Blisters can form spontaneously when transferring 2D materials on a substrate because of the small molecules trapped at the interface. Though extensive works have revealed a characteristic aspect ratio of these blisters by neglecting the bending effect of the layer, how the bending comes into play as the layer number increases has not been fully understood. Here, by simply measuring the profiles of blisters formed by transferred multilayer graphene and MoS2 sheets, the variable profiles of blisters and the transition of their characteristic shape from a constant aspect ratio to a constant dome curvature are observed. Taking variable profiles of blisters and different characteristics of the interface into consideration, a theoretical model is established, and the mechanism of such transition is further analytically unveiled. In addition, based on this theory, the bending stiffness of sheets and the adhesion energy between sheets and substrates can be obtained simultaneously. This method is simple but robust, providing a new experimental way to explore the mechanical behavior of 2D material structures.

No abstract

We consider how the bending stiffness of a multilayer graphene sheet relies on its bending geometry, including the in-plane length L and the curvature κ. We use an interlayer shear model to characterize the periodic interlayer tractions due to the lattice structure. The bending stiffness for the sheet bent along a cylindrical surface is extracted via an energetic consideration. Our discussion mainly focuses on trilayer sheets, particularly the complex geometry-dependency of their interlayer stress transfer behavior and the overall bending stiffness. We find that L and κ dominate the bending stiffness, respectively, in different stable regions. These results show good quantitative agreement with recent experiments where the stiffness was found to be a non-monotonic function of the bending angle (i.e., Lκ). Besides, for a given in-plane length, the trilayer graphene in the flat state (κ→0) is found to have the maximum bending stiffness. According to our analytical solution to the flat state, the bending stiffness of trilayer graphene sheet can vary by two orders of magnitude. Furthermore, once multilayer graphene sheets are bent along a cylindrical surface with small curvature, the sheets perform similar characteristics. Though the discussion mainly focuses on trilayer graphene, the theoretical framework presented here can be readily extended for various van der Waals materials beyond graphene of arbitrary layer numbers.

No abstract

No abstract