Role of electrostriction on the electrical aging of polymers

It is shown that the major parameters affecting most electrical properties of dielectrics, especially aging, are more poorly known than believed. This paper points out three major problems: the real values of the field-induced stress and strain, the strain saturation under high fields and the exact role of the sample size. One mechanism allowing to take those difficulties into account is electrostriction and although it is limited in low dielectric constant dielectrics, it appears to be significant in the cases studied here. The influence of sample size requires further work but it is already clear that many parameters involved in electrostriction are depending on sample thickness and possibly also on volume. Application to conduction and breakdown is briefly evoked.

I. Introduction

It is well known that apart the electrical F and temperature T, electrical aging and breakdown depend on many other parameters, including frequency and sample size [1]–[3]. The dependence of several electrical properties on the square of the applied field, led us to associate this dependence to the Maxwell stress , i.e. the Coulombic attraction exerted by field-induced charges on both electrodes, whose value is . In the case of electrical aging, the life t is given by

$$\begin{equation*} \mathrm{t}=(\mathrm{h}/\text{kT})\exp[(\mathrm{E}-0.5\sigma\Delta \mathrm{V})/\text{kT}] \tag{1} \end{equation*}$$ where is the permittivity of free space, the dielectric constant, h and k are the Planck and Boltzmann constants, E is the so-called activation energy and the activation volume. In our model, aging is due to bonds breaking which implies that E must be associated with the backbone bonds strength [3]. For many polymers, this means C-C bonds with . Recently, it was shown by Suo et al. [4] that Maxwell stress could not entirely explain solid dielectrics deformation. However, there is a problem with Suo theory: it cannot explain the sample size effect and it is a major parameter, as shown in Fig. 1. Another difficulty is the fact that some very high field results do not yield a linear relation between F² and log t, as shown in Fig. 2. These observations led us to consider other phenomena that could better explain electrical aging. The main objectives of this paper are to discuss the actual significance of some parameters and to show that electrical aging depends somehow on electrostriction, in which Maxwell stress plays a more or less important role. Fig. 1.

Examples of F² vs. Log time in ac aging of XLPE at 22 °C [5]–[8]. Note the different slopes for different sample sizes.

Fig. 2.

Deviation at high fields from a linear relation between F² vs. Log t for polypropylene [9].