Fractal analysis of electrical trees in a cross-linked synthetic resin

A statistical picture of dielectric breakdown in cross-linked polyester resins for a two-dimensional geometry is presented and discussed in this paper. A connection is established between the dielectric breakdown model (DBM) and the physical properties of the resin. Distribution propagation times of simulated trees obey a Weibull statistics, as was experimentally found. This adjustment is achieved by a redefinition of the unit of time, which is different from the one employed up to date. The experimental dependence of characteristic propagation times on the fractal dimension D can be reproduced in the range 1.2<D<1.5. A relationship is established between the glass transition temperature T(g) and the DBM parameter eta, which is in agreement with thermodynamical considerations. It is suggested that fractal characteristics of electrical trees should be related to a basic material property, such as the cross-linking density, which implies a notion of universality that deserves to be explored.