Aljedani Jabr, Chen Michael J, Cox Barry J
School of Mathematical Sciences, University of Adelaide Adelaide Australia
Faculty of Applied Studies, King Abdulaziz University Jeddah Saudi Arabia.
RSC Adv. 2020 Apr 22;10(27):16016-16026. doi: 10.1039/c9ra10439a. eCollection 2020 Apr 21.
The calculus of variations is utilised to study the behaviour of a rippled graphene sheet supported on a metal substrate. We propose a model that is underpinned by two key parameters, the bending rigidity of graphene , and the van der Waals interaction strength . Three cases are considered, each of which addresses a specific configuration of a rippled graphene sheet located on a flat substrate. The transitional case assumes that both the graphene sheet length and substrate length are constrained. The substrate constrained case assumes only the substrate has a constrained length. Finally, the graphene constrained case assumes only the length of the graphene sheet is constrained. Numerical results are presented for each case, and the interpretation of these results demonstrates a continuous relationship between the total energy per unit length and the substrate length, that incorporates all three configurations. The present model is in excellent agreement with earlier results of molecular dynamics (MD) simulations in predicting the profiles of graphene ripples.
变分法用于研究支撑在金属基底上的波纹状石墨烯片的行为。我们提出了一个由两个关键参数支撑的模型，即石墨烯的弯曲刚度和范德华相互作用强度。考虑了三种情况，每种情况都对应于位于平坦基底上的波纹状石墨烯片的特定构型。过渡情况假设石墨烯片长度和基底长度均受到约束。基底约束情况假设只有基底长度受到约束。最后，石墨烯约束情况假设只有石墨烯片的长度受到约束。给出了每种情况的数值结果，对这些结果的解释表明了单位长度总能量与基底长度之间的连续关系，该关系包含了所有三种构型。本模型在预测石墨烯波纹轮廓方面与早期分子动力学（MD）模拟结果非常吻合。
