Study of Thermal Expansion Coefficient of Graphene via Raman Micro-Spectroscopy: Revisited.

The thermal expansion coefficient (TEC) of a 2D material is a fundamental parameter for both material property and applications. A joint study is hereby reported, using Raman microspectroscopy and molecular dynamics (MD) simulations, of the substrate effects on thermal properties of graphene. It is found that besides the lateral strain induced by the substrate, out-of-plane coupling strongly affects the temperature-dependent vibrational modes and TEC of graphene. MD simulation shows significant reduction of the density of states for longer wavelength out-of-plane vibrations when the graphene is supported on an alkane substrate. The negative TEC of freestanding graphene becomes smaller when out-of-plane rippling is suppressed. In order to measure TEC of 2D materials with the out-of-plane coupling being taken into consideration, a Raman microspectroscopic scheme to separate the contributions of lateral strain and out-of-plane coupling to TEC is developed. The TEC of graphene on octadecyltrichlorosilane substrate is found to be (-0.6 ± 0.5) × 10 K at room temperature, which is fundamentally smaller than that of freestanding graphene. These results shed light on the fundamental understanding of the interaction between 2D material and substrate, and offer a general recipe for studying separately in-plane and out-of-plane couplings on supported materials.