A unified framework of slip controlled bending and rippled superlattice design of few-layer graphene

The out-of-plane bending of few-layer graphene (FLG) and other 2D materials have attracted increasing attention due to its practical significance in flexible electronics and soft robotics. Extensive studies have been carried out establishing the crucial role interlayer slip plays in the bending of FLG. Yet in previous analysis, slip was treated as the consequence of bending, rather than an independent variable, which makes sense physically but shadows part of its functionality. Here through a novel atomic simulation scheme, we select desired slip ratios r, a term we defined to quantify the ratio of the actual amount of slip to the maximum amount. The slip ratio serves as a gauge for determining the predominant deformation mechanism in curved FLG. We identified three regimes characterized with critical slip ratios r_c* and r_th. When r > r_c*, FLG behaves like the monolayer, and curvature is the primary quantity during its deformation. As r drops below r_c*, the accumulated in-plane strain imposes more impact, while when r < r_th, buckling and delamination may occur. By manipulating slip, we predict non-classical low-energy rippled superlattice of FLG, characterized by minimum periodicities, as small as a few nanometers, smaller than the FLG thickness itself.