Limits of mechanical energy storage and structural changes in twisted carbon nanotube ropes

Arrays of twisted carbon nanotubes and nanotube ropes are equivalent to a torsional spring capable of storing energy. The advantage of carbon nanotubes over a twisted rubber band, which is used to store energy in popular toys, is their unprecedented toughness. Using ab initio and parametrized density functional calculations, we determine the elastic range and energy storage capacity of twisted carbon nanotubes and nanotube ropes. We find that a twisted nanotube rope may reversibly store energy by twisting, stretching, bending, and compressing constituent nanotubes. We find that in the elastic regime, the interior of a twisted rope encounters hydrostatic pressures of up to tens of GPa. We examine the limits of reversible energy storage and identify structural deformations beyond the elastic limit, where irreversibility is associated with breaking and forming new covalent bonds. Under optimum conditions, the calculated reversible mechanical energy storage capacity of twisted carbon nanotube ropes surpasses that of advanced Li-ion batteries by up to a factor of 4 to 10.

Figure 1

Energy investment and structural snap shots of an isolated carbon nanotube subject to torsion [(a), (b)], stretching [(c, (d)], and bending [(e), (f)]. (a) Twist energy per atom $\Delta E_t/N$ as a function of the dimensionless twist strain ${\epsilon }_{\circ }$ of (10,10) and (5,5) nanotubes with metastable circular or flattened cross sections. (c) Stretch energy per atom $\Delta E_s/N$ of isolated and bundled (10,10) and (18,0) nanotubes as a function of the axial strain ${\epsilon }_{\parallel }$. (e) Bending energy per atom $\Delta E_b/N$ as a function of the bending strain ${\epsilon }_{\angle }$ for individual (5,5), (10,10), (15,15), and (20,20) nanotubes. Structural snap shots in (b), (d), and (f) are presented for the (10,10) nanotube. Only the low-energy branch of flattened nanotubes is presented in (b). All results, except where specified otherwise, are based on DFTB.

Figure 2

Changes in the total energy and equilibrium structure of a close-packed lattice of (18,0) nanotubes subject to hydrostatic pressure. (a) Structural changes during deformation pathways A, B, C, and D as a function of pressure, defined by the scale on the left, in end-on view. (b) Compression energy per atom $\Delta E_c/N$, (c) mass density ${\rho }_g$, and (d) fraction of $s{p}^3$ bonded carbon atoms as a function of hydrostatic pressure $p$. Conditions for abrupt structural changes are indicated by arrows.

Figure 3

Structural deformations and energy storage in twisted nanotube ropes. (a) Schematic of a rope, where individual nanotube strands of diameter $d_{(n,m)}$ form coils defined by radius $\rho$ and pitch length $\lambda$. (b) End-on and (c) side view of twisted ropes with different numbers of ($n,m$) nanotube strands at different values of the twist strain ${\epsilon }_{\circ }$. (d) Total gravimetric energy storage density $J$ of these ropes. DFTB results are represented by the data points. The solid lines are fits to these data points using Eq. (11). The red dashed lines represent the contribution of all energy storage mechanisms except twisting, based on Eq. (12). The notation $(n,m)-N_s$ describes a rope containing $N_s$ strands of $(n,m)$ nanotubes.

Figure 4

Gravimetric energy storage density $J$ and its components as a function of the dimensionless twist strain ${\epsilon }_{\circ }$ in ropes containing $2–19$ (10,10) nanotubes. Solid dots indicate branches of those mechanisms, where the elastic limit has been reached first. The dotted line indicates the maximum energy storage density of a Li-ion battery.

Figure 5

Optimum number of nanotube strands $N_{s,\mathrm{opt}}$ that maximizes energy storage in ropes of carbon nanotubes with diameter $d$. The dashed line is a guide to the eye.