A Theoretical Analysis of the Effect of the Hydrogenation of Graphene to Graphane on Its Mechanical Properties

We investigated the mechanical properties of graphene and graphane using first-principles calculations based on density-functional theory. A conventional unitcell containing a hexagonal ring made of carbon atoms was chosen to capture the finite wave vector ``soft modes", which affect the the fourth and fifth elastic constants considerably. Graphane has about 2/3 ultimate strengths in all three tested deformation modes -- {\em armchair}, {\em zigzag}, and {\em biaxial}-- compared to graphene. However, graphane has larger ultimate strains in {\em zigzag} deformation, and smaller in {\em armchair} deformation. We obtained the second, third, fourth, and fifth order elastic constants for a rigorous continuum description of the elastic response. Graphane has a relatively low in-plane stiffness of 240 N/m which is about 2/3 of that of graphene, and a very small Poisson ratio of 0.078, 44\% of that of graphene. The pressure dependence of the second order elastic constants were predicted from the third order elastic constants. The Poisson's ratio monotonically decreases with increasing pressure.