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In nanoparticles (NPs) static quenching of luminescence may be slower than in bulk media due to the space restrictions on acceptor location. Many-body cooperative quenching (manifesting itself as, e.g., down-conversion) occurs when the donor energy is transferred to two-, three-, or more particles (a cooperative acceptor) at once. Random distribution of acceptor particles in diluted media accounts for the non-exponential form of the kinetics. When the analytical expression for the kinetics form is known, it can be fitted to the experiment in order to find various micro- and macro-quenching parameters of the luminescent material. In this paper, we present an analytical law for cooperative quenching kinetics in NPs at longer time. Its clear and compact form reflects the fact that, on average, donors located on the surface of NPs are the last to decay having acceptors on one side only. We compared the resulting formula with the Monte-Carlo computer simulation, and they show good agreement. |
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