Graphyne is a theorized allotrope of carbon. Its structure is one-atom-thick planar sheets of sp and sp2-bonded carbon atoms arranged in crystal lattice. It can be seen as a lattice of benzene rings connected by acetylene bonds. Depending on the content of acetylene groups, graphyne can be considered a mixed hybridization, spn, where 1 < n < 2, and thus differs from the hybridization of graphene (considered pure sp2) and diamond (pure sp3).
Although not yet synthesized, periodic graphyne structures and their boron nitride analogues were shown to be stable on the basis of first-principles calculations using phonon dispersion curves and ab-initio finite temperature, quantum mechanical molecular dynamics simulations.
In 2016, the possible synthesis of graphyne on Ru(0001), Rh(111), and Pd(111) substrates have been proposed by Han et al. 
Graphyne has yet to be synthesized in significant quantities for study but through the use of computer models scientists have been able to predict several properties of the substance on assumed geometries of the lattice. The proposed structures of graphyne are derived from inserting acetylene bonds in place of Carbon-Carbon single bonds in a graphene lattice. Graphyne is theorized to exist in several different geometries. This variety is due to the multiple arrangements of sp and sp2 hybridized carbon. The proposed geometries include a hexagonal lattice structure and a rectangular lattice structure. It has been hypothesized as preferable to graphene for specific applications due to the potential of direction-dependent Dirac cones. Out of the theorized structures the rectangular lattice of 6,6,12-graphyne may hold the most potential for future applications.
The models for graphyne show that it has the potential for Dirac cones on its double and triple bonded carbon atoms. Due to the Dirac cones, there is a single point in the Fermi level where the conduction and valence bands meet in a linear fashion. The advantage of this scheme is that electrons behave as if they have no mass, resulting in energies that are proportional to the momentum of the electrons. Like in graphene, hexagonal graphyne has electric properties that are direction independent. However, due to the symmetry of the proposed rectangular 6,6,12-graphyne the electric properties would change along different directions in the plane of the material. This unique feature of its symmetry allows graphyne to self-dope meaning that it has two different Dirac cones lying slightly above and below the Fermi level. Graphyne samples synthesized to date have shown a melting point of 250-300 °C, low reactivity in decomposition reactions with oxygen, heat and light.
The directional dependency of 6,6,12-graphyne could allow for electrical grating on the nanoscale. This could lead to the development of faster transistors and nanoscale electronic devices.
Graphdiyne (graphyne with diacetylene groups) has successfully been synthesized on copper and silver substrates. Graphdiyne exhibits a nanoweb-like structure characterized by triangular and regularly distributed pores, which form a nanoporous membrane. Due to the effective size of its pores, which almost matches the van der Waals radius of the helium atom, graphdiyne could behave as an ideal two-dimensional membrane for helium chemical and isotopic separation. The application of a graphdiyne based membrane as an efficient two-dimensional sieve for water filtration and purification technologies has been proposed.
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