Cross-scale investigation of the size effect on thermal conductivity of monolayer graphene

It is known that the intrinsic thermal conductivity of a monolayer graphene highly depends on its in-plane dimensions which are at nanoscale. However, it remains not very clear how the thermal conductivity is quantitatively affected as the considered in-plane size undergoes a cross-scale variation, especially when temperature influence is involved. In this study, based on the ballistic-diffusion approximation theory, we propose a cross-scale model that can be used to calculate the thermal conductivity of monolayer graphene with prescribed length and width at selected temperatures by considering the temperature-dependent diffusive thermal conductivity (fitted from equilibrium molecular dynamics simulations). Then, the effects of the length, width, and temperature on the thermal conductivity of square-shaped and rectangular-shaped graphene are investigated separately. It shows that as the graphene length increases from the nanoscale to microscale, the thermal transport in square graphene will experience these three phonon thermal transport regimes in sequence (ballistic, quasi ballistic, and diffusive), corresponding to a rapid rise of the thermal conductivity, then a slower increase, and, eventually, a near-constant value, respectively. As the rectangular graphene gradually becomes square, the difference in the thermal conductivity in length and width directions will vanish due to the weakening of the boundary scattering. In addition, the thermal conductivity significantly drops with temperature increases because of the strong Umklapp scattering caused by high temperature.