热波动膜力学
Mechanics of thermally fluctuating membranes
摘要：
除了具有独特的电子特性外，石墨烯还被认为是自然界中最强的材料。在诺贝尔委员会的新闻稿中，声称由一平方米的单原子厚石墨烯制成的吊床可以承受4公斤猫的重量。更实际的是石墨烯的应用，如支架和传感器，这些都是关键依赖于机械强度。米大小的石墨烯甚至被考虑用于starshot项目中的光帆，以到达半人马座α星。石墨烯的预测强度是基于其非常大的杨氏模量，每原子层的杨氏模量比钢大得多。然而，这种推理将适用于传统的薄板，但没有考虑石墨烯作为热波动结晶膜的独特性质。最近的实验和理论表明，与原子尺度值相比，热波动导致微米级石墨烯样品的杨氏模量急剧降低，弯曲刚度增加。这使得标准的Föppl-von Karman弹性（FvK）理论不能直接应用于石墨烯和其他单原子层膜。这一事实很重要，因为目前对实验结果的解释是基于FvK理论。特别是，我们表明，FvK衍生的Schwerin方程，常规用于从压痕实验中获得的杨氏模量必须在室温下的石墨烯和微米尺寸的样品进行基本修改。基于标度分析和原子模拟，我们研究了石墨烯在横向载荷作用下的力学行为。我们确定的FvK理论的适用性的限制，并提供定量估计不同的制度。
英文摘要：
Besides having unique electronic properties, graphene is claimed to be the strongest material in nature. In the press release of the Nobel committee it is claimed that a hammock made of a squared meter of one-atom thick graphene could sustain the wight of a 4 kg cat. More practically important are applications of graphene like scaffolds and sensors which are crucially dependent on the mechanical strength. Meter-sized graphene is even being considered for the lightsails in the starshot project to reach the star alpha centaury. The predicted strength of graphene is based on its very large Young modulus which is, per atomic layer, much larger than that of steel. This reasoning however would apply to conventional thin plates but does not take into account the peculiar properties of graphene as a thermally fluctuating crystalline membrane. It was shown recently both experimentally and theoretically that thermal fluctuations lead to a dramatic reduction of the Young modulus and increase of the bending rigidity for micron-sized graphene samples in comparison with atomic scale values. This makes the use of the standard Föppl-von Karman elasticity (FvK) theory for thin plates not directly applicable to graphene and other single atomic layer membranes. This fact is important because the current interpretation of experimental results is based on the FvK theory. In particular, we show that the FvK-derived Schwerin equation, routinely used to derive the Young modulus from indentation experiments has to be essentially modified for graphene at room temperature and for micron sized samples. Based on scaling analysis and atomistic simulation we investigate the mechanics of graphene under transverse load up to breaking. We determine the limits of applicability of the FvK theory and provide quantitative estimates for the different regimes.
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