Theory of Fluorescence Depolarization by Anisotropic Brownian Rotations. Discontinuous Distribution Approach

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Abstract
In this paper, we generalize to molecules devoid of symmetry the phenomenological treatment of depolarization of the fluorescence by the Brownian rotations of a spherical molecule due to Spencer and Weber. There are six ways in which a system of orthogonal coordinates rigidly bound to the molecule may be made to coincide with the laboratory coordinates. The transitions between these permissible orientations gives rise to a system of six differential equations of transport, the solution of which entails that of a differential equation of sixth order. However, because of the equivalence of some of the rotations as regards the depolarizing effects, on account of the symmetry conditions, the solution of a differential equation of third order is only necessary. Consequently, after an instantaneous light pulse, a polarized component of the fluorescence will show a maximum of three exponential decays and the difference of parallel and perpendicular components a maximum of only two decays. The steady‐state fluorescence polarization from a completely assymetric molecule is given by a simple expression containing as only parameters a mean rotational rate, the variance of three orthogonal rates of rotation, and an average of these rates weighted according to their angles with the emission oscillator. A qualitative comparison of this treatment with previous theories of depolarization that make use of classical rotary diffusion theory shows that the former is better suited to an intuitive understanding of the phenomena and to experimental usage.