  Approach-to-equilibrium molecular dynamics simulations have been used to
study thermal transport in nanocrystalline graphene sheets. Nanostructured
graphene has been created using an iterative process for grain growth from
initial seeds with random crystallographic orientations. The resulting cells
have been characterized by the grain size distribution based on the radius of
gyration, by the number of atoms in each grain and by the number of atoms in
the grain boundary. Introduction of nanograins with a radius of gyration of 1
nm has led to a significant reduction in the thermal conductivity to 3% of the
value in single crystalline graphene. Analysis of the vibrational density of
states has revealed a general reduction of the vibrational intensities and
broadening of the peaks when nanograins are introduced which can be attributed
to phonon scattering in the boundary layer. The thermal conductivity has been
evaluated as a function of the grain size with increasing size up to 14 nm and
it has been shown to follow an inverse rational function. The grain size
dependent thermal conductivity could be approximated well by a function where
transport is described by a connection in series of conducting elements and
resistances (at boundaries).
