EXCITATION-ENERGY TRANSPORT IN FRACTAL AGGREGATES

A theory is developed to describe excitation energy transport in fractal aggregates. These fractal structures have densities which scale as a fractional power of the radius. Because of this, each donor is in a different environment with respect to donor and/or trap density. Consequently, ensemble averages cannot be performed using centro-symmetric coordinates. This problem has great similarities to the case of excitation energy transport in finite volumes. In this work the theory developed by Ediger and Fayer for the finite volume case is adapted to the fractal case. Forster limit (donor-trap transfer) and one-component (donor-donor transfer) systems are considered. Specific examples of Forster transfer are treated for the infinite size fractal, two-dimensional fractals and transfer from the aggregate to the excluded volume. A simple formalism for deriving expressions for the mean relaxation time of excitation is presented.