Statistical continuum theory for the effective conductivity of fiber filled polymer composites: Effect of orientation distribution and aspect ratio

Effective conductivity of polymer composites, filled with conducting fibers such as carbon nanotubes, is studied using statistical continuum theory. The fiber orientation distribution in the matrix plays a very important role on their effective properties. To take into account their orientation, shape and distribution, two-point and three-point probability distribution functions are used. The effect of fibers orientation is illustrated by comparing the effective conductivity of microstructures with oriented and non-oriented fibers. The randomly oriented fibers result in an isotropic effective conductivity. The increased fiber orientation distribution can lead to higher anisotropy in conductivity. The effect of fiber’s aspect ratio on the effective conductivity is studied by comparing microstructures with varying degrees of fiber orientation distribution. Results show that the increase in anisotropy leads to higher conductivity in the maximum fiber orientation distribution direction and lower conductivity in the transverse direction. These results are in agreement with various models from the literature that show the increase of the aspect ratio of fibers improves the electrical and thermal conductivity.