2017/06/29 by Andrea Cepellotti, Nicola Marzari
Engineering · Materials Science · Physics and Astronomy · #Advanced Thermoelectric Materials and Devices #Boltzmann constant #Boltzmann equation #Condensed matter physics #Materials science #Mean free path #Mechanics #Optics #Physics #Scattering #Thermal Radiation and Cooling Technologies #Thermal conductivity #Thermal properties of materials #Thermodynamics #cond-mat.mtrl-sci
paper · pdf · doi:10.1021/acs.nanolett.7b01202
published as Nano Lett., 2017, 17 (8), pp 4675-4682
openalex publication_date 2017/06/29 · arxiv created 2017/08/15 · arxiv updated 2017/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Surface scattering is the key limiting factor to thermal transport in dielectric crystals as the length scales are reduced or when temperature is lowered. To explain this phenomenon, it is commonly assumed that the mean free paths of heat carriers are bound by the crystal size and that thermal conductivity is reduced in a manner proportional to such mean free paths. We show here that these conclusions rely on simplifying assumptions and approximated transport models. Instead, starting from the linearized Boltzmann transport equation in the relaxon basis, we show how the problem can be reduced to a set of decoupled linear differential equations. Then, the heat flow can be interpreted as a hydrodynamic phenomenon with the relaxon gas being slowed down in proximity of a surface by friction effects, similar to the flux of a viscous fluid in a pipe. As an example, we study a ribbon and a trench of monolayer molybdenum disulfide, describing the procedure to reconstruct the temperature and thermal conductivity profile in the sample interior and showing how to estimate the effect of nanostructuring. The approach is general and could be extended to other transport carriers, such as electrons, or extended to materials of higher dimensionality and to different geometries, such as thin films.