Thermal conductivity of polymers: A simple matter where complexity matters

Thermal conductivity coefficient $\kappa$ measures the ability of a material to conduct a heat current. In particular, $\kappa$ is an important property that often dictates the usefulness of a material over a wide range of environmental conditions. For example, while a low $\kappa$ is desirable for the thermoelectric applications, a large $\kappa$ is needed when a material is used under the high temperature conditions. These materials range from common crystals to commodity amorphous polymers. The latter is of particular importance because of their use in designing light weight high performance functional materials. In this context, however, one of the major limitations of the amorphous polymers is their low $\kappa$, reaching a maximum value of about 0.4 W/Km that is 2--3 orders of magnitude smaller than the standard crystals. Moreover, when energy is predominantly transferred through the bonded connections, $\kappa \ge 100$ W/Km. Recently, extensive efforts have been devoted to attain a tunability in $\kappa$ via macromolecular engineering. In this work, an overview of the recent results on the $\kappa$ behavior in polymers and polymeric solids is presented. In particular, computational and theoretical results are discussed within the context of complimentary experiments. Future directions are also highlighted.