Thermal conductivity of composites of aligned nanoscale and microscale wires and pores

Two-dimensional composite materials made from aligned nano- and microwires hold great promise for various applications such as thermoelectric device. Similarly, two-dimensional composites made from aligned nanoscale pores are also very important for various technologies. Phonon transport along such composites primarily involves three nondimensional parameters based on the phonon mean paths in the host medium and the wire. The first of these is the ratio of interwire distance to the phonon mean free path in the host medium, the second is the ratio of the diameter of the wire to the phonon mean free path in the host medium, and the third is the ratio of the diameter of the wire to the phononmean free path in the wire. We develop an analytical model for the thermal conductivity in the longitudinal direction of these composites by solving the phonon Boltzmann transport equation. The analytical model includes the dependences of all three parameters and is in excellent agreement with a recently reported numerical model [Yang et al., Phys. Rev. B 72, 125418 (2005)]. Our solution shows that the scattering of phonons in the host medium at the wire interface reduces the thermal conductivity of the host medium.