Phonon Transport and Thermal Conductivity Percolation in Random Nanoparticle Composites

In this paper, we investigated the effective thermal conductivity of three dimensional nanocomposites composed of randomly distributed binary nanoparticles with large differences (contrast ratio) in their intrinsic (bulk) thermal conductivity. When random composites are made from particles with very different thermal conductivity (large contrast ratio), a continuous phase of high thermal conductivity constituent is formed when its volumetric concentration reaches beyond the percolation threshold. Such a continuous phase of material can provide a potentially low resistance pathway for thermal transport in random composites. The percolation theory predicts the thermal conductivity of the random composites to increase according to a scaling law with increasing concentration of the high thermal conductivity constituent after percolation. However, when the characteristic size of the particles in the nanocomposites is comparable to or smaller than the phonon mean free path, the phonon scattering at interfaces between two materials can introduce significant thermal resistance in the highly conductive phonon pathway. Such interfacial thermal resistance can reduce the thermal conductivity of the nanoparticle composites. The thermal conductivity of the random nanoparticle composites thus deviates significantly from the predictions of the percolation theory. In this study, the Monte Carlo simulation was employed to generate random distribution of nanoparticles and to simulate the phonon transport in random nanoparticle composites. The effects of particle size, thermal conDepartment of Mechanical Engineering, University of Colorado, Boulder, CO, USA, currently at Caterpillar Champaign Simulation Center, Champaign, IL, USA Department of Mechanical Engineering, University of Colorado, Boulder, CO, USA, Email: [email protected] ductivity contrast ratio, and the phonon-interface scattering characteristics on the effective thermal conductivity of random nanoparticle composites are scrutinized. The effective thermal conductivity of the random nanoparticle composites are mainly controlled by the interface density (interfacial area per unit volume) in the composites. The percolating pathway formed by the high thermal conductivity constituents is not as effective in improving the thermal conductivity of the random nanoparticle composites for a wide range of volumetric concentrations compared to a random composite with larger particle dimensions. Similarly, the thermal conductivity contrast ratio of the constituents only plays a limited role in determining the thermal conductivityof the composites studied. This study can be important in studying flexible thermoelectric materials and thermal interface materials. Keyword: nanocomposite, thermal conductivity, percolation theory, phonon transport, Monte Carlo simulation