Effect of comproportionation on voltammograms for two-electron reactions with an irreversible second electron transfer

Article abstract of DOI:10.1021/ac990066g

Many organic and organometailic compounds are reduced or oxidized in two steps with the addition or removal of the second electron occurring with greater difficulty than the first In such EE reactions, a comproportionation reaction can occur in solution near the electrode by which the final product exchanges an electron with the reactant to form two molecules of the intermediate species. Normally, this comproportionation reaction has little or no effect in voltammetry. In this paper, a substantial effect of comproportionation is predicted for the case where the second electron-transfer reaction is irreversible. In steady-state voltammetry, the normally symmetric, sigmoid-shaped second wave is predicted to rise more sharply near its base than is observed in the absence of comproportionation and, in the limit of a very fast comproportionation reaction, an "onset potential" develops at which the current at the second wave increases abruptly from the limiting current of the first plateau. Experimental examples of these effects are presented for the reduction of tetracyanoquinodimethane in acetonitrile by steady-state microelectrode voltammetry, normal-pulse voltammetry, and cyclic voltammetry.

Full text of DOI:10.1021/ac990066g

Anal. Chem. 1999, 71, 1947-1950
Effe c t o f Co m p ro p o rt io n a t io n o n Vo lt a m m o g ra m s
fo r Tw o -Ele c t ro n Re a c t io n s w it h a n Irre ve rs ib le
S e c o n d Ele c t ro n Tra n s fe r
Ma rk W. Le hm a nn a nd De nnis H. Eva ns *
Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716
2- + A ) 2A•-
(3)
Many organic and organometallic compounds are reduced
A
or oxidized in two steps with the addition or removal of
the second electron occurring with greater difficulty than
the first. In such EE reactions, a comproportionation
reaction can occur in solution near the electrode by which
the final product exchanges an electron with the reactant
to form two molecules of the intermediate species. Nor-
mally, this comproportionation reaction has little or no
effect in voltammetry. In this paper, a substantial effect
of comproportionation is predicted for the case where the
second electron-transfer reaction is irreversible. In steady-
state voltammetry, the normally symmetric, sigmoid-
shaped second wave is predicted to rise more sharply near
its base than is observed in the absence of compropor-
tionation and, in the limit of a very fast comproportion-
ation reaction, an “onset potential” develops at which the
current at the second wave increases abruptly from the
limiting current of the first plateau. Experimental ex-
amples of these effects are presented for the reduction of
tetracyanoquinodimethane in acetonitrile by steady-state
microelectrode voltammetry, normal-pulse voltammetry,
and cyclic voltammetry.
incoming A will react with electrogenerated A2- in the diffusion
layer to form the intermediate radical anion, A•-. Normally, the
effect of this comproportionation reaction on the voltammetric
response is negligible. In fact, it was shown many years ago that
comproportionation can have absolutely no effect in voltammetry
for the case of mass transport by diffusion only, equal diffusion
coefficients for all three species, reversible electrode reactions,
and the absence of other chemical reactions involving the three
species in the EE system.1
When one or more of these conditions is not met, the
comproportionation reaction will exert an effect on the voltam-
metric response. When diffusion is the only means of mass
transport, the largest effects are seen when other chemical
reactions are involved, e.g., conformational changes or isomer-
ization reactions.2,3 The effect of unequal diffusion coefficients was
explored recently,4 and it was found that small but detectable
effects could be seen in normal-pulse voltammograms for oxidation
of the dianion of tetracyanoquinodimethane, TCNQ2-, where the
diffusion coefficient of the reactant is about 35% smaller than that
of the intermediate (TCNQ•-) or the final product (TCNQ). It is
unusual for the diffusion coefficients of the structurally related
species in an EE system to differ as much as was seen for TCNQ,
so one expects that the effects of unequal diffusion coefficients
will normally be scarcely noticeable.
The consecutive addition or removal of two or more electrons
is a commonly observed phenomenon in organic and organome-
tallic electrochemistry. In systems featuring two electron-transfer
reactions (EE systems), the individual formal potentials, E°′1 and
E°′2, are normally separated by several tenths of a volt such that
addition or removal of the second electron is more difficult than
the first (reactions 1 and 2). For the sake of simplicity, the
Much more dramatic effects are seen when migration con-
tributes to mass transport in the voltammetric experiment.5-9 This
occurs when little or no supporting electrolyte is present. In
steady-state experiments (microelectrode voltammetry, for ex-
A + e- ) A•-
•- + e- ) A2-
E°′1, ks,1, R1
E°′2, ks,2, R2
(1)
(2)
(1) Andrieux, C. P.; Save´ant, J. M. J. Electroanal. Chem. Interfacial Electrochem.
1 9 7 0 , 28, 339.
(2) Matsue, T.; Evans, D. H. J. Electroanal. Chem. Interfacial Electrochem. 1984,
168, 287.
A
(3) Matsue, T.; Williams, D. G.; Evans, D. H. J. Electroanal. Chem. Interfacial
Electrochem. 1 9 8 7 , 233, 63.
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385, 201.
(5) Kamau, G. N.; Rusling, J. F. J. Electroanal. Chem. Interfacial Electrochem.
1 9 9 0 , 292, 187.
(6) Norton, J. D.; Benson, W. E.; White, H. S.; Pendley, B. D.; Abrun˜ a, H. D.
Anal. Chem. 1 9 9 1 , 63, 1909.
reactions are written as reductions and the initial reactant is
neutral. Transposition to oxidation reactions and other reactant
charge types is easily achieved. Each reaction is characterized
by a formal potential (E°′), standard heterogeneous electron-
transfer rate constant (ks), and transfer coefficient (R).
For the case where introduction of the second electron occurs
with greater difficulty than the first, it has long been recognized
that the comproportionation reaction (reaction 3) is favored so
that, at potentials where A2- is being formed at the electrode,
(7) Norton, J. D.; White, H. S. J. Electroanal. Chem. Interfacial Electrochem.
1 9 9 2 , 325, 341.
(8) Amatore, C.; Bento, M. F.; Montenegro, M. I. Anal. Chem. 1 9 9 5 , 67, 2800.
(9) Amatore, C.; Paulson, S. C.; White, H. S. J. Electroanal. Chem. Interfacial
Electrochem. 1 9 9 7 , 439, 173.
10.1021/ac990066g CCC: $18.00 © 1999 American Chemical Society
Published on Web 04/17/1999
Analytical Chemistry, Vol. 71, No. 10, May 15, 1999 1947

ample) the ratio of the two limiting currents can deviate markedly
from the value of unity that is seen at high supporting electrolyte
concentrations. Thorough theoretical treatments of migrational
effects in EE systems have been published.8,9
In a recent study,10 we determined the infinite-dilution standard
potentials, E°1 and E°2, for TCNQ (referred to the infinite-dilution
standard potential for the ferrocene/ ferrocenium couple) by using
steady-state microelectrode voltammetry at low ionic strength in
well-supported solutions (ratio of electrolyte to TCNQ concentra-
tion equal to 10). In the course of these studies, we noted an
unusual asymmetry in the shape of the second steady-state
voltammetric wave under certain experimental conditions. Instead
of exhibiting the normal-symmetric sigmoid shape, the second
TCNQ wave featured a rather sharply rising current near its foot
and a more normal drawn-out approach to the limiting current at
the crest. We then noted that similar unusually shaped curves
were present in our published normal-pulse voltammograms of
TCNQ4 and in channel-flow voltammograms of 2,3-dichloro-5,6-
dicyano-1,4-benzoquinone.11 In the present work, we have devel-
oped a probable explanation for these unusual wave shapes in
terms of the effect of the comproportionation reaction when the
second electron transfer exhibits sluggish electron-transfer kinet-
ics.
Fig u re 1 . Simulated steady-state voltammograms. E°1 ) 0 V, ks,1
) 104 cm/s, R1 ) 0.5, E°2 ) -0.5 V, ks,1 ) 10-4 cm/s, R2 ) 0.5, D
(all species) ) 10-5 cm2/s, C*reactant ) 10-3 M, r0 ) 10 µm, and kcomp
as indicated; temperature was 298 K. Dashed curve: Limiting
behavior for infinite kcomp with identification of the onset potential, Eos
.
form if a generally applicable set of theoretical responses is
needed. The values of input parameters are given in the caption
to Figure 1.
The first wave is of reversible shape with E1/ 2,1 ) E°1 and with
the slope of the “log plot” (E vs log[(Ilim,1 - I)/ I]) equal to the
reversible limit of 2.303RT/ F (59.16 mV at 298 K).12 Because of
the small value of ks,2 that was chosen, the second wave (with
comproportionation suppressed; kcomp ) 0) exhibits the normal
sigmoid shape for an irreversible process, the slope of the log
plot being 2.303RT/ R2F (118 mV for 298 K and R2 ) 0.5, as chosen
for the simulation).12 The second half-wave potential, E1/ 2,2, is
displaced12 (RT/ R2F) ln(ks,2r0/ D) to negative potentials from E°2
(236 mV for the values of parameters used in Figure 1). Thus, in
the absence of comproportionation, the voltammogram is perfectly
normal with the shape and position of the waves in accord with
theory. These results support the conclusion that the simulation
program is producing reliable results.
However, as comproportionation is introduced into the simula-
tion by increasing kcomp, a dramatic change in the shape of the
second wave is predicted. The wave tends to shift toward negative
potentials and a marked asymmetry sets in at kcomp near 108 M-1
s-1. The current rises very sharply at the foot of the wave while
the shape near the limiting current is almost normal. In the limit
of very large kcomp, the current-potential curve near the foot is
predicted to feature a sharp break (very large d2I/ dE2). This “onset
potential”, Eos, is indicated in Figure 1.
EXPERIMENTAL SECTION
Solvent, electrolyte, and reagents were as described earlier.4
Standard procedures were employed for microelectrode voltam-
metry, rotating disk electrode voltammetry, and cyclic voltamme-
try. The reference electrode comprised a silver wire in contact
with 0.010 M AgNO3, 0.10 M Bu4NPF6 in acetonitrile (AgRE).
Simulations were carried out using the software package
DigiSim (Bioanalytical Systems; Version 3.0). Hemispherical
diffusion geometry was employed for simulations of microelec-
trode voltammetry. The expanding space factor was 0.2, r0,min was
50, and the scan rate was 0.1 mV/ s. These input parameters were
found to produce very accurate values of the steady-state limiting
current. Simulation of the normal-pulse voltammogram was
accomplished using a mass transport coefficient for hemispherical
diffusion (D/ r0) set equal to the experimental mass transport
coefficient for normal-pulse voltammetry ((D/ πtp)1/ 2). Here D is
the diffusion coefficient of the reactant, r0 is the radius of the
hemisphere, and tp is the pulse duration. The simulated currents
were scaled to match the experimental values.
RESULTS AND DISCUSSION
It is of interest to see if we can understand the underlying
causes of the development of the onset potential. At first glance,
it is not obvious why a fast comproportionation will cause the
effects that are seen. It is particularly curious that the compro-
portionation reaction somehow works to keep the currents in the
range of about -0.6 to -0.7 V at the level of the first limiting
current although, in the absence of comproportionation, this
potential region encompasses a large part of the second wave.
Clearly, the rate of electrode reaction 2 (A•- + e f A2-) is
sufficiently high in this region to produce the second wave that
is seen in the absence of comproportionation. The answer to this
The concepts will be introduced by way of theoretical steady-
state microelectrode voltammograms. Figure 1 includes simula-
tions for an EE reaction occurring at a hemispherical microelec-
trode for the case where the first electron transfer occurs
reversibly and the second is quite irreversible, ks,2 ) 10-4 cm/ s.
The inputs to the model and the simulation output have been
expressed in real laboratory units rather than as dimensionless
quantities. The intention is to facilitate perception of the relevance
of the calculations to realistic laboratory conditions. Of course,
the simulation results can be easily expressed in dimensionless
(10) Lehmann, M. W.; Evans, D. H. J. Phys. Chem. B 1 9 9 8 , 102, 9928.
(11) Oyama, M.; Marken, F.; Webster, R. D.; Cooper, J. A.; Compton, R. G.;
Okazaki, S. J. Electroanal. Chem. Interfacial Electrochem. 1 9 9 8 , 451, 193.
(12) Oldham, K. B.; Zoski, C. G. J. Electroanal. Chem. Interfacial Electrochem.
1 9 8 8 , 256, 11.
1948 Analytical Chemistry, Vol. 71, No. 10, May 15, 1999

apparent contradiction is that the current produced by reaction 2
results in an equal suppression of the current arising from the
steady-state arrival of A and its reduction by reaction 1 because
the product of reaction 2, A2-, destroys an equivalent amount of
A when comproportionation is fast, i.e., A2- + A f 2A•-.
For the case of equal diffusion coefficients, the surface
considered, an analogous treatment gives eq 7 for Eos where tp is
2
tpks,2
RT
Eos - E°2 )
ln
(7)
(
)
2R2F
D
concentration of A•-, CA ,x)0, will equal the bulk concentration of
•-
the pulse duration. In fact, it was in the context of normal-pulse
voltammetry that unusually shaped voltammograms were first
noticed for an EE mechanism.4 Analogous expressions can easily
be derived for other steady-state (e.g., rotating disk voltammetry)
or pseudo-steady-state (classical polarography) techniques. To our
knowledge, the only earlier reference to phenomena like those
discussed here is in the theoretical work of Ruzic and Smith on
polarography and ac polarography.14
It is likely that similar effects on the second wave in EE
processes with an irreversible second step are possible for all
voltammetric techniques. In the present work, for example, we
have demonstrated that onset potentials can be seen in cyclic
voltammetry (see below). A substantially different but related
effect has been observed for the reduction of cyclooctatetraene,
for which the first electron-transfer reaction is quasireversible
while the second is reversible.15
A, C*A, at any point on the first limiting current plateau. The rate
of irreversible reaction 2 (expressed as the flux of A2- produced,
2-
JA ,x)0) will be given by eq 4, which invokes the normal Butler-
Volmer expression for the rate constant, kf,2. Also, the flux of A at
R2F
RT
JA2-,x)0 ) kf,2CA
,
•-
x)0 ) C*Aks,2 exp -
(E - E°2)
(4)
[
]
the electrode surface when the steady-state current is equal to
the first limiting current is given by eq 5.13 As long as the
DC*A
JA,x)0 ) -
(5)
r0
Returning to microelectrode voltammetry at hemispherical
electrodes, it is of interest to determine how large the parameter
r0ks,2/ D can be before eq 6 begins to fail. Simulations were
conducted for values of r0ks,2/ D ranging from 10-8 to 10. From
10-8 to 1, the simulations gave values of Eos in agreement ((1
mV) with eq 6, again attesting to the accuracy of the simulation
program. Only when this kinetic parameter exceeded 1 did the
simulations indicate a loss of definition of the onset potential under
conditions where the comproportionation reaction is very fast. This
information allows us to assess the likelihood that the unusually
shaped waves we have been discussing will actually be seen under
normal conditions and with typical EE systems. It is reasonable
to doubt that sharp onset potentials will be seen because it is
required that the comproportionation reaction be extremely fast
while the kinetic parameter r0ks,2/ D cannot be too large. A fast
comproportionation reaction implies a low barrier for this solution-
phase electron-transfer reaction which can result from a low
intrinsic barrier and/ or a large driving force. However, a low
intrinsic barrier will require that the barrier for the heterogeneous
electron transfer in reaction 2 will also be small, meaning that ks,2
will be large.
magnitude of the flux of A2- produced (eq 4) is less than the
potential flux of A that can arrive at the surface (eq 5), the
additional current due to production of A2- will be exactly offset
by suppression of the flux of arriving A by the fast compropor-
tionation reaction that converts A2- and A to two radical anions.
Following this line of argument, the onset potential, Eos, will
occur at the point where the flux of A2- produced (eq 4) first
exceeds the maximum flux of A arriving at the surface. By
equating the fluxes from eqs 4 and 5, we obtain an expression
for the onset potential, eq 6. Interestingly, this expression for Eos
r0ks,2
D
RT
R2F
Eos - E°2 )
ln
(6)
(
)
in the limit of a very fast comproportionation reaction is the same
as the expression for E1/ 2,2 in the absence of comproportionation.12
For the parameter values used in Figure 1, Eos is predicted to be
-236 mV from eq 6, and this is exactly what was found by
simulation, an observation that again supports the conclusion that
the simulation program is producing reliable results.
Taking unity as the upper limit of r0ks,2/ D for observing a well-
defined onset potential and using 10 µm as a very convenient
radius for a microelectrode along with a typical value of 10-5 cm2/ s
for the diffusion coefficient, we obtain the result that ks,2 cannot
exceed 0.01 cm/ s to allow well-defined Eos. This rate constant is
smaller than is typically observed for the electron-transfer reac-
tions of organic and organometallic species that might take part
in an EE scheme and may explain why sharp Eos values have not
been seen.
Another interesting feature of the second wave in the limit of
very large kcomp (dashed curve, Figure 1) is that its location and
shape are identical to those of the upper half of an irreversible
wave with a limiting current equal to Ilim,2. As was noted above,
the half-wave potential of this hypothetical expanded wave falls
at Eos, which is identical to E1/ 2,2 in the absence of compropor-
tionation. Furthermore, the slope of the log plot of the upper half
of the expanded wave (E vs log[(Ilim,2 - I)/ I] is exactly 2.303RT/
R2F. This result is mentioned here because it is interesting and,
to the authors, quite unintuitive.
In Figure 2, a normal-pulse voltammogram for the reduction
of TCNQ at a platinum working electrode in acetonitrile with 0.10
M Bu4NPF6 is presented4 (circles). Also shown in Figure 2 are
The geometry of the electrode does not play an explicit role
in the development of eq 6. Thus, for the technique of normal-
pulse voltammetry at planar electrodes for the EE system being
(14) Ruzic, I.; Smith, D. E. J. Electroanal. Chem. Interfacial Electrochem. 1 9 7 5 ,
58, 145.
(13) Bard, A. J.; Faulkner, L. R. Electrochemical Methods. Fundamentals and
Applications; Wiley: New York, 1980; p 145.
(15) Heinze, J.; Dietrich, M.; Hinkelmann, K.; Meerholz, K.; Rashwan, F.
DECHEMA Monogr. 1 9 8 8 , 112, 61.
Analytical Chemistry, Vol. 71, No. 10, May 15, 1999 1949

Fig u re 2 . Normal-pulse voltammogram for reduction of 6.9 × 10-4
M tetracyanoquinodimethane (TCNQ) in acetonitrile with 0.10 M Bu4-
NPF6 at 293 K (platinum disk working electrode (diameter: 0.31 cm)).
Pulse duration: 0.050 s. Data (circles) were taken from ref 4. Lines
are simulations with the following input parameters: E°1 ) -0.107
V, ks,1 ) 104 cm/s, R1 ) 0.5, E°2 ) -0.658 V, ks,1 ) 0.0065 cm/s, R2
) 0.35; diffusion coefficients of neutral, radical anion, and dianion
are 1.44 × 10-5, 1.35 × 10-5, and 9.1 × 10-6 cm2/s, respectively;4
kcomp as indicated.
Fig u re 3 . Cyclic voltammogram of 1.30 mM TCNQ in acetonitrile
with 0.10 M Bu4NPF6 at 298 K (platinum disk working electrode
(diameter: 0.33 cm). Scan rate: 2.00 V/s.
Apparently, larger rotation rates are required to cause such
behavior for TCNQ and the RDE.
Analogous behavior is easily seen in cyclic voltammetry. Figure
3 shows a voltammogram obtained at 2 V/ s in which a rather
sharp break is observed at the foot of the second cathodic peak.
Similar shapes were observed for concentrations ranging from
0.2 to 3 mM and scan rates from 1 to 50 V/ s. The voltammograms
are well accounted for by digital simulations that include fast
comproportionation though the agreement is not perfect, sug-
gesting that other factors are influencing the shape. If the
comproportionation reaction is eliminated from the simulations,
even qualitative agreement with the shape of the experimental
voltammograms is impossible to achieve.
As stated in the introduction, comproportionation will not affect
voltammograms if the diffusion coefficients of all species are equal,
mass transport is by diffusion only, the electron-transfer reactions
are reversible, and none of the species take part in other chemical
reactions. In this work, we have reported an experimental example
of the effect of comproportionation when the second electron-
transfer reaction is irreversible and for steady-state voltammetry
we have provided explanations for the development of asymmetry
in the second wave and the appearance of onset potentials. This,
together with the previous research cited above, completes the
suite of effects that can be observed when one or more of the
above constraints is released.
simulations in which E°1 - E°2 has been set at 0.55 V, in
agreement with our earlier measurements for this ionic strength.10
With fast comproportionation (kcomp ) 108 M-1 s-1) and a rather
small second electron-transfer rate constant (ks,2 ) 0.0065 cm/ s),
the second wave is positioned properly on the potential axis and
its asymmetric shape agrees well with experiment. To generate a
clear onset potential, the comproportionation reaction must
approach the diffusion-controlled limit, ca. 1010 M-1 s-1 (Figure
2). In the absence of comproportionation (kcomp ) 0, Figure 2),
the second wave has a symmetric shape and its half-wave potential
is about 60 mV less negative than when the comporoportionation
reaction is fast. Though kcomp ) 108 M-1 s-1 provides the best
agreement with the experimental data, the response is quite
insensitive to kcomp when it is large so this is not a practical way
to evaluate kcomp accurately.
We speculate that the rather small value of ks,2 required to
match the experimental data may have resulted from deactivation
of the electrode due to adsorption of impurities, electrolysis
products, etc. Some asymmetry is seen in the second wave of
steady-state voltammograms obtained with platinum microelec-
trodes (r0 ) 5 µm), but it is not as marked as the result in Figure
2. Freshly polished electrodes tend to give more symmetric
responses, implying that they exhibit larger values of ks,2. When
studied at a rotating platinum disk electrode (RDE), the second
wave for reduction of TCNQ was quite symmetric up to our
maximum rotation rate of 2000 rpm. In general, enhanced mass
transport should put stress on the second electron-transfer
reaction (reaction 2), bringing about a breakdown in symmetry
or even the development of a sharp break in the voltammogram.
ACKNOWLEDGMENT
This work was supported by the National Science Foundation,
Grant CHE-9704211.
Received for review January 27, 1999. Accepted March 12,
1999.
AC990066G
1950 Analytical Chemistry, Vol. 71, No. 10, May 15, 1999