At present time a monolayer of honeycomb-like packed carbon atoms, also known as graphene, seems to be one of the most promising materials for technologies dealing with membrane applications. As is well known, uniqueness of graphene is commonly associated with either or both peculiarities of its electronic structure and features of its spatial structure as well as mechanical properties of this material as a flexible membrane. The effect of surface inhomogeneity on the band structure and transport properties of graphene samples is the subject of intense investigations in both experimental and theoretical directions.

In presented work we report on the results of modeling of the graphene’s ground state evolution in dissipative mode under temperature-controlled environmental conditions. We estimate spatial extent of the surface corrugations to be of the order of several nanometers (up to 7–8 nm at 300 K), which represents the known experimental and theoretical data to adequate degree of accuracy. The effect of increase in out-of-plane fluctuations with consistent growth of deviations from equilibrium is also appeared in our simulations with the density functional method estimated binding energy potential. The effect however does not result in dangerous crumpling of the layer, keeping the finite height of normal deviations from the plane, which in our model samples reaches the magnitude of ~0.13 nm at high enough temperature. The results obtained confirm available in literature theoretical data concerning the effect of temperature conditions on variation of spatial scale of structural deformations in graphene sheets. We display the tendency of graphene structure to disorder with rising temperature via radial distribution function g(R). By comparing the obtained results with both experimental data and predictions of the other models we conclude on applicability of the used model of dissipative stochastic evolution to nanoscopic graphene structure dynamics.

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