Kinetics of Polypyrrole Films Doped with Sulphate Ions Electrodeposited Over Graphite - Epoxy Resin Electrode

Abstract

A kinetic study for the electrosynthesis of polypyrrole (Ppy) doped with SO 4 -2 ions is presented. Ppy films are electrochemically polymerized over graphite – epoxy resin electrode. Cyclic voltammetry shows a non-reversible process and the charge density increases as the number of cycles increases too. Current transients are obtained for three different potentiometric behaviors: anionic, cationic and a combination of both. Experimental data was statistically fitted to theoretical models to determine the nucleation and growth processes governing the polymer synthesis. Statistical fit suggests that the mechanism involved in the electropolimerization process is 3D nucleation limited by diffusion of the electroactive specie. The anionic-response polymer displays the lowest diffusion coefficient, while the cationic-response polymer displays the highest one. In all cases, both the active-sites number and the nucleation rate have considerably high values.

Full text

Nucleation and Growth Kinetics of Electrodeposited Sulfate-Doped Polypyrrole:
Determination of the Diffusion Coefficient of SO42-in the Polymeric Membrane
T. de J. Licona-Sa´nchez, G. A. A
´lvarez-Romero,* L. H. Mendoza-Huizar, and
C. A. Gala´n-Vidal
A
´rea Acade´ mica de Quı´mica, Laboratorio de Quı´mica Analı´tica, UniVersidad Auto´noma del Estado de
Hidalgo, Ciudad UniVersitaria, Carretera Pachuca-Tulancingo Km. 4.5, Mineral de la Reforma,
C.P. 42184, Hidalgo, Me´ xico
M. Palomar-Pardave´,* M. Romero-Romo, H. Herrera-Herna´ndez, and J. Uruchurtu†
Departamento de Materiales, UniVersidad Auto´ noma Metropolitana-Azcapotzalco, AV. San Pablo 180,
Col Reynosa Tamaulipas, C.P. 02200, Me´ xico, D.F
J. M. Jua´rez-Garcı´a
Laboratorio de Microana´ lisis, Centro Nacional de Metrologı´a, km 4.5 de la Carretera a los Cues,
municipio de El Marque´ s, Quere´taro, Me´xico
ReceiVed: March 24, 2010; ReVised Manuscript ReceiVed: June 29, 2010
A kinetic study for the electrosynthesis of polypyrrole (Ppy) doped with SO42-ions is presented. Ppy films
were electrochemically polymerized onto a graphite-epoxy resin electrode. Experimental current density
transients (j-t) were obtained for three different potentiometric behaviors: anionic, cationic, and a combination.
Theoretical models were used to fit the experimental j-tdata to determine the nucleation and growth processes
controlling the polymer synthesis. It was encountered that, in all cases, pyrrole electropolimerization involves
two concomitant processes, namely, a Ppy diffusion limited multiple 3D nucleation and growth and pyrrole
electro-oxidation on the growing surface of the Ppy nuclei. SEM analysis of the electrodes surfaces reveals
that Ppy deposition occurred over most of the electrode surface by multiple nucleation of hemispheres, as the
theoretical model used for the analysis of the current transients required. Hemispherical particles formed the
polymeric film displaying different sizes. The order for the particle size was as follows: anionic >
anionic-cationic >cationic. These results are congruent with those obtained by theoretical analysis of the
corresponding current transients. Analysis of the impedance measurements recorded on the anionic Ppy film,
immersed in an aqueous solution with different sulfate ion concentrations evidenced that SO42-ions diffuse
through the Ppy film provoking a decrease of its electrical resistance and an increase of its dielectric constant.
From the Warburg impedance coefficient, the sulfate coefficient of diffusion in the Ppy film was 1.38 ×10-9
cm2s-1.
1. Introduction
The analysis of experimental current density transients,
recorded during electrochemical phase formation processes,1,2
provides valuable information regarding the kinetics of this type
of electrochemical processes such as nucleation kinetics,
dimensional growth, superposition of growth centers, and
morphology. The knowledge of the electrosynthesis kinetics
helps to characterize the variables involved in the process, which
will have direct influence on the final properties and charac-
teristics of the so formed material.3In this case, the formation
of a new phase is induced by an electrical potential perturbation,
starting with a nucleation stage, that strongly depends on the
different electrosynthesis conditions and the overpotential
imposed.4-7The potentiostatic current density transients cor-
responding to these systems show a typical current increase with
time, which is related to the nucleation and growth processes
of the new phase over the electrode surface.4,8 Some examples
of electrochemical processes that involve a phase formation are
the following: metal electrodeposition,9anodic film formation,10
micelles adsorption,11 and the electrochemical synthesis of
conducting polymers.12-15 Theoretical models have been pro-
posed to explain the electrochemical behavior of conducting
polymers,16 that determine the kinetics for the formation and
growth of nuclei, and also the growth type (dimension); such
models describe also the rate law for the formation of nuclei
on a finite number of active sites, which are distributed randomly
over the electrode surface,17 taking into account the nature and
superficial texture of the substrate,18-20 the limiting stage of the
overall process, nuclei geometry, the possible formation of a
superficial layer because of ionization or anodic oxidation of
the electrode’s surface, and the electrochemical synthesis
procedure.21,22 The shape of the growing centers determines, in
many cases, the shape of the corresponding current density
transient for a specific potential.23 If nuclei growth is confined
to an x-yplane over the electrode’s surface, the nucleation and
growth processes are said to happen in two dimensions
* To whom correspondence should be addressed. E-mail: giaan@
uaeh.edu.mx and mepp@correo.azc.uam.mx.
†On sabbatical leave. Permanent address: Centro de Investigacio´n en
Ingenierı´a y Ciencias Aplicadas, Universidad Auto´noma del Estado de
Morelos, Av. Universidad 1001, Col. Chamilpa, Cuernavaca, Mor.
J. Phys. Chem. B 2010, 114, 9737–9743 9737
10.1021/jp102676q 2010 American Chemical Society
Published on Web 07/15/2010

(2D).24-26 When nuclei grow as hemispheres or cones, the
nucleation and growth process happens in three dimensions
(3D).22,24,27-30 Due to the increasing number of practical applica-
tions31-38 of conducting polymers, like polypyrrole (Ppy),37,38
experimental and theoretical reports also have increased during the
last years, especially those studying the relations between the
potentiostatic parameters used for the electropolymerization and
the resulting morphology and properties. However, there are few
reports about kinetic parameters for the conducting polymers
electrosynthesis occurring in the presence of doping agents. Sulfate
ion as polypyrrole dopant displays very peculiar characteristics that
significantly differ from those of other ions commonly used to dope
the polymer,37,38 which implies a significant number of possible
applications for this kind of polymers,31,39 like the development of
highly selective chemical sensors,40,41 application as artificial
muscles,12,42-44 anticorrosive coatings,45-48 etc.
In this work the kinetics of electrochemically synthesized
sulfate-doped polypyrrole films, Ppy-SO42-, with different
potentiometric response, namely those whose potential varies
with the presence of anions (anionic polypyrrole), with cations
(cationic polypyrrole), or both (anionic-cationic polypyrrole),49
is studied.
2. Experimental Section
2.1. Reagents. All reagents used in this work were analytical
grade. Na2SO4(Aldrich) was used as supporting electrolyte and
source of sulfate ions. Pyrrole (Py) (Aldrich) was purified by
distillation with N2atmosphere. Ultrapure monocrystalline
graphite powder 99,999% and Araldit epoxy resin with H.Y
hardener were used to construct the working electrode. All
solutions were prepared with deionized water obtained from a
Milli Q (Millipore) system with 18.2 MΩcm resistivity. The
solutions of Py containing SO42-were bubbled with pure N2
before each experiment.
2.2. Instrumentation. A typical three-electrode cell was
used: a platinum wire was used as counter electrode, an Ag/
AgCl (900200 Orion) as reference electrode, and carbon-epoxy
composite as working electrode. The composite electrode was
prepared by mixing graphite powder and Araldit epoxy resin-H.Y
hardener (agglomerating agent in a 1:0.4 proportion) components
in a 60:40 proportion relation. The proportion of the composite
was supported by using a 0.5 cm diameter PTFE tube with an
electrical contact, as shown in Scheme 1. The hardening of the
composite was achieved during a period of 12 h at a constant
temperature of 60 °C. Thereafter, the exposed surface was
polished before the electrochemical growth of the polypyrrole
film. Polypyrrole (Ppy) films were obtained potentiostatically
and potentiodinamically by using an electrochemical workstation
(Ecochemie) PGSTAT 30 AUTOLAB. For the electrochemical
impedance, EIS, measurements a BAS-Zahner IM6 electro-
chemical workstation was used. OriginLab version 6.1 software
was used for the fitting analysis.
2.3. Electrochemical Synthesis of Ppy-SO42-Films. Ppy-
SO42-films were synthesized by cyclic voltametry and
chronamperometric techniques over the exposed surface of the
composite electrode. In our previous research49 we have found
that depending on the potentiostatic conditions imposed, dif-
ferent potentiometric responses can be achieved for the Ppy-
SO42-film, namely, anionic, cationic, or anionic-cationic
combination; therefore these polymeric films can be used to
produce different kinds of electrochemical sensors.12,13,37 On the
basis of these results, we have already suggested the limiting
values for the electrochemical synthesis parameters; these are
shown in Table 1.
These results were used to synthesize a series of Ppy-SO42-
films with the three different behaviors.
2.4. SEM Characterization. Subsequent to the electrochemi-
cal synthesis of the Ppy-SO42-films, the samples were examined
by means of an Electron Probe Microanalyzer (EPMA) with 3
WDS/EDS combined JXA-8200 (JEOL), using an accelerating
voltage of 15 kV.
3. Results and Discussion
3.1. Potentiodynamic Synthesis. Figure 1 shows a typical
cyclic voltammogram obtained during potentiodynamic syn-
thesis of a Ppy-SO42-film: the potential scan started at the null-
current potential and cycles programmed in an interval from
-1200 to 1200 mV in the anodic direction with a scan rate of
100 mV s-1. The oxidation charge density, Q, obtained (Figure
1 inset) reaches a maximum value at about 50 cycles. This
behavior is typical for the electrochemical formation of conduct-
ing polymers12,13 and indicates that the amount of polymer on
the electrode surface increases as the number of cycles increases.
3.2. Potentiostatic Synthesis. Figure 2 shows families of
current-density transients for each of the potentiometric
responses encountered. The similarity in the shape of the
transients suggests that the nucleation and growth mechanisms
involved in all cases are the same. However, it is clear that the
charge involved (the area under the j-tplots) in each case is
quite different.
Recently, Palomar-Pardave´ et al.9have proposed a theoretical
physicochemical model that describes j-tplots with a very
similar shape to those shown in Figure 2. It is relevant to stress
that this model is not merely a mathematical description of the
experimental current transients, because each parameter involved
(see eqs 3-6) has a clear physical meaning. According to them,9
this sort of j-tplot is obtained when the potentiostatic formation
of a new phase, on the electrode surface, involves the presence
of two simultaneous electrode reactions, namely, a multiple
hemispherical 3D nucleation and growth limited by the mass
transfer reaction, J3D(t), presently, Ppy, nucleation and growth
as well as another faradaic process occurring on the growing
surfaces of the new phase, in this case pyrrole oxidation on the
Ppy surface, JPO(t). Thus, in our case, the equation derived
describing this process is:
where the overall current density-time transient, Jtotal(t), is given
by the addition of the contributions due to pyrrole oxidation on
SCHEME 1: Representation of the Graphite-Epoxy
Resin Composite Used As Working Electrodes for the
Electrochemical Synthesis of Ppy-SO42-Films
TABLE 1: Experimental Conditions Required to Produce
Ppy-SO42-Films with Different Potentiometric Responses
potentiometric response
synthesis
parameter anionic cationic anionic-cationic
E/V 0.86-0.96 0.80-1.00 0.52-0.86
t/min 10.8-15.0 6.0-10.0 4.00-15.0
[Py]/mol L-10.28-0.40 0.05-0.4 0.05-0.225
[SO42-]/mol L-10.35-0.54 0.005-0.5 0.005-0.35
Jtotal(t))J3D(t)+JPO(t)(1)
9738 J. Phys. Chem. B, Vol. 114, No. 30, 2010 Licona-Sa´ nchez et al.

the bare electrode surface, oligomer formation, and subsequently
after nucleation and growth of the polypyrrole deposit, J3D(t),
and that due to the pyrrole oxidation, JPO(t), on the growing
polypyrrole surface. Furthermore, this contribution to the overall
current density transient may also take into account that due to
polypyrrole oxidation, which is believed to occur at a much
lower potential than monomer oxidation thus occurring im-
mediately after the polymer is formed. Notwithstanding, even
when the polymer could be considered to have pores, which
may allow monomer diffusion and oxidation on the electrode
surface, in our model this contribution is considered negligible
when compared with monomer oxidation on the growing
polypyrrole surface.
Equation 1 can be parametrized as follows (see ref 9):
with
where c0is the pyrrole bulk solution concentration, Fis the
Faraday constant, Fis the density of the deposit, Mis its molar
mass, zPOFis the molar charge transferred during the pyrrole
oxidation process, kPO is the rate constant for pyrrole oxidation
reaction on the polypyrrole surface, Dis the pyrrole diffusion
coefficient, Ais the polypyrrole nucleation rate, and N0is the
number density of active sites for polypyrrole nucleation on
the electrode surface.
Figure 3 shows a comparison of the experimental j-tplot
recorded during polypyrrole nucleation and growth, see Figure
2, and the theoretical current density transient generated by
nonlinear fit of eq 2 to the experimental data.
The theoretical model represented by eq 1 describes ad-
equately the whole current density transient recorded in all cases.
From this analysis, the kinetics parameters Aand N0were
obtained, see Table 2, from which it is clear that the potentio-
static response of the Ppy-SO42-film does not change the
nucleation rate; however, the number density of active sites is
affected. It is important to mention that kPO could be estimated
from P1value, see eq 3, knowing the polypyrrole density, 1.5 g
cm-3, which is a physical constant, reported in the literature.50
However, in this work an estimate of kPO is not included due to
the difficulty in finding a reliable value for polypyrrole molar
mass.
From Figure 3 it is also possible to note that part of the current
measured during this sort of transients is effectively used for
the polymer growth on the electrode surface, related with J3D,
and the rest, JPO, is used for Py oxidation on the Ppy surface,
which helps for the subsequent Ppy growth. In this respect one
can infer by comparison of the transients presented in Figure 3
that the Ppy-SO42-film with a potential sensible to anions
involves a larger amount of deposited polymer. Moreover, that
the anionic-cationic response is in turn greater than that
associated with the cationic response.
3.2.1. SEM Characterization. Figure 4 shows the morphol-
ogy characteristics of the bare graphite-epoxy resin electrode
surface, see Figure 4a, and those coated with the Ppy-SO42-
films that display different potentiometric responses namely
cationic, Figure 4b, anionic-cationic, Figure 4c, and anionic,
Figure 4d. From these images one could clearly note that Ppy
deposition actually occurred over most of the electrode surface
by multiple nucleation of hemispheres, as the theoretical model
used for the analysis of the current transients required. In all
cases the hemispherical particles that form the polymeric film
Figure 1. Cyclic voltammograms for the potentiodynamic synthesis of Ppy-SO42-using a composite electrode, [Py] )0.1 M, [SO42-])0.1 M,
50 cycles, and a scan rate of 100 mV s-1. The inset shows the variation of the oxidation charge density recorded from integration of the anodic
branches of the voltammograms.
Jtotal(t))(P1+P4t-1/2)
(
1-exp
{
-P2
[
t-1-exp(-P3t)
P3
]
})
(2)
P1)
(
2c0M
πF
)
1/2
zPOFkPO (3)
P2)N0πk′D(4)
P3)A(5)
P4)zFD1/2c0
π1/2 (6)
k′)(8πc0/F)1/2 (7)
Electrodeposited Sulfate-Doped Polypyrrole J. Phys. Chem. B, Vol. 114, No. 30, 2010 9739

display different sizes depending on the electrochemical syn-
thesis parameters. The order for the particle size is as follows:
anionic >anionic-cationic >cationic. These results are
consistent with those obtained by theoretical analysis of the
corresponding current transients, see Table 2.
Figure 5 depicts the potentiometric response of the graphite-
epoxy resin composite electrode modified with the potentio-
statically formed anionic film in the presence of varying
concentration of sulfate ions in solution; a log relationship was
clearly obtained.
3.2.2. EIS EWaluation of the Electrode Coated with the
Ppy-SO42-Film That Displays a Potentiometric Anionic
Response. To evaluate the electrochemical properties of the
anionic Ppy-SO42-film, electrochemical impedance measure-
ments were recorded in the graphite-epoxy resin composite
electrode, coated with the anionic Ppy-SO42-film, immersed
Figure 2. Typical current-density transients recorded during the
electrochemical synthesis of Ppy-SO42-films, with different potentio-
metric response, on the graphite-epoxy resin composite: (a) anionic
[SO42-])0.5 M, [Py] )0.3 M, time (t))774 s; (b) cationic [SO42-]
)0.5 M, [Py] )0.05 M, t)480 s; (c) anionic-cationic [SO42-])
0.17 M, [Py] )0.13 M, t)570 s. The applied potentials used for the
synthesis are indicated in the figure.
Figure 3. Comparison between an experimental current-density
transient (---) recorded for each of the potentiostatic response (a) anionic
response, (b) cationic response, and (c) anionic-cationic response, see
Figure 2, and the theoretical current density transient (s) generated
by the nonlinear fitting of eq 2 to the experimental data. Individual
contributions due to JPO and J3D are also shown.
TABLE 2: Kinetic Parameters Obtained after the Statistical
Fit for the Three Different Potentiometric Responses
type of response of the
polymeric membrane 10-4N0/cm-2A/s-1
anionic 415 100
anionic-cationic 175 100
cationic 8.6 100
9740 J. Phys. Chem. B, Vol. 114, No. 30, 2010 Licona-Sa´ nchez et al.

in an aqueous solution with different Na2SO4concentrations.
Figure 6 shows both the Nyquist and Bode impedance plots
recorded.
On the basis of the shape of the Nyquist and Bode plots it
was decided to use the equivalent circuit presented in Figure
7 to fit into the impedance measurements. This is a
mathematical fitting of basic functions related to the classical
electrical components (resistors, capacitors, inductors) plus
a few specialized electrochemical elements (such as Warbug
diffusion elements), see Table 3. In this circuit constant phase
elements (CPE) were considered, rather than pure capacitors,
in order to take into account the electrode surface roughness.51
Mathematically, a CPE’s admittance is given by
where Qohas the numerical value of the admittance. When n
)1, this is the same equation as that for the impedance of a
capacitor, where Qo)C.
When nis close to 1, the CPE resembles a capacitor, the phase
angle not being 90°, but it is constant and somewhat less than
90°at all frequencies. In some cases, the true capacitance (C)
can be calculated from Qoand n.
For the case of a CPE in parallel with a resistance, Hsu and
Mansfeld52 proposed eq 10 for calculating the true capacitance,
C, as:
In this equation, ωMAX represents the frequency at which the
imaginary component reaches a maximum. It is the frequency
at the top of the depressed semicircle, and it is also the frequency
at which the real part (Zreal) is midway between the low and
high frequency x-axis intercepts.
The equivalent circuit in Figure 6 includes the solution
resistance (Rs), a CPE associated to the polymer film (CPEc),
the polymer resistance (Rc), a CPE associated to the double layer
interface (CPEdl), the charge transfer or polarization resistance
(Rp), and the Warburg impedance of the polymer (ZW).
Figure 6 compares the experimental impedance measurements
(see Figure 6a) with those obtained by nonlinear fitting of the
experimental data with the equivalent circuit shown in Figure
7. The best fitting parameters obtained are shown in Table 3.
From Table 3, it becomes clear that Ppy-SO42-film resistance
Rcvalues decreased and its capacitance values Ccincreased with
the increase of sulfate ion concentrations. Since the geometry
of the polymeric film, namely, the surface area Aand thickness
δ, were the same in all cases; the observed increase in the
Figure 4. Secondary electron images, ×100, of the bare graphite-epoxy resin electrode surface (a) and those coated with the Ppy-SO42-films
with different potentiometric responses: cationic (b), anionic-cationic (c), and anionic (d). The insets show, in each case, three different magnifications
(×1000, ×2000, and ×5000).
Figure 5. Electrode potential variation (b) of the graphite-epoxy resin
composite electrode modified with the potentiostatically formed anionic
film as a function of sulfate ions concentration. The line represents the
linear fitting of the experimental points.
1/Z)Y)Qo(jω)n(8)
1/Z)Y)jωQo)jωC(9)
C)Qo(ωMAX)n-1(10)
Electrodeposited Sulfate-Doped Polypyrrole J. Phys. Chem. B, Vol. 114, No. 30, 2010 9741

capacitance should be associated to an increment in the local
dielectric constant; as can be noted from the well-known
Helmholtz model:
where ωcis the dielectric constant of the polymer, ε0is the
vacuum permittivity, Ais the electrode surface area, and δis
the thickness of the protective layer. The previous observation
regarding variations of Rcand Ccwith sulfate ions in solution
strongly suggests that the SO42-ions in solution can penetrate
the polymeric film. Moreover, the diffusion coefficient for the
ionic transport in the polymeric matrix can be obtained with
the impedance measurements by using the Warburg impedance
coefficient Zw, from eq 12:53
where Dis the diffusion coefficient of sulfate ions (cm2s-1), A
is the area of electrode (cm2), Zwis the Warburg impedance
coefficient (Ωcm2s-1/2), Cis the concentration of sulfate (mol
cm3), Ris the gas constant (J K-1mol-1), Tis the absolute
temperature (K), and Fis the Faraday constant (C mol-1). The
result of the calculation is 1.38 ×10-9cm2s-1. It is important
to stress that Otero et al.,54,55 using chronoamperometry, reported
similar values for the perchlorate diffusion coefficient in swelling
polypyrrole (0.4 ×10-9to 2.2 ×10-9cm2s-1)54 and in
polypyrrole with different degrees of degradation (by overoxi-
dation) (0.4 ×10-9to 1.8 ×10-9cm2s-1).55 Morover, Ke¸ pas
and Grzeszczuk,56 using EIS measurements, determined the
diffusion coefficients for hexafluorosilicate and hexafluoroalu-
minate counterion systems in the order of 10-10 cm2s-1.
4. Conclusions
From the potentiostatic step technique and EIS it was shown
that sulfate-doped pyrrole electropolimerization involved two
concomitant processes, namely, a Ppy diffusion limited multiple
3D nucleation and growth and pyrrole electro-oxidation on the
growing surface of the Ppy nuclei. From SEM analysis it was
shown that Ppy deposition occurred over most of the electrode
surface by multiple nucleation of hemispheres, as the theoretical
model used for the analysis of the current transients required.
The order for the particle size was as follows: anionic >
anionic-cationic >cationic. These results are congruent with
those obtained by theoretical analysis of the corresponding
current transients. Analysis of the impedance measurements
recorded on the anionic Ppy film, immersed in an aqueous
solution with different sulfate ion concentrations evidenced that
SO42-ions diffuse through the Ppy film provoking a decrease
of its electrical resistance and an increase of its dielectric
constant. From the Warburg impedance coefficient, the sulfate
coefficient of diffusion in the Ppy film was 1.38 ×10-9cm2
s-1.
Acknowledgment. T.J.L.S. is grateful to CONACYT for the
stipend received for her Ph.D. studies. The authors are also
grateful to CONACYT and PROMEP for the financial support
Figure 6. Nyquist (a) and Bode (b) impedance plots recorded for the
graphite-epoxy resin composite electrode, coated with the Ppy-SO42-
film, immersed in an aqueous solution with different Na2SO4concentra-
tions as indicated in the figure. The solid lines in the Nyquist plots
were obtaned by nonlinear fitting of the experimental data with the
equivalent circuit shown in Figure 7. The inset in panel a depicts a
close-up of a higher frequency semicircle.
Figure 7. Proposed electrical equivalent circuit used to simulate the
experimental impedance plots.
Cc)
εcε0A
δ(11)
TABLE 3: Impedance Parameters of the Graphite-Epoxy
Resin Electrode Coated with the Ppy-SO42-Film, that
Display a Potentiostatic Anionic Response, Immersed in an
Aqueous Solution Containing Different [Na2SO4], Using the
Equivalent Circuit Shown in Figure 7
[Na2SO4]/
M
1010Cca/
Fcm
-2Rc/
Ωacm2n
104Cdla/
Fcm
-2Rct/
KΩcm2n
Zw/Ω
cm2s-1/2
10-54.98 510 1 8.6 3.74 0.3
10-35.13 340 1 4.2 4.01 0.3
10-111820 106 0.8 2.7 4.1 0.8 257.5
aBoth the capacitance of the polymeric film (Cc) and the double
layer capacitance (Cdl) were obtained from the values of CPEc and
CPEdl, respectively, using eq 10.
D)
[
RT
√
2AF2ZwC
]
2(12)
9742 J. Phys. Chem. B, Vol. 114, No. 30, 2010 Licona-Sa´ nchez et al.

given through projects 80058 and 46481, respectively. M.P.P.
thanks CONACyT for the support through projects 48854 and
24658 (“Nucleacio´ n y crecimiento electroquı´mico de nuevas
fases”). M.P.P. and M.R.R. wish to thank the Departamento de
Materiales, UAM-A, for the financial support given through
projects 2261203, 2261204, and 2261205. J.U. and H.H.H.
acknowledge Conacyt for the grant provided to pursue a research
sabbatical leave and a postdoctoral position, respectively, in the
Departamento de Materiales, UAM-A.
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