We report a comprehensive micro-Raman study of a pressurized suspended graphene membrane that hermetically seals a circular pit, etched in a Si/SiO$_2$ substrate. Placing the sample under a uniform pressure load results in bulging of the graphene membrane and subsequent softening of the main Raman features, due to tensile strain. In such a microcavity, the intensity of the Raman features depends very sensitively on the distance between the graphene membrane and the Si substrate, which acts as the bottom mirror of the cavity. Thus, a spatially resolved analysis of the intensity of the G- and 2D-mode features as a function of the pressure load permits a direct reconstruction of the blister profile. An average strain is then deduced at each pressure load, and Gruneisen parameters of $1.8\pm0.2$ and $2.4\pm0.2$ are determined for the Raman G and 2D modes, respectively. In addition, the measured blister height is proportional to the cubic root of the pressure load, as predicted theoretically. The validation of this scaling provides a direct and accurate determination the Young's modulus of graphene with a purely optical, hence contactless and minimally invasive, approach. We find a Young's modulus of $(1.05\pm 0.10) \rm TPa$ for monolayer graphene, in a perfect match with previous nanoindentation measurements. This all-optical methodology opens avenues for pressure sensing using graphene and could readily be adapted to other emerging two-dimensional materials and nanoresonators.

All-Optical Blister Test of Suspended Graphene Using Micro-Raman Spectroscopy

Analytical and molecular dynamics simulation approaches are used in this paper to study free-vibration behavior of multilayer graphene-based nanoresonators considering interlayer shear effect According to experimental observations, the weak interlayer van der Waals interaction cannot maintain the integrity of carbon atoms in the adjacent layers Hence, it is vital that the interlayer shear effect is taken into account to design and analyze multilayer graphene-based nanoresonators The differential equation of motion and the general form of boundary conditions are first derived for multilayer graphene sheets with rectangular shape using the Hamilton’s principle Then, by pursuing an analytical approach, closed-form results for the natural frequencies are obtained in the case of simply supported boundary conditions Molecular dynamics (MD) simulations of the graphene sheets are also accomplished to evaluate the accuracy of the presented analytical model’s results The numerical results indicate that by increasing the layers number, the natural frequency also increases until a specific number of layers, then the effect of layers number on the natural frequency significantly decreases Moreover, by a rise in aspect ratio of the multilayer graphene sheet, the natural frequency decreases until a specific aspect ratio, next, the changes in the sheet aspect ratio have no considerable effect on the natural frequency

Analytical and molecular dynamics simulation approaches to study behavior of multilayer graphene-based nanoresonators incorporating interlayer shear effect

In this paper, the atomic structure and mechanical stability of a new structural graphene modification—a 2D matrix of nanoscale cells in the form of a few-layer graphene substrate and nanoblister of a graphene monolayer—were studied for the first time. It is shown that such matrices are mechanically stable and are promising for environmentally friendly technologies. The calculated local atomic stress fields demonstrate that the atomic framework is not destroyed, even in the presence of defects in the atomic network of graphene nanoblister (Stone-Wales defect, double vacancies defect, ad-dimmer defect, and their combination). However, it was established that the presence of one or more SW defects leads to the appearance of critical stresses. These critical stresses can induce local bond breaking in the atomic network with an increase in temperature or external pressure. It was found that graphene nanoblister can store molecular hydrogen with a maximum density of 6.6 wt % for 1158 m2/g at 77 K under normal pressure.

High-Density Hydrogen Storage in a 2D-Matrix from Graphene Nanoblisters: A Prospective Nanomaterial for Environmentally Friendly Technologies

The effect of initial tension on mechanics of adhered graphene blisters is investigated by extending Hencky’s solution to cases with an initial tension The system parameters including maximum blister deflection, pressure difference across the membrane, and critical delamination pressure under various initial tensions are modeled and calculated The dependences of critical pressure on the radius and depth of etched microcavity are also demonstrated and compared with the previous work which does not consider the initial tension The results show that the added adhesion energy between monolayer graphene membrane and SiO2 substrate can reach 00954 J/m2 with a reported maximum initial tension of 24 N/m taken into account, which accounts for 212 % of the measured average value 045 J/m2 Thus, the initial tension should be considered in further adhesion energy measurements of graphene/substrate interfaces

Pei Xu

Papers

Effect of initial tension on mechanics of adhered graphene blisters