Kinetics of the p-aminodiphenylamine radical in organic solution: An electrochemical and electron spin resonance study

Article abstract of DOI:10.1021/jp952965o

In studying the reaction mechanism of anodic aniline oxidation the dimer p-aminodiphenylamine (ADPA) was found to be the main intermediate product in acidic solution. It is oxidized in both the free amine and the protonated form. The cyclic voltammograms have been simulated by taking into account an electrochemical reaction of both the protonated and the nonprotonated forms. Thus, it was also found that the ADPA concentration is determined by the protonation equilibrium. The oxidation product N-phenylquinone diimine (PQDI) undergoes a symproportionation reaction with ADPA forming the ADPA^?+ cation radical. The equilibrium constant for this reaction of PQDI in dimethyl sulfoxide was determined and found to be independent of the concentration of the protons in solution. The ADPA^?+ cation radical decay can be described by a rate equation based on a second-order reaction for the radical dimerization and a pre-equilibrium for the radical formation by symproportionation. The reaction mechanisms of the anodic oxidation of p-aminodiphenylamine and its chemical follow-up reactions are given.

Full text of DOI:10.1021/jp952965o

J. Phys. Chem. 1996, 100, 4867-4872
4867
Kinetics of the p-Aminodiphenylamine Radical in Organic Solution: An Electrochemical
and Electron Spin Resonance Study
A. Petr and L. Dunsch*
Institut fu¨r Festko¨rperforschung im IFW Dresden e. V., Abteilung Elektrochemie und leitfa¨hige Polymere,
Helmholtzstr. 20, D-01069 Dresden, Germany
ReceiVed: October 6, 1995; In Final Form: December 14, 1995X
In studying the reaction mechanism of anodic aniline oxidation the dimer p-aminodiphenylamine (ADPA)
was found to be the main intermediate product in acidic solution. It is oxidized in both the free amine and
the protonated form. The cyclic voltammograms have been simulated by taking into account an electrochemical
reaction of both the protonated and the nonprotonated forms. Thus, it was also found that the ADPA
concentration is determined by the protonation equilibrium. The oxidation product N-phenylquinone diimine
(PQDI) undergoes a symproportionation reaction with ADPA forming the ADPA•+ cation radical. The
equilibrium constant for this reaction of PQDI in dimethyl sulfoxide was determined and found to be
independent of the concentration of the protons in solution. The ADPA•+ cation radical decay can be described
by a rate equation based on a second-order reaction for the radical dimerization and a pre-equilibrium for the
radical formation by symproportionation. The reaction mechanisms of the anodic oxidation of p-
aminodiphenylamine and its chemical follow-up reactions are given.
1. Introduction
The role of p-aminodiphenylamine as an intermediate in the
anodic oxidation of aniline is widely recognized in former
studies.1-4 The reaction of this intermediate is important for
the preparation of polyaniline as one of the most prominent
members of the family of electrically conducting polymers. This
polymer is studied in detail because of its great potential
applications in, e.g., sensor materials, electrochromic devices,
corrosion protection, photochemical devices, and other fields.
It is studied to a large extent with respect to the influence of
the preparation conditions on the polymer properties.1 As the
initial stages of the electropolymerization of aniline in aqueous
solutions are very important for the polymer formation, it was
pointed out by other authors2 that p-aminodiphenylamine is the
dominant intermediate in these early stages. In acidic aqueous
solutions the anodic oxidation of aniline goes through further
different intermediates to form finally polyaniline (PANI), which
was formerly called aniline black.1 Large differences in the
structure of PANI due to various influences in the electropo-
lymerization were found. The dimeric intermediate p-amino-
diphenylamine (ADPA) is formed by an alternate electron
transfer2 and dimerization step of aniline. Due to the various
ways it takes part in redox and/or chemical reactions, it is the
main intermediate in aniline oxidation.1-4 Its occurrence was
already qualitatively proved by numerous studies in the past.
and not in a one-electron oxidation. This symproportionation
reaction has been compared with that of the p-phenylenedi-
amine.10
In their extensive and fundamental work on the electrochem-
istry and ESR spectroscopy of ADPA, Allendoerfer et al.8 draw
the conclusion from electrochemical measurements of the
differences in the peak potentials that Keq in aqueous solutions
must be less than 1. Due to this fact, the ESR spectrum was
weak.
A further point in the ESR spectroscopic and electrochemical
study of ADPA oxidation is the formation of a polymer layer
on the electrode giving rise to an ESR signal interfering with
that of the less intense signal from the ADPA radical. Thus,
conditions had to be found to avoid this interference.
Because of the slow, radical decay and the special ESR
technique applied in this study as described below, it will be
shown that the determination of that equilibrium constant is
possible within an estimated error of 30%. The error is
reasonable for that technique and nevertheless the best value
available in the present state of the technique.
Furthermore, there is a contradiction in the literature concern-
ing the follow-up reaction. In ref 10 an acid-catalyzed coupling
rate of PQDI is discussed which should be of second order with
respect to PQDI. On the other hand in refs 7 and 11 a
dimerization of the ADPA radical cation is assumed. It is also
important for the discussion of further polymer-growing steps
that this radical reaction in the aniline polymerization is different
Their have been several studies on the anodic oxidation of
ADPA itself5-9 to follow both the mechanism of the oxidation
and the formation of a polymer which is obviously different
from polyaniline.
The ADPA•+ radical, which can be detected by ESR
spectroscopy,8 is formed by symproportionation of ADPA and
N-phenylquinone diimine (PQDI) according to
* E-mail: dunsch@ifw-dresden.de.
X Abstract published in AdVance ACS Abstracts, February 15, 1996.
0022-3654/96/20100-4867$12.00/0 © 1996 American Chemical Society

4868 J. Phys. Chem., Vol. 100, No. 12, 1996
Petr and Dunsch
from that of the polymerization of PQDI. Therefore, there is a
need for a detailed study of the kinetics of the anodic reaction
of ADPA especially with respect to the equilibrium of ADPA
and PQDI. It is the aim of this work to find the valid rate
equation for the ADPA radical decay, and to estimate the
equilibrium constant of the symproportionation and the rate
constant of the chemical reaction by measuring the absolute
radical concentrations as a function of time. Thus, we can find
the most probable reactions by excluding different rate equa-
tions. Therefore, a reasonable reaction scheme is provided.
2. Experimental Section
2.1. Substances. p-Aminodiphenylamine (ADPA) was
purchased from Fluka in analytical grade and was recrystallized
twice from a methylene chloride-petroleum ether mixture under
inert conditions in a glovebox. The product obtained by this
procedure was faintly colored. The melting point was 66-67
°C (lit. mp 66-67 °C12). Dimethyl sulfoxide (DMSO) with a
maximum water content of 0.02% was used as the organic
solvent. Concentrated H2SO4 p.a. (Merck) and Na2SO4‚10H2O
were the supporting electrolytes for nonaqueous and aqueous
solutions, respectively. In general, 0.1 M H2SO4/DMSO
solutions have been used. The aqueous solutions were prepared
with deaerated bidistilled water.
2.2. Equipment. ESR spectroscopy was done with an
X-band spectrometer ESP 300 E (Bruker) with an H102 cavity.
All measurements were carried out at room temperature with
100 kHz modulation and a microwave power of 1 or 2 mW.
Electrochemical generation of the radicals as well as the
different electrochemical measurements in the electrochemical
ESR cell were carried out with a potentiostat PG 285 (HEKA
Lambrecht). The potentiostat was PC controlled. The potential
was varied under control of a locally written Turbo Pascal
program. For DA conversion a plug-in board ACAO (Straw-
berry Tree) was used, which was also the trigger source for the
ESR spectrometer and the pump of the electrolyte solution. A
block diagram of the apparatus setup used in this study is given
in ref 13. Cyclic voltammetry was done in either a conventional
electrochemical cell or the ESR flat cell using the potentiostat
PG 285 (HEKA Lambrecht).
For the simulations of the cyclic voltammograms, the program
DIGISIM 2.0 (Bioanalytical Systems) was used. For those of
the ESR spectra, the program SIMFONIA (Bruker) was used.
2.3. Cell Design. For the EC-ESR investigations, we used
a special flat cell situated in a rectangular cavity as shown in
Figure 1. The central part of this flat cell is 0.5 mm thick, 8
mm wide, and 40 mm long. This part is situated inside the
cavity. The working electrode for the standard procedure
consists of a coil made from platinum wire 12 cm in length
and 0.5 mm in diameter. This coil is mounted at the end of the
quartz tube on top of the flat part of the EC-ESR cell, which is
therefore used in an ex situ mode.
As the reference electrode a AgCl-coated silver wire within
a Luggin capillary was used. The end of this capillary and an
additional glass tube for gas bubbling were inside the Pt coil.
However, all potentials mentioned in this paper are referred to
the potential of the ferrocene couple. The counter electrode
was a Pd sheet situated below the flat part of the cell.
For our kinetic investigations we used the following proce-
dure: In the beginning of the measurement we brought exactly
1 mL of the ADPA solution in the upper part of the cell and
applied a definite charge to the solution. The simultaneous
bubbling with nitrogen provided both a homogeneous solution
of PQDI as well as ADPA and allows the application of higher
current densities in the electrolysis.
Figure 1. View of the ESR electrochemical cell for low-volume
measurements in the three-electrode system. The thin layer part of
the flat cell inside the ESR cavity is 0.5 mm thick, having an effective
probe volume of 45 µL.
When an appropriate charge had been applied to the ADPA
solution, the working electrode was disconnected immediately
by an electronic switch. Then gas bubbling was stopped, and
a volume of 0.5 mL of the electrolyzed solution was moved
down as fast as possible from the upper part of the ESR cell
into the flat cell region where the ESR measurement was done.
It was done by pumping off the electrolyte solution in the flat
cell Via the counter electrode compartment (Figure 1). This
solution was replaced by the electrolyzed one. By this way it
could be ensured that the whole part of the flat cell was filled
with the homogeneous reaction mixture. This procedure was
carried out with the help of a syringe connected to the lower
end of the cell. The volume of the solution in the upper part
of the cell was determined to get the exact concentration of the
reaction product. For this purpose the glassware was marked
for a certain volume. For the in situ EC-ESR investigations of
the kinetics of ADPA formation, the in situ EC-ESR cell
described earlier13 was used.
2.4. Solutions. The organic ADPA solutions were prepared
under nitrogen atmosphere in a glovebox. They were fed
through a Teflon tube directly from the glovebox into the EC-
ESR cell. In the spectra accumulation technique, the electrolyte
at the working electrode was renewed by transferring the
electrolyte using a computer-driven injection pump. For
measurements in DMSO, the sulfuric acid concentration was
varied in the range between 0.1 and 0.5 M. Any contact of the
acidic electrolyte solutions with other metal parts except
platinum was avoided. For measurements in aqueous solutions,
the solid ADPA was added to a thoroughly deaerated 0.1 N
Na2SO4-water solution. After the dissolution of ADPA, the
pH value of the solution was adjusted to 1.5 by the addition of
0.1 N H2SO4.

Kinetics of the p-Aminodiphenylamine Radical
J. Phys. Chem., Vol. 100, No. 12, 1996 4869
•+
AH2 + H+ a AH3
(2)
(3)
(4)
(5)
(6)
AH+3 a AH2•+ + e- + H+
•+
AH+3 + H+ a AH4
AH42+ a AH2•+ + e-1 + 2H+
AH2•+ a QH+ + e- + H+
Q + H+ a QH+
(7)
(8)
•+
AH+3 + QH+ a 2AH2
with AH2 ) unprotonated ADPA, AH+ ) single-protonated
3
ADPA, AH24+ ) double-protonated ADPA, AH2 ) radical
•+
cation of ADPA, and Q ) PQDI. It meets all results mentioned
in the present paper and is based on three one-electron transfer
reactions of three different protonated ADPA species forming
the corresponding cation radicals. These cation radicals undergo
quick protonation/deprotonation reactions and are oxidized to
PQDI, which also undergoes protonation/deprotonation. With
this mechanism we were also able to fit the experimental cyclic
voltammograms. The following parameter set was found to be
representative but probably overvalues the amount of the double-
protonated ADPA: formal potentials according to eq 1, E )
-0.15 eV; eq 2, E ) 0.49 V; eq 5, E ) 0.66 V; eq 6, E ) 0.06
V, and equilibrium constants for eq 2, K ) 2 × 105 L/mol; eq
4, K ) 10 L/mol; eq 7, K ) 105 L/mol.
Figure 2. (a) Cyclic voltammogram of ADPA measured at a Pt
working electrode in 0.5 M H2SO4/DMSO with an Ag/AgCl wire as a
reference electrode. Potentials are referred to the potential of the
ferrocene couple; sweep rate was 150 mV/s; concentration of ADPA
was 10-3 M. (b) Simulated cyclic voltammogram of ADPA with E1
) 0.15 V, E2 ) 0.49 V, E3 ) 0.66 V, and E4 ) 0.06 V. For
explanation, see text; for mechanism see eqs 1-8.
3. Results
A cyclic voltammogram of ADPA in acidic DMSO solution
is shown in Figure 2, curve a. The peak separation of the
oxidation and the re-reduction peak is 320 mV. This result is
quite different from that in neutral and HClO4-acidic acetonitrile
(MeCN).5,14 The H2SO4/DMSO solution gives a quite different
protonation equilibrium of ADPA and PQDI from that in HClO4/
MeCN, resulting in different cyclic voltammograms. The
current increase at potentials higher than 800 mV is due to the
starting formation of an oxide layer on the platinum electrode
in DMSO. This effect is not as significant as it is in sulfuric
acid solution where it has been known for a long time from
potentiodynamic measurements.15 The current increase is also
due to the beginning decomposition of the electrolyte. The weak
voltammetric wave at the foot of the anodic peak increases and
results in an additional peak at lower sweep rates.
It is known from in situ UV-vis electrochemical measure-
ments16 that within the time scale of our measurements PQDI
is the only product formed during oxidation of ADPA. In the
same study it is shown that the amount of the starting material
is re-formed during re-reduction.
For the simulation of the cyclic voltammograms, we tried
different reaction mechanisms like deprotonation before and
after oxidation or the electron transfer reaction of only the
protonated ADPA, but the simulations of the voltammograms
failed.
The equilibrium constant for the symproportionation reaction
(eq 8) is not determined by simulation but by our independent
measurement to be K ) 0.027 as described later. On the basis
of these simulations we can interpret the measured cyclic
voltammograms as follows:
The weak voltammetric wave at the foot of the anodic peak
is due to the oxidation of the nonprotonated ADPA. Its
concentration is low because the equilibrium according to eq 2
is shifted to the right side. This wave becomes the most intense
peak at very slow sweep rates due to the back reaction (eq 2).
The main oxidation peak at 0.49 V is due to the oxidation of
the single-protonated ADPA, while the small amount of twice-
protonated ADPA is oxidized at 0.66 V where the electrolyte
starts to decompose. As it can be concluded from the proto-
nation constants resulting from the simulation, nearly the whole
amount of the cation radicals is present in the nonprotonated
form which has a low formal potential for their oxidation. This
causes the immediate oxidation to PCDI and the large volta-
mmetric peak separation.
At the very beginning of this study of ESR spectroscopy of
ADPA, it turned out that neither the lifetime of the radical nor
the low radical concentration was the main problem in the ESR
measurements, but it was the formation of an adhering polymer
layer at the electrode surface. This polymer itself gives a strong
single ESR line (Figure 3a) well-known for polyaniline and other
conducting polymers which interferes with the highly resolved
ESR spectra of the low molecular structures. Especially, the
quantitative determination of the ADPA•+ radical concentration
is impossible. Therefore, DMSO was used as the solvent. Thus,
the polymer layer formation is suppressed, and no single ESR
line of the polymer observed by making sensitive ESR measure-
ments of the monomeric radical structures is possible. It was
found furthermore that the addition of DMSO in a small amount
of an aqueous electrolyte of 0.5 mM ADPA is the reason for
the suppression of the polymer layer formation. Figure 3b
Furthermore, we simulated the cyclic voltammograms on the
basis of three two-electron transfer reactions at three different
potentials according to three different protonated species of
ADPA. With this mechanism a good fit was possible, but the
fitted constants for the protonation equilibria showed that the
PQDI should be unprotonated. This fact is contradictory to our
in situ UV-vis measurements, where only the spectra of the
protonated PQDI were found. All our attempts to find a data
set with protonation constants which meet these facts failed.
We propose the following mechanism
AH2 a AH2•+ + e-
(1)

4870 J. Phys. Chem., Vol. 100, No. 12, 1996
Petr and Dunsch
TABLE 1: Equilibrium and Rate Constants of the ADPA
Symproportionation Determined for Different ADPA, PQDI,
and Acid Concentrationsa
concentration concentration concentration
rate
of H2SO4
(mol/L)
of ADPA
of PCDI
equilibrium
constant
(10-3 mol/L) (10-3 mol/L)
constant (L mol-1 s-1
)
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.20
0.20
0.20
0.50
0.50
0.15
0.36
0.40
0.41
0.43
0.52
0.55
0.60
0.67
0.79
2.60
3.67
4.00
4.49
2.03
2.04
2.40
1.80
2.10
0.80
0.57
0.52
0.50
0.53
0.40
0.37
0.34
0.28
0.19
0.30
1.03
0.74
0.32
0.74
0.74
0.41
0.10
0.67
0.024
0.026
0.030
0.032
0.029
0.028
0.031
0.019
0.019
0.031
0.028
0.025
0.027
0.026
0.031
0.031
0.028
0.021
0.022
34
34
30
40
31
35
31
31
35
40
33
a The mean value of the equilibrium constants is Keq ) 0.027
(standard deviation 0.004) and of the rate constants kd ) 34 L mol-1
s-1 (standard deviation 3.4 L mol-1 s-1).
radical concentration increases after switching off the working
electrode (point B). This increase is caused by the high
concentration of PQDI near the electrode surface and its low
concentration in the bulk electrolyte. In pure solutions of ADPA
and PQDI, the radical concentration is zero but turns to the
maximum if the concentrations of both species are equal.
Homogenization of the solution by either diffusion or convection
is therefore responsible for the increase in the radical concentra-
tion after off-circuiting the electrode. This is important for the
interpretation of the radical decay because in that case the pre-
equilibrium condition is fulfilled. Two things facilitate the
estimation of the kinetic data. First, the bubbling with nitrogen
during the generation of PQDI provides a homogeneous solution.
Therefore, the rate equations for homogeneous reactions can
be applied. Without homogenization a gradient in the ADPA
and PQDI concentrations has to be taken into account. There-
fore, the analysis of the kinetic data would be more difficult.
Secondly, the fulfilled pre-equilibrium condition simplifies the
rate equation. Otherwise we had to consider two further rate
constants according eq 9. To check our assumption concerning
the equilibrium
Figure 3. ESR spectrum of the electrochemically formed ADPA radical
cation from 5 × 10-4 M ADPA (a) in aqueous 0.1 M H2SO4 and (b)
in aqueous 0.1 M H2SO4 with 3% DMSO added.
Figure 4. Formation and decay of the ADPA radical cation in acidic
DMSO solution. The Pt electrode is situated in the center of the cavity.
At point A the potential is switched from 0.1 to 0.5 V. At point B the
electrode was off-circuited.
ADPA + PQDI T 2ADPA•+
(9)
[ADPA•+]2
shows the ESR spectrum of the ADPA•+ cation radical measured
in an aqueous solution containing 3% DMSO. This ESR
spectrum is well resolved and equals that described in the
literature.8 A high signal to noise ratio made the comparison
of simulated spectra with the experimental ones more stringent.
An ESR spectrum simulated on the basis of the hyperfine
coupling constants given in ref 8 was in good agreement with
our experimental spectrum. Therefore, the spin density at the
radical is not influenced by the change from water to DMSO
containing water as the solvent.
The radical cation of ADPA•+ is formed due to the sympro-
portionation of ADPA and PQDI according to eq 9. Further-
more, a series of in situ EC-ESR investigations was done to
demonstrate that the radicals are formed immediately after
oxidation of ADPA (Figure 4). At point A (Figure 4), the
potential was changed from -0.1 to 0.5 V. Without any time
delay, the increase of the radical concentration is observed. The
Keq
)
(9a)
[ADPA][PQDI]
we determined the equilibrium constants for different ADPA,
PQDI, and acid concentrations. The radical concentrations were
measured by ESR spectroscopy, the concentrations of PQDI
were known from the transferred charge corrected by one-half
of the radical concentration, and the ADPA concentrations were
given by the starting concentration minus the PQDI and the
radical concentration. The equilibrium constant was determined
for different PQDI and ADPA concentrations and also for
different H2SO4 concentrations.
The results are summarized in Table 1. As expected from
eq 9, the equilibrium constant did not depend on the acid
concentration. In the case of the PQDI reaction with the
nonprotonated or double-protonated form of ADPA in contrast
to that reaction with the single-protonated one, the equilibrium

Kinetics of the p-Aminodiphenylamine Radical
J. Phys. Chem., Vol. 100, No. 12, 1996 4871
By subsequent substitution we obtained a rate equation in the
different form
-Keqkd[ADPA•+]2 ([ADPA] + [PQDI])
(4[ADPA•+] + (Keq([ADPA] + [PQDI])))
d[ADPA•+]
)
dt
(14)
Considering the slope of the measured decay curves at t ) 0
in Figure 5, the behavior of the radical can be interpreted in
the following manner. Taking a fixed starting concentration
of ADPA, the slope of the decay curves at t ) 0 increases with
increasing radical concentration. The term (2[ADPA•+] + Keq-
([ADPA] + [PQDI])) considerably influences the theoretical
decay curves. When the rate constant is derived by the initial
stage method, the experimental error becomes however too large.
An analytical solution of the differential rate equation was not
possible. For a more precise evaluation of the rate constant,
we did not try to find a numerical solution of the rate equation
but solved the following system of equations
[ADPA•+]2
du
dt
Keq
)
and
) kd[ADPA•+]2 (15)
[ADPA][PQDI]
with du ) d([ADPA] + [ADPA•+] + [PQDI]) by the polygon
method which is equivalent to eq 14 and gives the same result
in a more evident way.
Figure 5. Time dependence of the ADPA radical cation concentration
at different concentrations of ADPA and PQDI in acidic DMSO
solution. Starting concentrations of ADPA were 3 mM for the curves
at the top and 1 mM for the curves at the bottom.
The numerical procedure was as follows: The rate for the
product formation is calculated for a small time interval. The
new concentrations of ADPA and PQDI were calculated on the
basis of the converted starting material. Then the new ADPA•+
radical concentration according to the equilibrium was calcu-
lated, and the procedure was started again. As a step width, 1
s was used. A further reduction of the step width by a factor
of 2 had only a slight influence. It is worth mentioning that
the rate of the product formation (ADPA-ADPA) is not the
reaction rate of the radical cation. The concentration of the
radical cation changes slowly because of its formation in the
symproportionation equilibrium.
By this given calculation method we obtained in any case
the same rate constants for different experimental conditions
as shown in Table 1. The full lines drawn in Figure 5 are the
calculated decay curves. Thus, this supposed reaction mech-
anism of the electrode reaction of ADPA is strongly supported.
The occurrence of a cationic intermediate in the reaction of
ADPA and PQDI is also supported by our attempts to prepare
PQDI by electrochemical synthesis in polar solvents which failed
throughout, and only higher dimerization products were ob-
tained. It was demonstrated already in the classical work of
Willsta¨tter and Moore19 that PQDI can only be produced in
nonpolar solvents where the cationic intermediate is not formed
and not stabilized by solvation. This result is important for the
interpretation of the influence of the solvent on the rate of the
aniline electropolymerization and on the mechanism and the
structure of the polymer formed.
constant should be influenced by the acid concentration, which
was not observed. Furthermore, the decay of the radical
concentrations was followed. Some of the measured decay
curves are shown in Figure 5. The data of the single experi-
ments were fitted by first- as well as second-order rate equations,
but in varying the concentrations of the reactants the obtained
rate constants changed to a great extent.
In the most favorable mechanism, the radical cation is
produced (eq 9) by a symproportionation (ADPA + PQDI T
2ADPA•+) and is diminishing (eq 10) according to
2ADPA•+ f ADPA-ADPA
(10)
In contrary to the reaction of thiophene oligomer cation
radicals17,18 where a π dimer is reversibly formed, the ADPA•+
radical of this study undergoes an irreverisble chemical reaction.
Using both reactions 9 and 10, it is possible to find a rate
equation for the radical cation reaction.
The starting point of the calculations are the equations
-d[ADPA•+]
) kd[ADPA•+]2 + k-1[ADPA•+]2 -
2 dt
k1[ADPA][PQDI] (11)
-d[ADPA•+]
2 dt
d[ADPA]
dt
) kd[ADPA•+]2 +
(12)
4. Conclusions
where k-1,k1 and kd are the rate constants of the backward
reaction, the forward reaction, and the dimerization reaction,
respectively.
(1) The rate of the slow ADPA•+ radical decay made the
evaluation of the equilibrium constant for the symproportion-
ation of ADPA and PQDI possible.
To get the expression d[ADPA]/dt the equation
(2) The equilibrium constant for the symproportionation of
[ADPA•+]2
ADPA with PQDI in organic solutions like DMSO is Keq
)
[ADPA] )
(13)
2.7 × 10-2
.
Keq[PQDI]
(3) The equilibrium constant is independent of the acid
concentration.
was differentiated, which is a good approximation in this case.

4872 J. Phys. Chem., Vol. 100, No. 12, 1996
Petr and Dunsch
(6) Knobloch, P. Collect. Czech. Chem. Commun. 1972, 37, 3356.
(7) Kitani, A.; Yano, J.; Kunai, A.; Sasaki, K. J. Electroanal. Chem.
1987, 221, 69.
(4) Using the dimerization reaction of the ADPA cation
radical, all of the experimental data could be described by the
rate equation with a single rate constant.
(8) Male, R.; Allendoerfer, R. D. J. Phys. Chem. 1988, 92, 6237.
(5) The rate constant for ADPA radical dimerization at room
(9) Genie`s, E. M.; Penneau, J. F.; Lapkowski, M.; Boyle, A. J.
Electroanal. Chem. 1989, 269, 63. Albery, W. J.; Compton, R. G.; Kerr,
I. S. J. Chem. Soc., Perkin Trans. 2 1981, 825.
temperature is k ) 34 L mol-1 s-1
.
Acknowledgment. The authors thank Mrs. Chr. Boge for
many careful measurements of the spin concentration and Dr.
A. Neudeck for helpful discussions.
(10) Albery, W. J.; Compton, R. G.; Kerr, I. S. J. Chem. Soc., Perkin
Trans. 2 1981, 825.
(11) Hand, R. L.; Nelson, R. F. J. Am. Chem. Soc. 1973, 96, 850.
(12) Beilsteins Handbuch der organischen Chemie, 4th ed.; Springer:
Berlin, 1930; Vol. 13, p H 77.
References and Notes
(13) Dunsch, L.; Petr. A. Ber. Bunsen-Ges. Phys. Chem. 1993, 97, 436.
(1) Dunsch, L. J. Electroanal. Chem. 1975, 61, 61. Dunsch, L. J. Prakt.
Chem. 1975, 314, 409 and the earlier literature cited therein. The latest
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