(331e) On the Thermal Conductivity of Carbon Nanotubes

Carbon nanotubes are nanostructures with diameters less than 1 nm and length of several microns. Iijima discovered CNT in 1991. They have found that CNTs exhibit interesting physical properties. One of the observation is that the thermal conductivity for CNT can be as high as 2000 W/m/k, higher than copper and gold. Why is the k value so high for CNT ? The fundamental mechanisms of heat conduction such as by free electron transport, phonon lattice vibrations etc are examined in detail. In the free electron theory the obstacle effect is removed and the thermal conductivity predicted for CNTs. The Fourier model needs to me modified to a generalized Fourier model. The Fourier's law of heat conduction, generalized Fourier's law of heat conduction (Cattaneo & Vernotte equation), and Boltzmann transport equations are examined for suitability to predict the higher heat conduction observed in CNTs. The EPRT, equation of phonon radiative transport due to Mazumdar is also examined. The challenge is in accounting for the quantum effects and the dual nature of electrons. The wave -partice duality. Newtonian mechanics can be used and the acceleration of molecules and that of electrons can be taken into account to better represent the transient heat conduction observations. The laws of thermodynamics such as Clausius's inequality have to be obeyed as well. The dichotomy is during the transport by lattice vibrations wouldn't there be a reverse flow of heat during vibrational transfer ? How can this be modeled ?