Representative simulation of a wrinkle-to-fold transition ((a) and (b)) of monolayer graphene upon uniaxial compression. The length of the domain along the uniaxial compression is 200 nm, the adhesion energy is 0.45 J/m2, and equilibrium separation of the potential is 6 nm. A lateral view of the fold is given in (c), to be compared with the fold morphology obtained with a smaller equilibrium separation ( ) shown in (d).
Critical strains for the onset of wrinkling and the wrinkle-to-fold transition under uniaxial compression, for different van der Waals parameters and for a graphene film of length L = 200 nm. Comparisons between analytical model (lines) and numerical simulations (symbols) for both wrinkling (dashed lines, triangles) and wrinkle-to-fold (solid lines, squares) strains as a function of the equilibrium spacing of the interaction potential h 0, and the adhesion energy γ (different colors). The inset shows the features of the interaction potential.
Illustration of the sliding of graphene as the system transits from wrinkling, with distributed excess graphene area relative to substrate area, to folding, with localized excess area (a). Critical strain for wrinkling and for the transition from wrinkling to multiple folds as a function of the frictional parameter , for a uniaxially compressed graphene sheet of length L = 1 μm (b).
Separation between folds L as a function of the friction parameter predicted by the theoretical model (top), checked against the simulations for four selected frictional coefficients (bottom). The color represents the out-of-plane deviation w(x). The inset shows L as a function of in a log-log scale, to highlight the fact that the relation is not a power-law.
Different stages during the wrinkle-to-fold transition of supported graphene upon biaxial compression for a 500 nm × 500 nm sample. (a) Randomly distributed labyrinth wrinkles; (b) nucleation of short folds; (c) extension of folds at the expense of wrinkles; (d) network of folds. The areal strain is −0.01 in (a) and −0.04 in (d).
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