Temperature-dependent graphene wrinkle formation: A theoretical study

The topic of wrinkle-free graphene has currently garnered significant attention from scientists. Understanding the mechanism of wrinkle formation is imperative for fabricating ultra-flat graphene sheets. Here, molecular dynamics (MD) simulations were conducted for graphene on single and multi-layer Cu substrates, respectively, to mimic the cooling process in chemical vapor deposition (CVD) growth. Wrinkles were initially observed in graphene on a single-layer Cu substrate during cooling from 1300 to 630 K, while the initiation temperature for wrinkle formation on a multi-layer Cu surface was approximately 1080 K. Based on these simulations, we proposed a two-step wrinkle formation process: Hill-shaped atomic structures first form on the Cu substrate for wrinkle nucleation, followed by wrinkle propagation at these locations. Moreover, we found a linear decrease in the critical temperature corresponding to the adhesion between the graphene layer and Cu substrate. Notably, we explored the impact of friction on wrinkle density and determined that residual compressive strain was approximately linearly related to distance from the wrinkle. Consequently, we developed an analytical model that considered the frictional forces between graphene and the Cu(111) substrate balanced with external compressive loads. Both simulation results and the analytical model demonstrate that the distance between neighboring wrinkles decreases with increasing friction.