Torsional Vibrations of Ester Groups as a Mechanism of Dielectric Relaxation of Poly(p-hydroxybenzoic Acid)

Dielectric relaxation of poly(p-hydroxybenzoic acid) (PHBA) due to torsional vibrations of the dipoles of ester groups in the main chain is considered. A dynamic model of elastically coupled rotators interacting with the crystal lattice is applied. The model is characterized by two sets of force constants which determine intrachain correlations between rotators along a given chain and interchain interactions in the crystal lattice. Correlation functions for the cosines of the rotation angles of different rotators in a chain are calculated. Fluctuations of the components of dipole moments normal to the chain axis (transverse components) and fluctuations of the components along the chain axis (longitudinal components) are considered. The transverse component is connected with the previously considered crank-shaft type of internal rotational motions of ester groups. The origin of the longitudinal component is ascribed to a complicated superposition of internal rotations and bending vibrations. The fluctuations of the transverse and longitudinal components depend on intrachain and interchain interactions, and their contributions to the dielectric relaxation of PHBA are comparable in magnitude. The thermal averaged magnitude of fluctuations of the total dipole moment is calculated. The calculated results are compared with experimental data on the dielectric relaxation of PHBA and also with predictions based on previous molecular mechanics calculations. It is concluded that consideration of only transverse fluctuations of the dipole moment does not provide an adequate description of the experimentally observed dielectric relaxation of PHBA. On the contrary, consideration of a superposition of both transverse and longitudinal contributions results in good agreement with experiment using force constants estimated from torsional potentials (calculated by the AM1 method) and from the experimental activation energy. The activation energy corresponding to dipolar motions in noncrystalline regions of a PHBA bulk sample is obtained from the experimental dielectric relaxation.