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of the change in the slope of the linear behavior in the two cases corresponds to the glass transition temperature for pure polymer and the nanotube-polymer composite. The results show that, due to mixing of 8% by volume of SWNT in polyethylene the glass transition temperature increases by about 20% and more significantly, the thermal expansion coefficient above glass transition temperature increases by as much as 142%. The enhanced thermal expansion coefficient of the composite is attributed mostly due to an equivalent increase in the excluded volume of the embedded CNT as a function of temperature.

Because both excited vibrational phonon modes and Brownian motion contribute to the dynamic excluded volume of the embedded CNT, as the temperature is increased their contributions towards excluded volume increase significantly. The cross-linking of polymer with CNT was not allowed in these initial simulations. It is possible that the cross-linking of polymer matrix with embedded CNTs may further reduce the motions of polymer molecules or the CNT; the predicted changes in the glass transition temperature and the thermal expansion coefficients in that scenario could be different. The increase in glass transition temperature and thermal expansion coefficients of carbon nanotube polymer composites has been also observed in experiments [55].

The simulation and experimental observations of thermal conductivity or thermal conductance across polymer-CNT interfaces are few and have been attempted recently. The pico-second transient absorption spectra have been measured to deduce interface thermal conductance for carbon nanotubes suspended in surfactant micelles in water. The experimental findings have been analyzed using the MD simulations of heat transfer from a carbon nanotube to a model hydrocarbon liquid surrounding it. The heat transport in a nanotube composite material has been found to be limited mainly by exceptionally small interface thermal conductance ~12 MW/m2K. The net thermal conductivity of the composite thus has been found to be significantly smaller than the intrinsically high thermal conductivity of carbon nanotubes and that would be allowed by the homogeneous mixing rule [56].

The observed low interface thermal conductance in the above case has been explained by a limited coupling between only a small number of low-frequency modes of carbon nanotubes and the surrounding matrix molecules. The energy contained in the high-frequency modes of the carbon nanotubes thus needs to be transferred to the low-frequency modes before it can be transported across the interface. The interface thermal resistance has been investigated also as a function of nanotube length. The longer nanotubes have been characterized by smaller thermal resistence or larger thermal conductance [57]. The thermal coupling between rather rigid carbon nanotubes and the soft polymer molecules has been attributed to the low-frequency weak dispersion forces, which limit the thermal transport across the CNT-polymer molecule interfaces. At higher temperatures and/or compressed composites, perhaps, the thermal interface conductance can be increased by increasing the coupling between the carbon nanotubes and the polymer matrix materials.

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