Atomic-scale finite element modelling of mechanical behaviour of graphene nanoribbons

Abstract

Experimental characterization of Graphene NanoRibbons (GNRs) is still an expensive task and computational simulations are therefore seen a practical option to study the properties and mechanical response of GNRs. Design of GNR in various nanotechnology devices can be approached through molecular dynamics simulations. This study demonstrates that the Atomic-scale Finite Element Method (AFEM) based on the second generation REBO potential is an efficient and accurate alternative to the molecular dynamics simulation of GNRs. Special atomic finite elements are proposed to model graphene edges. Extensive comparisons are presented with MD solutions to establish the accuracy of AFEM. It is also shown that the Tersoff potential is not accurate for GNR modeling. The study demonstrates the influence of chirality and size on design parameters such as tensile strength and stiffness. A GNR is stronger and stiffer in the zigzag direction compared to the armchair direction. Armchair GNRs shows a minor dependence of tensile strength and elastic modulus on size whereas in the case of zigzag GNRs both modulus and strength show a significant size dependency. The sizedependency trend noted in the present study is different from the previously reported MD solutions for GNRs but qualitatively agrees with experimental results. Based on the present study, AFEM can be considered a highly efficient computational tool for analysis and design of GNRs.

Width Dependent Elastic Properties of Graphene Nanoribbons

“…It is worth mentioning that an insensitivity of the mechanical behavior of AGNRs on their width has been also found using an atomic scale finite element method, while a qualitatively similar picture with our DFT data has been observed in the case of ZGNRs, though with a weaker width dependence, as can be seen from Figure 8 of Ref. [ 84 ].…”

“…Numerical data from a structural mechanics approach examining GNRs of different lengths and widths up to 10 nm has found that the Young’s modulus increases with the width in zigzag edged nanoribbons, while it exhibits a non-monotonous behavior for relatively narrow AGNRs [ 83 ]. Finally, an atomic scale finite element method has calculated stress-strain curves for ribbons of different widths and found a response insensitive to width for AGNRs, while the Young’s modulus and the intrinsic strength of ZGNRs is a decreasing function of ribbon width, in contrast to the width independent case of AGNRs [ 84 ].…”

Atomistic Modelling of Size-Dependent Mechanical Properties and Fracture of Pristine and Defective Cove-Edged Graphene Nanoribbons

“…Moreover, the mechanical response of CGNR with varying widths was different from the response previously observed for AGNR and ZGNR. Chu et al [ 21 ] and Damasceno et al [ 25 ] concluded that AGNR shows little size dependency with width whereas the size dependency with width is higher in the case of ZGNR. However, both authors [ 21 , 25 ] showed that in the case of the ZGNR as the width increased the ultimate strength and the failure strain decreased.…”

“…Chu et al [ 21 ] and Damasceno et al [ 25 ] concluded that AGNR shows little size dependency with width whereas the size dependency with width is higher in the case of ZGNR. However, both authors [ 21 , 25 ] showed that in the case of the ZGNR as the width increased the ultimate strength and the failure strain decreased. Moreover, other studies also concluded that the ultimate strength is larger as the width is decreased [ 38 , 39 ], while the fracture strain is increased.…”

“…The armchair ( ar ) and zigzag ( zz ) edges are the most investigated types by both theoretical and experimental approaches. Several studies using molecular dynamics (MD) simulations [ 20 , 21 , 22 , 23 , 24 ], atomic-scale finite element method [ 25 ] and experimental measurements [ 26 , 27 ] have been used to investigate the mechanical properties of GNR along the ar and zz directions. A study of the electronic properties of zigzag graphene nanoribbons with constructed edges representing pentagonal and heptagonal defects has been presented by Pincak et al [ 28 ], whereas the effects of edge vacancies on the electronic properties of zigzag nanoribbons have been addressed by Smotlacha and Pincak [ 29 ].…”