  In this study, we investigate the thermal rectification and thermal
resistance in the hybrid pillared-graphene and graphene (PGG) system. This is
done through the classical molecular dynamics simulation (MD) and also with a
continuum model. At first, the thermal conductivity of both pillared-graphene
and graphene is calculated employing MD simulation and Fourier low. Our results
show that the thermal conductivity of the pillared-graphene is much smaller
than the graphene by an order of magnitude. Next, by applying positive and
negative temperature gradients along the longitudinal direction of PGG, the
thermal rectification is examined. The MD results indicate that for the lengths
in the range of 36 to 86nm, the thermal rectification remains almost constant
(~3-5%). We have also studied the phonon density of states (DOS) on both sides
of the interface of PGG. The DOS curves show that there is phonon scattering at
low frequencies (acoustic mode) that depends on the imposed temperature
gradient direction in the system. Therefore, we can introduce the PGG as a
promising thermal rectifier at room temperature. Furthermore, in the following
of this work, we also explore the temperature distribution over the PGG by
using the continuum model. The results that obtained from the continuum model
predict the MD results such as the temperature distribution in the upper half
layer and lower full layer graphene, the temperature gap and also the thermal
resistance at the interface.
