Hydrodynamic properties of a rigid molecule: Rotational and linear diffusion and fluorescence anisotropy

Abstract

Abstract The fluorescence anisotropy of a general rigid body is formally the sum of five exponentials. We show that, to a high degree of approximation, there are relationships between the five time constants. As we define the time constants here, τ 1 ≅ τ 5 , τ 2 ≅ τ 3 , and τ 1 −1 + 3τ 4 −1 ≅ 4τ 2 −1 . In practical cases, at most only three exponentials will be observed, and, of these, only two are independent. Using a numerical integration procedure, Perrin's equations for the rotational and translational diffusion of a general ellipsoid are solved. Rotational friction coefficients, frictional ratio, rotational relaxation times, and the five exponential terms in the fluorescence anisotropy are tabulated as functions of the axial ratios of the ellipsoid. In principle, the three axes of a general ellipsoid may be determined by a simultaneous measurement of the anisotropy and the linear diffusion constant. We examine, and illustrate, the effect of experimental error on such a determination.