Extended graphynes: simple scaling laws for stiffness, strength and fracture

The mono-atomistic structure and chemical stability of graphene provides a promising platform to design a host of novel graphene-like materials. Using full atomistic first-principles based ReaxFF molecular dynamics, here we perform a systematic comparative study of the stability, structural and mechanical properties of graphynes - a variation of the sp(2) carbon motif wherein the characteristic hexagons of graphene are linked by sp(1) acetylene (single- and triple-bond) carbyne-like chains. The introduction of acetylene links introduces an effective penalty in terms of stability, elastic modulus (i.e., stiffness), and failure strength, which can be predicted as a function of acetylene repeats, or, equivalently, lattice spacing. We quantify the mechanical properties of experimental accessible graphdiyne, with a modulus on the order of 470 to 580 GPa and a ultimate strength on the order of 36 GPa to 46 GPa (direction dependent). We derive general scaling laws for the cumulative effects of additional acetylene repeats, formulated through a simple discrete spring-network framework, allowing extrapolation of mechanical performance to highly extended graphyne structures. Onset of local tensile buckling results in a transitional regime characterized by a severe reduction of strength (ultimate stress), providing a new basis for scaling extended structures. Simple fracture simulations support the scaling functions, while uncovering a "two-tier" failure mode for extended graphynes, wherein structural realignment facilitates stress transfer beyond initial failure. Finally, the specific modulus and strength (normalized by areal density) is found to be near-constant, suggesting applications for light-weight, yet structurally robust molecular components.