Predicting the thermal conductivity of inorganic and polymeric glasses: The role of anharmonicity

The thermal conductivity of several amorphous solids is numerically evaluated within the harmonic approximation from Kubo linear-response theory following the formalism developed by Allen and Feldman [Phys. Rev. B 48, 12581 (1993)]. The predictions are compared to the results of molecular dynamics (MD) simulations with realistic anharmonic potentials and to experimental measurements. The harmonic theory accurately predicts the thermal conductivity of amorphous silicon, a model Lennard-Jones glass, and a bead-spring Lennard-Jones glass. For polystyrene and amorphous silica at room temperature, however, the harmonic theory underestimates the thermal conductivity by a factor of about 2. This result can be explained by the existence of additional thermal transport via anharmonic energy transfer. More surprisingly, the thermal conductivity of polystyrene and amorphous silica at low temperature (MD and experimental) are significantly below the predictions of the harmonic theory. Potential reasons for the failure of the harmonic theory of disordered solids to predict the thermal conductivity of glassy polymers are discussed.