Optimal matching of thermal vibrations into carbon nanotubes*

Carbon nanotubes (CNTs) are promising candidates to improve the thermal conductivity of nano-composites. The main obstacle to these applications is the extremely high thermal boundary (Kapitza) resistance between the CNTs and their matrix. In this work our goal is to maximize the heat flux through the CNT by functionalizing their ends. We develop theoretical continuum models in which we vary the elasticity and density from surrounding medium to the CNT so as to maximize the transmission of thermal vibrations. We calculate the transmission coefficients using a scalar wave equation. Since the transport in CNT is strictly one dimensional, a Landauer formula is used to estimate the heat flux into the CNT. We determine the optimal continuous variation of elasticity and density with position for different geometries. We also investigate how to optimally match the nano-tubes to their matrix using a small number of discrete interfaces. Finally, we discuss the implications of these models for experiment.