Limitations of the rate-distribution formalism in describing luminescence quenching in the presence of diffusion

When encountering complex fluorescence decays that deviate from exponentiality, a very appealing approach is to use lifetime or rate constant distributions. These are related by Laplace transform to the sum of exponential functions, stretched exponentials, Becquerel's decay function, and others. However, the limitations of this approach have not been sufficiently discussed in the literature. In particular, the time-independent probability distributions of the rate constants or decay times are occasionally used to describe bimolecular quenching. We show that in such a case, this mathematical formalism has a clear physical interpretation only when the fluorophore and quencher molecules are immobile, as in the solid state. However, such an interpretation is no longer possible once we consider the motion of fluorophores with respect to quenchers. Therefore, for systems in which the relative motion of fluorophores and quenchers cannot be neglected, it is not appropriate to use the time-independent rate or decay time distributions to describe, fit, or rationalize experimental results on fluorescence decay.