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-e 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.