A Network Model for the Thermal Conductivity of Pillared-Graphene Architectures

Carbon nanotubes and graphene are promising for thermal management applications due to their high thermal conductivities. However, their thermal properties are anisotropic and the radial or out-of-plane thermal conductivity is low. A graphene-CNT 3D structure has previously been proposed to overcome such limitation, and direct molecular dynamics simulations have been used to predict its thermal conductivity. In this work, by recognizing that the thermal resistance comes primarily from CNT-graphene junctions, we have proposed a simple network model of thermal transport in pillared graphene structures. Using non-equilibrium molecular dynamics, the resistance across an individual CNT-graphene junction is found to be around 6 × 10⁻¹¹ m² K/W, which is significantly lower than the typical values reported in literature for planar interfaces between dissimilar materials. The size-dependence of the CNT-graphene junction resistance is also explored in our work. The CNT pillar length between two graphene sheets is found to be an important parameter affecting the junction resistance, which decreases as the pillar length decreases. We explain this behavior by calculating the local phonon density of states near the junction. The junction resistance is then used in the network model to obtain the thermal conductivity, and the results agree well with the direct MD simulation data, demonstrating the effectiveness of our model.