Effects of size and surface on the auxetic behaviour of monolayer graphene kirigami

Graphene is an active element used in the design of nano-electro-mechanical systems (NEMS) owing to its excellent in-plane physical properties on mechanical, electric and thermal aspects. Considering a component requiring negative Poisson's ratio in NEMS, a graphene kirigami (GK) containing periodic re-entrant honeycombs is a natural option. This study demonstrates that a GK with specific auxetic property can be obtained by adjusting the sizes of its honeycombs. Using molecular dynamics experiments, the size effects on the auxetic behaviour of GK are investigated. In some cases, the auxetic difference between the hydrogenated GK and continuum kirigami (CK) is negligible, in which the results from macro CK can be used to predict auxetic behaviour of nano kirigami. Surface effect of GK is demonstrated from two aspects. One is to identify the difference of mechanical responses between the pure carbon GK and the hydrogenated GK at same geometry and loading condition. Another is from the difference of mechanical responses between the GK model and the CK model under same loading condition and geometric configuration. Generally, surface energy makes the GK possess higher variation of auxetic behaviour. It also results in higher modulus for the GK as comparing with that of the CK.