Ares Pablo, Wang Yi Bo, Woods Colin R, Dougherty James, Fumagalli Laura, Guinea Francisco, Davidovitch Benny, Novoselov Kostya S
Department of Physics and Astronomy, University of Manchester, M13 9PL Manchester, United Kingdom;
National Graphene Institute, University of Manchester, M13 9PL Manchester, United Kingdom.
Proc Natl Acad Sci U S A. 2021 Apr 6;118(14). doi: 10.1073/pnas.2025870118.
Nonlinear mechanics of solids is an exciting field that encompasses both beautiful mathematics, such as the emergence of instabilities and the formation of complex patterns, as well as multiple applications. Two-dimensional crystals and van der Waals (vdW) heterostructures allow revisiting this field on the atomic level, allowing much finer control over the parameters and offering atomistic interpretation of experimental observations. In this work, we consider the formation of instabilities consisting of radially oriented wrinkles around mono- and few-layer "bubbles" in two-dimensional vdW heterostructures. Interestingly, the shape and wavelength of the wrinkles depend not only on the thickness of the two-dimensional crystal forming the bubble, but also on the atomistic structure of the interface between the bubble and the substrate, which can be controlled by their relative orientation. We argue that the periodic nature of these patterns emanates from an energetic balance between the resistance of the top membrane to bending, which favors large wavelength of wrinkles, and the membrane-substrate vdW attraction, which favors small wrinkle amplitude. Employing the classical "Winkler foundation" model of elasticity theory, we show that the number of radial wrinkles conveys a valuable relationship between the bending rigidity of the top membrane and the strength of the vdW interaction. Armed with this relationship, we use our data to demonstrate a nontrivial dependence of the bending rigidity on the number of layers in the top membrane, which shows two different regimes driven by slippage between the layers, and a high sensitivity of the vdW force to the alignment between the substrate and the membrane.
固体非线性力学是一个令人兴奋的领域，它既包含优美的数学，如不稳定性的出现和复杂图案的形成，也有多种应用。二维晶体和范德华（vdW）异质结构使得在原子层面上重新审视这个领域成为可能，能够对参数进行更精细的控制，并为实验观测提供原子层面的解释。在这项工作中，我们考虑二维vdW异质结构中围绕单层和少数层“气泡”形成的由径向排列的皱纹组成的不稳定性。有趣的是，皱纹的形状和波长不仅取决于形成气泡的二维晶体的厚度，还取决于气泡与衬底之间界面的原子结构，而这可以通过它们的相对取向来控制。我们认为这些图案的周期性源于顶部膜的抗弯曲阻力（倾向于大波长的皱纹）与膜 - 衬底vdW吸引力（倾向于小皱纹幅度）之间的能量平衡。利用弹性理论的经典“文克勒地基”模型，我们表明径向皱纹的数量传达了顶部膜的弯曲刚度与vdW相互作用强度之间的重要关系。基于这种关系，我们利用我们的数据证明了弯曲刚度对顶部膜层数的非平凡依赖性，这显示出由层间滑动驱动的两种不同状态，以及vdW力对衬底与膜之间对齐的高灵敏度。
