Dielectric relaxation of polymer chains

Dielectric spectroscopy is a valuable tool for studying the conformational and dynamic properties of polar macromolecules. The conformational features can be determined by dielectric relaxation strength measurements, whereas the dielectric spectrum provides information on the dynamics of the macromolecules. Phenomenological and molecular theories of dielectric permittivity and dielectric relaxation of polymers have also been developed to elucidate the experimentally observed phenomena. As Adachi and Kotaka have stressed (see Further reading), experimental information depends on each monomer s dipole vector direction as related to the chain contour. A classification of polar polymers into three categories was introduced by Stockmayer type-A polymers, where the dipole is parallel to the chain contour (Fig. 12.4), type-B, where it is perpendicular to the chain contour, and type-C, where the dipoles are located on mobile side groups. For type-A chains, the global dipole moment of each chain is directly proportional to the chain s end-to-end vector R. 

In the presence of an external electric field, polar chains reorient themselves in the direction of the field (Fig. 12.5). The orientational motions of polar macromolecules give rise to dielectric absorption. The rotational rearrangement of macromolecules in a solution takes a finite time, increasing the polarization P of the system in the direction of the field, where P is the sum of the constituent dipoles per unit 

The experimentally observed quantity is the complex dielectric per-nuttivity, defined as 

8 is the static permittivity and 8oo is the permittivity limit at high frequencies. 

The fluctuation-dissipation theorem dictates that the response of a system to a weak perturbation is entirely determined by the equilibrium correlation of the fluctuating dynamic variable that couples with the field, i.e., ili p (f) = cmm (0 where cmm is the correlation function of the fluctuations of the total dipole moment in equilibrium  

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