Solitons in inharmonic lattices: Application to achiral carbon nanotubes

Abstract

In this paper we demonstrate that soliton solutions, whose existence is well known in one-dimensional (1D) model anharmonic systems, can also exist in more complex systems such as carbon nanotubes (CNT). We investigate armchair and zigzag nanotubes and show that both can be simplified to anharmonic 1D lattice models with reduced internal degrees of freedom. Because of the differences in chirality, the armchair and zigzag nanotubes are represented, respectively, by homogeneous (one site per unit cell) and dimerized chains. Starting with the Brenner potential we expand the tube energy into Taylor series and construct effective interaction potentials for model lattices of armchair and zigzag CNTs. We then construct a continuous approximation for the model lattices and derive the Korteweg--de Vries (KdV) equation by applying the reductive perturbation method. The stability of KdV solitons are checked by molecular dynamics simulations of model lattices with parameters specific for CNTs. Numerical simulations attest to the stability of even narrow solitons in most CNTs. We show that solitons can be generated by shock compression at one end of the model chains. The formalism developed can also be applied to many quasi-1D objects such as polymers, nanowires, and others.