Theory of Fluorescence Depolarization by Anisotropic Brownian Rotations

The recently detected inertial effect on the behaviour of the fluorescence anisotropy r = \ j /J — \ as a function of the viscosity rj of a solvent for prolate luminescent molecule, the transition moment of which lies along its longer axis (see [1,2] and refs. quoted there), was explained using the non-Markovian generalized d i f fus ion equat ion [1], The a im of the present note is to extend the previous results to the case of anisotropic d i f fus ion and to derive the general expression for a steadystate depolarizat ion. T h e p rob lem is solved by reducing it to the case of Markov ian d i f fus ion and use of the final results of C h u a n g and Eisenthal [3]. It is worthy of ment ion that the inertial effect upon r was recently considered by Sarshevskii et al. [4] who used the d i f fus ion equa t ion with t ime-dependent d i f fus ion constant. This app rox ima t ion is however worse in compar ison with our approach [2]. The different t rea tments of the rotat ional Brownian motion of a nonpsher ical body in terms of a Fokker-Planck-Kramers equa t ion or stochastic integrodifferential equa t ion were presented in papers of Ford, Lewis, McConnel l , Scaife, and Morita (see [5] and refs. quo ted there) together with an application to the theory of dielectric relaxation.