Joule-heating field phase-amplification in particulate-doped dielectrics

Doping dielectric materials with particulates for use in electronic device applications is wide-spread, particularly for energy-storage devices such as ultracapacitors and batteries. This work investigates the resulting distortion of the electrical fields in multiphase (particle and matrix) material systems. Of particular interest is to ascertain safe overall electrical loading conditions in order to avoid current overload in heterogeneous media. Specifically, it is important to determine the phase-wise Joule-type heating field, formed by the inner product of the current and electric fields. General estimates are developed, and two asymptotic cases are studied: (1) high-conductivity (“superconducting”) particles added to a lower relative-conductivity matrix and (2) low-conductivity (“insulator”) particles added to a higher relative-conductivity matrix. The expressions developed provide a relatively easy guide for the selection of dopants in dielectric material design.