Nanoscale Bending of Multilayered Boron Nitride and Graphene Ribbons: Experiment and Objective Molecular Dynamics Calculations

By combining experiments performed on nanoribbons in situ within a high-resolution TEM with objective molecular dynamics simulations, we reveal common mechanisms in the bending response of few-layer-thick hexagonal boron nitride and graphene nanoribbons. Both materials are observed forming localized kinks in the fully reversible bending experiments. Microscopic simulations and theoretical analysis indicate platelike bending behavior prior to kinking, in spite of the possibility of interlayer sliding, and give the critical curvature for the kinking onset. This behavior is distinct from the rippling and kinking of multi- and single-wall nanotubes under bending. Our findings have implications for future study of nanoscale layered materials, including nanomechanical device design.

Figure 1

a) Bending (1), (2) and recovery (2), (3) cycle of 12-layer BNNR. Scale bars are 50 nm. Width is 82 nm, length is $\approx 300\mathrm{nm}$. b) Bending (1)–(3) and recovery (4) cycle of 9-layer GNR, showing critical curvature for kinking predicted from simulations (dotted line). Scale bars are 200 nm. Width is 34 nm, length is $\approx 1\mu \mathrm{m}$.

Figure 2

Kink developed in 9-layer GNR. This HRTEM image was taken towards the end of the bending stage [different experiment than Fig. 1b]. It shows typical dark fringes, the cause of which is shown in Fig. 3a. Scale bar is 5 nm.

Figure 3

Objective MD simulations for the bending of 4-layer $h$-BN. Three stages are indicated—(i) ideal platelike (no layers wrinkled—unshaded on graphs), (ii) intermediate (some layers wrinkled—shaded light gray), and (iii) final (only outer layer not wrinkled—shaded dark gray). (a) Morphology, revealing the origin of the dark fringes seen in the TEM Fig. 2. (b) Energy—dashed line indicates plate behavior as described by Ref. 10, solid line indicates total bending energy, dotted line indicates interlayer vdW component. (c) In-plane strain in individual layers.

Figure 4

Critical curvatures for kinking. Continuous lines show fitting with Eq. (1) using $B=6.6$ and $4.53\mathrm{deg}/\mathrm{nm}$ for graphene and $h$-BN, respectively.