Mechanical properties of hypothetical graphene foams: Giant Schwarzites

The mechanical properties of four different families of ordered porous graphene or giant Schwarzites, up to 12,288 atoms per cubic cell, were studied theoretically in order to shed light on the properties of newly synthesized graphene-like foams. It is shown that as the Schwarzite grows in size, the structure becomes flatter and not only more energetically stable, but also more elastically stable, thus opening the possibility of being synthesized in the near future. The mechanical properties such as bulk modulus, Young's modulus, and Poisson's ratio have been calculated with first principles for the smaller cells and with empirical methods for the larger cells. The bulk and Young moduli decrease as the structures grow. The "P" and the "I-WP" geometries favor smaller values of Poisson's ratio, likely to be synthesized experimentally. For the larger gyroid "G" and "D" cases, elastic instabilities appear, and these can be alleviated by breaking the symmetry of the associated space group. In addition, ripples in the graphene sheet stabilize the giant "D" family as the crystal cell dimensions increase. Finally, based on density functional theory calculations, the electronic properties of the high genus I-WP were examined for the first time finding semiconducting, semimetallic, and metallic behaviors.