Page 208 - Carbon Nanotube Fibres and Yarns

198 Carbon Nanotube Fibers and Yarns

bond stiffness and angle stiffness, while r 0 and θ 0 represent the equilibrium
spring length and the angle between neighboring springs. More precisely,
a dihedral contribution can also be introduced in the form E T = k T (1 + m
cosβ), where β is the dihedral angle associated with four adjacent beads,
m = 1 or − 1 corresponds to an equilibrium dihedral angle equal to β 0 = 180
degree or 0 degree [113]. The adjacent CNTs interact with each other via
12
6
vdW forces between the beads by E pair = 4ε [(σ/d) − (σ/d) ], where σ is
the distance parameter, ε is the energy well depth at equilibrium, and d is
the distance between two interacting beads. In principle, such CG model is
also valid for describing polymers infiltrated into CNT yarns [114].
Liu et al. [111] investigated the tensile behaviors of CNT yarns with
random and regular CNT stackings using CGMD simulations. In both
cases, CNTs are curled up under external twist loading and bundled by the
intertube vdW forces. A remarkable difference in crisscross and winding
patterns can be found (see Fig. 8.9). In the yarn obtained from the random
stacking, CNTs in different layers bundle into a uniform cylinder under
the coupling effect of twisting and vdW interactions (Fig. 8.9A). On the
other hand, the yarn obtained from the regular stacking displays a different
morphology (Fig. 8.9B). The CNTs form a distinct, uniform crisscross
pattern in some regions, and this pattern unravels at the overlapped regions
due to insufficient vdW interactions. This result indicates that a certain
entanglement of CNT is very helpful to the spinning of CNTs into a yarn,
similar to fiber migration in conventional textile yarn spinning. The tensile

Fig. 8.9 Structural reorganization of CNT yarns with different CNT stacking after twist-
ing. The initial structures were two CNT films with random stacking (A) or regular stack-
ing (B). The CNTs in the top and bottom layers are colored in red and blue, respectively.
(Reproduced with permission from X. Liu, W. Lu, O.M. Ayala, L.-P. Wang, A.M. Karlsson, Q.
Yang, T.-W. Chou, Microstructural evolution of carbon nanotube fibres: deformation and
strength mechanism. Nanoscale 5 (5) (2013) 2002–2008.)