A capacitive model for dielectric breakdown in polymer materials

In the present paper, we introduce a capacitive model to simulate the dielectric breakdown process. Two different protocols are presented to select the capacitor that will be broken out of the set that meet breakdown conditions. Protocol 1 is associated with the entropic contribution of the electrical tree growth process, whereas Protocol 2 is identified with the corresponding internal energy contribution. A linear combination of both protocols, f(p), is considered in order to partially reproduce the experimental information of the dependence of the fractal dimension, D, on the applied voltage. f(p) can be associated with an equivalent free energy function governing the electric growth process. Thus, in the CDBM, the dependence of the fractal dimension on the applied voltage has its thermodynamic origin in the interplay between energy injection and space charge formation processes. Also the CDBM makes it possible to consider the influence of different phases in the material, on the breakdown process, as well as their different spatial distribution. In this regard, it is important to note that a volume segregation of the different phases occurs in the manufacturing process of electrical insulators, and this kind of segregation can easily be modeled by CDBM. The CDBM is also capable of qualitatively reproducing the temporal dependence of the breakdown process.