The electroreduction kinetics of silver sulfite complexes

Article abstract of DOI:10.1016/j.electacta.2008.04.038

The electroreduction kinetics of silver sulfite complexes was investigated by rotation disk electrode (RDE) voltammetry, chronopotentiometry (CP) and electrochemical impedance spectroscopy (EIS). The stability constants of the silver sulfite complexes, pβ₂ = 7.9 and pβ₃ = 8.53 were determined. For the series of isopotential solutions investigated, a reaction order of 0.67 was obtained, the diffusion coefficient of the silver complexes varies in the range of 3.36 × 10^-6 to 5.54 × 10^-6 cm² s^-1 and the silver degree of complexation (2.31-2.67) were found. The analysis of the RDE, CP data and EIS spectra indicate the existence of a slow stage of the silver electrocrystallization in the region of the equilibrium potential and at stronger polarization of the electrode at initial time moments.

Full text of DOI:10.1016/j.electacta.2008.04.038

Electrochimica Acta 53 (2008) 6513–6520
Contents lists available at ScienceDirect
Electrochimica Acta
journal homepage: www.elsevier.com/locate/electacta
The electroreduction kinetics of silver sulfite complexes
a,∗
a
a
a
b,1
ˇ
Gintaras Baltr u¯ nas , Au sˇ ra Vali u¯ nien e˙ , Zana Margarian , Gintar e˙ Viselgien e˙ , George Popkirov
a
Department of Physical Chemistry, Vilnius University, Naugarduko 24, LT-2006 Vilnius, Lithuania
Faculty of Engineering, University of Kiel, Kaiserstr. 2, D-24143 Kiel, Germany
b
a r t i c l e i n f o
a b s t r a c t
Article history:
The electroreduction kinetics of silver sulfite complexes was investigated by rotation disk electrode (RDE)
voltammetry, chronopotentiometry (CP) and electrochemical impedance spectroscopy (EIS). The stabil-
ity constants of the silver sulfite complexes, pˇ2 = 7.9 and pˇ3 = 8.53 were determined. For the series of
isopotential solutions investigated, a reaction order of 0.67 was obtained, the diffusion coefficient of the
silver complexes varies in the range of 3.36 × 10 to 5.54 × 10 cm s and the silver degree of com-
plexation (2.31–2.67) were found. The analysis of the RDE, CP data and EIS spectra indicate the existence
of a slow stage of the silver electrocrystallization in the region of the equilibrium potential and at stronger
polarization of the electrode at initial time moments.
Received 7 February 2008
Received in revised form 10 April 2008
Accepted 14 April 2008
Available online 22 April 2008
−6
−6
2
−1
Keywords:
Silver sulfite
Electrocrystallization
Charge transfer stage
Mechanism
©
2008 Elsevier Ltd. All rights reserved.
1
. Introduction
X-ray photoelectron spectroscopy (XPS) investigation [4], has
revealed that in the presence of sulfite ions, the silver diox-
ide adsorption on a silver monocrystalline (1 0 0) surface is
accompanied by the build-up of a layer of chemisorbed sulfite.
Surface-enhanced Raman scattering (SERS) spectra of electrochem-
ically roughen silver surface [5], have shown that the adsorption
behavior of the silver oxianion can be characterized by (i) weak
electrostatic adsorption of sulfate and dithionate and (ii) by strong
sulfite and tiosulfate chemisorption on the silver surface. The
Silver electrodeposition from sulfite electrolytes is considered
to be one of the most promising processes to replace the extremely
toxic traditional cyanide-based silver plating solutions with the
additional advantage, that sulfite electrolytes can be successfully
applied for silver deposition for micro-electro-mechanical systems
(
MEMSs).
There are very few works dedicated to the chemistry and elec-
trochemistry of silver sulfite complexes. Most publications related
with this subject are concerned with the question of applicability.
Silver sulfite complexes are stable in low alkaline solutions, thus
the silver plating process based on electroreduction of these com-
plexes is quite a prospective one [1,2]. The authors of [3] have used
the rotating disk electrode (RDE) technique to measure the limiting
current density of the electroreduction of sulfite complexes in solu-
authors of [5] have, thus, assumed that a coating of Ag SO3 builds
up on silver surface.
In order to investigate the mechanism of electrochemical reac-
tion, i.e. to identify the complex particle, which directly participates
in the charge transfer stage we may apply the well known [6,7]
2
equation which relates the exchange current density, j , to the free
0
ligand concentration CL:
tions, prepared with 0.025 M free sulfite ions and 0.925 M NaNO .
3
;
−
4
∂ ln j0
zF ∂E(0)
The complexes concentrations in the analyzed solutions were 10
=
RL + ˛
(1)
−
4
−4
∂ ln CL
RT ∂ ln CL
2
× 10 and 5 × 10 M. Further, the limiting current density was
found to depend linearly on the square root of the RDE rotation
speed. The diffusion coefficient of Ag(SO3)
where RL is the electrode reaction order depending on the ligand,
˛ is the charge transfer coefficient, and E(0) is the equilibrium elec-
trode potential. As follows from Eq. (1) in order to determine the
reaction order, we need to know the value of the charge transfer
coefficient. Fortunately, in the case of isopotential solutions Eq. (1)
simplifies [7] to:
3−
complexes calculated
2
−
6
2
−1
from the experimental data was reported to be 5.6 × 10 cm s , a
value approximately three times less then the diffusion coefficient
−
5
2
−1
of free (hydrated) silver ions 1.55 × 10 cm s as determined in
the same study.
ꢀ
ꢁ
∂
∂
ln j0
ln CL
=
RL
(2)
∗ Corresponding author. Tel.: +370 5 233 6419; fax: +370 5 233 0987.
E
(0)
E-mail address: gintaras.baltrunas@chf.vu.lt (G. Baltr u¯ nas).
1
Thus performing the measurements in a series of isopoten-
tial solutions we were able to determine the reaction order RL
On leave from Central Laboratory for Solar Energy and New Energy Sources,
Bulgarian Academy of Sciences, Sofia, Bulgaria.
0
013-4686/$ – see front matter © 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.electacta.2008.04.038

6
514
G. Baltr u¯ nas et al. / Electrochimica Acta 53 (2008) 6513–6520
by simple measurement of the exchange current density. Val-
ues of the current density measured upon equilibrium potential
with the RDE were extrapolated to infinite rotation rate, this, it
was possible ‘to purify’ the charge transfer overvoltage and to
determine exchange current density by using the classic kinetic
equation [8]:
The specific objectives of this study was to investigate the kinetics
of silver sulfite complexes electroreduction, i.e. to determine the
limiting stages of the electrochemical reaction; to determine the
dependences of the exchange current density on the free sulfite
ions concentration in a series of isopotential solutions; to make
clear the mechanism of electrochemical reaction (to identify the
particle participating in the charge transfer reaction).
ꢂ
ꢀ
ꢁꢅ
ꢃ
ꢄ
˛
zF
ˇzF
RT
j = j0 exp
ꢀEct − exp
−
ꢀEct
(3)
RT
2. Experimental
where ˛ and ˇ are the charge transfer coefficients (˛ + ˇ = 1), and
Ect is the charge transfer overvoltage. For higher values of the
The solutions prepared were based on distilled water and p.a.
ꢀ
quality Na SO and Ag SO The electrolytes were prepared freshly
2
3
2
4.
overvoltage, |ꢀEct| ꢀ RT/zF, one of exponential terms of Eq. (3)
becomes negligible and a linear dependence is obtained in the
plot of ln (j) vs. ꢀEct. An extrapolation towards ꢀEct = 0, thus yields
before every new experimental series, in order to avoid the sulfite
ion oxidation by air oxygen. All experiments were performed at
◦
2
0 C temperature.
the value of ln j . It should be possible to avoid the requirement
0
Theelectroreductionofsilversulfite complexeswasinvestigated
|
ꢀEct| ꢀ RT/zF by applying the coordinates of Allen–Hickling [9],
using a rotating disk electrode of 0.2 cm2 surface area made of a
silver rod embedded in Teflon to isolate its side surface. An Ag disk
of 25-mm diameter was fitted in parallel to the working area of the
working electrode and served as counter electrode.
when ln (Y) is plotted instead of ln (j), where
j
Y = 1
− exp(± zF/RTꢀEct)
(4)
The silver electrode potential was measured potentiometrically
using a saturated Ag/AgCl, KCl electrode as the reference electrode
Here the sign ‘−’ is for anodic currents, whereas ‘+’ is for cathodic
currents. Using these new coordinates one of the exponential terms
in Eq. (3) will also be eliminated and for the case of a charge trans-
fer controlled process rate the dependence ln (Y) vs. ꢀEct must be
linear even for low polarizations.
(EH = 0.2 V). In this work, all potentials are referred to the scale of
the standard hydrogen electrode: E(0) = EAg/AgCl + 0.2 V.
Chronopotentiometry and EIS measurements were performed
using an ordinary three-electrode cell. The working electrode was
a platinum wire of 0.5 mm in diameter and 1.08 cm in length, which
During the process of metal electrodeposition a new phase
is formed, thus the total rate of the process should also depend
on (possibly) slow crystallization phenomena. The deposition
can be slowed down by: (i) slow formation of two- and/or
three-dimensional crystallization centres and (ii) by slow sur-
face diffusion of ad-atoms [7,10]. Obviously, these two stages are
strongly related—the more crystallization centers are formed, the
less is the distance, which ad-atoms have to diffuse on the sur-
face. The concentration of crystallization centers very fast increases
receding from equilibrium potential [10], i.e. the input of slow
crystallization stage decreases. Therefore, the influence of the
slow electrocrystallization can be easily avoided by performing
measurements at a relatively high electrode polarization, i.e. at
potentials rather far from the equilibrium potential. Conversely,
in order to investigate the crystallization separately, the electrode
potential should be chosen as close as possible to its equilib-
rium value. In the later case, the electrochemical impedance
spectroscopy (EIS) represents the method of choice, because an
impedance data can be obtained in a measurement with very low
deviation from the equilibrium state. The formation of the crystal-
lization centers, their growth, and the surface diffusion of ad-atoms
will show up in the measured impedance spectra, however a good
understanding of these processes and their effect on the obtained
spectra is to be developed yet [11–13]. Probably the most successful
model describing the surface diffusion impedance was proposed
in [13]. The authors succeeded in modeling the surface diffusion
impedance by parallel connected surface diffusion resistance and
capacitance [13]. Unfortunately, these both parameters depend
on the alternating current frequency as this is the case with the
Warburg impedance. In our analysis we have chosen a simplified
approach, taking into account that the non-dimensional alternating
current frequency term of the mathematical expressions given in
−2
was coated (10 ␮m) with silver galvanostatically (3 mA cm ) in
a sulfite-based electrolyte (2 M Na SO3 and 0.3 M AgNO ) before
2
3
each measurement. The surface area of the working electrode was
2
2
0
.17 cm . The counter electrode was made of an Ag spiral of 40 cm .
The reference electrode was a saturated Ag/AgCl, KCl electrode,
placed as close as possible to the working electrode by means of
a Lugin capillary.
The EIS measurements were performed galvanostatically at
controlled zero current using a fast Fourier transform (FFT)
impedance spectrometer as described in[14,15]. Chronopotentiom-
etry measurements were performed using ␮AUTOLAB (Type III)
measurement system.
3. Results and discussion
3.1. Stability of complexes
It was determined experimentally that anodic and cathodic
yields of the electroreduction of silver sulfite complexes are prac-
tically equal to 100%. This shows that electrochemical reaction
1
−2x
0
2−
Ag(SO3)
+ e ꢀ Ag + xSO
3
could be treated as equilibrium.
x
Since literary data concerning stability of silver sulfite com-
plexes are rather contradictionary [16,17], we attempted to
determine the dissociation constants of complexes experimentally.
We have measured the silver electrode potential as a function
of Na SO3 concentration for different concentrations of Ag(I) in
2
the solution. At higher concentration of the sulfite (>0.3 M), the
2−
slopes (∂E(0)/∂log[SO3 ]) of all curves become −150 to −160 mV.
Such values can be related to the dominating role of the com-
5−
plex Ag(SO3)
3
in the solutions. For lower concentrations of the
sulfite ions, the potential dependence on the sulfite concentra-
tion becomes more complicated. This may be explained either by
[
13] becomes sufficiently large for higher frequencies. As a result,
the surface diffusion impedance becomes qualitatively similar to
the conventional Warburg impedance, with a constant B charac-
terizing the surface diffusion of ad-atoms instead of the Warburg
constant for the case of three-dimensional diffusion:
3
−
the possible coexistence of two kinds of complexes Ag(SO )
3
2
5−
and Ag(SO3)
3
or by the suggestion that part of the sulfite ions
2−
are bounded into complexes, i.e. [SO3
]
ꢂ= [Na SO ]. The less the
2
3
total concentration of sulfite is, the more these both factors influ-
ence the value of the equilibrium potential. In order to describe
Zꢁ = −Zꢁꢁ = Bω−1/2
(5)

G. Baltr u¯ nas et al. / Electrochimica Acta 53 (2008) 6513–6520
6515
the Ag(I)–SO32 system, the following system of equations was
−
3.2. Slow silver electrocrystallization
solved:
At first, in order to investigate the kinetics of the electrochem-
ical reaction, voltammograms were measured in the range around
the equilibrium potential, while the rotation speed of the rotating
disk electrode was held fixed. Unfortunately, consecutive mea-
surements yielded voltammograms with slightly lower current
densities in every further measurement. This complicates the data
extrapolation to ı = 0, where ı is the diffusion layer thickness,
because the slope of the curves depends additionally on the time
interval, the electrode has been immersed into the solution. There-
fore, the tactic of the measurements was changed: mechanically
(polishing) and electrochemically (deposition of a new Ag layer)
prepared rotating disk electrode surface was held for 5 min at a
selected potential, and thereafter the current density was measured
at five different rotation speeds. Subsequently, the electrode sur-
face was subjected to mechanical and electrochemical preparation
again and the experiment was repeated for the next polariza-
tion potential value. This measurement sequence has significantly
decreased the deviation of measured data. Almost linear depen-
Ag ] + [AgSO −] + [Ag(SO3) 23 −] + [Ag(SO3) 35 −] = A;
+
[
3
−
+
2−
2−
−
3−
ˇ [AgSO ]=[Ag ] · [SO3 ]; [SO ] + [AgSO ] + 2[Ag(SO )
]
1
3
3
3
3
2
2
3[Ag(SO3) −] = L;
5
ˇ [Ag(SO ) ] = [Ag ] · [SO3 ] ;
3−
+
2−
+
3
2
3
3
3
5
−
+
2−
ˇ [Ag(SO ) ] = [Ag ] · [SO3
]
(6)
3
3
3
where ˇ , ˇ and ˇ1 are the stability constants of complex
3
2
5
−
+
+
2−
3−
+
2−
and
3
ions Ag(SO )
ꢀ Ag + 3SO
; Ag(SO3)2 ꢀ Ag + 2SO
3
3
3
−
2−
Ag(SO3)3 ꢀ Ag + SO
, respectively. A is the total concentration
3
of silver complexes, and L is the total concentration of sodium sul-
fite.
Electrochemical system of silver–silver sulfite complexes is sta-
ble in aqueous solutions only at L/A ꢀ 1. Analyzing potentiometric
data according to Eq. (6) we found that for all investigated solu-
+
−
3−
5−
tions expression [Ag ] + [AgSO3 ] ꢃ [Ag(SO )
] + [Ag(SO3)3 ] is
3
2
−
1
dencies of j vs. ı could be found (Fig. 2). This enabled us to find
the cathodic and anodic current densities, when ı = 0, i.e. to find
how the current density depends on the electrode potential in the
case when the process rate is not influenced by diffusion. As an
example, this is shown in Fig. 3, curve 1 for a solution containing
valid. Obtained result characterizes only volumetric concentra-
tion of ions, but it does not mean anyhow that in the charge
transfer reaction the ions of Ag+ or/and AgSO3− cannot domi-
nate. In that case analytical expressions of Eq. (6) become simpler.
Using simplified Eq. (6) and the Nernst equation the equilib-
rium potential of the silver electrode (E(0)) as a function of
free sulfite concentration at any values of ˇ2 and ˇ3 can be
calculated:
0
.05 M Ag(I) and 1.0 M Na SO . This curve is similar to the typi-
2 3
cal case of a charge transfer reaction. However, unlike the classic
charge transfer Eq. (3), characterized by exponential dependence
between j and ꢀEct only at considerable deviations from equi-
librium (|ꢀEct| ꢀ RT/zF) in our case the exponential dependence
appears already from equilibrium (Fig. 3, curve 1). As a compari-
ꢆ
ꢉ
+
RT
Aˇ3
Ag/Ag
E(0) = E(0)
+ F ln
(7)
ꢇ
ꢈ
ꢇ
ꢈ
2
3
−2
−1
2−
2−
son a voltammogram calculated from Eq. (3) for j = 1.1 mA cm ,
ˇ ˇ
3
SO3
+
SO3
0
2
and ˛ = ˇ = 0.5 is presented in Fig. 3, curve 2. The calculated curve
is linear in almost the entire polarization interval of interest with
deviations to appear only for |ꢀE| > 40 mV. A fit of the experimen-
tal data with Eq. (3) provides satisfactory coincidence only when
Fig. 1 shows the experimental data (symbols) compared with
computer simulated curves (lines) obtained upon best fit of the
both constants according to Eq. (7). The best fit value of the product
˛
≈ ˇ > 5, what is not consistent with the classical kinetic equa-
−
1
ˇ ˇ
3
was 0.25. Calculated values of ˇ have an average value
3
2
tion. Furthermore, by calculating the polarization resistance ∂E/∂j,
−
9
−9
−9
of ˇ =2.79×10 ± 0.08 (or pˇ =8.53), with ˇ
=2.99×10
;
;
5
2
3
3
3(0.005M)
ˇ3(0.03M)=3.08×10
when ꢀE = ± 5 mV, values of the order of 10 ꢁ cm was obtained
−
−
9
−9
;
ˇ
=3.57×10
;
ˇ
=2.8×10
−2
3(0.01M)
3(0.02M)
corresponding to an extremely low value (0.25 ␮A cm ) of the
9
−9
ˇ3(0.04M)=2.57×10
and ˇ3(0.05M)=2.79×10 . The average value
exchange current density. For higher values, |ꢀE| > 35 mV, i.e. at the
−8
of ˇ=1.2×10 , thus pˇ =7.9, respectively.
2
onset of the linear regime (q.v. Fig. 4, filled circles), extrapolation
Fig. 1. Dependence of the equilibrium Ag electrode potential on the concentration of
reversible [SO32 ] concentrationinsolutionscontaining Ag(I): (1) 0.01 M;(2) 0.03 M;
(
(
−
Fig. 2. Dependence of silver dissolution/deposition current densities on the diffu-
sion layer thickness. Solution composition: 0.05 M Ag(I); 1.0 M Na2SO3; pH 9.5. The
numbers indicate the electrode polarization value.
3) 0.05 M. Symbols show the experimental data; solid curves are calculated via Eq.
7).

6
516
G. Baltr u¯ nas et al. / Electrochimica Acta 53 (2008) 6513–6520
Fig. 5. Electrochemical FFT impedance spectra. Solution composition: 0.05 M Ag(I),
0.5 M Na2SO3, pH 9.5. Time passed after immersing the Ag electrode into the solu-
tion: (1) 3 s; (2) 10 s; (3) 26 s; (4) 56 s; (5) 102 s; (6) 193 s; (7) 375 s; (8) 565 s and (9)
748 s.
Fig. 3. Voltammograms determined without influence of diffusion. (1) obtained
from experimental data presented in Fig. 2 and (2) theoretically calculated charge
−2
transfer voltammogram for j0 = 1.1 mA cm and ˛ = ˇ = 0.5.
on the theory proposed in [13]. A freshly prepared silver electrode
was quickly immersed into the solution containing 0.05 M Ag(I)
towards ꢀE = 0, yields j ≈ 0.25 mA cm−2, i.e. it is about three orders
0
of magnitude higher. A similar result could be obtained under
conditions of equilibrium with the slow crystallization stage deter-
mining the total process rate [10]. It can be seen from Fig. 4, open
circles, that applying the coordinates of Allen–Hickling extends
the linear range, however apparent deviation still remains. This
demonstrates, that the charge transfer stage is not the solely rate
determining process in the vicinity of the equilibrium potential
and 0.49 M Na SO3 (pH 9.5). Impedance spectra in the range from
2
1.5 Hz to 5.1 kHz were recorded in galvanostatic regime at zero dc
current in order to assure equilibrium potential conditions (Fig. 5).
Thereafter, the electrode was held in the solution for 1 h in order to
establish an equilibrium surface structure and an electrochemical
impedance spectrum was obtained in a frequency range extended
in the lower range to 0.0305 Hz, q.v. Fig. 6.
(
± 30 mV). The extrapolation of experimental points, far from equi-
Initially, we tried to fit the impedance data yielded for frequen-
cies above 6.4 Hz using the simplified equation (5) and the typical
equivalent circuit taking into account charge transfer, Rct, diffusion,
ZW, and adsorption, R , C on the surface, as shown in Fig. 7. After-
−
2
librium towards ꢀE = 0 intercepts j ≈ 0.4 mA cm , however, the
0
coefficients ˛ ≈ 0.96 and ˇ ≈ 1.1, found from the slopes, unambigu-
ously show that the cathodic and anodic polarization were not
sufficiently high to fully avoid the influence of a slow electrocrys-
tallization stage. Unfortunately, the rotating disk electrode method
cannot be applied successfully for higher polarizations.
A
A
wards whole spectrum (up to 0.0305 Hz) was analyzed according to
model presented in [13]. From the obtained results we succeeded
to calculate the silver surface ad-atom diffusion coefficient, D, to
mean diffusion distance, r, relation and quite approximately eval-
uate the mean duration of silver ad-atom diffusion on the surface,
ꢂ:
The slow crystallization stage is most strongly expressed in the
region of the equilibrium potential, thus the EIS method was chosen
for its investigation. The experimental data were interpreted based
D1/2
r
−1
= 3 s−1/2
;
ꢂ = D−1r2 = 0.11 s = 0.1 s
∼
Analogously, the impedance spectra, Fig. 5, measured after
different time intervals of contact with the electrolyte at their equi-
librium potential were analyzed. We have attempted to estimate
Fig. 4. Dependence of the current density on the electrode polarization (Fig. 3,
data from curve 1) in half-logarithmic coordinates (Y = j)—filled circles, and in
Allen–Hickling coordinates—open circles.
Fig. 6. Electrochemical FFT impedance spectrum, determined 1 h after the electrode
was immersed into the solution. Solution composition as in Fig. 5.

G. Baltr u¯ nas et al. / Electrochimica Acta 53 (2008) 6513–6520
6517
Fig. 7. Equivalent circuit modeling adsorption and charge transfer on the surface
of the electrode. R0: uncompensated electrolyte resistance; CD: electrical double
layer capacity; Rct: charge transfer resistance; ZW: diffusion impedance; RA and CA:
adsorption resistance and capacity.
the single impedance components which mainly determine the
impedance. The fluctuation of the adsorption components (CA and
RA) was rather large, thus they could not be evaluated accurately,
probably due to their negligible effect on the total impedance. The
obtained variation of the three major values Rct, B (q.v. Eq. (5)), and
CD (Fig. 8) was consistent enough. Initially, during the first 100 s of
contact with the electrolyte, CD increases rather drastically whereas
Rct decreases, respectively. This unambiguously could be explained
by growing of active silver surface due to recrystallization. There-
after, this variation stabilizes (CD even decreases). The coefficient B,
which characterizes the silver ad-atom surface diffusion (Eq. (5)),
increases with an almost constant rate. This could be explained
with the decrease of the number of crystallization centers (or struc-
ture defects) during the process of recrystallization. During the
first 750 s of contact with the electrolyte, B increases from 760 to
Fig. 9. Time dependence of the silver electrode polarization. Solution composition
−
2
(M)—Ag(I): 0.05; Na2SO3: 0.49. Cathodic current density: 8 mA cm
.
Insofar, the processes under study are complicated by the slow
electrocrystallization stage of Ag at equilibrium potential condi-
tions, it would be of interest to perform measurements at relatively
high electrode polarization. The chronopotentiometric (CP) method
would be the best choice, because at sufficiently large current den-
sities high electrode polarization, even at the early stages could
be expected. However, some unexpected results were obtained
experimentally—upon subjecting the cell to a cathodic current den-
−
2
sity of −8 mA cm . As can be seen from Fig. 9, in contrast, the
electrode potential decreases initially, and only after 30 ms starts
increasing. Taking in consideration the technical characteristics of
our galvanostat, this phenomenon cannot be related to a transi-
tional process of the measurement set-up itself.
2
1/2
1010 ꢁ cm s . It is interesting to observe, that this phenomenon
lasts further. The measurements performed after 1 h of contact
2
1/2
with the electrolyte (Fig. 6) yield B values of about 1500 ꢁ cm s
.
The electrical double layer capacity CD, decreased further to
−2
1
8.3 ␮F cm . The charge transfer resistance (and respectively
Such electrode polarization variation could be explained
assuming that despite the comparatively strong deviation from
equilibrium, the electroreduction of silver sulfite complexes shortly
after the current switching is still controlled by a slow silver elec-
trocrystallization process. In other words, even at sufficiently large
electrode polarization, a particular time interval is necessary for
a sufficient concentration of crystallization centers to be formed.
Otherwise, the limitations of diffusion will assert in the range of
longer times. The larger it will become, the more difficult will be
to exactly “purify” the charge transfer overvoltage. Thus, for the
successful investigation of the charge transfer stage, the identifi-
cation of the time interval in which the slow electrocrystallization
influence is not considerable and limitations of diffusion are not
dominating, appears to be essential. This is not very convenient, but
still significantly better, as to perform investigations at equilibrium
potential range.
exchange current density) has changed slightly in the first 750 s,
3 ꢁ cm (j = 0.76 mA cm ) to 27 ꢁ cm2 (j = 0.95 mA cm ) but
2
−2 −2
3
0
0
2
−2
after 1 h its value has increased up to 206 ꢁ cm (j = 0.12 mA cm ).
0
Even qualitatively, we cannot explain this phenomenon yet. It is
important to notice that the exchange current densities determined
by the impedance method, are in good agreement with values
for j , obtained from voltammogram measurements, analyzed in
0
Allen–Hickling coordinates (Fig. 4).
3.3. The kinetics of electrochemical reaction
The chronopotentiometry method was chosen for j0 exper-
imental determination. In many cases, the measured electrode
polarization was the sum of the charge transfer and diffusion over-
voltages. Since only the diffusion overvoltage depends on time,
its effect on the total electrode polarization should be eliminated
using coordinates ꢀE vs. t1 . Investigating systems without com-
plex ions, the extrapolation of the linear parts of the curves obtained
in these coordinates towards t1 = 0, enabled us to determine the
exact values of the charge transfer overvoltage. From Fig. 10 it is
seen that in our system the experimentally determined ꢀE vs. t1
dependence is not linear, thus the elimination of the effect of dif-
fusion becomes problematical. The determination of the charge
/2
/2
/2
Fig. 8. Dependence of the electrical double layer capacity (CD), charge transfer resis-
tance (Rct) and coefficient B on the time as determined by analyzing FFT impedance
spectra (from Fig. 5).

6
518
G. Baltr u¯ nas et al. / Electrochimica Acta 53 (2008) 6513–6520
Fig. 10. Time dependence of the silver electrode polarization. Solution composition
Fig. 11. Dependences of the limiting current densities on the rotation speed of the
disk electrode. Numbers on the lines correspond to solution numbers as presented
in Table 1.
−2
(
M)—Ag(I): 0.1; Na2SO3: 0.77. Cathodic current densities used (mA cm ): (1) 10; (2)
2; (3) 14; (4) 16; (5) 18; (6) 20 and (7) 22.
1
transfer overvoltage becomes complicated as well. In our case the
electrochemical reaction proceeds in the presence of complex ions,
thus, we attempted to determine the influence of diffusion on the
total electrode polarization by taking into account not only the
metal complex ions, but also the effect of free ligand molecules on
the diffusion overvoltage dependence on time. If a complex com-
pound MeLx forms in the solution with an equilibrium constant
the current density of the cathodic process can be expressed by
a simplified Sand equation:
ꢋ
ꢋ
S
S
C
C
2j
t
C
C
x2j
zFCR0
t
O
R
=
1 −
and
= 1 +
(10)
0
O
0
O
0
R
zFC
ꢃDO
ꢃDO
where DO is the diffusion coefficient of the oxidized form. Introduc-
ing the obtained expressions into Eq. (9), we find that the electrode
polarization for the cathodic and anodic processes, respectively is
equal:
n+
ˇx, of the reaction MeLx ꢀ Me + xL and insert this into the Nernst
equation we obtain:
RT
zF
RT
zF
xRT
zF
ꢂ ꢀ
ꢁ
ꢀ
ꢁꢅ
E = E +
ln ˇx +
ln[MeLx] −
ln[L]
(8)
0
RT
zF
aj
√
axj √
ꢀEdif
=
ln 1 ∓
t
− x ln 1 ±
t
(11)
0
O
0
C
C
The oxidation–reduction process is proceeding during the elec-
trochemical reaction, thus for the reaction MeLx + n e¯ ꢀ Me + xL
we could write instead of: [MeLx] – oxidized form CO and instead
of [L] – reduced form CR. The electrode equilibrium potential
depends on the bulk concentrations of the oxidized and reduced
R
ꢊ
where a = 2/(zF ꢃD ). By calculating the diffusion overvoltage of
O
the cathodic process of the electrochemical reaction under study,
the ‘−’ sign has to be written in the first term under the logarithm,
because the total concentration of Ag complexes decreases dur-
ing the cathodic reaction. In the second member we write the ‘+’
sign, because the concentration of free sulfite ions increases during
the cathodic process. The signs in the terms under the logarithms
should be opposite for the case of an anodic process.
0
0
forms CO and C . When current is applied, the electrode poten-
R
tial E(j) is determined by the surface concentrations CS and C .
S
O
R
Since the concentrations are dominant in these equations, the total
electrode polarization will be equal to the diffusion overvoltage
ꢀEdif = E(j) − E(0) and can be expressed as
In order to use the obtained Eq. (11), it is necessary to find the
degree of complexation of the silver complex x and its diffusion
RT
zF
xRT
zF
RT
zF
xRT
zF
S
S
ln C −
R
0
O
ln CR0
ꢀEdif
=
=
ln C
−
−
lnC
+
O
coefficient D . Both these parameters depend on the solution com-
0
position. The diffusion coefficient, D0 of silver sulfite complexes
in all solutions, as presented in Table 1 were determined with a
rotating disk electrode. Experimentally determined limiting cur-
rent densities depend linearly on the square root of RDE rotation
speed as shown in Fig. 11. Thus, the values of D0 were easily cal-
culated for all series of isopotential solutions. As seen from the
data presented in Table 1, the values of D0 decrease by increasing
S
O
0
O
S
RT
zF
C
ln
xRT
zF
C
R
ln
(9)
0
C
C
R
If the current passing through the electrochemical system is
low enough or the duration of the process is short enough:
ꢊ
2
j/zFC0 t/ꢃD ꢃ 1, the concentration dependence on time and
Table 1
Composition of isopotential solutions (E(0) = 0.300 V) and parameters of the electrochemical system
No.
Solution composition (M)
System parameters
[SO32 ] (M)
−
3−
5−
DO × 10 (cm2
6
−1
s )
Ag(I)
Na2SO3
[Ag(SO3)2 ] (M)
[Ag(SO3)3 ] (M)
x
1
2
3
4
5
.
.
.
.
.
0.003
0.01
0.03
0.05
0.1
0.115
0.2
0.33
0.49
0.77
0.108
0.176
0.255
0.359
0.499
0.002
0.006
0.015
0.02
0.0009
0.004
0.015
0.029
0.067
5.54
5.45
4.97
4.33
3.36
2.31
2.41
2.51
2.59
2.67
0.033

G. Baltr u¯ nas et al. / Electrochimica Acta 53 (2008) 6513–6520
6519
the solution concentration. This effect could be due to the Na SO3
2
influence on the solution viscosity or to migration influence due to
decrease of Na SO to Ag(SO3)x1
−2x
concentration ratio.
2
3
In Section 3.1, we have proved that in a system of silver–silver
sulfite complexes the degree of complexation could vary between
2
and 3. Thus, we can write:
Ag(SO3)35
−
]
[SO3
−
2−
]
x = 2 + [
= 2 +
(12)
−1
A
[
SO32 ] + ˇ ˇ
3
2
5
−
Under limiting conditions, if Ag(SO )
is not formed, i.e. if
3
3
5−
5−
Ag(SO3)3 ] = 0, x = 2, and if Ag(SO ) is formed with a maxi-
3
mum concentration of [Ag(SO3)3 ] = A, x = 3. By using Eq. (12), it is
simple to calculate the degree of complexation of silver–silver sul-
fite complexes in the all isopotential solutions under consideration
[
3
5−
(
q.v. Table 1). Since the surface layer composition changes during
the experiments, the degree of complexation depends on time too.
We have derived the corresponding equations, but the calculations
performed showed that a change of x over the time has a negligible
influence on the calculated values of ꢀEdif. Therefore, we do not
present these equations here.
Fig. 13. Dependence of cathodic current density on the polarization of the silver
electrode in the coordinates of Allen–Hickling. Numbers on the lines correspond to
solution numbers as presented in Table 1.
The diffusion overvoltage of silver sulfite complexes could be
simply evaluated knowing all values presented in Eq. (11). Further-
more, following these equations, even before performing detailed
calculations, a conclusion might be made that in the case of complex
of the electrochemical reaction. The values determined vary from
−
2
solutions, the dependences ꢀEdif vs. t1/2 should not be necessar-
0.9 mA cm (for solution prepared with 0.003 M Ag(I) and 0.115 M
−
2
Na SO ) to 2.46 mA cm (solution prepared with 0.1 M Ag(I) and
ily linear. The dependence of the electrode polarization on time
is linear only at small current densities and only for short time
intervals.
2
3
0
.77 M Na SO ).
2 3
In order to identify the composition of the complex particles,
which directly participates in the charge transfer stage, the depen-
dence of the exchange current density on the free sulfite ions
For the further analysis, the charge transfer overvoltage Ect was
found from the experimentally measured total electrode polar-
ization by eliminating the calculated diffusion overvoltage. As
seen from Fig. 12, curve c, a practically time-independent polar-
ization was obtained, which can be identified as charge transfer
overvoltage. Thus, it becomes possible to avoid a fairly problemat-
ical non-linear data extrapolation. It was determined, that for all
isopotential solutions, changing the cathodic current densities, the
charge transfer overvoltages vary from−60 to −160 mV. Since in the
obtained overvoltage region Tafell dependences ln j vs. ꢀEct were
not entirely valid, Allen–Hickling coordinates (ln Y vs. ꢀEct) were
used as shown in Fig. 13. Upon extrapolation of these dependences
towards ꢀE = 0 yielded the respective exchange current densities
2
−
concentration was plotted in coordinates ln |j | vs. ln[SO
] (q.v.
0
3
Fig. 14). In this figure, one can easily find the reaction order to be
equal to 0.67. This result suggests that an unambiguous conclusion
concerning the mechanism of the electrochemical system under
−
study not possible. It is very probable, that AgSO3 participates
in the charge transfer reaction and experimental data can be dis-
torted due to adsorption of sulfite ions or to not exactly estimate
slow electrocrystallization of Ag.
We would like to note that any considerations regarding
the chemical, mechanical, morphological, etc. properties of the
deposited Ag film are not reported in this study because these data
were published in our study [18].
Fig. 12. Chronopotentiograms of silver sulfite complexes: (a) experimentally deter-
mined, (b) calculated via Eq. (11) and (c) difference between a and b. Solution
Fig. 14. Dependence of the exchange current density on the free sulfite ions con-
centration.
−2
composition as in Fig. 10. Cathodic current density: 12 mA cm
.

6
520
G. Baltr u¯ nas et al. / Electrochimica Acta 53 (2008) 6513–6520
4
. Conclusions
tion of silver ad-atom diffusion on the surface is approximately
equals 0.1 s.
Potentiometry investigations were carried out in order to
References
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(
2
3
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[
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[
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2−
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SO3 . The slow silver ad-atom diffusion on the surface strongly
reduces the total rate of electrochemical process. The mean dura-