Elastic bending modulus of monolayer graphene

By Qiang Lu, Marino Arroyo, Rui Huang. 2009

411 citations recorded by the source corpus.

An analytic formula is derived for the elastic bending modulus of monolayer graphene based on an empirical potential for solid-state carbon atoms. Two physical origins are identified for the non-vanishing bending stiffness of the atomically thin graphene sheet, one due to the bond-angle effect and the other resulting from the bond-order term associated with the dihedral angles. The analytical prediction compares closely with ab initio energy calculations. Pure bending of graphene monolayers into cylindrical tubes is simulated by a molecular mechanics approach, showing slight nonlinearity and anisotropy in the tangent bending modulus as the bending curvature increases. An intrinsic coupling between bending and in-plane strain is noted for graphene monolayers rolled into carbon nanotubes.

Subfields: Electrical and Electronic Engineering, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/991201358aae80b4ae8f8698c2c1e4dfe9418928

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Electrical and Electronic Engineering

1. Wei Gao
2. Rui Huang
3. Q. Zheng
4. Qiang Lu
5. Harold S. Park
6. Huajian Gao
7. Yong Zhu
8. Teng Zhang

In Materials Chemistry

1. Rui Huang
2. Wei Gao
3. Qiang Lu
4. Teng Zhang
5. Huajian Gao
6. Z. Aitken
7. Harold S. Park
8. Yong Zhu

Citations in the corpus

• NONLINEAR MECHANICS OF SINGLE-ATOMIC-LAYER GRAPHENE SHEETS (2009, background): “However, we found that the derivative of the dihedral term with respect to the bond angle does not vanish even at the ground state [Lu et al., 2009], leading to a noticeably higher bending modulus than that predicted by the first generation Brenner potential (no dihedral term).”
• A review on mechanics and mechanical properties of 2D materials—Graphene and beyond (2016, background): “Instead, they are independent properties resulting from multibody interactions among carbon atoms in a monolayer [29,44,46,54,55,58].”
• Effects of mismatch strain and substrate surface corrugation on morphology of supported monolayer graphene (2010, background): “(7) is similar to that for thin film wrinkling [23], except for the fact that the bending modulus of monolayer graphene is not directly related to the in‐plane modulus by the classical elastic plate theory [13].”
• Thermomechanics of monolayer graphene: Rippling, thermal expansion and elasticity (2014, methodology): “The present work combines MD simulations of graphene with a statistical mechanics (SM) approach for the study of thermomechanical properties of monolayer graphene.”
• Mechanical properties of two-dimensional materials and their applications (2018, neutral): “For theoretical prediction, various simulations have been carried out [36, 128].”
• Effects of functional groups on the mechanical and wrinkling properties of graphene sheets (2010, background): “framework of nonlinear continuum mechanics for GSs and a formula for the elastic bending modulus of GSs have also been developed [26].”
• Tailoring the mechanical properties of 2D materials and heterostructures (2018, background): “The physical origin of B in a single layer graphene is due to the carbon bonds torsional stiffness and the bond-order term associated with the dihedral angles [118] which differs from the tensile/ compression seen above/below the neutral surface in continuum thin plates [123].”