Department of Physics, University of Gothenburg, SE-41296 Göteborg, Sweden.
Nano Lett. 2012 Jul 11;12(7):3526-31. doi: 10.1021/nl301080v. Epub 2012 Jun 20.
Classical continuum mechanics is used extensively to predict the properties of nanoscale materials such as graphene. The bending rigidity, κ, is an important parameter that is used, for example, to predict the performance of graphene nanoelectromechanical devices and also ripple formation. Despite its importance, there is a large spread in the theoretical predictions of κ for few-layer graphene. We have used the snap-through behavior of convex buckled graphene membranes under the application of electrostatic pressure to determine experimentally values of κ for double-layer graphene membranes. We demonstrate how to prepare convex-buckled suspended graphene ribbons and fully clamped suspended membranes and show how the determination of the curvature of the membranes and the critical snap-through voltage, using AFM, allows us to extract κ. The bending rigidity of bilayer graphene membranes under ambient conditions was determined to be 35.5−15.0 +20.0 eV. Monolayers are shown to have significantly lower κ than bilayers.
经典连续介质力学被广泛用于预测石墨烯等纳米材料的性能。弯曲刚度κ是一个重要的参数，例如，它用于预测石墨烯纳机电设备的性能和波纹形成。尽管它很重要，但对于少层石墨烯的κ理论预测存在很大的差异。我们利用凸弯曲石墨烯膜在静电压力作用下的突然弯曲行为，实验确定了双层石墨烯膜的κ值。我们展示了如何制备凸弯曲悬空石墨烯带和完全固定悬空膜，并展示了如何通过原子力显微镜（AFM）确定膜的曲率和临界突然弯曲电压，从而提取κ值。在环境条件下，双层石墨烯膜的弯曲刚度被确定为 35.5-15.0+20.0 eV。结果表明，单层的κ明显低于双层。
