Measurements of piezoelectric and pyroelectric activity, density, and x-ray pole figures were used to study the effect of thermal aging on the state of polarization in polyvinylidene fluoride. A rolled and poled β-phase specimen of polyvinylidene fluoride was subjected to thermal aging which consisted of temperature cycling between room temperature and successively higher maximum temperatures, TMAX, where TMAX ranged from room temperature to 164 °C. We found that the room temperature piezo and pyroelectric activity decreased linearly as a function of TMAX from 75 °C to 164 °C at which temperature the specimen had 30% of its original activity; a linear extrapolation of these data to zero activity yielded a temperature Tc=207 °C. From density measurements at room temperature, crystallinity was calculated and found to remain constant during thermal cycling. X-ray pole-figure observations of the (200) (110) composite diffraction of the β-phase crystal showed single-crystal texture of the rolled specimen and confirmed the six-site model of dipole orientation. Changes in x-ray intensity at the six sites on the pole figure, as a function of thermal aging, were associated with the depolarization process which occurs via a 60° rotation of dipoles away from the direction of primary polarization. Based on these data, we propose a model which describes the state of polarization in polyvinylidene fluoride and from which we calculate the fraction of dipoles in the crystalline state contributing to the polarization.
We study the sine-Gordon soliton model of the dielectric α relaxation in crystalline polyethylene and similar polymers. These systems are characterized by a coupling constant which is essentially the ratio of intramolecular to intermolecular interaction strengths. We perform a stochastic molecular dynamics computer simulation for a wide range of coupling constants. We investigate analytically the high coupling (continuum) limit, modeled as free particle Brownian motion of the soliton, and the low coupling (pinned) limit, treated as hopping diffusion of the soliton over barriers at the sites on the polymer chain. We compare the simulation with these analytical theories and with experimental results for polyethylene. Agreement between simulation and theory for nonpolar polymers is excellent in the continuum limit down to relatively small coupling constants, and we also find quite reasonable agreement with experiments in that limit, considering the neglect of defects on the chains. The best fits of the pinned limit theory with the simulation are identical to those of the continuum limit in the lower coupling regime, and are not very successful. The continuum limit analytical theory is extended to polar polymers and qualitative agreement with other theories is shown, in the absence of experimental data for comparison. It is suggested that a more specific theoretical treatment in the intermediate to low coupling regime might improve agreement with the simulation and that the inclusion of defect effects is necessary for more successful agreement with experimental results.
The study of the sine-Gordon soliton model of the dielectric α relaxation in crystalline polymers is continued. We examine the intermediate range of the coupling constant, which is essentially the ratio of intramolecular to intermolecular interaction strengths, via another stochastic molecular dynamics computer simulation. The model is that of Currie et al. of the soliton as a pseudo-relativistic particle moving in an effective periodic potential. Comparison with the previous sine-Gordon chain simulation results in increasingly poor agreement with decreasing coupling constant, probably because of the neglect of multiple soliton effects. However, we find in the process the interesting result that relativity lowers the effective rate constant in such barrier-crossing problems. Finally, we also note that the continuum limit theory which is successful for nonpolar polymers may apply to other soliton-related physical systems as well.
Although a number of measurements of the frequency dependence of biological and botanical samples have been reported in the literature and there is agreement that three dielectric dispersion regions are present (Schwann, 1957;Pethig, 1984), it has not been possible to find agreement between the experimental data and the conventional models of dielectric response. This is, in part, due to the limited frequency ranges over which measurements have been made and has resulted in a limited understanding of the basic mechanisms of dielectric response in cellular tissues.Here we report extended frequency measurements of the real and imaginary parts of the complex permittivity of leaves of the succulent Crassula Portulacaceae (Jade), and show that these can be fitted over the frequency spectrum 10 -3 Hz to 10 +9 Hz by an electrical analog model comprised of three series elements.It is shown that these elements represent the electrical properties of individual cells, of imperfect charge transport within the matrix of cells, and of the electrical barrier at the epidermal surface layers of the leaf, in decreasing order of frequency.Elsewhere it will he shown (Hill et al., 1986) that the technique of dielectric response gives quantitative information about the efficiency of charge transport and charge blocking in leaf tissue and hence forms a useful and non-invasive tool for the comparison and detailed examination of biological tissues. Figure 1 shows the measured responses of the permittivities of the Jade samples as functions of frequency on log/log scales.Three different measuring techniques have been used to cover the frequency range and these are indicated in the figure by the use of three different pairs of symbols.The highest frequency data, 106 to 6.10 8 Hz, were obtained using an impedance analyzer (Hewlett Packard model4191A) and the midfrequency range measurements, 80 to 10 7 Hz, by means of a Hewlett Packard network analyzer (model 3570A).
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