Electric birefringence, rotational diffusion coefficient

The rotational diffusion coefficient Dr of a rodlike polymer in isotropic solutions can be measured by electric, flow, and magnetic birefringence, dynamic light scattering, and dielectric dispersion. However, if the polymer has some flexibility, its internal motion makes it difficult to extract Dr for the end-over-end rotation of the chain from data of these measurements. In other words, Dr can be measured only for nearly rodlike polymers. 

Three methods are mainly used to determine rotational diffusion coefficient. They are (1) flow birefringence, (2) electric birefringence, and (3) polarization of fluorescence. Of these, although electric birefringence can yield , its main use is in the study of dipole moments. All the three methods of determining 0 are discussed m the following pages. 

The rise and decay of birefringence (Figure 9.17) provide two different informations about the macromolecule. At the onset of the electric pulse, the shape of the rise of birefringence provides information about the orientation of the induced and permanent dipole moments of the moleeule. The decay of birefringence is due to rotational diffusion coefficient of the macromolecule. The decay, then, provides a precise measure of the rotational difiiision coefficient, which as we have seen earlier can provide an idea about the shape of the macromolecule. 

A similar formula (Eq. 5.30) as that given in Eq. 5.29 exists for the rotational diffusion coefficient. In Eq. 5.30, B is a reciprocal of the equivalent hydrodynamic diameter of a sphere and is listed in Table 5.3 for several common shapes. The mean value for the rotational diffusion coefficient Dg an be obtained from the angular dependence of the mean characteristic decay f in a multiangle PCS experiment following Eqs. 5.19 and 5.20. If another independent experiment, such as depolarized PCS or transient electric birefringence can be performed to determine Dr, a combination of Dt and Dr... 

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