Theory of electrical conduction in particulate systems

Abstract

Abstract A model is developed which describes the conductivity of a mixture of touching particles of two or three different species as a function of the volume fractions of the species present. The approach is based on an effective-medium treatment, in which the contact resistance between particles is taken to be a variable. It is shown that if a linear distribution of contact resistances exists in the sample then the deviation from the normal effective-medium solution (or percolation theory) is fairly small. If, however, a higher density of high values of contact resistance between particles exists, then substantial deviations from the normal effective-medium solution may occur and are recognizable as the behaviour that is observed in many practical systems. A simple model of the effect of unequal particle size between species is presented within the framework of effective-medium theory, and demonstrates semiquantitatively how the relative particle size between species affects the value of volume fractio...