We develop an effective medium model of thermal conductivity that accounts for both percolation and interface scattering. This model accurately explains the measured increase and decrease of thermal conductivity with loading in composites dominated by percolation and interface scattering, respectively. Our model further predicts that strong interface scattering leads to a sharp decrease in thermal conductivity, or an insulator transition, at high loadings when conduction through the matrix is restricted and heat is forced to diffuse through particles with large interface resistance. The accuracy of our model and its ability to predict transitions between insulating and conducting states suggest it can be a useful tool for designing materials with low or high thermal conductivity for a variety of applications.The ability to obtain high or low thermal conductivity makes composite materials of great technological interest. Materials with low thermal conductivity are needed for insulating thermoelectrics (TE), 1,2 while materials with high thermal conductivity are needed for thermal interface materials (TIM).3,4 Since the efficiency of a TE device increases with the figure of merit ZT , 5 which is proportional to temperature, improving the insulation of a TE device leads to less lateral heat loss, larger operating temperatures, and thus higher efficiency.2 On the other hand, TIMs are needed to transfer heat from semiconductor devices such as transistors to a heat sink or heat spreader.3,4,6 Improving the thermal conductivity of TIMs reduces the thermal resistance of the heat transfer system and lowers the operating temperature of the underlying device, improving lifetime and reliability.The current approaches for achieving high or low thermal conductivity have considerable limitations. For example, the porous silica aerogels 1,2 used to insulate TE devices are mechanically brittle, leading to short lifetimes and high maintenance costs, while the thermal conductivity of TIMs consisting of ceramic particles in a polymer matrix is limited by thermal resistance associated with the mismatch in elastic properties at the interfaces.
3,4To improve the performance of insulators and TIMs, it is necessary to develop models that account for all of the physical phenomena that affect thermal conductivity. For composite materials, this includes two competing effects: percolation and interface scattering.4,7-9 Percolation, which occurs at high loading when a continuous path is formed through the conductive phase, increases the effective thermal conductivity. Interface scattering, which arises from the difference in the phonon density of states between the particle and matrix, 10 reduces the effective thermal conductivity, and is particularly important for nanoparticles with large surface-to-volume ratio.The most accurate models for calculating thermal conductivity of composite materials are based on molecular dynamics simulations or the Boltzmann transport equation.6,11 While accurate, these models are computationally expensive, pa...