Torsional Vibrations of Ester Groups as a Mechanism of Dielectric Relaxation of Poly(p-hydroxybenzoic Acid) Marina G. Saphiannikova,* Natalia V. Lukasheva, Anatolii A. Darinskii, and Yulii Ya. Gotlib Institute of Macromolecular Compounds, Russian Academy of Sciences, Bol’shoi pr. 31, 199004 St. Petersburg, Russia Ju 1 rgen Brickmann Institut fu ¨ r Physikalische Chemie I and Darmsta ¨ dter Zentrum fu ¨ r Wissenschaftliches Rechnen, Technische Hochschule Darmstadt, Petersenstrasse 20, D-64287 Darmstadt, Germany Received December 17, 1998; Revised Manuscript Received August 16, 1999 ABSTRACT: 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. 1. Introduction The homopolyester of 4-hydroxybenzoic acid (PHBA) is a polar macromolecule which according to X-ray data 1-4 can exist in two conformations. We will refer to them as cis and trans. In the cis-conformation the oxygen atoms of neighboring carbonyl groups are found to be at opposite sides of the main chain; in the trans- conformation these atoms are located at the same side. 5 The trans-conformation is observed only in homopoly- mers with low degrees of polymerization at room tem- perature (phase II). 1,2 In all other phasessthe low- temperature phase I and two high-temperature phases III and IVsthe PHBA chains exist in the cis-conforma- tion. 1,3,4 In the cis-conformation the signs of the trans- verse projections of the dipole moments normal to the main chain alternate along the chain (Figure 1). There- fore, the transverse projection of the total dipole moment M of the PHBA chain is equal to zero in a regular chain conformation. The directions of the longitudinal projec- tions of all the dipoles coincide; therefore, every chain has a considerable longitudinal component of M which is proportional to the degree of polymerization. How- ever, in a highly ordered crystalline sample, the chain cannot reorient as a whole and the total dielectric relaxation is related only to small fluctuations of dipole moments near their equilibrium positions. Thus, the contributions from both transverse and longitudinal components of the total dipole moment may be impor- tant. Kalika and Yoon 6 studied the dielectric relaxation of PHBA near the transition from the crystal phase to the smectic-E -like phase beginning at 325 °C. They measured the dielectric susceptibility as a function of frequency and found the value of the dielectric strength Δǫ ) ǫ 0 - ǫ ∞ . Here, ǫ 0 is the static susceptibility, and ǫ ∞ is the infinite frequency limit. The measured value of the dielectric strength was found to be between 0.7 and 1.0 for different samples. It was compared to that calculated using Onsager’s formula 7 for an isotropic system of freely rotating dipoles with each dipole Figure 1. PHBA chain in the cis-conformation. The rotation of the ester group around a long bond of the main chain is shown by a curved arrow. 606 Macromolecules 2000, 33, 606-612 10.1021/ma9819440 CCC: $19.00 © 2000 American Chemical Society Published on Web 12/31/1999