Effectiveness of the elastic moduli characterization of graphene or other 2D materials via Raman spectroscopy

Abstract

Raman spectroscopy is a new technique to properly measure the strain of two dimensional (2D) materials, based upon which a new characterizing approach for the elastic moduli of graphene membranes was proposed from the central strain of the bulged membrane under a given pressure measured via Raman spectroscopy. In the present work, using finite element modeling (FEM), it is found that the aforementioned approach cannot properly determine the elastic moduli of free standing 2D materials. The reasons are that the membranes measured in the bulge test are not pre-strain free, and that the central strain measured via Raman spectroscopy includes both the pre-strain and the strain induced by the applied pressure. From FEM results, the negative apparent pre-strain in the membranes (corresponding the slack membranes) can result in the overestimation of their elastic moduli. The present results can be further validated by the reported experimental results, in which the measured elastic moduli of graphene membranes were significantly overestimated. Effectively estimating the apparent pre-strain is the necessary condition to properly determine the elastic moduli of graphene membranes via the central strain measured via Raman spectroscopy.