Dielectric relaxation of poly(p-hydroxybenzoic acid): Torsional vibrations of ester groups

Dielectric relaxation of poly(p-hydroxybenzoic acid) due to torsional vibrations of the dipoles of ester groups in the main chain is considered. A dynamic model of harmonically bound rotators interacting with the crystal lattice is applied. The model contains two sets of force constants, which determine either intrachain correlations between rotators along a given chain or interchain interactions in the crystal lattice. The correlation functions for the cosines of rotational angles of different rotators in the chain are calculated. These correlation functions are manifested in the dielectric relaxation of poly(p-hydroxybenzoic acid). The fluctuations of the components of dipole moments in a plane normal to the chain axis (i.e., the transverse components) and the dipole moment fluctuations in the plane of the chain (i.e., the longitudinal components) are considered. The transverse component is related to the simplest crankshaft type of the internal rotational motion of ester groups. This type of motion was considered previously. The origin of the longitudinal component is the superposition of internal rotations and bending vibrations. The amplitudes of the transverse and longitudinal fluctuations depend on intrachain and interchain interactions. Their contributions to the dielectric relaxation of poly(p-hydroxybenzoic acid) are comparable with each other. The fluctuations of the total dipole moment are calculated with both transverse and longitudinal components taken into account. The obtained results are compared with the experimental data and predictions based on the molecular mechanics calculations performed previously. Consideration of only transverse fluctuations of the dipole moment is insufficient to adequately describe the experimentally observed dielectric relaxation of poly(p-hydroxybenzoic acid). On the contrary, consideration of a superposition of both transverse and longitudinal contributions agrees well with the experimental data if the force constants estimated from the torsion potential (which was calculated by the AM1 method) are used. In this case, the activation energy corresponding to activation of the mobility of ester dipoles in noncrystalline regions of the sample of poly(p-hydroxybenzoic acid) is obtained from the experimental data on dielectric relaxation.