Emission anisotropy ellipsoids

Box 5.3 Emission anisotropy of totally asymmetric rotors and ellipsoids... 

In the particular case of prolate and oblate ellipsoids, the number of exponentials is reduced to three because two of the three axes are equivalent. The rotation diffusion coefficients around the axis of symmetry and the equatorial axis are denoted Di and D2, respectively. The emission anisotropy can then be written as... 

The three decay constants appearing in the expression for r(t) for an ellipsoid of rotation have been calculated and are own in Table 13. As may be seen, the three relaxation times diverge rapidly with increasing axial ratio for a prolate ellipsoid. However, for an oblate ellipsoid the deviations are small even for hi axial ratios and experimentally it m prove difficult to resolve more than a single, nean relaxation time for r(t) in this case. Thus, three situatrens exist in which the emission anisotropy may decay exponentially and it is not po le, therefore, to distingui ... 

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. ... 

---