Study of the mechanism of the vanadium 4+/5+ redox reaction in acidic solutions

Article abstract of DOI:10.1149/1.1630594

The mechanism of the vanadium VO²⁺/VO₂⁺ redox couple has been examined in acidic aqueous solutions. A detailed understanding of this chemistry is of interest for improving and optimizing the performance of vanadium redox-flow batteries, a promising electrochemical electricity storage technology. The vanadium 4+/5+ redox reactions were studied at a rotating disk graphite electrode and polarization curves were obtained in sulfuric acid and perchloric acid, with varying pH and vanadium concentrations. The results were compared to model predictions for different mechanisms. The data were consistent with a model with a multistep chemical-electrochemical-chemical mechanism at low overpotentials, which changes to a multistep electrochemical-chemical-chemical mechanism at higher anodic or cathodic overpotentials. Unusually high Tafel slopes (350-450 mV/decade) were observed for the reduction of VO₂⁺ at higher overpotentials. While this could not be directly explained by the model, insights gained through the use of the model can provide the basis for some suggestions.

Full text of DOI:10.1149/1.1630594

Journal of The Electrochemical Society, 151 ͑1͒ A123-A130 ͑2004͒
A123
0013-4651/2003/151͑1͒/A123/8/$7.00 © The Electrochemical Society, Inc.
Study of the Mechanism of the Vanadium 4¿Õ5¿ Redox
Reaction in Acidic Solutions
,z
b
c
M. Gattrell,a, J. Park,a B. MacDougall,a, J. Apte, S. McCarthy,
*
*
and C. W. Wuc
aInstitute for Chemical Process and Environmental Technology, National Research Council of Canada,
Ottawa, Ontario K1A 0R6, Canada
bMcGill University, Montreal, Quebec, Canada
cUniversity of Waterloo, Waterloo, Ontario, Canada
The mechanism of the vanadium VO2ϩ/VO2ϩ redox couple has been examined in acidic aqueous solutions. A detailed understand-
ing of this chemistry is of interest for improving and optimizing the performance of vanadium redox-flow batteries, a promising
electrochemical electricity storage technology. The vanadium 4ϩ/5ϩ redox reactions were studied at a rotating disk graphite
electrode and polarization curves were obtained in sulfuric acid and perchloric acid, with varying pH and vanadium concentra-
tions. The results were compared to model predictions for different mechanisms. The data were consistent with a model with a
multistep chemical-electrochemical-chemical mechanism at low overpotentials, which changes to a multistep electrochemical-
chemical-chemical mechanism at higher anodic or cathodic overpotentials. Unusually high Tafel slopes ͑350-450 mV/decade͒
were observed for the reduction of VOϩ2 at higher overpotentials. While this could not be directly explained by the model, insights
gained through the use of the model can provide the basis for some suggestions.
© 2003 The Electrochemical Society. ͓DOI: 10.1149/1.1630594͔ All rights reserved.
Manuscript received March 27, 2003. Available electronically December 9, 2003.
A more detailed understanding of vanadium redox chemistry is
of interest because of its application in vanadium-based redox flow
batteries. Redox flow batteries are an electrochemical energy storage
technology where the energy, rather than being stored at the elec-
trodes like batteries, is stored by chemical changes to species dis-
solved in a working fluid. Various systems based on different species
have been proposed over the years with two presently being com-
of the renewable energy storage.3 It is hoped that the different cost
relationships of the vanadium redox batteries will improve this situ-
ation. A further advantage is the much higher cycle life and simple
cycling considerations for redox flow batteries, because the active
materials are kept in solution and are not lost nor degraded by bat-
tery cycling. Thus this relatively new electrochemical technology
seems well suited for enhancing the utilization of renewable
energy.4-7 It has also been reported that the life cycle environmental
impact of using VRBs is lower than that for lead acid battery power
storage systems.8
The typical electrodes are carbon based because of their wide
operating potential range ͑minimal hydrogen and oxygen evolution͒,
stability as both an anode and a cathode, and availability in high
surface area at reasonable cost. Carbon has a very wide range of
characteristics depending on the methods of manufacturing and
preparation. Commercial vanadium battery electrodes typically use
carbon felt, made by pyrolysis of polymers ͑either rayon or poly-
acrylonitrile based9͒, which can be treated to increase the number of
surface oxide sites,10,11 or heated to increase its crystallinity and
conductivity.12 The electrolyte usually has from 1 to 3 M of vana-
dium sulfates in 1 to 2 M H2SO4 .
Ϫ
1
mercialized. One system is based on S/SϪ2 and BrϪ/Br3 and the
other based on V2ϩ/V3ϩ and VO2ϩ/VOϩ2 .2 While the polysulphide/
bromine system has a higher cell voltage ͑ca. 1.52 V͒, the
vanadium-based system ͑ca. 1.40 V͒ is simpler and more rugged, in
part because it is less affected by membrane crossover problems.
Thus, the vanadium system has an advantage for remote or unat-
tended operation.
Figure 1 shows the main components of a vanadium redox-flow
battery ͑VRB͒ system. The electrochemical cell stores or releases
power by shifting the ratio of the two vanadium species present at
each electrode. The system power is determined by the rate of reac-
tion of the vanadium species at each electrode and the total surface
area of the electrodes. The amount of energy stored in the system is
determined by the concentration of the vanadium species and the
volume of the reservoirs.
The reactions occurring at both electrodes during discharging of
the VRB are typically written as shown below
Because the solubility of the redox species in the working fluid is
limited, the volumetric and specific energy densities are low. There-
fore, the development of these systems has focused on stationary
applications. The cost of a system will increase with the power
output of the system based on the cost of the electrochemical cell,
and the cost will increase with the energy storage capacity of the
system based on the ͑typically lower͒ cost of the reservoirs and the
vanadium solution. Thus, redox flow-type batteries are particularly
suited for longer-term energy storage.
As well as applications such as load levelling and reliable power,
redox flow batteries seem well suited for storing electricity produced
by intermittent renewable energy sources such as wind or solar
power. Present systems typically use lead acid batteries. Because
lead acid batteries store energy in a coating on the electrode plates,
the system energy storage and power output are both related to the
electrode area. For lead acid batteries this makes increased energy
storage ͑and so increased capture of wind or solar energy͒ propor-
tionally more expensive, a fact that limits the most cost efficient size
V2ϩ ꢀ V3ϩ ϩ e-
VOϩ2 ϩ e- ϩ 2Hϩ ꢀ VO2ϩ ϩ H2O
͓1͔
͓2͔
The standard potential for Reaction 1 is reported to be Ϫ0.255 V
vs. normal hydrogen electrode ͑NHE͒13,14 However, standard poten-
tials of Ϫ0.258 and Ϫ0.291 V have been reported based on mea-
surements in 0.5 and 3 M H2SO4 solutions, respectively.13 For Re-
action 2, the standard potential is reported as 1.00013 or 1.004 V14
with values of 1.008 and 1.103 V reported based on measurements
in 1 and 3 M H2SO4 solutions, respectively.13 Thus, for VRB cells,
the open circuit cell voltage at 50% state of charge is often found to
be higher than the theoretical value of about 1.257 V due to the high
concentrations of sulphuric acid and vanadium sulfates used.
The redox reaction of the VO2ϩ/VOϩ2 couple in acid has been
studied on platinum, but the data is complicated because the degree
of surface oxide coverage of the platinum electrodes strongly influ-
enced the results.13 Reduction of 1 mM VOϩ2 on graphite in a mix of
1 M H2SO4 and 1 M H3PO4 has been reported to be irreversible and
result in a double wave.15 The reaction has recently been more ac-
tively studied as part of its development as a candidate for redox
* Electrochemical Society Active Member.
z E-mail: michael.gattrell@nrc-cnrc.gc.ca
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A124
Journal of The Electrochemical Society, 151 ͑1͒ A123-A130 ͑2004͒
Figure 2. The experimental setup. A sealed, water-jacketed RDE cell, with a
removable second counter electrode compartment for preparing oxidized or
reduced solutions.
Figure 1. VRB system with electrodes, membrane separator, pumps, and
reservoirs.
energy storage.16,17 In this work, the reactions were studied using
cyclic voltammetry, and some polarization curves were measured at
a rotating disk electrode ͑RDE͒. In the latter tests, the oxidation of
VO2ϩ appeared to be straightforward and amenable to standard elec-
trochemical measurement approaches, but the reduction of VOϩ2 did
not yield an easily interpreted polarization curve.17 In earlier work,
we also have found that the polarization curves for the VO2ϩ/VO2ϩ
redox reactions cannot be fit using a simple Butler-Volmer kinetic
equation.18 In this work we therefore attempt to study in more detail
the mechanism of Reaction 2, which can be seen from its equation
to be a multistep reaction.
have found that the activity of the electrodes can be increased
through more complex polishing methods.20 However, it was the
intent of this paper to study the influence of the solution chemistry
on the reaction, and so our goal was simply to prepare a reproduc-
ible surface.
Removing dissolved oxygen by sparging the solutions with argon
was observed to have no effect on the VO2ϩ/VO2ϩ couple, though it
was of course required to obtain the V2ϩ/V3ϩ couple. Because of
possible contamination from the SCE electrode, a test was carried
out where chloride was added to the cell, which resulted in no sig-
nificant change to the voltammetry.
The concentrations of the vanadium species were measured from
the limiting currents at various RDE rotation rates. Unfortunately,
no clear limiting current plateau was observed for the reduction of
VOϩ2 prior to the onset of other possible reactions such as VO2ϩ to
V3ϩ (Eؠ ϭ 0.377 V vs. standard hydrogen electrode, SHE͒ or to
Experimental
The rotating disk system, including glassy carbon ͑GC͒ and
graphite disc electrodes ͑0.196 cm2͒, an AFMSRX electrode rotator,
and the RDE cell ͑modified with a water jacket͒ was obtained from
Pine Instruments. An EG&G 263 potentiostat was used with Scrib-
ner CorrWare and CorrView 2.3f data collection and analysis soft-
ware. For most of the work, a cracked bead low flow junction stan-
dard calomel electrode ͑SCE͒ reference ͑Fisher Scientific Accumet,
Ͻ5 uL/h flow rate͒ was used to minimize possible solution contami-
nation over long run times. A platinum wire pseudo-reference was
used in parallel, connected via a series 10 ␮F capacitor, in order to
decrease the reference electrode impedance and improve the poten-
tiostat stability.19 A carbon rod counter electrode was used during
experimental measurements, while a platinum wire counter elec-
trode in a separate compartment was used ͑with the carbon rod as
the working electrode͒ to prepare oxidized or reduced solutions ͑see
diagram in Fig. 2͒. This allowed oxidized (VOϩ2 ) or reduced solu-
tions (V2ϩ or V3ϩ) to be prepared.
The chemicals used include VOSO4 from Alfa Aesar ͑with cer-
tificates of analysis showing 99.9ϩ% on a metals basis͒, ACS grade
H2SO4 , HClO4 , and Na2CO3 from EM Science, and deionized wa-
ter from a Millipore Milly-Q Plus system.
The electrodes were initially hand polished with 600 and 1200
grit paper, then polished with a Buehler polisher at 100 rpm using
Nanocloth with 1, 0.3, and 0.05 ␮m alumina, followed by a thor-
ough rinsing on the wheel. Some tests were done where the elec-
trode was placed in an ultrasonic bath for periods from 5 to 15 min,
which resulted in a slightly lower activity, but the same shape of
polarization curve ͑i.e., a slightly lower k0). Thereafter, between
experiments, a simple polish with 0.05 ␮m alumina and a thorough
rinsing on the wheel was used. It should be noted that other workers
14
V2ϩ (Eؠ ϭ Ϫ0.255 V vs. SHE͒ ͑see Fig. 3͒. However, known
solutions of VOSO4 could be used to estimate the diffusion coeffi-
cient for VO2ϩ. The value obtained in 1 M H2SO4 was 3.0 Ϯ 0.3
ϫ 10Ϫ6 cm2/s ͑calculated using a density of 1.066 g/cm3 and vis-
cosity of 1.23 g/cms21͒. The high degree of uncertainty is due to the
high oxygen evolution background ͑as can be seen by the sloped
limiting current plateaus in Fig. 3͒. Following this, mixtures of
VO2ϩ and VOϩ2 were produced by galvanostatic oxidation using a
cathode in a separate compartment ͑as described above͒. The con-
centration of VO2ϩ in the test mixture could then be determined
using the limiting current for VO2ϩ oxidation. The VO2ϩ was then
found by difference from the known starting total vanadium concen-
tration. The open circuit potential was also used as a check on the
solution composition, but due to the slow kinetics for the
VO2ϩ/VO2ϩ system, it was not as reliable. For the V2ϩ/V3ϩ system
the ability to clearly measure both limiting current plateaus, plus
knowing the total vanadium concentration, can provide a method for
determining the diffusion coefficients in the solution of interest and
thus checking solution compositions.
Note also that the choice of sweep rates for the various measure-
ments was typically a compromise. In order obtain steady-state data,
a slow sweep rate is desirable. However, too great a combination of
anodic potential and time leads to oxidation of the carbon surface
and a resulting loss in electrode activity ͑attributed to the formation
of a multilayer oxide film22͒. For measuring the limiting current
plateau, which required fairly anodic potentials to reach the mass
transfer limited region, sweep rates around 10 to 30 mV/s were
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Journal of The Electrochemical Society, 151 ͑1͒ A123-A130 ͑2004͒
A125
Figure 3. RDE polarization curves at various rotation rates. Graphite elec-
trode, 1 M H2SO4 , 21 mM V͑IV͒, and 29 mM V͑V͒.
Figure 5. Polarization curve for the graphite electrode. Sweep rate 0.1
mV/s, 20°C, 4000 rpm, approximately 90 mM VO2ϩ and 110 mM VO2ϩ , 1
M H2SO4 . Theoretical lines based on k0 ϭ 3.0 ϫ 10Ϫ7 cm/s, E0 ϭ 0.785
V, and Tafel slope for VO2ϩ to VOϩ2 of 138 mV/decade.
used. For measuring the polarization curves a lower anodic limit
was used and so sweep rates from 0.1 to 1 mV/s were used. Even so,
in some experiments, hysterisis and a slow drift in activity with
sweep number was noted. Because of this, for most of the results
that follow, both the forward and reverse sweeps are shown.
Fig. 5 that there are significant deviations from a simple mechanism.
A shoulder is apparent on the anodic Tafel slope from 0.785 to 0.95
V, and possibly a similar shoulder from 0.785 to 0.6 V on the ca-
thodic side. Also the linear part of the negative going polarization
curve ͑from 0.35 to 0.6 V͒ has a slope corresponding to ␣ ϭ 0.15
͑385 mV/decade͒. Even if the diffusion coefficient for VOϩ2 was as
low as 2.0 ϫ 10Ϫ6 cm2/s, the expected limiting current for its
reduction would be about 0.1 A/cm2, and so the high Tafel slope was
not due to mass transport limitations. This is also supported by Fig.
3, where the curves for VOϩ2 reduction only show divergence with
rotation rate at potentials below about 0.2 V.
While these shoulders occur at low current densities ͑they are
barely noticeable on linear plots͒ they are of interest because the
typical real current densities in operating VRBs are very small.
While high current density operation can be sustained if demanded
by a load, a typical operating target for energy storage is an overall
efficiency of around 80%.23 This would correspond to 90% energy
conversion efficiency and hence a maximum cell overvoltage of
0.126 V during the charge and discharge steps. As this total must
include the polarization overpotentials of both electrodes and the
resistive drop of the cell membrane, one can see that the initial parts
of the polarization curve are of significant interest. ͑One can also
understand the interest in specially prepared, high surface area car-
bon felt electrodes10-12 to get useful membrane current densities in
commercial units.͒
Results and Discussion
Typical polarization curves measured at the RDE are shown in
Fig. 4 and provide a good overview of the redox battery reactions.
The reversible potentials ͑i.e., corrected to equimolar concentra-
tions͒ are located at Ϫ0.50 and 0.76 V, giving a difference of about
1.26 V. It can also be seen that the kinetics of the VO2ϩ/VO2ϩ couple
were slower than the Vϩ/V2ϩ couple.
A Tafel type plot of the polarization curve for the VO2ϩ/VO2ϩ
reaction is shown in Fig. 5. Also plotted is the calculated response
expected for a simple electrochemical system. This calculation used
the Butler-Volmer equation with a formal potential of E0 ϭ 0.781 V
͑estimated from the zero crossing point of the curves and the vana-
dium species’ concentrations͒, and a standard rate constant of k0
ϭ 3.0 ϫ 10Ϫ7 cm/s with a Tafel slope for VO2ϩ to VOϩ2 of 138
mV/decade equal to a transfer coefficient ͑␣͒ of 0.42 ͑taken from the
straight line region from about 1.0 to 1.175 V͒. It can be seen from
The shoulder on the anodic side of the curves increased slightly
with electrode cycling, to increase linearly with vanadium concen-
tration, to not increase with rotation rate, and to increase roughly
with the square root of sweep rate ͑after background correcting for
the carbon electrode alone͒. If the shoulder was due to the mass
transfer limited reaction of a solution impurity, it would be expected
to change with rotation rate. If it was due to a surface bound species
it would be expected to increase linearly with sweep rate. It was
therefore decided to examine possible mechanisms for the
VO2ϩ/VOϩ2 couple, to see what they might predict.
Expected mechanism and model.—The VO2ϩ ion is reported to
exist in noncomplexing acidic solutions as the blue oxovanadium
24
ion VO͑H O) ]2ϩ
.
The complex is described as a tetragonal bi-
͓
2
5
pyramid ͑see Fig. 6͒ with four equatorial waters having residence
times of 1.35 ϫ 10Ϫ3 s and the axial water being more weakly held
with a residence time of 10Ϫ11 s.25 In strong acid, VOϩ2 exists as the
Figure 4. Graphite RDE, 4000 rpm, 0.1 mV/s, 1 M H2SO4 , 20 C. For
V͑II͒/V͑III͒, ca. 16 and 36 mM V3ϩ. For V͑IV͒/V͑V͒, 31 mM VO2ϩ, and 19
24,25 which has also
ϩ
yellow dioxovanadium ion, cis- VO (H O)
͔
4
,
͓
2
2
mM VOϩ2
.
been drawn in Fig. 6. It should be noted that, at the high vanadium
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A126
Journal of The Electrochemical Society, 151 ͑1͒ A123-A130 ͑2004͒
is the estimate of the thickness of the zone near the electrode surface
where the intermediate ͑B͒ has been depleted and is being replaced
by the reaction of the starting compound ͑A͒.
Thus reaction rates can be calculated for each possible rate de-
termining step. These calculated rates were then combined to give a
model for the overall system. For steps in series, the slowest calcu-
lated rate would limit the rate for that pathway. To allow the model
to shift smoothly between changing rate determining steps, the ex-
pressions for the different possible rate determining steps were
added as conductors in series
Figure 6. Structures for VO2ϩ and VOϩ2 in noncomplexing acidic solutions
͑based on Ref. 24 and 25͒.
ratepath1,total ϭ 1/ 1/rate
ϩ 1/ratepath1,step2
͒
͓5͔
͑
path1,step1
The overall reaction rate was then estimated as the sum of the
different parallel pathways. That did not allow for depletion of the
concentrations of intermediates shared by two pathways, but was
felt to be sufficiently complex to compare against measured data to
determine the key rate determining step or steps.
For the purposes of these calculations the forward reaction direc-
tion is taken to be the oxidation of VO2ϩ ͑cell charging͒. Then each
pathway can be written in terms of chemical ͑C͒ and electrochemi-
cal ͑E͒ steps as follows ͑where the rate determining step is under-
lined for each case͒.
and sulfuric acid concentrations encountered in commercial batter-
ies, more complex species have been reported, including V2O33ϩ
26
and complexes with sulfate and bisulfate.27-29 However, for this
work, lower concentrations were used, and because it is hoped to
obtain an initial basic understanding of the reaction mechanisms,
only the aqua complexes were considered.
The overall reaction as written in Eq. 2 would be expected to
consist of three elementary steps: one electron transfer and two pro-
ton transfers. Using the structures for the ions in noncomplexing
acidic solutions, a schematic of the possible mechanism can be writ-
ten based on various combinations of electron and proton transfers
͑shown in Fig. 7͒. It is interesting to note that, while the starting and
final vanadium species are the most stable forms around pH 0, the
intermediates would only be expected to predominate at higher or
lower pH values. The existence of VO3ϩ has been suggested from
the variation of the equilibrium potentials of V͑IV͒/V͑V͒ mixtures in
strong acid.13 It is also unclear what would be the form of VO2 . The
hydrated form of VO2 is usually written as VO͑OH)2 and the dry
oxide as V2O4 .25,14 A simpler version of this mechanism has also
been proposed by other workers.30
Three different reaction pathways are possible. However, be-
cause no transfer coefficients greater than 0.5 were observed, one
can conclude that on the dominant pathway the rate determining step
cannot come after the electron transfer step. For the cases where a
chemical step proceeding the electrochemical step is rate determin-
ing, the rate expression used is that suggested for the case where the
equilibrium of the chemical step favors the starting compound ͑A in
Eq. 3͒ ͑i.e., Keq ϭ kf /kr Ӷ 1).31,32 This assumes that the reaction is
governed by the rate of conversion of the starting compound in a
depleted zone near the electrode surface
Path 1 (ECC).—The rate is given by
EគCC: rate ϭ VO2ϩ
k
Ϫ k
VO3ϩ
͓ ͔
1f 1r
͓
͔
ϭ
VO2ϩ k0 exp 1 Ϫ ␣ ͒F E Ϫ E0͒/RT
͓͑ ͔
͓
͔
͑
1
1
1
Ϫ
VOϩ Hϩ 2/ K5eqK7eq͒ k0
͔͓
͓͓
ϫ exp Ϫ␣ F E Ϫ E0͒/RT
͔
͔
͑
͔
2
1
͓6͔
͓7͔
͓
͑
1
1
Path 2 (CEC).—The rates for the individual steps in Eq. 5 are
Cគ EC: rate ϭ VO2ϩ
k
D/ Hϩ k ͒
͑ ͓ ͔
4f 4r
1/2
͓
͔
CEគC: rate ϭ HVOϩ
k
Ϫ k
HVO2ϩ
͓ ͔
2f 2r
2
͓
͔
2
ϭ
VO2ϩ
K
4eq /͓Hϩ )k0 exp 1 Ϫ ␣ ͒
͓͑
͔
͔
͓͑
2
2
ϫ F E Ϫ E0͒/RT
Ϫ
VOϩ
͑
͔
͓͑
͔
2
2
ϫ
Hϩ /K ͒k0 exp Ϫ␣ F E Ϫ E0͒/RT
͔
͓8͔
͓9͔
͓
͔
͓
͑
2
7eq
2
2
Path 3 (CCE).—The rates for the individual steps in Eq. 5 are
Cគ CE: rate ϭ VO2ϩ D/͓Hϩ k )1/2
k
ϩe
f
A ꢀ B ꢀ C
͓3͔
͓4͔
k
͓
͔
͑
4f
͔
4r
k
Ϫe
r
CCគ E: rate ϭ HVOϩ k ͑D/͓Hϩ]k )1/2
͓
͔
1/2
1/2
i ϭ FD1/2
A k K ͒ ϭ Fk ͓A] DKeq /kf͒
͔͑ ͑
f eq f
6f
6r
2
͓
ϭ
VO2ϩ
K
/ Hϩ ͒k ͑D/͓Hϩ]k )1/2 ͓10͔
͓͑
͔
͓
͔
4eq
6f
6r
Equation 4 also assumes that the diffusion coefficients of the
reacting species are equal ͑i.e., DA ϭ DB ϭ D). Then (DKeq /kf)1/2
CCEគ: rate ϭ VO
k
Ϫ
VOϩ
k
͔
2
͓
͔
͓
2
3f
3r
ϭ
VO2ϩ
K
4eqK6eq /͓Hϩ 2)k0 exp 1 Ϫ ␣ ͒
͓͑
͓͑
͔
͔
3
3
ϫ F E Ϫ E0͒/RT
Ϫ
VOϩ k0
͑
͔
͓
͔
3
3
2
ϫ exp Ϫ␣ F E Ϫ E0͒/RT
͓11͔
͓
͑
͔
3
3
Similarly, for the reverse reaction of the reduction of VOϩ2 ͑cell
discharging͒, the equations would be
Path 1 (CCE).—The rates for the individual steps in Eq. 5 are
Cគ CE: rate ϭ VOϩ Hϩ k ͑D/k )1/2
͔͓
͓12͔
͓13͔
͓
͔
7r
7f
2
CCគ E: rate ϭ HVO2ϩ Hϩ k ͑D/k )1/2
͓
͔͓
͔
5r
5f
2
Figure 7. Schematic of the possible reaction pathways between VO2ϩ and
VOϩ Hϩ 2/K7eq͒k5r͑D/k5f)1/2
͔͓
VOϩ2 with the individual steps labeled.
2
ϭ
͓͑
͔
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Journal of The Electrochemical Society, 151 ͑1͒ A123-A130 ͑2004͒
VO2ϩ
A127
CCEគ: rate ϭ VO3ϩ
k
Ϫ
k
͔
1f
͓
͔
͓
1r
ϭ
VOϩ Hϩ 2/ K5eqK7eq͒ k0
͔͓
͓͓
͔
͑
͔
1
2
ϫ exp Ϫ␣ F E Ϫ E0͒/RT
Ϫ
VO2ϩ k0
͔
1
͓
͑
͔
͓
1
1
ϫ exp 1 Ϫ ␣ ͒F E Ϫ E0͒/RT
͓͑
͓14͔
͓15͔
͑
͔
1
1
Path 2 (CEC).—The rates for the individual steps in Eq. 5 are
Cគ EC: rate ϭ VOϩ Hϩ
k
D/k ͒
͑
7f
1/2
͓
͔͓
͔
7r
2
CEគC: rate ϭ HVO2ϩ
k
Ϫ
HVOϩ
k
͓
͔
͓
͔
2r
2f
2
2
ϭ
VOϩ Hϩ /K ͒k0 exp Ϫ␣ F E Ϫ E0͒/RT
͔͓
͓͑
͔
͓
͑
2
͔
7eq
2
2
2
Ϫ
VO2ϩ
K
4eq /͓Hϩ )k0 exp 1 Ϫ ␣ ͒
͓͑
͔
͔
͓͑
2
2
ϫ F E Ϫ E0͒/RT
͓16͔
͑
͔
2
Path 3 (ECC).—The rate is given by
EគCC: rate ϭ VOϩ
k
Ϫ
VO
k
3f
͓
͔
͓
͔
3r
2
2
ϭ
VOϩ k0 exp Ϫ␣ F E Ϫ E0͒/RT͒
͓
͔
͑
͑
3
2
3
3
Ϫ
VO2ϩ
K
4eqK6eq /͓Hϩ 2)k03
͓͑
͔
͔
ϫ exp 1 Ϫ ␣ ͒F E Ϫ E0͒/RT
͓͑
͓17͔
͑
͔
3
3
For each chemical step there are two unknowns (kf and kr).
However, for reaction step 4, the equilibrium is reported in the lit-
erature (pKa4 ϭ 5.3614͒, eliminating one unknown. Also, for each
path the overall free energy changes must be the same. Therefore
each E0 can be specified in terms of an overall E0 as shown below
nFE0overall ϭ nFE0 Ϫ RT ln K5eqK7eq
͒
͒
͒
͓18͔
͓19͔
͓20͔
͑
1
nFE0overall ϭ nFE0 Ϫ RT ln K4eqK7eq
͑
2
Figure 8. ͑A͒ The model fitted to a set of data. ͑B͒ The contribution of the
various reaction pathways to the complete model fit. Data measured at a
graphite electrode, 4000 rpm, 33 mM V͑IV͒, and 17 mM V͑V͒, 1.9 M
H2SO4 ϩ 1.4 M KHCO3 .
nFE0overall ϭ nFE0 Ϫ RT ln K4eqK6eq
͑
3
The model was then tested to see how well it could fit data
measured with different vanadium concentrations, pHs, electrolytes,
and electrode materials. To further reduce the number of adjustable
parameters and because the goal was simply to see the quality of the
qualitative fit to the data, values for the various pKas were arbitrarily
set (pKa5 ϭ Ϫ3, pKa6 ϭ 5.6, and pKa7 ϭ Ϫ2) and the literature
value of E0overall ϭ 1.004 V vs. SCE14 was used.
would both be expected to be pH independent. The reversible po-
tential will be dependent on the square of pH, while the shoulder
regions, being limited by potential independent acid-base reaction
steps ͓͑Cគ EC͒ pathways͔, would vary linearly with pH. This is best
tested using a perchloric acid electrolyte, because of its simpler
acid-base chemistry.
Comparison to data at various pH values and concentra-
tions.—A fit of the model to a polarization curve is shown in Fig.
8A, with a breakdown of the model prediction into its various com-
ponents shown in Fig. 8B. It can be seen that, except for the region
below 0.4 V, the model fit the data quite well. Figure 8B shows how
each of the three possible reaction pathways contributed to the over-
all fit. Near the reversible potential, reaction pathway 2 ͑CEC͒ domi-
nated. In that region, the fit was adjusted through ͓Hϩ͔ value and k20
͑there is insufficient data to adjust ␣2 so it was left at 0.5͒, and the
shoulders were then fit by adjusting the associated chemical rate
determining steps through k4f and k7r . As the potential became
more anodic, reaction pathway 1 ͑EគCC͒ took over ͑which was fit
using k01 and ␣1). Similarly, for the reduction reaction, at more
cathodic potentials reaction pathway 3 ͑EគCC͒ might dominate
͑which would be fitted using k30 and ␣3 , though this is not possible
because the model did not fit well in this region, as will be discussed
later͒. Thus rather than one mechanism dominating, this would ap-
pear to suggest that the preferred mechanistic pathway changes with
potential.
The effect of pH on the polarization curves is shown in Fig. 9A
for a 2 M HClO4 solution that was neutralized stepwise with
NaHCO3 . As the pH increased, the reversible potential moved to
more cathodic potentials. However, the anodic linear Tafel regions
͑from about 1.3 to 1.5 V͒ remain roughly the same and so the shoul-
der region anodic to the reversible potential becomes more pro-
nounced. The cathodic region also shows little pH dependence be-
low 0.5 V. This is consistent with the idea that the preferred
mechanistic pathway changes with potential. In Fig. 9B the model
predictions are shown. The model was fitted to the data for pH
Ϫ0.04, then the various constants were kept fixed and changing the
Hϩ value was used to match the reversible potential of the model
with the data. ͑It should be noted that because of the ionic strength
of these solutions, this value actually would relate to the activity of
hydrogen ion rather than the concentration.͒ Thus, without having to
readjust the parameters, the model correctly predicted the experi-
mental results above about 0.6 V. Though it should be noted, that at
pH values above 1 ͑not shown͒, the polarization curves began to
shift upward and no longer fit the model.
͓
͔
One way to test this idea is by varying the solution pH, because
the different reaction pathways are expected to have different pH
dependencies. At the extreme potentials, oxidation of VO2ϩ to VO2ϩ
Similar work was also carried out using sulfuric acid. In this case
the sulfate/bisulfate equilibrium added complexity both because of
the changing ionic strength and changing relative amounts of vari-
ous anions in the solutions. Two types of tests were conducted. One
via path 1 ͑EគCC͒ and reduction of VOϩ2 to VO2ϩ via path 3 ͑EគCC͒,
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A128
Journal of The Electrochemical Society, 151 ͑1͒ A123-A130 ͑2004͒
Figure 9. The effect of pH, showing data at three different pH values and
the trends predicted for the three pH values using the modeled mechanism.
Data measured at
ϩ NaHCO3 , 34 mM V͑IV͒, and 16 mM V͑V͒. ͑A͒ pH Ϫ0.50, ͑B͒ pH
Ϫ0.04, and ͑C͒ pH 0.27.
a graphite electrode, 4000 rpm, 2 M HClO4
Figure 10. Polarization curves in different sulfuric acid electrolytes. ͑Mea-
sured at a graphite electrode, 4000 rpm, and 0.2 mV/s.͒ ͑A͒ 33 mM V͑IV͒
and 14 mM V͑V͒, H2SO4/K2SO4 buffer ͑2 M total sulfate͒. ͑B͒ 31 mM
V͑IV͒ and 16 mM V͑V͒, 2, 0.5, and 0.2 M H2SO4 solutions.
dependence. However, the high Tafel slope region is relatively pH
independent ͑no apparent dependence in Fig. 9A and Fig. 10B and
roughly a 0.5 power dependence in Fig. 10A͒. It is also interesting
that when examining the model diagrammed in Fig. 7, the product
test started with 2 M H2SO4 , which was step wise neutralized with
NaHCO3 ͑hence closer to constant ionic strength͒, and the other
started with 0.05 M H2SO4 to which acid was added. The results are
shown in Fig. 10A and B. Several differences from the results with
perchlorate were noted. The currents near the reversible potential
were much lower, while those in the anodic Tafel region were
higher, thus requiring an adjustment in the scan limits to see the
regions of interest. Between the two set of data in sulfate solutions,
the results with constant sulfate ϩ bisulfate ͑Fig. 10A͒ had a depen-
dence on pH of the currents in the cathodic region, which is not
apparent in Fig. 9A nor Fig. 10B. This indicates that the amounts of
sulfate and bisulfate present may also have an influence.
The effect of total vanadium concentration is shown in Fig. 11.
The observed currents increased proportionally with the concentra-
tion as would be expected for a first order reaction. It is interesting
to note the general shape of the curves remains the same, thus all
parts of the curves including the shoulder increase by the same
proportion. The effect of changing the ratio of VO2ϩ to VO2ϩ is
shown in Fig. 12. Model fits are also shown. One set of kinetic
parameters was used and the three curves were then generated by
changing the entered vanadium concentrations. While not providing
a perfect fit, the model does however correctly predict the observed
trends.
One problem with the model is its inability to predict the very
unusual Tafel slope in the cathodic region ͑about 400-500 mV/
decade͒. Even if an unusually low symmetry factor is used for the
path 3 EគCC step, the model will then not correctly fit in the area
near the reversible potential. The unusual Tafel slope does, however,
appear to be related to the path 3 EគCC step. This is because path 2
would predict a horizontal plateau ͑see Fig. 8B͒ with a linear pH
Figure 11. Polarization curves at various vanadium concentrations. Graphite
electrode, 4000 rpm, 0.1 mV/s, 1 M H2SO4 . 100 mM is ca. 55 mM V͑IV͒
and 45 mM V͑V͒, 200 mM is ca. 110 mM V͑IV͒ and 90 mM V͑V͒, and 400
mM is ca. 250 mM V͑IV͒ and 150 mM V͑V͒.
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Journal of The Electrochemical Society, 151 ͑1͒ A123-A130 ͑2004͒
A129
possible adsorption and desorption steps. The role of surface sites
may also be important for understanding the unusual Tafel slope for
the reduction of VOϩ2 at higher cathodic overpotentials. The com-
petitive and possibly potential dependent adsorptions of VOϩ2 and
VO2ϩ may lead to a complex potential dependence of the reaction
rate. Also, as mentioned above, blocking of the reaction sites on the
carbon surface by a slowly desorbing or slowly dissolving species
͑such as a VO2-type compound͒, might also affect the apparent Tafel
slope.
Conclusions
The mechanism of the redox reactions between vanadyl (VO2ϩ
)
and vanadic (VOϩ2 ) were investigated. A model was developed
based on the various possible steps in the overall reaction as shown
in Fig. 7. The model could be used to fit the observed data over a
range of pH, concentrations, and ratios of species. The results of the
fit are consistent with a mechanistic path that changes depending on
the overpotential.
The unusual Tafel slope at higher overpotential for the reduction
of VOϩ2 of 400 to 500 mV/decade could not be directly explained by
the model, though it could be related to a VO2•4 H2O ͑or equiva-
lent͒ intermediate species. However, while the model can clarify the
underlying steps of the redox reactions, other aspects related to the
role of carbon surface sites and solution complexes, need to be
further investigated in order to completely understand the system.
Figure 12. Data ͑in black͒ and predicted curves using the modeled mecha-
nism ͑gray͒ for different ratios of V͑IV͒ to V͑V͒. Graphite electrode, 6000
rpm, 0.2 mV/s, 1 M H2SO4 . ͑A͒ ca. 49.9 mM V͑IV͒ and 0.1 mM V͑V͒, ͑B͒
25 mM V͑IV͒ and 25 mM V͑V͒, ͑C͒ ca. 0.2 mM V͑IV͒ and 49.8 mM V͑V͒.
Acknowledgments
The authors thank Dr. S. Miyake and Professor M. Skyllas-
Kazacos for useful discussions, and Colin Stewart for carrying out
some additional tests to help complete this paper.
of the path 3 EគCC step is written as VO2•4 H2O. Being a neutral
species, it might be expected to precipitate and possibly foul the
electrode if the concentration of this intermediate exceeds its solu-
bility. Pourbaix lists this species in solid form as V2O4 .14 Thus, an
unusual Tafel slope in this region of the polarization curve is not
actually inconsistent with the model. However, more work is re-
quired to understand the true cause of the unusual Tafel slope at
higher overvoltages in the cathodic region, as other factors may also
need to be considered.
The National Research Council of Canada assisted in meeting the pub-
lication costs of this article.
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