Elementary Theory of Dielectric Relaxation

The relative permittivity tensor for the system ik is defined (see, for example, Born and Wolf 1970 Landau et al. 1987) by the relation 

We have taken into account here, according to the conventional theory (Pokrovskii 1978), that the relaxation time of the first-order moment is three times bigger than the relaxation time of the moment of the second order in equation (7.49). A solution of equation (7.53) can be written in the form 

One can consider the oscillating amplitude of the field E exp(— iu ), while assuming that the second-order moment does not depend on the field, to have from equation (7.54) 

When velocity gradient is absent, the above formula looks like any other formula for dielectric permittivity for a system with the only relaxation process, which is used for estimation of dielectric relaxation time. 

A frequency dependence of complex dielectric permittivity of polar polymer reveals two sets or two branches of relaxation processes (Adachi and Kotaka 1993), which correspond to the two branches of conformational relaxation, described in Section 4.2.4. The available empirical data on the molecular-weight dependencies are consistent with formulae (4.41) and (4.42). It was revealed for undiluted polyisoprene and poly(d, /-lactic acid) that the terminal (slow) dielectric relaxation time depends strongly on molecular weight of polymers (Adachi and Kotaka 1993 Ren et al. 2003). Two relaxation branches were discovered for i.s-polyisoprene melts in experiments by Imanishi et al. (1988) and Fodor and Hill (1994). The fast relaxation times do not depend on the length of the macromolecule, while the slow relaxation times do. For the latter, Imanishi et al. (1988) have found 

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