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• W2034677673 abstract "The equilibrium structure and strain energy per atom of $(n,n)$ and $(n,0)$ single-walled carbon nanotubes (SWNTs) are analyzed by developing a simple force-field based atomistic model, in which the pyramidalization angle is used to characterize the inversion term energy associated with the curvature at an atom. Their closed-form expressions are obtained. Good agreements with existing numerical results based on ab initio calculations for various tube diameters from $0.5phantom{rule{0.3em}{0ex}}text{to}phantom{rule{0.3em}{0ex}}2phantom{rule{0.3em}{0ex}}mathrm{nm}$ (curvatures from $4phantom{rule{0.3em}{0ex}}text{to}phantom{rule{0.3em}{0ex}}1phantom{rule{0.3em}{0ex}}{mathrm{nm}}^{ensuremath{-}1}$) validate the present analysis. When the curvature is less than $4phantom{rule{0.3em}{0ex}}{mathrm{nm}}^{ensuremath{-}1}$, the present results show that the strain energy is mainly due to the inversion term, the effects of helicity and bond angle variation are smaller than 10%. Also, the first term of the Taylor expansion of the strain energy expressions is dominant in the strain energy, which is ${C}_{ensuremath{omega}}{a}_{0}^{2}∕(8{d}^{2})$ where ${C}_{ensuremath{omega}}$, ${a}_{0}$, and $d$ are the force constant associated with the pyramidalization angle, bond length in graphene sheet and tube diameter. Based on the proportional relation of the strain energy and $1∕{d}^{2}$, the bending stiffness of SWNTs is obtained by comparing with the strain energy of a corresponding cylindrical shell. However, when the curvature becomes larger, the helicity effect and the energy due to the bond angle variation will become significant. As a result, the nonlinear behavior of the tube bending may occur." @default.
• W2034677673 created "2016-06-24" @default.
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• W2034677673 date "2005-04-21" @default.
• W2034677673 modified "2023-10-06" @default.
• W2034677673 title "Equilibrium structure and strain energy of single-walled carbon nanotubes" @default.
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• W2034677673 doi "https://doi.org/10.1103/physrevb.71.165427" @default.
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