Rigorously solvable model for the electrical conductivity of dispersions of hard-core-penetrable-shell particles and its applications

We generalize the compact group approach to conducting systems to give a self-consistent analytical solution to the problem of the effective quasistatic electrical conductivity of macroscopically homogeneous and isotropic dispersions of hard-core-penetrable-shell particles. The shells are in general inhomogeneous and characterized by a radially symmetrical, piecewise-continuous conductivity profile. The local value of the conductivity is determined by the shortest distance from the point of interest to the nearest particle. The effective conductivity is expressed in terms of the constituents' conductivities and volume concentrations; the latter account for the statistical microstructure of the system. The theory effectively incorporates many-particle effects and is expected to be rigorous in the static limit. Using the well-tested statistical physics results for the shell volume concentration, this conclusion is backed up by mapping the theory on available 3D random resistor network simulations for hard spheres coated with fully penetrable concentric shells. Finally, the theory is shown to fit experimental data for real composite solid electrolytes. The fitting results indicate that the effect of enhanced electrical conduction is generally contributed to by several mechanisms. These are effectively taken into account through the shell conductivity profile.