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Radiative and non-radiative decay processes of the excited state of the colored form of photochromic furylfulgide
8 April 1994
CHEMICAL
PHYSICS LETTERS Chemical Physics Letters 220 ( 1994) 443-447
Radiative and non-radiative decay processes of the excited state of the colored form of photochromic furylfulgide J. Takeda ‘, T. Tayu ‘, S. Kurita a, Y. Yokoyama b, Y. Kurita b, T. Kuga c,l, M. Matsuoka c oLaboratoryofAppliedPhysics,FacultyofEngineering, YokohamaNationalUniversity,Hodogaya, Yolwhatna240, Japan b Departmentof MaterialsScience and ChemicalEngineering, Faculty of Engineering, YokohamaNationalUniversity, Hodogaya, Yokohama240, Japan ’ Institutefor Solid State Physics,Universityof Tokyo,Roppongi,Minato-ku106, Tokyo,Japan
Received 1 November 1993;in final form 13 January 1994
Abstract The time evolution of the luminescence of the colored form of a furylfulgide dispersed at various concentrations in a poly (methyl methacrylate ) film was measured as a function of the luminescence photon energy. The observed decay time of the luminescence is about l-2 ns and one order of magnitude shorter than the radiative lifetime ( 14 ns) estimated from the absorption intensity. The decay time is independent of temperature below 77 K. These results suggest that the non-radiative tunneling process from the excited state to the ground state is responsible for the decay.
1. Introduction Rewritable photon mode optical memories using photochromic organic compounds have attracted much interest because of their potentially superior properties for the application of photomemory. Since Heller and co-workers reported that 2-[ 1-(2,5-d& methyl-ffuryl)ethylidene]-3-isopropylidenesuccinic anhydride (fulgide 1) is a highly efficient photochromic compound [ l-3 1, fulgides have been considered to be one of the most promising candidates for such memory. Various studies on the syntheses of different kinds of fulgides [ 4-6 1, the dynamics of the photoreaction [7-91 and a method for a non-destructive readout of a photon mode optical memory [ 10 ] have been carried out. However, the fundamental studies for elucidating ’ Present address: Collegeof Arts and Science, University of Tokyo, Komaba, Meguro-ku 153,Tokyo, Japan.
the properties of the excited state and its relaxation processes for fulgides have not been well performed. We report a study of the time evolution of the luminescence from the colored form (C-form) of the fulgide in order to elucidate the relaxation processes of the excited state of the C-form of the fulgide.
2. Experimental (E)-2- [ l-( 2,5dimethyl-3-furyl)-2-methylpropylianhydride ( fulgide 2 ) was dispersed in a poly (methyl methacrylate ) film (PMMA film) with concentrations of 0.0 1,0.02 and 0.1 M ( 1 M= 1 mol/dm3) by a previously reported method [ $61. The typical thickness of a sample was 50 pm. The absorption spectra were measured at 4.2 K using the monochromatic light obtained from W and Xe lamps. Time-integrated luminescence spectra and
dene ] -3Gsopropyhdenesuccinic
0009-2614/94/$07.00 8 1994 Elsevier Science B.V. All rights reserved SSDIOOOS-2614(94)00190-2
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J. Takeda et al. / Chemical Physics Letters 220 (I 994) 443-44 7
the time evolution of the luminescence were measured at 4.2 and 77 K with the light excitation of the second harmonic of a mode-locked cw YAG laser. The excitation energy, repetition rate and pulse width of this laser were 18.8x lo3 cm-’ (532 nm), 82 MHz and 70 ps, respectively. The excitation light was irradiated at near-normal incidence on the sample’s surface. The time-integrated luminescence from the irradiated surface was detected by a photomultiplier and the time response of the luminescence analyzed by a synchroscan streak camera. The overall time resolution of the present experiments including the temporal broadening due to a 0.5 m grating monochromator was 90 ps and the spectral resolution 16 cm-‘. The average power of the excitation light was less than 2 mW/mm* to avoid damage to the samples.
3. Results and discussion 3. I. The oscillator strength and the radiative lifetime of the C-form of the fulgide in the visible light region On irradiation with ultraviolet light the E-form (colorless form) of the fulgide is transformed to the C-form and on irradiation with visible light the Cform turns back to the E-form. Fig. 1 shows the absorption spectrum of the C-form of fulgide 2 with concentration 0.02 M in a PMMA film at 4.2 K. The thickness of the sample is 50 pm. The molecular Wavelength (nm)
,,.
800700 600
500
400 ,
3?0 110
structure of the C-form is also shown in Fig. 1. From the integrated absorption intensity within the energy range of the visible light region ( ( 16-25) x lo3 cm-‘), we estimated the oscillator strength and the radiative lifetime of the C-form of fulgide 2. The oscillator strength fcp and the radiative lifetime rR are givenby [11,12]
(1) and ‘,=
* c3m*fiz( lEeg I) 2e*n&( jE,,l’) ’
(2)
Here, N is the molecular density, n the refraction index of the matrix, m* the effective electron mass, c the light velocity, e the electron charge, fi the reduced Planck constant and peg(E) the absorption coeffrcient. The ( IEegI ) and the ( IEge( ) are the average energies of the absorption and the luminescence spectra, respectively, being taken as equal to the peak energies of the absorption spectra (Z 19.9~ lo3 cm-‘) and the luminescence spectra (S 15.8~ lo3 cm- ’ ) [ 13 1. The refractive index n is taken to be 2 for the PMMA [ 14 1. We found that the values of the oscillator strength& and the radiative lifetime rR of fulgide 2 are 6.6 x lo-* and 14 ns, respectively, by using the above equations. The value off, suggests that the absorption of the C-form in the visible light region is due to the allowed ~-IL*transition [ 15 1. 3.2. The non-radiative decay process of the excited state of the C-form of thefilgide
4.2K 0.8-
A .Ti i 0.68
0.02M
0.4-
0 0.2-
Photon Energy (x103cm“)
Fig. 1. Absorption spectrum of the C-form of fidgide 2. The ordinate shows both the optical density and the molar extinction coeffkient c. The structure of the C-form is also shown in the fgure (R=isopropyl).
Some fraction of the fulgide molecules in a PMMA film is unable to change from the C- to the E-form at low temperature on irradiation of visible light, and then the luminescence of the C-form can be observed at low temperature [ 13 1. Fig. 2 shows the decay profile of the luminescence of the C-form fulgide with different concentrations and various spectral positions at 4.2 K. The numerical value on the left of each spectrum indicates the photon energy of the spectral position in units of lo3 cm-‘. The broken curves are the tits from a single exponential decay convoluted with the time profile of the laser pulse (the fitting parameter is 7). The value on the right of each spectrum
J. Takda et al. /Chemical PhysicsLetters220 (1994) 443-447
445
In the low-concentration cases (0.0 1 and 0.02 M ) , on the other hand, luminescence occurs from every
0
1
Time ( ns )
2
2 -1 Time ( ns )
/
I
I
0
1
2
Time (ns)
Fig. 2. Time behavior of the luminescence from the C-form fulgide with different concentrations and various spectral positions. The numerical value on the left of each spectrum indicates the photon energy of the luminescence in units of 1O3cm-‘. The broken curves show the tits from a single exponential decay convoluted with the time profile of the laser pulse. The titting parameter r is also shown on the right of each spectrum.
shows the value of the fitting parameter r in units of ns. According to our recent study, the energy of the excited state of the C-form of the fulgide molecule in a polymer film is slightly different from molecule to molecule because the environment around each fulgide molecule in a polymer film is different. In this situation, a Fiirster transfer proceeds from molecules having higher energy excited states (energy donors) to molecules having lower energy excited states (energy acceptors) in the high-concentration case. The estimated critical distance of the Fiirster transfer R. is x 40 A. The average distance between fulgide molecules, R, is about 30 A (0.1 M) and 55 A (0.02 M) [ 13 1. The ratio of the transition probability of the Fijrster transfer to the radiation decay rate of the donor molecules is given by (Ro/R)6. The values of the ratio in the cases of 0.1 and 0.02 M are about 6 ( > 1) and 0.15 ( < 1 ), respectively. Therefore, we assume that a Forster transfer takes place in the case of 0.1 M and can be neglected in the cases of 0.01 and 0.02 M. In the case of 0.1 M, luminescence takes place only from the fulgide molecules having a lower energy excited state after the Forster transfer is completed, and the luminescence spectrum may consist of almost a single luminescence band. The luminescence intensity at every luminescence photon energy thus decays exponentially with time and T represents the decay time of the luminescence as shown in Fig. 2.
photo-excited molecule without a Fiirster transfer implying that the luminescence spectrum consists of multiple luminescence bands. The luminescence intensityL(E,t)isgivenbyC,L@)exp(-t/ri),where Lj(E) and ri denote the luminescence intensity at energy E and the decay time of the ith luminescence band, respectively. The observed luminescence intensity actually seems to decrease single exponentially with time as shown in Fig. 2. Thus the decay time Tobtained experimentally should be taken as the averaged value of ri over the luminescence bands concerned for a given value of E. Fig. 3 shows the values of the decay time r (closed circles) as a function of the luminescence photon energy for various concentrations. Also, the time-integrated luminescence spectra are shown in the figure. The down arrows indicate the energy position of the excitation light by the second harmonic of a cw modelocked YAG laser. We also found that the shape of the luminescence spectra and the decay time of the luminescence at 77 K were almost the same as those for 4.2 K. The decay time of the luminescence is one order of magnitude shorter than the estimated radiative lifetime ( 14 ns) and does not depend on temperature
a)O.lM
A
4.2 K
2 i
Photon Energy ( xl 0 3 crri’)
Fig. 3. Value of the decay time T (closed circles) as a function of the luminescence photon energyfor various concentrations.Timeintegrated luminescence spectra are also shown in the figure. Down arrows indicate the energy position of the excitation light.
J. Takedaet al. / ChemicalPhysicsLetters220 (I 994) 443-447
446
below 77 K. This suggests that the non-radiative tunneling process from the excited state to the ground state is responsible for the decay of the luminescence. In the high-concentration case (0.1 M), the decay time of the luminescence is about 0.9 ns and independent of the spectral position indicating that the luminescence spectrum consists of almost a single luminescence band. On the other hand, the decay time r decreases from 2.3 to 0.9 ns with decreasing luminescence photon energy in the low-concentration cases (0.0 1 and 0.02 M). These experimental results are explained by the model of the non-radiative transition in a localized electron system [ 16,17 1. Fig. 4 shows typical potential diagrams in a localized electron system. Labels a and b correspond to two different fulgide molecules whose excited states have different energies due to the different environment around each molecule. The notation 1e,) and ]ei,) denotes the excited states of the C-form in the a and b molecules, and 1g) the ground state of the fulgide molecules, where the energy of the ground state is taken as the same for every molecule. IV, represents the relaxation energy of a localized electron, and & the energy difference between the minimum point of the potential curve of the excited state and that of the ground state. We assume that the curvature of the E
lea>
43’
potential curves and the lattice distortion QO,which gives the minimum point of the potential curve of the excited state, do not change from molecule to molecule in a polymer. The latter assumption was employed to explain why the peak energy of the luminescence spectrum of the C-form fulgide at low concentrations decreases with decreasing excitation photon energy [ 13 1. Under these assumptions, W,, does not vary but E,, changes from molecule to molecule in a polymer. Gutsche [ 161 calculated the non-radiative multiphonon transition rate W from the excited state to the ground state in the localized electron system represented in Fig. 4 using non-Condon approximations and found that W is given by wcc exp( -S)Sp-I
P!
xew( -+V
Fig. 4. Typical potential diagrams in a localized electron system for the C-form of the fulgide in a polymer film. Labels a and b correspondto two diRerentfulgide molecules whose excited states have different energies. The notation 1e.) and )e,,) denotes the excited states of the C-form in the a and b molecules, and Jg) the ground state of the fulgide molecules. W, represents the relaxation energy of a localized electron, and EOthe energy difference between the minimum point of the potential curve of the excited state and that of the ground state. The lattice distortion & gives the minimum point of the potential curve.
(3)
for the low temperature limit. Here, S (the HuangRhys factor) and Pare equal to W&iw and E,,/hw, respectively, n, is the phonon occupation number and fiw the phonon energy relevant to the tunneling process. In the present case, the values of W, and E. are about 2.1 x lo3 and 17.9 x 10’ cm- ‘, respectively, judging from the peak positions of absorption and luminescence spectra. Then P is about one order of magnitude larger than S, and Eq. (3) is simplified using Stirling’s formula, WccP3’2exp(-aP)
Lattice Distortion Q
(P-S)Z(n,+1)2
(cu=ln(P/S)-1).
(4)
This equation shows that the non-radiative decay rate W decreases with increasing P in the case of large P (P>3/2ax 1.5). In the low-concentration case, the energy transfer among the fulgide molecules is negligible and the luminescence proceeds from every excited molecule in a polymer. The lower energy part of the luminescence spectrum consists of the luminescence from the b-type molecules and the higher energy part of the luminescence is due to the luminescence from the a-type molecules. The non-radiative decay rate of the lower part of the luminescence spectrum is larger than that of the higher part of the luminescence spectrum because P for the b-type molecule is smaller than that for the atype molecule as shown in Fig. 4. Thus the non-radia-
J. Takzabet al. / ChemicalPhysicsLetters220 (1994) 443-447
tive decay time of the luminescence is longer at higher luminescence photon energy. A quantitative evaluation of the observed decay time is possible by using Eq. (3) if the vibrational frequency w of fulgide 2, relevant to the decay process, is known. Assuming that the magnitude of the vibrational frequency is about 2000-3000 cm-‘, which is adequate for organic molecules, we can well explain the experimental result that the decay time of the luminescence decreases with decreasing photon energy from 2.3 to 0.9 ns. A detailed discussion including the vibrational structure of fulgide 2 will be developed elsewhere. 4. Conclusion The oscillator strength and the radiative lifetime of the C-form of fttlgide 2 were estimated as 6.6 x 1O-’ and 14 ns, respectively. Judging from these values, the absorption of the C-form in the visible light region is due to the allowed x-x* transition. The decay time of the luminescence of the C-form of the fulgide is about l-2 ns and one order of magnitude shorter than the radiative lifetime. The decay time of the luminescence at high concentration (0.1 M) is independent of the luminescence photon energy, while, at low concentration (0.01 and 0.02 M), the decay time decreases with decreasing luminescence photon energy. These results suggest that the non-radiative tunneling process from the excited state to the ground state is responsible for the decay. Acknowledgement This work was partially supported by a Grant-inaid for Scientific Research (No. 05452039) from the
447
Ministry of Education, Science and Culture of Japan. One of the authors (JT) also acknowledges the tinancial support for this study by the Nissan Science Foundation, The Foundation “Hattori-Houkokai” and Sumitomo Foundation.
References [ 1 ] H.G. Heller and R.J. Hart, Chem. Sot. Perkin Trans. I (1972) 1321. [ 21 H.G. Heller and J.R. Langan, J. Chem. Sot. Perkin Trans. II (1981) 341. [ 3 ] P.J. Darcy, H.G. Heller, P.J. Strydom and J. Whit@ J. Chem. Sot. Perkin Trans. I ( 198 1) 202. [4] A. Kaneko, A. Tomoda, M. Ishizuka, H. Suzuki and R. Matsushima, Bull. Chem. Sot. Japan 61 (1988) 3569. [ 5 ] Y. Yokoyama, T. Goto, T. Inoue, M. Yokoyama and Y. Kurita, Chem. Letters (1988) 1049. [ 6 ] Y. Yokoyama, T. Iwai, N. Kera, I. Hitomi and Y. Kutita, Chem. Letters (1990) 263. [7] S. Kurita, A. Kashiwagi, Y. Kurita, H. Miyaaaka and N. Mataga, Chem. Phys. Letters 17 1 ( 1990) 553. [ 8 ] H.-D. IIge, M. Kaschke and D. Khechinashvili, J. Photochem. 33 (1986) 349. [9] D.A. Parthenopoulos and P.M. Rentzepis, J. Mol. Struct. 224 (1990) 297. [lo] Y. Yokoyama, T. Yamane and Y. Kurita, J. Chem. Sot. Chem. Commun. ( 199 1) 1722. [ 111 D.L. Dexter, in: Solid state physics, Vol. 6, eds. F. Seitz and D. Tumbull (Academic Press, New York, 1972) p. 370. [ 121 S.J. Strickler and R.A. Berg, J! Chem. Phys. 37 (1962) 814. [ 131 J. Takeda, N. Nakayama, N. Nagase, T. Tayu, K Kainuma, S. Km-ha, Y. Yokoyama and Y. Kurita, Chem. Phys. Letters 198 (1992) 609. [ 141 J. Brandrup and E.H. Immergut, eds., Polymer handbook, 2nd Ed. (Wiley, New York, 1975) chs. 3,8. [ 151 C. Lenoble and R.S. Becker, J. Phys. Chem. 90 ( 1986) 265 1. [ 161 E. Gutsche, Phys. Stat. Sol. (b) 109 (1982) 583. [ 171 N.J. Turro, Modem molecular photochemistry (Benjamin/ Cummings, Menlo Park, 1978) p. 183.
CHEMICAL
PHYSICS LETTERS Chemical Physics Letters 220 ( 1994) 443-447
Radiative and non-radiative decay processes of the excited state of the colored form of photochromic furylfulgide J. Takeda ‘, T. Tayu ‘, S. Kurita a, Y. Yokoyama b, Y. Kurita b, T. Kuga c,l, M. Matsuoka c oLaboratoryofAppliedPhysics,FacultyofEngineering, YokohamaNationalUniversity,Hodogaya, Yolwhatna240, Japan b Departmentof MaterialsScience and ChemicalEngineering, Faculty of Engineering, YokohamaNationalUniversity, Hodogaya, Yokohama240, Japan ’ Institutefor Solid State Physics,Universityof Tokyo,Roppongi,Minato-ku106, Tokyo,Japan
Received 1 November 1993;in final form 13 January 1994
Abstract The time evolution of the luminescence of the colored form of a furylfulgide dispersed at various concentrations in a poly (methyl methacrylate ) film was measured as a function of the luminescence photon energy. The observed decay time of the luminescence is about l-2 ns and one order of magnitude shorter than the radiative lifetime ( 14 ns) estimated from the absorption intensity. The decay time is independent of temperature below 77 K. These results suggest that the non-radiative tunneling process from the excited state to the ground state is responsible for the decay.
1. Introduction Rewritable photon mode optical memories using photochromic organic compounds have attracted much interest because of their potentially superior properties for the application of photomemory. Since Heller and co-workers reported that 2-[ 1-(2,5-d& methyl-ffuryl)ethylidene]-3-isopropylidenesuccinic anhydride (fulgide 1) is a highly efficient photochromic compound [ l-3 1, fulgides have been considered to be one of the most promising candidates for such memory. Various studies on the syntheses of different kinds of fulgides [ 4-6 1, the dynamics of the photoreaction [7-91 and a method for a non-destructive readout of a photon mode optical memory [ 10 ] have been carried out. However, the fundamental studies for elucidating ’ Present address: Collegeof Arts and Science, University of Tokyo, Komaba, Meguro-ku 153,Tokyo, Japan.
the properties of the excited state and its relaxation processes for fulgides have not been well performed. We report a study of the time evolution of the luminescence from the colored form (C-form) of the fulgide in order to elucidate the relaxation processes of the excited state of the C-form of the fulgide.
2. Experimental (E)-2- [ l-( 2,5dimethyl-3-furyl)-2-methylpropylianhydride ( fulgide 2 ) was dispersed in a poly (methyl methacrylate ) film (PMMA film) with concentrations of 0.0 1,0.02 and 0.1 M ( 1 M= 1 mol/dm3) by a previously reported method [ $61. The typical thickness of a sample was 50 pm. The absorption spectra were measured at 4.2 K using the monochromatic light obtained from W and Xe lamps. Time-integrated luminescence spectra and
dene ] -3Gsopropyhdenesuccinic
0009-2614/94/$07.00 8 1994 Elsevier Science B.V. All rights reserved SSDIOOOS-2614(94)00190-2
444
J. Takeda et al. / Chemical Physics Letters 220 (I 994) 443-44 7
the time evolution of the luminescence were measured at 4.2 and 77 K with the light excitation of the second harmonic of a mode-locked cw YAG laser. The excitation energy, repetition rate and pulse width of this laser were 18.8x lo3 cm-’ (532 nm), 82 MHz and 70 ps, respectively. The excitation light was irradiated at near-normal incidence on the sample’s surface. The time-integrated luminescence from the irradiated surface was detected by a photomultiplier and the time response of the luminescence analyzed by a synchroscan streak camera. The overall time resolution of the present experiments including the temporal broadening due to a 0.5 m grating monochromator was 90 ps and the spectral resolution 16 cm-‘. The average power of the excitation light was less than 2 mW/mm* to avoid damage to the samples.
3. Results and discussion 3. I. The oscillator strength and the radiative lifetime of the C-form of the fulgide in the visible light region On irradiation with ultraviolet light the E-form (colorless form) of the fulgide is transformed to the C-form and on irradiation with visible light the Cform turns back to the E-form. Fig. 1 shows the absorption spectrum of the C-form of fulgide 2 with concentration 0.02 M in a PMMA film at 4.2 K. The thickness of the sample is 50 pm. The molecular Wavelength (nm)
,,.
800700 600
500
400 ,
3?0 110
structure of the C-form is also shown in Fig. 1. From the integrated absorption intensity within the energy range of the visible light region ( ( 16-25) x lo3 cm-‘), we estimated the oscillator strength and the radiative lifetime of the C-form of fulgide 2. The oscillator strength fcp and the radiative lifetime rR are givenby [11,12]
(1) and ‘,=
* c3m*fiz( lEeg I) 2e*n&( jE,,l’) ’
(2)
Here, N is the molecular density, n the refraction index of the matrix, m* the effective electron mass, c the light velocity, e the electron charge, fi the reduced Planck constant and peg(E) the absorption coeffrcient. The ( IEegI ) and the ( IEge( ) are the average energies of the absorption and the luminescence spectra, respectively, being taken as equal to the peak energies of the absorption spectra (Z 19.9~ lo3 cm-‘) and the luminescence spectra (S 15.8~ lo3 cm- ’ ) [ 13 1. The refractive index n is taken to be 2 for the PMMA [ 14 1. We found that the values of the oscillator strength& and the radiative lifetime rR of fulgide 2 are 6.6 x lo-* and 14 ns, respectively, by using the above equations. The value off, suggests that the absorption of the C-form in the visible light region is due to the allowed ~-IL*transition [ 15 1. 3.2. The non-radiative decay process of the excited state of the C-form of thefilgide
4.2K 0.8-
A .Ti i 0.68
0.02M
0.4-
0 0.2-
Photon Energy (x103cm“)
Fig. 1. Absorption spectrum of the C-form of fidgide 2. The ordinate shows both the optical density and the molar extinction coeffkient c. The structure of the C-form is also shown in the fgure (R=isopropyl).
Some fraction of the fulgide molecules in a PMMA film is unable to change from the C- to the E-form at low temperature on irradiation of visible light, and then the luminescence of the C-form can be observed at low temperature [ 13 1. Fig. 2 shows the decay profile of the luminescence of the C-form fulgide with different concentrations and various spectral positions at 4.2 K. The numerical value on the left of each spectrum indicates the photon energy of the spectral position in units of lo3 cm-‘. The broken curves are the tits from a single exponential decay convoluted with the time profile of the laser pulse (the fitting parameter is 7). The value on the right of each spectrum
J. Takda et al. /Chemical PhysicsLetters220 (1994) 443-447
445
In the low-concentration cases (0.0 1 and 0.02 M ) , on the other hand, luminescence occurs from every
0
1
Time ( ns )
2
2 -1 Time ( ns )
/
I
I
0
1
2
Time (ns)
Fig. 2. Time behavior of the luminescence from the C-form fulgide with different concentrations and various spectral positions. The numerical value on the left of each spectrum indicates the photon energy of the luminescence in units of 1O3cm-‘. The broken curves show the tits from a single exponential decay convoluted with the time profile of the laser pulse. The titting parameter r is also shown on the right of each spectrum.
shows the value of the fitting parameter r in units of ns. According to our recent study, the energy of the excited state of the C-form of the fulgide molecule in a polymer film is slightly different from molecule to molecule because the environment around each fulgide molecule in a polymer film is different. In this situation, a Fiirster transfer proceeds from molecules having higher energy excited states (energy donors) to molecules having lower energy excited states (energy acceptors) in the high-concentration case. The estimated critical distance of the Fiirster transfer R. is x 40 A. The average distance between fulgide molecules, R, is about 30 A (0.1 M) and 55 A (0.02 M) [ 13 1. The ratio of the transition probability of the Fijrster transfer to the radiation decay rate of the donor molecules is given by (Ro/R)6. The values of the ratio in the cases of 0.1 and 0.02 M are about 6 ( > 1) and 0.15 ( < 1 ), respectively. Therefore, we assume that a Forster transfer takes place in the case of 0.1 M and can be neglected in the cases of 0.01 and 0.02 M. In the case of 0.1 M, luminescence takes place only from the fulgide molecules having a lower energy excited state after the Forster transfer is completed, and the luminescence spectrum may consist of almost a single luminescence band. The luminescence intensity at every luminescence photon energy thus decays exponentially with time and T represents the decay time of the luminescence as shown in Fig. 2.
photo-excited molecule without a Fiirster transfer implying that the luminescence spectrum consists of multiple luminescence bands. The luminescence intensityL(E,t)isgivenbyC,L@)exp(-t/ri),where Lj(E) and ri denote the luminescence intensity at energy E and the decay time of the ith luminescence band, respectively. The observed luminescence intensity actually seems to decrease single exponentially with time as shown in Fig. 2. Thus the decay time Tobtained experimentally should be taken as the averaged value of ri over the luminescence bands concerned for a given value of E. Fig. 3 shows the values of the decay time r (closed circles) as a function of the luminescence photon energy for various concentrations. Also, the time-integrated luminescence spectra are shown in the figure. The down arrows indicate the energy position of the excitation light by the second harmonic of a cw modelocked YAG laser. We also found that the shape of the luminescence spectra and the decay time of the luminescence at 77 K were almost the same as those for 4.2 K. The decay time of the luminescence is one order of magnitude shorter than the estimated radiative lifetime ( 14 ns) and does not depend on temperature
a)O.lM
A
4.2 K
2 i
Photon Energy ( xl 0 3 crri’)
Fig. 3. Value of the decay time T (closed circles) as a function of the luminescence photon energyfor various concentrations.Timeintegrated luminescence spectra are also shown in the figure. Down arrows indicate the energy position of the excitation light.
J. Takedaet al. / ChemicalPhysicsLetters220 (I 994) 443-447
446
below 77 K. This suggests that the non-radiative tunneling process from the excited state to the ground state is responsible for the decay of the luminescence. In the high-concentration case (0.1 M), the decay time of the luminescence is about 0.9 ns and independent of the spectral position indicating that the luminescence spectrum consists of almost a single luminescence band. On the other hand, the decay time r decreases from 2.3 to 0.9 ns with decreasing luminescence photon energy in the low-concentration cases (0.0 1 and 0.02 M). These experimental results are explained by the model of the non-radiative transition in a localized electron system [ 16,17 1. Fig. 4 shows typical potential diagrams in a localized electron system. Labels a and b correspond to two different fulgide molecules whose excited states have different energies due to the different environment around each molecule. The notation 1e,) and ]ei,) denotes the excited states of the C-form in the a and b molecules, and 1g) the ground state of the fulgide molecules, where the energy of the ground state is taken as the same for every molecule. IV, represents the relaxation energy of a localized electron, and & the energy difference between the minimum point of the potential curve of the excited state and that of the ground state. We assume that the curvature of the E
lea>
43’
potential curves and the lattice distortion QO,which gives the minimum point of the potential curve of the excited state, do not change from molecule to molecule in a polymer. The latter assumption was employed to explain why the peak energy of the luminescence spectrum of the C-form fulgide at low concentrations decreases with decreasing excitation photon energy [ 13 1. Under these assumptions, W,, does not vary but E,, changes from molecule to molecule in a polymer. Gutsche [ 161 calculated the non-radiative multiphonon transition rate W from the excited state to the ground state in the localized electron system represented in Fig. 4 using non-Condon approximations and found that W is given by wcc exp( -S)Sp-I
P!
xew( -+V
Fig. 4. Typical potential diagrams in a localized electron system for the C-form of the fulgide in a polymer film. Labels a and b correspondto two diRerentfulgide molecules whose excited states have different energies. The notation 1e.) and )e,,) denotes the excited states of the C-form in the a and b molecules, and Jg) the ground state of the fulgide molecules. W, represents the relaxation energy of a localized electron, and EOthe energy difference between the minimum point of the potential curve of the excited state and that of the ground state. The lattice distortion & gives the minimum point of the potential curve.
(3)
for the low temperature limit. Here, S (the HuangRhys factor) and Pare equal to W&iw and E,,/hw, respectively, n, is the phonon occupation number and fiw the phonon energy relevant to the tunneling process. In the present case, the values of W, and E. are about 2.1 x lo3 and 17.9 x 10’ cm- ‘, respectively, judging from the peak positions of absorption and luminescence spectra. Then P is about one order of magnitude larger than S, and Eq. (3) is simplified using Stirling’s formula, WccP3’2exp(-aP)
Lattice Distortion Q
(P-S)Z(n,+1)2
(cu=ln(P/S)-1).
(4)
This equation shows that the non-radiative decay rate W decreases with increasing P in the case of large P (P>3/2ax 1.5). In the low-concentration case, the energy transfer among the fulgide molecules is negligible and the luminescence proceeds from every excited molecule in a polymer. The lower energy part of the luminescence spectrum consists of the luminescence from the b-type molecules and the higher energy part of the luminescence is due to the luminescence from the a-type molecules. The non-radiative decay rate of the lower part of the luminescence spectrum is larger than that of the higher part of the luminescence spectrum because P for the b-type molecule is smaller than that for the atype molecule as shown in Fig. 4. Thus the non-radia-
J. Takzabet al. / ChemicalPhysicsLetters220 (1994) 443-447
tive decay time of the luminescence is longer at higher luminescence photon energy. A quantitative evaluation of the observed decay time is possible by using Eq. (3) if the vibrational frequency w of fulgide 2, relevant to the decay process, is known. Assuming that the magnitude of the vibrational frequency is about 2000-3000 cm-‘, which is adequate for organic molecules, we can well explain the experimental result that the decay time of the luminescence decreases with decreasing photon energy from 2.3 to 0.9 ns. A detailed discussion including the vibrational structure of fulgide 2 will be developed elsewhere. 4. Conclusion The oscillator strength and the radiative lifetime of the C-form of fttlgide 2 were estimated as 6.6 x 1O-’ and 14 ns, respectively. Judging from these values, the absorption of the C-form in the visible light region is due to the allowed x-x* transition. The decay time of the luminescence of the C-form of the fulgide is about l-2 ns and one order of magnitude shorter than the radiative lifetime. The decay time of the luminescence at high concentration (0.1 M) is independent of the luminescence photon energy, while, at low concentration (0.01 and 0.02 M), the decay time decreases with decreasing luminescence photon energy. These results suggest that the non-radiative tunneling process from the excited state to the ground state is responsible for the decay. Acknowledgement This work was partially supported by a Grant-inaid for Scientific Research (No. 05452039) from the
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Ministry of Education, Science and Culture of Japan. One of the authors (JT) also acknowledges the tinancial support for this study by the Nissan Science Foundation, The Foundation “Hattori-Houkokai” and Sumitomo Foundation.
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