Size and porosity effects on thermal conductivity of nanoporous material with an extension to nanoporous particles embedded in a host matrix

•Original extended irreversible thermodynamic model for thermal conductivity in nanoporous systems.•Validation by experimental data and comparison with five other models.•Physical interpretation of size and porosity dependence of the thermal conductivity.•Extension to porous nanocomposites.

A formula for the effective thermal conductivity of nanoporous media is derived, following a thermodynamic approach. An extension to nanocomposites composed of a homogeneous matrix wherein porous nanoparticles are dispersed is proposed as well. The originality of the model is that it is based on extended irreversible thermodynamics, a theory specifically designed for sub-scaled systems. Two different situations are discussed: in the first one, nanoporous silicon with spherical porous inclusions of micro-, meso- and macro-dimension respectively is considered. The description is validated by comparison with experimental data and five other models. Analysis of the results shows an excellent agreement of our theoretical approach with experiments in the whole range of porous radii, from 2 to 100 nm. In the second part of the work, thermal conductivity of porous silicon nanoparticles embedded in a germanium host matrix is investigated. The coupled influence of the pore and nanoparticles sizes is emphasized.