SUMMARY

The phonon gas model (PGM) originated from the behaviors observed and rationalized in homogenous crystalline solids and it has exhibited remarkable success in describing the behavior of a wide variety of solids, microstructures, nanostructures and molecules. Given its success, it has become the primary lens with which phonon transport is viewed. However for amorphous materials, or other structurally/compositionally-disordered systems, due to the lack of periodicity, one cannot clearly define the group velocity. Since the PGM hinges on knowledge of the group velocities, application of the PGM to amorphous materials is highly questionable. We developed a new method for direct calculation of the modal contributions to thermal conductivity, which is termed Green-Kubo modal analysis (GKMA). The GKMA method combines the lattice dynamics formalism with the Green-Kubo formula for thermal conductivity, such that the thermal conductivity becomes a direct summation of modal contributions, where one need not define the phonon velocity. The predicted temperature dependent thermal conductivity for amorphous silicon (a-Si) shows the best agreement with experiments to date. In 1955 Fermi, Pasta, and Ulam (FPU) made a “shocking little discovery” that even an anharmonic system can exhibit infinite thermal conductivity. The classes of materials that most closely resemble the 1D chains that have been studied previously are polymers, specifically individual polymer molecules. Towards improving understanding of this phenomenon, I sought out to answer several key questions that lingered from previous analysis. We used molecular dynamics simulations, the GKMA method as well as sonification to study the modal contributions to thermal conductivity in individual polythiophene chains. The simulations suggest that it is possible to achieve divergent/infinite thermal conductivity in individual polythiophene chains and the GKMA method allowed for exact pinpointing of the modes responsible for the anomalous behavior.