A kinetic model of time-dependent dielectric breakdown for polymers is presented. The micromechanism of thermally activated bond-breakdown is developed for polymers to account for the dynamical process of dielectric breakdown. We first prove that the thermally activated polymer bond-breakdown processes can explain not only the burst of a conducting pathway nucleated in any defect and the following successive propagation, but also the time-dependent dielectric breakdown strength of polymers. The formulae for conducting microcrack growth rate and time to failure are derived and applied to the experimental data for polyethylene terephthalate films.

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A non-equilibrium statistical theory of water treeing in polymeric cable insulators, which treats water tree growth as a stochastic process, is presented. In this treatment the deterministic equation for the rate of water tree growth is made stochastic by the addition of a fluctuation term. The fluctuations are used to model the effect of the complex topologically connected microstructure of the polymeric insulator on water tree growth. Such considerations lead to a generalized Langevin equation for the water tree's growth rate as well as an equivalent Fokker - Planck equation for the probability density distribution of the water tree length. Many of the major attributes of water tree growth are shown to be a natural consequence of this equation. The self-affine fractal object for water tree morphology is first constructed, based both on the self-affinity of the time-correlating fluctuations and on the scale-invariance of the fundamental dynamic equation dominating water tree growth. The empirical two-parameter Weibull distribution of water tree length in the literature is also derived. Good quantitative agreement between theory and previously reported experimental results is shown.

An electro-chemical reaction model is proposed in this paper to describe electrical ageing of solid dielectrics under ac voltage. The present model has the ability to predict not only the scale-invariance property of the electrical ageing function, but also the classical electrical ageing law, i.e. the electric field strength - lifetime inverse power law relationship. The micromechanisms inherent in the model enable a direct physical interpretation of the macroscopic electrical ageing behaviour in terms of the microscopic processes. We argue that the fractal behaviour of electrical ageing and breakdown processes in solid dielectrics are by essence determined by the scale-invariance of the electrical ageing evolution equation.