Density dependence of elastic properties of graphynes

Graphyne is a two-dimensional carbon allotrope of graphene. Its structure is composed of aromatic rings and/or carbon-carbon bonds connected by one or more acetylene chains. As some graphynes present the most of the excellent properties of graphene and non-null bandgap, they have been extensively studied. Recently, Kanegae and Fonseca reported calculations of four elastic properties of 70 graphynes, ten members of the seven families of graphynes [Carbon Trends 7, 100152 (2022)]. They showed that the acetylene chain length dependence of these properties can be simply modelled by a serial association of springs. Here, based on those results, we present the density dependence of these properties and show that the elastic moduli, $E$, of graphyne are less dependent on density, $\rho$, than porous cellular materials with an exponent of $E \sim \rho^{n}$, smaller than 2. We discuss the results in terms of the shape of the pores of the graphyne structures.