Excitons incoherent motion

Reineker, P. (1982). Exciton Dynamics in Molecular Crystals and Aggregates. Stochastic Liouville Equation Approach Coupled Coherent and Incoherent Motion, Optical Lineshapes, Magnetic Resonance Phenomena. Springer Tracts in Modern Physics, Vol. 94, Springer, Berlin, Heidelberg. 

The hopping probabilities between the two one-dimensional stacks in sublattices I and II are found from the analysis of the ESR spectra at room temperature to be Pi n = 1.6 10 s and Pn = 2.8 10 s. Their ratio is about the same as the Boltzmann factor, exp(-AE/feT) = 0.8 at T= 300 K, and the energy difference between I and II is AE/hc = 50 cm . The incoherent motion of the triplet excitons between the one-dimensional stacks is thus at least 1000 times slower than that within the stacks the triplet excitons in DBN crystals are therefore indeed one-dimensional. 

The description of excitation motion outlined in the previous sections assumes completely incoherent nearest neighbor hopping. This was treated in detail because it is the case of widest applicability especially with the materials of interest discussed in the final section. However, it should be noted that in some cases excitons can move coherently over several lattice spacings before being scattered i). For this case the diffusion coefficient is expressed in terms of the group velocity of the exciton v and the time between scattering events r. 

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). 

At r< 16 K, the triplet exciton motion within the one-dimensional stacks is coherent and is determined by the exchange integral Iaa = Ibb = 7 cm". This corresponds to an exchange frequency of coaa = 2 lAA/h = 2.7 10 s . For T> 16 K, the exciton motion within the stacks becomes increasingly incoherent. 

A considerable amount of theoretical work has been done on the lineshape of the EPR absorption under the influence of exciton motion. Haken and Strobl (1967, 1973) developed a stochastic model for the description of energy transfer by excitons that includes both the coherent and incoherent... 

In general the exciton dynamics exhibits both coherent and incoherent behaviour, where the incoherence arises from the couphng of the system to a dissipative environment. This is conveniently modelled by an equation of motion for the reduced density operator, p, defined by... 

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