Abstract
We derive an approximate expression for the time-dependent reaction rate coefficient, k(t), of the Smoluchowski equation for the step function nonradiative lifetime (SFNL) model in the case of structureless liquid (i.e., if there are no spatial correlations between molecules of reactants). The SFNL model assumes that a reaction occurs with equal probability for reactants at distances between r0 and r1. The accuracy of the obtained analytical formula for k(t) is absolutely sufficient for practical applications like the interpretation of experiments on fluorescence quenching. A molecular dynamics has shown that the SFNL model much better describes the simulation results than the Smoluchowski–Collins–Kimball model if the distance between r1 and r0 cannot be neglected.
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