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J. Phys. Chem. 1996, 100, 16466-16471
ARTICLES External Electric Field Effects on Fluorescence in an Electron Donor and Acceptor System: Ethylcarbazole and Dimethyl Terephthalate in PMMA Polymer Films Nobuhiro Ohta,* Masaru Koizumi, Shiro Umeuchi, Yoshinobu Nishimura, and Iwao Yamazaki Department of Molecular Chemistry, Graduate School of Engineering, Hokkaido UniVersity, Sapporo 060, Japan ReceiVed: April 17, 1996; In Final Form: July 17, 1996X
Fluorescence of ethylcarbazole doped in PMMA polymer films is quenched by an external electric field in the presence of dimethyl terephthalate, indicating that the rate of the intermolecular electron transfer from a photoexcited molecule of ethyl carbazole to dimethyl terephthalate is enhanced by an applied electric field. The field effect on the electron transfer as well as the transfer rate at zero field increases with a decrease of the electron donor-acceptor distance. The free energy change of the electron transfer reaction from photoexcited ethylcarbazole to dimethyl terephthalate is estimated to be about -0.7 eV in PMMA polymer films, based on the external electric field effect on fluorescence intensity of ethylcarbazole combined with the fluorescence lifetime. The molecular polarizability of fluorescent exciplex formed in a mixture of ethylcarbazole and dimethyl terephthalate is also estimated, based on the Stark shift of the exciplex fluorescence.
1. Introduction It is well-known that the electron transfer rate depends on the energy gap between the reactant and product states of the initial electron transfer processes.1-5 Since a radical-ion pair produced by electron transfer processes usually has a large dipole moment, the energy gap between the reactant and product (radical-ion pair) may be to a great extent influenced by an external electric field, F. Then, the electron transfer rate is expected to be influenced by F, depending on the magnitude of the electric dipole moment of the radical-ion pair and the orientation of the dipole moment relative to the direction of the applied field. Radical-ion pairs produced by the electron transfer are recombined by the Coulomb attraction. Electric field, which biases the Coulomb attraction, as well as Brownian motion may lead to dissociation of radical-ion pairs in competition with the attraction.6 Thus, the electric field effects on electron transfer processes are expected in two mechanisms: one is the field effect on the initial step of electron transfer and the other is the effect on dissociation or recombination process of the produced radical-ion pair. Poly-N-vinylcarbazole (PVCz) film doped with an electron acceptor is well-known as a typical photoconductive polymer, and the external electric field effects on fluorescence of this polymer film have been extensively examined in order to elucidate the photocarrier generation mechanism.7-10 Electric field effects on fluorescence have been examined also in other organic photoconductors,11-15 and the electric field has been confirmed to assist dissociation of radical-ion pairs into free carriers in the photoconductors. The field effects on the charge separation in photosynthetic reaction center are interpreted in terms of the field effect on the initial step of electron transfer.16 In contrast with the field effects on dissociation of radical pairs, however, the number of studies concerning the field effect on the initial step of intra- or intermolecular electron transfer processes is very limited, though charge transfer elementary X
Abstract published in AdVance ACS Abstracts, September 15, 1996.
S0022-3654(96)01125-2 CCC: $12.00
process and related one at zero field have been discussed in detail on the basis of the laser photolysis studies.17 A mixture of N-ethylcarbazole (ECZ) and dimethyl terephthalate (DMTP) doped in poly(methyl methacrylate) (PMMA) exhibits intermolecular exciplex fluorescence besides the monomer fluorescence of ECZ following excitation into ECZ, suggesting that a photoinduced intermolecular electron transfer occurs from ECZ to DMTP. Further, the intensity ratio between the monomer fluorescence of ECZ and exciplex fluorescence depends on the concentration of DMTP, suggesting that the intermolecular electron transfer rate depends on the distance between electron donor and acceptor molecules, i.e., the distance between ECZ and DMTP. In the present study, external electric field effects on fluorescence of ECZ doped in PMMA polymer films with DMTP having different concentrations have been examined with particular regard to the field effects on the initial step of the intermolecular electron transfer from ECZ to DMTP. 2. Experimental Section ECZ (Nakarai) was recrystallized several times from an ethanol-benzene solution. DMTP (Nakarai) was recrystallized several times in benzene and then vacuum sublimated. PMMA (MW ) 120 000, Aldrich) was purified by a precipitation with a mixture of methanol and benzene and by extraction with hot methanol. ECZ and DMTP were dissolved in benzene solution of PMMA with various concentrations. The sample solution was poured onto an semitransparent aluminum-coated quartz plate or onto an ITO-coated plate and kept in a dark room at room temperature for a few days. Then, the sample was evaporated in vacuo to eliminate benzene completely. The concentration of DMTP ranged from 0 to 10 mol % in the ratio to the monomer unit of PMMA. Following the cast of the polymer film, a semitransparent aluminum film was deposited by using vacuum vapor deposition. The aluminum films and ITO films were used as electrodes. The thickness of the polymer films was directly determined with a Mitutoyo scaling system (Surftest-SV-9700) to provide standard references for the © 1996 American Chemical Society
External Electric Field Effects on Fluorescence measurements of thickness. The thickness was determined by comparing the absorption intensity of ECZ of the sample with those of the standard. The thickness of the sample used for the optical measurements was typically 2 µm. All the optical measurements were carried out at room temperature under vacuum conditions. Fluorescence measurements were made with a fluorescence spectrometer equipped with an electric field modulation apparatus.18 Light from a 150 W xenon lamp dispersed by a monochromator was focused on a sample of the polymer film. Fluorescence emitted at right angle to the propagation direction of the excitation light was dispersed by a monochromator and detected by a photomultiplier. In order to minimize the influence of the scattered light, the excitation light reflected by the coated aluminum film was directed opposite to the propagation direction of the detected fluorescence, and a UV cutoff filter (Toshiba, UV31) was inserted in front of the monochromator for emission. A sinusoidal ac voltage was applied between the electrodes, with a function generator combined with a home-made power supply. A small amount of ac component of fluorescence at wavelength λ, ∆If(λ), synchronized with the applied voltage, was detected with a lock-in amplifier (NF, LI-574, and P-51) at the second harmonic (2f) of the modulation frequency (typically 40 Hz). A dc component corresponding to the total fluorescence intensity at λ, If(λ), was simultaneously obtained. Unless otherwise noted, the excitation wavelength is fixed at 294 nm for the fluorescence measurements, at which ECZ shows a maximum absorption intensity of the S0 f S2 transition. The absorbance of ECZ at the excitation wavelength of 294 nm was less than 0.4 in the samples used for the optical measurements. The angle between the direction of the external electric field and the propagation direction of the detected fluorescence as well as the propagation direction of the excitation light is 45°, and the dispersed fluorescence was detected without polarizer not only for emission but also for excitation. Fluorescence decays were measured by using a femtosecond pulse laser and a single-photon-counting system. The laser system was a mode-locked titanium:sapphire laser (Coherent, Mira 900) pumped by an argon ion laser (Coherent, Innova 300) combined with a pulse picker (Coherent, Model 9200). The third harmonic generated by an ultrafast harmonic system (Inrad, Model 5-050) was used as an excitation light. The decays were obtained with an excitation wavelength of 295 nm by using a microchannel plate photomultiplier (Hamamatsu R2809U-01).19
J. Phys. Chem., Vol. 100, No. 41, 1996 16467
Figure 1. Fluorescence spectra (dotted line) and electrofluorescence spectra (solid line) of N-ethylcarbazole (ECZ) doped in PMMA polymer films both in the absence and in the presence of dimethyl terephthalate (DMTP). The concentration of DMTP is 0, 0.5, 2.0, and 10.0 mol % from top to bottom, while the concentration of ECZ is 1.0 mol % in every case.
3. Results and Discussion Figure 1 shows the electrofluorescence spectra, ∆If(λ), of a mixture of ECZ and DMTP doped in a PMMA polymer film, together with the fluorescence spectra. These spectra were obtained in the presence of the external electric field with a strength of 6 × 105 V/cm. Hereafter, applied electric field is denoted by F. The concentration of ECZ is 1 mol % in every case, while the concentration of DMTP is varied from 0 to 10.0 mol %. Note that the maximum intensity of the fluorescence spectra shown in Figure 1 is normalized to unity in every case. As the concentration of DMTP increases, a broad fluorescence with a peak at around 440 nm appears besides the structured fluorescence emitted from ECZ. The broad fluorescence is assigned as the exciplex fluorescence resulting from intermolecular electron transfer from the photoexcited molecule of ECZ to DMTP.20 The magnitude of ∆If(λ) has been confirmed to increase with increasing F. An example for a sample with a DMTP concentration of 2 mol % is shown in Figure 2, where the values of ∆If(λ)/If(λ) observed at λ ) 354 and 475 nm are plotted as a function of the field strength. The former
Figure 2. Plots of ∆If(λ)/If(λ) of a mixture of ECZ (1 mol %) and DMTP (2 mol %) as a function of external electric field strength observed at λ ) 354 nm (open circles) and at λ ) 475 nm (closed circles).
wavelength corresponds to the peak of the fluorescence spectrum of ECZ, while the latter corresponds to the peak of the electrofluorescence spectrum in the longer wavelength region at 2 mol % of DMTP. ∆If(λ) is regarded as nearly proportional to the square of the strength of F (see Figure 2). Note that ∆If(λ) was observed at the second harmonic of the modulation frequency, i.e., 2f, as mentioned previously. As is shown in Figure 1, the electrofluorescence spectrum of ECZ depends on concentration of DMTP. The electrofluorescence spectrum observed in the absence of DMTP is nearly identical with the first derivative spectrum of the fluorescence spectrum of ECZ (see Figure 3). This result indicates that the field effect on the fluorescence spectrum of ECZ in the absence of DMTP is
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Figure 3. Electrofluorescence spectrum (solid line), fluorescence spectrum (broken line) and its first derivative spectrum (dotted line) of ECZ at 1 mol % in the absense of DMTP.
attributed to the so-called Stark shift. ∆If(νj) is shown in Figure 3, instead of ∆If(λ), where νj represents wavenumber. A conversion from wavelength to wavenumber in the abscissa of the spectrum was made by using a relation of λ2If(λ) ) If(νj). As is shown in Figure 1, the electrofluorescence spectrum of ECZ observed in the presence of DMTP is not identical with the first derivative of the ECZ fluorescence spectrum. As the concentration of DMTP increases, the electrofluorescence spectrum becomes closer in shape to the fluorescence spectrum of ECZ. As is shown in Figure 1, further, ∆If(λ) gives a negative value in the region of the ECZ fluorescence, implying that the quantum yield of the ECZ fluorescence is reduced by F in the presence of DMTP. Actually, the observed electrofluorescence spectra of ECZ are nearly reproduced by a linear combination of the fluorescence spectrum with its first-derivative spectrum with a constant value of a and b as follows:
∆If(νj) ) aIf(νj) + b(dIf(νj)/dνj)
Figure 4. Plots of ∆If(λ)/If(λ) of ECZ (1 mol %) observed at λ ) 354 nm (open circles) and at 455 nm (solid circles) as a function of concentration of DMTP doped in PMMA films.
(1)
The first term of eq 1 is attributed to the field-induced change in fluorescence quantum yield, while the second term corresponds to the Stark shift. A sharp minimum of the electrofluorescence spectrum observed in the absence of DMTP is located at 348 nm, which is shorter than that at the peak of the fluorescence spectrum of ECZ. The position of this minimum is monotonically red-shifted and approaches the peak position of the fluorescence spectrum (354 nm) as the concentration of DMTP increases. These results indicate that the first term relative to the second one in eq 1 becomes more significant with increasing concentration of DMTP; the value of a decreases with increasing concentration of DMTP. It should be stressed that a of the ECZ fluorescence is negative in the presence of DMTP. The amount of the field-induced change in fluorescence quantum yield relative to the total fluorescence quantum yield is considered to be evaluated from ∆If(λ)/If(λ) at λ ) 354 nm, at which the first derivative of the fluorescence spectrum is zero. Plots of ∆If(λ)/If(λ) at λ ) 354 nm obtained at 6 × 105 V/cm are shown in Figure 4, as a function of concentration of DMTP. Figure 4 shows that the ECZ fluorescence is quenched by F in the presence of DMTP, i.e., the fluorescence quantum yield is decreased by F, and that the efficiency of quenching becomes higher with increasing concentration of DMTP. Electric field effects are observed also for the exciplex fluorescence. As shown in Figure 1, the peak position in the longer wavelength region of the electrofluorescence spectrum is not identical with that of the peak of the exciplex fluorescence, but red-shifted. This disagreement is considered to come from the Stark shift, as in the case of the ECZ fluorescence observed in the absence of DMTP. As shown in Figure 5, the electrofluorescence
Figure 5. (a) Electrofluorescence spectrum at 10 mol % of DMTP (solid line), the first derivative of the exciplex fluorescence spectrum (dotted line), and the ECZ fluorescence spectrum (broken line); (b) fluorescence spectrum at 10 mol % of DMTP (solid line) and its decomposition into the ECZ fluorescence spectrum and exciplex fluorescence spectrum (dotted line). The concentration of ECZ is 1 mol %, and the maximum intensity of the fluorescence spectrum is normalized to unity.
spectrum of the exciplex observed at 10 mol % of DMTP is nearly identical with the first-derivative spectrum of the exciplex fluorescence. Note that the fluorescence spectrum of ECZ shown by a broken line in Figure 5 is the same in shape as the spectrum observed in the absence of DMTP and that the exciplex fluorescence spectrum given by another broken line in the figure was obtained by subtracting the ECZ fluorescence spectrum from the total fluorescence spectrum. It is also noted that the first-derivative spectrum multiplied by 18 is shown in Figure 5. At other concentrations of DMTP, the observed electrofluorescence spectra of exciplex are reproduced by a linear combination of the fluorescence spectrum with its first-derivative spectrum, since the quantum yield of the exciplex fluorescence is slightly enhanced by F as mentioned below. The field dependence of the intensity of the exciplex fluorescence was estimated at various concentrations of DMTP by measuring ∆If-
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Figure 7. Plots of ket and ∆ket at 6 × 105 V/cm for a mixture of ECZ (1 mol %) and DMTP as a function of the inverse cube root of concentration of DMTP.
Figure 6. Fluorescence decays of ECZ (1 mol %) with different concentrations of DMTP (0, 0.5, 1.0, 2.0, 5.0, 10.0 mol % from top to bottom) observed at 354 nm.
(λ)/If(λ) at λ ) 455 nm. The results are also shown in Figure 4. It is mentioned that the maximum intensity of the exciplex fluorescence spectrum given by If(νj) is at around 21 950 cm-1, which corresponds to ∼455 nm. In the presence of DMTP, ∆If(λ)/If(λ) at 455 nm gives a positive value at concentrations of DMTP less than 5 mol %, i.e., (1.0-2.0) × 10-3, while this value is close to zero at 10 mol %. It should be also noted that the field-induced change in absorption intensity at the excitation wavelength of 294 nm has been confirmed to be very small, i.e., ∆Iabs/Iabs e 3 × 10-4, where Iabs and ∆Iabs are the absorbance and its field-induced change, respectively. These results indicate that the exciplex fluorescence is a little enhanced by F at concentrations of DMTP less than 5 mol %. As the concentration of DMTP increases from 5 to 10 mol %, the amount of the field-induced increase of the quantum yield of the exciplex fluorescence decreases. At higher concentrations of DMTP more than 10 mol %, a quenching of the exciplex fluorescence may be expected to be induced by F . Time-resolved fluorescence intensity, If(t), observed for the ECZ fluorescence in the absence of DMTP shows a nearly single-exponential decay, and the lifetime is determined to be 12.5 ns. Here, t presents the time. In the presence of DMTP, the ECZ fluorescence shows a nonexponential decay, as shown in Figure 6. Actually, these decays can be analyzed by a multiexponential decay. At 10 mol %, for example, fluorescence decay is nearly reproduced by assuming a tripleexponential decay, where the lifetime of each component is estimated to be 0.5, 2.7, and 10.4 ns, respectively. In the present treatment, the average lifetime of fluorescence, denoted by jτf, was determined from the decays which show a nonexponential decay; jτf is given by ∫If(t) dt/If(0). jτf was obtained to be 9.2, 7.6, 5.3, 3.0, and 1.7 ns at 0.5, 1, 2, 5, and 10 mol %, respectively. Thus, the average lifetime monotonically decreases with increasing concentration of DMTP, implying that the rate of electron transfer from the photoexcited molecule of ECZ to DMTP increases with increasing concentration of DMTP. Here, it is assumed that electron transfer processes are negligible in the absence of DMTP. It is also assumed that the rate constants for processes other than the electron transfer are independent
of the concentration of DMTP. Then, the average rate constant of the electron transfer from photoexcited ECZ to DMTP, ket, is evaluated by using the following equation:
ket ) 1/τjf - 1/τ0
(2)
Here, τ0 is the fluorescence lifetime in the absence of DMTP, i.e., 12.5 ns. It is usually assumed that ket depends on the donor-acceptor distance exponentially.21,22 The present results, however, show that ket determined with eq 2 increases multiexponentially with decreasing the donor-acceptor distance, i.e., R, as shown in Figure 7. Note that R is inversely proportional to c1/3, where c is the concentration of DMTP. A field-induced change in quantum yield of the ECZ fluorescence is proposed to be caused by a field-induced change in ket, i.e, ∆ket. The quantum yield of the ECZ fluorescence at zero field and its field-induced change are denoted by Φf and ∆Φf, respectively. By assuming that the relaxation processes of the photoexcited molecule of ECZ are irreversible, Φf and Φf + ∆Φf are given by kr/(kr + knr + ket) and kr/(kr + knr + ket + ∆ket), respectively. Here, kr and knr represent the rate constants of radiative process and nonradiative processes other than the electron transfer, respectively. Further, jτf is assumed to be given by 1/(kr + knr + ket). Then, ∆ket at each concentration of DMTP is related to ∆Φf/Φf and jτf by the following equation:
∆ket ) -(∆Φf/Φf)/[{1 + (∆Φf/Φf)}τjf]
(3)
As mentioned previously, ∆Φf/Φf is regarded as the same as ∆If(λ)/If(λ) at λ ) 354 nm. In the present study, therefore, ∆ket was evaluated with eq 3 by using the values of ∆If(λ)/If(λ) at λ ) 354 nm, instead of ∆Φf/Φf, and jτf. The ∆ket thus obtained is plotted in Figure 7 as a function of the inverse cube root of concentration of DMTP, together with ket. ∆ket as well as ket increases with increasing concentration of DMTP, suggesting that both ∆ket and ket increase monotonically with decreasing the electron donor-acceptor distance. According to the Marcus theory,1-2 the rate constant of electron transfer is given by
ket )
[
(∆G + λ0) J2 2π exp 1/2 p (4πk Tλ ) 4kBTλ0 B 0
]
2
(4)
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Here, J, p, kB, T and ∆G are the transfer integral, Planck’s constant divided by 2π, the Boltzmann constant, the temperature, and the free energy change of the reaction, respectively. λ0 is the so-called reorganization energy given by the following equation:
λ0 )
(
)(
)
e2 1 1 1 1 2 + 2 op s Rd Ra R
(5)
where e is the electronic charge, op and s are the optical and static dielectric constants of the solvent, respectively, Rd and Ra are the radii of the donor and acceptor, respectively, and R is the donor-acceptor distance. External electric field is regarded as a perturbation, and the electron transfer rate can be expanded as a power series in F. Hereafter, the zeroth-, first-, and the second-order terms in F are considered, and other higher terms are neglected. By assuming that only ∆G is affected by F, i.e., ∆G is replaced by ∆G0 - µF, ket in the presence of F, denoted by ket(F), is given by
ket(F) ) A exp[B(∆G0 + λ0)2][1 - 2B(∆G0 + λ0)(µF) + B{1 + 2B(∆G0 + λ0)2}(µF)2] (6) where ∆G0 is the free energy change in the absence of F and µ is the dipole moment of the produced radical-ion pair. Here, A and B are given by
A)
J2 2π p (4πk Tλ )1/2 B 0
B ) -1/4kBTλ0
(7)
ket in the absence of F, ket(F)0), is given by A exp[B(∆G0 + λ0)2]. Then, ∆ket, which is defined as ket(F) - ket(F)0), divided by ket(F)0) is given by
∆ket/ket(F)0) ) -2B(∆G0 + λ0)(µF) + B{1 + 2B(∆G0 + λ0)2}(µF)2 (8) In the PMMA polymer films under the present study, the sample is regarded as distributed homogeneously. Then, the average value of µF and (µF)2 is given by zero and 1/3|µ|2|F|2, respectively. In such a case, eq 8 can be rewritten as
∆ket/ket(F)0) ) B{1 + 2B(∆G0 + λ0)2}(1/3|µ|2|F|2)
(9)
In the present experiments, 1 + (∆Φf/Φf) ≈ 1, and ∆ket is nearly proportional to ∆Φf according to eq 3. Then, the quadratic dependence of ∆Φf/Φf of the ECZ fluorescence on the strength of F shown in Figure 2 is well understood since ∆ket is expected to be proportional to |F|2 (see eq 9). As is shown in Figure 7, ∆ket as well as ket increases monotonically with decreasing the donor-acceptor distance, and ∆ket at 6 × 105 V/cm is about 2 orders of magnitude smaller than ket . The donor-acceptor distance may be estimated to be 7, 9, 12, and 16 Å at 10, 5, 2, and 1 mol % of DMTP with the specific gravity of 1.19 for PMMA.23 Then, λ0 is estimated with eq 5 to be 0.41, 0.47, 0.53, and 0.57 eV, respectively, at 10, 5, 2, and 1 mol %, by using s ) 3.6 and the relation of op ) 1.05n2, where n is the refractive index, and by assuming that Rd ) Ra ) 3 Å. The dipole moment of the radical ion pair produced by intermolecular electron transfer is estimated to be 35, 43, 60, and 76 D at 10, 5, 2, and 1 mol %, respectively. With a field strength of 6 × 105 V/cm, therefore, |µ||F| is estimated to be 44, 56, 75, and 95 meV, respectively. By
adopting the data of ∆ket and ket(F)0) given in Figure 7 to eq 9, the values of ∆G0 are estimated to be -0.62 or -0.20 eV at 10 mol %, -0.66 or -0.28 eV at 5 mol %, -0.71 or -0.35 eV at 2 mol %, and -0.75 or -0.39 eV at 1 mol %. Since ∆G0 is considered to be nearly independent of the concentration of DMTP, ∆G0 of the photoinduced intermolecular electron transfer system composed of ECZ and DMTP in PMMA polymer films may be regarded as about -0.7 eV. Tachiya and Murata24 reported that the distance dependence of ket results from the interplay of the distance dependence of J and λ0 and depends on the magnitude of ∆G. According to their calculations, ket decreases monotonically with decreasing the donor-acceptor distance when ∆G is relatively large. On the other hand, ket was shown to have a maximum at a certain distance, when ∆G is small. Note that ∆G e 0. The present result shows that ket increases multiexponentially with decreasing the distance, R. This kind of distance dependence is predicted to be observed for the case ∆G0 is quite large. In fact, ∆G0 evaluated above, i.e., -0.7 eV, is quite large. Quantum yield of the exciplex fluorescence is slightly enhanced by F at concentrations of DMTP less than 5 mol %, as mentioned previously. The fluorescent exciplex composed of ECZ and DMTP is assumed to be formed through the radicalion pair state following the electron transfer from photoexcited ECZ to DMTP, as proposed for PVCz doped with an electron acceptor.8,9 If a charge recombination occurs in the radicalion pair state, therefore, a quenching of the exciplex fluorescence occurs because of the decrease of the fluorescent exciplex formation yield. If such a charge recombination is prevented, the exciplex fluorescence increases. Accordingly, a small amount of field-induced increase of the exciplex fluorescence observed at concentrations of DMTP less than 5 mol % seems to indicate that a charge recombination of the radical-ion pair produced by the electron transfer slightly occurs in the absence of F and that such a recombination is presumably inhibited by F. As the concentration of DMTP increases, the negative charge can move to a neighboring molecule of DMTP more easily; i.e., the dissociation of the ion pair may be able to occur easily. Then, the probability of the formation of the exciplex becomes lower, and the field-assisted dissociation of the radical-ion pair, which leads to the fluorescence quenching, becomes more efficient. Therefore, fluorescence enhancement is considered to be observed only at low concentrations of DMTP, and the field-induced quenching is expected to become more important with increasing concentration. The fact that the field-induced change in fluorescence quantum yield of the exciplex fluorescence is nearly zero at 10 mol % of DMTP implies that the fluorescence quenching caused by the field-assisted dissociation just begins at around 10 mol % of DMTP; i.e., electron carries are considered to be produced at high concentrations of DMTP more than 10 mol %. In methylene-linked carbazole and terephthalic acid methyl ester doped in PMMA films, exciplex fluorescence is much efficiently quenched by an electric field at 10 mol %,25 in comparison with the present case. These results imply that hole carriers can be produced much more easily than electron carriers in the electron donor and acceptor system consisting of carbazole and dimethyl terephthalate. As mentioned previously, the Stark shift which induces the electrofluorescence spectrum corresponding to the first derivative of the fluorescence spectrum must be considered both for the ECZ fluorescence and for the exciplex fluorescence, besides the field-induced change in quantum yield. An expression for such a field-induced change in emission intensity was derived by Liptay and his co-workers.26,27 In rigid matrices such as a PMMA film, the original isotropic distribution is assumed to
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be maintained even in the presence of applied field.28 With these assumptions, ∆If induced by a change in electric dipole moment and polarizability following the radiation can be expressed in terms of the field-free emission intensity as
∆If ) [{∆R j /2 + (∆Rm - ∆R j )(3 cos2 χ - 1)/10}(hc)-1 × νj-3{d(If/νj3)/dνj} + (∆µ)2{5 + (3 cos2 ξ - 1)(3 cos2 χ 1)}30-1h-2c-2νj-3{d2(If/νj3)/dνj2}]|F|2 (10) Here, ∆µ and ∆R are related to the difference in dipole moment and polarizability, respectively, between the ground state and the emitted state; ∆µ ) µg - µe and ∆r ) rg - re.
∆µ ) |∆µ|; ∆R j ) (1/3) Tr ∆r
(11)
ξ and χ are the angle between the direction of ∆µ and the transition moment and the angle between the direction of F and the electric vector of the probing fluorescence, respectively. ∆Rm denotes the diagonal component of ∆r with respect to the direction of the transition moment. Note that If represents the emitted photon current density. In the present experimental setup, all the fluorescence was observed without passing through the polarizer, and the average value of cos2 χ is evaluated to be 0.25. As mentioned previously, the first derivative of the fluorescence spectrum is important for simulation of the electrofluorescence spectra, indicating that ∆µ is negligible and that the Stark shift mainly comes from a change in polarizability (see eq 10). By comparing the first-derivative part between eqs 1 and 10, ∆r can be evaluated. If the polarizability is assumed to be isotropic, j , ∆R j of ECZ is estimated to be about 100 in i.e., ∆Rm ) ∆R units of 4π0 Å3 by using the coefficient b of eq 1 obtained in j of the the present study, i.e., 1.0 cm-1. Similarly, ∆R fluorescent exciplex is estimated to be 1780 in units of 4π0 Å3 at 10 mol % of DMTP, by assuming that ∆Rm ) ∆R j (see Figure 5). The fact that ∆µ of the fluorescent exciplex is very small seems to show that the fluorescent exciplex formed in PMMA films exists not in a single donor-acceptor pair but in an aggregated form where dipole moments of different pairs are cancelled out on the average. Usually, the internal electric field (Fint) is not the same as an applied electric field (F) because of the dielectric properties of the environment. In the present analysis, this correction is not made because of the lack of the precise knowledge of this factor, but the relation between these two may be assumed that
Fint ) fF
(12)
where f is the local field correction. With a rough approximation for the internal field, the Lorentzian field correction may be used; f ) ( + 2)/3 with the dielectric constant of the material.29 By using 3.6 as the value of of PMMA, f is
obtained to be 1.87. When this Lorentzian field correction is used, the values of ∆R j evaluated above for the ECZ fluorescence and the exciplex fluorescence, i.e., 100 and 1780, respectively, must be replaced by 28 and 510 in units of 4π0 Å3, respectively. The free energy change of the electron transfer reaction, ∆G0, estimated with this correction is slightly larger than the aboveestimated value in every concentration of DMTP. Acknowledgment. We thank Mr. Hayashi at Mitutoyo for assistance of measuring the film thickness. This work was supported in part by Grant-in-Aids for Scientific Research on Priority Area “Photoreaction Dynamics” from the Ministry of Education, Science and Culture of Japan and by the Sumitomo Foundation. References and Notes (1) Marcus, R. A. J. Chem. Phys. 1956, 24, 966. (2) Marcus, R. A. Annu. ReV. Phys. Chem. 1964, 15, 155. (3) Rehm, D.; Weller, A. Isr. J. Chem. 1964, 15, 155. (4) Miller, J. R.; Beitz, J. V.; Huddleston, R. K. J. Am. Chem. Soc. 1984, 106, 5057. (5) Wasielewski, M. R.; Niemczyk, M. P.; Svec, W. A.; Pewitt, E. B. J. Am. Chem. Soc. 1985, 107, 1080. (6) Onsager, L. J. Chem. Phys. 1934, 2, 599; Phys. ReV. 1938, 54, 39. (7) Comizzoli, R. B. Photochem. Photobiol. 1972, 15, 399. (8) Yokoyama, M.; Endo, Y.; Mikawa, H. Chem. Phys. Lett. 1975, 34, 597; Bull. Chem. Soc. Jpn. 1976, 49, 1538. (9) Yokoyama, M.; Endo, Y.; Matsubara, A.; Mikawa, H. J. Chem. Phys. 1981, 75, 3006. (10) Sakai, H.; Itaya, A.; Masuhara, H. J. Phys. Chem. 1989, 93, 5351. (11) Menzel, E. R.; Popovic, Z. D. Chem. Phys. Lett. 1978, 55, 777. (12) Popovic, Z. D.; Menzel, E. R. J. Chem. Phys. 1979, 71, 5090. (13) Popovic, Z. D. Chem. Phys. 1984, 86, 311. (14) Weiss, D. S.; Burberry, M. Thin Solid Films 1988, 158, 175. (15) Kalinowski, J.; Stampor, W.; Di Marco, P. G. J. Chem. Phys. 1992, 96, 4136. (16) Boxer, S. G. in The Photosynthetic Reaction Center, eds. Deisenhofer, J.; Norris, J. R., Eds.; Academic Press: San Diego, CA, 1993; Vol. II, p 179. (17) Mataga, N. Pure Appl. Chem. 1984, 56, 1255. (18) Ohta, N.; Nomura, T.; Okazaki, S.; Yamazaki, I. Chem. Phys. Lett. 1995, 241, 195. (19) Ohta, N.; Tamai, T.; Kuroda, T.; Yamazaki, T.; Nishimura, Y.; Yamazaki. I. Chem. Phys. 1993, 177, 591. (20) Hoyle, C. E.; Guillet, J. E. Macromolecules 1979, 12, 956. (21) Eads, D. D.; Dismer, B. G.; Fleming, G. R. J. Chem. Phys. 1990, 93, 1136. (22) Song, L.; Dorfman, R. C.; Swallen, S. F.; Fayer, M. D. J. Phys. Chem. 1988, 127, 249. (23) Polymer Handbook; Brandrup, J., Immergut, E. H., Eds.; John Willey & Sons: New York, 1975. (24) Tachiya, M.; Murata, S. J. Phys. Chem. 1992, 96, 8441. (25) Ohta, N; Koizumi, M.; Nishimura, Y.; Yamazaki, I.; Tanimoto, Y.; Hatano, Y.; Yamamoto, M.; Kono, H. Submitted for publication. (26) Liptay, W. In Excited States; Lim, E. C., Ed.; Academic Press: New York, 1974; p 129 (27) Wortmann, R.; Elich, K.; Liptay, W. Chem. Phys. 1988, 124, 395. (28) Reimers, J. R.; Hush, N. S. J. Phys. Chem. 1991, 95, 9773. (29) Bottcher, C. J. F.; Bordewijk, P. Theory of Electric Polarization; Elsevier: Amsterdam, 1978; Vol. 1.
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