Electric birefringence, rotational diffusion

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. 

The rotational diffusion constant in water at 25° and neutral pH as measured by electric birefringence (258) is 230 X 105 sec-1 or 0.73 X HT8 sec as a relaxation time. For a hydrodynamic ellipsoid of dimensions 66 X 22 A and a molecular weight of 14,000, the calculated relaxation tilde is 0.72 X 10-8 sec. However, the apparent asymmetry of the molecule from the X-ray structure corresponds to an axial ratio of no more than 2 1 rather than 3 1. 

This electro-optical effect, commonly observed as transient changes in optical birefringence of a solution following application, removal, or reversal of a biasing electric field E(t), has been used extensively as a probe of dynamics of blopolymer solutions, notably by O Konski, and is a valuable tool because it gives information different in form, but related to, results from conventional dielectric relaxation measurements. The state of the subject to 1975 has been comprehensively presented in two review volumes edited by O Konski (25). The discussion here is confined to an outline of a response theory treatment, to be published in more detail elsewhere, of the quadratic effect. The results are more general than earlier ones obtained from rotational diffusion models and should be a useful basis for further theoretical and experimental developments. 

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. 

In addition to the substantial literature on solvent and small-molecule translational diffusion, there is also a significant literature on small-molecule rotational diffusion. Experimental methods that report rotational diffusion behavior include VH tight scattering, as examined in different time domains with Fabry-Perot interferometry and photon correlation methods, nuclear magnetic resonance, oscillatory electrical birefringence, and time-resolved optical spectroscopy. 

Quadratic Kerr effect has been mainly studied in polydiacetylene solutions and gels (Kapitulnik et al.(1984), Lim and Heeger (1985) Lim et al. (1985) Kapitulnik et al. (1986)). Strong electric birefringence was observed with large rotational diffusion constants (t 0.1 -r 0.2 s), characteristic for very long molecules. 

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... 

The rise and decay of the electric birefringence of a fluorinated surfactant are shown in Fig. 9.18 [283]. The birefringence relaxation time, Tb, is related to the rotational diffusion constant, D/ ... 

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