Thermodynamics of water treeing

The paper examines the models proposed by Zeller for the development of water trees within the polyethylene (PE) insulation of underground distribution cables. Those models are of two different geometries idealizing a water tree: a prolate spheroid and ageometry where two spheres are linked by a narrow conducting channel. In these models a dissolved species, within a solution permeating the water tree, enhances the conductivity of the solution, distorting the electric field and increasing the Gibbs\´ free energy. Consequently, the solute species have a chemical potential that is greater than that in the absence of an electric field and this potential is suggested as leading to reaction of the solute with PE. Zeller used sodium chloride as the solute and did not take into account (nor suggest) any reaction product in solution. Consequently, the chemical potential difference between reactants and products, the true "driving force" for reaction, was not obtainable from this previous work. The present paper suggests alternative species (ferric and ferrous iron) that can serve as reactant and product in a plausible reaction with PE. Calculation of chemical potential differences, based on both aspheroidal model and a uniform property dumbbell model, suggests that these species might indeed be involved in PE degradation but only at low solute concentrations. The paper concludes by hypothesizing how such low concentrations may occasionally occur.