Theory for Rotational Diffusion of Ellipsoids

In the preceding sections we described the rotationa) behavior of ellipsoids with transiticms directed along one of the symmetry axes. Although not frequently used, the complete expression for an dlipsoid with three nonequivalent axes(Hguie 12.1. left), derived without restricting one of the transitions to be on an axis, is useful to have. In this case die anisotrt decays with flve appvrat ccwielatitm times  

In this expression, D is the mean rotational diffusion coefficient, 

In the limiting case of spherical symmetry with Di = D2 = D = D, Eq. [12.22] reduces to a single ctHrelation time with 6 = (6D) For ellipsoids of revolution, these equations (12.22 to 12.28) reduce to those given in Section 12.2. 

TIME DOMAIN STUDIES OF ANISOTROPIC ROTATIONAL DIFFUSION 

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The theory for rotational diffusion of ellipsoids, and measurements by fluorescence polarization, can be traced to the classic reports by F. Perrin. Since these seminal reports, the theory has been modified to include a description of expected anisotropy decays. Hiis theory has been summarized in several reviews.For a rigid ellipsoid with three unequal axes, it is now agreed that the anisotropy decays with five correlation times. The correlation times depend on the three rotational diffiision coefficients, and the amplitudes depend on the orientation of the absorption and emission transition moments widiin the fluoroi iore and/or ellipsoid. While the the( predicts five correlation times, it is known diat two pairs of correlation times will be very close in magniOide, so that in practice only three correlation times are expect for a nonsf oical molecule. ... 

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