A R T I C L E S
Neuteboom et al.
(∼31 Å) of P1 the electronic coupling of the OPV and PERY
chromophores is negligible in the excited state and, hence, a
low rate for electron transfer, causing a decreased quenching
of the PERY emission. Because singlet energy transfer is less
dependent on the distance than electron transfer, the OPV
fluorescence in P1 is quenched to the same extent as in P2.
The conformational freedom of P1 can thus be used to
For the former process we have considered the cases where the
charge transfer is induced by excitation of either the OPV donor
(D*A f D+A- process; that is the direct transfer, corresponding
to electron transfer from D to A) or the acceptor (DA* f D+A-
process; that is the indirect transfer, corresponding to hole
transfer from A to D).
The ground-state geometries of the full chemical structures
have been optimized by means of the AM1 (Austin Model 1)
method.52 In the case of M1, the intermolecular geometric
parameters were optimized at the molecular mechanics level
using the Dreiding force field. To build the excited-state and
charge-separated geometrical structures, the equilibrium geom-
etries of the isolated donor and acceptor chromophores were
first optimized in the lowest singlet excited state and in the
singly (positively and negatively) charged ground state at the
AM1/CAS-CI (complete active space-configuration inter-
action)53 and AM1/ROHF (restricted open-shell Hartree-Fock)
level, respectively; these were then combined into the whole
structure to yield the relaxed geometries of the D*A, DA*, and
D+A- electronic states.
i
rationalize the widely different values obtained for kcs using
PL quenching and PIA spectroscopy.
d
The rate for charge separation in the films of P1 and P2, kcs
g 2.3 × 1012 s-1, is at the limit of the time resolution of the
pump-probe setup. The recombination, krec ) 9.5 × 109 s-1
,
is much slower. Both processes, however, are significantly faster
than the corresponding reactions in toluene solution. The
increased rate for charge separation can be understood by
assuming that in the films face-to-face orientations of the OPV
and PERY chromophores (like the one in M1) are present
(Figure 13). Although we have no evidence from morphological
studies, several polymer materials45-48 exist in which electron-
rich (donor) and electron-deficient (acceptor) segments form
alternating stacks in solution and in the solid state. The driving
force for such orientations is the π-stacking in combination with
electrostatic or weak charge-transfer interaction.49,50 Also, in
D-A molecular crystals the usual case is to have stacks with
alternating D-A molecules.51 A preference for face-to-face
D-A interactions, as schematically drawn in Figure 13, contrast
with the microphase separation that often occurs in block
copolymers. Apparently, the tendency for the OPV and PERY
segments to give alternating stacks in thin films of P1 and P2
is stronger than the antagonistic interactions that direct the
microscopic phase separation. One likely explanation for this
result is the limited length of the D and A segments in P1 and
P2. The proposition of the presence of alternating stacks of OPV
and PERY in films of P1 and P2 is supported by the similar
The transfer rate kCS and kCR, corresponding to the probability
for charge separation (D*A or DA* f D+A-) and charge
recombination (D+A- f DA) to occur after photoexcitation,
respectively, are evaluated using Jortner’s expression.54,55 Going
from reactant R to product P, the expression writes
1/2
2π
1
Sυ
kRP
)
VRP
e-S
×
2
∑
(
)
p
4πλskT
υ!
υ
(∆G° + λs + υp ω )2
exp -
(4)
(
)
4λskT
Here, VRP is the electronic coupling representing the tunneling
probability between the reactant and product potential-energy
surfaces (approximated as harmonics),∆G° is the variation in
Gibbs free energy during the reaction, S () {λi}/{p ωi }) is
the Huang-Rhys factor expressed in terms of the intramolecular
reorganization energy λi and the effective mode vibrational
energy p ωi , and λs is the solvent reorganization energy
including contributions from the polarization changes in the
dielectric (solvent) environment.
d
values of kcs obtained for M1 and the polymer films (Table
2). In full agreement with this view, the initial recombination
in the films is fast and the rate constant (krec ) 9.5 × 109 s-1
)
is again similar to the one observed for M1 (krec ) 6.9 × 109
s-1). The long-lived charge carriers in the films result from those
charges that escape from geminate recombination and diffuse
to different sites in the films. The relatively low number of
charges (<20%, Figure 9) that live up to 1 ns explains, at least
in part, the low currents observed in photovoltaic cells made
from P1 and P2. If the face-to-face orientations of OPV and
PERY are predominant in the films, this could be a more
important reason for the low currents, because such orientation
would severely limit charge transport.
∆G° is estimated from the enthalpies of formation, ∆Hf °,
with the solvent taken into account through the use of the
COSMO model56 implemented in the AMPAC package:57
∆G° ) ∆HP° - ∆HR° + Ecb
Theoretical Modeling of Charge Separation and Recom-
bination. Correlated semiempirical quantum-chemical calcula-
tions have been performed on the model compound M1 and a
monomer unit of P2 to assess the various molecular parameters
relevant in the charge separation and recombination processes.
with
D
A
∑∑ q q
1
i j
Ecb
)
4πꢀ0
ꢀsrij
j
i
∆HP° ) ∆Hf,D+° + ∆Hf,A-°;
(5)
(45) Lokey, S. R.; Iverson, B. L. Nature 1995, 375, 303.
(46) Zych, A. J.; Iverson, B. L. J. Am. Chem. Soc. 2000, 122, 8898.
(47) Nguyen, J. Q.; Iverson, B. L. J. Am. Chem. Soc. 1999, 121, 2639.
(48) Lokey, S. R.; Kwok, Y.; Guelev, V.; Pursell, C. J.; Hurley, L. H.; Iverson,
B. L. J. Am. Chem. Soc. 1997, 119, 7202.
(49) Hunter, C. A.; Lawson, K. R.; Perkins, J.; Urch, C. J. J. Chem. Soc., Perkin
2 2001, 651.
∆HR° ) ∆Hf,D*° + ∆Hf,A° or ∆Hf,D° + ∆Hf,A*
°
ꢀ0 and ꢀs are the vacuum and solvent dielectric constants,
(50) Hill, D. J.; Mio, M. J.; Prince, R. B.; Hughes, T. S.; Moore, J. S. Chem.
ReV. 2001, 101, 3893.
(51) Wright, J. D. Molecular Crystals, 2nd ed.; Cambridge University Press:
Cambridge, 1995.
(52) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J. Am.
Chem. Soc. 1995, 107, 3702.
(53) Typically 6-10 molecular orbitals were included in the CI active space.
9
8634 J. AM. CHEM. SOC. VOL. 125, NO. 28, 2003