Thermal or electrical bulk properties of rod-filled composites

The cell model (or self-consistent scheme) has been largely used to estimate the bulk thermal properties for dilute slender rods embedded in a matrix by applying a thermal gradient perpendicular to the main axis of the rod. This approach is then extended by considering a thermal gradient along the particle, or in other words a thermal flux through the end surfaces of the fiber. For a slender-body, this additional contribution is found to be negligible. Then, to circumvent the diluteness assumption, particle-particle contacts are considered when determining the effective thermal conductivity of the composite. This involves adding to the dilute result a new contribution depending on the magnitude of the Biot number (defined later) and on the micro-structures of the particles, and exhibiting a quadratic dependence on the particle concentration. Two assumed contact surface areas are investigating leading to the development of two micro-mechanical models, the difference being in the choice of the contact area. In addition, the model predictions are in good agreement with previously published data, where in-plane measurements of effective thermal conductivity are performed on highly conductive copper fibers impregnated with a poorly conductive PMMA matrix, for a wide range of fiber orientations and concentrations. When an appropriate cell size dimension for the dilute model is adopted, its predictions are also found to give an accurate fitting. Although this paper focuses on the thermal properties, the derivation can be carried over to the electrical properties with very minor modifications. This has been carried out for estimating the effective electrical conductivity of several CNTs (i.e., SWCNT and MWCNT) embedded in an epoxy matrix, leading again to good agreements.