  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 theoretical work our goal is to maximize the heat flux through
the CNT by functionalizing the CNT ends. We use a Landauer approach to
calculate and optimize the energy flux from a soft to a hard material in one
dimension through a connecting continuous medium of varying elasticity and
density. The transmission probability of phonons through the system is
calculated both numerically and analytically. We find that over 90% of the
maximum heat flux into CNT is possible for 1nm length of the intermediate
material at room temperature (300K).
