The rate of fluorescence quenching is derived for the continuum model of a diffusion-controlled reaction, using the exact solution to the Smoluchowski equation with a Coulomb potential derived earlier. The first two terms in the long-time expansion of the reaction rate are formally the same as the result obtained by Smoluchowski for no long-range forces. However, the sum of the hard-core radii in Smoluchowski’s expression is replaced by an effective encounter distance. Our expression for the reaction rate with the Coulomb interaction constitutes an extension of Debye’s steady-state result to the transient case.
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Hong et al. (1978) studied this question.