Thermal conductivity determination of conductor/insulator composites by fractal: Geometrical tortuosity and percolation

The thermal conductivity prediction of a conductor/insulator composite with various geometrical structures of the conducting phase is one of the top challenges in disordered composites. To determine the effects of the geometrical structure of the second phase on the thermal conductivity of a conductor/insulator composite, Cu₂O/Cu composites were prepared with spherical or branch-like Cu by hot-pressing technology. The box-counting fractal dimension was applied to characterize the geometrical structure of the second phase. The fractal dimension of branch-like Cu shows significantly lower values than the spherical Cu with a same filling content. The fractal dimension increasing rate with increasing Cu content was first introduced to predict the thermal conductivity of the composites. These results provide a pathway to determine the effects of the geometrical structure of the second phase on the thermal conductivity and shed some lights on building relationships between the tortuosity, fractal dimension, and overall performances of conductor/insulator composites.