Energetics of nanoscale graphitic tubules

Robertson, Daniel H.; Brenner, Donald W.; Mintmire, J. W.

doi:10.1103/physrevb.45.12592

Cited by 943 publications

(569 citation statements)

References 15 publications

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“…The molecular potential energy of the molecular model of a graphene sheet subjected to cylindrical bending (to form a nanotube) was equated with the strain energy of an equivalent-continuum plate subjected to cylindrical bending. [43] 0.021 Sawada and Hamada [44] 0.017 Miyamoto et al [45] 0.020 Hernandez et al . (n,n) [46] 0.021 Hernandez et al (n,0) [46] 0.022 Average 0.018 …”

Section: Discussionmentioning

confidence: 99%

“…Values of the force constant, K ω , have been determined using computational chemistry data from several studies [36,[43][44][45][46] and equation (25). Even though the computational chemistry data was obtained for the specific case of bending of graphene sheets to form complete nanotubes or nanotube-like structures, the concepts of structural mechanics can be implemented such that these values could apply to any bending mode of graphene sheets.…”

Section: Molecular Mechanics Modelmentioning

confidence: 99%

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Equivalent-continuum modeling of nano-structured materials

Odegard

2002

Composites Science and Technology

581

302

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A method has been proposed for developing structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with equivalent-continuum models. It has been shown that this substitution may be accomplished by equating the molecular potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As important examples with direct application to the development and characterization of singlewalled carbon nanotubes and the design of nanotube-based structural devices, the modeling technique has been applied to two independent examples: the determination of the effectivecontinuum geometry and bending rigidity of a graphene sheet. A representative volume element of the chemical structure of graphene has been substituted with equivalent-truss and equivalentcontinuum models. As a result, an effective thickness of the continuum model has been determined. The determined effective thickness is significantly larger than the inter-planar spacing of graphite. The effective bending rigidity of the equivalent-continuum model of a graphene sheet was determined by equating the molecular potential energy of the molecular model of a graphene sheet subjected to cylindrical bending (to form a nanotube) with the strain energy of an equivalent-continuum plate subjected to cylindrical bending.

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Section: Discussionmentioning

confidence: 99%

Section: Molecular Mechanics Modelmentioning

confidence: 99%

Equivalent-continuum modeling of nano-structured materials

Odegard

2002

Composites Science and Technology

581

302

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“…The most extensively used (e.g. [17,18,32,35,39,40]) potential function (mainly in Molecular Dynamics simulations) is the Tersoff-Brenner (TB) potential [37,38]. However, its formulation is relatively complicated for further numerical implementation due to effects of variation in length and angle are coupled, hence can be approached by the Morse potential [9,30] function for longitudinal strains below 10%, which is given by:…”

Section: Interatomic Potentialsmentioning

confidence: 99%

“…A special issue not explicitly included in MSM models (although the wall-curvature was included in the equations) is the preenergy, defined as the excess of strain energy from an infinite planar graphene sheet to the nanotube [17,32]. As has been shown [5,33,34,35], this preenergy is proportional to the curvature of the wall 1/R 2 (where R is the tube radius) leading to an stabilization effect into its cross-sectional area. In this paper, we introduce the preenergy as a system of initial strains which produces a 'prestressed state' previous to the action of any external loading.…”

Section: Introductionmentioning

confidence: 99%

A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation

Merli

Lázaro

Monleón

et al. 2013

Computers & Structures

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ElsevierMerli Gisbert, R.; Lazaro, C.; Monleón Cremades, S.; Domingo Cabo, A. (2013). A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation. Computers and Structures. 127:68-87. doi:10.1016/j.compstruc.2012.11.023 AbstractA new general formulation for the mechanical behavior of Single-Walled Carbon Nanotubes is presented. Carbon atoms are located at the nodes of an hexagonal honeycomb lattice wrapped into a cylinder. They are linked by covalent C − C bonds represented by a truss or spring element, and the three-body interaction among two neighboring covalent bonds is reproduced by a rotational spring. The main advantage of our approach is to allow general load conditions (and any chirality) with no need of specific formulation for each load case, in contrast with previous works [26], [27], [31]. Four load configurations are adopted: tension, compression, bending and torsion of cantivelered SWCNTs. Calculations with our own codes for both AMBER and Morse potential functions have been carried out, aimed to compare their final results. Initial positions of the atoms (nodes) into nanotube cylindrical geometry has been reproduced in great detail by means of a conformal mapping from the planar graphene sheet. Therefore, the effect of initial SWCNTs curvature has been introduced explicitly through a system of initial stresses (prestressed state) which contribute to maintain their circular cross-section. Numerical results and deformed shapes for nanotubes with several diameters and chiralities under each load case are used to obtain their mechanical parameters with the only objective of checking the present formulation with previous works [28], [30], [20], [24]. Also, the significance of the atomistic discrete simulations at the nano-scale size against other continuum models is underlined.

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“…Stiffness of CNTs measured experimentally [1] and calculated from simulations [2] is of the order of 1000 GPa, while the nearest competitive fiber (SiC whiskers) has utmost 400 GPa in stiffness [3]. CNTs have tensile strength of up to 150 GPa [4].…”

Section: Introductionmentioning

confidence: 99%