Binding energy and mechanical stability of single- and multi-walled carbon nanotube serpentines

Recently, Geblinger et al. [Nat. Nanotechnol. 3, 195 (2008)] and Machado et al. [Phys. Rev. Lett. 110, 105502 (2013)] reported the experimental and molecular dynamics realization of S-like shaped single-walled carbon nanotubes (CNTs), the so-called CNT serpentines. We reported here results from continuum modeling of the binding energy γ between different single- and multi-walled CNT serpentines and substrates as well as the mechanical stability of the CNT serpentine formation. The critical length for the mechanical stability and adhesion of different CNT serpentines are determined in dependence of E_iI_i, d, and γ, where E_iI_i and d are the CNT bending stiffness and distance of the CNT translation period. Our continuum model is validated by comparing its solution to full-atom molecular dynamics calculations. The derived analytical solutions are of great importance for understanding the interaction mechanism between different single- and multi-walled CNT serpentines and substrates.