- Email: [email protected]
Dynamic studies of conjugated polymers by phase–modulation IR-spectroscopy
Vibrational Spectroscopy 19 Ž1999. 77–83
Dynamic studies of conjugated polymers by phase–modulation IR-spectroscopy Yukio Furukawa
)
Department of Chemistry, School of Science and Engineering, Waseda UniÕersity, Shinjuku-ku, Tokyo 169-8555, Japan Received 9 July 1998; revised 5 October 1998; accepted 9 October 1998
Abstract The application of phase–modulation infrared spectroscopy to the photoexcitation dynamics of conjugated polymers is described. The modulation-frequency dependencies of the intensity and phase delay of photoinduced absorption have been observed and simulated numerically on the basis of a model based on second-order kinetics involving a neutralization process between the positive and negative charge carriers Žpolarons. that are formed from a photogenerated interchain charge-transfer exciton Žpolaron pair.. The rate constant of the bimolecular recombination process has been obtained. This numerical simulation is useful in analyzing the observed responses of a nonlinear system in the phase–modulation measurements. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Conjugated polymers; Phase–modulation infrared spectroscopy; Photoexcitation dynamics
1. Introduction Infrared absorption spectroscopy is useful in studying time-dependent phenomena of various materials. Transient phenomena can be studied by either time-domain transient experiments such as timeresolved techniques or frequency-domain steady-state experiments such as phase–modulation techniques. The phase–modulation method has not been used in infrared spectroscopy, whereas this method has been used in fluorescence spectroscopy w1,2x. In the phase–modulation experiments, the magnitude and phase of the dynamic response of a system to a sinusoidal stimulus are measured as functions of the
)
Tel.: q81-3-5286-3244; E-mail: [email protected]
frequency Žor angular frequency. of the external stimulus; they are associated with the dynamics of the system w3x. Noda et al. w4x have reported the infrared dichroic spectral changes of polymers induced by a stress modulation at a given modulation frequency. In addition, Noda w5x has proposed a two-dimensional correlation analysis of the obtained data, and this method is called two-dimensional infrared spectroscopy. These steady-state methods have been applied to liquid crystals w6x, electrochemical interfaces w7x, thermo-induced structural changes of proteins w8x, etc. In particular, it has been demonstrated that the phase–modulation method is a powerful tool for studying photoexcitation dynamics of conjugated polymers w9–11x. A new group of organic conjugated polymers ŽFig. 1. have attracted much attention of researchers,
0924-2031r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 2 0 3 1 Ž 9 8 . 0 0 0 6 6 - 6
78
Y. Furukawar Vibrational Spectroscopy 19 (1999) 77–83
Fig. 1. Chemical structures of conjugated polymers: Ža. polythiophene ŽPT.; Žb. polyŽ p-phenylenevinylene. ŽPPV.; Žc. polyŽ2,5dioctyloxy-p-phenylenevinylene. ŽDOO-PPV.; Žd. polyŽ2,5thienylenevinylene. wPTVx.
because they show high electrical conductivities upon chemical doping and are expected to be used as the organic semiconductors of electronic devices such as transistors and diodes w12–15x. Recently, polyŽ pphenylenevinylene. ŽPPV. and its derivatives are expected to be used for light emitting diodes w16x. A deep understanding of charge transport properties is needed in order to advance the electronic polymer devices. When a conjugated polymer is photo-irradiated across the band gap of the polymer, excitons or charge carriers are expected to be generated. In the picosecond time scale, singlet excitons and interchain charge-transfer excitons Žpolaron pairs. are generated. On the micro- to millisecond time scale, photoinduced absorptions in the region from visible to infrared have been measured by the phase– modulation method. In the modulation measurements of photoinduced absorptions from PPV w17x, poly Ž2,5-dimethoxy-p-phenylenevinylene . w18 x, polyŽ2,5-thienylenevinylene. ŽPTV. w19,20x, polythiophene w9x and polyŽ3-alkylthiophene.s w20–22x, the observed photoinduced absorption intensity decreases as f myn Ž n s 0.4–0.6.. In the case of various states of polyaniline, the values of n are in the range between 0.17 and 0.8 w23,24x. The observed f m dependency of the photoinduced absorption intensity has shown that the decay kinetics of photogenerated charged species is not unimolecular w3x. However, it is difficult to further analyze the observed data, although bimolecular kinetics has been suggested from the excitation-power dependency w25x. The difficulty comes from the nonlinearity of the photoinduced response from conjugated polymers. It has been reported w11x that a numerical simulations based on a model including a bimolecular recombination
process of charge carriers are useful in analyzing the f m dependencies of the intensity and the phase delay of photoinduced absorption from conjugated polymers. In this paper, we describe the outline of phase– modulation infrared spectrometry and a numerical simulation of the observed f m dependencies of the intensities and the phase delays of the photoinduced infrared absorption bands for polyŽ2,5-dioctyloxy-pphenylenevinylene. ŽDOO-PPV..
2. Phase–modulation measurements Let us assume that the intensity of laser light I Ž t . used for exciting a conjugated polymer is sinusoidally modulated as I Ž t . s I0 Ž 1 q sin 2p f m t .
Ž 1.
where I0 represents a constant and f m is the modulation frequency. The absorbance change of an infrared band at n˜ , D AŽ n˜ , f m ,t ., induced by the excitation laser light is in general expressed as 0
D A Ž n˜ , f m ,t . s D A Ž n˜ . q D A Ž n˜ , f m .
X
=sin 2p f m t y f Ž n˜ , f m . 4 q w higher-order terms x
Ž 2.
For a linear system, where photoinduced intensity is proportional to the power of excitation laser, the higher-order terms vanishes. The first term represents the time-independent dc component. The second vibrates sinusoidally with the same frequency as the external stimulus and called the f m term. The amplitude Žphotoinduced intensity. of the f m term is D AŽ n˜ , f m . X and the phase of this term is delayed by f Ž n˜ , f m . relative to the external stimulus because of the finite lifetime of the photogenerated species. The intensity and the phase delay expressed as functions of the modulation frequency are the response in the frequency domain. The intensity and the phase delay which result from an exponential decay, first-order kinetics, is given in a previous paper w3x. For a nonlinear system, where photoinduced intensity is not proportional to the power of excitation
Y. Furukawar Vibrational Spectroscopy 19 (1999) 77–83
laser, the higher-order terms Ž2 f m , 3 f m , etc. components. survive. In the present measurements, only the f m term is detected. No analytical forms of the f m dependencies of the intensity and the phase delay can be generally derived. It should be noted that the lower limit of the modulation frequency f m depends on the velocity Ž Õ cmrs. of the moving mirror and the wavenumber range Ž0 y n˜max cmy1 . of the infrared light in the measurements on a continuous-scan FT-IR spectrophotometer. The interferogram modulated by the external stimulus, Fm Ž x ., can be expressed as follows by considering the dc and the f m components: `
Fm Ž x . s
Hy`
0
B Ž n˜ . q D B Ž n˜ . q D B Ž n˜ , f m .
79
region between yn˜max and yn˜max cmy1 . In order to avoid the overlap of these spectra and obtain correct spectra, the following condition must be satisfied. f m G 4Õn˜max
Ž 4.
The modulation frequency in actuality is set sufficiently higher than 4Õn˜max . This restriction is lifted for either a step-scan FT-IR spectrometer or a dispersive-type spectrometer.
3. Experimental
X
=sin 2p f m t y f Ž n˜ , f m . 4 cos 2pn˜ xd n˜
Ž 3. where B Ž n˜ . denotes the infrared intensity spectrum Žthe magnitude of the transmitted intensity on an arbitrary scale. with the laser light off; D B Ž n˜ . 0 and D B Ž n˜ , f m .X are the photoinduced infrared intensity spectrum arising from the dc and the f m terms, respectively. The frequency f of the interferogram corresponding to the light of wavenumber n˜ is given by f s 2 Õn˜ w26x. By using this relation, the infrared spectra obtained from the modulated interferogram are schematically shown in Fig. 2. The D B Ž n˜ , f m . spectrum locates around the wavenumber f m r2 Õ corresponding to the modulation frequency f m , whereas the B Ž n˜ . q D B Ž n˜ . 0 spectrum exists in the
Fig. 2. Schematic infrared spectra obtained from Ža. an unmodulated interferogram and Žb. a modulated interferogram.
Our experimental setup for the phase–modulation infrared spectroscopy mainly consists of an Ar ion laser ŽCoherent Radiation Innova 90-6., an acoustooptic modulator ŽCoherent Associates Model 304., a lock-in amplifier ŽEG & G PARC 5209. and a Fourier transform infrared spectrophotometer ŽJEOL JIR5500. equipped with a mercury–cadmium–telluride ŽMCT. detector ŽEG & G Judson.. This detector has a D) value of 4.7 = 10 10 cm Hz 1r2 Wy1 with a long-wavelength cutoff around 700 cmy1 . A thin film of DOO-PPV was prepared on a BaF2 plate by the spin-coating technique. A thin film of DOO-PPV on a plate was placed on the cold head of a cryostat ŽOxford Instruments DN1754.. The temperature of the sample was kept at 78 K. The intensity of the 514.5-nm laser line was sinusoidally modulated by the acousto-optic modulator. A sinusoidal electric wave was provided from a function generator ŽWAVETEK Model 191. to the driver of the acousto-optic modulator. The higher limit of the wavenumber range of infrared light from an FT-IR spectrophotometer was set at about 2000 cmy1 by an optical filter. The velocity of the movable mirror of the FT-IR spectrophotometer was set to be 0.01 cm sy1 . Thus an unmodulated interferogram involves frequencies lower than 40 Hz. A signal from the MCT detector was passed through an electric bandpass filter and then was delivered to the lock-in amplifier. The reference signal of the lock-in amplifier was provided from the function generator. In this procedure, only the f m term was detected. After the output of the lock-in amplifier was returned to the spectrophotometer, the D B Ž n˜ , f .X spectrum was calculated. When the photoinduced absorbance arising
Y. Furukawar Vibrational Spectroscopy 19 (1999) 77–83
80
from the f m term is weak Žless than 10y4 ., the absorbance can be approximately expressed as X
D A Ž n˜ , f m . f y
0.434D B Ž n˜ , f m . kB Ž n˜ .
X
Ž 5.
where k is the factor of amplification of the lock-in amplifier. The D AŽ n˜ , f m .X spectrum was calculated from the observed D B Ž n˜ , f m .X and B Ž n˜ . spectra and the k value.
4. Experimental results Fig. 3a and b show the photoinduced infrared absorption spectra of DOO-PPV for the phase delays of 308 and y608, respectively. The modulation frequency is 1 kHz. In the 308 phase-resolved spectrum ŽFig. 3a., photoinduced absorption bands are observed at 1624, 1485, 1462, 1416, 1217, 1086, 1028 and 953 cmy1 . The observed spectrum is essentially the same as that obtained by the difference-spectrum method w10,27x. In the y608 phase-resolved spectrum ŽFig. 3b., the photoinduced infrared bands disappear completely. Thus, all the observed bands show the same temporal behavior. The photoinduced infrared absorption bands are attributed to charge carriers w10,27x, because these bands are similar to those of chemically doped DOO-PPV. The observed peak intensities and phase delays of the photoinduced 1485-cmy1 band of DOO-PPV are plotted
Fig. 4. Modulation-frequency dependencies of Ža. the intensities and Žb. the phase delays of the photoinduced 1485-cmy1 band of DOO-PPV. Excitation wavelength, 514.5 nm; excitation-power density, 300 mW cmy2 ; temperature, 78 K. Solid lines represent simulated results.
against the modulation frequencies between 0.8 and 20 kHz in Fig. 4a and b, respectively. The intensity decreases in proportion to f my0.6 with increasing modulation frequency in the range higher than 1 kHz. This result means that the decay kinetics of the photogenerated species is not unimolecular but is more complicated, because a unimolecular decay should show an f my1 dependence w3x.
5. Simulations
Fig. 3. Photoinduced infrared absorption spectra of DOO-PPV. Phase delays in Ža. and Žb. are 308 and y608, respectively. Excitation wavelength, 514.5 nm; excitation-power density, 300 mW cmy2 ; modulation frequency, 1 kHz; temperature, 78 K.
We have simulated the observed data by using the model based on a bimolecular process associated with the positive and negative polarons Žcharge carriers. that are formed from a photogenerated polaron pair Žcharge-transfer exciton. w10x. Elementary processes of this model are shown in Fig. 5. Transient absorptions persisting for longer than 1 ns have been attributed to the CT exciton w28,29x. In this model, it is assumed that the CT exciton decays by a unimolecular process with the rate constant k m Ž1.0 = 10 9 sy1 . and a bimolecular process with the rate constant k b . A positive polaron and a negative po-
Y. Furukawar Vibrational Spectroscopy 19 (1999) 77–83
81
cmy2 . This power density is equivalent to the photon flux of 7.8 = 10 17 photons cmy2 sy1 . In the present experiments, the modulation frequencies are lower than 20 kHz. The lifetime of the CT exciton is about 1 ns. Thus, it is reasonable to assume that the following condition for a steady state holds; dwExrdt s 0. Thus, we can derive the following equation from Eqs. Ž1., Ž6. and Ž7.. d wPx s dt Fig. 5. Proposed processes. N, Neutral polymer chain; E, CT exciton; Pq, positive polaron; Py, negative polaron.
laron are generated in a pair from the CT exciton with the rate constant k c , because of the two experimental results; the photoinduced absorption due to the CT exciton is enhanced with the excitation light polarized perpendicular to the chain for polyŽ2methoxy-p-phenylenevinylene. w27x, and the photoinduced bands due to polarons are also more strongly induced by perpendicular excitation for PPV w30x. The polarons formed from the CT excitons disappear bimolecularly with the rate constant k r . Let us assume that the positive polaron and the negative polaron give rise to the same infrared absorption bands. When the sample is irradiated by the sinusoidally modulated light I Ž t . with a frequency f m ŽEq. Ž1.., the following rate equations have been obtained for the concentration of the CT exciton wEx and the concentration of the positive Žnegative. polaron wPx. d wEx dt d wPx dt
s fa I Ž t . y k c w E x y k m w E x y k b w E x s k c wEx y k r wPx
2
2
Ž 6. Ž 7.
where f is the quantum efficiency of the creation of the CT exciton; a is the absorption coefficient at 514.5 nm. Since Yan et al. w31x have reported that the quantum efficiency of the creation of the CT exciton in PPV is 0.9, it is reasonable to consider that the f value of DOO-PPV is 0.9. The value of a at 514.5 nm of DOO-PPV is 1.2 = 10 5 cmy1 . In the present experiments the values of I0 are 300 mW
kc 2kb
½
= yŽ k c q k m .
(
2
q Ž k c q k m . q 4 k b fa I0 Ž 1 q sin 2p fm t . yk r w P x
2
5
Ž 8.
We have numerically integrated Eq. Ž8. by using the Runge–Kutta method w32x. The photoinduced absorbance can be obtained by the following equation. X
D A Ž n˜ , f m . s 2 K w P x
Ž 9.
where K is a constant. Under the sinusoidal modulation, the photoinduced absorbance has been reached to a steady state after a transient rise. The steady-state signal contains the f m and higher-order components. From this signal, we have obtained the intensity and the phase delay of the f m component by Fourier transformation. By calculating the intensities and the phase delays for various frequencies, we have obtained the modulation-frequency dependencies of the intensity and the phase delay. Four parameters k b , k c , k r and K have been adjusted by trial and error in such a manner that the calculated intensities and phase delays fit the observed. The values of k b , k c and k r are, respectively, determined to be 1.2 = 10y2 sy1 cm3 , 2.4 = 10 9 sy1 and 3.3 = 10y1 4 sy1 cm3 , respectively. The calculated modulation-frequency dependencies of the intensity and the phase delay are shown in Fig. 4 as solid lines. The calculated data agree with the observed.
6. Discussions The intensity of photoinduced absorption decreases in proportion to f my0.6 with increasing f m in the range higher than 1 kHz for DOO-PPV. The observed modulation-frequency dependencies of the
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Y. Furukawar Vibrational Spectroscopy 19 (1999) 77–83
intensity and the phase delay of the photoinduced absorptions from DOO-PPV have been explained by bimolecular recombination between oppositely charged polarons. Thus, the f myn Ž n s 0.4–0.6. dependencies in the literature w9,17–22x are attributable to bimolecular Žsecond-order. processes. Charged excitations such as polarons are expected to decay by a neutralization recombination process between oppositely charged species, which is equivalent to a second-order process. It has been demonstrated that high-quality photoinduced infrared absorption spectra are obtained by the modulation method, although the photoinduced absorptions are very weak. Few papers dealing with time-resolved absorption measurements of conjugated polymers in the micro- to millisecond range have been reported, although the time-resolved method is used for studies of the dynamics of various systems. Since the decay of the charge carriers in polymer films are bimolecular, their lifetimes are long. In time-resolved measurements, the repetition rate of pulsed light for photoexcitation must be reduced to a very low frequency. Thus it seems that it is difficult to obtain the high-quality data. It should be noted that the time-resolved measurements with the ac amplification method w33x may give a wrong temporal behavior when the photogenerated charge carriers do not return completely to the ground state because of high repetition rate of the excitation laser.
7. Conclusions We have studied the photoexcitation dynamics on the micro- to millisecond time scale in polyŽ2,5-dioctyloxy-p-phenylenevinylene. by phase–modulation infrared spectroscopy. We have demonstrated that the observed modulation-frequency dependencies of the intensity and the phase delay of photoinduced infrared absorptions can be successfully simulated by a model based on second-order kinetics, which is derived from the neutralization recombination process between the positive and the negative charge carriers Žpolarons.. A combination between the phase–modulation method and numerical simulation is useful in studying the photoexcitation processes of conjugated polymers in the micro- to millisecond time scale.
Acknowledgements The author is grateful to Prof. M. Tasumi and Dr. Y.-H. Cha for their collaborations in the studies on photoexcitation dynamics of conjugated polymers. The author would like to thank Dr. T. Ohnishi and Dr. T. Noguchi for the sample of DOO-PPV.
References w1x J.R. Lakowicz, Principles of Fluorescence Spectroscopy, 3rd edn., Plenum, New York, 1983. w2x F.V. Bright, Appl. Spectrosc. 49 Ž1995. 14A. w3x Y. Furukawa, Appl. Spectrosc. 47 Ž1993. 1405. w4x I. Noda, A.E. Dowrey, C. Marcott, Appl. Spectrosc. 42 Ž1988. 203. w5x I. Noda, J. Am. Chem. Soc. 111 Ž1989. 8116. w6x V.G. Gregoriou, J.L. Chao, H. Toriumi, R.A. Palmer, Chem. Phys. Lett. 179 Ž1991. 491. w7x F. Ozanam, J.-N. Chazalviel, Rev. Sci. Instrum. 59 Ž1988. 242. w8x M. Muller, R. Buchet, U.P. Fringeli, J. Phys. Chem. 100 ¨ Ž1996. 10810. w9x N. Yokonuma, Y. Furukawa, M. Tasumi, J. Mol. Struct. 379 Ž1996. 25. w10x Y.-H. Cha, Y. Furukawa, M. Tasumi, T. Noguchi, T. Ohnishi, Chem. Phys. Lett. 273 Ž1997. 159. w11x Y.-H. Cha, Y. Furukawa, M. Tasumi, T. Noguchi, T. Ohnishi, Chem. Phys. Lett. 280 Ž1997. 464. w12x H. Kiess ŽEd.., Conjugated Conducting Polymers, Springer, Berlin, 1992. w13x T. Kobayashi ŽEd.., Relaxation in Polymers, World Scientific, Singapore, 1993. w14x Y. Furukawa, J. Phys. Chem. 100 Ž1996. 15644. w15x N.S. Sariciftci ŽEd.., Primary Photoexcitations in Conjugated Polymers: Molecular Exciton versus Semiconductor Band Model, World Scientific, Singapore, 1997. w16x J.H. Burroughes, D.D.C. Bradley, A.R. Brown, R.N. Marks, K. Mackay, R.H. Friend, P.L. Burns, A.B. Holmes, Nature 347 Ž1990. 539. w17x N.F. Colaneri, D.D.C. Bradley, R.H. Friend, P.L. Burn, A.B. Holmes, C.W. Spangler, Phys. Rev. B 42 Ž1990. 11670. w18x H.S. Woo, S.C. Graham, D.A. Halliday, D.D.C. Bradley, R.H. Friend, P.L. Burn, A.B. Holmes, Phys. Rev. B 46 Ž1992. 7379. w19x A.J. Brassett, N.F. Colaneri, D.D.C. Bradley, H. Murata, S. Tokito, T. Tsutsui, S. Saito, Phys. Rev. B 41 Ž1990. 10586. w20x C. Botta, S. Luzzati, R. Tubino, D.D.C. Bradley, R.H. Friend, Phys. Rev. B 48 Ž1993. 14809. w21x J. Ruhe, N.F. Colaneri, D.D.C. Bradley, R.H. Friend, G. ¨ Wegner, J. Phys. Condens. Matter 2 Ž1990. 5465. w22x C. Botta, S. Luzzati, R. Tubino, A. Borghesi, Phys. Rev. B 46 Ž1992. 13008.
Y. Furukawar Vibrational Spectroscopy 19 (1999) 77–83 w23x M.G. Roe, J.M. Ginder, P.E. Wigen, A.J. Epstein, M. Angelopoulos, A.G. MacDiarmid, Phys. Rev. Lett. 60 Ž1988. 2789. w24x N.S. Sariciftci, L. Smilowitz, Y. Cao, A.J. Heeger, J. Chem. Phys. 98 Ž1993. 2664. w25x A.J. Heeger, H.E. Schaffer, Solid State Commun. 59 Ž1986. 415. w26x P.R. Griffiths, J.A. de Haseth, Fourier Transform Infrared Spectrometry, Wiley, New York, 1986, p. 6. w27x K.F. Voss, C.M. Foster, L. Smilowitz, D. Mihailovic, S. Askari, G. Srdanov, Z. Ni, S. Shi, A.J. Heeger, F. Wudl, Phys. Rev. B 43 Ž1991. 5109.
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w28x J.W. Hsu, M. Yan, T.M. Jedju, L.J. Rothberg, B.R. Hsieh, Phys. Rev. B 49 Ž1994. 712. w29x E.M. Conwell, H.A. Mizes, Phys. Rev. B 51 Ž1995. 6953. w30x D.D.C. Bradley, N.F. Colaneri, R.H. Friend, Synth. Met. 29 Ž1989. E121. w31x M. Yan, L.J. Rothberg, F. Papadimitrakopoulos, M.E. Galvin, T.M. Miller, Phys. Rev. Lett. 72 Ž1994. 1104. w32x W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in FORTRAN: the Art of Scientific Computing, 2nd edn., Chapter 16, Cambridge University, Cambridge, 1992. w33x K. Iwata, H. Hamaguchi, Chem. Phys. Lett. 157 Ž1989. 300.
Dynamic studies of conjugated polymers by phase–modulation IR-spectroscopy Yukio Furukawa
)
Department of Chemistry, School of Science and Engineering, Waseda UniÕersity, Shinjuku-ku, Tokyo 169-8555, Japan Received 9 July 1998; revised 5 October 1998; accepted 9 October 1998
Abstract The application of phase–modulation infrared spectroscopy to the photoexcitation dynamics of conjugated polymers is described. The modulation-frequency dependencies of the intensity and phase delay of photoinduced absorption have been observed and simulated numerically on the basis of a model based on second-order kinetics involving a neutralization process between the positive and negative charge carriers Žpolarons. that are formed from a photogenerated interchain charge-transfer exciton Žpolaron pair.. The rate constant of the bimolecular recombination process has been obtained. This numerical simulation is useful in analyzing the observed responses of a nonlinear system in the phase–modulation measurements. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Conjugated polymers; Phase–modulation infrared spectroscopy; Photoexcitation dynamics
1. Introduction Infrared absorption spectroscopy is useful in studying time-dependent phenomena of various materials. Transient phenomena can be studied by either time-domain transient experiments such as timeresolved techniques or frequency-domain steady-state experiments such as phase–modulation techniques. The phase–modulation method has not been used in infrared spectroscopy, whereas this method has been used in fluorescence spectroscopy w1,2x. In the phase–modulation experiments, the magnitude and phase of the dynamic response of a system to a sinusoidal stimulus are measured as functions of the
)
Tel.: q81-3-5286-3244; E-mail: [email protected]
frequency Žor angular frequency. of the external stimulus; they are associated with the dynamics of the system w3x. Noda et al. w4x have reported the infrared dichroic spectral changes of polymers induced by a stress modulation at a given modulation frequency. In addition, Noda w5x has proposed a two-dimensional correlation analysis of the obtained data, and this method is called two-dimensional infrared spectroscopy. These steady-state methods have been applied to liquid crystals w6x, electrochemical interfaces w7x, thermo-induced structural changes of proteins w8x, etc. In particular, it has been demonstrated that the phase–modulation method is a powerful tool for studying photoexcitation dynamics of conjugated polymers w9–11x. A new group of organic conjugated polymers ŽFig. 1. have attracted much attention of researchers,
0924-2031r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 2 0 3 1 Ž 9 8 . 0 0 0 6 6 - 6
78
Y. Furukawar Vibrational Spectroscopy 19 (1999) 77–83
Fig. 1. Chemical structures of conjugated polymers: Ža. polythiophene ŽPT.; Žb. polyŽ p-phenylenevinylene. ŽPPV.; Žc. polyŽ2,5dioctyloxy-p-phenylenevinylene. ŽDOO-PPV.; Žd. polyŽ2,5thienylenevinylene. wPTVx.
because they show high electrical conductivities upon chemical doping and are expected to be used as the organic semiconductors of electronic devices such as transistors and diodes w12–15x. Recently, polyŽ pphenylenevinylene. ŽPPV. and its derivatives are expected to be used for light emitting diodes w16x. A deep understanding of charge transport properties is needed in order to advance the electronic polymer devices. When a conjugated polymer is photo-irradiated across the band gap of the polymer, excitons or charge carriers are expected to be generated. In the picosecond time scale, singlet excitons and interchain charge-transfer excitons Žpolaron pairs. are generated. On the micro- to millisecond time scale, photoinduced absorptions in the region from visible to infrared have been measured by the phase– modulation method. In the modulation measurements of photoinduced absorptions from PPV w17x, poly Ž2,5-dimethoxy-p-phenylenevinylene . w18 x, polyŽ2,5-thienylenevinylene. ŽPTV. w19,20x, polythiophene w9x and polyŽ3-alkylthiophene.s w20–22x, the observed photoinduced absorption intensity decreases as f myn Ž n s 0.4–0.6.. In the case of various states of polyaniline, the values of n are in the range between 0.17 and 0.8 w23,24x. The observed f m dependency of the photoinduced absorption intensity has shown that the decay kinetics of photogenerated charged species is not unimolecular w3x. However, it is difficult to further analyze the observed data, although bimolecular kinetics has been suggested from the excitation-power dependency w25x. The difficulty comes from the nonlinearity of the photoinduced response from conjugated polymers. It has been reported w11x that a numerical simulations based on a model including a bimolecular recombination
process of charge carriers are useful in analyzing the f m dependencies of the intensity and the phase delay of photoinduced absorption from conjugated polymers. In this paper, we describe the outline of phase– modulation infrared spectrometry and a numerical simulation of the observed f m dependencies of the intensities and the phase delays of the photoinduced infrared absorption bands for polyŽ2,5-dioctyloxy-pphenylenevinylene. ŽDOO-PPV..
2. Phase–modulation measurements Let us assume that the intensity of laser light I Ž t . used for exciting a conjugated polymer is sinusoidally modulated as I Ž t . s I0 Ž 1 q sin 2p f m t .
Ž 1.
where I0 represents a constant and f m is the modulation frequency. The absorbance change of an infrared band at n˜ , D AŽ n˜ , f m ,t ., induced by the excitation laser light is in general expressed as 0
D A Ž n˜ , f m ,t . s D A Ž n˜ . q D A Ž n˜ , f m .
X
=sin 2p f m t y f Ž n˜ , f m . 4 q w higher-order terms x
Ž 2.
For a linear system, where photoinduced intensity is proportional to the power of excitation laser, the higher-order terms vanishes. The first term represents the time-independent dc component. The second vibrates sinusoidally with the same frequency as the external stimulus and called the f m term. The amplitude Žphotoinduced intensity. of the f m term is D AŽ n˜ , f m . X and the phase of this term is delayed by f Ž n˜ , f m . relative to the external stimulus because of the finite lifetime of the photogenerated species. The intensity and the phase delay expressed as functions of the modulation frequency are the response in the frequency domain. The intensity and the phase delay which result from an exponential decay, first-order kinetics, is given in a previous paper w3x. For a nonlinear system, where photoinduced intensity is not proportional to the power of excitation
Y. Furukawar Vibrational Spectroscopy 19 (1999) 77–83
laser, the higher-order terms Ž2 f m , 3 f m , etc. components. survive. In the present measurements, only the f m term is detected. No analytical forms of the f m dependencies of the intensity and the phase delay can be generally derived. It should be noted that the lower limit of the modulation frequency f m depends on the velocity Ž Õ cmrs. of the moving mirror and the wavenumber range Ž0 y n˜max cmy1 . of the infrared light in the measurements on a continuous-scan FT-IR spectrophotometer. The interferogram modulated by the external stimulus, Fm Ž x ., can be expressed as follows by considering the dc and the f m components: `
Fm Ž x . s
Hy`
0
B Ž n˜ . q D B Ž n˜ . q D B Ž n˜ , f m .
79
region between yn˜max and yn˜max cmy1 . In order to avoid the overlap of these spectra and obtain correct spectra, the following condition must be satisfied. f m G 4Õn˜max
Ž 4.
The modulation frequency in actuality is set sufficiently higher than 4Õn˜max . This restriction is lifted for either a step-scan FT-IR spectrometer or a dispersive-type spectrometer.
3. Experimental
X
=sin 2p f m t y f Ž n˜ , f m . 4 cos 2pn˜ xd n˜
Ž 3. where B Ž n˜ . denotes the infrared intensity spectrum Žthe magnitude of the transmitted intensity on an arbitrary scale. with the laser light off; D B Ž n˜ . 0 and D B Ž n˜ , f m .X are the photoinduced infrared intensity spectrum arising from the dc and the f m terms, respectively. The frequency f of the interferogram corresponding to the light of wavenumber n˜ is given by f s 2 Õn˜ w26x. By using this relation, the infrared spectra obtained from the modulated interferogram are schematically shown in Fig. 2. The D B Ž n˜ , f m . spectrum locates around the wavenumber f m r2 Õ corresponding to the modulation frequency f m , whereas the B Ž n˜ . q D B Ž n˜ . 0 spectrum exists in the
Fig. 2. Schematic infrared spectra obtained from Ža. an unmodulated interferogram and Žb. a modulated interferogram.
Our experimental setup for the phase–modulation infrared spectroscopy mainly consists of an Ar ion laser ŽCoherent Radiation Innova 90-6., an acoustooptic modulator ŽCoherent Associates Model 304., a lock-in amplifier ŽEG & G PARC 5209. and a Fourier transform infrared spectrophotometer ŽJEOL JIR5500. equipped with a mercury–cadmium–telluride ŽMCT. detector ŽEG & G Judson.. This detector has a D) value of 4.7 = 10 10 cm Hz 1r2 Wy1 with a long-wavelength cutoff around 700 cmy1 . A thin film of DOO-PPV was prepared on a BaF2 plate by the spin-coating technique. A thin film of DOO-PPV on a plate was placed on the cold head of a cryostat ŽOxford Instruments DN1754.. The temperature of the sample was kept at 78 K. The intensity of the 514.5-nm laser line was sinusoidally modulated by the acousto-optic modulator. A sinusoidal electric wave was provided from a function generator ŽWAVETEK Model 191. to the driver of the acousto-optic modulator. The higher limit of the wavenumber range of infrared light from an FT-IR spectrophotometer was set at about 2000 cmy1 by an optical filter. The velocity of the movable mirror of the FT-IR spectrophotometer was set to be 0.01 cm sy1 . Thus an unmodulated interferogram involves frequencies lower than 40 Hz. A signal from the MCT detector was passed through an electric bandpass filter and then was delivered to the lock-in amplifier. The reference signal of the lock-in amplifier was provided from the function generator. In this procedure, only the f m term was detected. After the output of the lock-in amplifier was returned to the spectrophotometer, the D B Ž n˜ , f .X spectrum was calculated. When the photoinduced absorbance arising
Y. Furukawar Vibrational Spectroscopy 19 (1999) 77–83
80
from the f m term is weak Žless than 10y4 ., the absorbance can be approximately expressed as X
D A Ž n˜ , f m . f y
0.434D B Ž n˜ , f m . kB Ž n˜ .
X
Ž 5.
where k is the factor of amplification of the lock-in amplifier. The D AŽ n˜ , f m .X spectrum was calculated from the observed D B Ž n˜ , f m .X and B Ž n˜ . spectra and the k value.
4. Experimental results Fig. 3a and b show the photoinduced infrared absorption spectra of DOO-PPV for the phase delays of 308 and y608, respectively. The modulation frequency is 1 kHz. In the 308 phase-resolved spectrum ŽFig. 3a., photoinduced absorption bands are observed at 1624, 1485, 1462, 1416, 1217, 1086, 1028 and 953 cmy1 . The observed spectrum is essentially the same as that obtained by the difference-spectrum method w10,27x. In the y608 phase-resolved spectrum ŽFig. 3b., the photoinduced infrared bands disappear completely. Thus, all the observed bands show the same temporal behavior. The photoinduced infrared absorption bands are attributed to charge carriers w10,27x, because these bands are similar to those of chemically doped DOO-PPV. The observed peak intensities and phase delays of the photoinduced 1485-cmy1 band of DOO-PPV are plotted
Fig. 4. Modulation-frequency dependencies of Ža. the intensities and Žb. the phase delays of the photoinduced 1485-cmy1 band of DOO-PPV. Excitation wavelength, 514.5 nm; excitation-power density, 300 mW cmy2 ; temperature, 78 K. Solid lines represent simulated results.
against the modulation frequencies between 0.8 and 20 kHz in Fig. 4a and b, respectively. The intensity decreases in proportion to f my0.6 with increasing modulation frequency in the range higher than 1 kHz. This result means that the decay kinetics of the photogenerated species is not unimolecular but is more complicated, because a unimolecular decay should show an f my1 dependence w3x.
5. Simulations
Fig. 3. Photoinduced infrared absorption spectra of DOO-PPV. Phase delays in Ža. and Žb. are 308 and y608, respectively. Excitation wavelength, 514.5 nm; excitation-power density, 300 mW cmy2 ; modulation frequency, 1 kHz; temperature, 78 K.
We have simulated the observed data by using the model based on a bimolecular process associated with the positive and negative polarons Žcharge carriers. that are formed from a photogenerated polaron pair Žcharge-transfer exciton. w10x. Elementary processes of this model are shown in Fig. 5. Transient absorptions persisting for longer than 1 ns have been attributed to the CT exciton w28,29x. In this model, it is assumed that the CT exciton decays by a unimolecular process with the rate constant k m Ž1.0 = 10 9 sy1 . and a bimolecular process with the rate constant k b . A positive polaron and a negative po-
Y. Furukawar Vibrational Spectroscopy 19 (1999) 77–83
81
cmy2 . This power density is equivalent to the photon flux of 7.8 = 10 17 photons cmy2 sy1 . In the present experiments, the modulation frequencies are lower than 20 kHz. The lifetime of the CT exciton is about 1 ns. Thus, it is reasonable to assume that the following condition for a steady state holds; dwExrdt s 0. Thus, we can derive the following equation from Eqs. Ž1., Ž6. and Ž7.. d wPx s dt Fig. 5. Proposed processes. N, Neutral polymer chain; E, CT exciton; Pq, positive polaron; Py, negative polaron.
laron are generated in a pair from the CT exciton with the rate constant k c , because of the two experimental results; the photoinduced absorption due to the CT exciton is enhanced with the excitation light polarized perpendicular to the chain for polyŽ2methoxy-p-phenylenevinylene. w27x, and the photoinduced bands due to polarons are also more strongly induced by perpendicular excitation for PPV w30x. The polarons formed from the CT excitons disappear bimolecularly with the rate constant k r . Let us assume that the positive polaron and the negative polaron give rise to the same infrared absorption bands. When the sample is irradiated by the sinusoidally modulated light I Ž t . with a frequency f m ŽEq. Ž1.., the following rate equations have been obtained for the concentration of the CT exciton wEx and the concentration of the positive Žnegative. polaron wPx. d wEx dt d wPx dt
s fa I Ž t . y k c w E x y k m w E x y k b w E x s k c wEx y k r wPx
2
2
Ž 6. Ž 7.
where f is the quantum efficiency of the creation of the CT exciton; a is the absorption coefficient at 514.5 nm. Since Yan et al. w31x have reported that the quantum efficiency of the creation of the CT exciton in PPV is 0.9, it is reasonable to consider that the f value of DOO-PPV is 0.9. The value of a at 514.5 nm of DOO-PPV is 1.2 = 10 5 cmy1 . In the present experiments the values of I0 are 300 mW
kc 2kb
½
= yŽ k c q k m .
(
2
q Ž k c q k m . q 4 k b fa I0 Ž 1 q sin 2p fm t . yk r w P x
2
5
Ž 8.
We have numerically integrated Eq. Ž8. by using the Runge–Kutta method w32x. The photoinduced absorbance can be obtained by the following equation. X
D A Ž n˜ , f m . s 2 K w P x
Ž 9.
where K is a constant. Under the sinusoidal modulation, the photoinduced absorbance has been reached to a steady state after a transient rise. The steady-state signal contains the f m and higher-order components. From this signal, we have obtained the intensity and the phase delay of the f m component by Fourier transformation. By calculating the intensities and the phase delays for various frequencies, we have obtained the modulation-frequency dependencies of the intensity and the phase delay. Four parameters k b , k c , k r and K have been adjusted by trial and error in such a manner that the calculated intensities and phase delays fit the observed. The values of k b , k c and k r are, respectively, determined to be 1.2 = 10y2 sy1 cm3 , 2.4 = 10 9 sy1 and 3.3 = 10y1 4 sy1 cm3 , respectively. The calculated modulation-frequency dependencies of the intensity and the phase delay are shown in Fig. 4 as solid lines. The calculated data agree with the observed.
6. Discussions The intensity of photoinduced absorption decreases in proportion to f my0.6 with increasing f m in the range higher than 1 kHz for DOO-PPV. The observed modulation-frequency dependencies of the
82
Y. Furukawar Vibrational Spectroscopy 19 (1999) 77–83
intensity and the phase delay of the photoinduced absorptions from DOO-PPV have been explained by bimolecular recombination between oppositely charged polarons. Thus, the f myn Ž n s 0.4–0.6. dependencies in the literature w9,17–22x are attributable to bimolecular Žsecond-order. processes. Charged excitations such as polarons are expected to decay by a neutralization recombination process between oppositely charged species, which is equivalent to a second-order process. It has been demonstrated that high-quality photoinduced infrared absorption spectra are obtained by the modulation method, although the photoinduced absorptions are very weak. Few papers dealing with time-resolved absorption measurements of conjugated polymers in the micro- to millisecond range have been reported, although the time-resolved method is used for studies of the dynamics of various systems. Since the decay of the charge carriers in polymer films are bimolecular, their lifetimes are long. In time-resolved measurements, the repetition rate of pulsed light for photoexcitation must be reduced to a very low frequency. Thus it seems that it is difficult to obtain the high-quality data. It should be noted that the time-resolved measurements with the ac amplification method w33x may give a wrong temporal behavior when the photogenerated charge carriers do not return completely to the ground state because of high repetition rate of the excitation laser.
7. Conclusions We have studied the photoexcitation dynamics on the micro- to millisecond time scale in polyŽ2,5-dioctyloxy-p-phenylenevinylene. by phase–modulation infrared spectroscopy. We have demonstrated that the observed modulation-frequency dependencies of the intensity and the phase delay of photoinduced infrared absorptions can be successfully simulated by a model based on second-order kinetics, which is derived from the neutralization recombination process between the positive and the negative charge carriers Žpolarons.. A combination between the phase–modulation method and numerical simulation is useful in studying the photoexcitation processes of conjugated polymers in the micro- to millisecond time scale.
Acknowledgements The author is grateful to Prof. M. Tasumi and Dr. Y.-H. Cha for their collaborations in the studies on photoexcitation dynamics of conjugated polymers. The author would like to thank Dr. T. Ohnishi and Dr. T. Noguchi for the sample of DOO-PPV.
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