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Effective acetylene length dependence of the elastic properties of different kinds of graphynes

Graphyne is a planar network of connected carbon chains, each formed by $n$ acetylene linkages. Uncountable ways to make these connections lead to uncountable structural graphyne families (GFs). As the synthesis of graphynes with $n > 1$ has been reported in literature, it is of interest to find out how their physical properties depend on $n$ for each possible GF. Although literature already present specific models to describe the dependence on $n$ of the elastic properties of specific GFs, there is not yet enough amount of data for the physical properties of different graphynes with different values of $n$. Based on fully atomistic molecular dynamics simulations, the Young's modulus, shear modulus, linear compressibility and Poisson's ratio of 10 graphyne members of 7 different GFs are calculated. A simple elastic model consisting of a serial combination of $n$ springs is proposed to describe the dependence on $n$ of the elastic properties of these 7 GFs. We show that except for the Poisson's ratio, this simple unique elastic model is able to numerically describe, with good precision, the Young's modulus, shear modulus and linear compressibility of all different graphynes, including anisotropy and negative values of linear compressibility of some GFs.