Anomalous phonon behavior of carbon nanotubes: First-order influence of external load

Amin Aghaei, Kaushik Dayal, Ryan S. Elliott

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External loads typically have an indirect influence on phonon curves, i.e., they influence the phonon curves by changing the state about which linearization is performed. In this paper, we show that in nanotubes, the axial load has a direct first-order influence on the long-wavelength behavior of the transverse acoustic (TA) mode. In particular, when the tube is force-free, the TA mode frequencies vary quadratically with wave number and have curvature (second derivative) proportional to the square-root of the nanotube's bending stiffness. When the tube has non-zero external force, the TA mode frequencies vary linearly with wave number and have slope proportional to the square-root of the axial force. Therefore, the TA phonon curves - and associated transport properties - are not material properties but rather can be directly tuned by external loads. In addition, we show that the out-of-plane shear deformation does not contribute to this mode and the unusual properties of the TA mode are exclusively due to bending. Our calculations consist of 3 parts: First, we use a linear chain of atoms as an illustrative example that can be solved in close-form; second, we use our recently developed symmetry-adapted phonon analysis method to present direct numerical evidence; and finally, we present a simple mechanical model that captures the essential physics of the geometric nonlinearity in slender nanotubes that couples the axial load directly to the phonon curves. We also compute the density of states and show the significant effect of the external load.

Original languageEnglish (US)
Article number023503
JournalJournal of Applied Physics
Issue number2
StatePublished - Jan 14 2013

Bibliographical note

Funding Information:
Amin Aghaei and Kaushik Dayal thank AFOSR Computational Mathematics (FA9550-09-1-0393) and AFOSR Young Investigator Program (FA9550-12-1-0350) for financial support. Ryan Elliott acknowledges support from the NSF CAREER Grant No. CMMI-0746628 and The University of Minnesota Supercomputing Institute. Kaushik Dayal also acknowledges support from NSF Dynamical Systems (0926579), NSF Mechanics of Materials (CAREER-1150002), and ARO Solid Mechanics (W911NF-10-1-0140). Amin Aghaei also acknowledges support from the Dowd Graduate Fellowship. This work was also supported in part by the NSF through TeraGrid resources provided by Pittsburgh Supercomputing Center. Kaushik Dayal thanks the Hausdorff Research Institute for Mathematics at the University of Bonn for hospitality. We thank Richard D. James for useful discussions.


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