Theory of Electrical Conductivities of Ferrogels

Conductive organic polymers can be formulated with polymers that incorporate fine dispersed metallic particles. In this work, we present a general model for ferrogels which are chemically cross-linked polymer networks swollen with a ferrofluid. Our aim is to study the effect of the shape and/or material (conductivity) anisotropy on the effective electrical conductivity of the ferrogel in the presence of an external magnetic field. Our theory can reproduce the known results and provides a link between the particle properties and orientation distribution and the effective electrical conductivity. To this end, we find that material (conductivity) anisotropies are more important for yielding a high effective electrical conductivity than shape anisotropies, while magnetic fields can offer a correction.