Relaxation and trapping of excitons in J-aggregates of a thiacarbocynine dye

E L S E V I E R Chemical Physics 211 (1996) 455-468

Chemical Physics

Relaxation and trapping of excitons in J-aggregates of a thiacarbocynine dye

M.A. Drobizhev a, M.N. Sapozhnikov a, I.G. Scheblykin a, O.P. Varnavsky M. Van der Auweraer b, A.G. Vitukhnovsky a

a Lebedev Physics Institute, Russian Academy of Sciences, Leninsky pr. 53, ] 17924 Moscow, Russian Federation b LaboratoryJbr Moleeular Dynamics and Spectroscopy, K.U. Leuven, Celestijnenlaan 200 F. 3001 Leuven, Belgium

Received 19 October 1995; in final form 12 April 1996

a

9

Abstract

Exciton relaxation processes in J-aggregates of 3,3',9-triethyl-5,5'-dichlorothiacarbocyanine iodide (TDC) dye have been studied by means of site-selective, steady-state and time-resolved spectroscopy. We found that TDC forms three different types of J-aggregates (J1,J2, and J3) in frozen solutions. Fluorescence polarization measurements showed that exciton diffusion between randomly oriented segments of aggregates plays a minor role in exciton relaxation. Optical properties of J3-aggregate fluorescent states are well described by the theoretical model of barrierless self-trapping of an exciton in a strictly one-dimensional discrete lattice. Upon optical excitation J3-aggregates also show thermally activated transformation to J2-aggregates. The height of the related potential barrier is approximately equal to 30 cm ~. Hence, two different exciton relaxation processes are proposed to take place in the system under study: barrierless self-trapping in J3-aggregates and thermally activated J3 ----> J2 photorearrangement.

1. In t roduct ion

It was discovered a long time ago that cyanine dyes can form specific aggregates that show a very narrow absorption band which is shifted to the red relative to the monomer band [1,2]. In honour of Jelley, these systems were called J-aggregates.

Polarization data obtained in streaming solutions suggest that J-aggregates have a linear extended structure [3]. The physical length of J-aggregates is not well established and estimated to be 10-10 5 molecules [4]. These systems are quite well orga- nized and, as in the case of molecular crystals, their excited states can be described by Frenkel excitons. The exciton motion in J-aggregates is considered to be restricted by one dimension and by a finite chain

length. However, modelling such systems as an ideal rigid linear chain cannot describe all their optical properties observed. J-aggregates are usually embedded in amorphous media that possess a greater structural disorder as compared to molecular crystals. This disorder can be described by an inhomogeneous distribution of site energies (diagonal disorder) and a distribution of resonance coupling constants between sites (non-diagonal disorder) ([5,6] and references therein). In addition, in reality some defects can break the chain into relatively decoupled segments. This effect can be considered within the framework of the model [7], which involves spatially correlated local disorder. In some papers these segments are assumed to be disorder-free linear chains of finite lengths. The disorder results in inhomogeneous line

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456 M.A. Drobizhev et al. / Chemical Physics 211 (1996) 455-468

broadening, although the stationary states are still delocalized over particular segment lengths. In addition, a real chain is not rigid and its vibrations affect the exciton dynamics through exciton-phonon coupling. Thus, J-aggregates in solutions are highly anisotropic (quasi-one-dimensional) restricted systems with static and dynamic disorder.

The excitation in such systems can relax either by exciton diffusion between different segments (parts of the chain) [4] or by intrasegment exciton energy conversion. A knowledge of relaxation mechanisms is of crucial importance for the variety of possible applications of such systems in non-linear optics, optical communications, and photosensitive devices.

As to the intrachain relaxation in J-aggregates, not so much attention has been paid to the possibility of photoinduced chain deformation as a mechanism of exciton relaxation. In particular, exciton self-trapping by chain distortion can be considered as a channel of relaxation in a deformable lattice. This process cru- cially depends on the system dimensionality and size restrictions [8-11]. It was found theoretically for three-dimensional (3D) systems that if the parameter of exciton-phonon coupling exceeds some critical value, the stable self-trapped state (ST) appears below the bottom of the band of free exciton states (F) [12,13]. In this case, two energy minima are separated by a potential barrier. On the other hand, as has been shown by Rashba [12], in infinite, strictly 1D chain, self-trapping occurs for any non-vanishing exciton-phonon coupling and the barrier between ST and F states is absent. Note that this model implies strictly 1D character of exciton motion and displace- ments of molecules. If the system is not strictly 1D, but still possesses a high anisotropy (quasi-one-dimensional), the potential barrier reappears [8,14,15].

The degree of topological anisotropy and therefore applicability of the 1D chain model for J-aggregates have not been established experimentally so far. There is even indirect evidence in the literature for the existence of the fractal dimensionality [16]. The investigation of self-trapping or related phenom- ena in J-aggregates can shed light on their meso- scopic dimensionality.

Self-trapping in J-aggregates has not been established directly, but some indirect indications to this process are present in the literature [17-20]. In [17,18], the authors observed a very extended and

intense red tail in the fluorescence spectrum at liquid helium temperature. This tail transformed to a sepa- rate wide red-shifted peak at 77 K [18]. The authors attributed these spectral features to self-trapping of excitons assisted by excimer formation. The mathe- matical analysis of the fluorescence decay kinetics in the region of the red peak provides evidence against the trapping by low-energy monomer traps [18]. In addition, the observed non-exponential fluorescence decay and the red shift of the time-resolved fluorescence spectrum suggest emission from the unrelaxed ST state. In [19], the appearance of the red tail in the fluorescence spectrum and broadening of the spectrum during hundreds of picoseconds were attributed to the self-trapping mechanism as one of the possi- bilities.

Our paper is devoted to the experimental investigation of exciton relaxation in molecular J-aggregates of a thiacarbocyanine dye and to the effect of electron-phonon coupling on their optical spectra. It is shown that the exciton relaxation in the system under study involves at least two different mechanisms that are related to the lattice distortion. The first one is the barrierless self-trapping inherent in the 1D chain, resulting in the Stokes shift of luminescence even at very low temperatures. The second one is a temperature-activated photorearrangement of one J-aggregate form (J3) to another (J2).

2. Experimental

The 3,3',9-triethyl-5,5'-dichlorothiacarbocyanine iodide (TDC) dye was synthesized at Niikhimfoto- proekt PLC, Moscow and used without further pu- rification.

For preparation of J-aggregates, TDC was dis- solved in a 3 : 2 ( v / v ) water-ethylene glycol (WEG) mixture under heating up to 70°C. The solutions with a dye concentration of = 3 X 10-3 M were cooled to room temperature, put into a dismountable glass cell 200 or 400 /xm in thickness, then cooled in a CF-204 Oxford Instruments helium cryostat to 250 K and kept at this temperature for 10-30 min. At this stage, a narrow J-band appeared at 618 nm in the absorption spectrum of the dye. Then the samples were placed into liquid nitrogen where they were frozen for about 30 s, again placed into a cryostat at

M.A. Drobizhev et al. / Chemical Physics 211 (1996) 455-468 4 5 7

80 K and finally cooled down to liquid helium temperature. Some experiments were performed at 77 K in a liquid nitrogen cryostat.

Fluorescence excitation and hole burning were performed with an argon laser-pumped CR-699-21 Coherent cw ring dye laser operated with Rhodamine 6G in the multimode regime with a linewidth of about 0.1 cm -~. The transmission spectra were recorded using a stabilized filament lamp and a double spectrometer or polychromator coupled with an optical multichannel analyzer. The hole spectra were detected with a resolution of 0.6-1 cm- ]. The procedure of estimation of the true hole width was described elsewhere [21].

Gated frequency mixing (up-conversion) tech- nique was used for fast fluorescence decay measurements. The picosecond laser setup based on a Coher- ent Antares system consists of a synchronously pumped cavity-dumped dye laser (Model 702) driven by a Nd:YAG laser (Antares 76s). Upon passing through a variable optical delay line, picosecond light pulses from the dye laser were mixed with the fluorescence signal from the sample in a non-linear LilO 3 crystal. The sum frequency light generated in the non-linear crystal was spatially (non-linear ge-

ometry) and spectrally (filters and an MDR-2 monochromator) separated from the laser light and the fluorescence was detected by a FEU-106 cooled photomultiplier. This system provided measuring picosecond fluorescence kinetics with a time resolution of about 3 ps with the excitation wavelength tuned within the 565-620 nm range.

3. Results and discussion

3.1. General view of spectra of samples with J-aggregates of TDC

Three types of J-aggregates can be observed in concentrated solutions of TDC at different preparation conditions. Each type of J-aggregates can be identified by: (1) the J-band position in the absorption spectrum, (2) the width of absorption and fluorescence bands, (3) the value of the Stokes shift, and (4) a general view of the entire absorption spectrum. We use the designations JL, J2, and J3 following the paper [22,23] where these three types of aggregates were observed in solutions of the TDC dye with another counterion. The J~ type of aggregates has the

2.5

c I

20 / \ +.+ _.

~,, r-

Ul 1.5 0 J2 "0 -band + dime o

residual ~,.~ • ~ 1.0 / ~ o n o m e r s

0 c

0 . 0 , I , I , I i I , I ~ i , I ,

440 460 480 500 520 540 560 580 600 620 640

Wavelength, nm Fig. 1. Absorption and fluorescence spectra of 3,3',9-triethyl-5,5'-dichlorothiacarbocyanine iodide (TDC) in water-ethylene glycol glass at 77 K at a concentration of 10 -3 M. The molecular structure of TDC is shown in the inset.

458 MA. Drobizhev et al. / Chemical Physics 211 (1996) 455-468

2.5 0.2

2.0 f J3 /'' ]~ 0.1

~." 1.5 /!'

°.s f ' - - . . . . , / -0.1

0 . 0

I = I , I I I [ f i i i t

1 5 4 0 0 1 5 6 0 0 1 5 8 0 0 1 6 0 0 0 1 6 2 0 0 1 6 4 0 0 1 6 6 0 0

Wavenumber, cm -1 Fig. 2. Fluorescence anisotropy as a function of emission frequency at 77 K upon off-resonance excitation at 575 nm. The fluorescence spectrum is also shown for comparison.

lowest transition energy of the J-band (approximately at 640 nm). It is relatively unstable and is not observed in a low-temperature glass.

In this work we restrict ourselves to the study of J2- and J3-aggregates only. Fig. 1 shows the absorption and fluorescence spectra of a concentrated frozen solution of TDC in WEG at 77 K. According to the spectral position and taking into account the blue shift upon freezing we assign our J absorption peak at 611 nm (16360 cm -~) at low temperatures to J3.

We found that the fluorescence spectrum of J-aggregates is much more sensitive to temperature changes in the 5 - 1 4 0 K range as compared to the absorption spectrum (see below). At intermediate temperatures (77 K), another long-wavelength fluorescence J-peak, which can be assigned to J2-aggregates, is observed. However, the J2-peak is absent in the absorption spectrum of fresh samples (Fig. 1).

3.2. Fluorescence polarization

The fluorescence anisotropy spectrum of WEG solution of TDC containing J-aggregates at 77 K is shown in Fig. 2. The steady-state fluorescence

anisotropy value A = ( I lL- I ± ) / ( I i i + 21<), (where II1' and I . are the fluorescence intensities polarized parallel and perpendicular to the excitation polarization) in a rigid matrix carries information on the angle between the excitation and emission transition dipoles. One can see from Fig. 3 that A for the

0.4

o3 1o3

02 - - o2 >

o 0.1 / .:," o

-0.1 J

-0.2 , , , i 0.0 16000 16400 16800 17200

Wavenumber, cm "1 Fig. 3. Fluorescence anisotropy as measured at (0 ) the maximum of the J2-peak and (D) at the maximum of the J3-peak at 77 K. The absorption peak is also presented.

M.A. Drobizhev et a l . / Chemical Physics 211 (1996) 455-468 459

Jj-peak is negative and has a high absolute value if the fluorescence is excited outside the J-band. This fact agrees well with the assumption that the angle between the absorption dipole (the H-band) and the emission dipole (the J-band) is close to 90 °, which is consistent with the model involving two molecules per unit cell [23,24]. A rather more intriguing fact is the small variation (by less than 30%) of anisotropy in passing to the J2-peak and the correlation between structures of the fluorescence and anisotropy spectra. Note that the absolute value of A decreases slightly between 16360 cm ] (the absorption maximum) and 16260 cm-] (the fluorescence maximum) of Jj-aggregates (Fig. 2). The persistence of the anisotropy value from the JJ- to the J2-peak suggests the absence of energy transfer between randomly oriented segments. Indeed, if the latter occurs, the fluorescence would be virtually almost depolarized after a single transfer act [25]. Therefore, if the energy transfer process really populates the red states of our system, the angle between the dipole moments of segments responsible for the JJ- and J2-peaks in fluorescence should be small enough. In other words, the segments cannot belong to different chains randomly oriented with respect to each other. Moreover, the fluorescence anisotropy values recorded at the maxima of each peak vary in parallel as a function of the excitation wavelength and become positive upon resonance excitation in the J-band, (Fig. 3). These results show that the orientations of the emission dipole moments of both peaks are highly correlated.

3.3. Optical properties of J~-aggregates

In this section we consider the optical properties and related photophysics of the Jj-band only.

Fig. 4 shows the fluorescence and absorption spectra of J-aggregates of TDC. The former is obtained upon selective laser excitation at 17240 cm- at different temperatures. The fluorescence spectrum at 6 K appeared to be virtually independent of the excitation frequency tuned from 17240 to 16320 cm -] Therefore, the Stokes shift measured as a difference between absorption and fluorescence maxima at 6 K does not depend on the excitation frequency and is equal to 100 cm -~.

We found that it is possible to burn persistent holes in the absorption band of the TDC Jj-aggre-

.k...

9 0 K j /

o 4 0 K 6" IT _ _ _ _ :3

........ ' ' ' . . . ....

I i I ~ I ~ I ~ I , ~ I

15400 15600 15800 16000 16200 16400 16600

-1 W a v e n u m b e r , c m

Fig. 4. Fluorescence (solid lines) and absorption (dotted lines) spectra of J-aggregates of TDC at different temperatures.

gates in the spectral range at least from 16220 to 16360 cm -L. The possibility of hole burning in the absorption band of aggregates suggests that this band is inhomogeneously broadened at low temperatures.

The temperature dependence of the width (FWHM) of the hole burnt near the absorption maximum is shown in Fig. 5. One can see that the hole width is independent of the temperature at low temperatures. The hole width in our case is apparently determined by the dephasing rate only (the spectral diffusion contribution is negligible) [21] and therefore is equal to twice the homogeneous linewidth -),. Note that the low-temperature limit of the hole width Fu(T= 0 ) = 2y 0 = 3.3 cm-1, which corresponds to the dephasing time T 2 = 6.4 ps, turned out to be an order of magnitude greater in our case than that in pseudoisocyanine (PIC) aggregates [26]. We found that the fluorescence decay at 77 K is close to a monoexponential one with a decay time T~ -- 40 ps. Thus, the temperature-independent homogeneous linewidth "/0 = 1.65 cm-1 is determined by sponta-

460 MA. Drobizheu et a l./Chemical Physics 211 (I 996) 455-468

7 -

• 5

1:3 "I~ 4- (I) o

"I'-

3 -

f 2 i i i i

0 5 10 15 20 25

T e m p e r a t u r e , K

Fig. 5. Temperature dependence of the spectral hole width

(FWHM) burnt near the maximum of the absorption J3-band.

neous phonon emission within the excited electronic state rather than by the relaxation to the ground state. The relaxation with the phonon emission can occur from optically populated levels of free excitons (at the bottom of the band) to the lower-lying levels of self-trapped excitons. This process is allowed at low temperatures because of the absence of the potential barrier between the F and ST states in the strictly 1D system. This type of relaxation processes can, in principle, result in the Stokes shift.

The homogeneous linewidth of TDC estimated from our hole burning data is in good agreement with that obtained by photon echo for two other carbocyanine dyes TC and TDBC [16,27]. As in our case, TC and TDBC J-aggregates have a noticeable Stokes shift (compared to the absorption bandwidth) at low temperature and their dephasing rate measured in the absorption maximum is determined by the phonon emission rather than by the transition to the ground state (in contrast to PIC [26]).

Note that in J-aggregates of PIC the Stokes shift was not observed in frozen solutions at low temperatures [28]. The presence of the Stokes shift in our case (see Fig. 2), as well as in other J-aggregate systems [16,19,27-29], can, generally speaking, be caused by different exciton relaxation processes, such as: (a) energy transfer between segments of the chain (or of different chains), (b) energy relaxation within the exciton band of a particular undeformable segment, which implies the optical population of not only band bottom state [this is facilitated by suffi-

ciently strong disorder (static or dynamic)], and (c) self-trapping of exciton via exciton-phonon interac- tion to the states under the bottom of the band.

According to the fluorescence polarization data, an energy transfer between the segments of different randomly oriented chains is insignificant in the formation of the fluorescence spectrum, see Section 3.2. Nevertheless, we cannot completely exclude an energy transfer between decoupled, but correlated in direction segments of different lengths belonging to the same chain. Our Monte Carlo computer simula- tions show, however, that in the case of a Gaussian distribution of lengths of rigid segments the Stokes shift is much smaller than the width of the absorption band.

Within the framework of model (b), the absolute value of the fluorescence anisotropy should not decrease after relaxation in undeformable chain. Such is not the case in the experiment (see Section 3.2). In addition, the Stokes shift can be calculated within this model if we assume, according to Hochstrasser and co-workers [30], that in an ensemble of disordered 1D chains of length N the fluorescence occurs only from the lowest state of each chain. The Stokes shift in this model depends on three parameters: the disorder parameter D, the half-width of the exciton band B and the number N. It was assumed in [30] that excitation was able to find the lowest state of the whole chain. Hence, the number of sites covered by an exciton during its lifetime in a real system can be used as a chain length N in the model calculations. The N can be estimated from exciton-exciton anni- hilation measurements. For PIC J-aggregates at room temperature it was measured to be about (15-50) × 103 [4]. However, for thiacarbocyanine dyes similar to TDC, it was shown [31,32] that increasing the excitation photon density by up to three orders of magnitude as compared to the critical value for PIC did not alter the fluorescence kinetics of J-aggregates. This means that the length accessible to exciton is at least three orders of magnitude smaller, all other factors being equal. Taking this fact into account, we can evaluate N for our system to be about 15-50. The static disorder parameter D can be estimated from the absorption bandwidth at low temperature to be D ~ 200 cm -t using calculations reported in [6]. Therefore, taking the half-width of the exciton band B = 1400 cm - j , estimated as the

M.A. Drobizhev et al. / Chemical Physics 21 l (1996) 455-468 461

difference between the positions of the monomer band and J3-band at 6 K in WEG, we obtain for D/B = 0.14. With these particular values of D/B and N we calculated the Stokes shift for a 1D linear chain with diagonal disorder using the analytic expression for the density of excitonic states (DOS) from [33] and Eq. (7) for the fluorescence spectrum from [30]. The Stokes shift resulting from the calculations was 0.05-0.1 FWHM of the absorption band, which was an order of magnitude smaller than the observed shift.

Within the framework of the self-trapping process (c), the Stokes shift gradually increases from zero with increasing exci ton-phonon coupling in I D systems [34,35]. Therefore, this implies very small exciton-phonon coupling in PIC J-aggregates. By assuming that only the self-trapping contributes to the Stokes shift observed, we can estimate the value of dimensionless exci ton-phonon parameter g from calculations [35]. (Here g = S/B and S is the lattice relaxation energy in the case of complete localization on a single site.) By assuming that the half-width of the exciton band for J3-aggregate is B = 1400 c m - and using the measured Stokes shift of 100 cm-~ at 6 K, we obtain g = 0.35 from Fig. 4 in [35]. This value of the coupling parameter implies that an average number N b of unit cells covered by the lattice distortion in the ST exciton is about 7 [35].

It is somewhat surprising that the trapped state has a narrow fluorescence band with a rather small spectral shift (about 100 cm -~) with respect to the free state. However, broadband fluorescence and large Stokes shifts are inherent only in 3D systems where localized excitation tends to occupy only single site [36,37]. This is because in this case the lattice relaxation energy S must be greater than B for self-trapping to occur. On the other hand, the stable ST state in the 1D lattice occupies a great number of sites if the parameter g does not exceed some critical value ( = 0.75) [34,35,38]. In the 1D case, the Stokes shift for large-radius ST states can have any value, which vanishes when the coupling constant g tends to zero [34]. In addition, the temperature broadening of the fluorescence lines for large-radius ST exciton states is slower than that of an exciton localized on a single site because of the smaller relaxation energy in the former.

Let us now attempt to describe the temperature

broadening of optical lines of J3-aggregates by a model that assumes both dynamic and static disorder. The effect of dynamic (temperature induced) disorder on excitonic optical spectra was considered by Schreiber and Toyozawa [39,40]. In this model, the linewidth is governed by a disorder parameter D r. The latter describes the mean-square fluctuations of the transition energy (e ) induced by phonons lin- early coupled to an exciton. Thus, if the displacement of the configurational coordinate is A Q, that of the transition energy is A e = cAQ. The coupling constant c can be obtained if the adiabatic potentials Po(Q) and P(Q) in the ground and excited states are known:

c= dQde Q=Q ..... = d(P(Q)-d~QP°(Q))-- Q=Q,,,°, (1)

where Qmin is the coordinate of the minimum of potential from which the optical transition occurs. The disorder parameter is related to the mean square of the displacement as follows:

D 2 = ( ( A E ) 2 ) = c 2 ( ( A Q ) 2 ) . (2)

In the classical case, ( ( ~ Q ) 2 ) = kT and

D 2 = c 2 k r . ( 3 /

The quantum statistics of phonons results in:

C 2

D 2 = - - h 0) coth( h 0)/2 kT), (4) 2

where 0) is the effective phonon frequency [39,40]. If both static D O and dynamic D r disorder contribute to the optical linewidth, the total disorder parameter is

D= fbT+v , (5)

because of the Gaussian statistics of the transition energies [39]. In the strong scattering regime (D >> B), the optical line half-width is given by the well- known expression for localized states:

A = f2-1n 2 D . (6)

In the weak scattering case (D << B), the linewidth near the band edge E 0 is given by

q'i" A = - - h 0)c 2 coth( h 0)/21~T) p(Eo), (7)

2

462 M.A. Drobizhev et a l . / Chemical Physics 211 (1996) 455-468

160

140 - "7

120

i 100-

8 0 -

-~ 60- ,'r

40 -

[] D

D []

/ / . . . . . . . :

Temperature, K

160

140

120 ~"

100 0

8o .~

x 6o

40

200

Fig. 6. ( • ) Temperature dependence of the blue-side HWHM of the J3 fluorescence peak and ([]) temperature dependence of the FWHM of the absorption peak. Fitting of the fluorescence peak broadening is presented, see text.

if the density of exciton states (DOS) p(E) can be considered constant. Taking into account the energy dependence of the DOS the authors [39] found in the classical approximation (h o) << kT) that the absorption line of the free exciton in the lattice disordered by phonons broadens as T" with a = 2 /3 , 1, and 1.5 for d = 1, 2, and 3, respectively, as compared to T j/2 in the strong scattering case of Eqs. (3) and (6).

The temperature dependence of the absorption band width is shown in Fig. 6 (top). The FWHM is constant at low temperatures and begins to increase only at T > 40 K. This is in qualitative agreement with the model of Klafter and Jortner [5], which involves the effect of both static and dynamic disorder on free excitons.

The temperature dependence of the width of the spectral hole burnt into the inhomogeneous absorption band (Fig. 5) is free from the static disorder contribution and is well described by Eq. (7) with the effective phonon frequency o)= 20 cm ~ (see solid line in Fig. 5). This suggests the free exciton nature of absorbing states since the weak scattering regime is realized in this case (D O <<B = 1400 cm-~). The density of excitonic states can presumably be considered as constant in a sufficiently narrow region of energies E o - 2 0 c m - = < E < E 0 + 2 0 c m - ~ .

Let us now consider the temperature broadening of the fluorescence line which differs considerably from that of the homogeneous line in absorption. Because the red side of the fluorescence spectrum changes non-monotonically (Fig. 4), we investigated

the blue-side half-width of the J3-peak as a function of temperature. Fig. 6 (bottom) demonstrates this dependence.

It is evident from Fig. 6 that the temperature line broadening curve displays the negative second derivative in the entire temperature range. This fact is in contradiction with the temperature line broadening laws of 2D and 3D free excitons in the lattice disordered by phonons [39]. Therefore, these states are either localized (independently of the dimensionality) or free in the 1D lattice. The negative second derivative at T < 10 K suggests that lattice vibrations can be treated classically even at low temperatures. Indeed, Eq. (7) has a positive second derivative at low temperatures for any reasonable value of o) (see temperature broadening of spectral hole in the absorption spectrum, Fig. 5). This result can be under- stood taking into account that the frequency of a phonon bound to ST exciton in 1D lattice tends to zero [41,42].

To describe quantitatively the temperature broadening of the fluorescence line we will treat the fluorescent states as belonging to those of ST excitons. Then the temperature-induced part of the broadening will be correlated with the value of the Stokes shift obtained earlier. The specific form of the adiabatic potential of the ST exciton is given by the sum [34,35]:

P(Q) = E ( Q ) + Q2/2, (8)

where Q is the average lattice distortion, and E(Q) is the binding energy of an exciton in the lattice deformed by the exciton itself. By definition [34,35], a positive direction of Q is decided so that E(Q) < 0 for Q > 0 and E ( Q ) = 0 for Q < 0 The function E(Q) can be calculated if only the parameter g of the exciton-phonon coupling is known [34,35]. Tak- ing this parameter equal to 0.35 (which was obtained from the Stokes shift within the same model, see above) we calculated the 1D adiabatic potential P(Q) for our system (Fig. 7). It is evident that this potential is asymmetric. In the energy range from - 3 4 to 0 cm-~ (0-49 K), it can be well described by a parabola with a minimum at Qm~n = 10.7. Therefore, we can obtain, using Eq. (1),

c = d ( E ( Q ) +02/2) Q=Q ..... d (Q2/2) O dQ dQ =Q ....

M.A. DrobiJmo et al. / Chemical Physics 211 (1996) 455-468 463

1oo

6080 ~ : ' l

"7 40 ELR

20 - ~ - •

o . . . . :i _ . . . .

• j -20 - i

-40 -

-20 -10 0 10 20

Q

Fig. 7. Adiabatic potentials (appropriate to J3-aggregates) calculated according to[35], B=1400cm t and g=0.35, Eur is the energy of lattice relaxation, SS is the Stokes shift, Q is the effective configurational coordinate. The bold arrows present optical transitions.

for this temperature range. As the first term is equal to zero for the fluorescence transition, c = -Qm~n = - 1 0 . 7 . This constant is related to the lattice relaxation energy as Et, R = c2/2 = 57 cm i. Substituting the value of c 2 in Eqs. (3), (5), and (6) we obtain the approximating function in the strong scattering regime:

A = ¢2 In 2 ( D 2 + c2kT) (9)

for the temperature broadening with only one ad- justable parameter D 2. Its variation gives the best fit at D 0 2 = 5 1 0 ± 7 5 cm 2. This approximation is shown in Fig. 6. Note that the value of c 2 obtained from the Stokes shift deviates only by 10-15% from that obtained from a priori fitting by function A = (a + bT) 1/2 with two fitting parameters a and b in the same temperature range.

The high-temperature behavior of the linewidth

can be explained as follows. The optical transitions that occur during the time, when Q < 0, does not contribute to the linewidth because in this region the potential curves of the ground and excited states are not shifted (see Fig. 7). Therefore, the temperature broadening should slow down. To describe semi- quantitatively this effect, we estimated the effective mean-square displacement of coordinate for particular potential (Fig. 7) at T > 50 K and substituted it into Eqs. (2), (5), and (6) with D 2 and c 2 obtained for the low-temperature region. This approximation is shown in Fig. 6 by the dotted line. Note that approximating functions in two temperature regions were obtained directly from the particular form of the adiabatic potential involving the ST state. The only fitting parameter was the static disorder.

Note that the strong scattering limit (D >> B) is adequate in the case of fluorescence line broadening because the exciton band collapses after self-trapping [8,381.

The value of the static disorder obtained from the fluorescence linewidth D o = 23 + 2 cm-J is an order of magnitude smaller than that obtained from the absorption bandwidth. Note that the small effect of the static disorder on the relaxed states also follows from the Urbach tail measurements (see Section 3.5). The particular mechanism of considerable decrease in the static disorder contribution into the fluorescence linewidth is not clear at the moment. One of the explanations could be based on the assumption that inhomogeneous broadening of the absorption band is due to distribution of segment lengths. In this case the narrowing of the chain length distribution is possible during a self-trapping process resulting in localization of an exciton on a particular length N b.

In conclusion, we emphasize that the fluorescence line broadening is well described assuming the ST nature of fluorescent states in the I D chain. On the other hand, the temperature dependence of the homogeneous linewidth in absorption (the hole width) obeys the taw derived for free-exciton in the weak scattering regime.

3.4. Temperature-dependent Js ~ J2 photoconver- sion

A rather interesting result is the temperature-dependent phototransformation of the J3 form to the J2

464 M.A. Drobizhev et al. / Chemical Physics 211 (1996) 455-468

form. One can see from Fig. 4 that an additional red-shifted shoulder (or resolved peak in some samples, shown in Figs. 1 and 2) appears at 30-40 K against the background of the smooth J3 wing. The relative intensity of this red J;-peak reaches a maximum at 40-65 K and decreases gradually with increasing temperature. One can see that the red shoulder disappears at 90-140 K. At these temperatures, the fluorescence spectrum has again the red wing without any inflections and maxima. It should be noted that the disappearance of the red band at elevated temperatures is not due to the simultaneous broadening of both peaks. The spectrum at 140 K is even narrower than that at 65 K. The second peak is absent in the absorption spectrum at any temperature.

The relative intensity of the J2-band depends on the sample preparation procedure, but has a similar temperature dependence for different samples (Fig. 8). The Jz-peak (if resolved) has a width 1.5-2 times greater than that of the J3-peak (see Fig. 2).

In addition, the relative intensity of the two peaks depends only slightly on the excitation frequency (Fig. 9), while their individual absorption spectra are qualitatively different in this frequency range [22].

These facts can be explained either by the energy transfer from J3-aggregates to J2-aggregates or by structural rearrangement upon excitation. There are, however, several experimental findings that are diffi- cult to interpret within the framework of the energy transfer model. The non-monotonic temperature dependence of the fluorescence spectrum is the

1 4 -

1 .2-

1 . 0 ,

u - 0 . 8 -

0,6-

0 . 4 .

o

~ m "i m "~

[] o

5; ,;0 4;0 Temperature, K

Fig. 8. Temperature dependence of the ratio of intensities of J2- and J3-peaks. ( • ) Fresh sample, (El) two weeks aged sample.

2 5 1 0

absorption [ ~

2.0 J3 [~ J 0 8

. . . . . . . . f i ! • •

1 6 06

e ~, 10 04 -~

OC I , I , k , I , h , I , I , I , I O0 15800 16000 16200 16400 16600 16800 17000 17200 17400

W a v e n u m b e r , c m "1

Fig. 9. Dependence of the ratio of fluorescence intensities F(J 2)/F(J 3) of J2- and J3-peaks on excitation wavelength ( • ) at 77 K. The absorption and fluorescence spectra at this temperature are also shown.

strongest indication against simple energy transfer mechanism of population of the states responsible for the J2-peak. Although in some doped molecular crystals the energy transfer rate is found to be temperature dependent [43,44], the relative luminescence intensity of donor and acceptor changes monotonically [43].

Our experiments are well described by the model of two energy minima in the excited state separated by the potential barrier. The disappearance of the red peak at T > 100 K can be due to the thermal population of the J3 form having greater oscillator strength.

One can clearly see from Fig. 8 that there are two different temperature regions with monotonically increasing and decreasing ratio F(J2)/F(J3). In the first region, T = 65-140 K, the temperature is assumed to be higher than the potential barrier height and therefore the two states (J2 and J3) are in thermal equilibrium. It is also assumed that the non-radiative decay channel is common for these states. Therefore,

F ( J 2 ) _ f2 exp ( A E ] , F(J3) f3 - ~ ] (10)

where f2 and f3 are the oscillator strengths of the J2 and J3 transitions, respectively, and A E is the energy difference between the two states. The best fit of our data by Eq. (10) in the above temperature range g i v e s f2 / / f3 = 0.36 + 0.03 and A E = 40 + 5 cm- ~.

In the second temperature region, T = 6-30 K, we assume the role of potential barrier to become

M.A. Drobizhev et al. / Chemical Physics 211 (1996) 455-468 465

important. In this case the rate kn~ of the transformation is determined by temperature-independent (tun- nelling through potential barrier) and temperature- activated (overcoming of the barrier) terms k 0 and k , = k I e x p ( - E b / k T ) , where E b is the barrier height. Assuming the radiative rate k~ of J3 state and the quantum yield ~ of fluorescence of Jz-aggregate to be independent on temperature in region men- tioned above one can describe the data by

F(J2) k.r k 0 + k I exp( -Eb/kT ) q). ( l l )

F(J3)

The best fitting procedure at low temperatures (6 -27 K) gives q~ko/k r = 0.43 _+ 0.02, q~k~/k r = 2.7 ___ 1.9, E b = 36 +_ 11 c m - i.

There is close agreement between our spectral results and kinetic measurements in J-aggregates of another dye (BIC) [19,20]. The activation energy of the non-radiative channel of the electronic relaxation was measured [20] to be 30 -40 c m - ~. The broadening of the fluorescence spectrum and the red tail appear during 300-500 ps at 4.5 K [19], but these changes occur without any measurable delay at T > 50 K [45]. The presence of a potential barrier of comparable height for non-radiative decay of excited J-aggregates of two other carbocyanine dyes was also reported [16,32].

Thus, the self-preparation of the J2 form from the excited J3 form can be reasonably related to the process involving the chain deformation or realign- ment by the electronic excitation. It should be men- tioned that this process is different from the exciton self-trapping in the strictly I D chain discussed above (see Section 3.3). The two states J3 and J2 are separated by a potential barrier and their interconver- sion results in considerable changes in the exciton band. This can mean changes of some other coordi- nates than the chain-axis coordinate (e.g., rotation or displacement of molecular planes).

The molecular structure of two forms of aggregates under investigation (J2 and J3) in solution is not established at present. Note, however, that the TDC J3-aggregate in solution possesses a strong H-transition, whereas the J-transition is weaker (see [22,23] and Fig. 1). On the other hand, for the system revealing only J2-aggregates, the H-band absorption and related circular dichroism are not observed

[22,23]. This can imply W-like arrangements with two molecules per unit cell making a tilt angle a > 45 ° [24] for the J3 form. The J2 form can have either the staircase and W-like structures with small angles or the brickstone work arrangement. There- fore the structures of J3 and J2 differ considerably. The particular height of the potential barrier obtained and the rearrangement mechanism is not clear at the molecular level and further investigation is required.

3.5. The long-wavelength tail of the fluorescence spectrum and its relation to the Urbach rule

It has been well established experimentally (see reviews [46,47]) that the long-wavelength tail of absorption spectra in many condensed systems can be described by the exponential:

( ~ ° - ~ ) A ( E ) = A e x p - o - kr ' (12)

where E 0 is the energy near the absorption maximum, A is the absorption at E 0, and o- is a dimensionless 'steepness coefficient ' . The exponential dependence was proven for impurity centres, free and localized excitons, and band-to-band transitions. Theoretical models give different temperature behavior of o- at low temperatures dependent on a particular physical system. The crucial point is a limiting value of o- at T--*0. It is evident that an ideal dielectric crystal should not absorb the energy of the band gap at T = 0 and therefore the absorption edge should be abrupt. This means that in a perfect crystal o- --* constant :/: 0 at T ~ 0. At T =# 0, transitions with phonon absorption can lead to the appearance of the long-wavelength tail below the absorption edge. Tak- ing this into account, it has been found that for localized excitations [48-50], free excitons [51 ], and band-to-band electron transition [52] in crystals the absorption tail has the exponential form from Eq. (12) and o r=o - 0 + aT at low temperatures with cr 0 ~ l .

On the other hand, any structure imperfections (impurities [53] or static disorder [54]) result in the exponential absorption tail even at T = 0. Klafter and Jortner [54] showed that o-~ kT in a wide temperature range and therefore o" ~ 0, as T --* 0.

Another possible mechanism accounting for the presence of the Urbach tail even at T = 0 is a set of exci ton-phonon transitions to the momentarily self-

466 M.A. Drobizhev et a l . / Chemical Physics 211 (1996) 455-468

trapped states lying below the free exciton edge if the ST state exists [36,40,55]. This model gives, however, an exponential behavior only in the restricted energy region above the adiabatic minimum of the ST state. In this case, also cr ~ kT, but in the region kT << h a) [36].

As for the fluorescence spectrum F(E) , if thermal equilibrium in the exci ton-phonon system takes place, it is described in the tail region by [36]:

E0 - E ] (13) F(E) = F e x p - ( o - - 1) kT ]

An experimental evidence of equivalence of cr values obtained independently from Eqs. (12) and (13) was given in [56].

The detection of the red tail in luminescence in solutions of moderate optical density is more conve- nient than in absorption because of the greater signal-to-noise ratio in the former. Note that according to Eq. (13), as opposed to the absorption, there exists the exponential tail in the fluorescence spectrum at very low temperatures, where o" ~ 1.

The first experimental observation of the Urbach tail over several decades of the absorption tail of P I e J-aggregates in solution at room temperature was reported in [57]. Very recently, the temperature de- pendencies of o" in absorption and fluorescence were measured in J-aggregates embedded in a Lang- muir-Blodgett film [58]. However, the absorption data were obtained only for one decade of the intensity decrease from a maximum, where the absorption spectrum can be described by a Gaussian (see [57]). In this case, the dependence o-~ kT at low temperatures can also mean the temperature independence of the Gaussian width in this temperature range, which was indeed established [58]. On the other hand, the steepness coefficient cr obtained from the fluorescence red tail using Eq. (13), is well described by the relation o-= 1 + aT at low temperatures and was not interpreted by authors anyhow.

We observed the exponential fall in the fluorescence spectrum to the red from the J2-peak, Fig. 10, right part. The steepness coefficient in the region E < 16050 cm-~ was calculated as a function of temperature using Eq. (13). This dependence is shown in Fig. 10, left part. One can see that it is similar to that observed in [58]. The linear asymp-

18

,2

lO 008

=~0.0 ~ 04 F

O ' J 0 2 1

[ i ~ / ~ l , I , I , I I , ' , , f , , , i , . . i . .

4 0 8 0 1 2 0 1 5 6 0 0 1 5 8 0 0 1 6 0 0 0 1 6 2 0 0 1 6 4 0 0 1 6 6 0 0

Temperature,K Wavenumber, cm -1

Fig. 10. Logarithmic plot of fluorescence spectra of J-aggregates of TDC at different temperatures (shown by numbers in K at each curve) (right part). Temperature dependence of the steepness coefficient in the Urbach rule (left part) and its fitting by Eq. (15), see text.

totic tending of o- to 1 at T ~ 0 K is very important evidence in favour of the conclusion made in Section 3.3 for low contribution of the static disorder to the fluorescence spectrum.

To describe our data quantitatively, we used the simple model of Davydov and Lubchenko [48], that considers coupling of localized excitations with phonons. It gives the following temperature dependence of o- :

In 14) or= I + h~o a e h w ( n + 1) '

where e is the base of the natural logarithm, o) is the frequency of an effective phonon in the ground electronic state, a is the Huang-Rhys factor, and n is the Bose-Einstein occupation number of a phonon of frequency w. It is obvious from Eq. (14) that at low temperatures cr is a linear function of T. Putting E 0 - E = 500 c m - I , we find from the best fit o9= 110 cm -I and a = 0 . 5 in Eq. (15). The fitting curve with these parameters is shown in Fig. 10. The close vibronic frequency is observed in selectively excited fluorescence of the TDC monomer, which can imply almost complete localization of states in the red tail of luminescence and, therefore, the applicability of the model [48,49].

The important conclusion of this Section is the following: if the thermal equilibrium in the exciton-

M.A. Drobizhev et al. / Chemical Physics 211 (1996) 455-468 467

phonon system occurs, then the relaxed excitons belonging to the tail states in molecular TDC J-aggregates are weakly affected by a static disorder. This agrees with independent results of Section 3.3.

(2) Thermally activated structural photorearrangement of the aggregate chain resulting in the J3 ~ J2

phototransformation observed in our system.

4. Conclusions

We found that TDC forms three types of J-aggregates. Two of them (J2 and J3 ) have been studied at different temperatures in frozen solutions.

It has been shown that the short-wavelength J3-

peak possesses a large negative value of fluorescence anisotropy upon non-resonance excitation at 77 K. This can imply that transitions to the top of the band are allowed, which imposes some limitations on the molecular structure of this aggregate. The fluorescence anisotropy spectra show that the emission transition dipoles of J3- and J2-aggregates are highly directionally correlated.

Optical properties of the J3-band have been studied in detail. Temperature dependence of persistent spectral hole width can be described by a model of free excitons in a weak scattering limit. At low temperatures, T < 10 K, the homogeneous linewidth is determined by one-phonon emission rather than by a relaxation to the ground state. A possible intermediate state can be the ST state. A combined analysis of the temperature broadening of the J3 fluorescence peak and the Stokes shift suggests that this peak is attributed to the self-trapped excitons of a large radius.

It has been found that the J3-aggregate can trans- form to the J2-aggregate upon photoexcitation. This process is shown to be temperature activated with a barrier height of approximately 30 cm- ~.

The exponential decrease in the fluorescence intensity with decreasing photon energy has been established in the long-wavelength spectral range. The low-temperature value of the steepness parameter o- of the Urbach role indicates a decrease in the relative contribution of static disorder to the spectra of relaxed states.

Finally, the following excitonic relaxation chan- nels are proposed to be of possible relevance to the dynamics in our system:

(1) Exciton self-trapping in the strictly 1D chain in the case of J3-aggregates.

Acknowledgement

This work was supported by the International Science Foundation, Grant MR 8300, the Russian Foundation for Fundamental Research, project No. 93-02-3656, INTAS Grant 93-85, F.K.F.O. and D.W.T.C. through IUAP II-16. We thank Mr. G. Im- eshev and Dr. A. Lobanov for valuable help, Dr. V.F. Kamalov for stimulating discussions and Dr. M.N. Ushomirsky for providing us the TDC dye and useful discussions.

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Relaxation and trapping of excitons in J-aggregates of a thiacarbocynine dye

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