Anomalous diffusion by tunnelling on a square lattice: trapping and fusion of triplet excitons in mixed crystals of naphthalene

Abstract

This paper presents numerical simulations of dispersive hopping transport by tunnelling between random centres on a square lattice. The results are compared with two approximations, the continuous-time random walk and anomalous diffusion by hopping on percolation clusters. The continuous-time random walk is qualitatively and semi-quantitatively adequate for high concentrations, short times and weak disorder, but diverges from the simulations at long times. Hopping on percolation clusters does not adequately describe the results. Diffusion is in general anomalous, r2(t) infinity tx, 0<x<1, where the upper and lower bounds correspond respectively to weak and strong disorder. The simulations show the dependence of the apparent luminescence decay of a disordered material on the source of excitation. The stretched exponential decay of donor phosphorescence and the algebraic decay of delayed fluorescence of isotopically mixed crystals of naphthalene at 1.6 K are studied as a practical illustration.