The model of Forster excitation energy transfer on a spherical core−shell nanoparticle was presented. A general expression for fluorescence intensity decay was obtained for an arbitrary number of acceptors linked chemically to the shell. It was found that the dynamical behavior of the system is extremely sensitive to the number of acceptors and the size of the nanoparticle. Monte Carlo simulations performed for the energy transfer parameters taken from an independent experiment show excellent agreement with the model for donor fluorescence decay and its mean lifetime. The original model was then extended to the common experimental case of core−shell nanoparticle size distribution, assuming the Gaussian distribution function of their radii. This effect leads to slower fluorescence decays and longer mean fluorescence lifetimes, as revealed by Monte Carlo simulations.

Analytical model of nonradiative energy migration (homotransfer) within the set of chemically identical fluorophores distributed on the surface of a spherical nanoparticle is for the first time presented. The expression for emission anisotropy decay is obtained. The method of Green’s function was used to solve the master equation describing this stochastic process. An expansion in powers of the fluorophore density to investigate this finite volume problem was employed. A very good result for the Green function directly related to emission anisotropy was obtained by using the Padé approximant. It was found that emission anisotropy decay depends strongly not only on the number of fluorophores linked to the spherical nanoparticles but also on the ratio of critical radius to nanoparticle radius, which is crucial for the optimal design of antenna-like nanostructures. Coherence of the model was verified by Monte Carlo simulations and excellent quantitative agreement was found between theoretical and Monte Carlo simulation results.

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