  We report a joint study, using Raman micro-spectroscopy and molecular
dynamics simulations, on the substrate effect on thermal properties of 2D
materials and revisit measurement of thermal expansion coefficient (TEC) of
supported 2D film. Graphene is employed as a representative. We find that the
out-of-plane coupling between graphene and substrate strongly affects the
temperature-dependent vibrational modes and TEC of graphene. Density of states
for long-wavelength out-of-plane oscillations is significantly reduced when
graphene is supported on an alkane substrate. To account for the contribution
of the out-of-plane coupling to TEC, a Raman micro-spectroscopic scheme is
developed. The TEC of graphene on octadecyltrichlorosilane substrate is found
to be (-0.6+-0.5)*10-6/K at room temperature, which is fundamentally smaller
than that of free-standing graphene. Our results shed light on the
understanding of the interaction between 2D material and substrate, and offer a
general recipe for optical measurement of TEC of a supported 2D film.
