Density dependence of thermal conductivity in nanoporous and amorphous carbon with machine-learned molecular dynamics

Disordered forms of carbon are an important class of materials for applications such as thermal management. However, a comprehensive theoretical understanding of the structural dependence of thermal transport and the underlying microscopic mechanisms is lacking. Here we study the structure-dependent thermal conductivity of disordered carbon by employing molecular dynamics (MD) simulations driven by a machine-learned interatomic potential based on the efficient neuroevolution potential approach. Using large-scale MD simulations, we generate realistic nanoporous carbon (NP-C) samples with densities varying from 0.3 to 1.5 g ${\mathrm{cm}}^{\ensuremath{-}3}$ dominated by ${sp}^{2}$ motifs, and amorphous carbon (a-C) samples with densities varying from 1.5 to 3.5 g ${\mathrm{cm}}^{\ensuremath{-}3}$ exhibiting mixed ${sp}^{2}$ and ${sp}^{3}$ motifs. Structural properties including short- and medium-range order are characterized by the atomic coordination, pair correlation function, angular distribution function, and structure factor. Using the homogeneous nonequilibrium MD method and the associated quantum-statistical correction scheme, we predict a linear and a superlinear density dependence of thermal conductivity for NP-C and a-C, respectively, in good agreement with relevant experiments. The distinct density dependences are attributed to the different impacts of the ${sp}^{2}$ and ${sp}^{3}$ motifs on the spectral heat capacity, vibrational mean free paths, and group velocity. We additionally highlight the significant role of structural order in regulating the thermal conductivity of disordered carbon.