Study of the Electrodeposition of Rhodium on Polycrystalline Gold Electrodes by Quartz Microbalance and Voltammetric Techniques

Article abstract of DOI:10.1149/1.1643071

The electrodeposition of rhodium on different polycrystalline gold substrates from Na₃RhCl₆ · 12H₂O + NaCl solutions was investigated by electrochemical quartz crystal microbalance and voltammetric techniques. A study of the electrodeposition of rhodium from the concentrated chloride solutions used in this work show several features that are associated with potentiostatic transients with growth of the clusters controlled by mixed kinetics, charge transfer and diffusion. The results in this paper offer a clear warning against the blind interpretation of potentiostatic transients with models based on simple diffusion controlled growth. At low overpotentials the electrodeposition of rhodium is characterized by very slow charge transfer kinetics and starts with the formation of a submonolayer. Even at more negative potentials current transients and massograms recorded at constant potential exhibit an apparent induction time, indicating that growth initially is controlled by mixed kinetics, charge transfer and diffusion. Bulk deposition of rhodium is shifted to more negative potentials compared with other solutions, e.g., H₂SO ₄-based electrolytes, but the exact influence of rhodium speciation in the plating solutions remains unknown.

Full text of DOI:10.1149/1.1643071

Study of the Electrodeposition of Rhodium on Polycrystalline Gold
Electrodes by Quartz Microbalance and Voltammetric Techniques
Steven Langerock and Luc Heerman
J. Electrochem. Soc. 2004, Volume 151, Issue 3, Pages C155-C160.
doi: 10.1149/1.1643071
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2004 ECS - The Electrochemical Society
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Journal of The Electrochemical Society, 151 ͑3͒ C155-C160 ͑2004͒
C155
0
013-4651/2004/151͑3͒/C155/6/$7.00 © The Electrochemical Society, Inc.
Study of the Electrodeposition of Rhodium on Polycrystalline
Gold Electrodes by Quartz Microbalance and
Voltammetric Techniques
Steven Langerock and Luc Heerman*,z
Coordination Chemistry Group, Department of Chemistry, Katholieke Universiteit Leuven, B-3001 Leuven,
Belgium
The electrodeposition of rhodium on different polycrystalline gold substrates from Na RhCl •12H O ϩ NaCl solutions was
3
6
2
investigated by electrochemical quartz crystal microbalance and voltammetric techniques. A study of the electrodeposition of
rhodium from the concentrated chloride solutions used in this work show several features that are associated with potentiostatic
transients with growth of the clusters controlled by mixed kinetics, charge transfer and diffusion. The results in this paper offer a
clear warning against the blind interpretation of potentiostatic transients with models based on simple diffusion controlled growth.
At low overpotentials the electrodeposition of rhodium is characterized by very slow charge transfer kinetics and starts with the
formation of a submonolayer. Even at more negative potentials current transients and massograms recorded at constant potential
exhibit an apparent induction time, indicating that growth initially is controlled by mixed kinetics, charge transfer and diffusion.
Bulk deposition of rhodium is shifted to more negative potentials compared with other solutions, e.g., H SO -based electrolytes,
2
4
but the exact influence of rhodium speciation in the plating solutions remains unknown.
2004 The Electrochemical Society. ͓DOI: 10.1149/1.1643071͔ All rights reserved.
©
Manuscript submitted June 2, 2003; revised manuscript received September 15, 2003. Available electronically January 26, 2004.
Information on the initial stages of the electrodeposition of
rhodium is relatively scarce. Some groups studied the electrodepo-
precision of 0.1 Hz. A personal computer with GPIB and data ac-
quisition boards ͑National Instruments͒ was used for the simulta-
neous measurement of frequency and current ͑voltage drop across
the series resistor͒ with a minimum sample time of 10 ms. EQCM
measurements were performed with polished AT-cut gold-coated 10
MHz quartz crystals ͑Elchema, Potsdam, N.Y.͒ of 14 mm blank
1-3
4
5
sition of rhodium on platinum, vitreous carbon, and copper elec-
6
trodes. Kibler et al. reported the results of an in situ scanning tun-
neling microscope ͑STM͒ study of the initial stages of rhodium
7
electrodeposition on Au͑111͒. Arbib et al. investigated the nucle-
2
ation and growth kinetics of rhodium on polycrystalline gold and on
diam ͑mass sensitive area: 0.196 cm ͒. The sensitivity factor in the
8
19
Au͑100͒ single crystal electrodes. Recently, de Dios et al. studied
Sauerbrey equation ⌬f ϭ Ϫk⌬m (⌬f: the observed frequency
the preparation of Rh-adlayers on Pt͑100͒ electrodes and their elec-
change; ⌬m: mass change per area͒ was determined by galvano-
9
trocatalytic activity for the reduction of nitrous oxide. Baraka et al.
static copper deposition and is very close to the theoretical value
investigated the electrodeposition of rhodium metal on oxidized ti-
tanium electrodes. Interest in the electrodeposition of thin layers of
rhodium has been stimulated by the high activity of this metal for
the conversion of automotive exhaust fumes in three-way
2
Ϫ1
(
k ϭ 0.226 Hz cm ng ͒.
Rhodium metal cannot be dissolved anodically and therefore the
number of EQCM experiments had to be restricted because a ͑rather
expensive͒ quartz crystal could be used only once. Gold evaporated
on a silicon wafer ͓further indicated as Au͑Si͔͒ was used as the
disposable working electrode for other voltammetric experiments.
The wafer was cut into 2 ϫ 2 cm squares which fitted into an elec-
trochemical cell, constructed to ensure linear diffusion, with a cir-
1
0-13
catalysts.
This work reports a study of the nucleation and growth of
rhodium on polycrystalline gold electrodes by means of voltamme-
try and electrochemical quartz crystal microbalance ͑EQCM͒. The
advantage of the combined use of massograms and voltammograms
2
cular area of 0.35 cm exposed to the solution and a new working
for the study of different types of electrochemical reactions was
electrode was used for each experiment. Electrochemical experi-
ments were performed with Ecochemie Autolab PSTAT10 and Au-
tolab PGSTAT12 instruments. Before each experiment the solution
was thoroughly deoxygenated with purified, water-saturated nitro-
gen. All experiments were performed at room temperature (20
Ϯ 2°C).
illustrated recently by several authors.1
4-16
It is shown that the nucle-
ation and growth of rhodium on polycrystalline gold from concen-
trated chloride solutions is a typical example of the effect of slow
electrode kinetics on the morphology of potentiostatic transients.
Experimental
Potentials were measured vs. a mercury-mercurous sulfate refer-
0
20
The plating solution was prepared from Na RhCl •12H O ͑Alfa
ence electrode but were converted (E ϩ E ϭ 0.658 V ͒ to stan-
3
6
2
j
Aesar͒, NaCl and HCl ͑Fisher Chemicals͒, and double distilled wa-
ter. The pH of the solutions, aged for at least six months before use,
was 3-3.4 to avoid interference of the hydrogen evolution reaction.
Aquation is the principal reaction of the hexachlorocomplex in wa-
dard hydrogen electrode ͑SHE͒ to facilitate a comparison with the
results reported in other papers.
Results and Discussion
ter and aqueous solutions contain a mixture of Rh͑H O) Cl ,
2
3
3
A typical cyclic voltammogram ͑CV͒ and the corresponding
massogram for a 2 mM rhodium salt solution are shown in Fig. 1.
The potential was scanned from the conditioning potential, 0.450 V,
ϩ
2ϩ
Rh͑H O) Cl and, on ageing, Rh͑H O) Cl . Higher chlorocom-
2
4
2
2
5
plexes can exist in solutions with a sufficient large excess of chlo-
ride anions.1
7,18
Ϫ1
in the negative direction at a rate of 0.020 V s . The cyclic volta-
A home build quartz microbalance and oscillator were used for
EQCM experiments. The voltammetric measurements were per-
formed with a modified PAR model 174 polarographic analyzer with
the working electrode at hard ground and a resistor in series with the
mmogram shows a very sharp cathodic peak for rhodium deposition
at about Ϫ0.050 V in the forward scan and a very pronounced nucle-
ation loop in the reverse scan. The position of this peak shifts to
slightly more positive values when the concentration of the metal
ion is increased. A slight increase of the current is observed at 0.150
V, i.e., before the main peak in the CV. The voltammetric behavior is
essentially the same for the two types of gold substrates used in this
work. Anodic dissolution of rhodium has not been observed, in
platinum counterelectrode connection.19
A
Hewlett-Packard
HP53132a instrument was used for frequency measurements with a
4
-7
agreement with earlier reports, because a passivating oxide layer
is formed on the metal at positive potentials.
*
Electrochemical Society Active Member.
E-mail: luc.heerman@chem.kuleuven.ac.be
z
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C156
Journal of The Electrochemical Society, 151 ͑3͒ C155-C160 ͑2004͒
Figure 1. Cyclic voltammogram and massogram for rhodium deposition
from 2 mM Na RhCl •12H O ϩ 0.1 M NaCl on a polycrystalline gold elec-
3
6
2
Ϫ1
trode ͑conditioning and initial potential: 0.45 V; scan rate: 0.020 V s ͒.
The massogram shows a very small frequency decrease, ⌬f
Ӎ Ϫ1.5 Hz, in the potential region before the main peak in the CV.
In the background electrolyte containing no rhodium salt, a fre-
quency increase, ⌬f Ӎ 1 Hz, is observed over the same potential
interval. The formation of a monolayer of rhodium on an atomically
flat Au͑111͒ surface corresponds with ⌬f ϭ Ϫ54 Hz ͑667 ␮C
Ϫ2
cm ͒. Therefore, if the small current before the peak corresponds to
rhodium deposition, then the observed frequency response corre-
sponds to the formation of only 5-6% of a monolayer. Evidently it is
dangerous if not impossible to draw definite conclusions from such
CV experiments and this point is better investigated by constant
potential methods where the frequency response can be monitored
over longer time intervals. A comparison of the voltammogram and
the massogram for the main peak in the voltammogram shows rather
large deviations from the Sauerbrey equation. Thus, the frequency
decrease is much larger than expected on basis of the integrated
current and this point is addressed further in this paper ͑see Appen-
dix͒.
Figure 2. ͑a͒ Potentiostatic transients for rhodium deposition from
2
mM Na RhCl •12H O ϩ 0.1 M NaCl on Au͑Si͒ electrodes at different
3
6
2
electrode potentials ͑conditioning and initial potential: 0.450 V͒. ͑b͒ Dimen-
sionless plots of (i/imax)2 vs. t/t
for the transients of Fig. 2a. The solid
max
At this point it is already interesting to make some comparisons
4
lines are the theoretical lines for instantaneous respectively progressive 3D
nucleation with diffusion controlled growth.
with the results of earlier reports. Pletcher and Urbina studied the
deposition of rhodium from 10 mM Na RhCl ϩ 1 M NaCl ͑pH
3
6
6
3.9͒ on vitreous carbon electrodes. Kibler et al. ͑Fig. 2͒ studied
rhodium deposition on Au͑111͒ from 0.1 mM Na RhCl in
3
6
for deposition on a well-ordered Au͑111͒ crystal, with a small shoul-
der at 0.420 V; on a stepped crystal a single peak is observed at
0.410 V. They reported that there is no indication for underpotential
deposition ͑of course, the meaning of ‘‘upd’’ is not clear, because the
equilibrium potential is not known with certainty, vide infra͒. Kibler
7
0
.1 M H SO ϩ 10 mM HCl. Arbib et al. ͑Fig. 1͒ recorded CVs
2 4
for the deposition of rhodium from 10 mM Na RhCl • 12H O in
3
6
2
0
.1 M HClO on polycrystalline and ͑100͒Au substrates. However,
4
1/2
the value of i /cv ͑where ip is the peak current density of the
p
6
main peak in the CVs ͑vide infra͒, c is the concentration, and ␯ the
scan rate͒ estimated from these different papers is practically the
same as the value determined in this work. This shows that all the
rhodium species in solution, whatever the ionic speciation, can par-
ticipate in the deposition process as noted already by Pletcher and
et al. studied the deposition of rhodium by in situ STM at 0.430 V,
choosing this potential in order to slow down the deposition rate. At
this potential a rhodium bilayer is formed first, but the deposition
process is very slow ͑as expected at this potential͒ and it took about
20 min for completion of the bilayer. Further deposition on top of
the bilayer proceeds via a Stranski-Krastanov growth mode and is
accompanied by a strong roughening of the surface.
4
Urbina. However it remains unknown whether the different com-
plexes undergo charge transfer directly or the reduction process in-
volves chemical reaction steps.
7
Arbib et al. observed the start of rhodium deposition from
It is also interesting to make a comparison with the results ob-
Na RhCl •12H O in 0.1 M HClO on a Au͑100͒ single crystal elec-
3
6
2
4
6
Ϫ1
tained by other workers on gold electrodes. Kibler et al. reported
trode in a CV ͑scan rate: 0.020 V s ͒ at about 0.400 V, in essence
the same value as reported by Kibler et al. ͑taking into account the
different scan rates͒. However, Arbib et al. found only a rather
6
that rhodium deposition on Au ͑111͒ from 0.1 mM Na RhCl in
3
6
7
0
.1 M H SO ϩ 10 mM HCl starts at about 0.440 V. The peak in
2
4
Ϫ1
cyclic voltammetry ͑scan rate: 0.010 V s ͒ occurs at about 0.340 V
small peak at 0.325 V, which on the basis of the integrated charge
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Journal of The Electrochemical Society, 151 ͑3͒ C155-C160 ͑2004͒
was attributed to the formation of a ͑sub͒monolayer of rhodium.
C157
After this small first peak the current drops practically sharply and a
second much larger peak for rhodium deposition is observed at
about 0.050 V. Similar results were also reported for rhodium depo-
sition on polycrystalline gold electrodes. Chronoamperometric tran-
sients on Au͑100͒ showed two clearly distinct sections with two
current maxima. These transients were analyzed with a model that
associates the first peak at short times to 2D nucleation and growth
of the first two monolayers, followed at longer times by 3D nucle-
ation and growth of the metal on top of the first monolayer. How-
7
ever, Arbib et al. did not consider the well-documented fact that
rhodium or rhodanized electrodes are good catalysts for the elec-
2
1-25
troreduction of perchlorate ions to chloride.
The reduction of
perchlorate starts at about 0.300 V24 in 0.1 M HClO and the reduc-
4
tion rate follows the sequence Rh͑100͒ϾRh͑poly͒ϾRh͑111͒ under
transient conditions.2
3,24
Reduction of perchlorate is a pH-dependent
multistep reaction and accumulation of the reduction intermediates
2
3-25
and chloride can block the further reduction of this anion.
Therefore it seems quite plausible that the deposition of rhodium
starts at 0.400–0.450 V in 0.1 M HClO but that the further growth
4
of the rhodium islands is blocked by the intermediates of perchlorate
reduction and chloride. Chloride and intermediates are desorbed at
about 0.100 V and 3D nucleation occurs at slightly more negative
potentials. Such a scheme explains that the relative height of the two
peaks is not only a function of the rhodium concentration in solution
but also of the perchloric acid concentration.26 The reduction ofa
perchlorate on rhodium requires contact adsorption of this anion
and is suppressed in HClO solutions containing millimolar concen-
4
23-25
trations of chloride or sulfate.
However, when rhodium is
freshly deposited on a foreign substrate perchlorate reduction and
adsorption of other anions are competitive processes. Anyway, per-
chloric acid seems not to be well suited as a supporting electrolyte
for the fundamental study of rhodium deposition because of the
possible interference of perchlorate reduction on the deposited
metal.
Figure 3. ͑a͒ AFM surface morphology of the bare Au͑Si͒ substrate ͑area:
2 ϫ 2 ␮m ͒, which reveals some sputtering imperfections. ͑b͒ Surface mor-
3
Ϫ
2
The formal standard potential of the couple RhCl /Rh has been
6
given as 0.500 V,27 but this value is based on a rather uncertain
estimate of the stability constant of the hexachlorocomplex in HCl
solutions. Nevertheless, the potential where rhodium deposition
phology after recording
a transient for 10 s at Ϫ0.125 V (2 mM
Na3RhCl6•12H2O ϩ 0.1 M NaCl).
6
7
starts according to Kibler et al. and Arbib et al. is only slightly
more negative than this value of the standard which may indicate
rather facile electrode kinetics. The peak maximum in cyclic volta-
mmetry found in this work is shifted by about 0.400 V to more
negative potentials. The position of the peak maximum found in this
work corresponds well with the value reported by Pletcher and
2b, together with the theoretical lines for the limiting cases of in-
stantaneous and progressive 3D nucleation with diffusion-controlled
28-30
growth.
At short times there is an important contribution of
charging current which masks the initial rising part of the nucleation
transient. In the dimensionless plots, the experimental points after
the current maximum fall between the theoretical lines for both lim-
iting cases which may suggest slow nucleation with diffusion-
controlled growth.
4
Urbina for the deposition of rhodium from 10 mM Na RhCl
3
6
ϩ 1 M NaCl ͑pH 3.9͒ on vitreous carbon electrodes. This corre-
spondence between the positions of the peak maxima may be simply
accidental. In fact, the potential at which electrodeposition starts
In fact the current/time transients shown in Fig. 2a actually fit
quite well to a theoretical model for 3D nucleation on active sites
with purely diffusion-controlled growth ͑the fitting used the nonlin-
ear least square procedure based on the Levenberg-Marquardt algo-
͑
corresponding to the ‘‘critical overpotential’’͒ normally depends on
a set of experimental conditions ͑electrode material, pretreatment of
the electrode, surface roughness, . . . ͒. However, a limited number
of experiments with different electrode materials ͑gold, platinum,
vitreous carbon, . . . ͒ shows that the peak maximum occurs in a
very narrow region of potentials. This seems to indicate that a ki-
netic factor associated with the speciation of the rhodium complexes
in chloride solutions (pH Ӎ 3.5-4) is a dominating factor that de-
termines the onset of rhodium deposition.
2
9
rithm described previously ͒. This fitting yields seemingly ‘‘nor-
mal’’ values of the nucleation site density N , the nucleation rate
0
constant A, and the diffusion coefficient. For example, analysis of
6
the transient recorded at E ϭ Ϫ0.125 V yields N ϭ 7.2 ϫ 10
0
Ϫ2
Ϫ1
Ϫ6
2 Ϫ1
cm , A ϭ 8.1 s , and D ϭ 7.70 ϫ 10 cm s . Then, the ex-
pected number of nuclei equals the site density and the average
radius of a nucleus is calculated from the charge, which corresponds
roughly to the deposition of 10 monolayers, as 200 nm. However, a
scanning electron microscope did not reveal anywhere on the sur-
face nuclei of this anticipated size. Figure 3 shows an atomic force
microscope image of the sputtered gold electrode before and after
recording the transient.
Chronoamperometric transients recorded at different potentials
for nucleation on Au͑Si͒ are shown in Fig. 2a. The corresponding
2
dimensionless plots of (i/imax) vs. t/t , which are customary used
max
for the characterization of nucleation transients, are shown in Fig.
a
As pointed out recently by Lang and Hor a´ nyi,26 the reduction of perchlorate on
Ϫ
rhodium electrodes is better not described as a reaction of adsorbed ClO4 with adsorbed
The bare gold has a nanofibrous structure and the average depth
H atoms. Instead the reduction process corresponds to a slow decomposition of ad-
sorbed perchlorate followed by fast reduction steps. This conclusion is based on the fact
that reduction of perchlorate already proceeds at a measurable level in a potential range
where the surface concentration of adsorbed H atoms is negligible.
of the surface features R is a few nm. The surface after recording
a
the transient exhibits a strong increase of R and roughness. Evi-
a
dently, it is somewhat ambiguous to count nuclei sized in the na-
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C158
Journal of The Electrochemical Society, 151 ͑3͒ C155-C160 ͑2004͒
Figure 5. Dimensionless plot of (i/imax)2 vs. t/tmax for the transient of Fig.
4
3
a. The solid lines are the theoretical lines for instantaneous resp. progressive
D nucleation with diffusion controlled growth.
The experimental points fall below the theoretical line for pro-
gressive nucleation with diffusion-controlled growth for all times
except of course for t/tmax ϭ 1, which is the reference point͒. Such
behavior has also been observed by other authors, for example by J.
͑
3
1
C. Ziegler ͑copper deposition on a n-Si͑111͒:H surface from
0
.1 mM CuSO ϩ 0.1 MH SO solutions͒ and Schrebler et al.32
4
2
4
͑nucleation of rhenium on gold͒.
It thus is evident that the experimental results can not be de-
scribed by a model for 3D nucleation with simple diffusion con-
trolled growth ͑i.e., growth controlled by diffusion from the moment
the nuclei are born, vide infra͒. Such apparently ‘‘anomalous’’ plots
2
of (i/imax) vs. t/t
can be explained by a combination of slow
max
nucleation and slow charge transfer, i.e., kinetically hindered depo-
3
3
sition and growth. Cao and West described a numerical algorithm
to investigate the effect of slow charge transfer on potentiostatic
transients for 3D-nucleation and growth. The same problem was
3
4
investigated by Langerock et al. using an extension of the concept
of planar diffusion zones. In this context it is important to remember
Figure 4. ͑a͒ Potentiostatic current transient and corresponding massogram
for rhodium deposition from 2 mM Na RhCl •12H O ϩ 0.1 M NaCl on a
that the growth of a nucleus initially is always controlled by pure
3
6
2
35-37
charge transfer.
Growth controlled by diffusion will occur only
polycrystalline gold electrode at E ϭ Ϫ0.025 V ͑conditioning and initial
potential: 0.45 V͒. ͑b͒ Plot of Ϫ⌬f vs. time for the initial stages of rhodium
deposition on polycrystalline gold electrodes: ͑open circles͒ Ϫ0.025 V and
2
38
after an apparent induction time t Ӎ 0.2Dc/V v , where D is the
diffusion coefficient, c is the concentration of electroactive species,
Vm is the molar volume of the deposit, and vf
0
m
f
͑solid circles͒ 0 V.
ϭ (i /zF)exp(Ϫ␣zf␩) is the rate of the charge transfer reaction per
0
unit area. However, for this discussion it is nevertheless useful to
consider instantaneous nucleation with growth controlled purely by
diffusion at all times t as a reference to compare the effect of slow
nucleation or growth controlled by mixed kinetics, keeping other
factors as the site density, concentration, electrode potential, etc.
nometer range on a sputtered substrate like used in this work. But a
rough estimate indicates a nucleus number density in the range
9
10
Ϫ2
10 -10 cm , at least three orders of magnitude higher than ex-
pected on the basis of the fitting results for 3D nucleation and
growth. This clearly shows that analysis of nucleation transients
with theoretical models for simple diffusion-controlled growth can
lead to erroneous interpretations.
Some potentiostatic transients were also recorded with the
EQCM. A typical current transient ͑Ϫ0.025 V͒ and the correspond-
ing massogram are shown in Fig. 4a. The initial part of the gravi-
metric data is shown in Fig. 4b ͑for Ϫ0.025 V resp. 0 V͒. Both the
current and the EQCM results clearly show kind of an induction
time. Thus, it appears that rhodium deposition can start at quite
positive potentials but is kinetically very slow. The induction time
depends strongly on the applied potential and this explains why the
2
constant. In a plot of (i/imax) vs. time, this hypothetical situation
corresponds to the upper theoretical line shown in Fig. 5. Then one
can consider the effect of slow nucleation while still supposing
growth controlled purely by diffusion. The slower formation of nu-
clei results in a slower increase of the current and for the limiting
case of progressive nucleation ͑high value of the site density N0 ,
very low value of the nucleation rate constant A͒ the lower theoret-
ical line in Fig. 5 is obtained. For intermediate values of N /A the
0
2
points of (i/imax) vs. t/t
will fall between these two theoretical
max
limits and this is the basis to determine the values of N and A from
0
experimental transients if growth is supposed to be purely controlled
by diffusion. Now consider the case of instantaneous nucleation
with growth controlled by mixed kinetics. Again there is a retarda-
tion of the current increase, compared with diffusion controlled
deposition of the initially formed submonolayer is hardly seen in the
2
cyclic voltammetric experiments described earlier. A plot of (i/imax
)
vs. t/tmax for the transient recorded at Ϫ0.025 V is shown in Fig. 5.
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Journal of The Electrochemical Society, 151 ͑3͒ C155-C160 ͑2004͒
Conclusions
C159
The electrodeposition of rhodium on different polycrystalline
gold substrates from Na RhCl •12H O ϩ NaCl solutions was in-
3
6
2
vestigated by EQCM and voltammetric techniques. A study of the
electrodeposition of rhodium from the concentrated chloride solu-
tions used in this work show several features that are associated with
potentiostatic transients with growth of the clusters controlled by
mixed kinetics, charge transfer, and diffusion. The results in this
paper offer a clear warning against the blind interpretation of poten-
tiostatic transients with models based on simple diffusion controlled
growth. At low overpotentials the electrodeposition of rhodium is
characterized by very slow charge transfer kinetics and starts with
the formation of a submonolayer. Even at more negative potentials,
current transients and massograms recorded at constant potential
exhibit an apparent induction time, indicating that growth initially is
controlled by mixed kinetics, charge transfer, and diffusion. Kibler
6
et al. reported that rhodium deposition on Au͑111͒ from 0.1 mM
Na RhCl in 0.1 M H SO ϩ 10 mM HCl at low overpotentials
3
6
2
4
starts with the formation a bilayer and that further deposition pro-
ceeds via a Stranski-Krastanov growth mode, accompanied by a
strong roughening of the surface. This conclusion was based upon in
situ STM measurements with well-defined electrode surfaces. The
results of this study with polycrystalline gold substrates agree well
with the findings of Kibler et al. Bulk deposition of rhodium is
however shifted to more negative potentials compared with other
Figure 6. Plot of the ratio (d⌬fexp /dt)/(d⌬fdep /dt) vs. time for the transient
shown in Fig. 4a. The quantity (d⌬fexp /dt) was obtained from the experi-
mental frequency vs. time response. The quantity (d⌬fdep /dt) is calculated
from the current vs. time curve, using the Sauerbrey equation ⌬fdep
ϭ Ϫk⌬mdep with the experimentally determined value of the proportional-
ity factor.
solutions, e.g., H SO -based electrolytes. The effect of rhodium spe-
2
4
ciation in the plating solutions on charge transfer kinetics remains
however unknown and may explain eventually the divergent experi-
mental observations made by different workers.
growth, because initially the growth is controlled by pure charge
transfer. This means that qualitatively the effect of slow nucleation
or mixed kinetics on a potentiostatic transient cannot be distin-
guished. For the case of instantaneous nucleation with growth con-
Acknowledgment
The authors are indebted to the F.W.O.-Vlaanderen ͑Fonds voor
Wetenschappelijk Onderzoek͒ for financial support of this work and
for the award of a doctoral fellowship ͑Aspirant F.W.O.͒ to S.L. The
authors thank also Dr. J.-M. Friedt and Dr. Kang-Hoon Choi ͑IMEC,
Leuven͒ for help with the AFM measurements.
trolled by mixed kinetics the experimental points in a plot of
2
(
i/imax) vs. t/t
will also fall between the theoretical lines for
max
3
3,34,38
the limiting cases with diffusion controlled growth.
In the
case of progressive nucleation and a sufficiently low value of vf
Katholieke Universiteit Leuven assisted in meeting the publication costs
of this article.
ϭ (i /zF)exp(Ϫ␣zf␩), the experimental points in a plot of
0
2
(
i/imax) vs. t/t
show the behavior seen in Fig. 6. Thus, the ex-
max
Appendix
perimental results described earlier can be explained by the combi-
nation of progressive nucleation and growth controlled by mixed
kinetics. It is important however to realize that any other factor that
The expression for the experimental frequency response ⌬fexp during an EQCM
45,46
experiment can be quite generally written as
causes an apparent induction time, for example site birth effects as
*
⌬
fexp ϭ Ϫk͑⌬mdep ϩ ⌬m ͒ ϩ ⌬f␩ ϩ ⌬fr ¯
͓A-1͔
considered by Milchev,3
static transient.
9,40
will have the same effect on a potentio-
The first term on the right is the Sauerbrey term which accounts for the frequency shift
due to mass changes on the electrode (⌬mdep is the mass change due to faradaic
deposition/dissolution of electroactive material and ⌬m* includes the contributions of
adsorption, trapping of solvent molecules . . . ͒. Other possible contributions to the
frequency shift include changes of viscosity, roughening of the surface, . . . etc. If only
the mass changes corresponding with deposition/dissolution are considered, then
Again, remember that the case of so called progressive nucle-
ation corresponds to very high values of the ratio N /A so that the
0
maximum number of clusters is not limited by the number of active
sites. This is akin to saying that the limiting case of progressive
nucleation corresponds to nucleation on a homogeneous surface
⌬
fdep ϭ Ϫk⌬mdep
͓A-2͔
(
N /A → ϱ). Most theories of the potentiostatic transient for 3D
0
nucleation with diffusion controlled growth are based on the concept
Evidently ⌬mdep , hence ⌬fdep , can be calculated from the measured current, assuming
a 100% current efficiency. A typical plot of (d⌬fexp /dt)/(d⌬fdep /dt) vs. time during the
recording of a potentiostatic transient for deposition of rhodium on gold is shown in Fig.
͑this kind of plot has the advantage over a plot of ⌬fexp /⌬fdep vs. time that it shows
deviations of the Sauerbrey equation as a transient phenomenon͒.
of planar diffusion/exclusion zones.2
8,29
An exclusion zone is a cir-
cular area spreading around a growing cluster where the formation
of new nuclei is impossible because of the depletion of electroactive
6
material. For diffusion-controlled growth the radius of the zones
The frequency shift is much higher than anticipated on the basis of the Eq. A-2 but
only during the initial stages of electrodeposition. Similar results were obtained for
increases with t1/2 and the overlap of the zones will result in a finite
cyclic voltammetry. Large deviations from the ‘‘simple’’ Sauerbrey equation were re-
number of observable clusters, i.e., the nucleus saturation density
NS .41 If the growth is controlled by mixed kinetics the zones ini-
tially grow at a much smaller rate ͑compared with the diffusion
47-52
ported previously by other authors
but the interpretation of these deviations may be
highly case sensitive. A simple explanation for the observed behavior could be that the
development of surface roughness is accompanied by trapping of solvent molecules.
However it seems unlikely that the contribution of roughening and water trapping can
explain the observed deviations because the average depth of the surface features is too
controlled case͒. This can result in a value of N that can be several
S
orders of magnitude higher than would be estimated on the basis of
a model that is based on purely diffusion controlled growth, spe-
cially when the nucleus saturation density is not limited by the avail-
ability of active sites. This behavior has been observed in this work
and similar findings have been reported over the years by several
52
small. Stress caused by the large lattice misfit between the rhodium deposit and the
gold substrate ͑the lattice constants are 3.8043 and 4.0786 Å, respectively͒ is the most
5
1
likely cause for the excess frequency shift. This would explain that the ‘‘simple’’
Sauerbrey equation applies after the deposition of the first 4-5 monolayers. To test this
hypothesis more results are needed, including a complete impedance analysis of the
EQCM response during the initial stages of deposition, and experiments in this direction
are planned for the near future.
4
2-44
other workers.
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