Low temperature dielectric relaxation in polyethylene and related hydrocarbon polymers

The dielectric loss tangent, tan $\delta $, of a number of hydrocarbon polymers has been measured in the frequency range 10 Hz to 1 MHz between 1 and 4.2 K. Four different grades of polyethylene, together with poly(4-methyl pentene-1), shows a peak in tan $\delta $, and this has been studied in some detail in Rigidex 3, a high-density polyethylene, where it has a form indistinguishable from that predicted on the basis of a single relaxation time. The frequency of maximum loss decreases almost linearly with temperature from 4.3 kHz at 4.2 K to 950 Hz at 1 K, while the magnitude of the loss increases by a factor of less than 2 over the same temperature range. A large superposed static field reduces the magnitude of the loss, and enables an estimate to be made of the magnitude of the contributing dipole: p$_{0}$ = 0.58 $\pm $ 0.06 x 10$^{-29}$ C m (1.75 $\pm $ 0.15 D). This value, together with a typical value of tan $\delta $ of 10$^{-5}$, indicates that the dipole concentration is about 10$^{21}$ m$^{-3}$, although this can be increased by heating the polymer in air. In polypropylene and polystyrene tan $\delta $ is independent of both frequency and temperature. A simple quantum mechanical model of the relaxation process is used to explain the experimental results: a particle in a double potential well tunnels from one well to the other with emission or absorption of a phonon. It is deduced that the particle is a proton, and the loss peak is ascribed tentatively to hydroxyl rotation in the crystalline regions of the polymer.