Abstract
An analytical consideration of bimolecular reactions in nanostructures is presented. As a mathematical model, the two-particle Green's function approach for the diffusion problem with the Neumann boundary condition is proposed. Also, the special cases, when the solutions can be reduced to the simpler one-particle Green's function, are analysed. Despite such diffusion equations are almost always analytically intractable, Green's function technique allows to build an analytical expression for the distance-dependent annihilation rate. The observed model can describe non-spin-selective annihilation reactions and spin-selective annihilation reactions such as triplet–triplet annihilation (TTA) of excitons or quenching of triplets by doublet centers. Based on this model, the distance-dependent annihilation rates were calculated for circular (2D system) and spherical (3D system) nanostructures. As illustrations of this method, we show that the annihilation rate can be enhanced in circular and spherical nanostructures.
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