单层石墨烯杨氏模量的理论模型

Theoretical model of Young's modulus of graphene

石墨烯力学性能的研究对其在半导体技术中的应用是十分重要的,本文基于半连续体模型并结合石墨烯纳米结构特性,通过对原子的描述构建了石墨烯形变分量和位移分量的新关系,从而给出了单层石墨烯结构形变能,并计算了不同尺寸单层石墨烯的杨氏模量值.通过对不同方向杨氏模量的分析,讨论了单层石墨烯的手性行为.结果表明:随着尺寸的增加,单层石墨烯两个方向的杨氏模量分别趋于0.746 TPa和0.743 TPa,当尺寸相同时,两方向杨氏模量的最大差值不超过0.003 TPa,此结果与文献报道结果相符.在小应变情况下,单层石墨烯薄膜呈各向同性,且薄膜尺寸变化对该特性影响不大.该计算结果对研究石墨烯的其它力学特性提供一定的参考价值.

The mechanical properties of graphene are very important for its application in semiconductor technology. Based on the semi - continuum model and the structure characteristic of the graphene, a new relationship between the deformation and the displacement components of graphene is performed by atomic coordinates in this paper. The deformation energy of the graphene is calculated and then Young＇ s moduli of the graphene with different sizes have been obtained. Through the analysis of Young＇ s moduli in different directions, the chiral behavior of single layer graphene is discussed. The results show that Young＇ s moduli of different directions tend to 0. 758 TPa and 0. 744 TPa, respectively. As the same size, the greatest difference of Young＇ s modulus of the two directions is not more than 0. 015 TPa, which is consistent with the results from references. The monolayer graphene is isotropic and the change of its size has little effect on the properties under small strain. The study in this paper would be useful for the application of graphene.