Electroreduction of dialkyl peroxides. Activation-driving force relationships and bond dissociation free energies

Article abstract of DOI:10.1021/ja971416o

The electrochemical reduction of five dialkyl peroxides in DMF was studied by cyclic voltammetry. The electron transfer (ET) to the selected compounds is concerted with the oxygen-oxygen bond cleavage (dissociative ET) and is independent of the electrode material. Such an electrochemical behavior provided the opportunity to study dissociative ETs by using the mercury electrode and therefore to test the dissociative ET theory by using heterogeneous activation-driving force relationships. The convolution voltammetry analysis coupled to the double-layer correction led to reasonable estimates of the standard potential (E°) for the dissociative ET to dialkyl peroxides, as supported, whenever possible, by independent estimates. A thermochemical cycle based on the dissociative ET concept was employed to calculate the bond dissociation free energies (BDFEs) of the five peroxides, using the above E°s together with electrochemical or thermochemical data pertaining to the redox properties of the leaving alkoxide ion. The BDFEs were found to be in the 25-32 kcal/mol range, suggesting a small substituent effect. The dissociative ET E°s were also used together with the experimental quadratic free energy relationships to estimate the heterogeneous reorganization energies.

Full text of DOI:10.1021/ja971416o

J. Am. Chem. Soc. 1997, 119, 9541-9549
9541
Electroreduction of Dialkyl Peroxides. Activation-Driving
Force Relationships and Bond Dissociation Free Energies1a
Sabrina Antonello,1b Martin Musumeci,1b,c Danial D. M. Wayner,1d and
Flavio Maran*,1b
Contribution from the Dipartimento di Chimica Fisica, UniVersita` di PadoVa, Via Loredan 2,
35131 PadoVa, Italy, and the Steacie Institute for Molecular Sciences, National Research Council
of Canada, 100 Sussex DriVe, Ottawa, Ontario, Canada K1A 0R6
ReceiVed May 5, 1997X
Abstract: The electrochemical reduction of five dialkyl peroxides in DMF was studied by cyclic voltammetry. The
electron transfer (ET) to the selected compounds is concerted with the oxygen-oxygen bond cleavage (dissociative
ET) and is independent of the electrode material. Such an electrochemical behavior provided the opportunity to
study dissociative ETs by using the mercury electrode and therefore to test the dissociative ET theory by using
heterogeneous activation-driving force relationships. The convolution voltammetry analysis coupled to the double-
layer correction led to reasonable estimates of the standard potential (E°) for the dissociative ET to dialkyl peroxides,
as supported, whenever possible, by independent estimates. A thermochemical cycle based on the dissociative ET
concept was employed to calculate the bond dissociation free energies (BDFEs) of the five peroxides, using the
above E°s together with electrochemical or thermochemical data pertaining to the redox properties of the leaving
alkoxide ion. The BDFEs were found to be in the 25-32 kcal/mol range, suggesting a small substituent effect. The
dissociative ET E°s were also used together with the experimental quadratic free energy relationships to estimate the
heterogeneous reorganization energies.
Introduction
the classical limit, where Morse-like potential energy curves
are adopted to describe reagents and products of the ET and
the harmonic approximation is used to describe activation by
the solvent, the development of the model leads to the
formulation of a simple Marcus-like activation-driving force
relationship in which the activation free energy ∆G# depends
quadratically on the free energy ∆G° of the reaction, according
to eq 4:4
Radical anion formation by electron transfer (ET) to an
organic molecule AB (eq 1) can be followed by an irreversible
bond-breaking reaction (eq 2) leading to a radical, A•, and an
anion, B-,2 where the intermediate species AB•- may fragment
AB + e a AB•-
AB•- f A• + B-
(1)
(2)
2
∆G°
∆G# ) ∆G#0 1 +
(4)
#
with rates which can vary over a wide range. However, when
the lifetime of the radical anion is so short to be of the same
order of magnitude as that of the vibration of the bond which
is going to be broken, there is no bound state for AB•-. The
ET can no longer be considered as an outer sphere process3
and is now best described as taking place in the single step (eq
3) and referred to as dissociative ET. The theory for such a
(
)
4∆G0
The intrinsic barrier ∆G#0, i.e. the activation free energy at
zero driving force, is given by three contributions: two of them
are the outer or solvent reorganization λo and the inner
reorganization λi, where the latter term does not include the
contribution of the mode corresponding to the breaking A-B
bond; the third, very important term is the bond dissociation
energy, BDE. Accordingly,
AB + e f A• + B-
(3)
concerted mechanism has been described by Save´ant, who
considered the adiabatic aspects of this reaction.4 More recently
a corresponding nonadiabatic treatment has been proposed.5 In
λo + λi + BDE
∆G#0 )
(5)
4
X Abstract published in AdVance ACS Abstracts, September 1, 1997.
(1) (a) Issued as NRCC publication No. 40836. (b) Universita` di Padova.
(c) Permanent address: Chemistry Department, Junior College, University
of Malta, Msida, Malta. (d) National Research Council of Canada.
(2) (a) Saeva, F. D. In Topics in Current Chemistry; Mattay, J., Ed.;
Springer-Verlag: Berlin, 1990; Vol. 156, p 59. (b) Schuster, G. B. In
AdVances in Electron Transfer Chemistry; Mariano, P. S., Ed.; JAI Press:
Greenwich, 1991; Vol. 1, p 163. (c) Maslak, P. In Topics in Current
Chemistry; Mattay, J., Ed.; Springer-Verlag: Berlin, 1993; Vol. 168, p 1.
(d) Save´ant, J.-M. Acc. Chem. Res. 1993, 26, 455.
(3) See for example: (a) Newton, M. D.; Sutin, N. Annu. ReV. Phys.
Chem. 1984, 35, 437. (b) Marcus, R. A.; Sutin, N. Biochem. Biophys. Acta
1985, 811, 265.
(4) (a) Save´ant, J.-M. J. Am. Chem. Soc. 1987, 109, 6788. (b) Save´ant,
J.-M. In AdVances in Electron Transfer Chemistry; Mariano, P. S., Ed.;
JAI Press: Greenwich, 1994; Vol. 4, p 53.
Whereas there is a wide literature concerning stepwise
reductive cleavages, either thermally induced or photoinitiated,2
the number of investigations on dissociative ETs is still limited.
The dissociative ET mechanism has been studied in dipolar
aprotic solvents by using either inert electrodes or aromatic
radical anions as electron donors. Specific, relevant examples
concern the dissociative reduction of alkyl6,7 or benzyl halides,8,9
(6) (a) Andrieux, C. P.; Gallardo, I.; Save´ant, J.-M.; Su, K. B. J. Am.
Chem. Soc. 1986, 108, 638. (b) Andrieux, C. P.; Gallardo, I.; Save´ant, J.-
M. J. Am. Chem. Soc. 1989, 111, 1620. (c) Andrieux, C. P.; Ge´lis, L.;
Medebielle, M.; Pinson, J.; Save´ant, J.-M. J. Am. Chem. Soc. 1990, 112,
3509.
(7) German, E. D.; Kuznetsov, A. M.; Tikhomirov, V. A. J. Phys. Chem.
1995, 99, 9095.
(5) German, E. D.; Kuznetsov, A. M. J. Phys. Chem. 1994, 98, 6120.
S0002-7863(97)01416-9 CCC: $14.00 © 1997 American Chemical Society

9542 J. Am. Chem. Soc., Vol. 119, No. 40, 1997
Antonello et al.
and therefore the cleavage of C-halogen bonds, the cleavage
of the C-S bond in sulfur compounds,10,11 and the cleavage of
O-O bonds in peroxides.12 From a quantitative point of view,
the dissociative ET theory has been tested rather satis-
factorily4b,13,14 through comparison of experimental data pertain-
ing to the reduction of methyl, butyl, and benzyl halides, with
theoretical predictions.
errors can arise if the ET rate results are used to obtain bond
energies in solution.12 The ET to the above peroxides was
studied by using a family of aromatic electron donors, and the
experimental rates were found to be significantly smaller than
predicted by the theory of adiabatic dissociative ET.4b The
reasons for such a discrepancy were explained partly through
the presence of steric hindrance caused by the tert-butyl and
cumyl groups and partly due to an intrinsic nonadiabaticity of
the ET.
In this paper we examine the possibility of using ET rate
data to obtain the bond dissociation free energies (BDFEs) for
dissociative ETs using a different approach to avoid the above
difficulties. As mentioned above, due to the reaction being
completely irreversible, the standard potential for a dissociative
ET cannot be calculated directly, say, by cyclic voltammetry;
however, it can be conveniently calculated by using the
following thermodynamical cycle17
One of the most relevant problems is the difficulty of
estimating the standard potential for the dissociative process 3;
since the direct determination of this potential is unfeasible,
thermochemical data, such as the bond dissociation energy of
the A-B bond, are required. Such data may not be easily
available and are often approximate, for example, due to the
use of bond dissociation enthalpies instead of free energies.
Furthermore, the evidence for a quadratic activation-driving
force relationship, which is quite important in the analysis of a
dissociative ET process, is not clear-cut in some cases, such as
in, for example, the homogeneous reduction of tert-butyl
bromide, for which data are available for an overall variation
of the rate constant by 13 orders of magnitude.15 In other
reactions, the experimental data fit equally well to a parabola
or to a straight line, a matter that leads to discussion.13,15 From
a practical point of view, this is not a trivial aspect; for example,
it is impossible to use the rate data to trace back the unknown
standard potential of the acceptor AB molecule from a linear
activation-driving force relationship. On the contrary, this
target is reachable if a quadratic activation-driving force
relationship is beyond experimental error. As a matter of fact,
it should be noticed that the curvature of the parabola described
by eq 4, given by
AB a A• + B•
B• + e a B-
BDFE
(7)
(8)
-FE°B /B
•
-
AB + e a A• + B-
-FE°AB/A ,B
(9)
•
-
and therefore through the equation:
E°AB/A ,B- ) E° - - BDFE/F
(10)
•
•
B /B
•
-
If the aim is to estimate E°AB/A ,B , the problem is to have good
experimental data or estimates for the two terms on the right-
hand side of eq 10.12a Conversely, if one can obtain E°AB/A ,B
•
-
∂2∆G#
1
through the activation-driving force relationship for the
)
(6)
investigated process, a powerful tool is provided to calculate
∂∆G° 2 8∆G#0
•
-
BDFEs once E°B /B can be estimated or experimentally
determined. It is worth noting that in this approach neither the
internal and solvent reorganization energies nor the knowledge
of the degree of adiabaticity of the ET reaction are required.
In principle, activation-driving force relationships can be
obtained by using either direct electrochemical reduction or
homogeneous reduction carried out by soluble one-electron
donors. There are however two reasons to prefer an electrode
as the electron donor instead of a soluble species. The first
reason is that whereas in the heterogeneous case the reorganiza-
tion energy λ ) λo + λi is dependent only on the acceptor
molecule, the homogeneous λ depends also upon the dimension
and structure of the one-electron donor; since the curvature of
the activation-driving force relationship is given by eq 6, the
local curvature is dependent upon the donor. The second reason
is that in the heterogeneous approach the free energy of the
reaction, i.e. the applied potential, can be varied continuously,
and as a result the quantity of data that can be collected is
significantly larger.
is smaller the larger ∆G#0 is, which is a very common situation
in dissociative ETs owing to the weight of the BDE term in eq
5.
The calculation of bond energies in solution is particularly
important.16 In principle, when the dissociative nature of the
ET is assessed, this could be done by using experimental rate
data and comparing them with theoretical rate constants. This
requires that a value for the pre-exponential factor describing
the rate constant itself has to be assumed followed by the use
of eq 4 to obtain the BDE. What is needed is the reorganization
energy, with the problems associated with the calculation of
the λo and λi terms, and the free energy of the reaction. This
possible application of the dissociative ET theory has been
stressed.2d To calculate the BDE in this way, however, the
degree of adiabaticity of the ET step must be known. Very
recently, using data on the reduction of di-tert-butyl peroxide
and dicumyl peroxide in DMF and MeCN, we found that serious
There is, however, a severe drawback that, until now,
precluded the possible use of direct electrochemistry in the
determination of BDFEs. In general, when the electron donor
is an electrode instead of a soluble species, eq 4 is best written
as
(8) Andrieux, C. P.; Le Gorande, A.; Save´ant, J.-M. J. Am. Chem. Soc.
1992, 114, 6892.
(9) Huang, Y.; Wayner, D. D. M. J. Am. Chem. Soc. 1994, 116, 2157.
(10) Severin, M. G.; Farnia, G.; Vianello, E.; Are´valo, M. C. J.
Electroanal. Chem. 1988, 251, 369.
(11) (a) Saeva, F. D.; Morgan, B. P. J. Am. Chem. Soc. 1984, 106, 4121.
(b) Andrieux, C. P.; Robert, M.; Saeva, F. D.; Save´ant J.-M. J. Am. Chem.
Soc. 1994, 116, 7864.
(12) (a) Workentin, M. S.; Maran, F.; Wayner, D. D. M. J. Am. Chem.
Soc. 1995, 117, 2120. (b) Maran, F.; Wayner, D. D. M.; Workentin, M. S.
Manuscript in preparation.
(13) Save´ant, J.-M. J. Am. Chem. Soc. 1992, 114, 10595.
(14) German, E. D.; Kuznetsov, A. M.; Tikhomirov, V. A. J. Phys. Chem.
1995, 99, 9095.
(15) Lund, H.; Daasbjerg, K.; Lund, T.; Pedersen, S. U. Acc. Chem. Res.
1995, 28, 313.
2
E - E° - φ#
∆G# ) ∆G#0 1 + F
(11)
4∆G#0
(
)
where E and E° are the applied and the standard potential,
respectively, and φ# is the difference between the potential at
the average distance at which the substrate is located when the
(16) Bordwell, F. G.; Zhang, X.-M. Acc. Chem. Res. 1993, 26, 510.
(17) Wayner, D. D. M.; Parker, V. D. Acc. Chem. Res. 1993, 26, 287.

Electroreduction of Dialkyl Peroxides
J. Am. Chem. Soc., Vol. 119, No. 40, 1997 9543
mp ) 72-74 °C (lit.22 mp 168-169 °C). 1H NMR (400 MHz, CDCl3,
TMS) δ 1.26 (6H, s, 2Me), 7.1-7.3 (20H, m, 4Ph); 13C NMR (400
MHz, CDCl3, TMS) δ 28.36 (Me), 82.64 (CMe2), 90.92 (CPh3), 125.36,
126.57, 127.67, 145.64 (PhCMe2: C2, C4, C3, C1), 126.97, 127.20,
129.18, 143.25 (Ph3C: C4, C3, C2, C1).
ET takes place and the potential of the bulk solution. Problems
are associated with the knowledge of φ# and of its derivative
∂φ#(E)/∂E. The fact is that inert electrodes are required to
analyze heterogeneous ETs, and this is particularly true when
the determination of the kinetics of a dissociative ET is the goal.
From a practical point of view the electrode material that
minimizes the possible interaction between the electrode and
the electroactive dissociative-type substrate or its reduction
intermediates is glassy carbon;6,8,11,12 unfortunately, the double
layer properties of glassy carbon are almost unknown,18 although
some research is being devoted in this direction.19 On the other
hand, the electrode material that has been best characterized
from such a point of view is mercury; until now, however, the
mercury electrode could never have been used is such studies
because it is far from being inert with respect to typical
dissociative ET systems, such as the halides.
In this paper the first use of mercury as an inert electrode
material in the reduction of dissociative-type substrates is
reported. The heterogeneous reduction of a series of dialkyl
peroxides has been investigated by cyclic voltammetry in N,N-
dimethylformamide (DMF) containing 0.1 M tetrabutylammo-
nium perchlorate (TBAP); the selected peroxides were either
symmetrical molecules such as di-tert-butyl peroxide (DBP),
dicumyl peroxide (DCP), and bis(triphenylmethyl) peroxide
(DTP) or unsymmetrical ones such as tert-butyl triphenylmethyl
peroxide (BTP) and cumyl triphenylmethyl peroxide (CTP). It
will be shown that the dissociative ET theory works pretty well
when the activation-driving force relationship is obtained by
using a well-defined experimental procedure and the data are
analyzed by the convolution approach coupled to the double
layer correction. In this way and through comparison with
literature thermochemical data, good estimates of the standard
potential and the BDFE can be obtained.
Electrodes. The working electrode materials were either glassy
carbon or mercury. The glassy carbon electrode was built from a 3
mm length by 3 mm diameter glassy carbon rod (Tokai GC-20), sealed
in glass tubing. The disk electrode surface was then polished by using
silicon carbide papers (500, 1000, 2400, and 4000) and then diamond
pastes (Struers: 3, 1, and 0.25 µm). The electrode was stored in
ethanol. Before each measurement, the working electrode was polished
with the 0.25 µm diamond paste and ultrasonically rinsed with ethanol
for 5 min. Electrochemical activation was carried out in the background
solution by means of several cycles at 0.5 V s-1 between 0 and -2.8
V against the KCl saturated calomel electrode, SCE. In this way the
surface was checked to be clean and reproducible. The area was
calculated with reference to the diffusion coefficient of anthracene in
DMF/0.1 M TBAP, 7.8 × 10-6 cm2 s-1 23
.
As expected for a microdisk
electrode, the area proved to be quite constant, as checked in separate
experiments.
The mercury electrode was prepared by controlled electrodeposition
of mercury onto a platinum bead substrate. Full details of this procedure
are given in the Supporting Information. The particular method
employed leads to very stable Hg electrodes which can be used for
several years without problems. No effect due to the platinum
underneath was ever detected and the heterogeneous ET kinetics of
suitable test substrates proved to be those of a bulk mercury electrode.
Electrochemical activation was carried out in the background solution
by means of several cycles at 0.5 V s-1 between -0.5 and -2.7 V vs
SCE.
The reference electrode was a home-made Ag/AgCl.24 Its potential,
which is about -0.30 V vs SCE, was always calibrated after each
experiment by adding ferrocene as an internal standard; the ferrocene/
ferricinium couple is known to be a recommended redox reference
system for nonaqueous measurements.25 Our own calibrations (statistics
of ca. 50 independent experiments) indicated that the standard potential
for ferrocene oxidation in DMF/0.1 M (and 0.2 M) TBAP is 0.464 V
vs SCE. In the following, all of the potential values will be reported
against SCE. The counter-electrode was a 1 cm2 Pt plate, positioned
symmetrically under the working electrode.
Electrochemical Apparatus and Procedures. The electrochemical
instrumentation employed for cyclic voltammetry was an EG&G-PARC
173/179 potentiostat-digital coulometer, an EG&G-PARC 175 universal
programmer, a Nicolet 3091 12-bit resolution digital oscilloscope, and
an Amel 863 X/Y pen recorder. The feedback correction was applied
to minimize the ohmic drop between the working and reference
electrodes. The confidence in the correction was judged by using the
same setup, including the working and reference electrode, to check
the voltammetric behavior of a redox couple of known heterogeneous
kinetics, such as 2-nitro-2-methylpropane; when the IR compensation
was properly adjusted, the scan rate dependence of the redox peak was
as expected on the basis of our own19 and literature results.26
Electrochemical measurements were conducted in an all glass cell,
thermostated at 25 ( 0.2 °C. The solution was carefully deoxygenated
with Argon (SIAD, 99.9995%), and then a blanket of gas was mantained
over the liquid. After deoxygenation, the behavior of the electrode
was studied in the background solution, in a selected potential range
and for scan rates ranging usually from 0.1 to 100 V s-1. To reduce
the electrical noise, the electrochemical measurements were carried out
by using a line transformer, doubly shielded coaxial cables for the
electrical connections, and, most important, a special copper Faraday
cage, disigned and optimized to reduce to minimum the high-frequency
noise components. The cyclic voltammograms were recorded by the
digital oscilloscope and then trasferred to a PC. The substrate was
Experimental Section
Chemicals. N,N-Dimethylformamide (Janssen, 99%) was treated
for some days with anhydrous Na2CO3, under stirring, and then distilled
at reduced pressure (17 mmHg) under a nitrogen atmosphere. The
solvent was collected and stored under an argon atmosphere in dark
bottles; it was used only after having checked the absence of
electroactive impurities in the available potential window. The
supporting electrolyte was tetrabutylammonium perchlorate (99%,
Fluka) that was recrystallized from a 2:1 ethanol-water solution and
dried at 60 °C under vacuum. Dicumyl peroxide (98%, Aldrich) was
recrystallized from ethanol. Di-tert-butyl peroxide (98%, Aldrich) was
used as purchased. Bis(triphenylmethyl) peroxide was prepared by
reaction of triphenylmethyl chloride (Baker) with mercury followed
by exposure to air.20
tert-Butyl triphenylmethyl peroxide was prepared as described in
the literature,21 from triphenylmethanol and tert-butyl trimethylsilyl
peroxide in an acidic medium. The product had the same melting point
as reported,21 69-71 °C, and Rf 0.70 (toluene). 1H NMR (400 MHz,
CDCl3, TMS) δ 1.01 (9H, s, t-Bu), 7.25-7.38 (15H, m, 3Ph).
Cumyl triphenylmethyl peroxide was prepared by reacting tri-
phenylmethanol (Aldrich) with cumyl hydroperoxide (80% in cumene,
Fluka) in acidic conditions.22 The crude product was dissolved in
diethyl ether, treated with sodium hydrogen carbonate and brine, and
eventually dried (MgSO4). The resulting solution was concentrated
and the product chromatographed on a silica gel column with toluene
and recrystallized from ethanol to give cumyl triphenylmethyl peroxide
as colorless crystals having Rf 0.87 (toluene-ethyl acetate 10:1) and
(18) McCreery, R. L. In Electroanalytical Chemistry; Bard, A. J., Ed.;
Marcel Dekker: New York, 1991; Vol. 17, p 221.
(19) Maran, F.; Musumeci, M. Research in progress.
(20) Tanaka, J. J. Org. Chem. 1961, 26, 4203.
(21) Buncel, E.; Davies, A. G. J. Chem. Soc. 1958, 1550.
(22) Davies, A. G.; Foster, R. V.; White, A. M. J. Chem. Soc. 1954,
2200.
(23) Fawcett, W. R.; Jaworski, J. S. J. Phys. Chem. 1983, 87, 2972.
(24) Farnia, G.; Maran, F.; Sandona`, G.; Severin, M. G. J. Chem. Soc.,
Perkin Trans. 2 1982, 1153.
(25) Gritzner, G.; Kuta, J. J. Pure Appl. Chem. 1982, 54, 1527. Gritzner,
G.; Kuta, J. J. Pure Appl. Chem. 1984, 56, 461.
(26) Save´ant, J.-M.; Tessier, D. J. Electroanal. Chem. 1975, 65, 57.
Save´ant, J.-M.; Tessier, D. J. Phys. Chem. 1977, 81, 2192.

9544 J. Am. Chem. Soc., Vol. 119, No. 40, 1997
Antonello et al.
Table 1. Voltammetric Data for the Reduction of Dialkyl
Peroxides in DMF/0.1 M TBAP at 0.2 V s-1 and T ) 25 °C
Ep(GC)a,b
∆Ep/2(GC)a,c
Ep(Hg)b
(V)
∆Ep/2(Hg)c
substrate
(V)
(V)
(V)
DBP
DCP
DTP
BTP
CTP
-2.50d,e
-2.23
-1.91
-2.18
-2.04
0.188d,e
0.158
0.189
0.174
0.185
-2.47
-2.22
-1.89
-2.19
-2.04
0.130
0.128
0.178
0.150
0.147
a GC ) glassy carbon. b Potentials are against SCE. c ∆Ep/2 ) peak
width. d Reference 12a. e DMF/0.1 M Et4NClO4; see ref 29.
and CTP are shown in Figure 1. As expected for the reduction
of dialkyl peroxides in dipolar aprotic solvents,12 the peaks are
located at potentials which are close to or more negative than
-2 V. A common feature of the voltammetric pattern is the
presence of an irreversible, broad peak. In Table 1 some
voltammetric data obtained by averaging the results of different
experiments performed at 0.2 V s-1 with either electrode are
reported. Comparison of the data reveals that no appreciable
effects can be ascribed to the electrode material; for a given
compound, the peak potentials (Ep) are equal within 10-30 mV
and the peak widths, i.e., the differences between the potential
measured at half-peak height and Ep (∆Ep/2), are large and
usually equal within 10-20%.29 These observations, in par-
ticular the position of the peak, are worth noting because the
investigated systems appear to provide the first experimental
cases in which substrates undergoing a dissociative ET do not
interact with mercury.
Since one of the goals of the present work was to calculate
the standard potential for the dissociative ET process by accurate
analysis of the voltammetric data, the best test to verify the
reliability of the adopted approach was to focus initially on
dialkyl peroxides for which independent estimates of the
standard potential itself were available. Among the investigated
substrates, we had previously obtained reasonable estimates of
the standard potential of DBP, -1.44 V, and DCP, -1.29 V.12
Such values were obtained through eq 10 by using thermo-
chemical and electrochemical data and are valid for DMF as
the solvent. Preliminary experiments, however, revealed that
the voltammetric data pertaining to DBP were not ideal to
perform an accurate kinetic analysis because of the proximity
of the reduction process to the onset of the solvent/electrolyte
breakdown and therefore DCP was chosen as the model
compound.
Figure 1. Cyclic voltammetry for the reduction of DBP (a: 2.87 mM,
GC; b: 2.18 mM, Hg), DCP (c: 2.10 mM, GC; d: 2.10 mM, Hg),
DTP (e: 0.49 mM, GC; f: 0.52 mM, Hg), BTP (g: 2.03 mM, GC; h:
1.89 mM, Hg), and CTP (i: 2.16 mM, GC; j: 2.16 mM, Hg). Whereas
curves b-j were obtained in DMF/0.1 M TBAP, curve a was obtained
Previous results obtained by using a glassy carbon electrode
12b
in DMF/0.1 M Et4NClO4 indicated that the reduction takes
place according to the two-step process
(RO)2 + e f RO• + RO-
(12)
(13)
in DMF/0.1 M TEAP. T ) 25 °C, V ) 0.2 V s-1
.
then added to the solution and the same procedure repeated. The
corresponding background curves were subtracted from the cyclic
voltammograms to eliminate the contribution of the capacitive current.
The resulting curves were then analyzed by the conventional voltam-
metric criteria27 and the convolution approach,28 using specially designed
laboratory software.
RO• + e f RO-
and therefore to the overall stoichiometry
(RO)2 + 2e f 2RO-
(14)
Results and Discussion
where R ) CMe2Ph. In the present study, the reduction of DCP
was studied at the mercury electrode, using voltammetric scan
The reduction of the selected dialkyl peroxides was studied
in DMF/0.1 M TBAP at 25 °C by cyclic voltammetry, using
both glassy carbon and mercury as electrode materials. The
cyclic voltammograms corresponding to DBP, DCP, DTP, BTP,
(29) The only apparent exception to this trend is provided by the results
obtained with DBP because whereas at mercury we obtained a well-behaved
pattern, the reduction is more sluggish at the glassy carbon electrode.
Apparently, however, this problem is caused by the TBAP electrolyte at
such negative potentials because the corresponding curves obtained with
the two electrodes in the presence of Et4NClO4 are very similar to each
other. In fact, the results obtained at the Hg electrode in the presence of
either electrolyte are identical.
(27) (a) Nicholson, R. S.; Shain, I. Anal. Chem. 1964, 36, 706. (b) Bard,
A. J.; Faulkner, L. R. Electrochemical Methods, Fundamentals and
Applications; Wiley: New York, 1980.
(28) Imbeaux, J. C.; Save´ant, J.-M. J. Electroanal. Chem. 1973, 44, 169.

Electroreduction of Dialkyl Peroxides
J. Am. Chem. Soc., Vol. 119, No. 40, 1997 9545
Figure 2. Scan rate dependence of the voltammetric peak width for
the reduction of DCP in DMF/0.1 M TBAP at the Hg electrode.
Substrate concentration (mM): O, 2.05; 0, 2.09; ∆, 1.95; ∇, 2.10. T
) 25 °C.
Figure 3. Potential dependence of the logarithm of the heterogeneous
rate constant for the reduction of DCP in DMF/0.1 M TBAP at 25 °C.
The plot is formed from a collection of curves obtained at the Hg
electrode in three separate experiments where V was varied from 1 to
rates ranging from 0.2 to 50 V s-1
. The process was
investigated in DMF/0.1 M TBAP to use available double layer
50 V s-1
.
data.30
The reduction peak of DCP is irreversible at all of the scan
rates used, and its peak potential shifts toward more negative
potentials by increasing the scan rate, V, the average slope being
166 mV/log V. The peak width ∆Ep/2 is also scan rate dependent
as shown in Figure 2, which derives from separate experiments;
for example, whereas the average ∆Ep/2 at 0.2 V s-1 is 128
mV, it increases to 199 mV when V ) 20 V s-1. Finally, the
ratio between the peak current ip and C*V1/2, where C* is the
bulk concentration, tends to decrease upon increasing V. The
above observations indicate that the heterogeneous ET to DCP
cannot be described by a rate law of the Butler-Volmer form,31
according to which ∂Ep/∂ log ν, ∆Ep/2, and ip/C*V1/2 should be
independent of V for a completely irreversible electrode
process.27
the mid-potential of the range pertaining to the peak width (i.e.
the potential at 3/4 peak height), it turns out that dR/dE ) 0.51
V-1
.
The heterogeneous ET kinetics was therefore analyzed in a
much more rigorous way by the convolution analysis,28 which
has the great advantage of allowing one to analyze the
experimental voltammetric curves without the need of defining
the ET rate law. Our typical procedure consisted of the digital
acquisition of the background voltammetric curves, addition of
the peroxide, new acquisition of curves under otherwise identical
conditions, background subtraction, and convolution of the
resulting curves.
The limiting convolution current, Il, was found to be
independent of the scan rate as expected on the basis of its
definition, i.e. Il ) nFAD1/2C*,28 where n is the overall electron
consumption and D the diffusion coefficient. The diffusion
coefficient was therefore readily calculated to be 4.7 × 10-6
cm2 s-1, using a glassy carbon electrode of known area. Given
the constancy of Il, the convolution curves were then subjected
to logarithmic analysis to obtain the potential dependence of
the heterogeneous ET rate constant k, using the equation that
holds for a completely irreversible process:26
The reasons for such deviations can be ascribed to the non-
constancy of the heterogeneous transfer coefficient R with
respect to the potential,32 where R is defined as
∂∆G#
∂∆G°
R )
(15)
Whereas in Butler-Volmer kinetics R is independent of the
potential, a decrease of R with a negative increase of the
potential would indeed account for the observed behavior. In
fact, an irreversible voltammetric peak shifts toward more
negative potentials upon increasing the scan rate, and therefore
the peak width and current reflect what happens at different
potential regions. The peak width is a particularly sensitive
detector for a possible potential dependence of R; in the present
case its values, which can be estimated by using the equation
Il - I(t)
ln k ) ln D1/2 - ln
(16)
(
)
i(t)
which combines real and convoluted current values. A con-
volution curve derives from an integration procedure and
therefore is rather insensitive to the noise affecting the original
voltammetric curve; however, owing to the mixing of current
data in eq 16, the real curve has to be acquired by using all of
the possible expedients to reduce the noise to low levels (see
Experimental Section) as otherwise the quality of the resulting
ln k plots (and further elaborations) is greatly affected. The
result of the logarithmic analysis is shown in Figure 3, where
both the overall agreement between the sets of data pertaining
to the different scan rates, obtained upon 1 point/mV acquisition,
and the curvature of the plot can be noticed. By derivatization
of the (ln k)-E plots, the apparent transfer coefficient Rapp can
be obtained according to the equation
R ) 1.857RT/F∆Ep/2,
27 are e.g. 0.373 at 0.2 V s-1 and 0.240 at
20 V s-1. For the sake of argument, if one assumes rather
arbitrarily that the potential coordinate for a given R value is
(30) Are´valo, M. C.; Rodriguez, J. L.; Severin, M. G.; Vianello, E.
Unpublished results.
(31) Butler, J. A. V. Trans. Faraday Soc. 1924, 19, 734. Erdey-Gruz,
T.; Volmer, M. Z. Phys. Chem. 1930, 150A, 203.
(32) Although analogous effects might be caused by improper compensa-
tion for the ohmic drop, this possibility was ruled out in our experimental
conditions thanks to the parallel experiments that we run using redox couples
of known heterogeneous kinetics.

9546 J. Am. Chem. Soc., Vol. 119, No. 40, 1997
Antonello et al.
RT d ln k
Rapp ) -
(17)
F
dE
The equation is written in terms of the apparent value of the
transfer coefficient because such a value is not yet corrected
for the double layer. Derivatization was simply accomplished
by linear regression of the experimental data within small E
intervals (21 to 29 mV, depending on the quality of the ln k
plots), therefore avoiding the temptation of treating directly the
whole set of (ln k)-E plots according to a quadratic equation.
The result of this procedure is shown in Figure 4. The plot is
statisfactorily linear and the result of its regression analysis is
given by the equation:
Rapp ) 0.849 + 0.253E
(18)
Comparison of eqs 11, 15, and 17 shows that the real R
coefficient is linked to Rapp by
Figure 4. Potential dependence of the apparent transfer coefficient
for the reduction of DCP in DMF/0.1 M TBAP at the Hg electrode.
The dashed line derives from the linear regression analysis of the data.
T ) 25 °C.
Rapp
F
R ) 0.5 +
(E - E° - φ#) )
(19)
8∆G#0
1 - ∂φ#/∂E
were therefore treated in a different way that, though ap-
proximate, led to reasonable results. The experimental proce-
dure was the same as above, the only difference being in the
subsequent logarithmic analysis which required the knowledge
of the limiting convolution current Il. Since Il can be determined
for most of the scan rates only in the potential region affected
by the dip, we resorted to analyze the rising part of the
convolution curves according to a nonlinear sigmoidal fit that
led to the expected Il value for each scan rate.34 The result
was rather satisfactory in that the Il values were very close to
each other, almost within the 2% maximum difference that we
usually find for such limiting currents. Therefore, we proceeded
in the analysis, along similar lines as described above for DCP,
to obtain the following electrochemical estimate for the double-
layer corrected standard potential
and therefore R can be obtained once the function φ#(E) is
known. By using available data for the mercury electrode in
DMF/0.1 M TBAP,30 the Rapp data were transformed into the
correponding R values, under the usual hypothesis that the
reaction site can be identified with the outer Helmholtz
plane,27b,33 leading to equation:
R ) 0.870 + 0.259E
(20)
Since R ) 0.5 when E ) E° + φ#, and considering that the
diffuse layer potential is -0.11 V when E ∼ -1.3 V,30 use of
eq 20 leads to the double-layer corrected estimate of the standard
potential pertaining to step 12, i.e.
E°(PhMe CO) /PhMe CO ,PhMe CO- ) -1.32 V SCE (21)
•
2
2
2
2
E°(t-BuO) /t-BuO ,t-BuO- ) -1.62 V SCE
(22)
•
2
a value that is remarkably close to the value of -1.29 V that
was previously obtained by using thermochemical (BDFE) and
a value which, though obviously approximate, is not too far
from the completely thermochemical estimate of -1.44 V.12a,35
The results obtained with the above peroxides, in particular
DCP, the data of which were treated under the most favorable
conditions, led us to extend the same type of analysis to the
heterogeneous reduction of three compounds (DTP, BTP, CTP)
of unknown BDFE and characterized by having a common
moiety, Ph3CO-, and being reducible at not very negative
potentials, i.e. in a more convenient region. The voltammetric
curves, which for the three compounds were always of very
good quality in the 0.2-20 V s-1 range (up to 100 V s-1 for
DTP), were analyzed by convolution to yield the Rapp vs E plots,
12b
•
-
electrochemical (E°PhMe CO /PhMe CO ) data.
Such a result is
2
2
worth noting if one considers that the potential difference
corresponds in energy terms to only 0.7 kcal/mol.
As a final remark, we should observe that the use of eq 18
would have led to a double-layer uncorrected estimate of -1.38
V, thanks to a partial compensation between the effects brought
about by ∂φ#/∂E, which tends to increase the slope of the R vs
E plot compared to the Rapp vs E plot and therefore to push the
standard potential in the negative direction, and φ#, which is
negative and hence adjusts the potential to more positive values.
Compared to the -1.29 V value, this would increase the
difference to ca. 2 kcal/mol.
(34) The I-E curves are typical sigmoidal transition curves.28 Our best
convolution data, obtained in the 0.2-2 V s-1 range, were treated according
to equation
The reduction of DBP also takes place according to the two-
electron stoichiometry given by eq 14,12a where now R ) t-Bu.
As mentioned above, some experimental problems associated
with the study of the reduction of DBP were caused by the fact
that just prior to the solvent/electrolyte discharge the background
subtraction procedure proved to be inaccurate. In fact, the
background subtracted curves revealed a dip at very negative
potentials, which led us to conclude that the electrolyte
breakdown is somehow inhibited by the presence of the
electroactive substrate. On the other hand, the potential region
in which the background corrected data are unreliable is rather
narrow being of the order of 0.1-0.15 V. The data of DBP
a1
I(E) ) a0 +
1 + exp[-(E - a2)/a3]
in which a0, a1, a2, and a3 are constants.
(35) In our previous work (ref 12a) the standard potential was estimated
by using the BDFE for decomposition of the neat peroxide. Whereas the
BDE of DBP is believed to be solvent independent based on photoacoustic
calorimetric studies (Wayner, D. D. M.; Lusztyk, E.; Page´, D.; Ingold, K.
U.; Mulder, P.; Laarhoven, L. J.; Aldrich, H. S. J. Am. Chem. Soc. 1995,
117, 8737), it is not clear that this should be so with the entropy change
associated with homolysis. Since the standard potential in eq 22 leads to a
BDFE value of 32 kcal/mol (viz. 28 kcal/mol from ref 12a) in DMF, we
can estimate an entropy contribution to homolysis (-T∆S) of 6 kcal/mol
in this solvent.
(33) Severin, M. G.; Are´valo, M. C.; Maran, F.; Vianello, E. J. Phys.
Chem. 1993, 97, 150.

Electroreduction of Dialkyl Peroxides
J. Am. Chem. Soc., Vol. 119, No. 40, 1997 9547
Figure 6. Cyclic voltammetry for the reduction of 2.89 mM CTP in
DMF/0.1 M TBAP at the GC electrode. T ) 25 °C, V ) 1 V s-1
.
to the thermochemical cycle 7-9. The standard potential for
•
-
the alkoxyl radical/alkoxide ion couple, E°Ph CO /Ph CO , was
3
3
obtained by cyclic voltammetry measurements. The experi-
ments were carried out with use of a glassy carbon electrode
by scanning the potential initially toward negative values, to
include the reduction peak of the selected peroxide, and then
extending the backward scan to rather positive potentials,
typically +0.1 V. In this way it is possible to detect the anion
that is electrogenerated during the direct scan, as shown by the
cyclic voltammogram reported in Figure 6. The best data were
obtained with CTP, though very similar results were also
obtained with DTP and BTP. Concerning the nature of the
species undergoing the oxidation, it should be observed that
the two-electron reduction in the forward scan produces both
anionic fragments so that both oxidations might be observed in
the reverse scan. On the other hand, the basicity of the anion
plays a key role in the detection of the peak: whereas t-BuO-
is too basic to survive in appreciable amounts in a medium that
contains water traces, the basicity of PhMe2CO- and that of
Ph3CO- are such to allow the observation of the peak.36
Moreover, whereas V must be higher than 0.5 V s-1 in the first
case,12 the oxidation peak can be seen with Ph3CO- even at
scan rates as low as 0.05 V s-1. The consequence is that the
oxidation peak observed at low scan rates with CTP is essentially
due only to the oxidation of Ph3CO-.
The oxidation peak is located at -0.308 V at 0.2 V s-1 and
is irreversible, and the peak potential shifts by 28.4 mV/log V
in the 0.1-1 V s-1 range, though the shift becomes larger at
higher scan. The peak potential shift is in good agreement with
a first-order reaction,27 causing the disappearance of the
electrogenerated Ph3CO• radical, a species the lifetime of which
can be estimated to be ca. 10 ps.37 Given such kinetic
information, the standard potential for the radical/anion couple
is easily obtained from good experimental Ep values.27 The
average of the results obtained with CTP is -0.030 V, a value
that will be used subsequently; nevertheless, it should be
Figure 5. Potential dependence of the apparent transfer coefficient
for the reduction of DTP (plot a), BTP (plot b), and CTP (plot c) in
DMF/0.1 M TBAP at the Hg electrode. T ) 25 °C.
depicted in Figure 5. After correction for the double layer, the
following dissociative ET standard potentials were estimated:
E°(Ph CO) /Ph CO ,Ph CO- ) -1.13 V SCE
(23)
(24)
•
3
2
3
3
E°t-BuOOCPh /t-BuO ,Ph CO- ) -1.22 V SCE
•
(36) (a) Whereas the pKa(DMF) of t-BuOH and that of water can be
calculated to be 32.5 and 31.7, respectively,36b the pKa’s of PhMe2OH and
Ph3OH do not seem to be known; however, taking into account the acidity
scale of alcohols36c and substituent effects, it is reasonable to assume that
their pKa values are about 2-3 units smaller than that of water. (b) The
pKa(DMF) values can be obtained from the corresponding DMSO data36c
by using the correlation pKa(DMF) ) 1.56 + 0.96 pKa(DMSO): Maran,
F.; Celadon, D.; Severin, M. G.; Vianello, E. J. Am. Chem. Soc. 1991, 113,
9320. (c) Olmstead, W. N.; Margolin, Z.; Bordwell, F. G. J. Org. Chem.
1980, 45, 3295.
(37) (a) Falvey, D. E.; Khanbatta, B. S.; Schuster, G. B. J. Phys. Chem.
1990, 94, 1056. (b) See, also: Avila, D. V.; Ingold, K. U.; Di Nardo, A.
A.; Zerbetto, F.; Zgierski, M. Z.; Lusztyk, J. J. Am. Chem. Soc. 1995, 117,
2711.
3
3
E°
- ) -1.15 V SCE (25)
•
PhMe2COOCPh3/PhMe2CO ,Ph3CO
Assuming that we have corrected properly for the double-layer
effect, which is sustained by the self consistency of the results
concerning DCP, we can estimate that the experimental error
associated to such E° estimates is probably within (0.05 V.
The best way to check the reliability of such double-layer
corrected E°s is to make use of eq 10, which relates the
dissociative ET standard potentials to other quantities, thanks

9548 J. Am. Chem. Soc., Vol. 119, No. 40, 1997
Antonello et al.
Table 2. Calculated and Experimental Parameters for the
Reduction of Dialkyl Peroxides in DMF/0.1 M TBAP and T ) 25
°C
to the breaking O-O bond, is going to develop in only half of
the starting peroxide and therefore that some screening to the
solvent reorganization is brought about by the second, uncharged
molecular fragment.39 Analogous reasoning was applied to the
calculation of the radius of the leaving alkoxide ion. The solvent
reorganization energy was then calculated from such effective
radii, using both the Marcus and Hush approach,40a i.e. by the
equation
substrate
DBP
DCP
DTP
BTP
CTP
E°AB/A ,B (V)
-1.44a -1.32
-1.62
-1.13 -1.22 -1.15
•
-
•
-
E°B /B (V)
-0.23a -0.12b -0.03 -0.03 -0.03
BDFE (kcal/mol)
28a
32c
27.7
25.4
27.4
25.8
reffective (Å)
3.35d
3.53
4.34
3.92
3.87
λo(Marcus) (kcal/mol)
λo(Hush) (kcal/mol)
λo(K-B) e (kcal/mol)
λf (kcal/mol)
11.5
23.0
16.6
15.9g
10.9
21.8
15.8
10.8
8.9
17.8
12.9
8.2
9.8
19.6
14.2
12.8
9.9
19.8
14.4
9.8
1
1 1
λo ) e2
-
(26)
(
)
ꢀop ꢀs nr
where n ) 4 (Marcus) or 2 (Hush), e is the charge of the
electron, and ꢀop and ꢀs are the high-frequency and static
dielectric constants of the solvent, respectively. The solvent
reorganization energy was also calculated by using a rough
correlation which derives from several data pertaining to the
heterogeneous reduction of aromatic compounds,40b i.e.
a From ref 12a. b From ref 12b. c Obtained by convolution analysis.
d From the density of the compound; see ref 40b. e From selected
f
Kojima-Bard data,40b using eq 27. This work. g Using the convolution
BDFE.
mentioned that the more qualitative analysis carried out on BTP
and DTP led to -0.036 and -0.040 V, respectively.
1
r
•
-
The determination of E°Ph CO /Ph CO is important because this
λo ) 55.7
(27)
3
3
potential is to be used in eq 10, together with the standard
potentials obtained by convolution analysis of the reduction data
of DTP, BTP, and CTP; besides DTP, for which the formation
of Ph3CO- in the dissociative ET is obvious, it is in fact very
likely, on the basis of simple substituent effects, that the initially
formed anionic fragment is Ph3CO- also in the case of BTP
and CTP. Accordingly, the BDFE values pertaining to these
peroxides can be easily calculated and are reported in Table 2.
It is worth noting that the calculated values are very similar,
almost equal within experimental error. Since the entropy term
is not expected to be very different in the investigated series,35
the similarity of the BDFE values (including those of DCP and
DBP) reflects what is known about the small substituent effect
on the BDEs of such compounds.38 The double-layer corrected
convolution approach seems therefore to work rather satisfac-
torily for such compounds.
The self-consistency of the data can be used to perform some
other calculations that are related to a problem that arises when
experimental ET data are to be compared with theoretical ones,
i.e. the evaluation of the reorganization energy λ. This is
particularly true in the heterogeneous case owing to the fact
that the solvent reorganization term may be calculated in
different ways. To calculate the solvent reorganization energy
for the investigated peroxides the following procedure was
adopted. The Stokes radii of the starting molecules were
calculated starting from the experimental diffusion coefficients
through the Stokes-Einstein equation. The radii were then
transformed into the corresponding effective radii (Table 2),
following the concept that the incipient negative charge, owing
where λo is given in kcal/mol and r in Å. This approach was
previously adopted and preferred to analyze the reduction of
various substrates.4b,8,12 The result of the three different
calculations is given in Table 2. We used both the experimental
activation-driving force relationships and the E° determinations
to obtain an evaluation of λ. The slope of the regression analysis
of the R vs E plots, γ, is in fact directly linked (see eq 6) to the
intrinsic barrier through the equation
F
8γ
∆G#o )
(28)
The BDFEs obtained as described above can be transformed
into BDEs, using a common entropy contribution of T∆S ) 6
kcal/mol35 and thus allowing estimates of λ by using eq 5. The
values pertaining to the five peroxides are given in Table 2.
Comparison of the theoretical (eq 26) and empirical (eq 27)
data with the experimental estimates reveals that the latter values
are generally between the empirical and the Marcus predictions.
In general, while it is possible to determine the free energy
changes associated with a dissociative process with reasonable
accuracy, extracting the solvent reorganization energies still
represents a significant challenge. Our results, based on very
careful electrochemical measurements with convolution analysis,
provide heterogeneous kinetic data of unusually high quality
over a large potential range and provide convincing verification
of the Save´ant theory of dissociative electron transfer. Con-
sequently, we expect that this experimental approach will
ultimately provide better understanding of the reorganization
energies associated with electrode processes.
(38) (a) Baldwin, A. C. In The Chemistry of Peroxides; Patai, S., Ed.;
Wiley: New York, 1983; p 97. (b) Ando, W., Ed. Organic Peroxides;
Wiley: New York, 1992. (c) Bach, R. D.; Ayala, P. Y.; Schlegel, H. B. J.
Am. Chem. Soc. 1996, 118, 12758.
(39) (a) See for example ref 4b and: Peover, M. E.; Powell, J. S. J.
Electroanal. Chem. 1969, 20, 427. (b) The effective radii were calculated
by using the equation
Conclusions
The possibility of studying the heterogeneous ET to dialkyl
peroxides at the mercury electrode has provided the opportunity
to test the dissociative ET theory by using experimental
activation-driving force relationships. The convolution vol-
tammetry approach coupled to the double-layer correction
proved to be a remarkably powerful tool in evaluating the
standard potential for the dissociative ET to dialkyl peroxides,
as supported, whenever possible, by comparison with indepen-
dent estimates of the E° values.
rB(2rAB - rB)
r )
rAB
where AB is the starting molecule and B the ionic fragment. Such an
equation was initially used for the dissociative ET to halides8,13 and
then to peroxides.12 Whereas halide-ion solvation is symmetrical, in
the case of alkoxide ions the negative charge, being concentrated onto
the oxygen atom, is not expected to cause significant reorganization
of the solvent molecules around the bulky hydrocarbon side of the ion
itself. Therefore, an effective radius for the alkoxides was calculated
by using once again the above equation, where now AB is the alkoxide
and B the oxygen atom.
(40) (a) See ref 43b and pertinent references cited therein. (b) Kojima,
H.; Bard, A. J. J. Am. Chem. Soc. 1975, 97, 6317.

Electroreduction of Dialkyl Peroxides
J. Am. Chem. Soc., Vol. 119, No. 40, 1997 9549
The use of the thermodynamical cycle 7-9 and therefore of
eq 10 that allows one to estimate BDFEs from the above E°s
together with the standard potential for the B•/B- couple is also
worth noting. In fact, in favorable conditions, the latter quantity
can be determined through analysis of the voltammetric oxida-
tion of the B- anion. In this way, reasonable estimates of
solution BDFEs were obtained for some dialkyl peroxides.
In treating the heterogeneous data, the double-layer effect
has to be taken into account. However, our results showed that
the difference between the E° calculations carried out by using
either R or Rapp amounts to only 0.06-0.07 V. It appears
therefore that provided the potential is not more positive than,
say, -1 V, i.e. under the conditions in which the relative
compensation between the φ# and ∂φ#/∂E effects still holds, the
use of the experimental Rapp may lead to a fairly good estimate
of the double-layer corrected E°; this fact is particularly
important if it could be extended to good experimental data
obtained with electrode materials, the double-layer properties
of which are unknown.
Finally, the approach of combining the E° estimate, through
eq 10, with the curvature of the activation-driving force
relationship (eq 6) seems to be promising in finding new
guidelines to estimate the heterogeneous ET reorganization
energies.
Acknowledgment. This work was financially supported by
the Consiglio Nazionale delle Ricerche (CNR), the Ministero
dell’Universita` e della Ricerca Scientifica e Tecnologica
(MURST), and the National Research Council of Canada
(NRCC).
Supporting Information Available: Details of the prepara-
tion of mercury electrodes (3 pages). See any current masthead
page for ordering and Internet access instructions.
JA971416O