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Related Concept Videos

Network Covalent Solids02:18

Network Covalent Solids

Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
To break or to melt a covalent network solid, covalent bonds must be broken. Because covalent bonds are relatively strong, covalent network solids are typically...

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Related Experiment Video

Updated: May 17, 2026

Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding
14:52

Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding

Published on: September 23, 2018

Graphene as a prototype crystalline membrane.

Mikhail I Katsnelson1, Annalisa Fasolino

  • 1Institute for Molecules and Materials, Radboud University Nijmegen, The Netherlands. m.katsnelson@science.ru.nl

Accounts of Chemical Research
|October 18, 2012
PubMed
Summary
This summary is machine-generated.

Graphene, a two-dimensional (2D) membrane, offers a microscopic model for understanding membrane properties. Microscopic and phenomenological theories align on scaling properties but diverge on temperature-dependent bending rigidity.

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Area of Science:

  • Physics and Chemistry
  • Materials Science

Background:

  • Membrane properties are crucial across disciplines, but microscopic understanding is limited.
  • Phenomenological models are common, yet a detailed atomic-level description is challenging.
  • Graphene serves as an ideal two-dimensional (2D) model system for studying membrane behavior.

Purpose of the Study:

  • To review and compare microscopic and phenomenological theories of graphene's structural and thermal properties.
  • To investigate graphene's behavior at high temperatures and its melting process.
  • To provide a foundational understanding of 2D membrane physics.

Main Methods:

  • Microscopic theoretical analysis of graphene's atomic structure and thermal fluctuations.
  • Comparison of theoretical predictions with phenomenological models.
  • Examination of two-dimensional (2D) melting models applied to graphene.

Main Results:

  • Microscopic and phenomenological theories show good agreement for scaling properties of atomic displacements.
  • Phenomenological models fail to explain temperature dependence of bending rigidity.
  • Graphene melting at high temperatures involves decomposition into entangled carbon chains, differing from standard 2D melting.

Conclusions:

  • Graphene provides a valuable platform for validating and advancing membrane theories.
  • Microscopic approaches are essential for capturing complex thermal properties like bending rigidity.
  • The unique melting behavior of graphene highlights its distinct nature as a 2D material.