Temperature Dependent Radiative Lifetime of J-Aggregates

value of the center-of-mass wave vector can recombine radiatively. Nonradiative relaxation becomes efficient with a rise of temperature and is explain...
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J. Phys. Chem. 1996, 100, 8640-8644

Temperature Dependent Radiative Lifetime of J-Aggregates Valey F. Kamalov,†,‡,§ Irina A. Struganova,⊥ and Keitaro Yoshihara*,† Institute for Molecular Science, Myodaiji, Okazaki 444, Japan, Institute of Chemical Physics, Russian Academy of Sciences, Kosygin Street 4, Moscow 117977, Russia, and Laser for Photochemistry Ltd., NoVatoroV Street 7, Moscow 117421, Russia ReceiVed: August 2, 1995; In Final Form: March 19, 1996X

The emission quantum yield of carbocyanine dye J-aggregates decreased 4-fold when temperature increased from 20 to 80 K. Independent measurements of the emission quantum yield and decay were used to calculate both radiative and nonradiative rate constants in the temperature range of 4-140 K. The radiative lifetime is found to linearly increase as temperature rises and is explained by the two-dimensional structure of J-aggregates assuming thermal distribution of excitons with the requirement that only excitons with a small value of the center-of-mass wave vector can recombine radiatively. Nonradiative relaxation becomes efficient with a rise of temperature and is explained by exciton self-trapping.

Introduction Jelly1

Scheibe2

and reported formation of a new absorption band in concentrated aqueous solutions of pseudo-isocyanine (PIC) dye. This sharp band at the red tail of the monomer absorption spectrum is due to creation of molecular aggregates, often called J-aggregates. Recent activities in the investigation of the exciton transition of J-aggregates were stimulated by the work of De Boer and co-workers,3,4 who measured both the dephasing time (by the accumulated photon echo technique) and the emission decay of PIC aggregates in glass at low temperatures. They proposed the superradiant character of emission to explain the short decay time of 70 ps at 1.5 K. This experiment was explained with the theory of superradiant emission of molecular aggregates by Spano and co-workers.5,6 We observed with carbocyanine (BIC) J-aggregates a clear dependence of the emission quantum yield at temperatures below 100 K. It is necessary to correct the emission lifetime on the basis of the quantum yield when the radiative lifetime is calculated. Recently for PIC7 the fluorescence lifetimes corrected for nonradiative decay were reported and discussed. The features of Frenkel excitons in molecular crystals can be used to describe exciton behavior in J-aggregates. The theory of molecular excitons was developed in the 1960s.8,9 Exciton diffusion and mechanisms of relaxation were studied in detail in the 1970s.10,11 Progress in the technology of producing small size semiconductor structures (at the nanometer scale) stimulated a number of authors to study exciton behavior in lowdimensional systems such as quantum wells and quantum wires.12,13 The quantum confinement effect of excitons in CdS microcrystallites was studied by time-resolved spectroscopy.14,15 We discuss the dimensionality of J-aggregates on the basis of the temperature dependence of the radiative lifetime with a theory developed for Frenkel excitons in the low-dimensional semiconductor structures.16 In this paper we present the results of the study of relaxation of excitons formed from carbocyanine BIC in a poly(vinyl alcohol) (PVA) film. We carried out optical measurements at different temperatures to determine the characteristic lifetimes †

Institute for Molecular Science. Russian Academy of Sciences. Present address: Department of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, GA 30332. E-mail: Valey.Kamalov@ chemistry.gatech.edu. ⊥ Laser for Photochemistry, Ltd. X Abstract published in AdVance ACS Abstracts, May 1, 1996. ‡ §

S0022-3654(95)02247-7 CCC: $12.00

and relaxation mechanisms. All measurements were taken at low exciton intensity to prevent the two-exciton effects observed recently in J-aggregates at high excitation intensity.17-21 We found that carbocyanine dyes form crystals of micrometer size in PVA films. The radiative lifetime is found to linearly increase as temperature rises and is explained by the low dimensionality of J-aggregates. Nonradiative relaxation becomes efficient with a rise of temperature and is explained by exciton self-trapping. Experimental Details and Results The molecular structure of BIC (1,1′-diethyl-3,3′-bis(sulfopropyl)-5,5,6,6′-tetrachlorobenzimidacarbocyanine), shown in Figure 1, was purchased from Nippon Kankoh Shikiso. BIC monomer has an absorption band with a maximum at 515 nm in methanol solution. The radiative lifetime is 1.28 ns according to the emission decay measured at 4 K.22 J-aggregates were prepared in films of poly(vinyl alcohol) (PVA) by the standard spin coating method.23 PVA powder from Kuraray was dissolved in distilled water (1/50 volume ratio), and dye was dissolved at a concentration of 10-5 M and heated to about 130 °C. The color of this mixture corresponded to the monomer form of dye at such a temperature. Hot solution was dropped on a cold plate (20 °C), which was rotated at a speed of 5 cycles/s. The characteristics of both absorption and emission spectra of the film were similar to those of the sample in the water/ethylene glycol mixture.22 The sample in the film is much more stable than in solution. High optical quality of the film in the temperature range 4-300 K allows us to measure absorption spectra and the emission quantum yield. The microcrystals were formed in the film which were observed by a fluorescence microscope. The image was observed with excitation at 530 nm and examination at 600 nm. J-aggregates in the film looked like “red submarines” in shape with 10-20 µm length and one-third width. The thickness of these aggregates was difficult to estimate. They seemed to be planar. The geometrical forms and size of microcrystals depend on the conditions of film preparations, but optical characteristics were practically the same. This can be explained taking into account two parameters of J-aggregates: the physical size and effective coherent exciton size. The physical size is much larger than the effective coherent exciton size. The latter is the area where excitation is delocalized and is determined by the interaction between molecules. The effective coherent exciton size is responsible for the optical properties. © 1996 American Chemical Society

Radiative Lifetime of J-Aggregates

J. Phys. Chem., Vol. 100, No. 21, 1996 8641

a

b Figure 2. Temperature dependence of the relative quantum yield of BIC J-aggregate emission in the PVA film. Excitation 530 nm.

c

Figure 3. Emission decay time temperature dependence of BIC J-aggregates in the PVA film (squares) and water/ethylene glycol glass (open circles). Excitation 570 nm. Figure 1. Absorption (solid line) and emission (dashed line, excitation 570 nm) spectra of BIC J-aggregates in a film of PVA measured at 4 K (a) and 90 K (b). (c) Structural formula of BIC.

Emission decays of BIC J-aggregates in PVA films were measured at different temperatures. J-aggregates were excited by a mode-locked dye laser with a pulse duration of 10 ps at 580 nm. The description of the experimental system can be found elsewhere.22 Briefly, the time-correlated photon counting technique was used with a response function of 60 ps. A sample was held in an optical helium cryostat, Oxford CF1204. Emission decay curves were measured at the maximum of the emission band, 593 nm. The excitation intensity was always kept below 103 W/cm2 to prevent the possible contribution of two-exciton effects.17-21 The Global Unlimited program was used to analyze decay curves. Absorption spectra of J-aggregates in films are shown in Figure 1 together with their emission spectra. The solid line in Figure 1a is the absorption spectrum measured at 4 K with a maximum at 589 nm and width of 10 nm at the full width at half-maximum (FWHM). The monomer absorption band is absent in the spectrum which indicates complete aggregation of dye molecules. The emission spectrum (dotted line in Figure 1a) measured at 4 K with excitation at 570 nm had a maximum at 592 nm. The emission bandwidth is about 2 times narrower compared to that of the absorption spectrum. The steady-state emission spectra were measured with a Shimadzu spectrofluorimeter with slits at excitation and emission monochromators corresponding to 1.5 nm, so that the real emission spectrum of J-aggregates is even narrower than that presented in Figure 1a. The full width at half-maximum (FWHM) is estimated to be about 4 nm (110 cm-1). In Figure 1b the absorption and emission spectra measured at 90 K are shown. The absorption spectrum (solid line) has

the same maximum as that at 4 K, the half-width being about the same with 10% accuracy. The absorption maximum moved from 589 nm at 4 K to 593.5 nm at 300 K. The absorption bandwidth increased from 300 to 500 cm-1, correspondingly. All changes mentioned above take place at T > 100 K. The emission maximum changes from 592 nm at 4 K to 594 nm at 300 K, and all changes take place at T > 100 K, too. The emission bandwidth is increased at the full temperature range (including the low-temperature range, T < 100 K) from 150 cm-1 (4 K) to 350 cm-1 (300 K). The broadening can be seen by comparison of the emission spectra presented in parts a and b of Figure 1 (dotted lines). The temperature dependence of the emission intensity is presented in Figure 2. The emission is excited at 530 nm and is observed in the spectral range of 585-605 nm. The absorption spectral change is not more than 10% at this wavelength in the temperature range of 4-150 K. The emission bandwidth is smaller than 10 nm at such a temperature range so that practically all emission is integrated, and the data in Figure 2 represent the relative value of the emission quantum yield. The key experimental observation is a significant decrease of the relative quantum yield of about 5-fold in the temperature range of 4-150 K. A plateau can be seen at T < 10 K, which is the reason to assume the absolute quantum yield at the liquid helium temperature is unity. The data at T > 150 K show that the emission intensity was practically constant at higher temperatures. The temperature dependence of the emission decay is presented in Figure 3 by squares. The emission decay depends on the emission wavelength at low temperatures, as was shown in ref 24. Here we fitted decays measured at the maximum of the emission spectrum by a single exponential curve. The emission decay at 4 K was fitted by an exponential curve with a 102 ps decay time with high enough fitting quality (characterized by the standard parameter χ2 ) 1.733 with 104 counts at

8642 J. Phys. Chem., Vol. 100, No. 21, 1996

Kamalov et al.

Figure 4. Temperature dependence of the radiative lifetime of BIC J-aggregates in the PVA film.

the maximum). Decay times decrease from 100 ps at T < 40 K to about 80 ps at T > 60 K. The decrease of the decay time is evidence of the nonradiative decay process that takes place in J-aggregates at T > 40 K. Similar behavior was observed for J-aggregates in glass22 (open circles in Figure 3) so that the nonradiative decay characterizes the exciton itself but is not a specific feature of the glass or film. The value of the emission decay time, 102 ps, at 4 K in a PVA film is also comparable with that for an exciton in an ethylene glycol/water glass, where we obtained 100 ps. The emission quantum yield (Φ) is the ratio of emitted and absorbed photons and is determined by two independent constants: the radiative rate constant (krad) and nonradiative rate constant (knrad), Φ ) krad/(knrad + krad). The emission lifetime (τ) also depends on both radiative and nonradiative rate constants: τ ) 1/(krad + knrad). Independent measurements of Φ(T) and τ(T) are necessary to determine krad(T) and knrad(T) according to eqs 1 and 2, all the quantities being temperature dependent.

Φ(T) ) krad(T)/(krad(T) + knrad(T))

(1)

τ(T) ) 1/(krad(T) + knrad(T))

(2)

The radiative lifetimes τrad(T) obtained from Φ(T) (Figure 2) and τ(T) (Figure 3) are presented in Figure 4. The minimum value of τrad ) 102 ps was at 4 K. The rise of temperature leads to a 5-fold increase of the radiative lifetime in the temperature range of 4-150 K. The nonradiative rate constant is presented in Figure 5 for the temperature range of 4-150 K. knrad increases with temperature, reaching the value 1.1 × 1010 s-1 at 140 K. Discussion We explain the temperature dependence of the radiative lifetime (Figure 4) with the theory developed recently for lowdimensional systems.12,13,16 Feldman et al.12 realized that the time-resolved photoluminescent decay time has a temperature dependence, τ(T), that also depends on the dimensionality of the sample. Because of the k-conservation rule, the exciton with a large center-of-mass wave vector, k > ko, cannot decay radiatively, where ko is the wave vector of light with the same energy as the exciton.8 The effect of the thermalization is characterized by the parameter ζ(T), which expresses the fraction of excitons with k < ko. By assuming Maxwell-Boltzmann distribution for excitons,12 ζ(T) is given by

ζ(T) ) ∫0 D(E)e-E/kBT dE/∫0 D(E)e-E/kBT dE ∆

∞

(3)

Figure 5. Temperature dependence of the nonradiative rate constant of BIC J-aggregates in the PVA film.

where D(E) denotes the density of states (DOS) of excitons and ∆ ) p2ko2/2M the maximum kinetic energy of excitons that can decay radiatively. The values of M ) 15.4me (me is the free electron mass; estimation assuming exciton bandwidth at 0.6 eV) and the photon energy of the observed emission pν ) 2.1 eV for BIC J-aggregates give ∆ ) 0.6 µeV. Substituting DOS for one-dimensional and two-dimensional systems (∼1/xE and constant, respectively), and assuming T . ∆/kB, we obtain

ζ1D(T) ) (4∆/πkBT)1/2

(4)

ζ2D(T) ) ∆/kBT

(5)

The averaged radiative lifetime τ(T) is then given by

τ1D(T) ) τoζ1D(T)-1 ) τo(πkBT/4∆)1/2

(6)

τ2D(T) ) τoζ2D(T)-1 ) τokBT/∆

(7)

where τo is the intrinsic radiative lifetime of the exciton at k ∼ 0. Therefore, for a two-dimensional system, the assumption of a thermal distribution of excitons with the requirement that only excitons with small value of the center-of-mass wave vector can recombine radiatively leads to τ(T) ∼ T.16 The solid line in Figure 4 is a best fit of the radiative lifetime of J-aggregates assuming linear dependence on the temperature. This result contradicts the model of a one-dimensional chain usually used for J-aggregates, which should give square root temperature dependence. As a compromise the model can be proposed where one-dimensional chains of J-aggregates are packed in the crystal parallel to each other so that the effective interaction between them takes place. J-aggregates observed by a near field microscopy contained multiple chains woven together or parallel located chains.25 De Boer and Wiersma measured the temperature dependence of the emission decay of PIC J-aggregates.4 Recently for PIC7 the fluorescence lifetimes corrected for nonradiative decay were reported and discussed. The quantum yield correction reduces the temperature up to which the fluorescence lifetime remains constant from 50 K4 to less than 30 K. In the description of uncorrected data by Spano et al.,6 where dephasing was activated by a 240 cm-1 optical phonon, the constant regime up to 50 K was matched well due to negligible activation of the optical phonon up to this temperature. The lower onset temperature of the radiative lifetime lengthening, due to quantum yield correction, could be obtained by using a lower frequency optical phonon. It was pointed out in ref 7 that the lengthening of the fluorescence lifetime, both before and after the relative quantum yield correction, remains far too strong above 70 K for PIC in

Radiative Lifetime of J-Aggregates

J. Phys. Chem., Vol. 100, No. 21, 1996 8643

order to be understood in frames of exciton-phonon interaction on the basis of a thermalized exciton population. Our data for BIC show that the temperature dependence of radiative decay can be treated assuming thermal distribution of excitons with the requirement that only excitons with a small value of the center-of-mass wave vector can recombine radiatively. It is interesting that the discussion on the radiative lifetime was launched a long time ago. First, Frank and Teller pointed out in 193826 that “the lifetime in this state will be that of a single cell if radiating by itself, divided by the number of cells in which the interacting photon and exciton can be described by a pure sine wave and for which, therefore, interference of the emitted light can occur“. Kasha showed that the enhancement of the dipole moment of a linear chain of molecules by µJ ) (N)1/2µmon, where N is the effective coherent exciton size and µJ and µmon are dipole moments of the aggregate and monomer, respectively.27 The radiative rate constant for dipole-allowed transition is given by krad ) 4µ2/3pλ3c3. Due to enhancement of the dipole moment the effective coherent exciton size can be found (for a onedimensional chain) as

N ) (krad/kradmon)(λJ/λmon)3

(8)

Here λJ and λmon are the absorption maxima of exciton and monomer transitions, respectively. The effective coherent exciton size of a one-dimensional chain at 4 K is N ) 18, which is found using radiative rate constants of the exciton (krad ) 9.8 × 109 s-1) and monomer dye (kradmon ) 0.8 × 109 s-1 based on the measurement of BIC monomer emission decay in methanol at 4 K22). Similar consideration for a two-dimensional system following ref 8 gives an area of ca. 4 × 4 molecules where the excitation is delocalized. Deformations of all kinds (including structural inhomogeneity of the crystal and distribution of the energy of dipole-dipole interaction between neighboring molecules) prevent further delocalization of excitation. This is opposite to the interaction energy between dipoles, which leads to delocalization of the excitation. The motional narrowing averages structural inhomogeneity so that the off-diagonal disorder (distribution of dipole-dipole interaction considered in ref 28) is the main reason for the limited effective coherent exciton size. Our model of homogeneous two-dimensional aggregates nicely reproduces the results of radiative lifetime temperature dependence, so that the inhomogeneity of BIC J-aggregates does not seem to determine temperature dependence essentially. In Figure 5 the temperature dependence of the nonradiative rate constant is shown. The fitting curve is made by connecting two separate fits in two temperature ranges: (i) T < 60 K and (ii) T > 60 K. Ioselevich and Rashba developed a theory of the self-trapping rate.29,30 The rate is determined by the process in which the composite system consisting of the lattice and the exciton passes over a self-trapping barrier in configuration space. There are two distinct mechanisms for getting over the self-trapping barrier. At T > Tc, the process is purely one of activation, and its rate is described by exp(-W/kBT), where W is the height of the self-trapping barrier and the critical temperature Tc is on the order of phonon frequencies. This theory states that the exciton passes over the barrier, and the self-trapped exciton then decays either radiatively or nonradiatively. We reported previously24,31 on the red-shifted emission of a self-trapped exciton in J-aggregates, with dominantly nonradiative relaxation of electronic excitation. The solid line in Figure 5 in the temperature range of T > 60 K is the best fit of the nonradiative decay rate constant

according to

knrad(T) ) knrad0 exp(-W/kBT)

(9)

with knrad0 ) 1.38 × 1010 s-1 and W ) 0.6 kcal/mol. At T < Tc, Joselevich and Rashba proposed the mechanism of thermally activated tunneling.29 They constructed a solution for small radius excitons interacting with acoustic/optical phonons. We found the nonradiative rate knrad measured at T < 60 K in good agreement with their thermally activated tunneling of excitons interacting with optical phonons:

ln knrad ≈ const + exp(-ωo/kBT)

(10)

where ωo is the frequency of the optical phonon. The solid line in Figure 5 below 60 K is the best fit by eq 10 with ωo ) 25 cm-1. The temperature dependence of the nonradiative rate constant suggests the importance of the low-frequency mode of about 25-30 cm-1. This mode can be assigned to intermolecular oscillation, similar to the librational mode of molecular crystals. This low-frequency mode can contribute to the destruction of mutual coherence of dye molecules in the aggregates. Conclusions The emission quantum yield of BIC J-aggregates changes 4-fold in the temperature range 20-80 K. With emission decay measurement, both radiative and nonradiative decay rate constants were obtained. The radiative lifetime shows linear dependence on temperature for 20-140 K. Nonradiative relaxation of the exciton was observed. We suggest that self-trapping determines the nonradiative decay. The character of the nonradiative decay temperature dependence indicates that passing over the barrier is purely for activation at T > 60 K. The vibration with a frequency of ca. 30 cm-1 determines the ability to pass over the barrier in the temperature range 20-60 K. The temperature dependence of the nonradiative rate constant shows the important role of low-frequency vibration that determines the Frenkel-type exciton behavior. This vibration of about 30 cm-1 is probably intermolecular oscillation, similar to the librational mode of molecular crystals. Acknowledgment. V.F.K. was awarded a Visiting Professorship by the Japan Society of Promotion of Science. V.F.K. and I.A.S. appreciate the hospitality of the Institute for Molecular Science, Okazaki, Japan. We gratefully thank Professor V. M. Agranovich and Professor E. I. Rashba for their comments and discussion. V.F.K. thanks the Office of Naval Research (Grant No. N00014-95-1-0306) for support. References and Notes (1) Jelley, E. E. Nature (London) 1936, 138, 1009. (2) Scheibe, G. Angew. Chem. 1936, 49, 563. (3) De Boer, S.; Vink, K. J.; Wiersma, D. A. Chem. Phys. Lett. 1987, 137, 99. (4) De Boer, S.; Wiersma, D. A. Chem. Phys. Lett. 1990, 165, 45. (5) Spano, F. C.; Mukamel, S. J. Chem. Phys. 1989, 91, 683. (6) Spano, F. C.; Kuklinski, J. R.; Mukamel, S. Phys. ReV. Lett. 1990, 65, 211. (7) Fidder, H.; Wiersma, D. A. Phys. Status Solidi B 1995, 188, 285. (8) Agranovich, V. M. Theory of Excitons; Nauka: Moscow, 1968; Uspehi Fizicheskih Nauk 1974, 112, 143. (9) Davydov, A. S. Theory of Molecular Excitons; Plenum Press: New York, 1971. (10) Agranovich, V. M.; Galanin, M. D. Electronic Excitation Energy Transfer in Condensed Matter; Nauka: Moscow, 1978 (in Russian); North-Holland: Amsterdam, 1982 (in English). (11) Sumi, H.; Toyozawa, Y. J. Phys. Soc. Jpn. 1971, 31, 342.

8644 J. Phys. Chem., Vol. 100, No. 21, 1996 (12) Feldmann, J.; Peter, G.; Gobel, E. O.; Dawson, P.; Moore, K.; Foxon, C.; Elliot, R. J. Phys. ReV. Lett. 1987, 59, 2337. (13) Akiyama, H.; Koshiba, S.; Someya, T.; Wada, K.; Noge, H.; Nakamura, Y.; Inoshita, T.; Shimizu, A.; Sasaki, H. Phys. ReV. Lett. 1994, 72, 924. (14) Misawa, K.; Yao, H.; Hayashi, T.; Kobayashi, T. Chem. Phys. Lett. 1991, 183, 113. (15) Misawa, K.; Yao, H.; Hayashi, T.; Kobayashi, T. J. Chem. Phys. 1991, 94, 4131. (16) Citrin, D. S. Solid State Commun. 1994, 92, 851. (17) Gadonas, R.; Danelyus, R.; Piskarskas, A.; Rentsch, S. Bull. Acad. Sci. USSR, Phys. Ser. 1983, 47, 151. (18) Kamalov, V. F.; Struganova, I. A.; Koyama, Y.; Yoshihara, K. Chem. Phys. Lett. 1994, 226, 132. (19) Fidder, H.; Knoester, J.; Wiersma, D. A. J. Chem. Phys. 1993, 98, 6564. (20) Johnson, A. E.; Kumazaki, S.; Yoshihara, K. Chem. Phys. Lett. 1993, 211, 511. (21) Minoshima, K.; Taiji, M.; Misawa, K.; Kobayashi, T. Chem. Phys. Lett. 1994, 218, 67.

Kamalov et al. (22) Kamalov, V. F.; Struganova, I. A.; Tani, T.; Yoshihara, K. Chem. Phys. Lett. 1994, 220, 257. (23) Misawa, K.; Ono, H.; Minoshima, K.; Kobayashi, T. Appl. Phys. Lett. 1993, 63, 577. (24) Kamalov, V. F.; Struganova, I. A.; Yoshihara, K. Chem. Phys. Lett. 1993, 213, 559. (25) Barbara, P. F. Private communication. (26) Frank, J.; Teller, E. J. Chem. Phys. 1938, 6, 861. (27) Kasha, M. In Spectroscopy of the Excited State; di Bartolo, B., Ed.; Nato ASI Series, Series B, Physics; Plenum Press: New York, 1976; Vol. 12, p 337. (28) Fidder, H.; Knoester, J.; Wiersma, D. A. J. Chem. Phys. 1991, 95, 7880. (29) Ioselevich, A. S.; Rashba, E. I. SoV. Phys. JETP 1985, 61, 1110. (30) Rashba, E. I. Synth. Met. 1994, 64, 255. (31) Kamalov, V. F.; Yoshihara, K. Time ResolVed Vibrational Spectroscopy 7; Springer-Verlag: Berlin, to be published.

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