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Conductive organic polymers can be formulated with polymers that incorporatefine dispersed metallic particles. In this work, we present a general model for ferrogels which are chemicallycross-linked polymer networks swollen with a ferrofluid. Our aim is to studythe effect of the shape and/or material (conductivity) anisotropy on theeffective electrical conductivity of the ferrogel in the presence of anexternal magnetic field. Our theory can reproduce the known results, andprovides a link between the particle property and orientation distribution andthe effective electrical conductivity. To this end, we find that material(conductivity) anisotropies are more important to yield a high effectiveelectrical conductivity than shape anisotropies, while magnetic fields canoffer a correction.

Theory of Electrical Conductivities of Ferrogels