Dislocation onset and nearly axial glide in carbon nanotubes under torsion

D.-B. Zhang, R. D. James, T. Dumitrică
2009 Journal of Chemical Physics  
The torsional plastic response of single-walled carbon nanotubes is studied with tight-binding objective molecular dynamics. In contrast with plasticity under elongation and bending, a torsionally deformed carbon nanotube can slip along a nearly axial helical path, which introduces a distinct ͑+1,−1͒ change in wrapping indexes. The low energy realization occurs without loss in mass via nucleation of a 5-7-7-5 dislocation dipole, followed by glide of 5-7 kinks. The possibility of nearly axial
more » ... of nearly axial glide is supported by the obtained dependence of the plasticity onset on chirality and handedness and by the presented calculations showing the energetic advantage of the slip path and of the initial glide steps. The remarkable physical properties of carbon nanotubes ͑CNTs͒ originate in their objective atomic structure 1 where each carbon atom sees precisely the same environment up to rotation and translation. Modulating these properties is highly desirable for various applications and systematic ways to manipulate the perfect arrangement of hexagonal rings are needed. A wealth of experimental data 2 shows that the nearsublimation thermal agitation does not necessarily destroy CNTs. Instead, it can have a positive effect, especially when combining the significant random agitation of the atoms with a coherent component caused by an externally applied deformation. For example, recent experiments on superplasticity 3,4 obtained that CNTs under tensile load can undergo large elongation and thinning without abandoning their perfection. Theoretical studies 5-7 indicated that superplasticity relies on primary microscopic mechanisms, like a mass-conserving glide along a helical slip path, as well as on a nearly axial kink propagation with dimers directly breaking out of the lattice. Remarkably, each mass-conserving glide step lowers the CNT diameter and changes its index from ͑n , m͒ to ͑n , m −1͒ or ͑n −1,m͒. Plasticity under bending 8,9 was also described in terms of kink motion along a helical path. What other primary transformations can be induced by external deformation on the hot CNT lattice? To address this question we considered CNT plasticity under another fundamental type of deformation-torsion. Due to recent experimental advances, 10-12 it is now possible to probe CNTs as torsional springs. The popular atomistic modeling tools are unsuitable for modeling this type of deformation. Relying on recent theoretical innovations, 13,14 we describe the CNT's torsional response with objective molecular dynamics ͑MD͒ and predict the possibility of a new mass-conserving nearly axial glide. Such glide cannot be promoted by pure tension. We first indicate by direct calculation the susceptibility of twisted ͑n , m͒ CNTs to the new slip path. Next, we show that the practical realization can be largely accomplished without the need of preexisting defects as it can be triggered by the nucleation of a 5-7-7-5 dislocation dipole. Once nucleated, the 5-7 kinks glide away from each other, leaving behind an ͑n +1,m −1͒ CNT. Objective MD represents a generalization of the widely used MD under periodic boundary conditions ͑PBCs͒. In PBC MD, the solution satisfies the specified translational invariance of a CNT. In objective MD, the helical symmetry of a CNT is no longer concealed and the solution is invariant to the specified helical group operations of a CNT. Here, we describe an infinitely long CNT with Index i runs over the N 0 atoms at locations X i inside the objective simulation domain, which in general is different from the PBC one, and index labels the various domain replicas. Rotational matrix R of angle and the axial vector T characterize the helical transformations applied to the objective domain. Given the objective domain, the 0 value for a strain-free ͑n , m͒ CNT has analytical form. 13 Note that objective MD has been previously applied to study linear elasticity as well as torsional and bending instabilities of CNTs. 13,15 Here we show a new utility in the context of plasticity and defect glide. Atomistic simulations based on empirical potentials have been carried out recently on the torsional response of CNTs. [16] [17] [18] [19] To minimize the magnitude of the end effects introduced by the employed cluster representation of a realistic micrometer-long CNT, as well as the influence on the strain energy caused by the additional kinematic constraints introduced by fixed boundary conditions, accounting for a large number of atoms was necessary. The widely used PBC MD avoids the spurious end and fixed boundary effects but requires large translational cells or supercells and can describe only discrete torsional deformations compatible with the assumed translational symmetry. 20 The advantage of ob-a͒
doi:10.1063/1.3081627 pmid:19239277 fatcat:fthp5rdgpvfmhld4fuk2impaa4