The effect of contact resistance on electrical conductivity in filled elastomer materials

Abstract

This paper is focused on studying the charge transport between the particles in filled elastomer composites, and suggests a new modeling approach that would allow predicting the electrical conductivity of this material. Our approach is based on a combination of non-equilibrium Green's function (DFTB-NEGF) analysis for atomic-level electron quantum transport, and effective medium theory for calculating the said macroscopic transport properties of the material. The model can be used for predicting macroscopic material conductivity based on the information of material microstructure received by electron microscopy; explain changes of conductivity in deformed material and with temperature variation, and finally it can assist in finding the optimal material parameters such as particle shape, size distribution, and volume fraction to maximize the performance. The results of our modeling re-attest the known phenomenon that the electrical conductivity in percolated network is always dominated by direct particle-to-particle charge transport. We studied the electrical conductivity in a medium of high volume fraction of metallic particles dispersed in polymer matrix where thin polymer matrix layer covalently attached to the metallic particle contacts, and the thin polymer layer undergoes high local shear strain when hard particles slide along each other during deformation. These conditions allow the redistribution of electron density from metal to the polymer, and the conductance through normally insulating matrix can become comparable with the pinpoint conductance through the metal. These conditions can only occur in the place of direct particle contacts, therefore all criteria for percolated conductive network hold valid in this case. The integral conductance of thin “sandwiched” polymer layer strongly, but predictably depends on local contact geometry, mostly on particle surface curvature at place of contact. This allows predicting composite conductivity from the properties of each phase, loading, and particle shape and size distributions. Further, the conductance of polymer chain can significantly increase with the fluctuations of molecular shape caused by temperature and/or deformation. We infer that this effect is responsible for the major part of strain and temperature dependence of the conductivity that has been reported in the literature, although particle orientation and stacking at larger deformations may also contribute to the strain dependence.