Effect of Potential on the Early Stages of Nucleation and Growth during Silver Electrocrystallization in Ammonium Medium on Vitreous Carbon

Article abstract of DOI:10.1149/1.1646154

In this work, a systemic study of silver electrocrystallization process was performed on a vitreous carbon (VC) electrode in a medium of 1.6 M NH ₃, 1 KNO₃ at pH 11. The analysis of current transients, using different theoretical models, shows that the systematic evolution of electrocrystallization process is observable through the gradual modification of energetic conditions of the interface by either changing the concentration of electroactive species [10^-4 to 0.1 M Ag(NH₃) ₂^-] or the potential imposed to the electrode. At low concentrations of electroactive species (≤10^-3 M) and not so negative potentials, 2D-2D growth of silver may be observed forming deposits less than the monolayer coverage. At more negative potentials 2D-3D growths are obtained. In this type of transition, two kinds of silver growth sites are identifiable, first on the VC and afterward, on the recently deposited silver. At concentrations ≥10^-2 M and less negative potentials, 3D growth of nuclei can be seen, forming deposits far beyond a monolayer. Their growth is influenced by either diffusion of Ag(NH₃)₂^- or the incorporation of silver adatoms into the substrate lattice, depending on the conditions of imposed potential. At concentrations ≥10^-1 M and very negative potentials, where the deposited silver was much greater than a monolayer, 2D growths were found associated with the growth of Ag° on the previously deposited silver. It is worth noting that this is the first time, that in the same chemical system, the systematic evolution of electrocrystallization of 2D and 3D stages of nuclei growth on heterogeneous VC surfaces can be observed, through the gradual modification of energetic conditions at the interface by either changing the concentration of electroactive species or the potential imposed to the electrode.

Full text of DOI:10.1149/1.1646154

C220
Journal of The Electrochemical Society, 151 ͑3͒ C220-C228 ͑2004͒
0
013-4651/2004/151͑3͒/C220/9/$7.00 © The Electrochemical Society, Inc.
Effect of Potential on the Early Stages of Nucleation and
Growth during Silver Electrocrystallization in Ammonium
Medium on Vitreous Carbon
a, ,z
b,
Margarita Miranda-Hern a´ ndez * and Ignacio Gonz a´ lez *
aCoordinaci o´ n de Superficies, Interfaces y Materiales Compuestos, Departamento Materiales Solares, Centro
de Investigaci o´ n en Energ ´ı a-UNAM, Temixco, Mor 62580, M e´ xico
b
Departamento de Qu ´ı mica, Universidad Aut o´ noma Metropolitana-Iztapalapa, 09340 M e´ xico,
D. F., M e´ xico
In this work, a systemic study of silver electrocrystallization process was performed on a vitreous carbon ͑VC͒ electrode in a
medium of 1.6 M NH , 1 KNO at pH 11. The analysis of current transients, using different theoretical models, shows that the
3
3
systematic evolution of electrocrystallization process is observable through the gradual modification of energetic conditions of the
Ϫ4
ϩ
2
interface by either changing the concentration of electroactive species ͓10 to 0.1 M Ag(NH ) ] or the potential imposed to the
3
Ϫ3
electrode. At low concentrations of electroactive species (р10 M) and not so negative potentials, 2D-2D growth of silver may
be observed forming deposits less than the monolayer coverage. At more negative potentials 2D-3D growths are obtained. In this
type of transition, two kinds of silver growth sites are identifiable, first on the VC and afterward, on the recently deposited silver.
At concentrations у10 M and less negative potentials, 3D growth of nuclei can be seen, forming deposits far beyond a
monolayer. Their growth is influenced by either diffusion of Ag(NH3)2 or the incorporation of silver adatoms into the substrate
Ϫ2
ϩ
Ϫ1
lattice, depending on the conditions of imposed potential. At concentrations у10 M and very negative potentials, where the
deposited silver was much greater than a monolayer, 2D growths were found associated with the growth of Ag° on the previously
deposited silver. It is worth noting that this is the first time, that in the same chemical system, the systematic evolution of
electrocrystallization of 2D and 3D stages of nuclei growth on heterogeneous VC surfaces can be observed, through the gradual
modification of energetic conditions at the interface by either changing the concentration of electroactive species or the potential
imposed to the electrode.
©
2004 The Electrochemical Society. ͓DOI: 10.1149/1.1646154͔ All rights reserved.
Manuscript submitted April 15, 2003; revised manuscript received September 25, 2003. Available electronically February 11,
004.
2
electroactive species, from very dilute to the concentrated (10Ϫ4 to
0.1 M͒. For each system, potential pulses were applied in a wide
range ͑Ϫ0.03 to Ϫ0.7 V vs. standard calomel electrode, SCE͒.
In general, electrocrystallization studies reported in the literature
are performed at small intervals of applied potential and therefore
take into account only one type of nucleation and growth in the
current-transient response analysis. This type generally fits the
model of three-dimensional ͑3D͒ growth limited by diffusion of the
Experimental
1
-9
electroactive species proposed by Scharifker and Hills. In the case
The studies were carried out in a typical three-electrode cell con-
sisting of a SCE as reference, a graphite bar as auxiliary electrode
of a complex response of current transients ͑presence of more than
1
0
2
one current maximum͒, these are not quantitatively analyzed or the
and VC disc with 0.071 cm area as working electrode. The system
11,12
ϩ
2
studies investigating that kind of response are very few
and only
was xAg(NH •) /1.6 M NH , 1 M KNO at pH 11, with x repre-
3
3
3
Ϫ4
show the effect of the electroactive species concentration in nucle-
senting different concentrations of complex metallic ion (10 M to
0.1 M͒. The electrochemical techniques employed were cyclic vol-
tammetry and chronoamperometry. Each system of different concen-
tration was characterized by voltammetry with scan rate of 50 mV/s
in the potential range between 0.7 to Ϫ0.7 V vs. SCE. The sweep
potential was always initiated in negative direction. Chronoampero-
metric studies were performed in the same Ag͑I͒ concentration
range as the voltammetric study, in a wide range of electrode poten-
tials ͑Ϫ0.03 to Ϫ0.7 V vs. SCE͒ with increases of 20 mV. The study
was always initiated applying a potential pulse in negative direction
ation and growth stages at small intervals of applied potential. In
these studies, other models1
3-18
associating transient responses with
simple or multiple growths ͑growth transitions͒ are used. These
models describe two-dimensional ͑2D͒ or 3D growths that comprise
different limiting stages, such as adatoms incorporation into sub-
strate lattice. Another study19 shows a methodology for quantitative
analysis of experimental current transients that display complex
shapes.
The aim of this work is to show that after modifying energetic
conditions of the electrode/electrolyte interface, it is possible to de-
scribe the evolution of electrocrystallization process ͑nucleation and
growth changes͒. It is demonstrated that transient responses may be
analyzed by applying different theoretical models without the limi-
Ϫ3
for 2 s ͑for concentrations above 10 M, the pulse time was 5 s͒;
after the potential was reversed to the value Eanodic
ϭ 0.7 V vs. SCE. On the other hand, before each sequence of per-
turbation, the working electrode was submitted to cleaning de-
scribed in Ref. 11 and 24 which assured realization of each experi-
ment on a clean surface. A PAR 270 potentiostat was coupled to a
computer for data acquisition and analysis by M-270 software.
1
-10,20-22
tation of a single model commonly reported in the literature.
It is well known that the initial stages of the nucleation are de-
termined by substrate surface properties: Step edges, defects, and
inhomogeneities. The influence of surface properties on the elec-
trode of vitreous carbon ͑VC͒ in ammonia medium has been de-
Results
scribed previously11,12,23
Figure 1 shows typical voltammograms corresponding to the sys-
therefore that effect is not discussed in this
Ϫ3
Ϫ2
ϩ
2
tems 10 and 10 M Ag(NH3) obtained at the potential range
paper. This work associates the quantity of monolayers formed on
the substrate with the type of growth analyzed. Hence its impor-
tance, because to our knowledge, there are no similar results re-
ported in the literature. The study was carried out using a VC elec-
trode and ammonium baths with different concentrations of
between 0.7 to Ϫ0.7 V vs. SCE at 50 mV/s. In both cases, the
reduction peak C1 was detected in the direct sweep potential ͑nega-
ϩ
tive direction͒, corresponding to the reduction of Ag(NH3)2 species
to metallic silver. In the reverse sweep potential, two crossovers are
observed, one at more negative potentials and the other at zero cur-
rent, characteristic of metal deposition onto substrates of different
nature. There is also a sharp peak A associated with the thorough
dissolution of metal on the substrate surface. Voltammetric re-
*
Electrochemical Society Active Member.
E-mail: mmh@cie.unam.mx
1
z
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Journal of The Electrochemical Society, 151 ͑3͒ C220-C228 ͑2004͒
C221
Table I. Values of conditional potential „EЈ… as a function of con-
¿
centration the electroactive species Ag„NH …
.
3
2
ϩ
͓
Ag(NH ) ͔/M
EЈ/V vs. SCE
3
2
Ϫ4
Ϫ3
Ϫ2
Ϫ1
10
10
10
10
Ϫ0.128
Ϫ0.068
Ϫ0.008
0.052
System: 10Ϫ4 M Ag(NH ) /1.6 M NH , 1 KNO3 at pH
ϩ
2
3
3
1
1.—Figure 2 shows potentiostatic current transients obtained in a
Ϫ4
ϩ
solution with 10 M Ag(NH ) /1.6 M NH , 1 KNO at pH 11 in
3
2
3
3
different overpotential pulses between 0.078 and Ϫ0.572 V. All tran-
sients show a similar behavior: first the transient current declined
sharply due to the double-layer ͑dl͒ charging process; after a current
maximum M1 observed within the time range of 0.04-0.1 s. At
longer times, the current transients present another maximum M2 .
On comparing the transients of Fig. 2 with the theory reported in
the literature, this suggests that both maxima (M1 2and M ) can be
2
5-27
analyzed by the model proposed by Bewick et al.
That model
describes the kinetics of electrolytic phase formation at the early
stages of 2D growth determined by the lattice incorporation of ada-
toms to the periphery of a growing nucleus, taking into account the
overlap of nuclei. This model considers two kinds of nucleation
processes, instantaneous and progressive, which can be described by
Eq. 2 and 3, respectively
2
2 2
2
2
␲nFMhN k t
␲N M k t
o
g
o
g
jinstantaneous
ϭ
exp
ͩ
Ϫ
ͪ
ͪ
͓2͔
͓3͔
␳
␳2
2
g
2
2
2
3
␲
nFMhAN k t
␲AN M k t
o
o
g
jprogressive
ϭ
exp
ͩ
Ϫ
␳
3␳2
where, N is the number density of active sites, k is the growth rate
o
g
constant of a nucleus, A corresponds to the nucleation rate constant,
M is the molar mass, ␳ is density of the deposited material, nF is the
molar charge transferred during electrodeposition and h is height of
the monolayer.
Figure 1. Typical cyclic voltammetric curves obtained in the x/M
ϩ
Ag(NH ) /1.6 M NH 1 M KNO at pH 11 system on vitreous carbon elec-
3
2
3
3
A quick way to demonstrate the applicability of this model to the
transient responses shown in Fig. 2 is to undertake a comparative
diagnosis between the theoretical response, in dimensionless coor-
dinates, of Eq. 2 and 3 (I/I vs. t/t ) and the experimental
Ϫ3
trode, at two different concentrations of electroactive species ͑a͒ x ϭ 10
b͒ x ϭ 10 M. The scan potential rate was 50 mV/s.
Ϫ2
͑
m
m
2
6,27
response,
where Im and tm are the coordinates of the current
sponses for other systems of different concentrations were similar to
the above-described behavior. It is important to note that the current
response is characteristic of the concentration of the system. These
results show that the reduction reaction at the electrode in all sys-
tems is the following
ϩ
Ϫ
o
Ag͑NH3͒2 ϩ e → Ag ϩ 2NH
3
ϩ
͓
Ag͑NH ͒ ͔
3
2
o
EЈ ϭ E Ј ϩ 0.06 log
͓1͔
NH ͔2
͓
3
where EЈ is the conditional potential represented by the Nernst Eq.
, which depends on the electroactive species and ͓NH ͔ concentra-
1
3
o
tions. In this case, ͓NH ͔ ϭ 1.6 M and E Ј
ϭ 0.136 V vs.
3
Ag(NH ) /Ag
ϩ
2
o
3
SCE. EЈ refers to the silver complexes in the ammonia bath. The
estimated values of EЈ for each experimental condition are reported
in Table I. More details of EЈ determination have been reported
elsewhere ͑see Appendix, Ref. 11͒. In order to made a energetic
comparison, in all cases the overpotentials were considered ͑evalu-
ated from imposed potentials and the potentials of Table I͒.
Below results are shown corresponding to the chronoamperomet-
ric study obtained for systems at different concentrations, applying a
wide range of potentials.
Figure 2. Family of current transients for the electrodeposition of silver onto
Ϫ4
ϩ
vitreous carbon from 10 M Ag(NH ) /1.6 M NH , 1 KNO solution at
3
2
3
3
pH 11, obtained at different overpotentials ␩/V: ͑छ͒ 0.078, ͑᭹͒ Ϫ0.022, ͑᭺͒
Ϫ0.122, ͑᭡͒ Ϫ0.322, ͑᭝͒ Ϫ0.372, ͑᭿͒ Ϫ0.472, and ͑ᮀ͒ Ϫ0.572.
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C222
Journal of The Electrochemical Society, 151 ͑3͒ C220-C228 ͑2004͒
Table II. Types of growth, nucleation, and kinetic parameters corresponding to the mechanism of silver electrocrystallization obtained for the
À4
¿
a
10
M Ag„NH … Õ1.6 M NH , 1 M KNO system at pH 11, as a function of the overpotential „␩….
3
2
3
3
System 10Ϫ4 M Ag͑I͒
M1
M2
5
*h ϫ 108
͑cm͒
t I ϫ 105
͑C cm ͒
*h ϫ 108
͑cm͒
**h ϫ 108
͑cm͒
␩
t I ϫ 10
Nucleation
and growth
m
m
m m
Ϫ2
Ϫ2
͑V͒
͑C cm
͒
0
0
.078
.028
1.94
1.46
1.57
1.74
1.94
1.83
1.61
1.72
1.89
1.89
3.91
3.03
3.54
5.54
6.53
2.12
2.28
0.20
0.15
0.16
0.18
0.20
0.19
0.17
0.18
0.20
0.20
0.41
0.31
0.37
0.57
0.68
0.22
0.24
1.09
1.12
1.23
1.48
1.72
1.95
1.95
2.04
2.44
2.34
3.82
3.43
4.52
4.90
6.29
4.04
4.88
0.11
0.12
0.13
0.15
0.17
0.20
0.20
0.21
0.25
0.24
0.40
0.35
0.47
0.51
0.65
0.42
0.51
Transition
2D-2D
progressive
0.18
0.23
0.29
0.37
0.43
0.55
0.57
0.61
0.69
0.67
1.09
0.98
1.18
1.35
1.56
Ϫ0.022
Ϫ0.072
Ϫ0.122
Ϫ0.172
Ϫ0.192
Ϫ0.222
Ϫ0.272
Ϫ0.322
Ϫ0.372
Ϫ0.422
Ϫ0.472
Ϫ0.522
Ϫ0.572
Ϫ0.122
Ϫ0.572
M1
M2
dl
Ϫ3
kg1 ϫ 103
Ϫ3
kg2 ϫ 103
3
␩
A
͑s
No ϫ 10
A
͑s
No ϫ 10
kads ϫ 10
͑A cm
k
1
1
2
2
des
Ϫ1
Ϫ2
͑mol cm sϪ1
Ϫ2
Ϫ1
Ϫ2
͑mol cm sϪ1
Ϫ2
Ϫ2
Ϫ1
͑V͒
͒
͑cm
͒
͒
͒
͑cm
͒
͒
͒
͑s ͒
Ϫ0.122
Ϫ0.572
19.04
25
1.58
1.98
33.46
31.62
2
2.86
0.2
0.27
78.1
67.08
2.33
7.8
90.21
109
a
The thickness of a monolayer of silver deposited is 1.59 ϫ 10Ϫ8 cm ͑this term was evaluated from characteristics parameters͒. The thickness (*h) of
silver layer was obtained for Imtm using Eq. 6. The thickness of the silver formed (**h) was evaluated from the charge associated to the deposit ͑area
under the curve of the corresponding current transient͒.
It also is very important to note that, in the entire range of overpo-
tentials ͑Table II͒, the thickness ͑h͒ of the deposit is less than a
monolayer. The monolayer is estimated to have a thickness of 1.59
maximum and tm is the time associated to this maximum. The analy-
sis of each successive maximum M1 and M2 ͑Fig. 2͒ allows the
association with a progressive 2D growth which suggests a 2D-2D
transition for all of the transient current responses.
A detailed analysis is presented below of the transient responses
shown in Fig. 2, in order to demonstrate if a 2D-2D transitions may
effectively be associated with progressive growth.
Ϫ8
ϫ 10 cm, considering the number of silver atoms required to
2
cover the geometric area of the electrode ͑0.0707 cm ͒ and the area
Ϫ16
2
of a silver atom is 9.62 ϫ 10
cm . Therefore, the charge needed
1
3
Ϫ5
to form a monolayer (7.35 ϫ 10 atoms) is 1.19 ϫ 10 C.
The reason that this does not strictly obey the product of Eq. 6 is
due precisely to the fact that there are different contributions to the
total current: the current necessary to charge the dl (Idl) and for the
Considering Eq. 3, the maximum current occurs at a time defined
by
␳2
1/3
2
2
2D-2D growth transition, the current which corresponds to 2D pro-
tm
ϭ
͓4͔
͓5͔
͓6͔
ͩ
2
g
ͪ
␲
M AN k
o
gressive growth in the maximum M1 (I2DP(M1)) and the current of
the 2D progressive growth in the maximum M2 (I2DP(M2)). In this
manner, the total current may be represented as follows
the maximum current density is given by
2
1/3
4
␲AN k ␳
o
g
Itotal ϭ Idl ϩ I2DP͑M1͒ ϩ I2DP͑M2͒
͓7͔
Im ϭ zF
ͩ
ͪ
h exp͑Ϫ2/3͒
M
In order to separate each of the contributions in the total current
response, a nonlinear fit of Eq. 7 ͑see details of nonlinear fit pro-
cesses in the Appendix͒ was made to the experimental results and
presented in its completely developed form in the following equa-
tion, where Idl ϭ kads exp( Ϫ kdest) and I2DP are defined for Eq. 3
the product Imtm yields
2
zF␳h exp͑Ϫ2/3͒
I t
m m
ϭ
M
I ϭ kads exp͑Ϫkdest͒
As may be observed, the product Imtm should be a constant deter-
mined by the height of the silver monolayer independent of the
electrode potential, concentration and pH.
2
2
2
2
2
3
3
n␲FMh A N k t
␲M A N k t
1
1
o
g1
1
o
g1
1
1
ϩ
ϩ
ͫ
ͫ
exp
exp
ͩ
ͩ
Ϫ
ͪ
ͪ
ͬ
ͬ
␳
3␳2
Table II shows the values of the product Imtm and of h ͑height of
the deposited layer͒ evaluated with Eq. 6. It may be observed that
both Imtm and h are relatively constant only up to a certain value of
overpotential ͑0.078 to Ϫ0.322 V͒. For more negative overpoten-
tials, the product Imtm changes. With this it is demonstrated that over
a large interval of overpotentials, the maxima M and M observed
2
g2
2
2
n␲FMh A N k t
␲M A N k t
2
2
o
2
o
g2
2
2
Ϫ
͓8͔
␳
3␳2
At the initial stage of the silver deposition transient, a sharp
1
2
in the transient current response may be associated with 2D growth.
decline in the current normally occurs ͑Fig. 2͒. According to the
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Journal of The Electrochemical Society, 151 ͑3͒ C220-C228 ͑2004͒
C223
Figure 3. ͑छ͒ Experimental current transient recorded at: ͑a͒
␩
Ϫ4
ϩ
ϭ Ϫ0.122 V, ͑b͒ ␩ ϭ Ϫ0.572 V, for the system 10 M Ag(NH ) /1.6 M
3
2
NH , 1 KNO at pH 11, and ͑*͒ a theoretical curve for the 2D-2D nucleation
3
3
transition ͑Eq. 8͒. Contributions to the transient current from the double layer
charging phenomenon (I ) and two consecutive 2D progressive nucleation
dl
processes (I2DP) are shown separately.
literature,1,13 this is related to the electrode dl charging effect initi-
ated by the potential pulse employed. Although this phenomenon
has been recognized and described qualitatively, a quantitative char-
acterization has rarely been performed. Kolb and co-workers
showed that such a charging effect can be correlated quantitatively
to the adsorption-desorption process of ions on the electrode
1
3
surface. To estimate quantitatively the dl charge contribution in
1
3
this silver overpotential deposition, the same approach as Kolb
was employed. The estimation of the current density contribution
Idl) in current transients due to the dl charging effect was based on
(
Figure 4. Potentiostatic current transients obtained for the deposition of sil-
a Langmuir-type adsorption-desorption equilibrium and previously
Ϫ3
ϩ
ver on a VC electrode from 10 M Ag(NH ) /1.6 M NH , 1 KNO solu-
established mathematical formalisms.2
8,29
3
2
3
3
From I ,k is related to
dl ads
tion at pH 11. The overpotential of the electrode was different; see in the
figures.
the total charge of the adsorption process Qads
Idl ϭ kads exp͑Ϫkdest͒
͓9͔
end of Table II, the value of Imtm for M and M is shown, obtained
1
2
where kads ϭ kdes Qads
from each individual fit, in other words without contributions. In this
In Fig. 3a-b, the result of the nonlinear fit is shown as an ex-
ample for two overpotentials Ϫ0.122 and Ϫ0.572 V. Also, the con-
tribution of each of the events described in Eq. 8 to the current as
well as the total current ͑the sum of all of the contributions͒ are
illustrated. Considering the response for each event, it was observed
table, the parameters found with the nonlinear fit of Eq. 3 (AN k ,
kads and kdes) are also reported, where the subscripts 1 and 2 are
o
g
used to denote the maxima M1 and M . The magnitude of these
2
parameters show a tendency very similar to those reported in Ref. 11
and 12. The thickness of the silver formed (**h) was evaluated
from the charge associated to the deposit ͑area under the curve of
the corresponding current transient͒. The values obtained in this
manner are always less than that required to form the monolayer.
that the transient response corresponding to the maximum M is the
1
largest contribution to the total current, for Idl as well as for I2DP(M2)
during the entire time interval in which the M1 was formed. At the
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C224
Journal of The Electrochemical Society, 151 ͑3͒ C220-C228 ͑2004͒
The fully developed form of Eq. 10 is shown in Eq. 11
I ϭ kads exp͑Ϫkdest͒
2
2
2
2
2
2
n␲FMh N k t
␲M N k t
1
o
g1
o
g1
1
1
ϩ
ϩ
ͫ
ͫ
exp
exp
ͩ
ͩ
Ϫ
ͪ
ͪ
ͬ
ͬ
␳
␳2
2
2
2
2
n␲FMh N k t
␲M N k t
2
o
g2
o
g2
2
2
Ϫ
͓11͔
␳
␳2
Table III summarizes the results obtained for this system. It is im-
portant to mention that in this table the values of tm and Im for the
overpotential range of Ϫ0.432 to Ϫ0.632 are not reported because in
the experimental results it is difficult to appreciate the presence of a
second maximum (M ). This becomes evident only after the differ-
2
ent contributions to the total current have been separated through the
nonlinear fit of the transient current responses of Fig. 4c, in such a
form that the product t I , which is practically constant, has been
m
m
evaluated ͑see Table III͒. In the same manner as the last case, **h
the thickness of the deposited silver͒ was evaluated. As before, this
͑
is less than that required to form the monolayer, which is in agree-
ment with the corresponding value of *h obtained from t I , for
m
m
overpotentials from Ϫ0.032 to Ϫ0.382. At more negative overpo-
tentials, *h as well as **h present values that correspond to the
formation of more than a monolayer ͑3D growth͒.
System: 10Ϫ2 M Ag(NH ) /1.6 M NH , 1 KNO at pH
ϩ
2
3
3
3
1
1.—Figure 6a-b shows potentiostatic current transients obtained in
Ϫ2
ϩ
10
M Ag(NH ) /1.6 M NH , 1 KNO solution at pH 11, upon
3 3 3
2
the application of different overpotential pulses in the range of
Ϫ0.09 to Ϫ0.69 V. The transient responses shown in Fig. 6a, are
similar to the those described by the theoretical model proposed by
1
,5,6
Scharifker and Hills.
Their models describe the kinetics of elec-
trolytic phase formation in the early stages when diffusion of the
electroactive species from bulk to the interface is the slowest step of
the process. The growth of the nuclei is considered to be 3D, taking
into account overlap of diffusion zones. The instantaneous and
progressive-type nucleation is described by Eq. 12 and 13
Figure 5. ͑छ͒ Experimental current transient recorded at: ͑a͒
␩
M
Ϫ3
ϭ Ϫ0.432 V,
͑b͒ ␩ ϭ Ϫ0.6372 V,
for the system 10
ϩ
Ag(NH ) /1.6 M NH , 1 KNO at pH 11, and ͑*͒ a theoretical curve for the
3
2
3
3
2D-2D nucleation transition ͑Eq. 11͒. Contributions to the transient current
from the dl charging phenomenon (I ) and two consecutive 2D instanta-
neous nucleation processes (I2DIns) are shown separately.
nFD1/2
dl
jinstantaneous
ϭ
͓1 Ϫ exp͑ϪN ␲kDt͔͒
͓12͔
͓12a͔
͓13͔
1/2 1/2
o
␲
t
1
/2
8
␲cM
Considering the results of Table II, the presence of 2D-2D growth
on the polycrystalline surface of ͑VC͒ is confirmed.
k ϭ
ͩ
ͪ
␳
nFD1/2
AN ␲k Dt
o g
2
System: 10Ϫ3 M Ag(NH ) /1.6 M NH , 1 KNO3 at pH
ϩ
2
3
3
jprogressive
ϭ
ͫ
1 Ϫ exp
ͩ
ͪ
Ϫ
ͪ
ͬ
1/2 1/2
1
1.—Figure 4a-c shows potentiostatic current transients obtained in
␲
t
2
Ϫ3
ϩ
a solution with 10 M Ag(NH ) /1.6 M NH , 1 KNO at pH 11,
3
2
3
3
1
/2
4
3
8␲cM
corresponding to different overpotentials between Ϫ0.032 and
Ϫ0.632 V. These responses have complex shapes, different from
each other. Figure 4a-b, for the same transient, shows more than one
kg ϭ
ͩ
͓13a͔
␳
current maximum (M1 and M ); after the dl charge. Note that the
2
where D is the diffusion coefficient, and c is the bulk concentration
of the silver species. Other parameters were described above for Eq.
2 and 3.
current of M in Fig. 4b is observed to be constant unlike that of M
2
2
in Fig. 4a. Figure 4c shows just one maximum, M . All transients
1
were analyzed using the model described for 2D growth proposed
This model is used to analyze experimental transients ͑Fig. 6a͒
and it shows that there is a progressive 3D growth limited by diffu-
sion of the electroactive species from the bulk dissolution toward the
interface ͑see details in Ref. 11͒. Figure 6b exemplifies two tran-
sients, one obtained at Ϫ0.49 V and the other at Ϫ0.69 V. The
current maxima are displaced at short times and cannot be analyzed
by the above model. Moreover, regarding the shape of the transient
changes ͑Ϫ0.69 V͒; first there is a current maximum that rapidly
decreases, then a small shoulder appears followed by an asymptotic
2
5-27
by Bewick in dimensionless coordinates from Eq. 2 and 3.
The
analysis reports a progressive 2D-2D transition for the overpotential
range between Ϫ0.032 and Ϫ0.132 V ͑Fig. 4a͒. The overpotential
range of Ϫ0.182 to Ϫ0.382 V ͑Fig. 4b͒ shows another 2D-3D tran-
sition. They are both limited by adatoms incorporation into the sub-
strate lattice ͑see detailed analysis in Ref. 12 and 24͒. At overpoten-
tials between Ϫ0.432 and Ϫ0.632 V ͑Fig. 4c͒, an instantaneous
2D-2D transition is present. In Fig. 5a-b, nonlinear fits of two ex-
perimental current transients are presented ͑Ϫ0.432 and Ϫ0.632 V͒,
using Eq. 10 and considering Eq. 2, which describes an instanta-
neous nucleation 2D (I2DIns) and Eq. 9 for Idl
current drop which does not reach zero. This type of transient is
scarcely reported in the literature. Budevski et al.1
7,27
consider that
this kind of response is due to a 2D growth of crystals on the pe-
riphery of the electrode. Table IV summarizes the results obtained as
a function of the potential applied.
Itotal ϭ Idl ϩ I2DIns͑M1͒ ϩ I2DIins͑M2͒
͓10͔
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Journal of The Electrochemical Society, 151 ͑3͒ C220-C228 ͑2004͒
C225
Table III. Types of growth, nucleation and kinetic parameters corresponding to the mechanism of silver electrocrystallization obtained for the
À3
¿
1
0
M Ag„NH … Õ1.6 M NH , 1 M KNO system at pH 11, as a function of the overpotential „␩….
3
2
3
3
System 10Ϫ3 M Ag͑I͒
M2 2D progressive
M1 2D progressive
*h ϫ 108
*h ϫ 108
͑cm͒
t I
ϫ10
t I
m m
ϫ10
m
m
5
5
**h ϫ 108
͑cm͒
␩
͑
͑cm͒
Nucleation
and growth
V͒
͑C cmϪ2͒
͑C cmϪ2͒
Ϫ0.032
Ϫ0.082
Ϫ0.132
1.43
1.51
1.68
0.15
0.16
0.17
1.09
1.20
1.58
0.11
0.12
0.16
Transition
2D-2D
progressive
0.32
0.38
0.46
Ϫ0.182
Ϫ0.232
Ϫ0.252
Ϫ0.282
Ϫ0.332
Ϫ0.382
2.84
3.11
3.87
3.17
3.93
4.37
0.29
0.32
0.40
0.33
0.41
0.45
M2 3D progressive
Transition
2D-3D
progressive
0.50
1.00
0.73
0.88
1.08
1.42
M1 2D instantaneous
M2 2D instantaneous
Transition
2D-2D
Ϫ0.432
Ϫ0.482
Ϫ0.532
Ϫ0.582
Ϫ0.632
6.09
7.95
9.19
12.07
14.95
1.07
1.39
1.61
2.12
2.62
1.90
2.35
2.70
3.06
3.40
instantaneous
Ϫ0.432
Ϫ0.632
2.53
2.61
0.44
0.46
13.31
13.52
2.33
2.37
dl
Ϫ3
3
Ϫ3
kg2 ϫ 103
kads ϫ 103
␩
No1 ϫ 10
kg1 ϫ 10
No2 ϫ 10
͑cm ͒
k
͑s
des
Ϫ1
͑V͒
Ϫ2
͑mol cm sϪ1
Ϫ2
͒
Ϫ2
͑mol cm sϪ1
Ϫ2
͒
Ϫ2
͒
͑cm
͒
͑A cm
͒
Ϫ0.432
Ϫ0.632
0.70
10.13
38.85
10.05
0.62
1.08
10.39
9.21
8.9
9.5
188.72
121.24
The thickness of a monolayer of silver deposited is 1.59 ϫ 10Ϫ8 cm ͑this term was evaluated from characteristics parameters͒. The thickness (*h) of
silver layer was obtained for Imtm using Eq. 6. The thickness of the silver formed (**h) was evaluated from the charge associated to the deposit ͑area
under the curve of the corresponding current transient͒.
System: 10Ϫ1 M Ag(NH ) /1.6 M NH , 1 KNO at pH
ϩ
2
2
2
3
3
3
3
Ϫ␲M k AN t
1
o
1
1.—Figure 7a-b shows the potentiostatic current transients obtained
jprogressive ϭ nFk2
ͫ
1 Ϫ exp
ͩ
␳2
ͪ
ͬ
͓15͔
3
Ϫ1
ϩ
2
in 10 M Ag(NH ) /1.6 M NH , 1 KNO solution at pH 11 upon
3
3
3
the application of different overpotential pulses in range of Ϫ0.08 to
Ϫ0.75 V. The transient response shown in each figure is different
and depends on the interval of the overpotential. Figure 7a shows a
family of current transients corresponding to the potential range of
Ϫ0.08 to Ϫ0.20 V. For all potentials, the rise of the deposition
current as a function of the deposition time was observed. In the
final stage, the current reached a steady-state condition. Figure 7b
shows that the shape of current transients are modified as the applied
overpotential becomes more negative. Within the overpotential
range between Ϫ0.22 and Ϫ0.35 V, a current maximum is well
defined, whereas at overpotentials ranging from Ϫ0.4 to Ϫ0.75 V,
an increase in current is observed which later decreases asymptoti-
cally to a determined value different of zero.
All parameters mentioned in these equations were described previ-
ously. The values obtained for kinetic parameters of nucleation are
reported in Ref. 11. The transients obtained in the interval of Ϫ0.22
to Ϫ0.35 V ͑Fig. 7b, i-v͒ were analyzed by the model proposed by
and Eq. 12 and 13 describes 3D growth of
nuclei limited by diffusion of the electroactive species. The current
1
,5,6
Scharifker and Hills,
transient obtained at overpotentials between Ϫ0.4 and Ϫ0.75 V ͑vi,
vii͒, shows that tm corresponding to current maxima (I ) occurred a
m
very short time and furthermore these cases are not possible to
evaluated through by Eq. 12 and 13, however similar responses are
17,30
reported for to 2D growth limited by diffusion.
Interestingly, in
Ϫ2
this case as well as in the previous case of 10 M ͑high concentra-
tions of Ag(NH3)2 species͒, current transient responses, at more
negative overpotentials, shows the 2D growth; this behavior is cu-
rious because for these conditions ͑high concentrations and more
negative overpotential͒, a 3D growth is expected. In order to eluci-
date the results, a detailed discussion of Tables II-V is given below.
ϩ
The transients of Fig. 7a were analyzed using the model pro-
posed by Armstrong.1
8,26
That model describes a 3D instantaneous
or progressive nucleation, limited by the lattice incorporation of
adatoms, and takes into account the overlapping of growing nuclei
with a specific geometry ͑right-circular cones͒. Each nucleus is
treated as a well-defined circular cone which grows on a foreign
substrate in a direction parallel to the surface with a rate constant
Discussion
Tables II and III corresponding to 10Ϫ4 and 10Ϫ3 M of Ag͑I͒
respectively, show that for the overpotential range between 0.078 to
Ϫ0.382 V, a 2D-2D transition are described. Furthermore, these
cases were reported to have formed less than a monolayer, not only
at less negative potential ranges but also at the intermediate and
more negative ranges. The low concentration of electroactive spe-
cies might be the cause of 2D growth on the VC surface. It is
(
k1). In the direction perpendicular to the substrate surface, nuclei
grow with a different rate constant defined as (k ). Equations 14
and 15 describe instantaneous and progressive nucleation, respec-
tively, in this model
2
2
2
2
Ϫ␲M k N t
1
o
jinstantaneous ϭ nFk2
ͫ
1 Ϫ exp
ͩ
ͪ
ͬ
͓14͔
␳2
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C226
Journal of The Electrochemical Society, 151 ͑3͒ C220-C228 ͑2004͒
Table IV. Types of growth and nucleation corresponding to the
mechanism of silver electrocrystallization obtained for the
À2
¿
1
0
M Ag„NH … Õ1.6 M NH , 1 M KNO system at pH 11 on
3
2
3
3
a
VC, as a function of the overpotential „␩….
1
0Ϫ2 M Ag͑I͒
6
␩
͑V͒
Nucleation
Growth
No. of
**h ϫ 10 /cm
monolayers
Ϫ0.09 Progressive
Ϫ0.14
3D
Controlled
by the
diffusion of
electroactive
species
59
65
62
0.94
1.03
0.98
Ϫ0.16
Ϫ0.18
Ϫ0.19
70
71
1.11
1.13
Ϫ0.24
Ϫ0.29
Ϫ0.31
Indefinite
2D
Limited
by the growth
on electrode
periphery
72
69
66
1.15
1.10
1.05
Ϫ0.34
Ϫ0.39
Ϫ0.44
Ϫ0.49
Ϫ0.54
Ϫ0.59
Ϫ0.69
69
67
61
60
70
62
73
1.10
1.07
0.98
0.96
1.12
0.98
1.16
a
The thickness of
a monolayer of silver deposited is 1.59
Ϫ8
ϫ 10 cm ͑this term was evaluated from characteristics param-
eters͒. The thickness of the silver formed (**h) was evaluated from
the charge associated to the deposit ͑area under the curve of the
corresponding current transient͒. The charge needed to form a mono-
layer (7.35 ϫ 1013 atoms) is 1.19 ϫ 10 C.
Ϫ5
Figure 6. Potentiostatic current transients obtained for the deposition of sil-
Ϫ2
ϩ
2
ver on a VC electrode from 10 M Ag(NH ) /1.6 M NH , 1 KNO solu-
3
3
3
These results prove the hypothesis proposed for this theory by Hills,
Sharifker, and Mostany regarding the diffusion-limited 3D
tion at pH 11. The overpotential of the electrode was different; see in the
figures.
1
,6
growth. At more negative overpotentials ͑Ϫ0.24 to Ϫ0.69 V͒, the
nucleation and growth are not ‘‘defined.’’ Following with a logical
behavior, for these experimental conditions, a 3D growth is ex-
pected, however distinctly transients, similar to those described by
important to note that the electrocrystallization processes occur in
Ϫ4
17
underpotential region ͑0.078, 0.028 V͒ in the solution of 10
M
the model of Budevski, appear. The shapes of these transients
Ag͑I͒, this is probably due to the specific interaction between the
correspond to a 2D growth limited by the substrate environment.
It is important to emphasize that when the Ag͑I͒ concentration is
10Ϫ3 M an instantaneous 2D growth is observed at more negative
overpotentials ͑Ϫ0.432 to Ϫ0.632 V͒, associated with the growth of
adatoms and substrate, provoked by the coordination sphere of silver
ϩ
2
ions ͓Ag(NH ) ͔ and the electrolyte (NH ). As the applied poten-
3
3
tial becomes more negative, the tendency to form the monolayer
increases, which indicates that new types of growth are induced by
changes in the potential conditions. The fact that growth zones may
be modified through the changes of potential shows that new silver
nuclei constantly develop in energetically preferential sites. This jus-
tifies the progressive nucleation in these cases. It is also likely to be
one of the causes of transitions observed in the growth ͑2D to 2D
and 2D-3D͒. Moreover, the growth transitions may also be attributed
to overlap effects between the deposited silver nuclei. For more
drastic energetic conditions ͑more negative overpotentials, Table
III͒, the growth of silver nuclei on silver can be observed because
more than one monolayer is formed. Therefore, the type of nucle-
Ϫ2
silver nuclei on silver. This indicates that for the 10 M Ag͑I͒
system at the overpotential of Ϫ0.24 to Ϫ0.69, the transient re-
sponse may be related to the nucleation and silver growth on silver.
Therefore, it could be speculated that at less negative potentials, the
response I vs. t is associated with the growth and nucleation of silver
on VC, whereas at more negative potentials, the growth and nucle-
ation of silver on silver is described.
Ϫ1
The results reported in Table V ͓10 M de Ag(I)͔, for less
negative overpotentials ͑Ϫ0.08 to Ϫ0.2 V͒, the type of growth re-
ported is 3D, limited by adatoms incorporation into the substrate
lattice. Moreover, the number of estimated monolayers is quite
large, which justifies the type of growth analyzed. Yet, in the de-
scription of experimental current transients using the model reported
o
ation probably changes from progressive (Ag /VC) to instantaneous
o
o
(
Ag /Ag ).
On the other hand, a 3D growth is observed for 10Ϫ2 M concen-
by Armstrong it was considered that at very short times ͑below 1 s,
18
tration of electroactive species ͑Table IV͒ at overpotentials range
between Ϫ0.09 to Ϫ0.19 V, whereas the number of monolayers and
thickness of the formed deposit is much greater than a monolayer,
which justifies the 3D growth. It is also worth noting that the num-
ber of monolayers and thickness of the formed deposit are practi-
cally constant at all overpotentials, indicating that once the nuclei
have grown and diffusion layers have overlapped, no additional
nucleation centers are formed, not even at more negative potentials.
Fig. 7͒ no overlap of formed nuclei takes place. Therefore, for such
conditions of overpotential, the initial growth of silver nuclei is
11
supposed to take place on VC. Furthermore, this model suggests
that at greater times, overlap effects show up through the formation
of a great number of monolayers ͑see Table V͒ that result in the
silver deposition onto silver. Unlike the 3D growth presented in
Table IV, the thickness and the number of monolayers grow consid-
erably as the overpotential becomes more negative. It is surprising
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Journal of The Electrochemical Society, 151 ͑3͒ C220-C228 ͑2004͒
C227
Table V. Types of growth and nucleation corresponding to the
mechanism of silver electrocrystallization obtained for the
À1
¿
1
0
M Ag„NH … Õ1.6 M NH , 1 M KNO system at pH 11 on
3
2
3
3
a
VC, as a function of the overpotential „␩….
1
0Ϫ1 M Ag͑I͒
6
␩
͑V͒
Nucleation
Growth
No. of
**h ϫ 10 /cm
monolayers
Ϫ0.08 Instantaneous
3D
Controlled
by the
lattice
incorporation
of adatoms
147
132
191
198
2.33
2.09
3.04
3.14
Ϫ0.10
Ϫ0.12
Ϫ0.14
Ϫ0.15
Ϫ0.16
Ϫ0.17
Ϫ0.20
301
250
262
332
4.79
3.96
4.16
5.28
Ϫ0.22
Ϫ0.24
Ϫ0.25
Progressive
3D
Controlled
by the
diffusion of
electroactive
species
381
429
458
6.06
6.81
7.27
Ϫ0.30
Ϫ0.35
448
518
7.11
8.22
Ϫ0.40
Ϫ0.45
Ϫ0.50
Ϫ0.55
Ϫ0.60
Ϫ0.75
Indefinite
2D
526
508
512
513
506
547
8.35
8.07
8.13
8.15
8.03
8.68
a
The thickness of
a monolayer of silver deposited is 1.59
Ϫ8
ϫ 10 cm ͑this term was evaluated from characteristics param-
eters͒. The thickness of the silver formed (**h) was evaluated from
the charge associated to the deposit ͑area under the curve of the
corresponding current transient͒. The charge needed to form a mono-
layer (7.35 ϫ 1013 atoms) is 1.19 ϫ 10 C.
Figure 7. Potentiostatic current transients obtained for the deposition of sil-
Ϫ1
ϩ
2
ver on a VC electrode from 10 M Ag(NH ) /1.6 M NH , 1 KNO solu-
3
3
3
Ϫ5
tion at pH 11. The overpotential ␩/V was different; Fig. 7a: ͑i͒ Ϫ0.08, ͑ii͒
Ϫ0.10, ͑iii͒ Ϫ0.12, ͑iv͒ Ϫ0.15, ͑v͒ Ϫ0.17, ͑vi͒ Ϫ0.20. Figure 7b: ͑i͒ Ϫ0.22,
͑ii͒ Ϫ0.24, ͑iii͒ Ϫ0.25, ͑iv͒ Ϫ0.30, ͑v͒ Ϫ0.35, ͑vi͒ Ϫ0.45, ͑vii͒ Ϫ0.75.
ϩ
of Ag(NH3)2 or the incorporation of silver adatoms into the sub-
strate lattice. Likewise, for these concentrations and very negative
overpotentials at which the amount of deposited silver is much
greater than a monolayer, 2D growths are observable, possibly as-
that for overpotentials between Ϫ0.22 to Ϫ0.35 V, a 3D growth
limited by diffusion of electroactive species appears. The nuclei
grow onto silver independent the amount of the monolayers formed
͑
Table V͒; yet, the energetic conditions are such that the process is
o
sociated with the growth of Ag on the previously deposited silver.
limited by diffusion. Once the conditions become energetically more
severe ͑Ϫ0.4 to Ϫ0.75͒, the amount of deposited metal becomes
significant and 2D growth of silver onto silver is observed again.
It is worth noting that, for the first time in the same chemical
system, the systematic evolution of electrocrystallization of 2D-3D
stages of nuclei growth on heterogeneous VC surfaces can be ob-
served through gradual modification of energetic conditions of the
interface by either changing the concentration of electroactive spe-
cies or the potential imposed to the electrode.
Conclusion
In this work, a systemic study of silver electrocrystallization pro-
cess was performed on a VC electrode in a medium of 1.6 M NH3 ,
Centro de Investigacion en Energia assisted in meeting the publication
costs of this article.
1
KNO at pH 11. It was carried out for a wide range of concentra-
3
ϩ
tions of electroactive species ͓Ag(NH ) ͔ and the potentials ap-
3
2
plied. It is important to emphasize that the potential pulse times for
these experiments are short ͑from 2 to 5 s͒, whereas in the literature
the times reported are much longer.
Appendix
Nonlinear Fit Procedure
The equations used for the nonlinear fit of the experimental current transients con-
tain different parameters that can be varied during the fitting procedure. In this Appen-
dix, the nonlinear procedure used in this work is shown for the case of Eq. 8 ͑as an
example͒.
In order to evaluate the kinetic parameters of nucleation and
growth, it was necessary to establish a methodology for identifica-
tion and analysis of current transients using different theoretical
models.
As described in the text, the total current for this case may be represented as follows
For low concentrations of electroactive species (10Ϫ4,10Ϫ3 M)
and not so negative overpotentials, it is possible to observe 2D-2D
and 2D to 3D growths. In these transitions, two types of silver
growth sites were identifiable, first on VC and after, on the recently
Itotal ϭ Idl ϩ I2DP M1 ϩ I2DP M2
͒
͓A-1͔
͓A-2͔
͑
͒
͑
where
and
Ϫ2
deposited silver. Concentrations greater than or equal to 10 M and
Idl ϭ kads exp͑Ϫkdest͒
not so negative overpotentials, 3D growth was observed of nuclei
forming deposits beyond a monolayer that depended on the diffusion
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C228
Journal of The Electrochemical Society, 151 ͑3͒ C220-C228 ͑2004͒
2
2
2
2
3
␲
nFMhANok t
␲ANoM k t
n␲FMh
g
g
ϭ 3.1124 ϫ 106
h
j2DP ϭ
exp
ͩ
Ϫ
ͪ
͓A-3͔
P1 and P9 are defined as equal to
␳
3␳2
␳
M1 and M2 in Eq. 1 correspond to each one maximum in the experimental current
transient and this equation is completely developed as
This procedure allows one to obtain the values of No , A, kg with physical meaning.
Furthermore, this procedure allows to independently determine values of kg and No .
This is the importance of this procedure.
The strategies used for the nonlinear fit procedure for different electrocrystallization
processes are more deeply discussed in a previous works.
n␲FMh1A1No1k t2
2
␲M A1No k t3
2
2
g1
1
g1
I ϭ kads exp͑Ϫkdest͒ ϩ
ͫ
exp
ͩ
Ϫ
ͪ
ͬ
3␳2
␳
n␲FMh2A2No k t2
2
␲M A2No k t3
2
2
2
g2
2
g2
ϩ
ͫ
exp
ͩ
Ϫ
ͪ
ͬ
͓A-4͔
␳
3␳2
References
this equation is parametrized such as
1
2
3
. B. Scharifker and G. Hills, Electrochim. Acta, 7, 879 ͑1983͒.
. R. T. Carlin, W. Crawford, and M. Bersh, J. Electrochem. Soc., 139, 2720 ͑1992͒.
. P. M. Rigano, C. Mayer, and T. Chierchie, J. Electroanal. Chem. Interfacial Elec-
trochem., 248, 219 ͑1988͒.
I ϭ k1 exp͑Ϫk2t͒ ϩ ͓P1P2P3P4t2 exp͑P5P2P3P4t ͔͒
3
ϩ ͓P9P6P7P8t2 exp͑P5P6P7P8t3͔͒
͓A-5͔
4
5
. L. Legrand, A. Tranchant, and R. Messina, J. Electrochem. Soc., 141, 378 ͑1994͒.
. B. R. Scharifker and J. Mostany, J. Electroanal. Chem. Interfacial Electrochem.,
where
1
77, 13 ͑1984͒.
6
. J. Mostany, J. Mozota, and B. R. Scharifker, J. Electroanal. Chem. Interfacial
Electrochem., 177, 25 ͑1984͒.
. G. Trejo, A. F. Gil, and I. Gonz a´ lez, J. Electrochem. Soc., 142, 3404 ͑1995͒.
. M. Palomar-Pardav e´ , M. T. Ram ´ı rez, I. Gonz a´ lez, A. Serruya, and B. R. Scharifker,
n␲FMh1
k1 ϭ kads , k2 ϭ kdes , P1 ϭ
,
P2 ϭ A1 , P3 ϭ No1 , P4 ϭ k2
,
g1
␳
7
8
␲
M2
␳2
J. Electrochem. Soc., 143, 1539 ͑1996͒.
P5 ϭ
´
´
3
9. A. Serruya, B. R. Scharifker, I. Gonzalez, M. T. Oropeza, and M. Palomar-Pardave,
J. Appl. Electrochem., 26, 45 ͑1996͒.
1
0. E. G o´ mez, E. Guaus, F. Sanz, and E. Vall e´ s, J. Electroanal. Chem., 465, 63 ͑1999͒.
11. M. Miranda-Hern a´ ndez, M. Palomar-Pardav e´ , N. Batina, and I. Gonz a´ lez, J. Elec-
n␲FMh2
P6 ϭ A2 , P7 ϭ No2 , P8 ϭ k2
, P9 ϭ
g2
␳
troanal. Chem., 443, 81 ͑1998͒.
1
2. M. Palomar-Pardav e´ , M. Miranda-Hern a´ ndez, N. Batina, and I. Gonz a´ lez, Surf.
Sci., 399, 80 ͑1998͒.
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͑1994͒.
17. E. Budevski, M. Fleischmann, C. Gabrielli, and M. Labram, Electrochim. Acta, 28,
925 ͑1983͒.
Kinetic parameters (P1 ,P2 ,P3 ......P9) were obtained as a result of the best fit ͑non-
linear regression͒ of Eq. A5 to experimental data. We performed the nonlinear fit using
the Statistica StatSoft software. This software requires the initial values of each param-
eter in Eq. A5, and these were estimated considering the following
1
1
1
1
the maximum current occurs at a time defined by
␳2
1/3
2
2
tm ϭ
͓A-6͔
ͩ
2
g
ͪ
␲
M ANok
1
8. R. D. Armstrong, M. Fleischmann, and H. R. Thirsk, J. Electroanal. Chem., 11, 208
1966͒.
the maximum current density is given by
͑
1
9. M. Palomar-Pardav e´ , M. Miranda-Hern a´ ndez, N. Batina, and I. Gonz a´ lez, Recent.
Res. Devel. in Electrochem., 1, 15 ͑1998͒.
20. G. Gunawardena, G. Hills, I. Montenegro, and B. Scharifker, J. Electroanal. Chem.
Interfacial Electrochem., 138, 225 ͑1982͒.
2
1/3
4
␲ANok ␳
g
Im ϭ zF
ͩ
ͪ
h exp͑Ϫ2/3͒
͓A-7͔
͓A-8͔
M
the product Imtm yields
2
1. A. Milchev and I. Montenegro, J. Electroanal. Chem. Interfacial Electrochem.,
33, 93 ͑1992͒.
22. G. Trejo, A. F. Gil, and I. Gonz a´ lez, J. Appl. Electrochem., 26, 1287 ͑1996͒.
ndez, N. Batina, and I. Gonz a´ lez, J. Phys. Chem. B, 105, 4214
3
2
zF␳h exp͑Ϫ2/3͒
Imtm ϭ
´
M
23. M. Miranda-Herna
2001͒.
͑
Using the experimental current transients, we obtained the different values of tm ͑A6͒,
Im ͑A7͒, and the product of Eq. A8, for each applied potential; these values are specific
and allowed to fix the initial limits of parameters in Eq. A5. Likewise, the convergence
24. M. Miranda-Hern a´ ndez, Ph.D. Thesis, Universidad Aut o´ noma Metropolitana Izta-
palapa, Mexico ͑1999͒.
25. A. Bewick, M. Fleischmann, and H. R. Thirsk, Trans. Faraday Soc., 58, 2200
criterion, means, and standard deviation for the fitting procedure was fixed in a factor of
͑
1962͒.
Ϫ4
1
0
. Furthermore the convergence criterion, means and standard deviation for the
2
2
6. R. Greef, R. Peat, L. M. Peter, D. Pletcher, and J. Robinson, Instrumental Methods
in Electrochemistry, Chap. 9, Ellis Horwood, Chichester, U.K. ͑1985͒.
7. H. R. Thirsk and J. A. Harrison, A Guide to the Study of Electrode Kinetics, Chap.
fitting, the values obtained in this manner, are accepted only when the magnitude ob-
tained for P5 , P1 , and P9 parameters ͑see below͒ are equals to those obtained by the
direct evaluation using previously reported values for: M ͑molecular weight of silver͒
and ␳ ͑silver density͒.
3
, Academic Press, London ͑1972͒.
2
2
8. F. E. Varela, L. M. Gassa, and J. R. Vilche, Electrochim. Acta, 37, 1119 ͑1992͒.
9. R. G. Barradas and E. Bosco, J. Electroanal. Chem. Interfacial Electrochem., 193,
␲
M2
␳2
2
3 ͑1985͒.
P5 ϭ constant value ϭ 110.37 ϭ
3
30. R. D. Armstrong and J. A. Harrison, J. Electrochem. Soc., 116, 328 ͑1969͒.
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