Monte Carlo simulations on concentration self-quenching by statistical traps

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Abstract
We present high accuracy Monte Carlo simulations on the steady state fluorescence quantum yield and anisotropy for systems in which concentration self‐quenching due to incoherent energy transfer between randomly distributed molecules occurs. A simple model of self‐quenching is considered, in which luminescent molecules within a critical distance of each other act as perfect traps. The simulations are based on the complete solution of the coupled rate equations for a randomly chosen distribution of molecules in a finite box. Finite size effects are systematically investigated. The results are used to assess the validity of simple analytic theories, such as Burshtein’s theory of hopping transfer, which is found to give a good semiquantitative description of the fluorescence quantities. Furthermore, we show that truncating the transfer rate in such a way that, on the average, 10–20 molecules are within reach of an excitation residing on a given molecule, induces large deviations in the yield. We point out that this is a serious source of error in previous simulations.