Photoinduced electron transfer of carbazole-acceptor dyads in solution and in a polymer solid

Article abstract of DOI:10.1039/b401951b

Photoinduced charge separation (CS) of carbazole-acceptor dyads (Cz-S-A) in solutions and in a polymer solid was examined by the measurement of fluorescence decay. For the discussion of CS from the viewpoint of thermal fluctuations in a solution and in a polymer solid, the separation distance between the Cz donor moiety and acceptor moiety was fixed with a rigid spacer. The photoinduced CS was observed for various solutions with different dielectric constants ranging from 3.06 to 37.5 at room temperature. The rate constant k_CS increased with an increase in the free energy gap of -ΔG_CS, indicating that CS is in the normal region of the Marcus theory. The temperature dependence of CS in a solution from 183 to 296 K was quantitatively explained by an electron transfer (ET) formula where solvent motions are treated as a classical mode and vibrational motions of the reactant are treated as a quantum mode. On the other hand, the photoinduced CS was also observed for a polymer solid with polar cyano groups over a wide temperature range from 100 to 400 K, although most motions are highly restricted compared with those in a solution. Above the glass transition temperature (T _g), CS was explained by the same ET formula as that in a solution with dielectric constants measured at a high frequency. Below T_g, CS was independent of temperature, indicating that CS is caused by nuclear tunneling at low temperatures.

Full text of DOI:10.1039/b401951b

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R E S E A R C H P A P E R
Photoinduced electron transfer of carbazole–acceptor dyads
in solution and in a polymer solid
Hideo Ohkita,* Hiroaki Benten, Arihiro Anada, Hitoshi Noguchi, Nobuaki Kido,
Shinzaburo Ito and Masahide Yamamoto
Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University, Katsura,
Nishikyo Kyoto 615-8510, Japan
Received 10th February 2004, Accepted 28th May 2004
First published as an Advance Article on the web 14th June 2004
Photoinduced charge separation (CS) of carbazole–acceptor dyads (Cz–S–A) in solutions and in a polymer solid
was examined by the measurement of fluorescence decay. For the discussion of CS from the viewpoint of thermal
fluctuations in a solution and in a polymer solid, the separation distance between the Cz donor moiety and
acceptor moiety was fixed with a rigid spacer. The photoinduced CS was observed for various solutions with
different dielectric constants ranging from 3.06 to 37.5 at room temperature. The rate constant kCS increased with
an increase in the free energy gap of ꢀDGCS, indicating that CS is in the normal region of the Marcus theory.
The temperature dependence of CS in a solution from 183 to 296 K was quantitatively explained by an electron
transfer (ET) formula where solvent motions are treated as a classical mode and vibrational motions of the
reactant are treated as a quantum mode. On the other hand, the photoinduced CS was also observed for a
polymer solid with polar cyano groups over a wide temperature range from 100 to 400 K, although most motions
are highly restricted compared with those in a solution. Above the glass transition temperature (Tg), CS was
explained by the same ET formula as that in a solution with dielectric constants measured at a high frequency.
Below Tg, CS was independent of temperature, indicating that CS is caused by nuclear tunneling at low
temperatures.
researchers have discussed ET in glassy solids from a theore-
tical standpoint.7–11 However, there are few experimental
1. Introduction
reports on intramolecular ET in polymer solids.12–14
Here we investigated photoinduced charge separation (CS)
The first-order rate constant for electron transfer (ET) kET
between two molecules with very weak electronic coupling is
simply expressed by eqn. (1):1–6
of intramolecularly linked donor (D) and acceptor (A) com-
pounds in a polymer solid and in various solvents. The D–A
2p
ꢀh
2
kET
¼
jVj ðFCÞ
ð1Þ
molecules have a carbazole and an A moiety whose separation
distance is fixed by a rigid cyclohexane spacer. In other words,
the electronic coupling V is considered to be constant in our
system. We focus on the latter term, FC, in eqn. (1) to discuss
intramolecular photoinduced ET in a polymer solid where the
orientational motions of polar group are partially restricted
and have various relaxation modes.
where V is the electronic coupling matrix element and FC is the
Franck–Condon factor. The former term, V, decreases expo-
nentially with an increase in the separation distance between
the reactants. The latter term, FC, is the probability of the
fulfilment of the Franck–Condon conditions: the Franck–
Condon principle and energy conservation, which is given by
a sum of products of overlap integrals of the wavefunctions of
the reactants with those of the products, weighted by
Boltzmann factors. Thus, ET will occur only when the total
energy of the reactants and surrounding medium is equal to
that of the products and surrounding medium. In a solution,
the energy matching takes place by thermal fluctuations in the
orientational coordinates of solvent molecules and in the
vibrational coordinates of the reactants. In other words, ET
requires not only a spatial approach of the reactants but also
the energy matching caused by thermal fluctuations.
In a polymer solid, molecular motions are highly restricted
compared with those in a solution. Above the glass transition
temperature (Tg), segments in the main chains are freely
mobile. Below the Tg, on the other hand, the free rotational
motions of the main chain are frozen but local motions such as
rotational motions of side chains and librational motions of a
few segments in the main chain are still allowed. The relaxation
time of these local motions shows a wide distribution, which is
heavily dependent on temperature in general. In other words,
the orientational fluctuations of polar groups in a polymer
solid are different from those in a solution. Thus, ET in a
polymer solid should be different from that in a solution. A few
2. Experimental
2.1. Materials
A series of nine carbazole (Cz; Donor) cyclohexane (S; Spacer)
acceptor (A; Acceptor) molecules (Cz–S–A) were synthesized
as described below. The synthetic scheme of the Cz–S–A
molecules is summarized in Scheme 1. N-Ethylcarbazole
(EtCz) was synthesized by N-alkylation of carbazole and was
purified by silica-gel column chromatography and recrystalli-
zation. 1,12-Di(9-carbazolyl)dodecane (Cz–12–Cz) was synthe-
sized by the reaction of carbazole with 1,12-dibromododecane
and purified by recrystallization and silica-gel column chromato-
graphy. Either EtCz or Cz–12–Cz was used as a reference.
Solvents used here were hexane (Hex; Nacalai Tesque, spectro-
scopic grade), dibutyl ether (DBE; Nacalai Tesque), 2-methyl-
tetrahydrofuran (MTHF; Nacalai Tesque), and acetonitrile
(MeCN; Nacalai Tesque, spectroscopic grade). Before use,
DBE was purified by distillation under reduced pressure and
MTHF was dried with solid KOH, passed through freshly
activated alumina, and then distilled from CaH2 with 2,6-di-
tert-butyl-p-cresol. Other solvents of spectroscopic grade were
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4
P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 3 9 7 7 – 3 9 8 4
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Scheme 1 Synthetic scheme of a series of nine carbazole (Donor)–cyclohexane (Spacer)–acceptor (Acceptor) molecules (Cz–S–A): A ¼ CF3 (1), 5F
(2), Cin (3), 2CF3 (4), TP (5), CN (6), DEF (7), NO2 (8), and 2NO2 (9).
used without further purification. The polymer used here was
cyanoethylated O-(2-hydroxypropyl)cellulose (CN-HPC),
which was kindly provided by Professor Takeaki Miyamoto
and Associate Professor Yoshinobu Tsujii.
remove the melt of cis-1,4-cyclohexylenedimethylene diacetate.
The residue was recrystallized from acetone and from metha-
nol to give trans-1,4-cyclohexylenedimethylene diacetate: yield
82.5 g (52.1%); mp 69.0–72.5 1C; IR (KBr) 2950, 2875 (nCH ),
3
2925, 2850 (nCH ), 1750 (nCQO), 1240 (nC–C–O–C), 1040
2
(nC–O) cmꢀ1
.
Synthesis of trans-1,4-cyclohexylenedimethylene diacetate. A
solution of acetic anhydride (160 g) was added dropwise to a
mixture of cis- and trans-cyclohexanedimethanol (100 g) stirred
at 140–165 1C, with the evolution of acetic acid. After the
removal of acetic acid, the solution was heated at 200 1C to
remove the residual acetic anhydride and cooled to room
temperature. The resulting white crystals were collected and
dried to afford a mixture of cis- and trans-1,4-cyclohexylene-
dimethylene diacetate. The mixture was heated at 35 1C to
Synthesis of trans-1,4-cyclohexanedimethanol. The trans-dia-
cetate (82.5 g) was added to 10 wt.% aqueous NaOH (825 g),
and refluxed for 10 h. After cooling to room temperature, the
reaction mixture was neutralized with aqueous HCl. The
reaction product was extracted into chloroform and the solvent
was evaporated. The residual powder was recrystallized from
ether to give trans-1,4-cyclohexanedimethanol: yield 24.1 g
3978
P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 3 9 7 7 – 3 9 8 4
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4

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(46.3%); mp 62.0–64.0 1C; IR (KBr) 3300 (nOH), 2920 (nCH ),
H, 4.55; N, 2.87; F, 19.49; found: C, 66.78; H, 4.33; N, 2.86;
F, 19.51%.
2
2850 (nCH ), 1040 (nC–O) cmꢀ1
.
2
1
Synthesis of trans-1,4-cyclohexanedimethanol monotosylate.
The dimethanol (30 g) was dissolved in a mixture solution of
chloroform (150 mL) and pyridine (150 mL) at 0 1C. To the
solution was added dropwise a mixture solution of chloroform
(100 mL) and pyridine (150 mL) with p-toluenesulfonyl chlo-
ride (39.6 g). After stirring for 4 h, the solvent was evaporated
below 35 1C. The reaction product was dissolved in excess
chloroform solution, washed with dilute aqueous H2SO4,
aqueous NaHCO3, and water. After the chloroform layer
was dried over anhydrous Na2SO4, the solvent was evaporated.
The residue was dissolved in methanol solution, cooled at 0 1C,
filtrated, and evaporated to afford yellow oil of trans-1,4-
cyclohexanedimethanol monotosylate: yield 34.2 g (55.1%);
1H NMR (CDCl3, 90 MHz) d 0.80–1.80 (m, 10H, cyclohexane
ring), 2.40 (s, 3H, CH3), 3.40 (t, 2H, CH2), 3.80 (d, 2H, CH2),
7.30 (d, J ¼ 6.0 Hz, 2H, ArH), 7.72 (d, J ¼ 6.0 Hz, 2H, ArH);
Cz–S–Cin (3). H NMR (CDCl3, 90 MHz) d 0.90–1.88 (m,
10H, cyclohexane ring), 4.00 (d, J ¼ 4.0 Hz, 2H, CH2), 4.16 (d,
J ¼ 4.0 Hz, 2H, CH2), 6.32 (s, 1H, ring) 4.00 (d, J ¼ 4.0 Hz,
2H, CH ), 4.16 (d, J ¼ 4.0 Hz, 2H, CH ), 6.32 (s, 1H, ꢀCH ),
Q
6.50 (s, 1H, CH–), 7.16–7.60 (m, 10H, ArH), 7.76 (s, 1H,
2
2
Q
ArH), 8.10 (d, J ¼ 4.8 Hz, 2H, ArH); IR (KBr) 2925, 2850
(nCH ), 1710 (nCQO), 1640 (nCQC), 1330 (nC–C–O), 1200 (nC–O),
2
750 (dAr–H) cmꢀ1; elemental anal. calcd: C, 82.24; H, 6.90; N,
3.31; O, 7.56; found: C, 82.36; H, 6.99; N, 3.35; O, 7.42%.
Cz–S–2CF3 (4). 1H NMR (CDCl3, 90 MHz) d 0.82–1.86 (m,
10H, cyclohexane ring), 4.13 (d, 4H, CH2), 7.08–7.52 (m, 8H,
ArH), 8.10 (d, J ¼ 4.8 Hz, 2H, ArH), 8.42 (s, 1H, ArH); IR
(KBr) 2925, 2850 (nCH ), 1740 (nCQO), 1280 (nC–C–O), 1250
2
(nC–O), 1240 (nC–O–C), 1150 (nCF ), 750 (dAr–H) cmꢀ1; elemental
anal. calcd: C, 65.28; H, 4.72; N, 2.63; F, 21.37; found: C,
65.39; H, 4.66; N, 2.59; F, 21.18%.
3
IR (KBr) 3550, 3375 (nOH), 2920, 2850 (nCH ), 1750 (nCQO),
2
1240 (nC–C–O–C), 1040 (nC–O) cmꢀ1
.
1
Cz–S–TP (5). H NMR (CDCl3, 90 MHz) d 0.92–1.90 (m,
Synthesis of trans-4-(carbazole-9-yl)methylcyclohexylmetha-
nol. Carbazole (6.9 g) was dissolved in a solution of N,N-
dimethylformamide (DMF, 50 mL). To the solution was added
sodium hydride (2.0 g) with stirring at 60 1C for 1 h. To the
solution cooled to room temperature, a DMF solution (20 mL)
of trans-1,4-cyclohexanedimethanol monotosylate (12.3 g) was
added dropwise and stirred for 2 h. The reaction solvent was
changed to dichloromethane from DMF. The mixture was
washed with water three times. After the dichloromethane
layer was dried over CaCl2, the solvent was evaporated. The
residue was recrystallized from benzene–hexane solution to
give trans-4-(carbazole-9-yl)methylcyclohexylmethanol: yield
2.5 g (20.7%); 1H NMR (CDCl3, 90 MHz) d 0.64–1.84
(m, 10H, cyclohexane ring), 3.20 (d, J ¼ 4.0 Hz, 2H, CH2),
4.12 (d, J ¼ 4.0 Hz, 2H, CH2), 7.12–7.44 (m, 6H, ArH), 8.10 (d,
10H, cyclohexane ring), 3.90 (s, 3H, CH3), 4.12 (m, 4H, CH2),
7.12–7.28 (m, 6H, ArH), 8.04–8.12 (m, 6H, ArH); IR (KBr)
2925, 2850 (nCH ), 1720 (nCQO), 1450 (nOCH ), 1270 (nC–C–O),
2
3
1120 (nC–O), 750 (dAr–H) cmꢀ1; elemental anal. calcd: C, 76.46;
H, 6.42; N, 3.08; O, 14.05; found: C, 76.43; H, 6.41; N, 3.05;
O, 14.17%.
1
Cz–S–CN (6). H NMR (CDCl3, 90 MHz) d 0.93–1.90 (m,
10H, cyclohexane ring), 4.13–4.24 (m, 4H, CH2), 7.16–7.50 (m,
6H, ArH), 7.72 (d, J ¼ 6.0 Hz, 2H, ArH), 8.10 (d, 4H, ArH);
IR (KBr) 2925, 2850 (nCH ), 1720 (nCQO), 1280 (nC–C–O),
2
750 (dAr–H) cmꢀ1; elemental anal. calcd: C, 79.59; H, 6.20; N,
6.63; O, 7.57; found: C, 79.77; H, 6.08; N, 6.48; O, 7.40%.
J ¼ 4.8 Hz, 2H, ArH); IR (KBr) 3375 (nOH), 2920, 2850 (nCH ),
2
1
1450 (Ar skeleton vibration), 750 (dAr–H) cmꢀ1
.
Cz–S–NO2 (8). H NMR (CDCl3, 90 MHz) d 0.92–1.90 (m,
10H, cyclohexane ring), 4.16 (d, 4H, CH2), 7.12–7.48 (m, 6H,
ArH), 8.08–8.32 (m, 6H, ArH); IR (KBr) 2930, 2850 (nCH ),
2
Synthesis of Cz–S–A (Cz–S–DEF excluded). Eight of the
nine Cz–S–A molecules (Cz–S–DEF excluded) were synthe-
sized by the esterification reaction of trans-4-(carbazole-9-
yl)methylcyclohexylmethanol with acyl chloride having an
acceptor moiety. To an acetone solution of trans-4-(carba-
zole-9-yl)methylcyclohexylmethanol and one molar equivalent
of pyridine was added one molar equivalent of acyl chloride
having an acceptor moiety and refluxed for 2 h. The reaction
solvent was changed to dichloromethane from acetone. The
mixture was washed with dilute aqueous HCl three times and
water two times. After the dichloromethane layer was dried
over CaCl2, the solvent was evaporated. The product was
purified by silica-gel column chromatography and recrystalli-
zation from a dichloromethane–hexane solution.
1720 (nCQO), 1525 (nNO ), 1340 (nNO ), 1260 (nC–C–O), 750
2
2
(dAr–H) cmꢀ1; elemental anal. calcd: C, 73.28; H, 5.92; N,
6.33; O, 14.46; found: C, 73.15; H, 5.78; N, 6.30; O, 14.57%.
Cz–S–2NO2 (9). 1H NMR (CDCl3, 90 MHz) d 0.92–1.90 (m,
10H, cyclohexane ring), 4.16–4.30 (m, 4H, CH2), 7.16–7.50 (m,
6H, ArH), 8.10 (d, J ¼ 4.8 Hz, 2H, ArH), 9.10–9.20 (m, 3H,
ArH); IR (KBr) 2930, 2850 (nCH ), 1720 (nCQO), 1525 (nNO ),
2
2
1340 (nNO ), 1260 (nC–C–O), 750 (dAr–H) cmꢀ1; elemental anal.
2
calcd: C, 66.52; H, 5.17; N, 8.62; O, 19.69; found: C, 66.24; H,
5.03; N, 8.64; O, 19.42%.
Synthesis of Cz–S–DEF. To a solution of carbon tetrachlor-
ide with trans-4-(carbazole-9-yl)methylcyclohexylmethanol
(1.2 g) and fumaryl chloride (2.5 g) was added AlCl3 (0.84 g).
After the solution was refluxed with stirring for 30 min, ethanol
(0.6 g) was added to the solution and the reflux was further
continued for 30 min. The product was purified by silica-gel
column chromatography and recrystallization from hexane.
1
Cz–S–CF3 (1). H NMR (CDCl3, 90 MHz) d 0.94–1.88 (m,
10H, cyclohexane ring), 4.10–4.20 (m, 4H, CH2), 7.13–7.46 (m,
8H, ArH), 7.68 (d, J ¼ 6.0 Hz, 2H, ArH), 8.10 (d, 4H, ArH);
IR (KBr) 2920, 2850 (nCH ), 1720 (nCQO), 1460 (Ar skeleton
2
vibration), 1320 (nC–O), 750 (dAr–H) cmꢀ1; elemental anal.
calcd: C, 72.24; H, 5.63; N, 3.01; F, 12.25; found: C, 72.49;
H, 5.39; N, 2.90; F, 12.28%.
Cz–S–DEF (7). 1H NMR (CDCl3, 90 MHz) d 0.84–1.90 (m,
13H, cyclohexane ring, CH3), 3.92–4.32 (m, 6H, CH2), 6.80 (s,
1
Cz–S–5F (2). H NMR (CDCl3, 90 MHz) d 1.02–1.88 (m,
10H, cyclohexane ring), 4.18 (d, 4H, CH2), 7.16–7.48 (m, 6H,
2H, CH CH), 7.12–7.44 (m, 6H, ArH), 8.08 (d, J ¼ 4.8 Hz,
Q
2H, ArH); IR (KBr) 2920, 2850 (nCH ), 1725 (nCQO), 1300
2
ArH), 8.10 (d, J ¼ 4.8 Hz, 2H, ArH); IR (KBr) 2925, 2850
(nQ CH, nC–C–O–C), 750 (dAr–H) cmꢀ1; elemental anal. calcd: C,
74.44; H, 6.97; N, 3.34; O, 15.26; found: C, 74.06; H, 6.98; N,
3.40; F, 14.00%.
(nCH ), 1740 (nCQO), 1500 (Ar skeleton vibration), 1320 (nC–O),
2
1240 (nC–F), 750 (dAr–H) cmꢀ1; elemental anal. calcd: C, 66.52;
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4
P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 3 9 7 7 – 3 9 8 4
3979

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Table 1 Potential difference between oxidation of Cz and reduction of A moieties
A moieties
CF3
3.05
5F
Cin
2CF3
2.89
TP
CN
DEF
2.59
NO2
2.04
2NO2
1.89
Eox ꢀ EredA/eV
D
2.99
2.97
2.84
2.80
Ag1. Scan rate was 100 mV sꢀ1. Direct-current polarogram
was obtained by a Yanagimoto model p-8 polarograph. Height
of the mercury reservoir of the dropping mercury electrode was
60 cm. An electrode of Ag/Ag1 (0.1 mol Lꢀ1) was used as the
reference electrode, which has the potential 0.36 V versus SCE
in the solution of 0.1 mol Lꢀ1 of tetra-n-butylammonium
iodide in MeCN. Polarographic measurements were all carried
out in MeCN containing 0.1 mol Lꢀ1 of tetra-n-butylammo-
nium iodide. Temperature of the electrolytic cell was main-
tained at 25 1C. The oxygen dissolved in the electrolytic
solution was removed by bubbling pure nitrogen gas through
2.2. Sample preparation
Samples dissolved in solvents were degassed by the freeze–
pump–thaw method and sealed in a 1 cm quartz cell. The
concentration of Cz compounds in the solutions was kept in
the order of 10ꢀ5 mol Lꢀ1 to prevent intermolecular inter-
action. Polymer films of CN-HPC doped with carbazole
compounds were prepared by the solvent-casting method.
The Cz compounds were dissolved in MeCN with the CN-
HPC so that the concentration of Cz compounds in the final
polymer films was in the order of 10ꢀ3 mol Lꢀ1. The polymer
solution was dropped onto a quartz plate (15 ꢁ 15 ꢁ 1 mm3),
dried for 2 days under atmospheric pressure and for 1 week in a
desiccator under reduced pressure at room temperature. The
polymer films had a thickness of about 15 mm.
D
A
the solution. The differences between Eox and Ered are
summarized in Table 1.
3. Results and discussion
3.1. Fluorescence spectra of Cz–S–A dyads in solutions
2.3. Absorption and fluorescence measurements
Fig. 1 shows the fluorescence spectra of EtCz and Cz–S–A
molecules in MeCN at room temperature. The fluorescence
spectra of Cz–S–A molecules were the same as that of the
reference compound EtCz and were almost mirror images of
absorption spectrum of EtCz. This proves that there are no
intra- and intermolecular interactions between Cz and A
moieties in the ground state. From the absorption and fluor-
escence spectra, the energy level of the lowest excited singlet
state of EtCz E(S1) was evaluated to be 3.56 eV. The fluores-
cence intensity of Cz–S–A was weak in comparison with that of
EtCz. This fluorescence quenching was ascribed not to energy
transfer but to electron transfer from the excited Cz moiety to
the A moieties, because there is no spectral overlap between
fluorescence of the Cz donor and absorption of the A moieties:
there is no absorption of the A moieties in the wavelength
range of 4300 nm where absorption spectra of Cz–S–A are
essentially the same as that of EtCz shown in Fig. 1.
Steady-state absorption and emission spectra were measured at
room temperature in a 1 cm quartz cell with a spectrophoto-
meter (Hitachi, U-3500) and a fluorescence spectrophoto-
meter (Hitachi, 850 or F-4500), respectively. Fluorescence
decay was measured by the time-correlated single-photon-
counting method. The excitation light source was third har-
monic pulses (295 nm) generated from
a mode-locked
Ti:sapphire laser (Spectra-Physics, Tsunami 3950) that was
pumped by an Ar1 laser (Spectra-Physics, BeamLok 2060).
The fluorescence emission was collected at 901 relative to the
incident excitation laser light pathway and detected by a
photomultiplier tube (PMT; Hamamatsu Photonics, R3234)
through a monochromator (Ritsu, MC-10N) or by a micro-
channel plate-photomultipiler tube (MCP-PMT; Hamamatsu
Photonics, R3809), with a polarizer set at a magic angle of
54.751 to the vertically polarized excitation light and a cut-off
filter (UV-360 or UV-34) for the excitation light. The details of
this apparatus have been described elsewhere.15 The total
instrument response function has an FWHM of ca. 750 ps
for the PMT system and ca. 60 ps for the MCP-PMT system.
The decay data were fitted with the sums of a function that
were convoluted with the instrument response function by the
nonlinear least-squares method.
The temperature of samples sealed in a 1 cm quartz cell was
controlled in a heat bath of isopentane or water and measured
with a thermocouple. For the measurement below 0 1C, the
quartz cell was dipped in a Dewar cell filled with isopentane
precooled by liquid nitrogen and the spontaneous heating rate
was slow enough to measure within a temperature precision
of ꢂ1 1C. For the measurement above 0 1C, the quartz cell was
dipped in a Dewar cell filled with water equipped with a heater
to control the temperature. Temperature of film samples cast
on a quartz plate was controlled in a cryostat (Iwatani Plantech
Corp., CRT510) with PID temperature control unit (Scientific
Instruments, Model 9650).
As shown in Fig. 2, the fluorescence of Cz–S–A decayed
rapidly compared with that of EtCz. The fluorescence decay
I(t) of Cz–S–A in solution was well fitted with a single or
double exponential function: I(t) ¼ SAi exp(ꢀt/ti). The lifetime
of the minor component is ascribable to a Cz molecule having
no A moiety, because it was similar to that of EtCz. The minor
fraction was less than 5%. Thus, the CS rate constant kCS was
ꢀ1
calculated by kCS ¼ tꢀ1 ꢀ t0 where t0 is the fluorescence
2.4. Electrochemical measurements
D
The standard potential of the one electron oxidation Eox of
A
EtCz and reduction Ered of all the Cz–S–A compounds used
here were determined by the cyclic voltammetry and polaro-
graphy techniques, respectively. The cyclic voltammogram was
measured in MeCN containing 0.1 mol Lꢀ1 of tetra-n-butyl-
ammonium perchlorate as the supporting electrolyte. Refer-
ence electrode was Ag in MeCN containing 0.01 mol Lꢀ1 of
Fig. 1 Fluorescence spectra of EtCz and Cz–S–A in MeCN at room
temperature: thick lines EtCz; thin lines Cz–S–CF3 (1), Cz–S–Cin (3),
Cz–S–TP (5), and Cz–S–DEF (7) from top to bottom (solid lines).
Absorption spectra of EtCz in MeCN at room temperature
(broken line).
3980
P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 3 9 7 7 – 3 9 8 4
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4

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Fig. 2 Fluorescence decay curves of EtCz (open circles) and Cz–S–TP
(5) (closed circles) in MeCN at room temperature. Excitation wave-
length was 295 nm. Monitor wavelength was 368 nm. Broken line
shows an excitation laser pulse: instrumental response function with an
FWHM of 750 ps.
Fig. 3 Free energy gap dependence of the charge separation rate kCS
of a series of nine Cz–S–A molecules in various solvents: square DBE;
triangle MTHF; circle MeCN. Solid lines is the theoretical prediction
calculated by using eqn. (3) with the following parameters: lV
¼
0.56 eV, V ¼ 5.8 cmꢀ1, io ¼ 1300 cmꢀ1. Broken line is the theoretical
prediction of the rate kCS in DBE calculated by using eqn. (2) with the
same parameters.
lifetime of EtCz and t the major component of the fluorescence
lifetime of Cz–S–A. The fluorescence lifetimes and kCS are
summarized in Table 2. On the other hand, the fluorescence
spectra of Cz–S–A molecules in a polymer film were also the
same as that of Cz–12–Cz and the intensity was quenched
compared with that of Cz–12–Cz, indicating that intramole-
cular CS from the excited Cz to the A moieties also occurred
even in a polymer film.
The free energy gap for the photoinduced CS (ꢀDGCS) and
reorganization energy for solvent (lS) were calculated by
eqn. (4) and (5), respectively,
ꢀDGCS ¼ EðS1Þ ꢀ ðEoDx ꢀ ErAed
Þ
ꢀ
ꢁ
ꢂꢁ
ꢂꢃ
e2
1
1
2
1
1
1
1
þ
þ
þ
ꢀ
ð4Þ
ð5Þ
4pe0 eS rDA
rD rA
37:5 eS
3.2. Solvent polarity effects of photoinduced CS in solutions
ꢁ
ꢂꢁ
ꢂ
e2
1
1
1
1
1
First, we investigated the intramolecular CS of D–S–A mole-
cules in various solvents. Fig. 3 shows the free energy gap
(ꢀDGCS) dependences of the kCS for D–S–A molecules in
various solvents. Solid and broken curves in the figure repre-
sent the theoretical prediction of the following ET formula. In
a classical ET formula of the Marcus theory,1,2 the Franck–
Condon factor FCCC can be expressed by eqn. (2), where both
orientational motions of solvents and vibrational motions of
the reactants are treated as a classical mode. In a single
quantum mode formula in the Jortner theory,16,17 the
Franck–Condon factor FCCQ can be expressed by eqn. (3),
where the orientational motion of solvents is treated as a
classical mode and the vibrational motion of reactants is
treated as a quantum one.
lS ¼
þ
ꢀ
ꢀ
4pe0 2rD 2rA rDA
e
eS
1
where e is the elementary charge, e0 the vacuum permittivity, eS
dielectric constant of the matrix, rDA separation distance
between donor (Cz) and acceptor (A) (12.2 A), rD and rA
spherical radii of donor and acceptor moieties (4.5 and 3.7 A),
respectively, and eN optical dielectric constant of the matrix,
which is equal to the square of the refractive index of the
matrix n2. In the eS range from 3.06 (DBE) to 37.5 (MeCN), as
shown in Fig. 3, kCS increased with increasing ꢀDGCS, indicat-
ing that CS is in the normal region of the Marcus theory. In a
non-polar solvent such as Hex, CS was not observed except for
DEF, NO2, and 2NO2 with large ꢀDGCS. This finding indicates
that CS in solutions is promoted by the orientational fluctua-
tions of polar solvents. The Marcus plots of kCS of Cz–S–A in
various solvents were well explained by eqn. (3) rather than
eqn. (2) with the following parameters: the electronic coupling
matrix element V ¼ 5.8 cmꢀ1, the reorganization energy for
intramolecular vibration of Cz–S–A molecules lV ¼ 0.56 eV,
2p
ꢀh
2
kCC
¼
¼
jVj FCCC
"
#
2
1
ðlS þ lV þ DGCS
4ðlS þ lVÞkBT
Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
FCCC
exp ꢀ
4pðlS þ lVÞkBT
and the vibrational energy io ¼ 1300 cmꢀ1 18–21
.
Thus, we
ð2Þ
conclude that intramolecular CS in solutions results from
vibrational motion of Cz–S–A molecules as well as classical
solvent motions.
2p
ꢀh
2
kCQ
¼
¼
jVj FCCQ
1
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4plSkBT
FCCQ
3.3. Temperature dependence of photoinduced CS in MTHF
"
#)
ꢀ
2
Sm expðꢀSÞ
ðlS þ mꢀho þ DGCS
4lSkBT
Þ
X
The CS rate depends on both dielectric constant eS of the
matrix and temperature. As shown by eqn. (4) and (5), both lS
and ꢀDGCS decrease with the decrease in eS, but lS þ DGCS is
independent of eS. Thus, kCS should decrease with the decrease
ꢁ
exp ꢀ
m!
m
ð3Þ
Table 2 Fluorescence lifetime and CS rate constant of Cz–S–A molecules in MeCN at room temperature
A moieties
EtCz
15.0
CF3
5F
Cin
2CF3
TP
CN
DEF
NO2
2NO2
t/ns
Log kCS
12.3
7.2
14.0
6.7
9.0
7.6
b
8.6
7.7
6.0a
8.0
4.2a
8.2
2.4a
8.6
0.26a
9.6
0.20a
9.7
b
a
ꢀ1
.
Major component (495%) of double exponential fitting. kCS ¼ tꢀ1 ꢀ t0
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4
P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 3 9 7 7 – 3 9 8 4
3981

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Fig. 5 Free energy gap dependence of the charge separation rate kCS
of a series of five Cz–S–A molecules in CN-HPC films at room
temperature: Cz–S–Cin (3), Cz–S–2CF3 (4), Cz–S–TP (5), Cz–S–CN
(6), and Cz–S–2NO2 (9). The solid curve is the theoretical prediction
Fig. 4 Upper: temperature dependence of dielectric constant eS of
MTHF.22 Bottom: kCS of Cz–S–Cin (3) (closed circles) and Cz–S–CN
(6) (open circles) in MTHF. Temperature range of the measurements
was from 183 to 296 K. Broken and solid curves are the theoretical
prediction calculated by using eqn. (2) and (3), respectively, with the
calculated by using eqn. (3) with the following parameters: lV
¼
0.56 eV, V ¼ 3.5 cmꢀ1, io ¼ 1300 cmꢀ1. Dielectric constant of CN-
following parameters: lV ¼ 0.56 eV, V ¼ 5.8 cmꢀ1, io ¼ 1300 cmꢀ1
.
HPC was measured at 1 MHz.
in eS at a temperature. On the other hand, kCS should increase
with increasing temperature at a fixed dielectric constant. In
the temperature range from 183 to 296 K, as shown in Fig. 4,
groups at room temperature above the Tg sufficient to fluctuate
the energy of the D–S–A system, which leads to ET.
k
CS of Cz–S–Cin and Cz–S–CN in MTHF gradually increased
3.5. Temperature dependence of photoinduced CS in a polymer
solid
with increasing temperature while dielectric constant eS of
MTHF decreased with increasing temperature.22 This shows
that thermal activation of the intramolecular kCS in a solution
is governed by temperature rather than eS of solvents. Broken
and solid lines in the figure are the theoretical prediction
calculated by eqn. (2) and (3), respectively. The temperature
dependence of kCS was well reproduced by eqn. (3) but not by
the classical ET theory (eqn. (2)). These findings shows that the
intramolecular CS of Cz–S–A in a solution is thermally
activated mainly by orientational motions of a polar solvent
but intramolecular vibrational motions of the reactants also
contribute to the activation.
As mentioned in the previous section, the fluorescence decay of
Cz–S–A in a polymer solid was well fitted with a three
exponential function. Fig. 6 shows the temperature dependence
of the lifetime ti of each fraction of Cz–S–CN over a tempera-
ture range from 100 to 400 K. One of them (open circles) was
independent of temperature and the lifetime was similar to that
of Cz–12–Cz. This fraction represented less than 5% of the
whole. Thus, this minor component was ascribed to a Cz
molecule having no A moiety. The lifetime of the other two
components decreased above Tg. A similar tendency was
observed for the other Cz–S–A dyads. Here we calculated the
averaged lifetime hti of Cz–S–A from the major two
components.
The relaxation time of rotational motions of polar groups in
polymer solids varies widely. Consequently, it is difficult to
evaluate eS of polymer solids: the dielectric constant of polymer
solids significantly depends on the measuring frequency. Fig. 7
shows the temperature dependence of dielectric constant e
evaluated by dielectric relaxation measurement. The value of
3.4. Free energy gap dependence of photoinduced CS in
a polymer solid
Next, we investigated the intramolecular CS in a polymer solid
where orientational fluctuations of polar groups are highly
restricted compared with those in a solution. Owing to in-
homogeneity of polymer solids, the fluorescence decay I(t) of
Cz–S–A in a polymer solid was well fitted with a sum of three
exponential functions: I(t) ¼ SAiexp(t/ꢀti). Since lifetime of
the minor component (less than 5%) is ascribable to a Cz
molecule having no A moiety, ꢀth1 e CS rate constant kCS was
calculated by kCS ¼ htiꢀ1 ꢀ t0 where t0 is the fluorescence
lifetime of EtCz and hti the average of major two components
in the fluorescence lifetime of Cz–S–A. Fig. 5 shows Marcus
plots of a series of five Cz–S–A molecules in CN–HPC films at
room temperature. As in a solution system, kCS increased with
increasing ꢀDGCS. Although the free energy dependence of kCS
was roughly explained by eqn. (3) with the same parameters as
those for a solution system, it was reproduced better with
V ¼ 3.5 cmꢀ1 smaller than that for a solution system
(5.8 cmꢀ1). This is probably because the mean separation
distance between Cz and A moieties in a solution is shorter
than that in a polymer solid because the conformational
change in a solution is so rapid that the mean separation
distance effectively decreases in the time scale of the photo-
induced CS. The CN–HPC polymer has a polar cyano group at
the end of the side chain and has a glass transition temperature
(Tg) of 248 K. Thus, there exist rotational motions of polar
Fig. 6 Temperature dependence of the lifetime ti of each fraction in
the decay analysis for Cz–S–CN (6). Open circles are the minor fraction
in the three decay components, being less than 5%. This fraction was
neglected in the lifetime evaluation: see text.
3982
P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 3 9 7 7 – 3 9 8 4
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4

View Article Online
temperature.16,17 The thick line in Fig. 7 is calculated by
eqn. (6) with a dielectric constant of 3.11.
2p
ꢀh
2
kQQ
¼
¼
jVj FCQQ
exp½ꢀSLð2nL þ 1Þ ꢀ SHð2nH þ 1Þꢃ
FCQQ
ꢀhoL
pðmÞ
ꢁ
ꢂ
n
o
X
2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
nL þ 1
ꢁ
ꢁ
ꢄ
I
2SL nLðnL þ 1Þ
jpðmÞj
nL
ꢂ
m
m
2
ꢁ
n
o
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
nH þ 1
I
2SH nHðnH þ 1Þ
jmj
nH
ꢁ
ꢂ
ꢅꢀ1
ꢄ
ꢁ
ꢂ
ꢅꢀ1
ꢀhoL
kBT
ꢀhoH
kBT
nL ¼ exp
ꢀ 1 ; nH
¼
exp
ꢀ 1
;
DGCS þ mꢀhoH
ꢀhoL
pðmÞ ¼ ꢀ
ð6Þ
The theoretical line well reproduced temperature independent
of kCS observed below Tg. Another possibility is that ET may
be no longer in thermal equilibrium at low temperatures,
because the relaxation time of most orientational motions of
polar groups is longer than the lifetime of D–S–A molecules in
the excited state. The non-thermal equilibrium ET also could
result in temperature independent ET at low temperatures.10,11
Although both situations are possible for ET in a polymer
solid, the former is probably the major cause of the tempera-
ture independence of kCS because there are some polar groups
with motions fast enough to cause ET even in a polymer solid,
which are probably in the thermal equilibrium.
Fig. 7 Top: temperature dependence of the dielectric constant e of
CN–HPC films over the temperature range from 77 to 380 K. Broken
and solid lines are the dielectric constants e measured by dielectric
relaxation measurement at a frequency of 20 Hz (broken) and 1 MHz
(solid). Bottom: temperature dependence of the charge separation rate
kCS of Cz–S–2CF3 in CN-HPC films over the temperature range from
100 to 400 K. Broken and solid lines are the theoretical prediction of
kCS calculated by using eqn. (3) with dielectric constants e evaluated by
dielectric relaxation measurement at a frequency of 20 Hz (broken) and
1 MHz (solid). Thick line is calculated by eqn. (6) with following
parameters: SLioL ¼ 0.31 eV, SHioH ¼ 0.56 eV, V ¼ 3.5 cmꢀ1
,
ioH ¼ 1300 cmꢀ1, ioL ¼ 500 cmꢀ1, e ¼ 3.11.
4. Conclusions
e was nearly constant from 100 to 248 K and steeply increased
at 248 K, which corresponds to the Tg. As mentioned above, e
depends on the measuring frequency: e measured at 20 Hz was
larger than that at 1 MHz.
Photoinduced CS of carbazole–acceptor dyads (Cz–S–A) in
solutions is caused by not only classical solvent motions but
also vibrational motions of the reactant. The temperature
dependence of CS in solutions results from mainly classical
solvent motions but also the quantum vibrational motions over
a wide temperature range. These results could be quantitatively
explained by a single quantum mode ET formula. As for the
photoinduced ET in a polymer solid, the CS of Cz–S–A was
also observed over a wide temperature range although most
motions are highly restricted compared with those in a solu-
tion. Above Tg, CS was explained with dielectric constants at a
high frequency by the same ET formula as that in a solution.
Below Tg, CS was independent of temperature, indicating that
ET is caused by nuclear tunneling. We conclude that these
features of ET in a polymer solid are due to the presence of a
variety of motions over a wide time domain.
Broken and solid lines in Fig. 7 show the theoretical predic-
tion of kCS calculated by eqn. (3) with the e measured at 20 Hz
and 1 MHz, respectively. Above the Tg, temperature depen-
dence of kCS was well reproduced by the solid line (1 MHz)
rather than the broken line (20 Hz). This is because CS
occurred in the time domain from sub-nanoseconds to a
hundred nanoseconds, which corresponds to 10 to 100 MHz
in the frequency domain. In other words, the slow motion of a
polar group in a polymer solid does not contribute to ET but
the fast motion of a polar group effectively causes ET. This
finding shows that a variety of motions of polar groups in
polymer solids allow ET although most of the motions are
restricted compared with those in a solution.
Below the Tg, kCS was nearly constant and independent of
temperature whereas the theoretical prediction by eqn. (3)
monotonously decreased with decreasing temperature. The
single-mode formula of eqn. (3) treats orientational motions
of polar groups as a classical mode and vibrational motions of
the reactant molecule as a quantum one. The classical mode
results in temperature dependence of the Arrhenius type. Thus,
this deviation shows that the classical mode has no contribu-
tion any more to intramolecular CS in a polymer solid. In fact,
e was nearly constant below the Tg, indicating that most
orientational motions of polar cyano groups are frozen. It is
worthwhile to note that ET still occurs even below Tg where
orientational motions of polar groups are highly restricted.
This tendency is similar to ET in the photosynthetic bacterium
Chromatium.23,24 In the low temperature range, ET is
probably caused by a high-frequency quantum mode such as
vibrational motions of the reactant molecule or the polar cyano
groups of the polymer matrix. These high-frequency motions
cause ET by nuclear tunneling, which is independent of
Acknowledgements
This work was supported by the Murata Science Foundation
and the Takeda Science Foundation. We would like to thank
Professor Takeaki Miyamoto and Associate Professor
Yoshinobu Tsujii for provision of CN-HPC and DSC measure-
ment of CN-HPC and Dr Yasuo Kita for dielectric relaxation
measurement of CN-HPC.
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T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4