MEAN FIELD-THEORY OF TRANSIENT FLUORESCENCE QUENCHING IN THE FREQUENCY-DOMAIN

A dynamical mean field theory is developed for the frequency dependence of the modulation and phase angle that are monitored in frequency domain fluorometric studies of diffusion-influenced fluorescence quenching. These quantities are obtained directly in the frequency domain by solving an implicit equation involving the Laplace transform [k̂(z) ] of the time dependent bimolecular rate coefficient [k(t) ] that plays a central role in the Smoluchowski approach to this problem. For several models of the quenching process, the mean field results are compared with those obtained by Fourier transforming the time domain response calculated using the Smoluchowski approach. The agreement is good except at high quencher concentrations. For models where k̂(z) is known analytically, the mean field approach is computationally simpler than the Smoluchowski one. This is even more so when it is not possible to find k(t) analytically from k̂(z) (e.g., a model in which the nonradiative lifetime of a quencher-fluorophore pair is constant up to a critical separation but infinite thereafter).