A study is made of the luminescence intensities associated with exciton diffusion and trapping on a three-dimensional anisotropic percolating lattice. The calculation is based upon a relationship that exists between the frequency dependent diffusion tensor at frequencies comparable to the inverse excitation lifetime, and luminescence observables such as the host and trap luminescence intensities for conditions of constant illumination. The present approach allows the study of crossover behavior in percolative systems that are of intermediate transport dimensionality 2 < dt < 3. Our results suggest that curvature seen in luminescence observables near the transition need not always be a direct reflection of the critical indices associated with classical isotropic percolation. We have identified three possible sources of deviation from the classical behavior: (1) the radiative time scale of the luminescence measurements, (2) the functional dependence of the luminescence yields on the diffusion tensor, and (3) the demands of dimensional crossover in the critical region arising from the anisotropy of the medium.
P. E. Parris, "Exciton Diffusion at Finite Frequency: Luminescence Observables for Anisotropic Percolating Solids," Journal of Chemical Physics, vol. 90, no. 4, pp. 2416-2421, American Institute of Physics (AIP), Jan 1989.
The definitive version is available at https://doi.org/10.1063/1.455984
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