Influence of interfacial surface conduction on the DC electrical conductivity of particle reinforced composites
We describe new effects associated with electrical conduction along phase interfaces for particle reinforced conductors. For particles of general shape we introduce a new quantity β1 called the 'surface to volume dissipation' of a particle. This quantity is a measure of the particle's ability to dissipate energy on its surface relative to the energy dissipated in its interior. It is described mathematically as the minimum value of a suitably defined Rayleigh quotient and is related to an eigenvalue problem posed on the particle surface. We consider the overall conductivity of a particle reinforced conductor when the particle conductivities are less than that of the matrix. It is shown that the overall conductivity will be increased by the presence of a specific particle when the particle's 'surface to volume dissipation' lies above a critical value. We calculate the surface to volume dissipation for a sphere and for starlike particles we provide a lower bound in terms of particle dimensions. These estimates allow for the prediction of new particle size effects. Second, we present a new criterion on the particle size distribution for which the overall conductivity lies below the matrix conductivity. © 1998 The Royal Society.
Publication Source (Journal or Book title)
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Lipton, R. (1998). Influence of interfacial surface conduction on the DC electrical conductivity of particle reinforced composites. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 454 (1973), 1371-1382. https://doi.org/10.1098/rspa.1998.0212