Thermal percolation in composite materials with electrically conductive fillers

Abstract

We measured thermal conductivity and electrical conductivity in organic/inorganic composites with Ag nanowires (NWs) embedded in a poly(vinylidene fluoride) matrix. High thermal and electrical conductivities of 8.43 W/(mK) and 1.02 ×106 S/m are achieved, respectively, when the volume fraction of Ag NWs reaches 28.34%. Both measured electrical and thermal conductivities obey the universal power law commonly described in the percolation theory. The percolation behaviors of thermal and electrical conductivities are clearly observed when the volume fraction of Ag NWs is above the critical volume fraction (2.25%), due to the formation of a percolation spanning cluster. Further calculations on the Lorenz number as a function of Ag NW volume fraction also confirm the percolation behaviors. The power-law exponent for the thermal percolation is slightly smaller than that for the electrical percolation, which is likely due to the “dead-end” structures that do not contribute to electrical percolation. To understand the effect of contact resistance between Ag NWs, we modeled the electron contribution to the electrical and thermal resistance at the contact. The non-ideal contact will cause the interfacial thermal resistance increase much more than the electrical contact resistance. The interfacial Lorenz number will decrease from the Sommerfeld value to a much lower value if the contact is non-ideal. Our work can shed some light on the thermal percolation in composite materials.