Concerted proton-electron transfers. consistency between electrochemical kinetics and their homogeneous counterparts.

Article abstract of DOI:10.1021/ja206561n

The concerted proton-electron transfer (CPET) oxidation of phenol with water (in water) and hydrogen phosphate as proton acceptors provides a good example for testing the consistency of the electrochemical and homogeneous approaches to a reaction, the com

Full text of DOI:10.1021/ja206561n

ARTICLE
pubs.acs.org/JACS
Concerted ProtonꢀElectron Transfers. Consistency between
Electrochemical Kinetics and their Homogeneous Counterparts.
Cyrille Costentin, Viviane Hajj, Cyril Louault, Marc Robert, and Jean-Michel Sav ꢀe ant*
Univ Paris Diderot, Sorbonne Paris Cit ꢀe , Laboratoire d'Electrochimie Mol ꢀe culaire, Unit ꢀe Mixte de Recherche Univ - CNRS No 7591,
B ^a timent Lavoisier, 15 rue Jean de Baïf, 75205 Paris Cedex 13, France
S Supporting Information
b
ABSTRACT: The concerted protonꢀelectron transfer (CPET)
oxidation of phenol with water (in water) and hydrogen phos-
phate as proton acceptors provides a good example for testing the
consistency of the electrochemical and homogeneous ap-
proaches to a reaction, the comprehension of which raises more
mechanistic and kinetic challenges than that of a simple outer-
sphere electron transfer. Comparison of the intrinsic kinetic
characteristics (obtained at zero driving force of the CPET
reaction) shows that consistency is indeed observed after a
careful identification and quantitation of side factors (electrical work terms, image force effects). Water (in water) appears as a
better intrinsic proton acceptor than hydrogen phosphate in both cases in terms of reorganization energy and pre-exponential factor,
corroborating the mechanism by which electron transfer is concerted with Grotthus-type proton translocation in water. Detailed
compared analysis of the approaches also revealed that modest but significant electric field effects may be at work in the
electrochemical case. Comparison with phenoxide ion oxidation, taken as a reference outer-sphere electron transfer, points to a
CPET precursor complex that possesses a precise spatial structure allowing the formation of one or several H-bonds as required by
the occurrence of the CPET reaction, thus decreasing considerably the number of efficient collisions compared with those
undergone by structureless spherical reactants.
’
INTRODUCTION
the case where the system does not give rise to a reversible dif-
fusion-controlled electrochemical response. One is that the “redox
potentials” thus obtained may not be a good estimate of the sought
Association between electron and proton transfers is ubiquitous
in natural and artificial systems. It is also likely to interfere in reac-
tions currently envisaged for the resolution of contemporary energy
challenges. These proton-coupled electron transfers (PCETs)
may follow stepwise or concerted pathways or both as illustrated
in Scheme 1 with the example of phenol oxidation. Concerted
4
standard (or formal) potentials. The second is that the available
kinetic and mechanistic information is not exploited despite the
fact that the kinetic models used in both areas are basically the
same after taking due account of the heterogeneous character of
the electrochemicalreactionsand henceof the interference ofreac-
tant transport in the overall kinetics.
These considerations are particularly true in the field of proton-
coupled electron transfers where both homogeneous and electro-
chemical approaches have been applied to the same systems,
although systematic comparisons are scarce. The discussion below
aims at illustrating the consistency of the two approaches with the
example of the oxidation of phenol with water (in water) and
hydrogen phosphate as proton acceptors and detailing the factors
that should be taken into account to make the comparison
between them meaningful. Homogeneous oxidation with water
1
2
pathways (CPET ) skip the high-energy intermediates involved
in the two stepwise pathways, PET (proton transfer followed by
electron transfer) and EPT (electron transfer followed by proton
transfer). They may therefore be more advantageous if the likely
additional kinetic cost is not too high. Although the concertedꢀ
stepwise competition is a completely general issue, oxidation of
phenols has been taken repeatedly as an illustrating example
keeping in mind the prominent role they play in reactions
occurring in natural systems particularly, but not exclusively, in
1,3
the oxidation of a tyrosine (Tyr ) in photosystem II.
z
Establishment of the reaction mechanism and analysis of the
kinetic characteristics have been tackled from two sides, usual
homogeneous kinetics, where the electron donor or acceptor is
present in solution, on the one hand, and electrochemical kinetics
where electron transfer takes place at the electrode surface, on the
other. Most homogeneous kinetic studies usually consider electro-
chemistry merely as a way to access “redox potentials”, actually
standard (or formal) potentials, rather than a source of kinetic and
mechanistic information. This state of affairs has two drawbacks in
(
in water) and hydrogen phosphate as proton acceptors has already
5
given rise to a detailed study. This is also the case for the elec-
trochemical oxidation of phenol with water (in water) as proton
acceptor. What is lacking at present to proceed to the com-
parison between the two approaches is data concerning the
6
Received: July 14, 2011
Published: November 09, 2011
r 2011 American Chemical Society
19160
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|J. Am. Chem. Soc. 2011, 133, 19160–19167

Journal of the American Chemical Society
ARTICLE
Scheme 1. PCET Stepwise (Blue) and Concerted (Red)
Pathways
electrochemical oxidation of phenol with hydrogen phosphate as
proton acceptor. This will be the object of the first part of the
following Results section. Electrochemical work terms will then
be seen to play an important role in the achievement of an
accurate comparison, calling for the determination of the poten-
tial difference between the reaction site and the solution. This is
described in the second part of the Results section together with
the ensuing correction of the standard rate constant. Other
results of interest for the analysis of the PCET reaction concern
the oxidation of phenoxide ion, which may serve as a pure ET
reference in the analysis of phenol oxidation. This is described in
the third part of the Results section. The Discussion section will
be devoted to testing the consistency of the homogeneous and
electrochemical approaches based on the whole set of experi-
mental results. In both cases, the intrinsic CPET reactivities when
water (in water) and hydrogen phosphate are the proton acceptors
are compared. Hydrogen phosphate is a stronger base than water.
This obvious thermodynamical advantage makes the CPET reac-
tion extrinsically faster in the first case than in the second.
Concerning the intrinsic reactivities, derived from the standard
rate constants in the electrochemical case and from the self-
exchange rate constants in the homogeneous case, the picture is
reversed. It will be indeed seen that water (in water) appears as a
better intrinsic proton acceptor than hydrogen phosphate, con-
sistently in the electrochemical and homogeneous cases.
Figure 1. Derivation of the Pourbaix diagram from slow scan cyclic
voltammetry: (a) Cyclic voltammetry of 0.2 mM phenol at 0.2 V/s in
0.05 M BrittonꢀRobinson buffers in the presence of 0.5 M KNO
3
. (b)
Peak potential, E , as a function of pH. (c) Pourbaix diagram obtained
p
after correction from the effect of follow-up dimerization according to
0
the equation (Eapp, apparent standard potential; kdim, dimerization rate
0
constant; v, scan rate; C , phenol concentration). The various standard
potentials derived from the Pourbaix diagram correspond to the pathway
indicated as subscript and, in the case of CPET, to the proton acceptor
indicated as superscript. All potentials in V vs NHE.
Scheme 2
’
RESULTS
could then be gathered (Figure 1c), but, in these conditions, no
assignment of the PCET mechanism and characteristic rate constant
could be achieved. This was obtained upon raising the scan rate as
depicted in Figure 2. The variations of the peak potential with scan
Electrochemical Oxidation of Phenol with Hydrogen
Phosphate As Proton Acceptor. Previous cyclic voltammetric
6,7
studies carried out at low scan rates allowed the establishment
of a Pourbaix diagram (Figure 1), based on the observation that
under these conditions, the electrochemical oxidation of phenol
involves a fast and reversible proton-coupled electron transfer
followed, whatever its mechanism, by a rate-determining dimerization
step (Scheme 2). Since the dimerization rate constant was known
from previous pulse radiolysis studies (kdim =1.3 ꢁ 10 M s ), its
effect on the cyclic voltammetric responses could be corrected for so
as to obtain the variation of the apparent standard potential of the
9
rate and phosphate concentration (Figure 3) may be simulated
according to the mechanism in Scheme 2 with a ButlerꢀVolmer rate
law for electron transfer and a transfer coefficient, α= 0.5 (in line with
4c
the thickness of the cyclic voltammetric responses):
ꢀ
ꢁ
9
ꢀ1 ꢀ1
8
i
F
app
0
app
¼
ꢂ
kS exp
ðE ꢀ E
Þ
ꢀ
FS
2RT
ꢁꢃ
•
+
F
PhOH/PhO + H couple with pH as summarized in Figure 1.
Standard potentials characterizing each putative proton acceptor
0
app
ꢁ
½Redꢂ ꢀ ½Oxꢂ exp ꢀ ðE ꢀ E
Þ
ð1Þ
∑
∑
RT
1
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Journal of the American Chemical Society
ARTICLE
Figure 2. Cyclic voltammetry of 0.2 mM phenol in a phosphate buffer at
2ꢀ
pH=7.2([HPO
4
] = 0.125 M) in the presence of KNO (0.5 M) as a func-
3
tion of scan rate, from bottom to top: (a) 0.1, 0.2, 0.5, 1, 2; (b) 5, 10, 20, 50 V/s.
Figure 3. Cyclic voltammetry of 0.2 mM phenol in a phosphate buffer at
3
pH = 7.2 in the presence of 0.5 M KNO . Variation of the peak potential
where i is the current, S is the electrode surface area, and ∑[Red] and
with the scan rate, for different buffer concentrations: 0.025, 0.05, 0.25,
and 0.5 M (magenta, green, red, and blue dots respectively). Colored
lines: simulation for each buffer concentration according to the mecha-
nism in Scheme 2 (see text). Black line: kinetic control by follow-up
dimerization.
∑[Ox] are the sums of concentrations of all reduced forms of phenol
and all oxidized forms of phenol, respectively (see Scheme 1). The
0
app
values of the apparent standard potential, E , used in the simulation
are those previously obtained at low scan rate under the form of the
Pourbaix diagram of Figure 1. The resulting values of the apparent
app
standard rate constant, kS , are gathered in Figure 4 for several
concentrations of phosphate buffer. The apparent standard rate
constant measures the superposition of all pathways, stepwise and
ꢀ
concerted, that are represented in Scheme 1, with Z = H O, HO ,
2
2ꢀ
HPO4 . Since the proton transfers in the stepwise pathways are
fast, they may be considered as being always at equilibrium. The
contribution of the stepwise pathways may therefore be consid-
ered as being a function of pH, independently from the particular
proton acceptor involved. This is not the case for the CPET
pathways, the kinetics of whichdepends ofthenatureoftheproton
acceptor in each case. It follows that (see Supporting In-
formation):
PET
k
app
S
S
k
¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðpK
•þ ꢀ pHÞ
ðpKPhOH ꢀ pHÞ
1
þ 10 PhOH
ꢁ
1 þ 10
EPT
k
Figure 4. Apparent standard rate constant as a function of phosphate
buffer concentration. Full line: representation of eq 3.
S
þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðpH ꢀ pK
•þ Þ
ðpH ꢀ pKPhOHÞ
1
þ 10
PhOH
ꢁ
1 þ 10
2
ꢀ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
CPETꢀHPO4
ꢀ
2ꢀ
k
½H2PO4 ꢂ ꢁ ½HPO4 ꢂ=CS
S
so as to make appear a term independent from phosphate
þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ꢀ
indepHPO
4
ðpK
•þ ꢀ pHÞ
ðpH ꢀ pKPhOHÞ
1
þ 10 PhOH
ꢁ
S
1 þ 10
concentration, k
, and a term proportionalto phosphate
S
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ꢀ
concentration. The very fact that the apparent standard rate
constant is a unity-slope linear function of phosphate concentra-
CPETꢀH2O
þ
CPETꢀHO
ꢀ
k
ð½H O ꢂ=C Þ þ k
½HO ꢂ=C
S
3
S
S
þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðpK
•þ ꢀ pHÞ
ðpH ꢀ pKPhOHÞ
2ꢀ
1
þ 10 PhOH
ꢁ
1 þ 10
tion points to the occurrence ofa CPETꢀHPO4 pathway. Since
the protonation step of the PET and EPT pathways are at
equilibrium, the contribution of phosphate to these pathways is
independent of its concentration, its role being merely to fix
the pH.
ð2Þ
where C is a normalizing concentration taken as equal to 1 M.
S
The notations for the concerted pathways’ standard rate con-
PET
stants are self-explanatory; kS stands for the electron transfer
Application of eq 3 to the experimental data in Figure 4
2ꢀ
CPETꢀHPO
4
from phenoxide ion in the framework of the PET mechanism and
provides the value of the constant of interest, kS
(Table 1).
Although not central to the determination of kS
is interesting to estimate the relative contributions of the various
EPT
S
k
stands for the electron transfer from phenol itself, leading to
2
ꢀ
CPETꢀHPO
4
the cation radical, in the framework of the EPT mechanism.
Equation 2 may be rewritten as, noting that the experiments are
carried out at pH = 7.2, the pK of hydrogen phosphate:
, it
2
ꢀ
pathways besides the contribution of the CPETꢀHPO
path-
4
indep HPO42
ꢀ
way. This is obtained by application of eq 2, using the following
set of parameters (Table 1), and leading to the diagrams in
app
S
k
¼ kS
2
ꢀ
CPETꢀHPO4
½HPO42ꢀꢂ
k
Figure 5. We note that in the phosphate buffer, the contribution
S
þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ꢀ
of the CPETꢀHPO4
pathway prevails. Concerning the
ðpK
•þ ꢀ pHÞ
ðpH ꢀ pKPhOHÞ
C
1
þ 10 PhOH
ꢁ
1 þ 10
S
assumption that the proton transfers in the stepwise pathways
are at equilibrium, we may note that in the opposite case, the
ð3Þ
1
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Journal of the American Chemical Society
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Table 1. Electrochemical Standard Rate Constants Charac-
terizing the Various Competing Pathways
standard rate constants (uncorrected
pathway
from double layer effects) at 25 °C
PET
S
EPT
S
CS PETꢀH
CS PETꢀD
ꢀ1 a
PET
EPT
k
k
k
k
k
k
k
k
= 1 cm s
ꢀ1 b
= 1 cm s
2
O
ꢀ16
ꢀ16
CPETꢀH
CPETꢀD
2
O
= 25 cm s
= 10 cm s
= 25 cm s
2
O
2
O
ꢀ
ꢀ
ꢀ
CPETꢀHO
ꢀ1 ꢀ1 c
CPETꢀHO
S
M
ꢀ
CPETꢀDO
ꢀ1 ꢀ1 c
CPETꢀDO
CPETꢀHPO
S
≈ 10 cm s
= 1.1 cm s
M
2
ꢀ
2
ꢀ
CS PETꢀHPO
CS PETꢀDPO
4
ꢀ1 ꢀ1
4
M
2
ꢀ
2ꢀ
4
ꢀ1 ꢀ1
CPETꢀDPO
4
= 0.4 cm s
M
Other Parameters (Values at 25 °C)
Figure 5. Contribution of the various pathways to the apparent standard
d
rate constant (eq 2) as a function of pH (see text) in H O (left) and D O
2
2
pK's
pKPhOH = 10.0, pKPhOD = 10.7
(
right). Blue, EPT; green, PET; red, CPETꢀH(D)
2
O; yellow, CPETꢀ
; cyan, CPETꢀ0.5 M
; black (right diagram), sum of all contributions.
1
0
e
pKPhOH•+ = ꢀ2, pKPhOD•+ ≈ ꢀ1.6
ꢀ
2ꢀ
4
H(D)O ; magenta, CPETꢀ0.25 M H(D)PO
1
1a
12
pK 2
H PO4
ꢀ
= 7.2,
pK 2
D PO4
ꢀ
= 7.8
HPO
2ꢀ
4
5 f
PhOH = 3.6 ꢁ 10ꢀ , DPhOD = 3.0 ꢁ 10ꢀ5 f
diffusion coefficients
D
2
ꢀ1
(
cm s
)
H
2
O
9 13
D
2
O
9 g
dimerization rate constants
k
dim = 1.3 ꢁ 10
k
dim = 1.0 ꢁ 10
ꢀ
1
ꢀ1
(
M
s )
a
b
From the cyclic voltammetry of phenoxide ion, see next section.
Approximate estimation assuming that solvent reorganization is
about the same as in the preceding case, taking into account that a
gross estimate is sufficient in view of the smallness of the contribu-
tion of this pathway in the pH range of interest (see Figure 5).
c
ꢀ
Assuming that the mechanism of the CPETꢀH(D)O reaction is
the exact reverse of the mechanism of the CPETꢀH(D)
2
O reaction.
The approximate character of this estimation has no important
consequences since the contribution of this pathway is modest,
ꢀ
due to the small concentration of HO in the pH range of interest
(
agreement with literature data.
0
d
see Figure 5). From the Pourbaix diagram in Figure 1c in
1
1b e
Estimated from pK
D
≈ pK
H
+
1
4 f
g
2
H O
dim
.4. From the CV peak currents. From k
, corrected by the
ratio of the diffusion coefficient.
2
Figure 6. Cyclic voltammetry of 0.2 mM phenol in D O in a phosphate
buffer at pD = pKD2PO4ꢀ = 7.8 in the presence of 0.5 M KNO . Variation
3
contributions of the PET and EPT pathway would be less than
that pictured in Figure 5, that is, even more negligible.
A similar, albeit simplified, procedure was used to obtained the
of the peak potential with the scan rate for 0.25 M buffer concentration.
Full line represents simulation according to the mechanism in Scheme 2,
in which H is replaced by D (see text and Table 1).
standard rate constant in D O. The variation of the peak potential
2
z being the charge number of the reactants,
with scan rate at one concentration of hydrogen phosphate is
shown in Figure 6. The apparent standard rate constant was
extracted from the data in Figure 6 in the same way, as in Figure 3
using the parameter values listed in Table 1, thus leading to the
standard rate constants in the same table.
Work Terms in the Electrochemical Reaction: Double
Layer Correction. In the application of the ButlerꢀVolmer
law (eq 1) to the electrochemical oxidation of phenol with water
and hydrogen phosphate, respectively, works terms that describe
Z
R
Z
P
w ¼ zFϕ , w ¼ ðz þ 1ÞFϕ
Z
Z
leading to
ꢀ
ꢁ
ð2z þ 1ÞFϕ
CPET ꢀ Z
¼ k CS PET ꢀ Z exp
Z
k
ð4Þ
S, corr
2
RT
Further analysis of the kinetic data therefore requires the
determination of the potential of the reaction sites and starting
with the potential in the outer Helmoltz plane (OHP, see Scheme 3),
the transfer of the reactant from the bulk of the solution to the
Z
R
reaction site, w , and of the products from the reaction site to
Z
P
the solution w , (Z being either water or hydrogen phosphate),
traditionally noted ϕ , that is, the potential at the boundary between
2
have to be introduced, leading to the following correction of the
raw standard rate constant data.
the compact double layer (portion of space between the electrode
and the OHP) and the diffuse double layer (portion of space between
15a
the OHP and the solution). This potential may be obtained, in
the framework of the GouyꢀChapman theory, from double layer
capacitance data according to
"
#
Fðw ZR þ w Þ
Z
CPET ꢀ Z
CPET ꢀ Z
¼ kS
P
k
exp
S, corr
2
RT
"
#
2
RT
CdðE ꢀ EpzcÞ
The work terms results from the application of the potential in
ϕ2 ¼
asinh
ð5Þ
1=2
zF
ð8RTε0εcÞ
the reaction site, ϕ , to the charge of reactant and products,
Z
1
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Journal of the American Chemical Society
ARTICLE
Scheme 3. Double Layer Effects
Figure 7. (a) Cyclic voltammetry of a solution in a 0.1 M phosphate
buffer at pH = 7.2 in the presence of 0.5 M KNO
3
showing the double
layer charging current in the region of the potential of zero charge, Epzc
.
Scan rate = 2 V/s. (b) Variation of the outer Helmholtz plane potential
with the electrode potential under the same conditions.
ꢀ
1
Table 2. Electrochemical Standard Rate Constants (cm s
for Phenol Oxidation, Correction of Double Layer Effects
)
1
6
dimensions (Å)
δH2O = 1.5, aNO3ꢀ = 2.9
5
b
5b
a
HPO42ꢀ = 3.5, aH2O = 6.5
ꢀ
1
k
= 4.2
= 0.125
HPO42ꢀ = 0.108, ϕH2O = 0.053
potentials (V)
ϕ
2
ϕ
2ꢀ
CPETꢀH
2
O
CPETꢀHPO
4
raw standard rate constants
k
S,25°C
= 25, kS,25°C
= 1.1
2
= 0.002
ꢀ
4
CPETꢀH
2
O
CPETꢀHPO
corrected standard rate constants
k
S,corr,25°C = 83, kS,corr,25°C
where z is the reactant electric charge ε is the vacuum permittivity, ε
0
is the dielectric constant of the solvent (here 78.8), c is the electrolyte
concentration (here 0.5 M, the concentration of KNO in excess over
3
the other components of the solution), C is the differential capacity of
d
the electrode, and Epzc is the potential of zero charge. From the shallow
minimum in Figure 7a, Epzc = 0.65 vs NHE, and from the approxi-
2
mately constant anodic capacitive current, C = 150 μF/cm , applica-
d
tion of eq 5 leads to an estimation of ϕ as a function of the electrode
2
potential (Figure 7b). In the zone of electrode potentials where the
experiments were carried out, we may estimate that, on average, ϕ ≈
2
0
.125 V at the peak potential. In view of the radius of the nitrate ion and
the radii of the proton in water and of hydrogen phosphate (Table 2),
the potential at the reaction site (Scheme 3), ϕ , is smaller than ϕ :
1
5a
Z
2
ϕ ¼ ϕ exp½ ꢀ kða ꢀ a
ꢀ
Þꢂ
Z
2
Z
NO3
ꢀ
1
where k is the Debye length for the electrolyte concentration used in
the experiments summarized in Figures 1ꢀ6 as reported in
Table 2.
The resulting values of the potential at the reaction site for
water and hydrogen phosphate are listed in Table 2, enabling the
correction of the raw standard rate constants according to eq 4,
and thus leading to the corrected values in Table 2.
Electrochemical Oxidation of Phenoxide Ion. The oxida-
tion of phenoxide ion was investigated to have at disposal a
reference ET reaction (Scheme 4) to be compared with the two
CPET reactions. While an extensive investigation of the varia-
tions with temperature and scan rate was hampered in the case of
phenol by the proximity of the oxidation wave to the discharge of
the supporting electrolyte, this was possible in the present case
1
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Journal of the American Chemical Society
ARTICLE
Scheme 4
Figure 9. Oxidation of phenoxide ion. Arrhenius plots derived from the
data in Figure 8, blue = raw data, red = corrected from double layer
effects.
Table 3. Phenoxide Ion Oxidation, Correction of Double
Layer Effects and Variations with Temperature
temp (K)
299
2.7
286
2.5
273
1.4
268
1.1
5
2
ꢀ1
a
D ꢁ 10 (cm s
)
ꢀ
9
ꢀ1 ꢀ1 b
k
dim ꢁ 10 (M
s
)
1.3
0.9
0.6
0.4
0
PhO
c
E
+
/PhO
ꢀ
(V vs NHE)
0.930 0.935 0.845 0.860
ꢀ
PhO
S
raw standard rate constant, k
1.00
0.80
0.12
0.45
0.07
0.35
0.05
ꢀ
PhO
corrected standard rate constant, kS,corr 0.15
a
b
From peak heights. From the measured temperature dependence of
the diffusion coefficient and the DebyeꢀSmoluchowski relationship
c
between bimolecular diffusion limit and the diffusion coefficient. The
standard potentials were obtained from the peak potential by the same
procedure as depicted in Figure 1.
properties, are concerned. This observation parallels the com-
parison between the same two proton acceptors in homoge-
III
5
neous oxidation of phenol by photogenerated Ru (bpy)
3
Figure 8. Oxidative cyclic voltammetry of a 0.2 mM phenol solution in a
when also made at zero driving force and in which the effect
0.1 M Britton buffer at pH = 12 in the presence of 0.5 M KNO
3
, featuring
of electrostatic work terms has also been corrected (Table 4).
2
ꢀ
the oxidation of phenoxide ion. Variation of the peak potential with the
scan rate at various temperatures (number in each diagram), blue dots =
experimental data, blue lines = simulation according to Scheme 4 with
The H O/HPO4 rate ratio is however substantially bigger
2
in the electrochemical case than in the homogeneous case.
These observations call for a more quantitative analysis of the
comparison between the electrochemical and homogeneous
reactions.
9
the parameter values listed in Table 3, red lines = rate-determining
dimerization.
The corrected electrochemical standard rate constants may be
17
expressed as:
since the oxidation of phenoxide ion is less positive. The results
are shown in Figure 8 where the variations of the peak potential
with scan rate at four temperatures are displayed as well as their
simulations according to Scheme 4 so as to derive the values of
the standard rate constants.
The resulting Arrhenius plot is displayed in Figure 9. The raw
values of the standard rate constant were then corrected from
double layer effects in the same way as for phenol oxidation,
"
#
CPET ꢀ Z
λ
el
π exp ꢀ
4RT
CPET ꢀ Z
¼ Z eC lPET ꢀ Z sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
πRT
k
S, corr
1 þ
CPET ꢀ Z
λ
el
CPETꢀZ
after introduction of the reorganization energy, λ
, and
el
considering that the reaction site sits at the OHP and that ϕ =
CPETꢀZ
2
of the pre-exponential factor, Zel
(Z being either water
0
.100 V on average in the potential domain where the oxidation
or hydrogen phosphate). The electrochemical reorganization
energy may be derived from the homogeneous self-exchange
reorganization energy, taking into account image force effects
peak of phenoxide ion is located, leading to the values listed in
Table 3 and to a corrected Arrhenius plot (Figure 9).
18
according to
ꢂ
ꢃ
’
DISCUSSION
aZ
dZ
CPET ꢀ Z
CPET ꢀ Z
λ
¼ λ
1 ꢀ
A first observation upon perusal of Table 4 is that, in the
el
se
CPET electrochemical oxidation of phenol, water (in water) is a
much more efficient proton acceptor than hydrogen phosphate
as far as corrected standard rate constants, that is, intrinsic
where a is the radius of the equivalent sphere and d =2(δ +aZ),
the distance between the reaction site and its electrical image (see
Z
Z
H O
2
1
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Journal of the American Chemical Society
ARTICLE
a
b
Table 4. Electrochemical and Homogeneous Kinetic
Characteristics
decrease of the pre-exponential factor when passing from a
simple ET reaction to the CPET reactions indicates that, in the
later case, the pre-exponential factor is not simply a combined
measure of proton tunneling (in which case, the KIE should be
very large) and structureless approach of the two reactants,
phenol and proton acceptor, assimilated to spheres, toward
the electrode surface as sketched in Scheme 3. The precursor
complex is actually likely to adopt a precise spatial structure so as
to allow the formation of one or several H-bonds as required by
the occurrence of the CPET reaction, thus decreasing consider-
ably the number of efficient collisions.
c
5
electrochemical
homogeneous
CPETꢀH
2
O
CPETꢀH
2
O
7 d
k
k
S,corr,25°C = 83
k
k
0,25°C
= 8.8 ꢁ 10
2
ꢀ
2ꢀ
CPETꢀHPO
4
CPETꢀHPO
0,25°C
4
4
S,corr,25°C
= 0.002
= 2 ꢁ 10
¼ 4:4 ꢁ 10
O
CPET
S, corr, 25°C
ꢀ
H2O
CPET
0, 25°C
ꢀ
H2O
k
k
4
3
¼
3:9 ꢁ 10
CPET
ꢀ
HPO2ꢀ
CPET
k
0, 25°C
ꢀ
HPO2ꢀ
4
4
k
S, corr, 25°C
CPETꢀH
2
O
e
CPETꢀH
2
KIEel,25°C
= 2.75
4
KIEhom,25°C = 4.0
2
ꢀ
2ꢀ
CPETꢀHPO
KIEel,25°C
e
CPETꢀHPO
4
= 2.4
KIEhom,25°C
= 3.5
Ce lPETꢀH
2
O
f
Cs ePETꢀH
2
O
λ
λ
Z
Z
= 0.27
λ
λ
Z
Z
= 0.45 eV
2
ꢀ
2ꢀ
Ce lPETꢀHPO
4
f
Cs ePETꢀHPO
4
= 0.56
= 0.86 eV
10
’
CONCLUDING REMARKS
eC lPETꢀH
2
O
ꢀ1
CPETꢀH
2
O
= 390 cm s
hom
= 1.2 ꢁ 10
2
ꢀ
2ꢀ
The CPET oxidation of phenol with water (in water) and
eC lPETꢀHPO
4
ꢀ1
ꢀ1
CPETꢀHPO
4
7
ꢀ1
= 0.16 cm s
hom
= 2 ꢁ 10 M s
!
!
hydrogen phosphate as proton acceptors has provided a good
example for testing the consistency of the electrochemical and
homogeneous approaches to a reaction, the comprehension of
which raises more mechanistic and kinetic challenges than that of
a simple outer-sphere electron transfer. In terms of driving forces,
hydrogen phosphate is a better proton acceptor than water (by
ca. 0.4 eV), but when comparison is made at zero driving force,
water (in water) appears as more efficient than hydrogen phos-
phate. This observation, originally derived from homogeneous
experiments, is confirmed by the value found for the electro-
chemical standard rate constants. A meaningful comparison
between the electrochemical and homogeneous intrinsic proper-
ties requires correcting the raw data from electrical work terms.
In the first case, this operation consisted in correcting from the
effect of the electrochemical double layer at the level of the
reaction site. This estimate was based on the reactant dimensions
revealed by the analysis of the homogeneous results. This is also
the case for the evaluation of the electrochemical reorganization
energy, derived from a detailed analysis of a large set of homo-
geneous experiments carried out as a function of temperature,
while analogous electrochemical experiments could not be
performed. Once the electrochemical reorganization energy
was thus determined, the electrochemical pre-exponential factors
could be obtained and compared with their homogeneous
counterparts. The intrinsic advantage of water (in water) over
hydrogen phosphate is therefore confirmed, corroborating
the mechanism by which electron transfer is concerted with
Grotthus-type proton translocation in water. More precise com-
parison between the pre-exponential factors and H/D kinetic
isotope effects revealed that electric field effects that favor
zwitterionic forms in the transition state may be at work in the
electrochemical case. The electrochemical oxidation of phen-
oxide ion could be investigated as a function of temperature,
providing a detailed picture of a system that can be used as a
reference outersphere electron transfer to be compared with the
CPET reactions. The huge decrease of the pre-exponential thus
observed points to a CPET precursor complex that possesses a
precise spatial structure allowing the formation of one or several
H-bonds as required by the occurrence of the CPET reaction, thus
decreasing considerably the number of efficient collisions com-
pared with those undergone by structureless spherical reactants.
In summary, consistency between the two approaches of the
same reaction is indeed observed after some specific, and rather
modest, effects, such as electric field effects, have been taken into
account. One worth noting consequence is the possibility of
transferring information from one domain to the other so as to
obtain a deeper comprehension of the reaction.
CPET
Zel
CPET
Zel
ꢀ
H2O
CPET
hom
ꢀ
H2O
Z
log
¼ 3:4
log
¼ 2:8
ꢀ
HPO2ꢀ
CPET
Zhom
ꢀ
HPO2ꢀ
4
4
ꢀ
Ee lTꢀPhO
λ
= 1.1 eV
ꢀ
Ee lTꢀPhO
4
Z
= 8 ꢁ 10 cm s
a
c
ꢀ1
b
ꢀ2 ꢀ1
Standard rate constants in cm s
Energies in eV. Taking into account image force effects with dH O
6, dHPO42ꢀ = 10 Å (see text). From the ratio of the uncorrected
standard rate constants in Table 1. corrected from work terms.
.
Rate constants in M
s
.
=
d
2
e
1
f
Scheme 3). The ensuing reorganization energies for water and
hydrogen phosphate are reported in Table 4, as well as the values
of the pre-exponential factor. It is again observed, as in the
homogeneous case, that the pre-exponential factor is substantially
larger in the case of water than in the case of hydrogen phosphate.
The electrochemical results thus confirm the very peculiar nature
of water (in water) as a proton acceptor previously characterized in
the homogeneous oxidation of phenol: the charge of the proton
generated in the reaction is delocalized over a large cluster of water
molecules; the electron transfer reaction is concerted with Grotthus-
type proton displacements by means of H-bond relays.
2
ꢀ
It is worth noting that the H O/HPO4 ratio of pre-expo-
2
nential factors is, after all work term corrections have been made,
substantially larger, by a factor of ca. 10, in the electrochemical
case than in the homogeneous case. A likely reason for this dif-
ference is the existence of an electric field effect in the reaction
site favoring the zwitterionic form of the reactant system in the
ꢀ
+
transition state, (PhO ,H nH O), as already observed in the
2
oxidation of an aminophenol in which the proton acceptor is an
1
9
internal base. The observation that the H/D kinetic isotope
effect (Table 3) is smaller in the electrochemical case (2.4ꢀ2.75)
than in the homogeneous case (3.5ꢀ4.0) can be interpreted as an
additional manifestation of the same phenomenon.
An additional source of information is provided by comparing the
electrochemical CPET reactions with the oxidation of phenoxide
ion taken as a reference ET reaction, for which the reorganization
energy and the pre-exponential factor could be derived from
20
temperature-dependent experiments, leading to the values re-
ported in Table 3. It is interesting to note that the pre-exponential
4
ꢀ1
factor 8 ꢁ 10 cm s , is substantially larger than the collision
1/2
3
ꢀ1
frequency, [RT/(2πM)] = 6.5 ꢁ 10 cm s (M = molar mass)
for phenoxide ion, which may be attributed to the fact that the
electron transfer reaction starts to take place before the reactant has
17,19
reached the outer Helmholtz plane as discussed earlier.
2ꢀ
The pre-exponential factors found for the HPO4 ꢀ and5
H OꢀCPET reactions are much smaller, by a factor of 5 ꢁ 10
2
in the first case and 205 in the second. This considerable
1
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dx.doi.org/10.1021/ja206561n |J. Am. Chem. Soc. 2011, 133, 19160–19167

Journal of the American Chemical Society
ARTICLE
’
ASSOCIATED CONTENT
S
Supporting Information. Experimental details, proof of
b
eq 2, details of ref 16. This material is available free of charge via
the Internet at http://pubs.acs.org.
’
AUTHOR INFORMATION
Corresponding Author
saveant@univ-paris-diderot.fr
’
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(
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(
(
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4
b,c
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(
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3
(
(
(
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20) This was not feasible in the homogeneous case because of a side
(
(
reaction between phenoxide ion and methylviologen serving as quench-
II
er of the excited Ru (bpy) complex.
3
1
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dx.doi.org/10.1021/ja206561n |J. Am. Chem. Soc. 2011, 133, 19160–19167