Nanomechanical Energy Storage in Twisted Nanotube Ropes

We determine the deformation energetics and energy density of twisted carbon nanotubes and nanotube ropes that effectively constitute a torsional spring. Using ab initio and parametrized density functional calculations, we identify structural changes in these systems and determine their elastic limits. The deformation energy of twisted nanotube ropes contains contributions associated not only with twisting but also with stretching, bending, and compression of individual nanotubes. We quantify these energy contributions and show that their relative role changes with the number of nanotubes in the rope.

Figure 1

Deformation energy of an individual carbon nanotube subject to stretching and torsion. (a) Stretch energy per length $\Delta E_s/l_0$ of a (10, 10) nanotube as a function of axial strain ${ϵ}_{\Vert }=l/l_0-1$, $l_0$ is the length of an unstrained nanotube segment. (b) Twist energy per length $\Delta E_t/l_0$ as a function of the dimensionless twist rate ${ϵ}_{\circ }$ for an armchair (10, 10) nanotube. (c) Snapshots of a deforming (18, 0) nanotube at different twist rates in side and end-on views. (d) A possible space-filling compact arrangement of individually twisted (18, 0) carbon nanotubes in end-on and side views.

Figure 2

DFTB calculation results for deformation energy of twisted carbon nanotube ropes. (a) Schematic of a rope and the constituting nanotubes deformed to a coil. (b) Snapshots of structural changes, including the flattening of individual nanotubes, induced by twisting of a rope containing 2 and 6 nanotubes. (c) Gravimetric deformation energy density $J$ in twisted nanotube ropes as a function of the rope twist rate $\phi /l_0$.

Figure 3

Structural changes and deformation energy of laterally compressed nanotube arrays, establishing the limits of elasticity and reversibility. (a) Compression energy per nanotube segment $\Delta E_c/l$ in an infinite nanotube lattice as a function of the intertube separation $d$. (b) Equilibrium geometries of stable nanotube array phases subject to different degrees of compression.

Figure 4

Contribution of individual terms of Eq. (5) towards the deformation energy density $J$ in nanotube ropes with 2, 7, and 19 strands. Solid dots terminate branches, where the elastic limit has been reached first.