Energy transport of surface phonon polaritons propagating along a chain of spheroidal nanoparticles

We analyze in detail the energy transport of surface phonon polaritons propagating in a chain of spheroidal polar nanoparticles with both longitudinal and transversal polarizations. Explicit and closed-form expressions for the dispersion relation and propagation length are derived and used to determine the values of the nanoparticle polarizability and the interparticle distance that maximize the polariton propagation length. The thermal conductance in the ballistic regime and the thermal conductivity in the diffusive one are also determined and examined as a function of the geometry of the nanoparticles and their temperature. For a chain of cigar-shaped SiC nanoparticles in contact, an aspect ratio of 5, and surrounded by air; it is shown that: (i) The surface phonon polaritons propagate a distance of 10 mu m along a chain of 100 nanoparticles. This propagation length is one order of magnitude longer than that for spherical nanoparticles. (ii) The polariton thermal conductivity is comparable with the one of air in a wide range of temperatures and is 41 mW m(-1) K-1 at 500 K. (iii) The polariton thermal conductance increases with the temperature and at 500 K is 44 pW K-1, which represents 9% of the quantum of thermal conductance. In view of the ultralow phonon thermal conductivity of a chain of polar nanoparticles in contact and their high surface area-to-volume ratios, the proposed theoretical model and obtained results are expected to be useful to experimentally quantify the energy transport of surface phonon polaritons propagating along these nanostructures.