Bending Rigidity and Gaussian Bending Stiffness of Single-Layered Graphene

• Published in: Nano letters Vol. 13; no. 1; pp. 26 - 30
• Main Authors: Wei, Yujie, Wang, Baoling, Wu, Jiangtao, Yang, Ronggui, Dunn, Martin L
• Format: Journal Article
• Language: English
• Published: Washington, DC American Chemical Society 09.01.2013
• Subjects: Bending; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Condensed matter: structure, mechanical and thermal properties; Cross-disciplinary physics: materials science; rheology; Density functional theory; Electron states; Exact sciences and technology; Fullerenes and related materials; diamonds, graphite; Gaussian; Graphene; Lipids; Low-dimensional structures (superlattices, quantum well structures, multilayers): structure, and nonelectronic properties; Materials science; Mathematical analysis; Mechanical and acoustical properties of condensed matter; Mechanical properties of nanoscale materials; Methods of electronic structure calculations; Physics; Rigidity; Single wall carbon nanotubes; Specific materials; Stiffness; Surfaces and interfaces; thin films and whiskers (structure and nonelectronic properties); Gaussian bending stiffness; Bending rigidity; Helfrich Hamiltonian; graphene; density functional theory; Singlewalled nanotube; Experimental result; Graphene; Hamiltonians; Morphology; Theoretical study; Bending; Fullerenes; Density functional method; Stiffness; Carbon; Lipid bilayers
• ISSN: 1530-6984; 1530-6992; 1530-6992
• DOI: 10.1021/nl303168w

Bending rigidity and Gaussian bending stiffness are the two key parameters that govern the rippling of suspended graphenean unavoidable phenomenon of two-dimensional materials when subject to a thermal or mechanical field. A reliable determination about these two parameters is of significance for both the design and the manipulation of graphene morphology for engineering applications. By combining the density functional theory calculations of energies of fullerenes and single wall carbon nanotubes with the configurational energy of membranes determined by Helfrich Hamiltonian, we have designed a theoretical approach to accurately determine the bending rigidity and Gaussian bending stiffness of single-layered graphene. The bending rigidity and Gaussian bending stiffness of single-layered graphene are 1.44 eV (2.31 × 10–19 N m) and −1.52 eV (2.43 × 10–19 N m), respectively. The bending rigidity is close to the experimental result. Interestingly, the bending stiffness of graphene is close to that of lipid bilayers of cells about 1–2 eV, which might mechanically justify biological applications of graphene.