Critical Stable Length in Wrinkles of Two-Dimensional Materials

The emergent two-dimensional (2D) materials are atomically thin and ultraflexible, promising for a variety of miniaturized, high-performance, and flexible devices in applications. On one hand, the ultrahigh flexibility causes problems: the prevalent wrinkles in 2D materials may undermine the ideal properties and create barriers in fabrication, processing, and quality control of materials. On the other hand, in some cases the wrinkles are used for the architecturing of surface texture and the modulation of physical/chemical properties. Therefore, a thorough understanding of the mechanism and stability of wrinkles is highly needed. Herein, we report a critical length for stabilizing the wrinkles in 2D materials, observed in the wrinkling and wrinkle elimination processes upon thermal annealing as well as by our in situ TEM manipulations on individual wrinkles, which directly capture the evolving wrinkles with variable lengths. The experiments, mechanical modeling, and self-consistent charge density functional tight binding (SCC-DFTB) simulations reveal that a minimum critical length is required for stabilizing the wrinkles in 2D materials. Wrinkles with lengths below a critical value are unstable and removable by thermal annealing, while wrinkles with lengths above a critical value are self-stabilized by van der Waals interactions. It additionally confirms the pronounced frictional effects in wrinkles with lengths above critical value during dynamical movement or sliding.