Dynamics of helical worm-like chains. IV. Dielectric relaxation

Abstract

Dielectric relaxation of both flexible and stiff chain polymers in dilute solution is studied on the basis of the discrete helical worm-like chain such that an electric dipole moment is attached rigidly or with a rotational degree of freedom to each of the subbodies composing the chain. The complex dielectric constant is formulated with the dipole correlation function, which may be expressed in terms of the L=1 time-correlation functions derived previously. Then, dielectrically active branches of the eigenvalue spectrum are identified for a given type of dipoles, and a mode analysis of them is made in order to inquire into the interaction between global and local modes. The decay behavior of the dipole correlation function is also examined numerically for various chains. A comparison of theory with experiment is made with respect to the dispersion and loss, and also the dielectric correlation time τD as determined from the loss peak. The theory cannot always well explain the asymmetry of the loss curve, especially for flexible chains without side chain motions. For flexible chains, however, the calculated values of τD agree rather well with the observed values, although the former are somewhat smaller than the latter. Furthermore, it is found that there is strong correlation between the static stiffness parameter λ−1 and the dynamic stiffness as defined as the ratio of τD to that of the isolated subbody (monomer unit). For stiff chains, an interpolation formula for τD is constructed, and it is shown to explain well the molecular weight dependence of τD. Finally, a possible direction toward improvement of the theory is suggested.