Thermal fluctuations of single layer hydrogenated graphene (graphane) are investigated using large scale atomistic simulations. By analyzing the mean square value of the height fluctuations $\langle h^2\rangle$ and the height-height correlation function $H\left(q\right)$ for different system sizes and temperatures, we show that hydrogenated graphene is an unrippled system in contrast to graphene. The height fluctuations are bounded, which is confirmed by a $H\left(q\right)$ tending to a constant in the long wavelength limit instead of showing the characteristic scaling law $q^{4-\eta }(\eta \simeq 0.85)$ predicted by membrane theory. This unexpected behavior persists up to temperatures of at least 900 K and is a consequence of the fact that in graphane the thermal energy can be accommodated by in-plane bending modes, i.e., modes involving C-C-C bond angles in the buckled carbon layer, instead of leading to significant out-of-plane fluctuations that occur in graphene.

• Received 12 April 2012

DOI:https://doi.org/10.1103/PhysRevB.86.041408