The thermal expansion of a hole, in a planar system, follows the same trend as the thermal expansion of the whole system, i.e., the hole expands (contracts) if the material expands (contracts) under thermal excitation. At nanoscale, this phenomenon has not been studied so far. Here, using tools of classical molecular dynamics simulations, we show that graphene nanomeshes (GNMs) behave oppositely: While the whole structure contracts (expands), the nanoholes expand (contract) under thermal excitation. We propose and test a simple mechanism to describe this unexpected behavior in terms of out-of-plane vibrations of the atoms close to and far from the edges of the holes. This mechanism allows us to see that, contrary to usual planar systems, this behavior comes from nonuniform thermal expansion along the structure. Although the thermal expansion of holes in GNMs is contrary to the classical prediction, we verify that the thermal expansion of the whole GNM structure is the same as that of pristine graphene.

Graphene possesses excellent mechanical, thermal and electronic properties, not to mention its optical transparency and chemical stability. Much effort has been made towards the control of its physical properties for technological applications. One way to achieve this control is by modifying graphene size and structure. Recently, in a search for the development of semiconducting graphene structures to be produced at large scale, a new structure called graphene nanomesh was synthesized by means of block copolymer lithography and other methods. Basically, a graphene nanomesh is a graphene structure made to possess a periodic array of nanoscale holes whose sizes and hole-to-hole (or neck) distances are considered as control parameters for its overall electronic properties. Although the electronic properties of graphene nanomeshes are being intensively studied, their mechanical properties are still to be investigated. This work, then, presents the first study of mechanical, structural and thermal properties of graphene nanomeshes as a function of hole and neck sizes, through atomistic molecular dynamics simulations. The dependence of the Young's modulus and coefficient of thermal expansion of graphene nanomeshes on the hole and neck sizes will be shown.