The Young's moduli of three types of carbon allotropes: a molecular mechanics model and a finite-element method

The close-form expressions of the Young's moduli and the fracture stresses of cyclicgraphene, graphyne and supergraphene along their armchair and zigzag directions are derived based on a molecular mechanics model. Checking against present finite-element calculations of their Young's moduli shows that the explicit solutions are reasonable. The obtained analytical solutions should be of great help for understanding the mechanical properties of the graphene-like materials.

An Analytical Molecular Mechanics Model for Elastic Properties of Graphyne-n

Graphynes, a new family of carbon allotropes, exhibit superior mechanical properties depending on their atomic structures and have been proposed as a promising building materials for nanodevices. Accurate modeling and clearer understanding of their mechanical properties are essential to the future applications of graphynes. In this paper, an analytical molecular mechanics model is proposed for relating the elastic properties of graphynes to their atomic structures directly. The closed-form expressions for the in-plane stiffness and Poisson's ratio of graphyne-n are obtained for small strains. It is shown that the in-plane stiffness is a decreasing function whereas Poisson's ratio is an increasing function of the number of acetylenic linkages between two adjacent hexagons in graphyne-n. The present analytical results enable direct linkages between mechanical properties and lattice structures of graphynes; thereby, providing useful guidelines in designing graphyne configurations to suit their potential applications. Based on an effective bond density analysis, a scaling law is also established for the in-plane stiffness of graphyne-n which may have implications for their other mechanical properties.