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Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, for example, it can bend without twisting, but cannot twist without bending. Given the ubiquity of ribbon-like biopolymers in biology and chemistry, here we study the statistical mechanics of microscopic inextensible, fluctuating ribbons loaded by forces and torques. We show that these ribbons exhibit a range of topologically and geometrically complex morphologies exemplified by three phases—a twist-dominated helical phase (HT), a writhe-dominated helical phase (HW), and an entangled phase—that arise as the applied torque and force are varied. Furthermore, the transition from HW to HT phases is characterized by the spontaneous breaking of parity symmetry and the disappearance of perversions (that correspond to chirality-reversing localized defects). This leads to a universal response curve of a topological quantity, the link, as a function of the applied torque that is similar to magnetization curves in second-order phase transitions.
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Symmetry-adapted tight-binding electronic structure analysis of carbon nanotubes with defects, kinks, twist, and stretch
In this paper, a symmetry-adapted method is applied to examine the influence of deformation and defects on the electronic structure and band structure in carbon nanotubes. First, the symmetry-adapted approach is used to develop the analog of Bloch waves. Building on this, the technique of perfectly matched layers is applied to develop a method to truncate the computational domain of electronic structure calculations without spurious size effects. This provides an efficient and accurate numerical approach to compute the electronic structure and electromechanics of defects in nanotubes. The computational method is applied to study the effect of twist, stretch, and bending, with and without various types of defects, on the band structure of nanotubes. Specifically, the effect of stretch and twist on band structure in defect-free conducting and semiconducting nanotubes is examined, and the interaction with vacancy defects is elucidated. Next, the effect of localized bending or kinking on the electronic structure is studied. Finally, the paper examines the effect of 5–8–5 Stone–Wales defects. In all of these settings, the perfectly matched layer method enables the calculation of localized non-propagating defect modes with energies in the bandgap of the defect-free nanotube.
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- Award ID(s):
- 1635407
- PAR ID:
- 10547028
- Publisher / Repository:
- SAGE Publications
- Date Published:
- Journal Name:
- Mathematics and Mechanics of Solids
- Volume:
- 26
- Issue:
- 5
- ISSN:
- 1081-2865
- Format(s):
- Medium: X Size: p. 667-682
- Size(s):
- p. 667-682
- Sponsoring Org:
- National Science Foundation
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