- Email: [email protected]
Temperature dependence of femtosecond time-resolved fluorescence intensity of a dye molecule in solution
Journal of Luminescence 102–103 (2003) 295–300
Temperature dependence of femtosecond time-resolved fluorescence intensity of a dye molecule in solution Hiroshi Murakami* Advanced Photon Research Center, Kansai Research Establishment, Japan Atomic Energy Research Institute, Umemidai 8-1, Kizucho, Sourakugun, Kyoto 619-0215, Japan
Abstract We have measured femtosecond time-resolved fluorescence intensity for coumarin in an ethanol/methanol mixture from 150 K to room temperature using an up-conversion technique. A liquid nitrogen flow-type cryostat was vibrated up and down during the measurement so that the same molecule in the sample might not be kept irradiated with a laser pulse. At 150 K, no fading of the fluorescence intensity due to the damage of the dye molecule under light irradiation was observed when the cryostat was moved, while the fluorescence intensity faded when it was not. The time profile of fluorescence intensity depends on temperature and wavelength of the detection on a time scale up to several picoseconds in the temperature range examined. This is considered to be ascribed to the temperature dependence of the energy relaxation in the excited state of the dye molecule due to solvation process of the surroundings of it. r 2002 Elsevier Science B.V. All rights reserved. PACS: 78.47.+p Keywords: Dye molecule; Fluorescence; Solvation; Energy relaxation
1. Introduction The structural dynamics of liquids have attracted much attention, because they play an important role in chemical reactions, and are an issue of the condensed matter physics. A very suitable method for studying the above is to employ a fluorescent probe of a dye molecule. As shown schematically in Fig. 1(a), the population is created on the potential curve in the electronic excited state of the dye molecule *Fax: +33-47688-2542. E-mail address: [email protected], [email protected] (H. Murakami).
according to the Franck–Condon principle by optical excitation, and then proceeds down to the bottom of the curve as the energy relaxation goes on. This relaxation is due to the configurational change of the surroundings of the dye molecule, i.e., solvation, in response to the electronic structure abruptly changed by optical excitation. Hence, the time-resolved fluorescence (TRF) spectrum originated from the population shifts to the low-energy side with time. This is called dynamic Stokes shift. At the same time, the time profile of the wavelength-resolved fluorescence (WRF) intensity in the high-energy side has a decay component other than the decay due to the fluorescence lifetime of the dye molecule which is
0022-2313/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 3 1 3 ( 0 2 ) 0 0 5 1 8 - 5
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Fig. 1. (a) A schematic energy diagram of a dye molecule in solution. (b) A three-dimensional graph of simulated timeresolved fluorescence spectra. The curve parallel to the time axis is the time development of the fluorescence intensity at a given energy, while that to the energy axis is the time-resolved fluorescence spectrum at a given time.
typical of the order of ns, while it has a rise one in the low-energy side, as seen in Fig. 1(b); the time scale of the decay and rise should be comparable to that of the shift of the TRF spectrum. If no energy relaxation in the electronic excited state occurs, the TRF spectrum shows no time-dependent shift, and the time profiles of the WRF intensity in the wavelength range of the fluorescence spectrum show only a decay due to the fluorescence lifetime. Thus we can study the energy relaxation process from the time development of the TRF spectrum and the rise and decay component in the WRF intensity. It has been shown from femtosecond TRF (FTRF) experiments for various dye molecules,
especially coumarin dyes, in solution that the ultrafast energy relaxation due to the solvation occurs in the electronic excited state of the dye molecule [1]. Moreover, molecular dynamics simulations have demonstrated that inertial or vibrational motions are responsible for the solvation process [2]. Most studies, however, have been focused on the dynamics at room temperature. One reason is that the FTRF measurement usually uses a sample-flow optical-cell system in order to prevent the dye molecule from damage due to dense light excitation. Therefore a cryostat is not applicable to the measurement, and temperature dependence of the energy relaxation is not accessible. The energy relaxation dynamics are usually analyzed using a sum of exponentials, often up to four ones, whose time constants are sometimes below several ps [1]. The relaxation processes with different origins are expected to show temperature dependence in some different ways. For example, in the energy relaxation due to diffusion-like process of the solvent, the relaxation time increases with decreasing temperature in accordance with Arrhenius equation or Vogel–Fulcher–Tammann one [3,4]; so the energy relaxation is distinguishable from the other relaxation processes. Thus it is significant to measure the temperature dependence of the energy relaxation in order to verify such many relaxation components with close time constants and to explore their origins. Further theories and molecular dynamics simulations for the energy relaxation should be tested on the temperature dependence of it also. What we should do to avoid damage of the dye molecule due to light irradiation is not to let the same molecule irradiated. For this end, we vibrate a cryostat in which the sample cell is fixed during the FTRF measurement. Ma et al. have examined the temperature dependence of femtosecond transient hole-burning (THB) spectra for a chromophore in solution, and shown that the relaxation process from 100 fs to ns in the electronic ground state of the chromophore is consistently explained by the mode coupling theory, in a temperature range above the glasstransition temperature of the liquid [5]. This analysis is impossible without measurement of
H. Murakami / Journal of Luminescence 102–103 (2003) 295–300
the temperature dependence, and the first case to apply the mode coupling theory to solutions. The energy relaxations in the electronic ground state and excited one after optical excitation are different, that is, the surroundings of dye molecules undergoing no optical excitation contribute to the relaxation in the ground state while those of molecules excited do in the excited state [4]. Hence it will be interesting to compare the temperature dependence of the energy relaxation in the excited state with that in the ground state on the same timescale as examined by them. Further since the time-dependent change of the THB spectrum is, in principle, due to the relaxation process both in the electronic excited and ground state, overlapping ground and excited state effects and the excited state absorption often make it difficult to extract the contribution of the ground state relaxation from the THB spectrum. The TRF spectrum comes from the excited state relaxation only and such difficulty is not involved. In this study, in order to study the temperature dependence of the ultrafast energy relaxation in the electronic excited state of a dye molecule in solution, we have demonstrated that the FTRF measurement for coumarin in a mixture of ethanol and methanol is free from light-induced damage of the dye molecule at low temperatures using our cryostat system, and measured the time profile of the WRF intensity of the sample in the low- and high-energy sides of the fluorescence spectrum at 150, 170, 230, and 296 K.
2. Experimental Coumarin 540A (Exciton, laser grade) dissolved in a mixture of ethanol and methanol (Nacalai Tesque, spectral grade) in a voluminal ratio of 4:1 (C540A/EtMt) was prepared without further purification. The liquid-glass transition temperature of the solvent is around 130 K, which is close to the temperature accomplished by our cryostat. The concentration of the dye molecule was around 7 104 mol/l, where the absorbance of it was about 1 per 1 mm optical path length at the excitation wavelength of 410 nm. The time profile of the WRF intensity of C540A/EtMt was
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measured up to 100 ps with an up-conversion technique with a temporal resolution of about 150 fs. The experimental system has already been described in detail [6]. A liquid nitrogen flow-type cryostat was used to control the temperature of the sample within about 1 K. The cryostat was attached to a translation stage equipped with computer-controlled stepping motors and vibrated up and down at a velocity of about 10 mm/s during the FTRF measurement. From the measurement of the fluorescence intensity of C540A/EtMt at 150 K at a constant delay time after photoexcitation, it has been found that the fluorescence intensity is constant if the cryostat is moved, while the intensity decays within a few ten seconds owing to light-induced damage of the dye molecule if it is not. Further, we have confirmed that the time profile of the WRF intensity does not vary among over ten data obtained in several hours under the same condition as long as the cryostat is moved.
3. Experimental results and discussion The time profiles of the WRF intensity of C540A/EtMt at 465 nm (circles) and 575 nm (stars) at 296 K are depicted in the temporal range of 5 ps in Fig. 2(a). It is apparent that the time behavior at 465 nm shows a fast decay other than the decay of the order of ns due to the fluorescence lifetime while it has a rise component at 575 nm. The wavelength of 465 nm is in the high-energy side of the fluorescence spectrum of C540A/EtMt while 575 nm in the low-energy side. Thus, as described above, the TRF spectrum at 296 K is expected to show dynamic Stokes shift due to the energy relaxation in the electronic excited state of the dye molecule in the time scale (the time-dependent shift of the TRF spectrum has been confirmed at 296 K in our preliminary study). In order to estimate the aspects of the energy relaxation from the decay and rise thus observed, fitted to the experimental results up to 100 ps is the convolution P of a sum of exponential functions ( i ai expðt=ti Þ where ai is the pre-exponential factor, ti the time constant and t the time) with the instrumental response function to the excitation
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Fig. 2. (a) The time behavior of the fluorescence intensity of C540A/EtMt at 465 nm (circles) and 575 nm (stars) at 296 K. The solid lines were obtained from the convolution of four exponentials with the instrumental response function to the excitation laser pulse. (b) At 170 K.
laser pulse. A good agreement is obtained between the experimental result and the calculation (solid lines) at each wavelength using four exponentials in Fig. 2(a), although not using two or three exponentials, where the time constant of one exponential is fixed at 3 ns in order to take account of the fluorescence lifetime. It has been found from this fitting that there are components with time constants of a few hundred fs, a few ps and the order of 10 ps in the decay and rise. Therefore, the energy relaxation will occur roughly with these time constants. Here, we do not intend that the energy relaxation should be explained in terms of a sum of exponential relaxations even if the above fitting is successful. The time constants derived
here are an approximate measure to characterize the energy relaxation. Also seen as symbols in Fig. 2(b) is the characteristic that a fast decay other than the decay due to the fluorescence lifetime is at 465 nm while a rise at 575 nm at 170 K. Hence, the timedependent shift of the TRF spectrum should also be observed at 170 K. The time behavior at 170 K, however, is quite different from that at 296 K in the variation of the decay and rise in 5 ps, namely, the variation at 170 K is smaller than at 296 K. This reveals that the time development of the energy relaxation at 170 K is different from that at 296 K. It has been found from the same fitting procedure (solid lines in Fig. 2(b)) as at 296 K that the time constants of the three exponentials, other than the exponential with a time constant of 3 ns, roughly coincide with those at 296 K, while the value of the pre-exponential factor is different between the exponential functions with the same time constant at the two temperatures. Therefore, the difference between the time behaviors at 296 and 170 K is considered to be due to that between the values of the pre-exponential factors at the two temperatures. This has been found to be valid among all the temperatures examined. Thus, we summarize the temperature dependence of the preexponential factors in the case of 465 nm in Fig. 3,
Fig. 3. Temperature dependence of the pre-exponential factors of four exponentials obtained from the fitting to the time behavior of the fluorescence intensity at 465 nm. The order of the time constants of the exponentials is listed in the explanatory note. The lines are to guide the reader’s eye.
H. Murakami / Journal of Luminescence 102–103 (2003) 295–300
where P the factor is represented as a ratio of ai = i ai ; and hereafter we refer to the factors as the ratio of 0.1, 1, 10 ps, and 3 ns with the order of the time constants. The ratios of 0.1 and 1 ps decline with decreasing temperature. On the other hand, the ratio of 3 ns increases dramatically below 170 K. This is considered to be because the time profile of the WRF intensity was measured only up to 100 ps after the photoexcitation although the fluorescence continues on a time scale of ns, and so all the decay components which are much long compared with 100 ps are regarded as the decay one with a time constant of 3 ns in the fitting procedure. The energy relaxation time due to the diffusion-like motion of the surroundings of the dye molecule is around 1 ns at 170 K in the ethanol/methanol mixture [7], and increases with decreasing temperature. Thus, it is considered that not only the decay component due to the fluorescence lifetime but also that due to the energy relaxation with the diffusion-like motion contributes to the ratio of 3 ns below 170 K. On the other hand, above 230 K, the energy relaxation time will be in the time window of the observation, and the decay component due to the energy relaxation will contribute to the ratio of 10 ps above 230 K. Hence, the ratio of 3 ns above 230 K is very small compared with those below 170 K, with a nearly constant value. It may be worth citing that the energy relaxation time due to the diffusion-like motion is of the order of 10 ps at room temperature in a dye molecule in ethanol [8]. The presence of the ratio of 10 ps below 170 K may suggest that of another energy relaxation mechanism, e.g. it might be related to Johari–Goldstein process which appears below the critical temperature (roughly 180 K for the solvent employed here) from the mode coupling theory [9]. From the temperature dependence of the ratios of 0.1 and 1 ps, we can say that the magnitude of the solvation process responsible for the energy relaxation on the time scale decreases with decreasing temperature, because the ratio is considered to be an approximate measure to characterize the magnitude of the energy relaxation process. It will be worth considering this solvation, together with the dynamics of glass-
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forming liquids studied extensively up to date. Boson peak in the low-frequency vibrational excitation and the so-called fast process have been observed in various glass-forming liquids irrespective of their chemical and structural characteristics, although their origins are not clear yet (see for a review, Ref. [10]). The low-frequency vibrational excitation extending up to 100– 200 cm1 is believed to be attributed to collective intermolecular vibrations, because its high-frequency wing is determined with molecular scales, and because its low-frequency one shows the transition to the Debye continuum. On the other hand, the fast process has a time constant of a few ps which is almost independent of temperature, and the magnitude of the process decreases with decreasing temperature. The process is often regarded cage rattling. It will be natural that such dynamics of the surroundings of the dye molecule make the electronic state of the molecule fluctuate and relax through the interaction between them. In fact, the phonon side band due to the boson peak has been observed in the optical spectra of dye molecules in glass-forming liquids, which reveals the presence of such an interaction [11]. Accordingly, we may assign the components of 0.1 and 1 ps to the energy relaxation due to the lowfrequency vibrational motions and that due to the fast process of the surroundings, respectively. The temperature dependence of the ratio of the slower component seems to correspond to that of the magnitude of the fast process. On the other hand, the temperature dependence of the magnitude of the faster solvation will be explained probably in terms of that of the phonon density and vibration anharmonicity. Also in coumarin 540A in glycerol, a typical glass-forming liquid, the energy relaxation components with a time constant of a few hundred fs and a few ps have been assigned to the above two, respectively [6]. On the assumption that the configurations of the surroundings of the dye molecule just after photoexcitation and at the equilibrium in the electronic excited state of the dye molecule do not depend on temperature, if the equilibrium is established by a sum of some independent relaxation processes, then the magnitude of each relaxation process will be constant irrespective of
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temperature. Therefore, the relaxation components here, whose ratios are temperature-dependent, cannot be regarded as independent relaxation processes, as long as the assumption is valid. The fast process has recently been interpreted in terms of the phonon density fluctuation due to vibration anharmonicity [12]. On the other hand, the fast process and the diffusion process are regarded as a two-step process in terms of a cage, namely, they correspond to rattling within the cage and the escape from the cage, respectively [10]. Further, we have explained the energy relaxation process in the electronic excited state of a dye molecule in polymer and myoglobin on the basis of hierarchically constrained dynamics in which there exist certain restrictions among structural motions with different time/space scales [13]. These examples seem to correspond to the above statement that the relaxation components seen in the energy relaxation of C540A/EtMt are not independent of each other. In conclusion, we have measured the temperature dependence of the femtosecond time-resolved fluorescence intensity for coumarin in an ethanol/ methanol mixture, and clarified that the dynamics of the fluorescence intensity depend on temperature on a time scale below a few picoseconds. The temperature dependence is considered to be due to that of the magnitude of the energy relaxation
rather than that of the relaxation time. The detailed analysis will be reported on the basis of the temperature dependence of the time-resolved fluorescence spectrum elsewhere.
References [1] M.L. Horng, J.A. Gardecki, A. Papazyan, M. Maroncelli, J. Phys. Chem. 99 (1995) 17311; P.F. Barbara, W. Jarzeba, Adv. Photochem. 15 (1990) 1. [2] S.J. Rosenthal, X. Xie, M. Du, G.R. Fleming, J. Chem. Phys. 95 (1991) 4715. [3] S. Kinoshita, N. Nishi, J. Chem. Phys. 89 (1988) 6612. [4] A. Kurita, K. Matsumoto, Y. Shibata, T. Kushida, J. Lumin. 76&77 (1998) 295. [5] J. Ma, D.V. Bout, M. Berg, Phys. Rev. E 54 (1996) 2786. [6] H. Murakami, J. Mol. Liq. 89 (2000) 33. [7] H. Murakami, S. Kinoshita, Y. Hirata, T. Okada, N. Mataga, J. Chem. Phys. 97 (1992) 7881. [8] S.G. Su, J.D. Simon, J. Phys. Chem. 91 (1987) 2693. [9] D. Richter, R. Zorn, B. Farago, B. Frick, L.J. Fetters, Phys. Rev. Lett. 68 (1992) 71. [10] E. Donth (Ed.), The Glass Transition: Relaxation Dynamics in Liquids and Disordered Materials, Springer, Berlin, 2001. [11] Y. Ichino, Y. Kanematsu, T. Kushida, J. Lumin. 66&67 (1996) 358. [12] V.N. Novikov, Phys. Rev. B 58 (1998) 8367. [13] H. Murakami, T. Kushida, Phys. Rev. B 54 (1996) 978; H. Murakami, T. Kushida, H. Tashiro, J. Chem. Phys. 108 (1998) 10309.
Temperature dependence of femtosecond time-resolved fluorescence intensity of a dye molecule in solution Hiroshi Murakami* Advanced Photon Research Center, Kansai Research Establishment, Japan Atomic Energy Research Institute, Umemidai 8-1, Kizucho, Sourakugun, Kyoto 619-0215, Japan
Abstract We have measured femtosecond time-resolved fluorescence intensity for coumarin in an ethanol/methanol mixture from 150 K to room temperature using an up-conversion technique. A liquid nitrogen flow-type cryostat was vibrated up and down during the measurement so that the same molecule in the sample might not be kept irradiated with a laser pulse. At 150 K, no fading of the fluorescence intensity due to the damage of the dye molecule under light irradiation was observed when the cryostat was moved, while the fluorescence intensity faded when it was not. The time profile of fluorescence intensity depends on temperature and wavelength of the detection on a time scale up to several picoseconds in the temperature range examined. This is considered to be ascribed to the temperature dependence of the energy relaxation in the excited state of the dye molecule due to solvation process of the surroundings of it. r 2002 Elsevier Science B.V. All rights reserved. PACS: 78.47.+p Keywords: Dye molecule; Fluorescence; Solvation; Energy relaxation
1. Introduction The structural dynamics of liquids have attracted much attention, because they play an important role in chemical reactions, and are an issue of the condensed matter physics. A very suitable method for studying the above is to employ a fluorescent probe of a dye molecule. As shown schematically in Fig. 1(a), the population is created on the potential curve in the electronic excited state of the dye molecule *Fax: +33-47688-2542. E-mail address: [email protected], [email protected] (H. Murakami).
according to the Franck–Condon principle by optical excitation, and then proceeds down to the bottom of the curve as the energy relaxation goes on. This relaxation is due to the configurational change of the surroundings of the dye molecule, i.e., solvation, in response to the electronic structure abruptly changed by optical excitation. Hence, the time-resolved fluorescence (TRF) spectrum originated from the population shifts to the low-energy side with time. This is called dynamic Stokes shift. At the same time, the time profile of the wavelength-resolved fluorescence (WRF) intensity in the high-energy side has a decay component other than the decay due to the fluorescence lifetime of the dye molecule which is
0022-2313/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 3 1 3 ( 0 2 ) 0 0 5 1 8 - 5
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H. Murakami / Journal of Luminescence 102–103 (2003) 295–300
Fig. 1. (a) A schematic energy diagram of a dye molecule in solution. (b) A three-dimensional graph of simulated timeresolved fluorescence spectra. The curve parallel to the time axis is the time development of the fluorescence intensity at a given energy, while that to the energy axis is the time-resolved fluorescence spectrum at a given time.
typical of the order of ns, while it has a rise one in the low-energy side, as seen in Fig. 1(b); the time scale of the decay and rise should be comparable to that of the shift of the TRF spectrum. If no energy relaxation in the electronic excited state occurs, the TRF spectrum shows no time-dependent shift, and the time profiles of the WRF intensity in the wavelength range of the fluorescence spectrum show only a decay due to the fluorescence lifetime. Thus we can study the energy relaxation process from the time development of the TRF spectrum and the rise and decay component in the WRF intensity. It has been shown from femtosecond TRF (FTRF) experiments for various dye molecules,
especially coumarin dyes, in solution that the ultrafast energy relaxation due to the solvation occurs in the electronic excited state of the dye molecule [1]. Moreover, molecular dynamics simulations have demonstrated that inertial or vibrational motions are responsible for the solvation process [2]. Most studies, however, have been focused on the dynamics at room temperature. One reason is that the FTRF measurement usually uses a sample-flow optical-cell system in order to prevent the dye molecule from damage due to dense light excitation. Therefore a cryostat is not applicable to the measurement, and temperature dependence of the energy relaxation is not accessible. The energy relaxation dynamics are usually analyzed using a sum of exponentials, often up to four ones, whose time constants are sometimes below several ps [1]. The relaxation processes with different origins are expected to show temperature dependence in some different ways. For example, in the energy relaxation due to diffusion-like process of the solvent, the relaxation time increases with decreasing temperature in accordance with Arrhenius equation or Vogel–Fulcher–Tammann one [3,4]; so the energy relaxation is distinguishable from the other relaxation processes. Thus it is significant to measure the temperature dependence of the energy relaxation in order to verify such many relaxation components with close time constants and to explore their origins. Further theories and molecular dynamics simulations for the energy relaxation should be tested on the temperature dependence of it also. What we should do to avoid damage of the dye molecule due to light irradiation is not to let the same molecule irradiated. For this end, we vibrate a cryostat in which the sample cell is fixed during the FTRF measurement. Ma et al. have examined the temperature dependence of femtosecond transient hole-burning (THB) spectra for a chromophore in solution, and shown that the relaxation process from 100 fs to ns in the electronic ground state of the chromophore is consistently explained by the mode coupling theory, in a temperature range above the glasstransition temperature of the liquid [5]. This analysis is impossible without measurement of
H. Murakami / Journal of Luminescence 102–103 (2003) 295–300
the temperature dependence, and the first case to apply the mode coupling theory to solutions. The energy relaxations in the electronic ground state and excited one after optical excitation are different, that is, the surroundings of dye molecules undergoing no optical excitation contribute to the relaxation in the ground state while those of molecules excited do in the excited state [4]. Hence it will be interesting to compare the temperature dependence of the energy relaxation in the excited state with that in the ground state on the same timescale as examined by them. Further since the time-dependent change of the THB spectrum is, in principle, due to the relaxation process both in the electronic excited and ground state, overlapping ground and excited state effects and the excited state absorption often make it difficult to extract the contribution of the ground state relaxation from the THB spectrum. The TRF spectrum comes from the excited state relaxation only and such difficulty is not involved. In this study, in order to study the temperature dependence of the ultrafast energy relaxation in the electronic excited state of a dye molecule in solution, we have demonstrated that the FTRF measurement for coumarin in a mixture of ethanol and methanol is free from light-induced damage of the dye molecule at low temperatures using our cryostat system, and measured the time profile of the WRF intensity of the sample in the low- and high-energy sides of the fluorescence spectrum at 150, 170, 230, and 296 K.
2. Experimental Coumarin 540A (Exciton, laser grade) dissolved in a mixture of ethanol and methanol (Nacalai Tesque, spectral grade) in a voluminal ratio of 4:1 (C540A/EtMt) was prepared without further purification. The liquid-glass transition temperature of the solvent is around 130 K, which is close to the temperature accomplished by our cryostat. The concentration of the dye molecule was around 7 104 mol/l, where the absorbance of it was about 1 per 1 mm optical path length at the excitation wavelength of 410 nm. The time profile of the WRF intensity of C540A/EtMt was
297
measured up to 100 ps with an up-conversion technique with a temporal resolution of about 150 fs. The experimental system has already been described in detail [6]. A liquid nitrogen flow-type cryostat was used to control the temperature of the sample within about 1 K. The cryostat was attached to a translation stage equipped with computer-controlled stepping motors and vibrated up and down at a velocity of about 10 mm/s during the FTRF measurement. From the measurement of the fluorescence intensity of C540A/EtMt at 150 K at a constant delay time after photoexcitation, it has been found that the fluorescence intensity is constant if the cryostat is moved, while the intensity decays within a few ten seconds owing to light-induced damage of the dye molecule if it is not. Further, we have confirmed that the time profile of the WRF intensity does not vary among over ten data obtained in several hours under the same condition as long as the cryostat is moved.
3. Experimental results and discussion The time profiles of the WRF intensity of C540A/EtMt at 465 nm (circles) and 575 nm (stars) at 296 K are depicted in the temporal range of 5 ps in Fig. 2(a). It is apparent that the time behavior at 465 nm shows a fast decay other than the decay of the order of ns due to the fluorescence lifetime while it has a rise component at 575 nm. The wavelength of 465 nm is in the high-energy side of the fluorescence spectrum of C540A/EtMt while 575 nm in the low-energy side. Thus, as described above, the TRF spectrum at 296 K is expected to show dynamic Stokes shift due to the energy relaxation in the electronic excited state of the dye molecule in the time scale (the time-dependent shift of the TRF spectrum has been confirmed at 296 K in our preliminary study). In order to estimate the aspects of the energy relaxation from the decay and rise thus observed, fitted to the experimental results up to 100 ps is the convolution P of a sum of exponential functions ( i ai expðt=ti Þ where ai is the pre-exponential factor, ti the time constant and t the time) with the instrumental response function to the excitation
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Fig. 2. (a) The time behavior of the fluorescence intensity of C540A/EtMt at 465 nm (circles) and 575 nm (stars) at 296 K. The solid lines were obtained from the convolution of four exponentials with the instrumental response function to the excitation laser pulse. (b) At 170 K.
laser pulse. A good agreement is obtained between the experimental result and the calculation (solid lines) at each wavelength using four exponentials in Fig. 2(a), although not using two or three exponentials, where the time constant of one exponential is fixed at 3 ns in order to take account of the fluorescence lifetime. It has been found from this fitting that there are components with time constants of a few hundred fs, a few ps and the order of 10 ps in the decay and rise. Therefore, the energy relaxation will occur roughly with these time constants. Here, we do not intend that the energy relaxation should be explained in terms of a sum of exponential relaxations even if the above fitting is successful. The time constants derived
here are an approximate measure to characterize the energy relaxation. Also seen as symbols in Fig. 2(b) is the characteristic that a fast decay other than the decay due to the fluorescence lifetime is at 465 nm while a rise at 575 nm at 170 K. Hence, the timedependent shift of the TRF spectrum should also be observed at 170 K. The time behavior at 170 K, however, is quite different from that at 296 K in the variation of the decay and rise in 5 ps, namely, the variation at 170 K is smaller than at 296 K. This reveals that the time development of the energy relaxation at 170 K is different from that at 296 K. It has been found from the same fitting procedure (solid lines in Fig. 2(b)) as at 296 K that the time constants of the three exponentials, other than the exponential with a time constant of 3 ns, roughly coincide with those at 296 K, while the value of the pre-exponential factor is different between the exponential functions with the same time constant at the two temperatures. Therefore, the difference between the time behaviors at 296 and 170 K is considered to be due to that between the values of the pre-exponential factors at the two temperatures. This has been found to be valid among all the temperatures examined. Thus, we summarize the temperature dependence of the preexponential factors in the case of 465 nm in Fig. 3,
Fig. 3. Temperature dependence of the pre-exponential factors of four exponentials obtained from the fitting to the time behavior of the fluorescence intensity at 465 nm. The order of the time constants of the exponentials is listed in the explanatory note. The lines are to guide the reader’s eye.
H. Murakami / Journal of Luminescence 102–103 (2003) 295–300
where P the factor is represented as a ratio of ai = i ai ; and hereafter we refer to the factors as the ratio of 0.1, 1, 10 ps, and 3 ns with the order of the time constants. The ratios of 0.1 and 1 ps decline with decreasing temperature. On the other hand, the ratio of 3 ns increases dramatically below 170 K. This is considered to be because the time profile of the WRF intensity was measured only up to 100 ps after the photoexcitation although the fluorescence continues on a time scale of ns, and so all the decay components which are much long compared with 100 ps are regarded as the decay one with a time constant of 3 ns in the fitting procedure. The energy relaxation time due to the diffusion-like motion of the surroundings of the dye molecule is around 1 ns at 170 K in the ethanol/methanol mixture [7], and increases with decreasing temperature. Thus, it is considered that not only the decay component due to the fluorescence lifetime but also that due to the energy relaxation with the diffusion-like motion contributes to the ratio of 3 ns below 170 K. On the other hand, above 230 K, the energy relaxation time will be in the time window of the observation, and the decay component due to the energy relaxation will contribute to the ratio of 10 ps above 230 K. Hence, the ratio of 3 ns above 230 K is very small compared with those below 170 K, with a nearly constant value. It may be worth citing that the energy relaxation time due to the diffusion-like motion is of the order of 10 ps at room temperature in a dye molecule in ethanol [8]. The presence of the ratio of 10 ps below 170 K may suggest that of another energy relaxation mechanism, e.g. it might be related to Johari–Goldstein process which appears below the critical temperature (roughly 180 K for the solvent employed here) from the mode coupling theory [9]. From the temperature dependence of the ratios of 0.1 and 1 ps, we can say that the magnitude of the solvation process responsible for the energy relaxation on the time scale decreases with decreasing temperature, because the ratio is considered to be an approximate measure to characterize the magnitude of the energy relaxation process. It will be worth considering this solvation, together with the dynamics of glass-
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forming liquids studied extensively up to date. Boson peak in the low-frequency vibrational excitation and the so-called fast process have been observed in various glass-forming liquids irrespective of their chemical and structural characteristics, although their origins are not clear yet (see for a review, Ref. [10]). The low-frequency vibrational excitation extending up to 100– 200 cm1 is believed to be attributed to collective intermolecular vibrations, because its high-frequency wing is determined with molecular scales, and because its low-frequency one shows the transition to the Debye continuum. On the other hand, the fast process has a time constant of a few ps which is almost independent of temperature, and the magnitude of the process decreases with decreasing temperature. The process is often regarded cage rattling. It will be natural that such dynamics of the surroundings of the dye molecule make the electronic state of the molecule fluctuate and relax through the interaction between them. In fact, the phonon side band due to the boson peak has been observed in the optical spectra of dye molecules in glass-forming liquids, which reveals the presence of such an interaction [11]. Accordingly, we may assign the components of 0.1 and 1 ps to the energy relaxation due to the lowfrequency vibrational motions and that due to the fast process of the surroundings, respectively. The temperature dependence of the ratio of the slower component seems to correspond to that of the magnitude of the fast process. On the other hand, the temperature dependence of the magnitude of the faster solvation will be explained probably in terms of that of the phonon density and vibration anharmonicity. Also in coumarin 540A in glycerol, a typical glass-forming liquid, the energy relaxation components with a time constant of a few hundred fs and a few ps have been assigned to the above two, respectively [6]. On the assumption that the configurations of the surroundings of the dye molecule just after photoexcitation and at the equilibrium in the electronic excited state of the dye molecule do not depend on temperature, if the equilibrium is established by a sum of some independent relaxation processes, then the magnitude of each relaxation process will be constant irrespective of
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temperature. Therefore, the relaxation components here, whose ratios are temperature-dependent, cannot be regarded as independent relaxation processes, as long as the assumption is valid. The fast process has recently been interpreted in terms of the phonon density fluctuation due to vibration anharmonicity [12]. On the other hand, the fast process and the diffusion process are regarded as a two-step process in terms of a cage, namely, they correspond to rattling within the cage and the escape from the cage, respectively [10]. Further, we have explained the energy relaxation process in the electronic excited state of a dye molecule in polymer and myoglobin on the basis of hierarchically constrained dynamics in which there exist certain restrictions among structural motions with different time/space scales [13]. These examples seem to correspond to the above statement that the relaxation components seen in the energy relaxation of C540A/EtMt are not independent of each other. In conclusion, we have measured the temperature dependence of the femtosecond time-resolved fluorescence intensity for coumarin in an ethanol/ methanol mixture, and clarified that the dynamics of the fluorescence intensity depend on temperature on a time scale below a few picoseconds. The temperature dependence is considered to be due to that of the magnitude of the energy relaxation
rather than that of the relaxation time. The detailed analysis will be reported on the basis of the temperature dependence of the time-resolved fluorescence spectrum elsewhere.
References [1] M.L. Horng, J.A. Gardecki, A. Papazyan, M. Maroncelli, J. Phys. Chem. 99 (1995) 17311; P.F. Barbara, W. Jarzeba, Adv. Photochem. 15 (1990) 1. [2] S.J. Rosenthal, X. Xie, M. Du, G.R. Fleming, J. Chem. Phys. 95 (1991) 4715. [3] S. Kinoshita, N. Nishi, J. Chem. Phys. 89 (1988) 6612. [4] A. Kurita, K. Matsumoto, Y. Shibata, T. Kushida, J. Lumin. 76&77 (1998) 295. [5] J. Ma, D.V. Bout, M. Berg, Phys. Rev. E 54 (1996) 2786. [6] H. Murakami, J. Mol. Liq. 89 (2000) 33. [7] H. Murakami, S. Kinoshita, Y. Hirata, T. Okada, N. Mataga, J. Chem. Phys. 97 (1992) 7881. [8] S.G. Su, J.D. Simon, J. Phys. Chem. 91 (1987) 2693. [9] D. Richter, R. Zorn, B. Farago, B. Frick, L.J. Fetters, Phys. Rev. Lett. 68 (1992) 71. [10] E. Donth (Ed.), The Glass Transition: Relaxation Dynamics in Liquids and Disordered Materials, Springer, Berlin, 2001. [11] Y. Ichino, Y. Kanematsu, T. Kushida, J. Lumin. 66&67 (1996) 358. [12] V.N. Novikov, Phys. Rev. B 58 (1998) 8367. [13] H. Murakami, T. Kushida, Phys. Rev. B 54 (1996) 978; H. Murakami, T. Kushida, H. Tashiro, J. Chem. Phys. 108 (1998) 10309.