10208 J. Am. Chem. Soc., Vol. 121, No. 43, 1999
Ferm´ın et al.
max
photo
A closer look into the potential dependence of j
revealed
that the increment of ket with increasing potential approaches a
Tafel behavior. The ratio ket/kd can be estimated by rearranging
eq 6
1
ket/kd )
(7)
max
(eI0σNs/j
) - 1
photo
In Figure 9b, this ratio is plotted as a function of the Galvani
potential difference assuming a value of Ns of 2.5 × 1014 cm-2
.
The exponential increment of ket/kd with increasing Galvani
potential can be described in terms of a Tafel relation with a
transfer coefficient close to R ) 0.5. These results have been
phenomenologically interpreted in terms of an activation barrier
for the electron-transfer process.11,12 In addition, taking the
lifetime of the triplet state as 30 µs after the report by Hugerat
et al.7 for a similar porphyrin ion pair, ket may lie in the range
of 104-105 s-1. The value of ket is within the same order of
magnitude to the estimated for the monomer ZnTPPC. Conse-
quently, these results seem to indicate that the larger photocur-
rent observed for the pair ZnTPPS-ZnTMPyP in comparison
to the porphyrin ZnTPPC is mostly connected to a higher
interfacial concentration of the porphyrin ion pair.
The value of ket, as extracted from the previous analysis,
corresponds to the integral of the electron-transfer rate over the
distance separating the adsorbed sensitizer and the organic redox
couple.11 Recent descriptions of the interfacial structure of ITIES
based upon lattice-gas approximation21 and molecular dynam-
ics22 suggest that the interfacial region between water and DCE
extends over an average distance of 1 nm. Taking this value as
a first approximation, the pseudo-first-order heterogeneous rate
constant is of the order of 10-2 cm s-1. Although this magnitude
is ∼10 times faster than previously reported rate constants for
heterogeneous electron transfer at ITIES in the dark,23-27 it is
still 2-3 orders of magnitude slower than the upper limit for
outer sphere adiabatic electron-transfer reactions from the
Marcus’ model.28-30
Figure 9. Potential dependence of the photocurrent associated with a
full monolayer of porphyrin heterodimer (a) obtained from the fittings
of the photocurrent isotherms (Figure 8). The ratio of the pseudo-first-
order electron transfer and decay of the excited rate constants as a
function of the Galvani potential difference (b) was estimated from eq
7, assuming 2.5 × 1014 cm-2 as the maximum surface density of dimer
species. Considering a Butler-Volmer dependence of ket, a transfer
coefficient of 0.5 is estimated.
the association equilibrium for the two porphyrin monomers as
defined in eq 2.
The dependence of the photocurrent on the concentration of
ZnTPPS and ZnTMPyP at various Galvani potential differences
is displayed in Figure 8. Fittings employing eq 5 are also shown
as continuous lines. Three parameters were adjusted for each
max
photo
According to the values obtained for â, the Gibbs energy of
Galvani potential difference, j
, KC and â. The parameters
adsorption (∆Gads) can be estimated as -22.8 ( 0.4 kJ mol-1
.
KC and â were found almost independent of the applied
potential. For instance, the association constant KC exhibited
an average value of (6 ( 1) ×107 mol-1 dm3 throughout the
potential range. This value is comparable to the preliminary
estimations based on the shift of the ZnTMPyP transfer potential
in the presence of ZnTPPS (cf. Figure 2). In turn, the increase
of the photocurrent with increasing potential is associated with
The magnitude of ∆Gads is approximately half of the value
reported for ZnTPPC under similar experimental conditions.11,12
This surprising result indicates that, although the adsorption
energy for ZnTPPC is larger, a smaller number of these
porphyrins can be accommodated at the liquid/liquid junction
in comparison to the heterodimer. The large adsorption energy
exhibited by ZnTPPC in comparison to ZnTPPS is also
responsible for the difference in photoreactivity of the corre-
sponding dimer structures. As mentioned earlier, no enhance-
ment of the photocurrent associated with the quenching of
ZnTPPC is observed upon addition of the cationic ZnTMPyP.
Although spectroscopic evidence suggests the formation of ion
pairs between ZnTPPC and ZnTMPyP in solution, the adsorp-
tion sites at the interface are expected to be mostly occupied
max
photo
max
photo
the parameter j
. The potential dependence of j
is
displayed in Figure 9a. This behavior reflects an increase of
the electron-transfer rate with respect to the relaxation of the
excited state. Another interesting aspect arising from this
max
photo
analysis is the rather high values obtained for j
in com-
parison to the responses observed for the monomer ZnTPPC.11
Taking a capture cross section of 10-17 cm2 at 543 nm for the
heterodimer, the photocurrent density is 4-5 times higher than
the value expected for a close packed layer of porphyrin
molecules lying coplanar to the interface.11 Assuming that
(21) Schmickler, W. J. Electroanal. Chem. 1997, 429, 123-127.
(22) Benjamin, I. Annu. ReV. Phys. Chem. 1997, 48, 407.
(23) Cheng, Y.; Schiffrin, D. J. J. Chem. Soc., Faraday Trans. 1993,
89, 199-205.
photocurrent arises from the first monolayer of adsorbed
max
photo
porphyrin species, the high values of j
can be taken as an
(24) Ding, Z.; Ferm´ın, D. J.; Brevet, P.-F.; Girault, H. H. J. Electroanal.
Chem. 1998, 458, 139-148.
evidence for a specific orientation of the adsorbed porphyrin
pairs at the interface. On the basis that porphyrin heterodimer
consists of an electrically neutral dipolar molecule, it could be
envisaged a kind of self-assembling mechanism for the adsorp-
tion process at the liquid/liquid junction. The interfacial orienta-
tion of heterodimer species may also play a fundamental role
on the kinetics of photoinduced electron transfer.
(25) Tsionsky, M.; Bard, A. J.; Mirkin, M. V. J. Phys. Chem. 1996, 100,
17881-17888.
(26) Tsionsky, M.; Bard, A. J.; Mirkin, M. V. J. Am. Chem. Soc. 1997,
119, 10785-10792.
(27) Shi, C.; Anson, F. C. J. Phys. Chem. B 1999, 103, 6283-6289.
(28) Marcus, R. A. J. Phys. Chem. 1990, 94, 4152-5.
(29) Marcus, R. A. J. Phys. Chem. 1990, 94, 1050-5.
(30) Marcus, R. A. J. Phys. Chem. 1991, 95, 2010-13.