Thermal rippling behavior of graphane

TL;DR

This study uses atomistic simulations to show that hydrogenated graphene (graphane) remains flat and un-rippled at high temperatures, unlike graphene, due to its unique in-plane bending modes absorbing thermal energy.

Contribution

It reveals that graphane exhibits bounded height fluctuations and does not follow membrane theory scaling, contrasting with graphene's rippling behavior.

Findings

Graphane remains un-rippled up to 900 K.

Height fluctuations in graphane are bounded and do not follow membrane theory.

Thermal energy in graphane is absorbed by in-plane bending modes.

Abstract

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 $<h^2>$ and the height-height correlation function $H(q)$ for different system sizes and temperatures we show that hydrogenated graphene is an un-rippled system in contrast to graphene. The height fluctuations are bounded, which is confirmed by a $ H(q) $ 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 behaviour 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.