. (5) will not be considered
−1
from now on, since, by considering a scan rate of 20 mV s
,
passive layer chemical dissolution will not have any influence
in the explored potential interval.
In order to check the relative contribution of both nickel
electrodissolution/nickel passivation to the overall anodic pro-
cess at each applied potential the analysis of the instantaneous
mass/charge ratio, Fdm/dQ function, as defined in Eq. (11), was
performed in the potential interval [−0.05, 0.5] V.
Calculated Fdm/dQ values are represented in Fig. 2 as a
function of the electrode potential between 0 and 0.5 V. In this
potential range the signal to noise ratio is high enough to make
Fdm/dQ values affected by a low uncertainty. The experimental
−2
calculated values show variations between −12 and −17 g cm
at all the explored potential range.
3
. EQCM measurements
Mass changes were followed on a nickel deposit in a voltam-
−1
metry experiment at an scan rate of 20 mV s , as represented
in Fig. 1.
Between −0.05 and 0.5 V measured mass loss is
−
2
ꢀ
ꢀ
m = −1.49 ␮g cm , and the calculated anodic charge is
2
−
Q = 9.5 mC cm . Thisanodicchargewascalculatedbymeans
of the integration of the intensity curve between −0.2 and 0.5 V.
This potential range included anodic peak I which is associated
to nickel oxidation. From these values, the averaged mass/charge
−
1
ratio could be calculated as Fꢀm/ꢀQ = −15 g mol . Based
on previous results obtained by other workers [49–51], this
value is consistent with a simultaneous nickel electrodissolu-
tion/nickel passivation taking place at the explored potential
interval. According to our previous obtained results, chemical
dissolution of the electrogenerated passive layer does not play
a significant role in these experimental conditions [33]. More-
over, according to our recent results in a similar pH, passive layer
chemical dissolution begins to become important after 30 s of a
Fig. 2. Voltammogram (solid line) and instantaneous mass/charge ratio function
circles) during the anodic scan for a nickel deposit. [−500, 500] mV, scan rate
20 mV/s, 0.32 M H3BO3, 0.26 M NH4Cl, 1.33 M Na2SO4, pH 5.1, T = 298 K.
(

J. Gregori et al. / Electrochimica Acta 52 (2006) 658–664
661
For the analysis of the Fdm/dQ behaviour it is considered that
for the electrodissolution process:
Ni → Niaq + + 2e−,
2
Fdm/dQ|diss = −29 g mol−1 (12)
Obviously, anions present in the solution may participate during
the electrodissolution process, but taking into account that there
is an adsorption followed by a desorption process, their influ-
ence may be neglected in the Fdm/dQ function if these processes
take place fast enough. On the other hand, according to recent
spectroscopic and electrochemical measurements, it can be con-
sidered that at the early stages of nickel passivation the passive
layer is mainly formed by Ni(OH)2, without any other anion
incorporation in the passive film structure [51,52]. When time
elapses, i.e. for successive voltammetric cycles, a bilayer struc-
ture is developed for the passive layer consisting in an inner more
crystalline layer and an outer more amorphous one [18,19,33].
Then, the passivation process may be written such as
Fig. 3. Total intensity current (solid line), intensity current due to passivation
process (dashed line) and layer thickness variation curves during the anodic scan
for a nickel deposit. Same experimental conditions as in Fig. 1.
−
−
Ni + 2OH → Ni(OH)2 + 2e ,
−
1
Fdm/dQ|pass = 17 g mol
(13)
According with the results represented in Fig. 2, nickel
deposit becomes readily passive in these experimental condi-
tions. Moreover, according with the results presented in Fig. 3,
passive layer thickness at E = 0 mV is about 0.6 nm. Consider-
ing that for crystalline nickel hydroxide the distance between
monolayers is about 0.3 nm [51], then, at E = 0 V approximately
two monolayers of Ni(OH)2 are electrogenerated, if the passive
layer generated during the first anodic scan is mainly formed
by Ni(OH)2 and a bilayer structure is not formed (as occurs
for greater times of anodic polarization [33]). This implies that
all the electrode surface is covered by a passive layer at the
beginning of the anodic peak, and, consequently, the PDM is
applicable. From a general point of view, the point defect model
theory is applicable for metal surfaces fully covered by a passive
layer, independently of their composition (oxide or hydroxide),
when the inherent hypothesis of the theory are fulfilled [19],
as discussed below. Within this context, Eq. (12) represents the
global process, which leads to nickel dissolution according to
Eqs. (1) and (2), whereas Eq. (13) represents the global process
which leads to nickel passivation according to Eqs. (3) and (4),
or Eq. (8), within the framework of the PDM.
This Eq. (13) is equivalent to Eq. (8) when written for the case of
the formation of nickel hydroxide, as indicated in Eq. (9).Then,
in this case:
Fdm/dQ|exp = −29γ1 + 17γ2
γ1 + γ2 = 1
(14)
(15)
where γ1 and γ2 are the charge fractions due to reactions (12)
and (13), respectively. γ2 values define the growth fraction as
defined by Landolt and co-workers [35–37] as the fraction of
charge consumed in passive layer thickening. γ2 can be calcu-
lated by solving the system of equation defined by (14) and (15).
This allows to calculate the current component exclusively due
to passivation process as i2 = iγ2. γ2 obtained values are between
0
.38 and 0.28. Therefore, only a minor part of the total current
leads to passive layer formation as observed in other experimen-
tal conditions [38,49,50]. The fact that only a minor part of the
total current leads to passive layer formation is in agreement
with the fact that the main charge carriers within passive layers
on nickel are cation vacancies (see Eqs. (1) and (2)) [53]. This
is because passive layers on nickel show p-type semiconductor
behaviour in passivity potential range [53].
i2 values are represented in Fig. 3 together with the total
measured current, i, for comparison. That way, by considering
valid the above hypotheses, the kinetics of the passive layer
growth can be really followed. In Fig. 3 the passive layer thick-
ness is also represented as a function of the applied potential.
4. Discussion
According to the PDM theory, the current consumed in pas-
sive film growth can be expressed as [18,35]:
i2 = i02eb2(E−εδ)
(16)
Passive layer thickness, δ, is calculated as δ = ꢀQpassV , where
f
−
4
3
−1
V = 1.848 × 10 cm C is the volume per unit charge for
For obtaining a theoretical expression for the passive layer
thickness evolution with the applied potential several hypothe-
sis, consistent with the PDM, are made. First, it is considered
that the electric field ε remains constant within the passive layer
almost in the rising part of the anodic peak for i2 in Fig. 3.
It is also considered that the potential drop variations at the
film/solution interface can be disregarded when they are com-
pared with potential drops at the metal/film and within the film
f
the Ni(OH)2 [11,54], and ꢀQpass calculated as ꢀQ2pass(t) =
ꢃ
t
i2 dt is the charge consumed in the passivation process from
t=0
t = 0 until each measured time, t. Initially, a non-linear and quick
increase in thickness was observed followed by a linear variation
region in passivity potential range. An inflexion point is defined
at E = 0.068 V, which corresponds to the peak potential for i2
values.

6
62
J. Gregori et al. / Electrochimica Acta 52 (2006) 658–664
and 0.4 V), where the intensity current i2 is quite potential inde-
pendent (see Fig. 3). Then Eqs. (16) and (17) imply that the
passive layer thickness is proportional to the applied potential.
This linear relationship is also represented in Fig. 4. Conse-
quently, in this potential range the calculated electric field is
6
−1
ε = 1.6 × 10 V cm . Then, the electric field does not remain
constant within the passive layer during a voltammetric experi-
ment. This electric field variation has been already observed at
more basic pH [11], and it is produced at the potential range
of negative slope of the voltammetric peak for i2 in Fig. 3.
Therefore, the ε variation is the cause for the deviation between
experimental and theoretical growth behaviour for the passive
layer under voltammetric conditions, since the hypothesis of ε
constant inherent to the PDM is no longer fulfilled. According
to previously published results, the ε variation is produced by
changes in the crystalline structure of the passive layer, which
becomes more protective with potential [11]. This more protec-
tive character implies a decrease in the slope of mass loss, as
can be seen in Fig. 1. However, this increase in the electric field
value causes a change in γ1 (charge fraction associated to nickel
electrodissolution process) and γ2 (charge fraction associated to
passive film growth) values, as can be deduced from Fig. 2. It
is observed in Fig. 2 that γ1 values increase (Fdm/dQ evolves
Fig. 4. Experimental (circles) and fitted curves (solid lines) for the passive layer
thickness variation. Same experimental conditions as in Fig. 1.
[
18,35,38]. In a voltammetry experiment E = E0i + νt, where ν is
−
1
form −12 to −17 g mol ) during the potential range of nega-
tive slope of the voltammetric peak I. This increase can be due to
an enhanced metal vacancies migration due to higher ε values.
This enhanced metal vacancy migration could be the origin of
the anodic shoulder defined between 0.15 and 0.25 V in Fig. 1,
since this anodic shoulder does not appear in i2 values poten-
tial evolution in Fig. 3. This enhanced metal vacancy migration
has associated another interesting effect: an increase in vacancy
recombination, which implies a greater degree of crystalline
structure of the electrogenerated passive layer enhancing the
passivation efficiency, in accordance with previous works [11].
According to the above discussion, nickel surface becomes
readily covered by a 3D passive layer in a weakly acid medium
under voltammetric conditions. In the following it is discussed
if the same is true under impedance measurements experimen-
tal conditions for a polycrystalline nickel electrode. It must to
be considered in the following that the impedance study has
been performed for a metallic nickel electrode, whereas the
above discussed voltammetric and EQCM results concerned a
nickel deposit. In Fig. 5 the anodic scan of the cyclic voltammo-
the scan rate and E0i represents the initial potential. Moreover
the film growth layer law is [35,55]:
dδ
=
K
film
i2
(17)
dt
where Kfilm is defined as Kfilm = Vfilm/(nF), and Vfilm is the
molar volume of the film. If we consider that the passive film
3
−1
is formed by Ni(OH)2 then V
= 36 cm mol [10], and
Ni(OH)
2
−
4
3
−1 −1 −1
A s . FromEqs. (16)and(17),
Kfilm = 1.9 × 10 cm mol
the following differential equation is obtained:
dδ
dt
dδ
→ e−
b2(E0i+νt−εδ)
Kfilmi02e
= Kfilmi02eb2(E0i+νt) dt
=
b2εδ
(18)
and if it is considered that at the potential E0i = −0.1 V, the initial
film thickness is δ0 = 0 nm, the integration of Eq. (18) leads to
ꢄ
ꢅ
1
K
i02ε
film
2 0
b E
δ =
ln
(e
− 0.14) + 1
(19)
εb2
ν
−1
The experimental passive layer thickness variation with the
applied potential has been fitted to the theoretical curve defined
by Eq. (19) and the result of the fitting is represented in Fig. 4.
To do this, several initial b2 values are fixed and proved, find-
gram recorded at a low scan rate of 0.5 mV s for a polycrys-
talline nickel electrode is represented. Anodic peak I marks the
active/passive transition of the nickel surface, but in passivity
potential range II, an upper rise in current is clearly observed.
The presence of chloride ions in the acid medium causes a local
attack of the electrogenerated passive layer and an enhanced
metal electrodissolution is produced [13]. After a complete cycle
in these experimental conditions pitting on electrode surface is
clearly observed.
−
1
ing the best fit for b2 = 20 V . This value is in good agreement
with the previously obtained one during nickel deposit potentio-
static passivation [38]. From this fitting procedure the following
5
−1
values for the electric field ε is obtained: ε = 2 × 10 V cm . As
can be seen in Fig. 4 there is a good agreement between experi-
mental and theoretical curves until the inflexion point in Fig. 3
Severalimpedancespectrahavebeenrecordedatstabilization
potentials located in the descending part of the anodic peak I in
Fig. 5, as are represented in Fig. 6.
(
or Fig. 4) at E = 0.068 V is reached. From this inflexion point
Eq. (19) cannot reproduce the experimental curve.
As mentioned above, there is a linear variation of the pas-
sive layer thickness in passivity potential range (between 0.2
In Table 1 intensities values, which correspond at each stabi-
lization potential are listed as a function of the applied potential.

J. Gregori et al. / Electrochimica Acta 52 (2006) 658–664
663
A progressive increase in the low frequency limit of the mea-
sured impedance is observed in Fig. 6. Moreover, in Table 1 it is
observed that the intensity values progressively decrease. Nickel
surface becomes more and more passive with the stabilization
potential. According to Eqs. (1) and (3), in the case of a nickel
electrode fully covered by a passive layer, measured intensity
values are determined by the potential drop at the metal/passive
layer interface, φm/f. No negative time constant is observed at any
stabilization potential at this pH. This fact can be explained by
considering that ꢀφm/f = φm/fE − φm/fE < 0 from the sta-
1
2
bilization potential E1 to the stabilization potential E2, this is to
say, if there is a decrease in φm/f values with the stabilization
potential. Then, the measured current values will also decrease,
as is experimentally observed. According to D’Alkaine and San-
tanna [11], φm/f decrease is due to a progressive increase in
electric field values at potentials located at the descending part
of the voltammetric peak, in agreement with the EQCM results
discussed above. An estimation of ꢀφm/f can be made by the
following procedure:
Fig. 5. Voltammetriccurverecordedat0.5 mV/sinthe[−940, 860] mVpotential
interval. 0.32 M H3BO3, 0.26 M NH4Cl, 1.33 M Na2SO4, pH 5.1, T = 298 K.
ln i2
ln i1
ln i2 − ln i1
=
bꢀφm/f → ꢀφm/f =
(20)
b
by considering b = 20 V 1. In these conditions, the correspond-
−
ing thickness increase ꢀδ can be calculated if a constant mean
5
electric field of ε = 9 × 10 V/cm is considered, as a first approx-
imation, since, as indicated above, ε values must increase.
5
According to the results discussed above, ε goes from 2 × 10 to
6
−1
1
.6 × 10 V cm under voltammetric conditions for a passive
layer on a nickel deposit in a EQCM experiment. Then,
ꢀ
E0 − ꢀφm/f
ꢀδ =
(21)
ε
The obtained values are listed in Table 1 as a function of the
stabilization potential together with the ꢀφm/f calculated ones.
As observed in Table 1, at E0 = −25 mV, passive layer thickness
can be estimated as δ = 3.3 nm. This value is of the same order of
magnitude than those measured in EQCM analysis. There exists
a good agreement between δ values determined by means the
two procedures tested.
Fig. 6. Experimental impedance spectra at E0 = −75 mV (circles), E0 = −50 mV
5. Conclusions
(
up triangles) and E0 = −25 mV (diamonds). 0.32 M H3BO3, 0.26 M NH4Cl,
1
.33 M Na2SO4, pH 5.1, T = 298 K.
Fdm/dQ analysis shows that a passive layer fully covers the
electrode surface at the beginning of the recorded anodic oxi-
dation peak. Then, the obtained results are analyzed within the
framework of the point defect model theory. Only a minor part
of the measured current values are consumed during the pas-
sive film growth (nickel passivation). This experimental finding
is consistent with cation vacancies being predominant within
passive layer. Fdm/dQ analysis allows to obtain the fraction
of charge consumed during passivation, and, in this way, fol-
lowing the passive layer thickness variation with the applied
potential. It is observed that two monolayers of Ni(OH)2 fully
covers the electrode surface at the beginning of the voltammetric
peak.
Table 1
Measured intensity currents as a function of the stabilization potential
E0 (mV)
i (␮A)
ꢀE0 (mV)
ꢀφm/f (mV)
ꢀδ (nm)
−
−
−
−
−
125
100
75
50
25
31
14
6
2
1
−125 → −100
−100 → −75
−75 → −50
−50 → −25
−47
−47
−65
−41
0.8
0.8
1.0
0.7
Calculated and estimated ꢀφm/f and ꢀδ values form Eqs. (20) and (21), respec-
5
tively. A constant electric field of E = 9 × 10 V/cm is considered as a first
approach.

6
64
J. Gregori et al. / Electrochimica Acta 52 (2006) 658–664
[25] S. Bruckenstein, K. Brzezinska, A.R. Hillman, Phys. Chem. Chem. Phys.
Acknowledgements
2
(2000) 1221.
[
[
26] S. Bruckenstein, K. Brzezinska, A.R. Hillman, Electrochim. Acta 45 (2000)
This work has been supported by Spanish Ministry of Sci-
ence and Technology (Project CICyT-CTQ2004-08026/BQU).
J. Gregori acknowledges a Fellowship from the Spanish Min-
istry of Education (FPU program). J.J. Garc ´ı a-Jare n˜ o would also
acknowledge the Spanish Ministry of Science and Technology
for their position (“Ram o´ n y Cajal” Program).
3801.
27] J.J. Garc ´ı a-Jare n˜ o, A. Sanmat ´ı as, F. Vicente, C. Gabrielli, M. Keddam, H.
Perrot, Electrochim. Acta 45 (2000) 3765.
[28] D. Benito, C. Gabrielli, J.J. Garcia-Jareno, M. Keddam, H. Perrot, F.
Vicente, Electrochim. Acta 48 (2003) 4039.
[
29] D. Gim e´ nez-Romero, P.R. Bueno, C. Gabrielli, C. Casta n˜ o, H. Perrot, J.J.
Garc ´ı a-Jare n˜ o, F. Vicente, Electrochem. Commun. 8 (2006) 195.
30] L. Grasjo, M. Seo, N. Sato, Corros. Sci. 31 (1990) 299.
[
[
References
31] D. Gim e´ nez-Romero, J.J. Garc ´ı a-Jare n˜ o, F. Vicente, J. Electroanal. Chem.
558 (2003) 25.
[
[
[
1] E.M.A. Martini, S.T. Amaral, I.L. M u¨ ller, Corros. Sci. 46 (2004) 2097.
2] P. Marcus, Electrochim. Acta 43 (1998) 109.
3] A. Gildenpfennig, U. Gramberg, G. Hohlneicher, Corros. Sci. 45 (2003)
[32] D. Gim e´ nez-Romero, J.J. Garc ´ı a-Jare n˜ o, F. Vicente, Electrochem. Com-
mun. 6 (2004) 903.
[33] F. Vicente, J. Gregori, J.J. Garc ´ı a-Jare n˜ o, D. Gim e´ nez-Romero, J. Solid
State Electr. 9 (2005) 684.
5
75.
[
[
4] S.G. Real, J.R. Vilche, A.J. Arv ´ı a, Corros. Sci. 20 (1980) 563.
5] M.R. Barbosa, S.G. Real, J.R. Vilche, A.J. Arv ´ı a, J. Electrochem. Soc. 135
[34] G. Sauerbrey, Z. Phys. 155 (1959) 206.
[35] C.O.A. Olsson, D. Hamm, D. Landolt, J. Electrochem. Soc. 147 (2000)
4093.
[36] M.G. Verg e´ , C.O.A. Olsson, D. Landolt, Corros. Sci. 46 (2004) 2583.
[37] C.O.A. Olsson, M.G. Verg e´ , D. Landolt, J. Electrochem. Soc. 151 (2004)
B652.
[38] J. Gregori, J.J. Garc ´ı a-Jare n˜ o, F. Vicente, Electrochem. Commun. 8 (2006)
683.
(
1988) 1077.
6] A. Jouanneau, M. Keddam, M.C. Petit, Electrochim. Acta 21 (1976)
87.
7] M.R. Barbosa, J.A. Bastos, J.J. Gac ´ı a-Jare n˜ o, F. Vicente, Electrochim. Acta
4 (1998) 957.
8] M. Keddam, in:P. Marcus, J. Oudar(Eds.), CorrosionMechanisminTheory
and Practice, Marcell Dekker, New York, 1995, p. 55.
9] M. Itagaki, H. Nakazawa, K. Watanabe, K. Noda, Corros. Sci. 39 (1997)
[
[
[
[
2
4
[39] J. Gregori, J.J. Garc ´ı a-Jare n˜ o, D. Gim e´ nez-Romero, F. Vicente, J. Solid
State Electr. 9 (2005) 83.
9
01.
[40] D. Gim e´ nez-Romero, J.J. Garc ´ı a-Jare n˜ o, F. Vicente, Materiales y Procesos
Electr o´ dicos (I), Ed. INSDE, Burjassot, 2002 (Chapter 3).
[41] S. Bruckenstein, K. Brzezinska, A.R. Hillman, Electrochim. Acta 45 (2000)
3801.
[42] J.J. Garc ´ı a-Jare n˜ o, C. Gabrielli, H. Perrot, Electrochem. Commun. 2 (2000)
195.
[43] E. Gileadi, V. Tsionsky, J. Electrochem. Soc. 147 (2000) 567.
[44] J.R. Macdonald, Solid State Ionics 58 (1992) 97.
[45] J.J. Garc ´ı a-Jare n˜ o, J.J. Navarro, A.F. Roig, H. Scholl, F. Vicente, Elec-
trochim. Acta 40 (1995) 1113.
[46] B.A. Boukamp, J. Electrochem. Soc. 142 (1995) 1885.
[47] P. Agarval, M.E. Orazem, L.H. Garcia-Rubio, J. Electrochem. Soc. 139
(1992) 1917.
[
[
[
10] C.V. D’Alkaine, M.A. Santanna, J. Electroanal. Chem. 457 (1998) 5.
11] C.V. D’Alkaine, M.A. Santanna, J. Electroanal. Chem. 457 (1998) 13.
12] L. Leroy, P. Girault, J.L. Grosseau-Poussard, J.F. Dinhut, Nucl. Instrum.
Meth. B 148 (2002) 49.
13] J. Gregori, J. Agrisuelas, D. Gimenez, M.P. Pe n˜ a, J.J. Garcia-Jareno, F.
Vicente, Rev. Metal. 39 (2003) 346.
14] S.G. Kim, S.P. Yoon, J. Han, S.W. Nam, T.H. Lim, I.H. Oh, S.A. Hong,
Electrochim. Acta 49 (2004) 3081.
15] V. Rashkova, S. Kitova, I. Konstantinov, T. Vitanov, Electrochim. Acta 47
[
[
[
[
[
[
(
2002) 1555.
16] X. Wang, H. Luo, H. Yang, P.J. Sebastian, S.A. Gamboa, Int. J. Hydrogen
Energy 29 (2004) 967.
17] C.Y. Chao, L.F. Lin, D.D. Macdonald, J. Electrochem. Soc. 128 (1981)
[48] A. Sadkowski, Solid State Ionics 176 (2005) 1987.
[49] B. Macdougall, J. Electrochem. Soc. 127 (1980) 789.
[50] B. Macdougall, D.F. Mitchell, M.J. Graham, J. Electrochem. Soc. 132
(1985) 2895.
1
187.
18] D.D. Macdonald, S.R. Biaggio, H. Song, J. Electrochem. Soc. 139 (1992)
70.
1
[
[
[
19] D.D. Macdonald, J. Electrochem. Soc. 139 (1992) 3434.
20] B.J. Feldman, O.R. Melroy, J. Electroanal. Chem. 234 (1987).
21] R. Hillman, M.J. Swann, S. Bruckenstein, J. Phys. Chem. 95 (1991)
[51] M. Nakamura, N. Ikemiya, A. Iwasaki, Y. Suzuki, M. Ito, J. Electroanal.
Chem. 566 (2004) 385.
[52] J. Scherer, B.M. Ocko, O.M. Magnussen, Electrochim. Acta 48 (2003)
1169.
[53] E. Sikora, D.D. Macdonald, Electrochim. Acta 48 (2002) 69.
[54] D.R. Lide (Ed.), Handbook of Chemistry and Physics, CRC Press, New
York, 1995.
[55] L. Zhang, D.D. Macdonald, E. Sikora, J. Sikora, J. Electrochem. Soc. 145
(1998) 898.
3
271.
22] A.R. Hillman, N.A. Hughes, S. Bruckenstein, Analyst 119 (1994)
67.
[
1
[
[
23] X. Zeng, S. Bruckenstein, J. Electroanal. Chem. 461 (1999) 131.
24] M.A. Malik, K. Miecznikowski, P.J. Kulesza, Electrochim. Acta 45 (2000)
3
777.