Excitation transfer in disordered two-dimensional and anisotropic three-dimensional systems: Effects of spatial geometry on time-resolved observables

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A unified treatment of dipole–dipole excitation transfer in disordered systems is presented for the cases of direct trapping (DT) in two-component systems and donor–donor transfer (DD) in one-component systems. Using the two-particle model proposed by Huber we calculate the configurational average of Gs(t), the probability of finding an initially excited molecule still excited at time t. For the isotropic three-dimensional case treated by Huber excellent correspondence is found with the previously reported infinite diagrammatic approximation. The anisotropy of the dipole–dipole interaction is included in the averaging procedure. Two regimes of orientational mobility are considered: the dynamic and static limit, rotations being much faster or slower, respectively, than the energy transfer. The following geometrical distributions are investigated: (a) Infinite systems of one, two, and three dimensions which lead to Förster-like decays. Two orientational distributions are considered for monolayers: dipoles confined to the plane or oriented isotropically. (b) Bilayers and multilayers. The averaging procedure for transfer from one layer to another is outlined in detail. The main parameters determining the decay of Gs(t) are the surface concentration and the ratio of the layer separation and the Förster radius. In a stack with a small number of layers, which is a finite system in one of the dimensions, an average over positions of the initially excited donor is included. At low surface concentration the decay gradually changes from two- to three-dimensional character as one increases the number of layers. This fractal-like behavior is solely due to the presence of excluded volumes and the finite nature of the system. Experimental observables are considered in detail. An analysis including a general formalism is presented to determine the loss of polarization memory if an excitation is transferred to a random distribution within the given geometrical constraints. It follows that after one transfer step, in the worst case, less than 10% of the initial anisotropy is conserved if the appropriate observation geometry is chosen. The anisotropy decay, which is manifested in a transient grating or fluorescence depolarization experiment, is thus a useful observable for Gs(t) in DD transfer.