  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.
