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Volumn 80, Issue 11, 2009, Pages

Polaron-induced deformations in carbon nanotubes studied using the bicontinuum model

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EID: 70350596029     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.113406     Document Type: Article
Times cited : (3)

References (23)
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    • L. Yang and J. Han, Phys. Rev. Lett. 85, 154 (2000). 10.1103/PhysRevLett. 85.154
    • (2000) Phys. Rev. Lett. , vol.85 , pp. 154
    • Yang, L.1    Han, J.2
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  • 18
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    • L. D. Landau and E. M. Lifshitz "Theory of Elasticity" Pergamon Press Oxford (1986). The density of elastic energy for an isotropic system has the form f=μ uij uij + λ 2 uii ujj, where λ, μ are the Lamé coefficients. Here we renormalize the coefficients to σg =1.
    • (1986)
    • Landau, L.D.1    Lifshitz, E.M.2
  • 19
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    • The expression for Vel is simplified in the long polaron approximation. Using the notation of Ref., we can neglect terms in i qj (the dispersion in the optical branches) as long as (μ- μ′) / a2, (λ- λ′) / a2 α, where a is the length of the polaron. Since (μ- μ′), (λ- λ′) are the order of the square of the speed(s) of sound in graphene or about 108 m2 s-2, whereas α can be expressed in terms of the graphitelike optical frequency α= ωΓ2 /4∼ 1028 s-2 and we have for the length of the polaron a∼10nm, those ratios are thus of the order of 10-4.
    • The expression for Vel is simplified in the long polaron approximation. Using the notation of Ref., we can neglect terms in i qj (the dispersion in the optical branches) as long as (μ- μ′) / a2, (λ- λ′) / a2 α, where a is the length of the polaron. Since (μ- μ′), (λ- λ′) are the order of the square of the speed(s) of sound in graphene or about 108 m2 s-2, whereas α can be expressed in terms of the graphitelike optical frequency α= ωΓ2 /4∼ 1028 s-2 and we have for the length of the polaron a∼10 nm, those ratios are thus of the order of 10-4.


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