Entropic Effects of Thermal Rippling on van der Waals Interactions between Monolayer Graphene and a Rigid Substrate

摘要

Graphene monolayer, with extremely low flexural stiffness, displaysspontaneous rippling due to thermal fluctuations at a finite temperature. Whena graphene membrane is placed on a solid substrate, the adhesive interactionsbetween graphene and the substrate could considerably suppress thermalrippling. On the other hand, the statistical nature of thermal rippling adds anentropic contribution to the graphene-substrate interactions. In this paper wepresent a statistical mechanics analysis on thermal rippling of monolayergraphene supported on a rigid substrate, assuming a generic form of van derWaals interactions between graphene and substrate at T = 0 K. The ripplingamplitude, the equilibrium average separation, and the average interactionenergy are predicted simultaneously and compared with molecular dynamics (MD)simulations. While the amplitude of thermal rippling is reduced by adhesiveinteractions, the entropic contribution leads to an effective repulsion. As aresult, the equilibrium average separation increases and the effective adhesionenergy decreases with increasing temperature. Moreover, the effect of a biaxialpre-strain in graphene is considered, and a buckling instability is predictedat a critical compressive strain that depends on both the temperature and theadhesive interactions. Limited by the harmonic approximations, the theoreticalpredictions agree with MD simulations only for relatively small ripplingamplitudes but can be extended to account for the anharmonic effects.