The stability of two-dimensional (2D) layers and membranes is subject of a long standing theoretical debate. According to the so called Mermin-Wagner theorem, long wavelength fluctuations destroy the long-range order for 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These dangerous fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes making that a two-dimensional membrane can exist but should present strong height fluctuations. The discovery of graphene, the first truly 2D crystal and the recent experimental observation of ripples in freely hanging graphene makes these issues especially important. Beside the academic interest, understanding the mechanisms of stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest for its unusual Dirac spectrum and electronic properties. Here we address the nature of these height fluctuations by means of straightforward atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear due to thermal fluctuations with a size distribution peaked around 70 \AA which is compatible with experimental findings (50-100 \AA) but not with the current understanding of stability of flexible membranes. This unexpected result seems to be due to the multiplicity of chemical bonding in carbon.

Intrinsic ripples in graphene

Mechanisms of metal sorption by biochars: Biochar characteristics and modifications

Biochar-based nano-composites for the decontamination of wastewater: A review.

A review of functionalized carbon nanotubes and graphene for heavy metal adsorption from water: Preparation, application, and mechanism.

Progress in the preparation and application of modified biochar for improved contaminant removal from water and wastewater

Removal of hexavalent chromium from aqueous solutions by a novel biochar supported nanoscale iron sulfide composite.

Preparation and characterization of a novel graphene/biochar composite for aqueous phenanthrene and mercury removal.

Immobilization of hexavalent chromium in contaminated soils using biochar supported nanoscale iron sulfide composite.

Preparation of a novel graphene oxide/Fe-Mn composite and its application for aqueous Hg(II) removal.

Different approaches for preparing a novel thiol-functionalized graphene oxide/Fe-Mn and its application for aqueous methylmercury removal

Yao Huang

Papers

Removal of hexavalent chromium from aqueous solutions by a novel biochar supported nanoscale iron sulfide composite.

Preparation and characterization of a novel graphene/biochar composite for aqueous phenanthrene and mercury removal.

Immobilization of hexavalent chromium in contaminated soils using biochar supported nanoscale iron sulfide composite.

Preparation of a novel graphene oxide/Fe-Mn composite and its application for aqueous Hg(II) removal.

Different approaches for preparing a novel thiol-functionalized graphene oxide/Fe-Mn and its application for aqueous methylmercury removal