Switch of d imensionality of e xciton d iffusion in a ggregates

. The ultrafast exciton dynamics in J-aggregates of a perylene bisimide dye is investigated for temperatures down to 77 K revealing at low temperatures a decrease of the exciton mobility and a change in the dimensionality. measurements. It works much better for both, the 150 K and the 77 K data, but fails at 293 K (see Fig. 2b). A diffusion constant D 3D of 0.016 nm²/ps is found for 150 K and of 0.005 nm²/ps for 77 K. This reduction of the exciton mobility can be traced back to the decrease of the spectral overlap between absorption and fluorescence. The stationary absorption spectra show upon cooling no new features pointing to a compact three-dimensional packing of the PBI-1 molecules and the structure responsible for the shape of the spectra is still the one-dimensional aggregate chain [3]. Furthermore, it seems highly unlikely that extended three-dimensional structures are formed for the following reasons. At cold temperatures clear samples are obtained and no pronounced scattering is observed, which would be


Experimental Results and Discussion
Fused silica cells with a layer thickness of 1 mm are filled with a 0.09 mM solution of PBI-1 in MCH and placed into a continuous flow cryostat operated with liquid nitrogen. Stationary spectroscopy shows that at this concentration J-aggregates are formed. Pumpprobe absorption measurements are carried out applying for excitation 30 fs long pulses centred at 530 nm from a non-collinearly phase-matched optical parametric amplifier (NOPA) and as probe a white light continuum generated in a calcium fluoride substrate [3].
Transient absorption spectra of PBI-1 in MCH are depicted in Fig. 1 for three different temperatures. They show a strong negative band due to ground state bleach and stimulated emission. Upon cooling, narrowing of the bands and a solvent induced red shift occur, which is also observed in the stationary spectra. In addition, a positive signal contribution, which is particularly visible at 77 K, exists at the blue side of the dominant band. It is attributed to the excited state absorption from the one-exciton to the two-exciton state. The decay of the signal is non-exponential and accelerates with increasing excitation density. It is dominantly caused by bimolecular exciton-exciton annihilation [2]. Accordingly, the evolution of the time dependent exciton density n(t) is described by the rate equation Equ. 1.
 is the intrinsic lifetime of the excitons and (t) the bimolecular annihilation rate. The latter depends on the dimensionality and reads for one-and three-dimensional diffusive exciton motion [2,3]: with the molecular density N0, the lattice constant a and the diffusion constant D1D. In the case of three-dimensional motion, D3D is the isotropically averaged diffusion constant and a the isotropic annihilation interaction distance that should be the lattice constant for next neighbour interaction. Figure 2 shows for the three considered temperatures the time dependent exciton densities as they are obtained from the spectrally integrated transient absorption (white regions in Fig. 1). At room temperature (293 K, green dots) the decay is faster than at lower temperatures and can be described by one-dimensional diffusion driven annihilation (Fig. 2a). The fit of Equ. 1 using the one-dimensional annihilation rate 1D reproduces the decay dynamics at room temperature very well and yields a diffusion constant of D1D = 0.36 nm²/ps. However, the one-dimensional model does not work for the lower temperatures, see Fig. 2a. Therefore, the three-dimensional model, i.e. 3D is applied to these measurements. It works much better for both, the 150 K and the 77 K data, but fails at 293 K (see Fig. 2b). A diffusion constant D3D of 0.016 nm²/ps is found for 150 K and of 0.005 nm²/ps for 77 K. This reduction of the exciton mobility can be traced back to the decrease of the spectral overlap between absorption and fluorescence. The stationary absorption spectra show upon cooling no new features pointing to a compact three-dimensional packing of the PBI-1 molecules and the structure responsible for the shape of the spectra is still the one-dimensional aggregate chain [3]. Furthermore, it seems highly unlikely that extended three-dimensional structures are formed for the following reasons. At cold temperatures clear samples are obtained and no pronounced scattering is observed, which would be typical for particles or microcrystals. Additionally, the cooling process is quite fast and the time window, during which the sample is liquid, is

Conclusions
The decay of the exciton density in PBI-1 aggregates can be modelled and understood in terms of diffusion driven exciton-exciton annihilation. It is found that the exciton motion is substantially slowed down at low temperatures. The temperature dependence of the fitted exciton diffusion constant resembles thereby almost perfectly the changes in the spectral overlap. This points to an incoherent hopping scenario based on Förster energy transfer. Static disorder in the aggregate chains results in energy barriers, which limit the delocalization of the excitons as well as their incoherent hopping rate and mobility. Surprisingly, we observe a change in the exciton decay dynamics that could be reproduced by switching from a one-dimensional model used at room temperature to a three-dimensional model for measurements at 150 K and 77 K. This variation of the exciton decay behaviour is most likely caused by a structural change from one-dimensional chain like aggregates at room temperature to more extended structures at low temperatures. The latter seem to consist of a limited set of weakly interlinked chains as it is frequently observed for dye aggregates often resulting in the formation of organogels.
Financial support by the German Science Foundation via the SFB 652 is gratefully acknowledged.