Pulsed electrodeposition of two-dimensional Ag nanostructures on Au(111)

Article abstract of DOI:10.1021/jp061780m

One-step pulsed potential electrodeposition of Ag on Au(111) in the underpotential deposition (UPD) region has been studied in 0.5 mM Ag ₂SO₄ + 0.1 M H₂SO₄ aqueous electrolyte at various pulse durations from 0.2 to 500 ms. Evolution of the deposited Ag nanostructures was followed by in situ scanning tunneling microscopy (STM) and by measurement of the respective current transients. At short pulse durations a relatively high number density (4 × 10 ¹¹ cm^-2) of two-dimensional Ag clusters with a narrow size and distance distribution is observed. They exhibit a remarkably high stability characterized by a dissolution potential which lies about 200 mV more anodically than the typical potential of Ag-(1 × 1) monolayer dissolution. To elucidate the underlying nucleation and growth mechanism, two models have been considered: two-dimensional lattice incorporation and a newly developed coupled diffusion-adsorption model. The first one yields a qualitative description of the current transients, whereas the second one is in nearly quantitative agreement with the experimental data. In this model the transformation of a Ag-(3 × 3) into a Ag-(1 x 1) structure indicated in the cyclic voltammogram (peaks at 520 vs 20 mV) is taken into account.

Full text of DOI:10.1021/jp061780m

J. Phys. Chem. B 2006, 110, 15905-15911
15905
Pulsed Electrodeposition of Two-Dimensional Ag Nanostructures on Au(111)
D. Borissov, R. Tsekov, and W. Freyland*
Institute of Physical Chemistry, UniVersity of Karlsruhe, D-76128 Karlsruhe, Germany
ReceiVed: March 22, 2006; In Final Form: May 19, 2006
One-step pulsed potential electrodeposition of Ag on Au(111) in the underpotential deposition (UPD) region
has been studied in 0.5 mM Ag SO + 0.1 M H SO aqueous electrolyte at various pulse durations from 0.2
to 500 ms. Evolution of the deposited Ag nanostructures was followed by in situ scanning tunneling microscopy
STM) and by measurement of the respective current transients. At short pulse durations a relatively high
2
4
2
4
(
11
-2
number density (4 × 10 cm ) of two-dimensional Ag clusters with a narrow size and distance distribution
is observed. They exhibit a remarkably high stability characterized by a dissolution potential which lies about
2
00 mV more anodically than the typical potential of Ag-(1 × 1) monolayer dissolution. To elucidate the
underlying nucleation and growth mechanism, two models have been considered: two-dimensional lattice
incorporation and a newly developed coupled diffusion-adsorption model. The first one yields a qualitative
description of the current transients, whereas the second one is in nearly quantitative agreement with the
experimental data. In this model the transformation of a Ag-(3 × 3) into a Ag-(1 × 1) structure indicated
in the cyclic voltammogram (peaks at 520 vs 20 mV) is taken into account.
I. Introduction
carried out by switching the electrode potential of the working
electrode in a conventional three-electrode electrochemical cell
from E1 ) 550 mV to E2 ) 20 mV vs Ag /Ag for a very
In recent years, pulsed potentiostatic deposition has been
employed to fabricate and tailor nanomaterials with specific
properties. This includes nanostructures such as long metal
+
short time; see Figure 1A. The silver wire of the reference
electrode had a diameter of 0.3 mm, and its tip was fixed 1
1
2
nanowires, thin homogeneous magnetic films, and nano-
2
mm above the working electrode with an area of 0.56 cm . The
3
particles or nanocrystals with excellent size monodispersity;
corresponding uncompensated iR drop we estimate to be 20 mV
for a recent review see ref 4. The particular advantage of the
pulsed electrodeposition technique is that nucleation and growth
can be controlled separately by varying the potential pulse
amplitudes and durations. In addition, the technique is fast and
inexpensive.
For the examples given above, square wave potential pulses
in the overpotential region (OPD) have been used and deposition
was studied typically on surfaces with low interfacial energy
2
for current densities of 15 mA/cm . The duration of the potential
pulse was varied from 0.2 to 500 ms. For these fast measure-
ments, the potentiostat was equipped with a special interface
card, ADC750 (AutoLab, Nederlands), which has a maximum
conversion speed of 750 kHz and can measure current-time
response of the conventional three-electrode electrochemical cell
with a shortest interval of 1.3 µs. After one potential pulse from
E1 ) 550 mV to E2 ) 20 mV, the electrochemical cell was
switched off and the scanning tunneling microscopy (STM)
experiment was performed at the open circuit potential (OCP).
In this work, a mechanically polished single-crystal Au(111)
was used as a working electrode with a size of 10 mm × 10
mm and a thickness of 2 mm and an orientation misfit of better
than 0.1 exhibiting a grain size less than 30 nm (MaTeck,
Germany). The following cleaning procedure was employed:
First, the crystal was electropolished in 0.1 M H2SO4 electrolyte
in a conventional electrochemical cell with platinum as a
reference and a counter electrode at a constant applied voltage
of +4 V for 1 min. Subsequently, the oxide layer was dissolved
in 1 M HCl. Then the crystal was thoroughly rinsed with Milli-Q
water. To get large monatomic flat terraces, the single-crystal
Au(111) was flame annealed in a hydrogen burner to a reddish
color for 10 min. Afterward, it was quenched in Milli-Q water,
and a droplet of Milli-Q water was left on the gold surface to
prevent adsorption of impurities. This procedure resulted in large
atomically flat and clean terraces.
5
,6
such as graphite. This leads to electrocrystallization of three-
dimensional (3D) metal particles under conditions of instanta-
neous nucleation and diffusion-controlled Vollmer-Weber
4
growth mode. In this investigation, we have focused on pulsed
electrodeposition in the underpotential range (UPD) where
usually homogeneous monolayer formation is expected by
gradually changing the electrode potential. In our experiments
we used a high-energy surface Au(111) substrate. Ag UPD has
been selected in these studies as here a detailed knowledge of
UPD phase formation and transitions in different electrolytes
7
-10
exists.
So, the main objective of this work is to study 2D
phase formation and growth of Ag on Au(111) under pulsed
electrodeposition conditions in comparison with conventional
UPD. The evolution of the 2D nanostructures as a function of
time and potential has been followed by in situ STM imaging.
II. Experimental Section
Pulsed electrodeposition in the UPD region of 0.5 mM Ag2-
SO4 (p.a, Merck, Germany) solution on Au(111) in 0.1 M H2-
SO4 (p.a, Merck, Germany) sulfuric aqueous electrolyte was
In situ STM investigations were carried out with a home-
built STM head employed with a 2µ scanner. The STM head
was driven by a Molecular Imaging (MI) Pico SPM controller.
STM tips used in this work were made of PtIr wire (90%-
*
Author to whom correspondence should be addressed. E-mail:
Werner.Freyland@chemie.uni-karlsruhe.de.
1
0.1021/jp061780m CCC: $33.50 © 2006 American Chemical Society
Published on Web 07/26/2006

15906 J. Phys. Chem. B, Vol. 110, No. 32, 2006
Borissov et al.
Figure 1. (A) Cyclic voltammogram recorded on single-crystal Au(111) in 0.5 mM Ag
shows a potential jump. (B) After one potential pulse from E1 ) 550 mV to E2 ) 20 mV the electrochemical cell is switched off and STM
experiment is performed.
2
SO
4
+ 0.1 M H
2
SO
4
at a sweep rate of 30 mV/s. The arrow
Figure 2. (A) 500 nm × 500 nm in situ STM image of Au(111) after one potential pulse from 550 to 20 mV with a duration of 0.2 ms in 0.5 mM
Ag
2
SO
4
+ 0.1 M H
2
SO
4
. (B) 250 nm × 250 nm area of the substrate recorded at OCP after 24 h. (C) Cross section analysis of 2D Ag clusters
yielding a height of 2 Å.
10% respectively, 0.25 mm in diameter, Advent, England). The
III. Results
tips were produced by electrochemical etching in 4 M NaCN
using the “drop-off” method. A PtIr wire, after being washed
with ethanol, was vertically anchored to a manipulator and fixed
in the middle of a ring wire of Pt acting as a counter electrode.
A thin lamella of NaCN solution was formed on the ring
electrode crossing the PtIr wire. Then an ac voltage of 4 V was
applied between the Pt ring electrode and PtIr wire. Due to the
After one potential pulse from 550 to 20 mV in 1 mM solution
of Ag with a duration of 0.2 ms, the Au(111) surface was
examined by in situ STM at OCP. The measured OCP was
stabilized at 70 mV. Figure 2A presents an STM image of the
surface showing a surprisingly large number of two-dimensional
+
(
2D) silver nanoclusters (islands) that have a narrow size
distribution suggesting an instantaneous nucleation.
“
necking-in” effect, the down part of the wire drops off when
its weight exceeds the tensile strength of the necking-in region.
Just before dropping the voltage was reduced to 2 V. The down
part was caught in a small plastic tip holder so that the apex of
the tip was not damaged. For a better control all tips were
checked by an optical microscope with 40× magnification
before use. To minimize Faradaic currents in STM measure-
ments carried out in the electrolyte, the freshly prepared tips
were insulated with an anodic epoxy paint (BASF, ZQ 84-3225
A detailed analysis of the STM images reveals that the 2D
Ag nanoclusters are formed all over the surface without any
preferential position on the gold terraces or at the step edges.
Also, it was found that they have a very high stability because
no significant change in their size and spatial distribution was
observed for a long span of time; see Figure 2B. A cross section
analysis (Figure 2C) reveals silver clusters which have a
monatomic height of about 2 Å. To test whether 2D Ag clusters
grow under potentiostatic conditions, the electrochemical cell
was switched on and the electrode potential was gradually
reduced from 70 mV (the actual value of OCP) to 0 mV. From
OCP to 30 mV there is no significant change on the surface
0
201, Germany). For this purpose 0.8 cm of PtIr tips were
immersed into the epoxy paint and a dc voltage of 25 V was
applied for 5 min between the tip (anode) and a counter Pt plate
electrode (cathode).

Electrodeposition of Ag on Au(111)
J. Phys. Chem. B, Vol. 110, No. 32, 2006 15907
Figure 4. A sequence of STM images showing the dissolution of the
Ag-(1 × 1) adlayer, size 250 nm × 250 nm: (A) at 0 mV; (B) at 30
mV; (C) at 40 mV; (D) at 50 mV. The white arrow shows that after
dissolution the same 2D pulsed Ag clusters appear on the surface as
before (Figure 3) indicating a very high stability.
stripped at positive potentials where usually the (1 × 1)-Ag
adlayer is completely dissolved in accordance with the CV (A3
process in the CV). This strongly indicates that the 2D clusters
exhibit an anomalous stability. Similar behavior of small Ag
and Au nanoclusters on HOPG has already been observed.1
Moreover, a striking result is that some kind of “memory effect”
is observed because after dissolution the STM pictures reveal
the pulse deposited 2D Ag clusters at the same places on the
surface as at the beginning of the deposition; see the white
arrows in Figure 4D and Figure 3A. The 2D Ag clusters are
evident even at 200 mV as displayed in Figure 5; see the arrows
in parts A and B of Figure 5. They start to dissolve slowly in
the potential range from 200 to 400 mV; see Figure 4B-D.
Possibly, the initial stability of the pulse deposited 2D Ag
clusters is due to surface alloying which was observed for this
2,13
Figure 3. A sequence of in situ STM images after 0.2 ms potential
pulse from 550 to 20 mV at various electrode potentials showing the
formation of one monolayer of Ag-(1 × 1), size 250 nm × 250 nm:
(A) at 30 mV; (B-D) at 20 mV; (E) at 10 mV; (F) at 0 mV. The time
span between different images is about 5 min.
(Figure 3A). In accordance with the CV, at 20 mV a new silver
phase is being formed at the step edges and at 2D silver clusters
as well; see Figure 3B. The development of the island growth
was continuously followed at constant applied electrode potential
of 20 mV. In Figure 3B-D sequential images are shown with
a time interval of about 5 min. The new Ag islands enlarge
relatively fast their size and indicate a strong tendency to merge
with each other as well as with the existing Ag clusters.
Apparently, the silver islands that stem from the pulsed clusters
grow with different rates. Approaching the Nernst equilibrium
potential, the surface coverage of Ag on Au(111) increases. It
is worth noting that almost one monolayer of Ag coverage is
reached at 0 mV and the pulsed clusters become almost an
unrecognizable part of it (Figure 3F). Interestingly, it seems
that before the monolayer of Ag covers the whole surface, some
islands are formed on the top of the silver monolayer, perhaps
due to the fact that the electrodeposition takes place at or near
nonequilibrium conditions. A pseudomorphic (1 × 1) adlayer
of Ag is formed that covers and follows the topography of the
Au(111) surface.7
7
system recently.
The effect of potential pulse duration on the nucleation density
and size of 2D Ag clusters has been studied for pulses in the
range from 0.2 to 500 ms. Qualitatively, the STM images show
that for larger pulse durations the cluster size increases whereas
the nucleation density decreases; see Figure 6.
A quantitative analysis of the nearest neighbor distance
distribution of 2D Ag clusters is presented in Figure 7 for a
pulse experiment of 0.2 ms; see also Figure 2 for the respective
STM images. In comparison to a random distribution the
experimental histogram is narrower. Distances below 5 nm are
missing indicating an average cluster size of 5 nm. The mean
nearest neighbor distance is determined to be 10 ( 2 nm,
whereas the value of the random distribution is 8.1 nm.14 The
average nucleation density, in this case, is found to be N0 )
-11
11
-2
4 × 10 cm .
Dissolution of the deposited monolayer of Ag was studied
by in situ STM as a function of the applied electrode potential.
In Figure 4 STM snapshots are displayed during the dissolution
process. It should be noted that although the 2D Ag clusters
become a part of the (1 × 1) Ag monolayer, they cannot be
For the pulsed electrodeposition of Ag on Au(111) in the
UPD range, we have recorded the current transients at different
pulse durations. Typical results are shown in Figure 8. For short
pulses the current decays continuously with time; see the
example of a 10 ms pulse time. At larger times a clear bump or

15908 J. Phys. Chem. B, Vol. 110, No. 32, 2006
Borissov et al.
Figure 7. Histogram of distances between nearest neighboring Ag
clusters after using a 0.2 ms potential pulse, for STM image; see Figure
1
4
2
A. The line is drawn according to the Poisson distribution law.
nucleation and growth mechanism of 2D pulsed electro-
deposition, in the following we concentrate on the discussion
of the current transients. For this aim we consider two simple
model descriptions. In the first case we start from standard
nucleation modelssinstantaneous or progressive nucleations
and assume that the rate-determining step of cluster growth is
the lattice incorporation of Ag adatoms at the expanding
periphery of the nucleation centers. Taking into account double
layer charging, the total current-time dependence in the case
of instantaneous nucleation is given by (see, e.g., refs 15 and
Figure 5. STM images (250 nm × 250 nm) of dissolution of 2D pulsed
Ag nanoclusters: (A) at 100 mV the pulse deposited 2D clusters are
still visible; (B) at 200 mV the clusters slowly start to dissolve; (C) at
4
00 mV and (D) at 500 mV they are almost completely dissolved.
1
6)
2
i (t) ) i exp(-t/τ) + p t exp(-p t /2)
(1)
tot
0
1
2
2
2
2
2
where p1 ) 2πFN0Mk h/F and p2 ) 2πN0M k /F . Here F is
the Faraday constant, N0 is the initial number density of
nuclei, k is the rate constant of lattice incorporation, h is the
height of 2D Ag clusters, and M and F are the atomic weight
and density of a 2D Ag cluster. The time constant of double
layer charging is denoted by τ. Figure 9 shows a fit by eq 1 of
the current transient measured for a pulse time of 50 ms. The
red curve corresponds to instantaneous nucleation, the blue
one to progressive nucleation. Both fits are in qualitative
agreement with the experimental result whereby the instanta-
neous nucleation fit gives a better description consistent with
the STM observations. The time constant τ is determined to be
∼
0.4 ms.
From the fit parameters p1 and p2 the following quantities of
nucleation and growth model can be derived. The ratio p1/p2
2
yields a charge coverage of about 19 µC/cm , which is
comparable in magnitude to the charge coverage of the (3 × 3)
2
structure (59 µC/cm ) occurring at 500 mV but is smaller by
roughly a factor of 10 in comparison with (1 × 1) structure
Figure 6. STM images show the effect of pulse duration on cluster
size after a potential pulse from 550 to 20 mV: (A) 0.5 ms; (B) 10
ms; (C) 100 ms; (D) 500 ms pulse duration.
2
7
2
(
222 µC/cm ) at 20 mV. Estimating the product N0k from p1
3
2
-2
-6
yields a value of 1.2 × 10 mol s cm , which is roughly 5
orders of magnitude larger than the corresponding kinetic
parameters determined in Cu UPD at near equilibrium condi-
1
8
-4
maximum is visible at times near 2-3 ms. The strong drop of
the current below 1 ms we ascribe to the double layer charging
effect; see below.
tions. This implies a large rate constant k of the order of 10
-
1
-2
11
-2
mol s cm taking for N0 the above value of 4 × 10 cm .
In conclusion it is difficult to say how far the simple lattice
incorporation model describes the experimental observations.
Since the simple 2D lattice incorporation model does not
allow a quantitative description of the measured current
transients, we have developed a new model based on coupled
diffusion-adsorption kinetics. In brief, the regular diffusion
equation has been solved with the following boundary and initial
conditions: in the bulk electrolyte, a constant concentration far
away from the Au(111) electrode, c∞ ) c(t,z)∞), is taken,
IV. Discussion
Several features of the STM observations of pulse deposited
2D Ag clusters on Au(111) are worth noting: an unusual
stability of clusters on dissolution, the high nucleation density
of nearly random distributed clusters, and the peaks in the
current transients at short times. To get further insight into the

Electrodeposition of Ag on Au(111)
J. Phys. Chem. B, Vol. 110, No. 32, 2006 15909
Figure 8. Current-time (i-t) responses recorded during the potential pulse from 550 to 20 mV in 0.5 mM Ag
at different pulse durations.
2
SO
4
2 4
+ 0.1 M H SO on Au(111)
Further analysis requires modeling of the adsorption kinetics.
From the STM and experimental CV results it is clear that the
Ag atoms can form two different stable surface phases on the
Au surface: the Ag-(3 × 3) phase occurring at 520 mV and
the Ag-(1 × 1) at 20 mV; see also ref 7. Let us denote the
dilute one as the R-phase and the condensed one as the â-phase.
If the electrode potential changes continuously, the R-phase
appears at about 520 mV and then it is transformed into the
â-phase at around 20 mV. However, in contrast to quasi-
equilibrium electrodeposition, if the potential jumps from 550
mV directly to 20 mV, there is no R-phase at the beginning
and, hence, the formation of the two phases will take place
simultaneously. It is conceivable, that the creation of the â-phase
requires first the presence of the R-phase. Thus, a linearized
kinetic model of the adsorption of Ag on Au electrode after the
potential jump reads
∞
R
∞
R
Figure 9. Best fits of theoretical i-t expressions for instantaneous or
progressive nucleation under assumption that the rate-determining step
is the lattice incorporation of Ag adatoms at the expanding periphery
of the nucleation centers.
∂ Γ ) k c (Γ - Γ ) ≈ k Γ c - k c Γ
(3)
t
R
a
s
R
R
s
a ∞ R
∞
â-R
∞
∂tΓâ - R ) k Γ c (Γ
- Γâ - R) ≈ k c Γ ΓR -
t
R
s
t ∞ â-R
∞
k c Γ Γ
∞ R â-R
(4)
t
whereas at the electrolyte/Au(111) interface the diffusion and
adsorption fluxes are equal, i.e., D(∂zc)z)0 ) ∂tΓ; here D is the
bulk diffusion coefficient and Γ is the adsorption of Ag atoms;
the initial conditions are constant concentration everywhere in
the bulk c(t)0,z) ) c∞ and a bare Au surface Γ(t)0) ) 0 at
the beginning of the process. Hence the local concentration is
given by the following Laplace image c˜ (s,z) (see, e.g., ref 18)
where ΓR is the number of atoms per unit area forming the
R-phase, Γâ-R is the number of atoms per unit area added
between the atoms of the dilute R-phase to convert it into the
∞
∞
â-R
denser â-phase, and ΓR and Γ
represent the saturation
coverages, cs ) c(t,z)0) is the subsurface concentration, kR is
the adsorption constant, and kt is the rate constant of transforma-
tion of R- into â-phase. Note, that desorption is completely
neglected in eqs 3 and 4. Solving these equations by Laplace
c˜ ) c /s - Γ˜
x x
s/D exp(- s/Dz)
(2)
∞

15910 J. Phys. Chem. B, Vol. 110, No. 32, 2006
Borissov et al.
transformation yields the following Laplace images of the
adsorptions
∞
R
Γ˜ ) k Γ c˜ /(s + k c )
(5)
(6)
R
a
s
a ∞
∞
∞
R
∞
Γ˜ â-R ) k c Γ k Γ c˜ /(s + k c )(s + k c Γ )
t
∞
â-R
a
s
a
∞
t ∞ R
The total adsorption of Ag atoms on the Au surface is a sum of
the partial adsorptions above, i.e.
∞
R
∞
â-R
s + k c (Γ + Γ
)
∞
R
t
∞
Γ˜ ) Γ˜ + Γ˜
) k Γ c˜
(7)
R
â-R
a
s
(
∞
â-R
s + k c )(s + k c Γ
)
a
∞
t
∞
Introducing eq 7 in eq 2 leads to an expression for the Laplace
image of the local concentration. Using it one can derive the
Laplace image of the subsurface concentration in the form
Figure 10. The theoretical dependence of current vs time for a 50 ms
potential pulse obtained from the coupled diffusion-adsorption model
according to eq 10 in comparison to experimental data points.
c˜ s )
∞
R
(
s + k c )(s + k c Γ )
a
∞
t
∞
c∞
∞
R
∞
∞
R
∞
â-R
s[(s + k c Γ ) + k Γ (s + k c Γ + k c Γ
)
x
s/D]
a
∞
a
R
t
∞
t
∞
(8)
which depends on both the diffusion in the bulk and the kinetics
of adsorption. Finally, the measured electric current is a sum
of the electric current due to Ag deposition and the current due
to the charging of the electric double layer
˜ı ) Fs Γ˜ + A/(s + 1/τ)
(9)
Here A is a constant and τ is the time constant of the double
layer charging. Substituting c˜ s from eq 8 and introducing the
result of Γ˜ in eq 9 leads to the following expression for the
Laplace image of the current
˜ı )
∞
R
∞
R
∞
â-R
Figure 11. Evolution of the relative subsurface concentration
Fk c Γ (s + k c Γ + k c Γ
)
a
∞
t
∞
t
∞
∞
c
Γ
s
/c
â-R/Γ
∞
(black line) and the relative coverage by the R-phase Γ
R
/ΓR
-
∞
R
∞
∞
R
∞
â-R
∞
∞
(
s + k c )(s + k c Γ ) + k Γ (s + k c Γ + k c Γ
)
x
s/D
â-R
(red line) and by the â-phase Γâ-R/Γ
â-R
(blue line),
a
∞
t
∞
a
R
t
∞
t
∞
respectively.
∞
R
i - Fk c Γ
0
a
∞
+
(10)
response for a 50 ms potential pulse as calculated from eq 10
is plotted in Figure 10. As is seen the theory reproduces very
well the characteristic maximum at about 2 ms after the double
layer charging. Obviously, this model gives a better fit to the
experimental data than the simple lattice incorporation descrip-
tion, although slight deviations remain in the time interval
between 10 and 20 ms. In Figure 11 the time dependence of
the surface concentration, cs(t), and the adsorption of R- and
â-phases, respectively, are plotted. Evidently, at the beginning,
the dilute phase (R) forms, which later completely transforms
into the condensed one (â). The surface concentration is
substantially decreased compared to the bulk one and the slow
diffusion kinetics determines the current-time response at larger
times. Due to the limitation approximation, the model applies
only in the limit of short times and does not describe the
evolution of the coverage at longer times.
s + 1/τ
where the constant A is expressed by the initial current i0 )
i(t)0). The analytical inversion of the Laplace image from eq
0 is impossible. For this reason numerical calculations have
1
been employed. Some of the parameters in eq 10 are known:
-
5
2
19
c∞ ) 1 mM, D ) 1.65 × 10 cm /s, and τ ) 0.4 ms. From
our previous investigations7 we conclude that the R-phase
corresponds to 0.25 ML, while the condensed phase (â-phase)
forms a complete monolayer. Thus, one can estimate that the
maximal adsorptions are equal to Γ ) 0.25NA/πd ) 1.6
) 0.75NA/πd ) 4.8 µmol/m , where d )
.89 Å is the distance between the surface Au atoms. Because
of the high electrolyte concentration, the relaxation of the double
layer is very fast, on the order of 1 ms. For the initial current,
we adopt the value of i0 ) 16 mA/cm in accordance with Figure
C. The remaining other two parameters are determined by a
∞
R
2
2
∞
â-R
2
2
µmol/m and Γ
2
2
8
Acknowledgment. We acknowledge financial support by
fit of the dependence i vs t for the 50 ms pulse experiment; see
Figure 8C. For this purpose, the inverse Laplace transformation
of eq 10 was performed numerically and then fitted to the
experimental i vs t for 50 ms pulse data varying the constants
Fonds der Chemischen Industrie.
References and Notes
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417, 217.
-
1
ka and kt. The best fit corresponds to kac∞ ) 0.1 ms and
(
∞
â-R
-1
ktc∞Γ
) 1 ms . The theoretical dependence of the i-t

Electrodeposition of Ag on Au(111)
J. Phys. Chem. B, Vol. 110, No. 32, 2006 15911
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