Emission anisotropy isotropic rotations

For isotropic motions in an isotropic medium, the values of the instantaneous and steady-state emission anisotropies are linked to the rotational diffusion coefficient Dr by the following relations (see Chapter 5) ... 

Equations (8.25) to (8.28) are no longer valid in the case of hindered rotations occurring in anisotropic media such as lipid bilayers and liquid crystals. In these media, the rotational motions of the probe are hindered and the emission anisotropy does not decay to zero but to a steady value rc0 (see Chapter 5). For isotropic rotations (rod-like probe), assuming a single correlation time, the emission anisotropy can be written in the following form ... 

The case of probes undergoing isotropic rotations in a homogeneous isotropic medium will be examined first. Rotations are isotropic when the probe has a spherical shape, but it is difficult to find such probes because most fluorescent molecules are aromatic and thus more or less planar. Nevertheless, when a probe interacts with the solvent molecules through hydrogen bonds, experiments have shown that in some cases the observed rotational behaviour can approach that of a sphere. In the case of rod-like probes whose direction of absorption and emission transition moments coincide with the long molecular axis (e.g. diphenylhexatriene Figure 8.4), the rotations can be considered as isotropic because any rotation about this long axis has no effect on the emission anisotropy. 

The timescale of fluorescence emission is comparable to that of rotational diffusion of proteins and the timescale of segmental motions of protein domains or individual amino acid residues. The polarization or anisotropy of the emission provides a measure of these processes. Suppose a sample is excited with vertically polarized light (Fig. 11), and that the sample is viscous so that the fluorophores do not rotate during the lifetime of the excited state. Then the emission is polarized, usually also in the vertical direction. This polarization occurs because the polarized excitation selectively excites those fluorophores in the isotropic solution whose absorption... 

Szabo proposed an interesting model-free formula for the time-resolved anisotropy in a macroscopically isotropic system [112]. He expressed r(f) as the autocorrelation function of orientations of the emission dipole moment at time t and absorption dipole moment at time t = 0 in a form suitable for general treatment of various systems, and particularly those with possible internal rotation ... 

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