Exciton diffusion constant

The 7 constant (in cm3s-1) of mobile excitons is directly related to the exciton diffusion constant D 7 = S-nDR, (in cm2s-1). 

Many papers have been devoted to the experimental determination of the exciton diffusion constant D. In most of the studies, D was determined by observing how the diffusion of excitons results in their capture by impurities (sensitized fluorescence) or in bimolecular quenching of excitons (reviews of these experiments may be found in (8),(21). The interpretation of such experiments requires that not only the diffusion of the excitons to the acceptor is taken into account, but also the character of the exciton interaction with the acceptor (i.e. with the impurity... 

We estimate that the IRAVs are photogenerated within 2 ps in the 10% Cgo-doped film, in contrast to the time constant of about 50 fs in 50% Ceo-doped films [160]. This indicates that the photoinduced charge transfer reaction in Ceo-doped films is actually limited by the exciton diffusion toward Qo molecules close to the polymer chains. Consequently, the exciton wavefiinc-tion in MEH-PPV films is not as extended as previously thought. The same conclusion was drawn for Ceo-doped DOO-PPV films, where it was estimated [161] that the exciton diffusion constant to reach the Cgo molecules is of the order of 10 crcd/s. 

A theory of exciton-phonon coupling is presented and the consequences of this coupling for spectral line shapes and exciton transport are discussed. The theory is valid for arbitrary phonon and exciton bandwidths and for arbitrary exciton phonon coupling strengths. The dependence of the diffusion constant on temperature and the other parameters is analyzed. 

Other important examples which exhibit both confinement and diffusion in the classical dynamics of their cyclic collective coordinates are the positronium [20] and the excitonic [14] atom. Because of the comparable masses of the two particles in both cases the mean CM velocity as well as the diffusion constant are orders of magnitude larger than the corresponding values of the hydrogen atom. 

Therefore the migration of excitons slows down when they reach the low-energy sites where they find fewer sites with lower energy in its neighborhood. Due to such dispersive migration, the exciton diffusion cannot be described using a constant diffusion coefficient, but a time-dependent one. 

As can be seen from eqn (14.8), the calculation of the tensor reduces to the calculation of two-particle correlation functions. The lack of sufficiently detailed data on the exciton band structure and the exciton-phonon coupling constants considerably complicates the accurate calculation of the two-particle correlation functions and the exciton diffusion coefficients. However, the temperature dependence of this coefficient differs significantly for coherent and incoherent excitons (see below). Therefore, studying the temperature dependence of diffusion has always been an important tool to analyze the character of the energy transfer in molecular crystals. In the remainder of this chapter, we will focus on the main characteristics of the diffusion constant and its temperature dependence... 

In some molecular crystals a crossover from coherent excitons (exciton mean free path l A) to incoherent ones ( k, A, Ioffe-Regel criterion) takes place with increasing temperature. We then expect that upon increasing the temperature from very low values, at some threshold temperature the decreasing behavior of the diffusion constant for coherent excitons goes over into an increasing behavior. 

FlG. 14.1. The decay rate of the transient grating signal versus 92 (9 is the angle between the pump pulses) for anthracene crystals at 10 and 20 K (23). The magnitude of the slope is proportional to the diffusion constant of the excitations in the crystal. With increasing temperature, the diffusion constant decreases. The average diffusion constant obtained from these data is about 10 times larger than the value expected for incoherent exciton motion (25). 

Here, th is the lifetime of the host excitons without traps. We furthermore make the simplifying assumption that every exciton is captured when it reaches a trap and that the excitation density is constant with time and remains homogeneous. If, in addition, the mean free path of the exciton is smaller than the capture radius R of the traps for excitons, and D is the exciton diffusion coefficient, then we obtain... 

Accordingly, the PAi onset dynamics can be attributed to cooling toward the new configuration equilibrium within the 1B manifold. This vibrational relaxation initially occurs with a time constant of 300 fs, which is followed by a slower component with a time constant of 830 fs. The onset dynamics may also be influenced by the exciton diffusion. However, the polarization decay on the sub-ps timescale shows a slower dynamics characterized by a time constant of 1.6 ps, suggesting that the exciton spatial diffusion occurs on a longer timescale compared to that of the intrachain exciton cooling. As shown in Figure 22.12b, the polarization ratio decay, and thus spatial diffusion, continues until PAi becomes isotropic at about 150 ps. 

The relatively low values of yss and Ds in quasi-amorphous solids might be underlain by disorder (see Sec. 2.4.3) and/or a contribution of triplet excitons in quenching of fluorescent singlets (cf. Sec. 2.5.1.2). The diffusion coefficient of triplets is expected to be lower than of singlets since both energy donor and acceptor transitions are disallowed. A low value of yss has been found for the triplet-triplet annihilation rate constant from biexcitonic quenching... 

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