Relations among steady-state, time domain, and frequency domain fluorescence quenching rates

Abstract

Methods of nonequilibrium statistical thermodynamics are used to study relations among rate expressions for steady-state, time domain, and frequency domain fluorescence quenching rates. Equations are derived that relate the Laplace transform, @(z), of the quenching rate coefficient in the time domain, P(t), to the steadystate rateconstant, k", and to themean field rate coefficient in the frequency domain, km'(o), These relationships can be useful in calculating steady-state and frequency domain results when the Laplace transform, @(z), is given. The equation linking @(z) with k" is a rigorous consequence of the statistical nonequilibrium thermodynamic theory and is equivalent to an equation derived by Szabo (J. Phys. Chem. 1989,93,6929). The equation relating @ ( z ) to kmf(w) is obtained for the case of low illumination intensity and is different from that conjectured by Zhou and Szabo (J. Chem. Phys. 1990,92,3874). The relationships between the steady-state, time-dependent, and frequency-dependent quenching rates illustrate a more general principle: the molecular rate coefficient, k(t), of a diffusion-controlled bimolecular process is coupled to the rates of concurrent unimolecular processes, e.g., particle generation and decay.

Relations among Steady State, Time Domain, and Frequency Domain Fluorescence Quenching Rates. 2

“…The treatment presented in this paper compliments and extends those in refs 1 We stress that the present theory is not equivalent to that of Sung et aL9 This is because our eq 21 ignores the excluded volume effects and, therefore, cannot produce the same result for ko. However, one can repeat the derivation of eq 40 for a more general reactivity model:…”

“…First, we derive an exact formula linking kd and @(z) in the linear harmonic regime. This formula follows exactly from ow formalism, and our previous result in ref 1 can be regarded as a useful approximation. We also discuss the relationships between the various approaches and show that our treatment of frequency domain fluorescence quenching is consistent with that by Sung et al?…”

“…Relation between k^fo) and k°(z). We begin by noting that the oscillatory illumination 7 causes oscillations not only of the concentration *( ) but also of the radial distribution Equation 26 was first derived by Szabo7 and rederived in ref 1 for the case with no static quenching. However, the fact that eq 26 is also valid in the present case should not be taken to imply that the macroscopic characteristics of fluorescence quenching are not affected by reaction (l.e).…”

“…when Kc = 0 or qq = 0). Thus, at steady state when K(t) = Kss = const, the ratio of the intensity in the absence (/0) and in the presence (1) of the quencher becomes…”

Spatially nonlocal fluctuation theory of rapid chemical reactions

“…Recently we have shown how that theory can be used to calculate the time dependence of both the nonequilibrium radial distribution function and bimolecular reaction rate constants. 8,9 As useful as that theory is, it suffers from an intrinsic limitation, namely, it is based on spatially local conceptions regarding density fluctuations due to reaction and diffusion. Indeed, the dynamics of density fluctuations in that theory involve only hydrodynamic length scales 2,3 with a molecular length scale for reaction appearing only in the definition of the rate coefficient in terms of the radial distribution function.…”