Interrupted tubules in filamentous crystals: Elastic analysis

Abstract

We have performed a linear elastic analysis of an interrupted tubule IT in a transversely isotropic, crystalline filamentous crystal. Elastic solutions for stresses, strains, and displacements are derived using the inherent antisymmetry about the plane of the IT defect. We show that the solutions can be expressed in terms of two related strain potentials evaluated in different transformed coordinate systems. The displacements are long range and the defects accumulate significant strain energy. We extend our elastic analysis to IT defects in crystalline nanotube ropes CNTR, where the coupled coordinate systems are necessarily real. We find that the stresses diverge within a dumbell-shaped core region, and the core shape is sensitive to the tube radius. Finally, we discuss finite-size effects and registry-dependent modifications to the analysis.