High density mechanical energy storage with carbon nanothread bundle

The excellent mechanical properties of carbon nanofibers bring promise for energy-related applications. Through in silico studies and continuum elasticity theory, here we show that the ultra-thin carbon nanothreads-based bundles exhibit a high mechanical energy storage density. Specifically, the gravimetric energy density is found to decrease with the number of filaments, with torsion and tension as the two dominant contributors. Due to the coupled stresses, the nanothread bundle experiences fracture before reaching the elastic limit of any individual deformation mode. Our results show that nanothread bundles have similar mechanical energy storage capacity compared to (10,10) carbon nanotube bundles, but possess their own advantages. For instance, the structure of the nanothread allows us to realize the full mechanical energy storage potential of its bundle structure through pure tension, with a gravimetric energy density of up to 1.76 MJ kg−1, which makes them appealing alternative building blocks for energy storage devices.

Benefiting from the excellent tensile properties of individual CNTs, the CNT bundles can maintain a much higher gravimetric energy density (over 6.0 MJ kg -1 ) compared with that of the carbon nanothread bundles. To note that current CNT bundles are normally fabricated through spinning or twisting to maintain a densely packed structure as a loose structure has low mechanical performance. 1 The low mechanical performance is majorly originated from low interfacial load transfer efficiency, which can be effectively enhanced by introducing certain percentage of initial torsion. 2 Researchers have tried to introduce inter-tubular covalent bonds between CNTs, which however results in detrimental effect on the mechanical properties of CNT bundles. 3

Supplementary Note 1 | Fracture mechanisms of the bundle structure
For the bundle structure, the fracture usually initiates from the boundary region, which is expected due to the loading condition. Under torsion, the bonds at the interface needs to transfer the external load to the deformable region through bond torsion, which inevitably induce a local stress/strain concentration. In other words, the fracture behavior of the bundle is expected to be independent on the sample length, and the applied boundary condition would not affect our predictions. As such, the sample length is not expected to influence the torsional behavior of the bundle structure. To further affirmed such phenomenon, two sets of simulations have been performed, including: a relaxation simulation continued from the twisted bundle-7 structure (for both CNT and carbon nanothread) and the twist deformation simulation for nanothread-A bundle-7 with different sample length. For the relaxation simulation, the twist loads were removed, and the bundle was relaxed for 500 ps with the fixed boundaries. For nanothread-A, the atomic structure at the twist angle of 8.38 rad was selected. For CNT, the atomic structure at the twist angle of 2.09 rad was considered.
As shown in Supplementary Figure 5, the potential energy of the bundle structure is very stable, suggesting no structural change during the relaxation process. By tracking the atomic configurations for CNT bundle and nanothread-A bundle, almost identical stress distribution patterns are observed before and after the relaxation. The stress concentration at the boundary regions are still existing after relaxation process.

Supplementary Note 2 | Theoretical description of the bundle deformation
The mechanical energy stored in the twisted nanothread bundle structure can be described by following the theoretical framework established by Tománek and coauthors for CNT, 4, 5 which is based on the Hooke's law with a consideration of linear elasticity. In detail, the total strain energy can be calculated from: (S1) Here, + = < / < ; /,2 = ?1 + ( 2 / < ) -− 1 ; 4 = < / , with 2 = 2 [1 + ( <  Given the same (dimensionless) torsional strain + and compression strain 5 for all nanothread filaments in the bundle configuration, the tensile and bending deformation of the filament is the same within each layer for a same coil radius.
Therefore, for the bundle with 1 < ≤ 7, Eq. S1 can be approximated as: ultra-thin bundle structures, the relationships between different strain components will be the same for larger bundles in experiments. In other words, it can be predicted that for larger bundles, tensile deformation will be the dominant deformation mode when the bundle is under twist. We should highlight that the theoretical model has assumed an ideal bundle with uniform filaments. Experimentally, the bundle may contain different types of filaments, the filaments may differ in length, or some filaments may be defective. All these different bundles deserve a substantial research effort in the future, and the theoretical predictions may serve as the upper limit of their mechanical performance.