Model Calculations on the Electric Conductivity of the Nc Phase

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Abstract
A theoretical study of the electric conductivity of a system consisting of a body-centered tetragonal lattice of insulating cylinders, embedded in a uniform and isotropic conducting medium is presented. The model is described by three parameters: the volume fraction occupied by the cylinders (here taken to be less than 50%); the diameter to length ratio of the cylinders, d/l; and the ratio of the minimum distances between cylinders normal and parallel to the cylinder axis, ζ. We find that the conductivity anisotropy is in general smaller than the value corresponding to infinitely long cylinders. The anisotropy can assume both positive and negative values. The sign is largely determined by the ratio ζ. The usefulness of the model in relation to the Nc lyotropic mesophase is discussed.