Electrical Strength of Polymer Film with Randomly Distributed Air Inclusions

A probabilistic model has been constructed to describe the physical state of a dielectric film that contains randomly distributed air inclusions with random radius \(\tilde {r}\). Analysis of this model has shown that the statistical distribution of electrical strength, which is less than that of a defect-free film, has exactly two maxima. It is realized at a sufficiently low density of air inclusions of random radius \(\tilde {r}\), which has an almost uniform probability distribution within the limits \({{r}_{*}}\) > \(\tilde {r}\) > 0. Moreover, the position of the first maximum is determined by the value of the parameter \({{r}_{*}}\). With increasing defect density or film thickness, the first maximum disappears and the electrical strength distribution becomes unimodal.