A new model for water tree propagation

Abstract

A quantitative, physical model for water tree formation based on Zeller's concept is presented. The water tree is assumed to be composed of cavities filled with aqueous salts connected by narrow cylindrical conducting links. This structure is formed in the amorphous region of a polymer. The difference in conductivity between the links and cavities and the un-treed polymer, introduces an electrical contribution to the free energy difference between these two regions under an ac electric field. Consequently, there is a pressure difference that acts to force aqueous sails into the un-treed polymer and to establish, first, a conducting link capable of transporting the salt under pressure, and second, a new cavity when the pressure builds up suitably at the end of the link. At all times the pressure gradient is directed away from the pre-existing tree structure. Our model suggests that there is no need to deform the polymer to form the link, and that the pressure difference is sufficient to force enough aqueous salts into the free volume to form a percolation system along the link cylinder. Expressions have been derived for the time required to form a link or a cavity in terms of the flow rate of aqueous salt into and through the link. This physically based model is suitable for computer simulation by defining a matrix of incipient links with nodes acting as incipient.