边界应力对石墨烯翘曲的影响

Effect of Stress on the Boundary of Graphene Sheets

对于边界应力引起的石墨烯薄膜边界翘曲问题,分别建立了理想边界模型和真实边界模型来分析边界尺寸对翘曲形貌的影响。通过建立弹性薄壳模型,将边界处理成只具有面积而没有几何尺寸的理想梁模型以及具有真实尺寸的真实边界壳模型,然后进行理论分析来确定石墨烯薄膜边界翘曲时的尺度关系(即翘曲波形的波长、腹向衰减表征尺度以及面外翘曲幅值)。理论分析发现,边界宽度的变化对石墨烯薄膜的能量、翘曲幅值及腹向衰减尺度的影响显著,且当边界宽度为0.1 nm时,总应变能有最小极值点出现在波长为7 nm左右,该发现与原子模拟研究所得结果基本一致;同时发现,石墨烯翘曲幅值在边界宽度为0.1 nm时幅值达到最大,腹向衰减尺度随边界宽度在边界宽度为0.1 nm时衰减得最快。

Theoretical and true edge models are established respectively to study the importance of edge width on edge warping of graphene nanoribbons,which is caused by the edge stress. In both models the graphene nanoribbon itself is treated as an elastic shell. The edge owns a nominal edge area and thus beam model is used for the edge in the theoretical model. In comparison the edge will behave like thin shell as the ribbon itself in the true edge model. The deformation parameters,such as warping period and amplitude and the damping scale inward are analyzed by seeking numerical solutions of a set of nonlinear equations. Theoretical analysis found that,the variation of edge width has significant effects on the three deformation parameters. When the edge width is 0. 1nm,total strain can be minimal extremum points about 7 nm wavelength which is consist with the predictions based on molecular dynamics. It is also found that only when the edge width is 0. 1nm,edge warping reaches the maximum amplitude and at the same time the warping descends at the rapidest scale inward.