The Permittivity Tensor for Polymer Systems

we have to return to the subchain model of macromolecule, which was used to calculate the stresses in the polymeric system, and express the tensor of the mean orientation of the segments of the macromolecule in terms of the subchain model. 

Equation (10.6), formulated in the previous section, defines the relative permittivity tensor in terms of the mean orientation of certain uniformly distributed anisotropic elements, which we shall interpret here as the Kuhn segments of the model of the macromolecule described in Section 1.1. We shall now discuss the characteristic features of a polymer systems, in which the segments of the macromolecule are not independently distributed but are concentrated in macromolecular coils. 

In the equilibrium situation, at a given end-to-end distance R of a macromolecule, the tensor of mean orientation of segments of a chain is determined (Flory 1969) as 

As before, we shall consider each macromolecule to be divided into N subchains and assume that every subchain of the macromolecule is in the equilibrium. So, using the above formula relating the tensor of the mean orientation of the segments of the macromolecules (ejek) to the distance between the ends of the subchains, we arrive from relation (10.6), taken in the first approximation, at Zimm s (1956) expression for the relative permittivity tensor 

The anisotropy of the coil has been calculated for other models of the macromolecule. Expressions for the anisotropy coefficient are known in the case where the macromolecule has been represented schematically by a continuous thread (the persistence length model) (Gotlib 1964 Zgaevskii and Pokrovskii 1970) and also in the case where the microstructure of the macromolecules has been specified. In the latter case, the anisotropy coefficient of the macromolecule is expressed in terms of the bond polarisabilities and other microcharacteristics of the macromolecule (Flory 1969). 

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