Radiative properties of solvated molecules in dielectric clusters and small particles

The radiative lifetime of molecules solvated in finite size clusters and particles is studied as a function of size. Four regimes of behavior are indicated by our present and previous theoretical results and by the available experimental data: The microscopic regime (up to a few tens of solvent molecules), where the lifetime is sensitive to microscopic structural details of the cluster; the electrostatic regime (up to sizes ∼0.1λ, where λ is the radiation wavelength in the cluster), where the lifetime follows the predictions of classical electrostatics of dielectric environments; the electromagnetic regime (sizes of the order of λ), where the behavior is dominated by electromagnetic resonances in the particles; and the bulk regime (sizes much larger than λ). In the last three regimes the radiative lifetime may be approximated as a product of a cavity factor and a solvent factor. The first depends on the shape of the microscopic cavity surrounding the molecule and the second depends on the shape and size of the solvent particle. For spherical particles and for spherical or mildly spheroidal cavities, the lifetime changes from being longer than that of the free molecule in the electrostatic regime to being shorter in the bulk regime, in agreement with recent experimental results. The transition region occurs in the electrodynamic size regime. In the "bulk regime" (very large particles) molecules near the particle surface (within ∼ one wavelength) are strongly affected by electromagnetic Mie resonances and show strong size-dependent deviation from the bulk behavior which characterizes molecules in the interior. The size dependence of the radiative lifetime stands in marked qualitative contrast to the size dependence of the solvent induced frequency shift, which approaches its bulk limit much earlier-when the cluster size becomes much larger than the microscopic cavity size. Finally, the ratio between the integrated absorption profile and the radiative decay rate does not depend on the cluster size.