Excitons in Molecular Aggregates of 3,3'-Bis-[3 ... - ACS Publications

Knoester, J.; Spano, F. In J-aggregates; Kobayashi, T., Ed.; World Scientific .... Scheblykin, I. G.; Bataiev, M. M.; Van der Auweraer, M.; Vitukhnovs...
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J. Phys. Chem. B 2001, 105, 4636-4646

Excitons in Molecular Aggregates of 3,3′-Bis-[3-sulfopropyl]-5,5′-dichloro-9ethylthiacarbocyanine (THIATS): Temperature Dependent Properties I. G. Scheblykin,† O. Yu. Sliusarenko,‡ L. S. Lepnev,‡ A. G. Vitukhnovsky,‡ and M. Van der Auweraer*,† Laboratory for Molecular Dynamics and Spectroscopy, K.U.LeuVen, Celestijnenlaan 200 F, 3001 LeuVen, Belgium, and P. N. LebedeV Physics Institute, RAS, P. N. LebedeV Research Center in Physics, Leninsky pr. 53, 117924 Moscow, Russia ReceiVed: NoVember 28, 2000; In Final Form: March 12, 2001

J-aggregates of the dye THIATS (triethylammonium salt of 3,3′-bis-[3-sulfopropyl]-5,5′-dichloro-9-ethylthiacarbocyanine) with a two-component Davydov splitting of the exciton band were investigated in the temperature range from 5 to 130 K and at room temperature. A wide set of excitonic and optical characteristics (absorption line broadening, fluorescence line broadening, Stokes shift, coherence length, exciton migration rate, and wavelength dependence of the fluorescence decay time) of the same J-aggregates is presented. The exciton migration rate was found to be the most temperature sensitive property. The temperature dependence of a whole set of exciton properties reveals two critical temperatures: 30 and 70 K. The observed phenomena are described qualitatively as an interplay of static and dynamic disorder effects. At low temperature (T < 20 K) static disorder is the main factor which limits the coherence length and exciton-exciton annihilation rate and determines the absorption width. An intraband, subnanosecond exciton relaxation toward the lower energy states is observed. Below 20 K only a limited number of exciton states of the molecular ensemble are reached by the exciton during downhill relaxation. While the temperature increases from 30 to 70 K, a wider set of states becomes accessible for the exciton during its relaxation. The “internal” structure of the exciton band becomes blurred by homogeneous broadening and the coherence length decreases. Very fast exciton wave packet motion occurs over 106-107 molecules. At temperatures higher than 80 K, we suggest dynamical processes to play the most important role. The Stokes shift becomes temperature independent. Exciton migration starts to be strongly blocked by scattering on optical phonons. The effective, long distance exciton migration in THIATS J-aggregates as well as peculiarities of the Stokes shift and line broadening temperature dependence allow us to conclude that no exciton self-trapping process occurs at temperatures higher than 20 K.

1. Introduction Molecular aggregates of organic dyes in solution1,2 are a brilliant example of quasi-1D (and also 2D and rodlike 3D)3,4 self-assembled nanostructures where Frenkel excitons can be generated. Large intermolecular coupling leads to the “semiconductor limit” for excitons when the exciton bandwidth is very large (2000-4000 cm-1) in comparison with the thermal energy kT, major lattice phonon frequencies (10-300 cm-1), and the energetic disorder. The application of the theory of excitons to explain the optical and electronic properties of J-aggregates has attracted a lot of effort from theoreticians and experimentalists.5,6 The physical phenomena under interest of both theoreticians and experimentalists are spectral line broadening, relaxation of the exciton-phonon system, and coherent and incoherent exciton energy migration. The temperature dependence of those properties is very useful for comparison with theoretical predictions. The role of energetic and structural disorder is also very important, especially in applications to natural molecular aggregates, such as light-harvesting antennae.7 Aside from considering them as a model system for natural aggregates, * To whom all correspondence should be addressed. Email: mark. [email protected]. † Laboratory for Molecular Dynamics and Spectroscopy. ‡ P. N. Lebedev Physics Institute.

J-aggregates themselves attract nowadays much of attention as an new active material for organic light emitting diodes8,9 and nonlinear optics.10,11 A set of investigations of exciton dynamics and spectroscopic properties of some J-aggregates at different temperatures has already been performed (see, for example, refs 12-17 and references therein). However, in those contributions only some of the mentioned phenomena were considered for a particular aggregate system. Herein we refer the reader to refs 12 and 18 for the temperature-dependent homogeneous line broadening, to refs 19 and 20 for the temperature-dependent properties of absorption spectra. There are also not much experimental data in the literature about the temperature-dependent fluorescence spectra.13,15,20,21 Some information about the Stokes shift can be found in refs 15 and 22. As for the temperature dependence of the Stokes shift of fluorescence in J-aggregates, to our knowledge, no systematic study is available so far. Note here that those papers deal with J-aggregates not only of different dyes but also with aggregates in different matrixes (solutions,12,14,17 LB-films,12,20 and polymer films21). This variety of materials and experimental conditions makes it difficult to compare experiment and theory and even to have a qualitative view on exciton physics in J-aggregates (e.g., ref 22). Thus, it seems to be very important to have a more global overview as possible for a particular molecular system.

10.1021/jp004294m CCC: $20.00 © 2001 American Chemical Society Published on Web 04/26/2001

Molecular Aggregates of THIATS

Figure 1. Absorption spectrum of J-aggregates of THIATS in water/ ethylene glycol (3/2) at room temperature and chemical structure of the dye.

In this contribution we will present the temperature dependence of such important excitonic and optical characteristics of J-aggregates of the dye triethylammonium salt of 3,3′-bis[3-sulfopropyl]-5,5′-dichloro-9-ethylthiacarbocyanine, THIATS (see Figure 1) as absorption line broadening, fluorescence line broadening, Stokes shift, coherence length, exciton migration rate, and waVelength dependence of the fluorescence decaytime. The whole set of data covers temperature range from 5 to 130 K, and we also have data obtained at room temperature (300K) from previous investigations.16,23 It will be shown that temperature dependencies of all investigated properties possess two “critical” temperatures: T ) 20-30 K and T ) 70 K. These two points split the whole temperature range on three intervals: low-temperature range [0-20 K], intermediate temperature range [30-70 K], and hightemperature range [80-300 K]. In those temperature intervals the temperature dependence of the investigated properties is clearly different. A qualitative description of the physical processes occurring in those temperature intervals will be given. We have to emphasize here again that all expected theoretical discussions will be done referring to particular values of the excitonic and spectroscopic parameters which were obtained experimentally for the J-aggregates of THIATS in water/ethylene glycol 3/2. Of course, particular values of the critical temperatures scale first of all with the absorption and fluorescence line widths. On this basis one can compare THIATS aggregates with others. It has been proved by various spectroscopic investigations16 that the THIATS dye under particular conditions builds a type of aggregates with two molecules per unit cell. Such an arrangement of the unit cell leads to Davydov splitting of the exciton band in two subbands.24 In this case in an infinite aggregate there are two states of different energy where the exciton wavevector B k is equal to zero. These states corresponds to the top and the bottom of the exciton band and contain most of the transition dipole moment of the molecular ensemble. In our system two bands are observed in the absorption spectrum15,16 (Figure 1): a “J-band” with a maximum at λJ ) 613 nm or νJ ) 16 310 cm-1 and a “H-band” with a maximum at λH ) 517 nm or νH ) 19340 cm-1 (the numbers are given for liquid nitrogen temperature, absorption spectra of the monomer has a maximum at 550 nm). Regardless of the excitation wavelength, the fluorescence occurs always from the J-state with a very small Stokes shift. Because no other bands reveal beyond the spectral region limited by the J- and H-band and because the fluorescence quantum yield is close to unity, we attribute

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Figure 2. Absorption (dashed line) and fluorescence (solid line) spectra of J-aggregates of THIATS in water/ethylene glycol (3/2) at 10 K. Numbered triangles show the analysis wavelengths where the fluorescence decays were determined: [1] 611.5 nm, [2] 613.5 nm, [3] 614.5 nm, [4] 615.5 nm, and [5] 617.5 nm. See section 3.2 for details.

J- and H-states to the top of the upper and the bottom of the lower Davydov subbands of the exciton band. Thus, the total width B of the exciton band is B ) (EH - EJ) ≈ 3030 cm-1. The largest part of the exciton transition dipole moment is concentrated in the upper Davydov component (H-transition). Furthermore, the lowest exciton state (J-state) contains only 1/30 of the total value. This peculiarity distinguishes J-aggregates of THIATS from other molecular aggregates in solution known from the literature. For all further details about the Davydov splitting in these aggregates, see refs 16 and 17. Because of a fast intraband exciton relaxation, only the fluorescence from the lowest level (J-state) is observed (Figure 2). A crude estimation of the time of the primary relaxation step from the H-state as 1/(H-bandwidth) gives the value of 10-15 fs even at helium temperatures.25 The total relaxation time to the J-state, of course, is larger. However, it is less than 10-20 ps at T > 77 as soon as we did not observe any component with negative amplitude in the fluorescence decays.16,23 Even if we observe such a component at low temperatures (section 3.2), this can still be due to “lateral” energy transfer between different exciton states near the bottom of the band (sections 3.1.2 and 3.2) rather than to “vertical” relaxation accompanied by a large change of the exciton wavevector B k. For such a system with Davydov splitting one has to use the following relation between radiative lifetimes of the aggregate τradJ and monomer τrad0 that takes into account the redistribution of the transition dipole moment:16,17

τrad J )

τrad µ2H 0 (1 + Q), Q ) 2 Nc µ

(1)

J

where NC is the exciton coherence length and µH and µJ are the transition dipole moments of upper (H) and lower (J) transitions of the exciton band. In THIATS aggregates we have Q ≈ 30. This leads to a 30-fold increase of the radiative lifetime of the exciton in comparison with that for an aggregate of the same coherence length Nc with one molecule per unit cell.16 The experiment yields a radiative lifetime of about 5.5 ns and a quantum yield of about unity at 5 K.17 In comparison with other aggregates, absorption and fluorescence lines of the J-transition are extremely narrow at low temperature. They possess a full width at half-maximum (fwhm) of 85 and 60 cm-1 respectively at 5 K. All other well-known J-aggregates except of pseudoisocyanine (PIC) aggregates12

4638 J. Phys. Chem. B, Vol. 105, No. 20, 2001 (dyes 1,1′-diethyl-3,3′-bis(sulfopropyl)-5,5′,6,6′-tetrachlorobenzimidacarbocyanine (BIC),26 5,5′,6,6′-tetrachloro-1,1′-diethyl3,3′-di(4-sulfobutil)-benzimidazolocarbocyanine (TDBC),14 and others13 in different frozen matrixes and films) reveal a line width which is at least 1.5-3 times larger (see also ref 15 and references therein). In comparison with classical bulk molecular crystals like anthracene (1La-band), the exciton coupling strength is approximately 10 times larger in J-aggregates. The exciton bandwidths are 3030 cm-1 for J-aggregates of THIATS and 100-400 cm-1 for anthracene depending of exciton wavevector orientation.27 On the other hand, dye molecules in aggregates are not packed with the same perfection as anthracene molecules in bulk single crystals. This leads to a static energetic disorder ∆, which plays an important role in the exciton dynamics especially at low temperatures.12,28 However the most important factor is the ratio of B and the disorder ∆ and the lattice intermolecular phonon frequencies Ω. For THIATS aggregates B is very large, hence B.Ω, ∆, kT for all reasonable experimental conditions. It means that excitons in J-aggregates can be considered in the framework of so-called “wide band semiconductor limit”.27,24 Moreover, the system under investigation reveals a very interesting combination of excitonic parameters. On one hand, it has a very strong intermolecular coupling and on the other hand the exciton decay time is very large (5 ns) due to the small value of the transition dipole moment of the lowest excited state (J-state). 2. Experimental Section The dye THIATS was a gift from AGFA. It has an extinction coefficient of 90000 L/(mol cm) at the maximum at 550 nm in methanol solution. J-aggregates were studied in a water/ethylene glycol 3/2 volume mixture at a dye concentration of C ) 1.5 × 10-4 M (see refs 15 and 16 for details). Most experiments have been done in a liquid helium cryostat (Ukraine, Kiev) at temperatures from 4.2 to 130 K. The temperature was controlled within 1 K or better. We have to note that the glass transition temperature of the water/ethylene glycol mixture is about 150 K. To avoid any possible influences of this phase transition on conclusions drawn about physical properties of J-aggregates, all measurements in the frozen solution were done at temperatures below 150 K. The absorption and fluorescence spectra were obtained by a linear CCD array (model MORS-UI-2048, Russia) coupled to the second output port of the monochromator. This experimental complex allowed us to measure a wide range of spectral characteristics without changing sample. We have to stress here that all data for the Stokes shift measurements were obtained for the same sample and that fluorescence and absorption spectra were detected on the same setup almost simultaneously. This allowed us to avoid sample- and instrumental-dependent artifacts. The fluorescence decays were determined by the time correlated single photon counting technique with an instrumental response function of 0.7 ns. The fluorescence was excited by a picosecond synchronically pumped dye laser17 at 565 nm and detected by Hamamatsu model H3836 photomultiplier with a multialkali photocathode. The time window of 50 ns was used in all experiments. To obtain fluorescence decays at different wavelengths within the narrow fluorescence line (section 3.2) a monochromator (model MDR-3, LOMO, Russia) with a resolution of about 0.5 nm (13 cm-1 at 610 nm) was installed before the detection photo

Scheblykin et al.

Figure 3. Temperature dependence of fluorescence fwhm (open circles), absorption fwhm (solid circles) and Stokes shift (squares). Excitation wavelength was 565 nm.

multiplier. Such spectral resolution was enough to measure decays at 5 different wavelengths within the fluorescence band possessed fwhm from 55 to 70 cm-1 (see Figure 2). The excitation photon flux (W) was kept every time as small as possible to avoid exciton-exciton annihilation (see section 3.4) and never exceeded 108 photons/cm2pulse. During experiments at different excitation power (investigation of exciton-exciton annihilation, section 3.4) a set of neutral density filters was used to change excitation intensity. An additional photomultiplier was used to control the primary laser intensity. A special attention was paid to avoid photo damage of the sample under laser irradiation. Degradation of the sample revealed as a decrease of the fluorescence intensity and shortening of the fluorescence decay time.29 Fortunately, in the frozen solution the photo degradation was much less important than at room temperature, however, each point of the sample was used only for a limited number of experiments. To be sure that photodegradation does not influence the results, additional decay measurements were carried out to compare decay curves before and after an experiment under the same conditions. 3. Results and Discussions 3.1. Spectral Line Broadening and Stokes Shift. The broadening of the absorption and fluorescence spectra as well as the Stokes shift are presented in Figure 3. There are 3 very easily distinguished temperature ranges (T < 30, 30 < T < 70, and T > 70) where the Stokes shift and the fluorescence line width show a different behavior. Here we will try to discuss in a qualitative way the reasons for the line broadening in J-aggregates. Several more or less equivalent languages are commonly used in the literature for explaining exciton properties of the J-aggregates. Here we discuss the exciton properties mostly in terms of the exciton coherence length NC. This parameter is equal to the number of molecules of the molecular aggregate over which the exciton wave function is delocalized. 3.1.1. Absorption Spectra. (i) Imperfection of the Chain of Molecules as a Source of Optical Transition Broadening. In this

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subsection the basic excitonic properties of a chain of dye molecules will be discussed in the framework developed by Davydov.24 For an ideal molecular crystal of an infinite number of molecules optical transitions are allowed only into an exciton state with an exciton wavevector B k equal to 0.24 Hence, the state |k B ) 0〉 carries the total dipole moment of the exciton transition. As soon as the crystal becomes non ideal (energy disorder or finite chain length for example), the free exciton states |k B〉 with a particular value of the wavevector are not longer eigenstates of the system. Let us designate the eigenstates of such an aggregate as |n〉 where n (without vector sign!) ) 1,2, ..., N number of the state, n ) 1 and N corresponds to the bottom and the top of the exciton band, respectively. The |n〉 states can be described as a linear combination (wave packet) of the free exciton states |k B〉: N

|n〉 )

ani|k Bi〉 ∑ i)1

(2)

The dipole moment of the transition |0〉 w |n〉 is proportional to the contribution of the |k B ) 0〉 state to the linear combination (eq 2). For example, let us consider an ideal chain of molecules of a finite length N. The energies of the states are given as follows:

E(n) ) -2V cos

(Nπn+ 1),

n ) 1, 2, ..., N

(3)

Only states with odd numbers of n carry a transition dipole moment:

{

(

)

2µ20 πn 2 µ (n) ) N + 1 cot 2(N + 1) , 0, 2

n ) 1, 3, 5, ...,

(4)

n ) 2, 4, ...

The transition dipole moment is concentrated in the lowest state |n ) 1〉 and tends to zero with increasing n. The energy difference between states |n ) 1〉 and |n ) 3〉 which are the lowest ones carrying a substantial transition dipole moment is

∆E13 ) E(3) - E(1) ≈

8π2V (N + 1)2

(5)

The typical value of the coherence length N for J-aggregates at low temperatures is 20-50.30 Thus, we can make a crude view on the level structure of J-aggregates. For the THIATS Jaggregates where V ≈ 3000/4 ) 750 cm-1 (ref 16) while N ) 10, 15, 20, 25, and 30 molecules, one can obtain from eq 5 ∆E13 ) 460, 220, 130, 90, and 60 cm-1, respectively. The positions of the levels of these two lowest optically allowed states in comparison with measured absorption spectrum (fwhm ) 85 cm-1) are shown on Figure 4. One can see, the energy shift ∆E13 is larger than the half-width of absorption spectra for all N used. In the framework of our oversimplified model this means that the dominant part of the observed absorption band are formed by transitions to the lowest state |n ) 1〉. The transitions to the state |n ) 3〉 are shifted to the blue quite a lot and form the “blue wing” of the absorption band. This very crude estimation has been done to give the reader an idea about contribution of different states to the total absorption spectra of J-aggregates. In the general case, any imperfection of the chain of molecules (nonequivalence of molecules in energy, position, orientation, etc.) results in a decreased coherence length NC of the

Figure 4. Low temperature (5K) absorption spectrum of J-aggregates of THIATS in water/ethylene glycol (3/2). The vertical rods reflect position and relative transition dipole moment (height of the rods) of the first (n ) 1) and the second (n ) 3) optically allowed exciton states of the ideal chain of molecules of a different length. Chain lengths (N) are 30, 25, 20, 15, and 10 molecules (see section 3.1.1).

exciton. One can replace N in the above equations by NC and considered the exciton states within the more or less the same formalism as for ideal chains of final length (ref 31 and references therein). This nonequivalence can be due to a distribution of the excited state energy levels of each molecule and of the interaction between molecules. Both factors are the result of a distribution of the properties of the environment, which, in terms of traditional spectroscopy, means inhomogeneous broadening. This inhomogeneity of the molecular array is usually called static disorder. The word “static” means that that type of disorder is time independent at least on the time scale of excited-state decay time. Excited states of such molecular ensembles consisting of many molecules residing in different environments can be characterized by a density of states (DOS) function for every energy.32 The static disorder and the finite chain length are the only reasons of absorption broadening at low temperature. There are two rather simple models of the static disorder discussed intensively in the literature: the broken rod model (BR model) and the model of the continuous energy disorder (CED model).33 The sketch of those models are presented on Figure 5. In the framework of the broken rod model all molecules of the same coherent segment have the same energy and this energy fluctuates from one “ideal” segment to another segment. It gives rise to the exciton states energy distribution with a width of σ (see Figure 5A). In the case of the CED model, the energy of the excited state of each molecule is distributed over a band of energy levels which is often given by a Gaussian distribution with a width of σ0 as shown in Figure 5B. In the framework of both models choosing suitable values of the modeling parameters allow one to obtain an agreement with the experimentally observed absorption spectrum.28,34 This means that in the framework of both models it is possible to obtain more or less the same shape of the density of states (DOS) function. For examples of the DOS for one-, two-, and three-dimensional crystals with disorder we refer the reader to the work of Schreiber and Toyowaza.32 Some groups are in favor of CED model;28,35 others prefer the BR model for calculations.34 In the current paper we will use the language of both models for the sake of clarity. (ii) Relaxation of the Exciton/Phonon System (Homogeneous Broadening). The transverse relaxation of the exciton-phonon states itself with relaxation times T2 (also called the exciton

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Figure 5. Models of exciton relaxation in J-aggregates. (A) Broken rod model. (B) Continuous energy disorder model. In the continuous energy disorder model ovals represent the delocalization length and the spatial location of the exciton wave function within the chain of molecules. σ, σ0: values of disorder. In both cases the thickness of the lines gives an indication of the transition dipole moments of the states.

dephasing times) as well as the relaxation to the ground state with characteristic time T1 lead to homogeneous broadening of the transitions. The reason for exciton dephasing is the exciton scattering on the phonons or in other language - on “dynamic disorder”. In general,

σhom ∝

∑i

1 T(i) 2

+

1 2T1

(6)

where the summation includes the whole set of exciton-phonon states involved in the transition. As far as phonon states are involved here, this type of broadening is very temperature dependent. At low-temperature, T2 is of the order of several picoseconds (see for example ref 22 and references therein. This time leads to homogeneous width of several wavenumbers, which is much less than absorption width observed in the experiment. However, upon increasing temperature, the homogeneous component of the line broadening can become more and more important. (iii) Phonon States Population. For nonzero temperatures the absorption from thermally populated vibrational states can occur. In the case of a different shape of the potential energy surfaces of the excited and ground states of the system this could lead to changes in the transition energies. In a first approximation this effect will lead to an enhancement of the low energy wing of the absorption band. Experimentally we found that almost no broadening of the absorption line occurs with increasing temperature below 70 K (Figure 3). Thus, we can conclude that for T < 70 K the absorption spectra corresponds directly to DOS(E) multiplied by µ(E), which are more or less temperature independent at these temperatures. It means that the mentioned temperature-dependent factors (ii) and (iii) are not of substantial importance for absorption spectra at this temperature region. It means also, that static disorder is temperature independent at T < 70. Any transitions to states with n g 3 are situated mostly at or beyond the short wavelength limit of the absorption band and do not influence the line width substantially (see above). We have to emphasize that the exact theoretical calculation of the absorption

line width is rather difficult and has not been performed so far. We just refer the reader to several classical works where such attempt was done.32,36 3.1.2. The Fluorescence Spectra and Stokes Shift. Mechanisms of fluorescence line broadening are even more complex, because they include an intraband relaxation of the exciton-phonon system, which can include a spatial motion of the exciton within the molecular ensemble as well. At the very first moment after excitation the population of the manifold of the exciton states is determined by the overlap of the excitation light spectra, density of states, and the oscillator strength dependencies on energy. Afterward a relaxation starts. The mechanisms of this relaxation can be very different for different molecular systems depending on the type of excitonphonon coupling, the exciton bandwidth B, the phonon spectrum, strength of the lattice,, and so on. In the general case there are two possibilities. The first one is a relaxation within the DOS only and the second onesdeformation of the DOS itself after excitation. For example, for several molecular systems (aggregates, polymers) self-trapping has sometimes been suggested as the origin of the luminescent states.22,27,37,38 This means that the exciton creates itself a specific permanent lattice deformation and carries it during its decay time. In the language of density of states it means that all evolution of the excitation occurs in a deformed DOS which is different from the initial one of the unexcited aggregate. Now let us consider these basic ideas in application to J-aggregates. In the BR model model there are two different relaxation processes: relaxation within level of the particular coherent segment (intrasegment relaxation) and energy transfer between different segments which can have a different length or energy (see Figure 5). Both processes lead to an energy decrease while the second one leads also to spatial motion of the exciton along the chain of molecules. As far as different excitonic states in the framework of CED model have a predominant amplitude at different sites of the chain,28,31 exciton spatial motion during relaxation is also an innate feature of this model. Let us for the sake of simplicity consider the case of T ) 0 and the absence of self-trapping. The relaxation process within excited states characterized by a DOS function allows the exciton to find states with lower energies. Note again that this relaxation process includes also an exciton transition from one aggregate to another as far as the states between which the relaxation occurs have maximum amplitude of the wave functions at different sites of the aggregate. As a result, we observe a Stokes shift of the fluorescence spectra and a narrowing of the fluorescence band in comparison with absorption spectrum. So, in the first approximation, we can say that at zero temperature the “fluorescent states” correspond to the set of the lowest “easily accessible” states. What does “easy accessible” mean? To clarify this point more, let us consider a very simple model when all states of the DOS can be reached by an exciton during its relaxation. We will refer hereafter to this assumption as the model of “totally accessible DOS”. In that case if the temperature is zero and the number of exciton states is finite, the fluorescence spectra should consist only of the line, which corresponds to the transition from the exciton state with the lowest energy. At the nonzero temperatures the exciton cannot remain permanently in the lowest energy level due to thermally induced population of the other states of the band. At thermal equilibrium in the DOS a crude estimation of the fluorescence spectrum can be obtained as a product of the low-temperature absorption spectrum, and an exponential function, namely:

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J. Phys. Chem. B, Vol. 105, No. 20, 2001 4641

F(ν) ) A(ν) exp(-ν/kT)

(7)

Assuming A(ν) is a Gaussian with fwhm ) σ:32

(

A(ν) ) exp -

ν2 ‚4 ln 2 σ2

)

(8)

we obtain

(

F(ν) ) exp(-ν/kT) exp -

[

)

ν2 ‚4 ln 2 ∝ σ2

(

exp - 4 ln 2 ν +

) ]

2 σ2 /σ2 (9) kT 8 ln 2

So, we obtain again a Gaussian of the same width σ as the absorption spectrum but shifted over an amount to lower energy, leading to a Stokes shift:

SS ) σ2/(kT 8 ln 2)

(10)

So, in the framework of the model of “totally accessible DOS”, the Stokes shift should increase upon cooling. In Figure 6 the experimental Stokes shift and the Stokes shift calculated from eq 10 assuming σ ) fwhmabs ) 80 cm-1 are presented. It is clear that, at low temperatures (T < 20) the calculated Stokes shift is extremely large and incompatible with the experimental observations. The deviation of the model of “totally accessible DOS” from the experimental results suggests that for T < 20 K only a limited fraction of the DOS states is involved in the exciton relaxation process. In other words, not every state of the DOS, which carries oscillator strength, can be populated by the exciton during its downhill relaxation. As we have seen already, in the framework of both the CED and BR models of the aggregate chain it is necessary for the exciton to be able to move along the chain, to obtain access to every state of the DOS. Thus, we can conclude that the exciton migration should be suppressed at those very low temperatures. A small increase of the experimental Stokes shift when the temperature raises from 4 to 30 K probably means that more states of the DOS become involved into the exciton relaxation process upon increasing temperature. We would like to emphasize, once again, that the only purpose of this discussion is to show that the assumption that the exciton can reach every state of the DOS is not valid at low temperatures. A Gaussian function (eq 10) for the absorption line was taken for the sake of simplicity. However, it has been shown that the low energy side of the absorption band of Frenkel excitons in crystals with disorder can be fitted to a some extent by a Gaussian.32 As for the low energy tail of the absorption spectra, for a diverse types of solids (and for J-aggregates as well15,20) it is described by exponential law which is also called “Urbach rule” (see ref 32, p 1544, and references therein). However, the amplitude of the exponential function decreases with decreasing energy ν much slower than the Gaussian given by eq 8. Thus, in the case of an Urbach tail the Stokes shift calculated in the framework of the model of totally accessible DOS will be even larger and deviate more from the experimental results. Note also, that experimental fluorescence line width at T < 20 K is less than the line width of absorption (see Figure 3), whereas according to our model, based on a thermal population of all levels in the DOS, they should be the same. While the absorption width does not change and amounts 87 cm-1, the fluorescence bandwidth decreases almost linearly from 80 to 60 cm-1 upon decreasing the temperature from 30 to 5K. The

Figure 6. Temperature dependence of the fluorescence Stokes shift. Solid circles, experimental values; solid line, calculation of the fluorescence Stokes shift in the framework of the model of a “totally available DOS” (section 3.1.2, eq 10).

same effect of an appreciable narrowing of fluorescence spectra relative to absorption spectra has been also observed for aggregates of other dyes at low temperature.14,20 For instance, the fluorescence width of TDBC J-aggregates was reported to decrease from 170 cm-1 at 80 K to 125 cm-1 at 5 K, while the absorption width was the almost constant (160 cm-1) at temperatures less than 150K.14 This fact undoubtedly shows a relaxation to and a preferable population of a more narrow distribution of states at such low temperature (see also ref 14). This phenomenon can be explained by suggesting the blocking of the exciton migration within the whole molecular ensemble at temperatures less than 30K. This “freezing” of the exciton motion will be discussed later (sections 3.2 and 3.4) in connection with exciton migration properties and with wavelength dependence of the exciton fluorescence decay time. The Stokes shift (SS) reflects the energy difference between the distribution of the exciton states carrying the oscillator strength (absorption spectra) and that of the relaxed states multiplied on their population (fluorescence spectra). As usual, the Stokes shift is larger for systems with stronger exciton-phonon interaction, for systems with more disorder and a "softer” lattice.22 The temperature dependence of Stokes shift can provide important information about the origin of the emitting states of J-aggregates. Although a lot of work has been done in J-aggregates photophysics the question concerning whether excitons after relaxation are “free” or self-trapped in these molecular ensembles is still far from clear. Hereafter we will try to estimate the relative importance of the self-trapping (or deformation of the DOS after excitation) for excitons in J-aggregates of THIATS by an analysis of temperature dependence of the Stokes shift and the width of the absorption and fluorescence spectra. We have to note here again that there are almost no reliable experimental data about the temperature dependence of the Stokes shift in J-aggregates. Unmatched data taken from different experiments with different aggregates do not allow one to make reliable general conclusions. As shown in Figure 3, the temperature dependence of the Stokes shift (excitation wavelength was 565 nm) is rather complex and nonmonotonic for J-aggregates of THIATS. The critical temperatures of 30 K as well as 70 K are clearly observed on the graph. To clarify the underlying physical processes we calculate the Stokes shift in units of the fluorescence bandwidth:

SSrel ) SS/fwhmfluor

(11)

The value of relative Stokes shift (SSrel) reflects the ratio of

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Figure 7. Temperature dependence of the Stokes shift relative to the fwhm of the fluorescence spectrum in the semilogarithmic scale. Functions plotted by solid lines are indicated in the figure. See section 3.1.2. for details.

the downhill relaxation of the excitons to the total energy “width” of the accessible relaxed DOS population. In Figure 7 the logarithm of the relative Stokes shift is plotted against the temperature. The fascinating features of this graph are a linear dependence of ln(SSrel(T)) in intermediate temperatures and a constant value at low temperatures and high temperatures (Figure 7). In the semilogarithmic scale, a linear decrease of Stokes shiftrel vs T means an exponential temperature dependence. The dependence SSrel(T) was well fitted by the function A‚exp(-T/Ta) in the intermediate temperature range (30-80 K). For the best fit, the parameter Ta was found to be about 65 K ) 45 cm-1 which is very close to the half-width of the spectral bands. We attribute this behavior to the process of “opening” more and more DOS states for exciton thermal population. Note that in this range the Stokes shift becomes closer and closer to the limit of a “totally accessible DOS” discussed above (see Figure 6). At low temperatures (T < 20 K), relative Stokes shift is constant and large. It reaches more than 50% of the fluorescence line width (SSrel ≈ 0.6). In the high temperature range (T > 90K), the relative Stokes shift is again temperature independent and equal to 0.2. At this sufficiently high temperatures (the absorption fwhm is of the order kT) an exciton-phonon equilibrium is established very rapidly within the DOS and this process is not limited by internal barriers and/or disorder as it was the case at low temperature. As soon as the width of the absorption spectrum becomes comparable with kT, the population induced broadening is saturated. In other words, there are no other possibilities for population induced broadening if the DOS remains the same. In this case, relaxation processes within a “rigid” DOS do not provide much difference between absorption and fluorescence spectra. Exactly this effect we observed in the experiment (Figure 3). As far as we observed, the same temperature dependence of the width of the absorption and fluorescence spectra at T > 70 and that the relative Stokes Shift is small, there are no significant deformations of the DOS after excitation. The further broadening of the both absorption and fluorescence spectra is going on mainly by a homogeneous mechanism. Since no significant deformation of the DOS was observed at T > 90 K it is possible to conclude that there is no self-trapping process in this temperature range. 3.2. Wavelength Dependence of the Exciton Decay Time within the Fluorescence Band. As we have mentioned already, exciton relaxation is accompanied by an energy transfer between

Figure 8. Fluorescence decays at different registration wavelengths at 10 K. Excitation wavelength, 565 nm; analysis wavelengths, 611.5, 613.5, 614.5, 615.5, and 617.5 nm; the time increment per channel, 98 ps.

different excited states in J-aggregates. To investigate this phenomenon we measured the fluorescence decay at different wavelengths within the fluorescence band (see section 2 for experimental details). We found the fluorescence kinetics f(t) to be very dependent on the detection wavelength (Figure 8) in the low-temperature range (T < 30 K). To acquire a qualitative description of those differences, we calculate the average fluorescence decay time given by

〈τ〉 )

∫o∞ f(t)dt

(12)

where f(t) is a fluorescence intensity normalized to one at t ) 0. At T < 30 K, the average decay time increases from ca. 3 ns to ca. 7 ns with increasing observation wavelength from 611 to 617 nm (blue and red wings of the fluorescence band respectively). In spectroscopic language, this means that one observed a time-dependent spectral shift of the fluorescence spectrum toward lower energy after excitation. The effect of wavelength dependence of the fluorescence decay time at low temperature has been observed for several aggregates in solution14,26,39 as well as for PIC aggregates in LB films.12 However, in all those cases fluorescence spectra were much broader (fwhm was more than 100 cm-1) than we observed for our system. This spectral shift on a subnanosecond time scale reflects a long time component of the Stokes shift formation. While the temperature increases above 30 K the fluorescence decay time becomes steadily less and less dependent on the wavelength within the emission band. There were no differences in kinetics observed at T > 50 K (Figure 9). Hence, the homogeneous component of the fluorescence bandwidth (1/T2) does not blur the identity of the exciton states contributing to the fluorescence spectra at T40 the homogeneous broadening and significant exchange between different exciton states take place. Therefore, no difference in fluorescence kinetics was observed at these temperatures. As we have already mentioned, particular values of critical temperatures scale together with the absorption and fluorescence line width. For example, for TDBC aggregates with a fluorescence fwhm of 125 cm-1 at 5 K, it was found that a wavelength dependence of the fluorescence decay time is observed at T < 80 K.14 It is easy to see that both those values are approximately 2 times larger than those for THIATS aggregates (60 cm-1 and 40 K, respectively). Recalling the previously suggested CED and BR models of the aggregates (section 3.1.1), one can easily see that the simple BR model of noninteracting coherent segments (no hopping between different segments)34 of different length N predicts exactly the opposite decay time behavior when the fluorescence

τ(n) ∝

n2 1 π2n2 ∝ ; E(n) ∝ - 1 + 2(N + 1) µ (n) (N + 1) 2

where n is the number of the exciton state (see section 3.1.1). Thus, the model predicts a shorter radiative decay time at lower energies (longer wavelengths). “To save” the model one has to introduce energy transfer between lowest levels of the neighboring ideal “rods”. Choosing particular values of the intra- and intersegment relaxation rates it is possible to obtain a least qualitative agreement with the experiment.40 The model of the continuous energy disorder (CED model) seems to be able to explain the observed decay time behavior. Actually, the lowest energy states of the chain possess a smaller transition dipole moment (longer radiative decay time) than that of the higher states, corresponding to the maximum of the absorption spectra.33,28 By choosing an appropriate value of the rate of downhill energy relaxation between different states, one can also obtain shorter decay time on the high energy side (“blue wing”) of the fluorescence spectra. 3.3. Temperature Dependence of the Exciton Coherence Length. As has been indicated above, the exciton coherence length is a very important parameter that influences all spectroscopic properties of the J-aggregates. One way to estimate the effective coherence length NC experimentally is to determine the radiative lifetime of the excitons, or, in the other words, to estimate transition dipole moment from the excited to the ground state. Afterward NC can be calculated using the eq 1:

Nc ) Φ

τ0 τfluores

(1 + Q)

(13)

where Φ is the fluorescence quantum yield and τfluores is the fluorescence decay time. The value of Q has been determined by eq 1. The temperature dependence of the fluorescence quantum yield Φ and the decay time τfluores has been measured17 for THIATS aggregates and the temperature dependence of the NC has been calculated.17 Knowledge of Nc(T) provides substantial information about dimensionality of the exciton coherent volume.41 In the case of THIATS J-aggregates, we demonstrated an applicability of the quasi-1D model to excitons in this system. All details can be found in ref 17. Such experiments have been done also for PIC J-aggregates.42 Several related experiments were carried out also for other dyes.14,43,44 The temperature dependence of the coherence length for THIATS aggregates is plotted in Figure 11.17 We should note that in those experiments the values of NC were determined from

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the average fluorescence decay times because the fluorescence was collected from the whole fluorescence band. Thus, such peculiarities as the wavelength dependence of the fluorescence decay time at T < 40 K (see the previous paragraph) are obscured by the detection procedure. Note here, that the effect of the decay time “inhomogeneity” at low temperatures was not considered in the experimental papers mentioned above too, as well as in all theoretical work (see for instance ref 41 and references therein). In a first approximation the effect of fast decaying components with a positive contribution (mainly present at the short wavelength side of the emission band) will be compensated by that of components with a negative contribution presented at the long wavelength side of the emission band. Comparing NC(T) (Figure 11) with the temperature dependence of other aggregate parameters indicates that NC(T) reveals the same critical temperature of 30 K. This temperature splits whole temperature interval in the lowest temperature range where NC≈constant and a high-temperature range where NC starts to decrease with increasing temperature. It is interesting to note that NC starts to decrease at the same temperature where the intensive exchange between adjacent exciton levels starts to take place (see section 3.2). 3.4. Long Distance Exciton Migration at Different Temperatures. One of the most attractive features of the J-aggregates is a long distance migration of the exciton through a molecular ensemble. This observation shows a potential application of such organic molecular nanoclusters as a very effective artificial light harvesting antennae. This energy migration can be observed by the occurrence of bi-exciton quenching or exciton-exciton annihilation (EEA) at high excitation intensities. In J-aggregates this phenomenon was first observed as a decrease of the fluorescence lifetime under high excitation intensity.23,45-48 However, up to now there is no final answer to the question on physical nature of the ultrafast exciton migration of highly delocalized excitons, which can be wave packet-like coherent motion or incoherent hopping. A crude rate equation, which describes biexciton quenching, is

dF 1 ) -KF - γF2 dt 2

(14)

where F is the excitation density [cm-3], K is the exciton decay rate in the absence of EEA (when F ) 0), and γ is the EEA rate constant [cm3 s-1]. At a crude approximation49 γ ∼ D, where D is the exciton diffusion constant. It means that determination of the biexciton annihilation rate γ provides us a substantial information about exciton migration itself. It is well-known from the theory of molecular excitons27,49 that the temperature dependence of the exciton diffusion constant D is completely different for coherent excitonic transport and for incoherent hopping. For incoherent hopping D increases with increasing temperature and scales as exp(-Ea/T) where Ea is the activation energy.27,49 In the case of coherent motion D decreases with increasing T and scales as T-m where m ) 0-1.5 depending on the particular parameters of the exciton-phonon system.27,49 At their turn, the mechanism of the exciton migration is determined by many different factors, of which the most important are exciton-phonon coupling, the ratio of the exciton bandwidth, and the phonon energies kT, and the extent of the crystal disorder.49,50 The EEA rate γ can be estimated from the measurements of the fluorescence quantum yield Φ at different excitation intensities W, relative to the value of Φ extrapolated to zero

Figure 12. Exciton-exciton annihilation rate γ at different temperatures. Solid line, the best-fit exponential function (see section 3.4); dashed line, guide for eyes. The excitation photon flux W in the units of number of molecules per created exciton is shown within the bar.

intensity. To obtain values of the relative fluorescence quantum yield fluorescence decays were measured at different excitation photon flux W. The fluorescence decays were measured by the same TCSPC set up described in sections 2 and 3.2. The sample was excited at 565 nm and the fluorescence light was collected from the whole emission band, which had a maximum at 614 nm. The excitation photon flux (W) was varied from 2.7 × 1010 to 108 photons/cm2pulse using a set of neutral filters. For all other details we refer the reader to the original paper.51 To estimate the EEA efficiency from the plot of Φ(W) vs W the excitation photon flux when 20% of exciton quenching have been reached (W20%) was determined. Under those conditions of rather weak biexciton quenching it can be shown52 that the annihilation rate γ is inversely proportional to experimentally determined W20%.51,52 The values of W20%(T) as well as the annihilation rate γ in arbitrary units are shown in Figure 12. The most pronounced feature of γ(Τ) is a strong nonmonotonic temperature dependence. The whole investigated temperature range can be divided in four temperature intervals: 0-20, 20-70, 70-110, and 110-300 K. In each temperature range the EEA rate γ and, in turn the ability of the exciton to migrate, show a completely different behavior. As one can see, these temperature intervals coincide very well with those observed for the linear spectroscopic properties described above. However, the EEA rate possesses a much stronger temperature dependence than the other excitonic characteristics and changes nonmonotonically with the temperature by orders of magnitude. We observed a strong blocking of the EEA process when T is below 10 K or above 80 K, and an almost constant EEA rate between 20 and 70 K. The most effective EEA process with almost constant γ was observed in the temperature range of 20-70 K. It was found that the exciton emission had been quenched already by 20% under an excitation photon flux of ca. 109 photons/cm2pulse. This intensity corresponds to approximately one absorbed photon per 107 dye molecules. Note that due to some experimental difficulties,51 an error by a factor 3-5 cannot be excluded in this estimation. The very effective and temperature independent EEA process suggests a coherent (wave packet-like) exciton motion for this temperature range. A “freezing” of the fast coherent exciton motion can be observed at T < 10 K. This phenomenon is attributed to the blocking of the exciton by energetic barriers in a disordered chain. In the case where kT is smaller than value ∆ of the disorder, the exciton, delocalized over the coherence length of 20-100 molecules, becomes blocked between energetic barriers. Thus, we assume that a thermally activated (phonon assistant)

Molecular Aggregates of THIATS hopping between two coherent segments is probably the main mechanism, which can provide exciton migration at such low temperatures. In Figure 12 the experimental data for T < 20 K were fitted to an Arrhenius equation with a hopping activation energy Ea ) 15 K ) 10.5 cm-1, which gives us an estimation of the energetic disorder ∆. We would like to emphasize here that there is a clear connection of this observation to the conclusion of the “incomplete” exciton relaxation within the DOS at low temperature and the “inaccessibility” of the whole set of states generated by static disorder (see section 3.2). However, even at 5 K the EEA is still pronounced corresponding to an exciton migration over ca. 104 dye molecules. This observation is not in agreement with the common opinion that the excitons in J-aggregates are almost immobile quasiparticles at such a low temperature.53 As soon as the temperature is more than 20 K, population of higher lying excitonic states with different B k vectors occurs. Exciton wave packets possess the kinetic energy larger than ∆ can migrate with a group velocity regardless to the disorder. This is a qualitative explanation how the incoherent hopping transmits coherent wave packet motion at higher temperatures. In the temperature range between 70 and 110 K, γ starts to be strongly temperature-dependent again. The diffusion coefficient decreases by almost 2 orders of magnitude when the temperature is increased only by 50%. This strong temperature dependence cannot be explained in the framework of exciton scattering on acoustic phonons or optical phonons with small frequencies (ω , kT). This mechanism can only lead to a rather slow power decrease of D (see above). Such strong decrease of the exciton migration rate means that in this temperature range another mechanism starts to become important. We attribute this effect to scattering of coherent excitons on optical phonons with frequencies Ωopt ) 40-60 cm-1. Optical phonon modes with such a frequency are often considered for explaining exciton dynamics in J-aggregates.41 The strong temperature dependence comes from the fact, that contrary to acoustic phonons the optical phonons are dispersionless. Therefore, the exciton does not interact with optical phonon mode at all as long as T < Ωopt. When T ∼ Wopt the interaction is turned on and exciton scattering starts to be strongly temperature dependent (D decreases by several orders of magnitude).50,49 When kT > Ωopt, we return back to the “normal exciton phonon coupling” however with another (than it was at lower temperatures when exciton coupling takes place with acoustic phonons only) exciton-phonon coupling constant due to the involvement of optical phonons into the scattering process. Note here that self-trapping of excitons that has been suggested in some aggregated systems22,54 is doubtful in this type of THIATS J-aggregates, as far as so effective long distance exciton migration is observed. There is no doubt that in the high temperature range (110 K < T < 300 K) the exciton dynamics is very strongly influenced by exciton-phonon scattering.41 We observed a decrease of γ of about 1 order of magnitude when the temperature increases from 110 to 300 K. However, even at room temperature the exciton is still delocalized over a coherence length of about 10 dye molecules.17,30 This means that the exciton migration cannot be considered as a simple incoherent hopping from one molecule to another. This feature also distinguishes J-aggregates from anthracene-like molecular crystals where excitons are completely localized on a single molecule at room temperature and migrate through the lattice by incoherent hops.27,49 Moreover, for incoherent hopping one should expect an increase of γ with increasing T,49 whereas we observed the opposite.

J. Phys. Chem. B, Vol. 105, No. 20, 2001 4645 TABLE 1: Critical Temperatures for Excitons in J-Aggregates of the Dye THIATS excitonic and optical properties absorption broadening fluorescence broadening stokes shift fluorescence lifetime wavelength dependence coherence length annihilation rate

critical temperature 30 K 70 K no yes yes yes

yes yes yes no

yes yes

no yes

It is perhaps interesting to know that a similar nonmonotonic temperature dependence (and with a similar rationalization) for is observed for charge carriers mobility in organic single crystals (perylene, anthracene, and naphthalene).55 We have to emphasize here that our results51 are completely different from those obtained for PIC monolayers with traps,56 where the energy transfer rate was found to be proportional to T in the temperature range of 20-300 K and associated with incoherent exciton hopping. 4. Summary and Conclusions The absorption line width, fluorescence line width, Stokes shift, coherence length, exciton migration rate, as well as fluorescence wavelength dependence of the fluorescence decay time of the J-aggregates of the dye THIATS are investigated in the temperature range 4-130 K and at room temperature. In comparison with other aggregates, absorption and fluorescence lines of the J-transition of THIATS aggregates are extremely narrow at low temperature. The full width at halfmaximum is 85 and 60 cm-1 at 5 K for absorption and fluorescence respectively, which is 1.5-3 times smaller than those of other well-known J-aggregates except aggregates of pseudoisocyanine dye. The temperature dependence of the whole set of exciton properties reveals two critical temperatures: 30 and 70 K (see Table 1). Among all investigated characteristics, excitonexciton annihilation rate possesses the most significant temperature dependence. The observed phenomena are described qualitatively as an interplay of static and dynamic disorder effects. For each temperature range we suggest the following physical mechanisms to be dominant: T ) 0-20 K, “static range”. Static disorder is the main factor which limits coherence length, EEA rate and absorption width. The internal structure of the DOS levels has not been “blurred” by homogeneous broadening. Slow subnanosecond exciton relaxation toward the lower energy states is observed. Only limited amount of DOS states are accessible for exciton during its relaxation. Exciton migration is suppressed by disorder. T ) 30-70 K, “static f dynamic” transition range. Homogeneous processes and intensive phonon-induced exchange between exciton states start to disturb “frozen picture”. A wide set of the DOS states starts to be accessible for exciton during its relaxation. The coherence length starts to decrease. A very fast wave packet like exciton migration occurs over more than 106 molecules. T ) 80-300 K, “dynamical range”. The population of the optical phonons states in the ground electronic state leads to a broadening of the absorption spectra. The Stokes shift becomes temperature independent. The exciton migration starts to be strongly blocked by scattering on optical phonons. The effective, long distance exciton migration in THIATS J-aggregates suggests that no exciton self-trapping process

4646 J. Phys. Chem. B, Vol. 105, No. 20, 2001 occurs at temperatures higher than 20 K. Also, below 20 K selftrapping in shallow traps is unlikely as it would lead to a reduction of the of the exciton coherence length when one proceeds from the “free” excitons above 70 K to the trapped excitons below 20 K, which is not observed. Even if selftrapping would occur below 20 K the traps must be quite shallow, as they are no longer populated at higher temperatures where self-trapping is excluded. Acknowledgment. This work was supported by NATO grant SfP97-1940 and RFBR grants 99-02-17326, 00-15-96707, 00-02-16607. I.G.Sch. thanks the F.W.O. (Fonds voor Wetenschappelijk Onderzoek Vlaanderen) for a “Visiting Postdoctoral Fellowship” and the Russian Federal Program “Integratsia AO-133” for support. I.G.Sch. personally thanks Dr. Andrei Lobanov (Lebedev Physical Institute) for stimulation of some experiments and useful discussions, Mikhail Skorikov and Vitalii Tsvetkov (Lebedev Physical Institute) for the technical help and Prof. R. Silbey (MIT, MA) for discussions. The authors gratefully acknowledge the continuing support from DWTC (Belgium) through grant IUAP-IV-11, the F.W.O.-Vlaanderen, and the Nationale Loterij. The authors are grateful for Agfa N.V. for the sample of THIATS. References and Notes (1) Jelley, E. E. Nature 1936, 138, 1009. (2) Scheibe, G. Angew. Chem. 1936, 49, 563. (3) von Berlepsch, H.; Bo¨ttcher, C.; Da¨hne, L. J. Phys. Chem. B 2000, 104, 8792. (4) von Berlepsch, H.; Bo¨ttcher, C.; Quart, A.; Burger, C.; Da¨hne, S.; Kirstein, S. J. Phys. Chem. B 2000, 104, 5255. (5) Scherer, P. O. J. In J-aggregates; Kobayashi, T., Ed.; World Scientific Publishing: Singapore, 1996; Chapter 4. (6) Knoester, J.; Spano, F. In J-aggregates; Kobayashi, T., Ed.; World Scientific Publishing: Singapore, 1996; Chapter 5. (7) van Oijen, A. M.; Ketelaars, M.; Ko¨hler, J.; Aartsma, T. J.; Schmidt, J. Biophys. J. 2000, 78, 1570. (8) Mal'tsev, E. I.; Lypenko, D. A.; Shapiro, B. I.; Brusentseva, M. A.; Milburn, G. H. W.; Wright, J.; Hendriksen, A.; Berendyaev, V. I.; Kotov, B. V.; Vannikov, A. V.; Appl. Phys. Lett. 1999, 75, 1896. (9) Bourbon, S.; Gao, M.; Kirstein, S. Synth. Met. 1999, 101, 153. (10) Gadonas, R. In J-aggregates; Kobayashi, T., Ed.; World Scientific Publishing: Singapore, 1996; Chapter 7. (11) Kobayashi, T.; Misawa, K. in J-aggregates; Kobayashi, T. Ed.; World Scientific Publishing: Singapore, 1996; Chapter 6. (12) Fidder, H.; Terpstra, J.; Wiersma, D. A. J. Chem. Phys. 1991, 94, 6895. (13) Fidder, H.; Wiersma, D. A. J. Phys. Chem. 1993, 97, 11603. (14) Moll, J.; Daehne, S.; Durrant, J. R.; Wiersma, D. A. J. Chem. Phys. 1995, 102, 6362. (15) Drobizhev, M. A.; Sapozhnikov, M. N.; Scheblykin, I. G.; Van der Auweraer, M.; Varnavsky, O. P.; Vitukhnovsky, A. G. Chem. Phys. 1996, 211, 455. (16) Scheblykin, I. G.; Varnavsky, O. P.; Verbouwe, W.; De Backer, S.; Van der Auweraer, M.; Vitukhnovsky, A. G. Chem. Phys. Lett. 1998, 282, 250. (17) Scheblykin, I. G.; Bataiev, M. M.; Van der Auweraer, M.; Vitukhnovsky, A. G. Chem. Phys. Lett. 2000, 316, 37. (18) Hirschmann, R.; Friedrich, J. J. Chem. Phys. 1989, 91, 7988. (19) Renge, I.; Wild, U. P. J. Phys. Chem. A 1997, 101, 7977. (20) Nabetani, A.; Tomioka, A.; Tamaru, H.; Miyano, K. J. Chem. Phys. 1995, 102, 5109.

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