Continuum Theory for Piezoelectric Response of Chiral Nanotubes Under Uniaxial and Torsional Stresses

We develop and solve a continuum theory for the piezoelectric response of nanotubes under applied uniaxial and torsional stresses. We find that the piezoelectric response is controlled by the chiral angle, the aspect ratio, and two dimensionless parameters specifying the ratio of the strengths of the electrostatic and elastic energies. The model is solved in two limiting cases and the solutions are discussed. These systems are found to have several unexpected physical effects not seen in conventional bulk systems, including a strong stretch-twist coupling and the development of a significant bound charge density in addition to a surface charge density. The model is applied to estimate the piezoelectric response of a boron nitride nanotube under uniform tensile stress. Disciplines Physical Sciences and Mathematics | Physics Comments Suggested Citation: Michalski, P.J. and Mele, E.J. (2007). Continuum theory for piezoelectric response of chiral nanotubes under uniaxial and torsional stresses. Physical Review B. 76, 205419. © 2007 The American Physical Society http://dx.doi.org/10.1103/PhysRevB.76.205419 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/123 Continuum theory for piezoelectric response of chiral nanotubes under uniaxial and torsional stresses P. J. Michalski and E. J. Mele Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA Received 10 August 2007; published 14 November 2007 We develop and solve a continuum theory for the piezoelectric response of nanotubes under applied uniaxial and torsional stresses. We find that the piezoelectric response is controlled by the chiral angle, the aspect ratio, and two dimensionless parameters specifying the ratio of the strengths of the electrostatic and elastic energies. The model is solved in two limiting cases and the solutions are discussed. These systems are found to have several unexpected physical effects not seen in conventional bulk systems, including a strong stretch-twist coupling and the development of a significant bound charge density in addition to a surface charge density. The model is applied to estimate the piezoelectric response of a boron nitride nanotube under uniform tensile stress. DOI: 10.1103/PhysRevB.76.205419 PACS number s : 73.63.Fg, 73.63.Bd, 77.65.Ly, 61.46.Fg