- Email: [email protected]
Vibrational energy relaxation rates in the S2 state of azulene in nitrogen and carbon dioxide
2 April 1999
Chemical Physics Letters 303 Ž1999. 223–228
Vibrational energy relaxation rates in the S 2 state of azulene in nitrogen and carbon dioxide Y. Kimura ) , T. Yamaguchi, N. Hirota 1 Department of Chemistry, Graduate School of Science, Kyoto UniÕersity, Kyoto 606-8502, Japan Received 10 November 1998; in final form 28 January 1999
Abstract The solvent density dependence of the vibrational energy relaxation rates in the S 2 state of azulene has been measured in nitrogen and carbon dioxide at 323.2 and 341 K. The vibrational energy relaxation rate is determined by measuring the time-dependent fluorescence spectra after photo-excitation at 283 nm. The density dependence of the vibrational energy relaxation rate is almost similar to that of the ground state. However, the vibrational energy relaxation rate in the S 2 state is faster than that of the ground state if they are compared at the same solvent density. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction The understanding of the vibrational energy relaxation mechanism in solution is one of the central subjects in solution chemistry. In recent years, various experimental and theoretical studies have been performed on this subject owing to the rapid development of the laser technology. The study of vibrational energy relaxation using the so-called supercritical fluids is an interesting approach for investigating the mechanism of the energy transfer in solution, since we can continuously change the ‘collision’ frequency which is an essential factor in discussing the vibrational energy relaxation. In the gaseous phase, the vibrational energy relaxation is well described by the isolated binary collision ŽIBC. model,
)
Corresponding author. Fax: q81 75 753 4000; e-mail: [email protected] 1 Also corresponding author
where the vibrational energy relaxation rate is described by the product of the collisional frequency and the energy dissipation rate per collision. By changing the solvent density continuously using the fluid above the critical temperature, we can study the effect of the ‘collision’. However, it is difficult to estimate the density dependence of the collisional frequency, since the collision frequency is not a simple function of solvent density. Although there have been several studies on the vibrational energy relaxation in fluids over wide solvent densities w1– 13x, the applicability of the IBC model to the liquid phase has not been fully tested yet. Recently, Zerezke and co-workers have investigated the vibrational energy relaxation rates of the ground state azulene by the transient absorption measurement w4–6x. By comparing the results with a Monte Carlo simulation, they have concluded that the IBC model is applicable to the understanding of the solvent density dependence of the vibrational energy relaxation rate w6x. On the other hand, Fayer and co-workers have
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 1 8 7 - 6
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Y. Kimura et al.r Chemical Physics Letters 303 (1999) 223–228
studied the vibrational energy relaxation rate from Õ s 1 to Õ s 0 of the anti-symmetric mode around 2000 cmy1 of WŽCO. 6 by pump–probe IR spectroscopy w9–13x. From the temperature dependence of the vibrational energy relaxation rate near the solvent critical density, they have suggested that the long-range correlation between solvent molecules is the key to understanding the vibrational energy relaxation near the critical density w13x. Further studies are required to clarify the mechanism of the density dependence of the vibrational energy relaxation. In this Letter, we present new experimental results on the vibrational energy relaxation rates in the electronically excited state ŽS 2 state. of azulene in nitrogen ŽN2 . and carbon dioxide ŽCO 2 . measured by the time-dependent fluorescence spectrum. Azulene is an unusual molecule that emits fluorescence
from the S 2 state, and the lifetime of the S 2 state is ; 2 ns in solution. It is known that the fluorescence lineshape and the fluorescence lifetime of an isolated azulene molecule Ži.e., without energy relaxation. is dependent on the excitation wavelength Žsee Fig. 1. w14,15x. We utilize this property as the thermometer of the molecule, i.e., we estimate the excess energy in the S 2 state of azulene in solution at each delay time after the photo-excitation by analyzing the lineshape of the fluorescence spectrum with reference to the spectrum measured in the vapor phase. From the decay profile of the excess energy thus estimated, we can evaluate the vibrational relaxation rate in the S 2 state of azulene. A similar kind of experiment has previously been performed for azulene in the rare gas matrix w16x. We have measured the vibrational energy relaxation rate in nitrogen ŽN2 . at 341 K from rr f 0 to 0.3 and in carbon dioxide ŽCO 2 . at 323.2 and 341 K from rr f 0 to 1.6, where rr is the reduced density by the critical density of the solvent.
2. Experimental
Fig. 1. Fluorescence spectra of azulene in the vapor phase at 323.2 K excited at various wavelengths. From the top to the bottom; 283, 294, 305, 313, 320, 331, 338, and 351 nm. The solid lines are the results of the spectral fitting. See detail in the text.
The time dependence of the fluorescence spectrum was measured by a streak camera using a picosecond pulsed dye laser. Briefly, a dye laser with a cavity-dumper built in it ŽCoherent 700. was pumped by a train of frequency-doubled output from a mode-locked Nd:YAG laser ŽCoherent Antares 76.. The dye laser produced 6–7 ps pulses Ž; 8 nJ. centered at 566 nm operated at 1.3 MHz using Rhodamine 6G for the gain dye. The output of the dye laser was frequency doubled by a BBO crystal of 1 mm thickness and used for the excitation. The fluorescence was detected by a streak camera ŽHamamatsu Photonics C4334. with a spectrograph ŽChromex 250IS. using the photon counting mode. No selection of the fluorescence polarization was done for the detection. The full width of the half maximum ŽFWHM. of the response function was typically 30 ps. The wavelength dependence of the sensitivity of the steak camera was corrected by measuring the reference sample Ž2-aminopyridine w17x.. For measuring the excitation wavelength dependence of the fluorescence spectra in the vapor phase of azulene, the dye laser was operated at 566,
Y. Kimura et al.r Chemical Physics Letters 303 (1999) 223–228
588, and 610 nm with Rhodamine 6G, and at 626, 640, 662, and 676 nm with DCM. Excitation at 351 nm was done by the frequency-doubled output of a Ti:sapphire laser ŽCoherent Mira 900-F, 100 fs FWHM, 76 MHz. pumped by an Arq laser ŽCoherent Innova 300.. The high-pressure optical cell used for the measurement has been described elsewhere w18x. The measurements in fluids were performed at 341 " 1 and 323.2 " 0.1 K, and the temperature was controlled by flowing thermostated water through the cell. The pressure of the cell was measured by a strain gage ŽKyowa PGM 500 KH., and the density of the solution was calculated with empirical equations of state w19,20x. The concentration of azulene was - 10y1 mM. In measuring the fluorescence spectra in the vapor phase, a small amount of azulene was enclosed in the quartz cell which was evacuated by a vacuum pump to 5 = 10y3 Torr with azulene trapped by liquid nitrogen. Then the cell was immersed into the cell holder which was temperature regulated at 323 or 341 K by the flowing of thermostated water. Azulene was purchased from Nacalai Tesque and purified by sublimation before use. N2 ŽSumitomo Seika, ) 99.999%. and CO 2 ŽSumitomo Seika, ) 99.98%. were used without further purification.
225
almost exponentially dependent on the excess energy as was reported by the quantum yield measurement w14x. Fig. 2 shows the fluorescence spectra in N2 at rr s 0.063 at several delay times after photo-excitation at 283 nm. Although the signal to noise ratio is not so good, the fluorescence lineshape clearly indicates the time dependence, which follows the decrease of the excess energy in the S 2 state as is indicated by Fig. 1. To estimate the corresponding excess energy possessed by azulene at each delay time, we first consider the modeling of the lineshape with the different excitation wavelengths in Fig. 1. To model the fluorescence lineshape as a function of the excess energy, we fit the fluorescence intensity at each probe wavelength Žfrom 330 to 440 nm, with a division of 0.16 nm. as a second-order polynomial of the excess energy. In the fitting, the integrated area of the fluorescence lineshape at each excitation wavelength is kept constant, and the constant value of the polynomial Žcorresponding to the zero excess energy value. is fixed to the fluorescence intensity excited at 351 nm. The solid lines in Fig. 1 correspond to the lineshapes thus estimated. As is shown in the figure, the fitting procedure works quite well, although some discrepancies are seen in the spectra excited at 313 and 338 nm. Using this ‘lineshape function’, we estimate the excess energy at each delay time after the photo-excitation in solution.
3. Results and discussion Fig. 1 shows the excitation wavelength dependence of the fluorescence spectra measured by our system. Excitation with a wavelength shorter than 294 nm corresponds to excitation from S 0 state to states energetically higher than the S 2 state, but internal conversion to the S 2 state is very fast, and in any case the fluorescence from the S 2 state was observed w15x. Since the 0–0 band of the transition from the ground state to the S 2 state in the vapor phase is ; 348 nm w14x, excitation at 351 nm corresponds to excitation to the S 2 state with no-excess energy. As shown in the figure, the fluorescence lineshape becomes structured with decreasing excitation photon energy. We have also measured the lifetime of the S 2 state, and obtained a value of ; 2 ns with excitation at 351 nm. The lifetime was
Fig. 2. Fluorescence spectra of azulene at various delay times after the photo-excitation at 283 nm. The results for N2 at 323.2 K and rr s 0.063. The solid lines are the results of the fitting to the reference spectrum.
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Y. Kimura et al.r Chemical Physics Letters 303 (1999) 223–228
Since the absorption and the fluorescence spectra at the equilibrium state show little solvent effect Ž; 1.5 nm shift of the 0–0 band of the absorption from the vapor to rr s 1.6 in CO 2 ., the excess energy dependence of the fluorescence lineshape in solution is expected to be similar to that without solvent. Therefore, we fit the fluorescence spectra as a function of the excess energy with reference to the above-constructed model. In this procedure, the reference spectrum was a little red-shifted to adjust the peak position of the relaxed fluorescence spectrum in solution to the peak position of the reference spectrum of no excess energy, in order to correct the small spectral shift due to the solvent. The solid lines in Fig. 2 that correspond to the fluorescence lineshapes evaluated in this way reproduce the features of each spectrum successfully. Fig. 3 shows the time dependence of the excess energy thus estimated together with the fluorescence intensity Žintegrated area.. As is shown in the figure, the excess energy decays almost exponentially with time. The initial first decay of the fluorescence intensity Ž I F Ž t .. is due to the shorter lifetime of the excited state with a large amount of the excess energy. In order to obtain the vibrational energy relaxation rate Ž k c ., we have analyzed these profiles by the following scheme. Firstly, we assume that the excess energy estimated from the lineshape corresponds to the average excess energy Ž² EŽ t .:. possessed by the azulene molecule at the time, and that
the integrated fluorescence intensity represents the number of the molecules in the S 2 state. The effect of the molecular rotation on the fluorescence intensity is considered to be small, since the rotational motion in fluids under study is much faster than the system response and the energy dissipation rate. Then, we fit these two profiles by the following equation: `
IF Ž t . s
H0 g Ž t y t . f Ž t . dt ,
Ž 1.
`
IF Ž t . ² E Ž t . : s
H0 g Ž t y t . f Ž t . h Ž t . dt ,
Ž 2.
where g Ž t . is the normalized instrumental response function, f Ž t . is the fluorescence decay function, and hŽ t . is the decay function of the excess energy, respectively. The response function is assumed to have the following functional form gŽ t. s
1 2t R
sech2
t y t0
ž / tR
,
Ž 3.
where t 0 and t R are parameters which signify the center and the width of the instrumental response time. Since the fluorescence lifetime depends on the excess energy possessed by the molecule, we assume that f Ž t . is given by t
H0 k h Ž t . 4 dt
f Ž t . s f 0 exp y
,
Ž 4.
where f 0 is the initial intensity of the fluorescence, and the fluorescence decay constant k is dependent on the excess energy at time t Ž hŽ t .. in the following way: k Ž h Ž t . . s k F exp a h Ž t . ,
Ž 5.
where k F is the fluorescence decay constant with no excess energy, and the constant a is determined as 4.0 = 10y4 cm by the excitation energy dependence of the lifetime determined in the vapor phase. The decay function of the excess energy is assumed to be h Ž t . s E0 exp Ž yk c t . , Fig. 3. The time dependence of the total fluorescence intensity and the vibrational excess energy in the excited state. The results for N2 at 323.2 K and rr s 0.063. The solid lines are the results of the best fit to Eqs. Ž1. and Ž7..
Ž 6.
where E0 is the initial excess energy Ž6850 cmy1 .. In fitting the transient, we first fit the total fluorescence intensity ŽEq. Ž1.. by adjusting the parame-
Y. Kimura et al.r Chemical Physics Letters 303 (1999) 223–228
ters Ž t 0 , t R , k F , f 0 . with a fixed value of k C of the initial guess. Then using the result, we fit the excess energy decay curve ŽEq. Ž2.. by adjusting k C . Using the new value of k C , we repeat the procedure iteratively to get self-consistent values. In our fitting procedure, the time origin and the width of the response function are also adjustable parameters, although ideally these values should be measured simultaneously with the accumulation of data by means of, for example, measurement of the pump light scattering, since the time origin and the width of the response function of the streak camera ŽC4334. are strongly dependent on the trigger condition of the streak scope in each experiment. However, our polychrometer could not cover such a wide wavelength region including the scattering light of the pump beam and the real fluorescence, simultaneous measurement was impossible. Therefore we have chosen the way to estimate the origin and the width from fitting the fluorescence time profile itself. It was assumed that the estimated response function almost simulates the system response measured by the scattering of the pump light just after or before the measurement of the signal for some data. In the real fitting, we used the following equation instead of Eq. Ž2. in order to correct the small broadening of the relaxed fluorescence spectrum shape in solution from that without solvent: `
IF Ž t . ² E Ž t . : y E b s
227
Fig. 4. Solvent density dependence of the vibrational energy dissipation rates in the S 2 state and the ground state. Ža. N2 ; v sS 2 state at 341 K, `s ground state at 383 or 420 K multiplied by a factor of 1.7. Žb. CO 2 ; B sS 2 state at 323.2 K, v sS 2 state at 341 K, `s ground state at 296, 385 or 445 K multiplied by a factor of 3.2.
H0 g Ž t y t . f Ž t . h Ž t . dt , Ž 7.
where E b is the correction term which is also adjusted in the fitting procedure. The maximum value of this correction term is ; 400 cmy1 at the highest density in CO 2 , which is considered to be sufficiently small in comparison with the excess energy. The solid lines in Fig. 3 are the results of the best fit to Eqs. Ž1. and Ž7.. The fitting is successful, although some deviation is detected in the early time dynamics. The vibrational energy relaxation rates estimated in this way are summarized in Fig. 4. The estimated error of the energy relaxation time is less than 20% of the value at the higher density region Ž rr ) 1.0., and the error is much smaller in the lower-density region. In the figure, we have also
plotted the vibrational energy relaxation rate measured in the ground state of azulene given in Ref. w4x. The values for the ground state are multiplied by a factor of 1.7 for N2 and 3.2 for CO 2 , in order to compare their density dependence with the results of the S 2 state clearly. In both solvent fluids, the density dependence of the energy relaxation rates in the S 2 state are quite similar to those in the ground state, although the relaxation rates are faster in the S 2 state. Since the solvent effects on the absorption and fluorescence spectra are small, the solute–solvent interaction in the S 2 state of azulene is not so different from that in the ground state. This indicates that the collisional frequency in the S 2 state is not so different from that in the ground state. From this result, it is natural to consider that the density depen-
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dence of the vibrational energy relaxation rate is dominated by the density dependence of the collisional frequency, and that the different energy relaxation rates between two electronic states originate from the difference in the efficiency of the energy loss per collision. The efficient energy dissipation in the electronic excited state has been reported previously in the case of pyrazine w21x. McDowell et al. measured the vibrational energy relaxation rate in the triplet state of pyrazine in the gaseous phase, and found that the energy loss per collision was ; 5–10 times larger in the triplet state than in the ground state. They consider that the ‘softening’ of the triplet vibration, especially among the low-frequency modes, is the origin of the larger energy loss in the triplet state. They speculate that lowering the vibrational frequency in the triple state enhances the energy transfer to the rotational or the translational modes of the solvent molecule. We consider the same mechanism to be applicable in the case of azulene. It has been reported that several vibrational frequencies of azulene in the S 2 state become lower than those of azulene in the ground state, and that the difference is larger in the lower-frequency modes w15x. This observation is consistent with our explanation. The different ratio of the energy relaxation rate in the S 2 state to that in the ground state between N2 and CO 2 represents the difference of the frequency dependence of the effective channel for the energy dissipation between these solvent molecules. In summary, we have measured the vibrational energy relaxation rate in the S 2 state of azulene in N2 and CO 2 . We have found that the density dependence of the rate is almost similar to that in the ground state, although the rate is larger in the excited state if they are compared at the same reduced density. Similar studies are now under way for various solvent fluids at wider solvent densities up to the liquid-like densities.
Acknowledgements This work is supported by CREST ŽCore Research for Evolutional Science and Technology. of Japan Science and Technology ŽJST.. References w1x M. Chatelet, J. Kieffer, B. Oksengorn, Chem. Phys. 79 ˆ Ž1983. 413. w2x M.E. Paige, C.B. Harris, Chem. Phys. 149 Ž1990. 37. w3x Q. Liu, C. Wan, A.H. Zewail, J. Phys. Chem. 100 Ž1996. 18666. w4x D. Schwarzer, J. Troe, M. Votsmeier, M. Zerezke, J. Chem. Phys. 105 Ž1996. 3121. w5x D. Schwarzer, J. Troe, M. Votsmeier, M. Zerezke, Ber. Bunsenges. Phys. Chem. 101 Ž1997. 595. w6x D. Schwarzer, J. Troe, M. Zerezke, J. Chem. Phys. 107 Ž1997. 8380. w7x J. Benzler, S. Linkersdorfer, K. Luther, Ber. Bunsenges. ¨ Phys. Chem. 100 Ž1996. 1252. w8x J. Benzler, S. Linkersdorfer, K. Luther, J. Chem. Phys. 106 ¨ Ž1997. 4992. w9x R.S. Urdahl, K.D. Rector, D.J. Myers, P.H. Davis, M.D. Fayer, J. Chem. Phys. 105 Ž1996. 8973. w10x R.S. Urdahl, D.J. Myers, K.D. Rector, P.H. Davis, B.J. Cherayil, M.D. Fayer, J. Chem. Phys. 107 Ž1997. 3747. w11x B.J. Cherayil, M.D. Fayer, J. Chem. Phys. 107 Ž1997. 7642. w12x M.J. Myers, R.S. Urdahl, B.J. Cherayil, M.D. Fayer, J. Chem. Phys. 107 Ž1997. 9741. w13x M.J. Myers, S. Chen, M. Shigeiwa, B.J. Cherayil, M.D. Fayer, J. Chem. Phys. 109 Ž1998. 5971. w14x Y. Hirata, E.C. Lim, J. Chem. Phys. 69 Ž1978. 3292. w15x M. Fujii, T. Ebata, N. Mikami, M. Ito, Chem. Phys. Lett. 77 Ž1983. 191. w16x J.B. Hopkins, P.M. Rentzepis, Chem. Phys. Lett. 117 Ž1985. 414. w17x W.H. Melhuish, Appl. Opt. 14 Ž1975. 26. w18x T. Yamaguchi, Y. Kimura, N. Hirota, J. Phys. Chem. A 101 Ž1997. 9050. w19x F.H. Huang, M.H. Li, L.L. Lee, K.E. Starling, F.T.H. Chung, J. Chem. Eng. Jpn. 18 Ž1985. 490. w20x T.H. Chung, M.M. Khan, L.L. Lee, K.E. Starling, Fluid Phase Equilib. 17 Ž1984. 351. w21x D.R. McDowell, F. Wu, R.B. Weisman, J. Chem. Phys. 108 Ž1998. 9404.
Chemical Physics Letters 303 Ž1999. 223–228
Vibrational energy relaxation rates in the S 2 state of azulene in nitrogen and carbon dioxide Y. Kimura ) , T. Yamaguchi, N. Hirota 1 Department of Chemistry, Graduate School of Science, Kyoto UniÕersity, Kyoto 606-8502, Japan Received 10 November 1998; in final form 28 January 1999
Abstract The solvent density dependence of the vibrational energy relaxation rates in the S 2 state of azulene has been measured in nitrogen and carbon dioxide at 323.2 and 341 K. The vibrational energy relaxation rate is determined by measuring the time-dependent fluorescence spectra after photo-excitation at 283 nm. The density dependence of the vibrational energy relaxation rate is almost similar to that of the ground state. However, the vibrational energy relaxation rate in the S 2 state is faster than that of the ground state if they are compared at the same solvent density. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction The understanding of the vibrational energy relaxation mechanism in solution is one of the central subjects in solution chemistry. In recent years, various experimental and theoretical studies have been performed on this subject owing to the rapid development of the laser technology. The study of vibrational energy relaxation using the so-called supercritical fluids is an interesting approach for investigating the mechanism of the energy transfer in solution, since we can continuously change the ‘collision’ frequency which is an essential factor in discussing the vibrational energy relaxation. In the gaseous phase, the vibrational energy relaxation is well described by the isolated binary collision ŽIBC. model,
)
Corresponding author. Fax: q81 75 753 4000; e-mail: [email protected] 1 Also corresponding author
where the vibrational energy relaxation rate is described by the product of the collisional frequency and the energy dissipation rate per collision. By changing the solvent density continuously using the fluid above the critical temperature, we can study the effect of the ‘collision’. However, it is difficult to estimate the density dependence of the collisional frequency, since the collision frequency is not a simple function of solvent density. Although there have been several studies on the vibrational energy relaxation in fluids over wide solvent densities w1– 13x, the applicability of the IBC model to the liquid phase has not been fully tested yet. Recently, Zerezke and co-workers have investigated the vibrational energy relaxation rates of the ground state azulene by the transient absorption measurement w4–6x. By comparing the results with a Monte Carlo simulation, they have concluded that the IBC model is applicable to the understanding of the solvent density dependence of the vibrational energy relaxation rate w6x. On the other hand, Fayer and co-workers have
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 1 8 7 - 6
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Y. Kimura et al.r Chemical Physics Letters 303 (1999) 223–228
studied the vibrational energy relaxation rate from Õ s 1 to Õ s 0 of the anti-symmetric mode around 2000 cmy1 of WŽCO. 6 by pump–probe IR spectroscopy w9–13x. From the temperature dependence of the vibrational energy relaxation rate near the solvent critical density, they have suggested that the long-range correlation between solvent molecules is the key to understanding the vibrational energy relaxation near the critical density w13x. Further studies are required to clarify the mechanism of the density dependence of the vibrational energy relaxation. In this Letter, we present new experimental results on the vibrational energy relaxation rates in the electronically excited state ŽS 2 state. of azulene in nitrogen ŽN2 . and carbon dioxide ŽCO 2 . measured by the time-dependent fluorescence spectrum. Azulene is an unusual molecule that emits fluorescence
from the S 2 state, and the lifetime of the S 2 state is ; 2 ns in solution. It is known that the fluorescence lineshape and the fluorescence lifetime of an isolated azulene molecule Ži.e., without energy relaxation. is dependent on the excitation wavelength Žsee Fig. 1. w14,15x. We utilize this property as the thermometer of the molecule, i.e., we estimate the excess energy in the S 2 state of azulene in solution at each delay time after the photo-excitation by analyzing the lineshape of the fluorescence spectrum with reference to the spectrum measured in the vapor phase. From the decay profile of the excess energy thus estimated, we can evaluate the vibrational relaxation rate in the S 2 state of azulene. A similar kind of experiment has previously been performed for azulene in the rare gas matrix w16x. We have measured the vibrational energy relaxation rate in nitrogen ŽN2 . at 341 K from rr f 0 to 0.3 and in carbon dioxide ŽCO 2 . at 323.2 and 341 K from rr f 0 to 1.6, where rr is the reduced density by the critical density of the solvent.
2. Experimental
Fig. 1. Fluorescence spectra of azulene in the vapor phase at 323.2 K excited at various wavelengths. From the top to the bottom; 283, 294, 305, 313, 320, 331, 338, and 351 nm. The solid lines are the results of the spectral fitting. See detail in the text.
The time dependence of the fluorescence spectrum was measured by a streak camera using a picosecond pulsed dye laser. Briefly, a dye laser with a cavity-dumper built in it ŽCoherent 700. was pumped by a train of frequency-doubled output from a mode-locked Nd:YAG laser ŽCoherent Antares 76.. The dye laser produced 6–7 ps pulses Ž; 8 nJ. centered at 566 nm operated at 1.3 MHz using Rhodamine 6G for the gain dye. The output of the dye laser was frequency doubled by a BBO crystal of 1 mm thickness and used for the excitation. The fluorescence was detected by a streak camera ŽHamamatsu Photonics C4334. with a spectrograph ŽChromex 250IS. using the photon counting mode. No selection of the fluorescence polarization was done for the detection. The full width of the half maximum ŽFWHM. of the response function was typically 30 ps. The wavelength dependence of the sensitivity of the steak camera was corrected by measuring the reference sample Ž2-aminopyridine w17x.. For measuring the excitation wavelength dependence of the fluorescence spectra in the vapor phase of azulene, the dye laser was operated at 566,
Y. Kimura et al.r Chemical Physics Letters 303 (1999) 223–228
588, and 610 nm with Rhodamine 6G, and at 626, 640, 662, and 676 nm with DCM. Excitation at 351 nm was done by the frequency-doubled output of a Ti:sapphire laser ŽCoherent Mira 900-F, 100 fs FWHM, 76 MHz. pumped by an Arq laser ŽCoherent Innova 300.. The high-pressure optical cell used for the measurement has been described elsewhere w18x. The measurements in fluids were performed at 341 " 1 and 323.2 " 0.1 K, and the temperature was controlled by flowing thermostated water through the cell. The pressure of the cell was measured by a strain gage ŽKyowa PGM 500 KH., and the density of the solution was calculated with empirical equations of state w19,20x. The concentration of azulene was - 10y1 mM. In measuring the fluorescence spectra in the vapor phase, a small amount of azulene was enclosed in the quartz cell which was evacuated by a vacuum pump to 5 = 10y3 Torr with azulene trapped by liquid nitrogen. Then the cell was immersed into the cell holder which was temperature regulated at 323 or 341 K by the flowing of thermostated water. Azulene was purchased from Nacalai Tesque and purified by sublimation before use. N2 ŽSumitomo Seika, ) 99.999%. and CO 2 ŽSumitomo Seika, ) 99.98%. were used without further purification.
225
almost exponentially dependent on the excess energy as was reported by the quantum yield measurement w14x. Fig. 2 shows the fluorescence spectra in N2 at rr s 0.063 at several delay times after photo-excitation at 283 nm. Although the signal to noise ratio is not so good, the fluorescence lineshape clearly indicates the time dependence, which follows the decrease of the excess energy in the S 2 state as is indicated by Fig. 1. To estimate the corresponding excess energy possessed by azulene at each delay time, we first consider the modeling of the lineshape with the different excitation wavelengths in Fig. 1. To model the fluorescence lineshape as a function of the excess energy, we fit the fluorescence intensity at each probe wavelength Žfrom 330 to 440 nm, with a division of 0.16 nm. as a second-order polynomial of the excess energy. In the fitting, the integrated area of the fluorescence lineshape at each excitation wavelength is kept constant, and the constant value of the polynomial Žcorresponding to the zero excess energy value. is fixed to the fluorescence intensity excited at 351 nm. The solid lines in Fig. 1 correspond to the lineshapes thus estimated. As is shown in the figure, the fitting procedure works quite well, although some discrepancies are seen in the spectra excited at 313 and 338 nm. Using this ‘lineshape function’, we estimate the excess energy at each delay time after the photo-excitation in solution.
3. Results and discussion Fig. 1 shows the excitation wavelength dependence of the fluorescence spectra measured by our system. Excitation with a wavelength shorter than 294 nm corresponds to excitation from S 0 state to states energetically higher than the S 2 state, but internal conversion to the S 2 state is very fast, and in any case the fluorescence from the S 2 state was observed w15x. Since the 0–0 band of the transition from the ground state to the S 2 state in the vapor phase is ; 348 nm w14x, excitation at 351 nm corresponds to excitation to the S 2 state with no-excess energy. As shown in the figure, the fluorescence lineshape becomes structured with decreasing excitation photon energy. We have also measured the lifetime of the S 2 state, and obtained a value of ; 2 ns with excitation at 351 nm. The lifetime was
Fig. 2. Fluorescence spectra of azulene at various delay times after the photo-excitation at 283 nm. The results for N2 at 323.2 K and rr s 0.063. The solid lines are the results of the fitting to the reference spectrum.
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Y. Kimura et al.r Chemical Physics Letters 303 (1999) 223–228
Since the absorption and the fluorescence spectra at the equilibrium state show little solvent effect Ž; 1.5 nm shift of the 0–0 band of the absorption from the vapor to rr s 1.6 in CO 2 ., the excess energy dependence of the fluorescence lineshape in solution is expected to be similar to that without solvent. Therefore, we fit the fluorescence spectra as a function of the excess energy with reference to the above-constructed model. In this procedure, the reference spectrum was a little red-shifted to adjust the peak position of the relaxed fluorescence spectrum in solution to the peak position of the reference spectrum of no excess energy, in order to correct the small spectral shift due to the solvent. The solid lines in Fig. 2 that correspond to the fluorescence lineshapes evaluated in this way reproduce the features of each spectrum successfully. Fig. 3 shows the time dependence of the excess energy thus estimated together with the fluorescence intensity Žintegrated area.. As is shown in the figure, the excess energy decays almost exponentially with time. The initial first decay of the fluorescence intensity Ž I F Ž t .. is due to the shorter lifetime of the excited state with a large amount of the excess energy. In order to obtain the vibrational energy relaxation rate Ž k c ., we have analyzed these profiles by the following scheme. Firstly, we assume that the excess energy estimated from the lineshape corresponds to the average excess energy Ž² EŽ t .:. possessed by the azulene molecule at the time, and that
the integrated fluorescence intensity represents the number of the molecules in the S 2 state. The effect of the molecular rotation on the fluorescence intensity is considered to be small, since the rotational motion in fluids under study is much faster than the system response and the energy dissipation rate. Then, we fit these two profiles by the following equation: `
IF Ž t . s
H0 g Ž t y t . f Ž t . dt ,
Ž 1.
`
IF Ž t . ² E Ž t . : s
H0 g Ž t y t . f Ž t . h Ž t . dt ,
Ž 2.
where g Ž t . is the normalized instrumental response function, f Ž t . is the fluorescence decay function, and hŽ t . is the decay function of the excess energy, respectively. The response function is assumed to have the following functional form gŽ t. s
1 2t R
sech2
t y t0
ž / tR
,
Ž 3.
where t 0 and t R are parameters which signify the center and the width of the instrumental response time. Since the fluorescence lifetime depends on the excess energy possessed by the molecule, we assume that f Ž t . is given by t
H0 k h Ž t . 4 dt
f Ž t . s f 0 exp y
,
Ž 4.
where f 0 is the initial intensity of the fluorescence, and the fluorescence decay constant k is dependent on the excess energy at time t Ž hŽ t .. in the following way: k Ž h Ž t . . s k F exp a h Ž t . ,
Ž 5.
where k F is the fluorescence decay constant with no excess energy, and the constant a is determined as 4.0 = 10y4 cm by the excitation energy dependence of the lifetime determined in the vapor phase. The decay function of the excess energy is assumed to be h Ž t . s E0 exp Ž yk c t . , Fig. 3. The time dependence of the total fluorescence intensity and the vibrational excess energy in the excited state. The results for N2 at 323.2 K and rr s 0.063. The solid lines are the results of the best fit to Eqs. Ž1. and Ž7..
Ž 6.
where E0 is the initial excess energy Ž6850 cmy1 .. In fitting the transient, we first fit the total fluorescence intensity ŽEq. Ž1.. by adjusting the parame-
Y. Kimura et al.r Chemical Physics Letters 303 (1999) 223–228
ters Ž t 0 , t R , k F , f 0 . with a fixed value of k C of the initial guess. Then using the result, we fit the excess energy decay curve ŽEq. Ž2.. by adjusting k C . Using the new value of k C , we repeat the procedure iteratively to get self-consistent values. In our fitting procedure, the time origin and the width of the response function are also adjustable parameters, although ideally these values should be measured simultaneously with the accumulation of data by means of, for example, measurement of the pump light scattering, since the time origin and the width of the response function of the streak camera ŽC4334. are strongly dependent on the trigger condition of the streak scope in each experiment. However, our polychrometer could not cover such a wide wavelength region including the scattering light of the pump beam and the real fluorescence, simultaneous measurement was impossible. Therefore we have chosen the way to estimate the origin and the width from fitting the fluorescence time profile itself. It was assumed that the estimated response function almost simulates the system response measured by the scattering of the pump light just after or before the measurement of the signal for some data. In the real fitting, we used the following equation instead of Eq. Ž2. in order to correct the small broadening of the relaxed fluorescence spectrum shape in solution from that without solvent: `
IF Ž t . ² E Ž t . : y E b s
227
Fig. 4. Solvent density dependence of the vibrational energy dissipation rates in the S 2 state and the ground state. Ža. N2 ; v sS 2 state at 341 K, `s ground state at 383 or 420 K multiplied by a factor of 1.7. Žb. CO 2 ; B sS 2 state at 323.2 K, v sS 2 state at 341 K, `s ground state at 296, 385 or 445 K multiplied by a factor of 3.2.
H0 g Ž t y t . f Ž t . h Ž t . dt , Ž 7.
where E b is the correction term which is also adjusted in the fitting procedure. The maximum value of this correction term is ; 400 cmy1 at the highest density in CO 2 , which is considered to be sufficiently small in comparison with the excess energy. The solid lines in Fig. 3 are the results of the best fit to Eqs. Ž1. and Ž7.. The fitting is successful, although some deviation is detected in the early time dynamics. The vibrational energy relaxation rates estimated in this way are summarized in Fig. 4. The estimated error of the energy relaxation time is less than 20% of the value at the higher density region Ž rr ) 1.0., and the error is much smaller in the lower-density region. In the figure, we have also
plotted the vibrational energy relaxation rate measured in the ground state of azulene given in Ref. w4x. The values for the ground state are multiplied by a factor of 1.7 for N2 and 3.2 for CO 2 , in order to compare their density dependence with the results of the S 2 state clearly. In both solvent fluids, the density dependence of the energy relaxation rates in the S 2 state are quite similar to those in the ground state, although the relaxation rates are faster in the S 2 state. Since the solvent effects on the absorption and fluorescence spectra are small, the solute–solvent interaction in the S 2 state of azulene is not so different from that in the ground state. This indicates that the collisional frequency in the S 2 state is not so different from that in the ground state. From this result, it is natural to consider that the density depen-
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Y. Kimura et al.r Chemical Physics Letters 303 (1999) 223–228
dence of the vibrational energy relaxation rate is dominated by the density dependence of the collisional frequency, and that the different energy relaxation rates between two electronic states originate from the difference in the efficiency of the energy loss per collision. The efficient energy dissipation in the electronic excited state has been reported previously in the case of pyrazine w21x. McDowell et al. measured the vibrational energy relaxation rate in the triplet state of pyrazine in the gaseous phase, and found that the energy loss per collision was ; 5–10 times larger in the triplet state than in the ground state. They consider that the ‘softening’ of the triplet vibration, especially among the low-frequency modes, is the origin of the larger energy loss in the triplet state. They speculate that lowering the vibrational frequency in the triple state enhances the energy transfer to the rotational or the translational modes of the solvent molecule. We consider the same mechanism to be applicable in the case of azulene. It has been reported that several vibrational frequencies of azulene in the S 2 state become lower than those of azulene in the ground state, and that the difference is larger in the lower-frequency modes w15x. This observation is consistent with our explanation. The different ratio of the energy relaxation rate in the S 2 state to that in the ground state between N2 and CO 2 represents the difference of the frequency dependence of the effective channel for the energy dissipation between these solvent molecules. In summary, we have measured the vibrational energy relaxation rate in the S 2 state of azulene in N2 and CO 2 . We have found that the density dependence of the rate is almost similar to that in the ground state, although the rate is larger in the excited state if they are compared at the same reduced density. Similar studies are now under way for various solvent fluids at wider solvent densities up to the liquid-like densities.
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