The van der Waals interactions of concentric nanotubes

Abstract

For sparse materials like graphitic systems and carbon nanotubes the standard density functional theory (DFT) faces significant problems because it cannot accurately describe the van der Waals interactions that are essential to the carbon-nanostructure materials behavior. While standard implementations of DFT can describe the strong chemical binding within an isolated, single-walled carbon nanotube, a new and extended DFT implementation is needed to describe the binding between nanotubes. We here provide the first steps to such an extension for parallel and concentric nanotubes through an electron-density based description of the materials coupling to the electrodynamical field. We thus find a consistent description of the (fully screened) van der Waals interactions that bind the nanotubes across the low-electron-density voids between the nanotubes, in bundles and as multiwalled tubes.

Van der Waals interactions of parallel and concentric nanotubes

“…The frequency integrals, now decoupled from the spatial integrals, do not depend on the nanotube separation d and are therefore identical to the frequency factors defined in Ref. [11] …”

“…For an external electric field of strength E 0 (u), oriented perpendicular to the nanotubes or along the nanotubes, we may factorize the electric potential as φ(s, u, u 0 ) = −E 0 (u)W (s, u, u 0 ) cos θ and solve ∇ · {(1 + 4πχ 0 ) ∇φ} = 0. The components of the effective susceptibility then become [11] …”

Nature and strength of bonding in a crystal of semiconducting nanotubes: van der Waals density functional calculations and analytical results

“…͑16͔͒ that invokes a longwavelength form of the electrodynamical response but respects the morphology of the interaction problem. 40 The main panel shows that the full vdW-DF calculations are necessary around the binding separations ⌬ bind ϳ 3.5 Å. Here, the interaction is significantly enhanced compared with estimates based on the asymptotic dipolar response.…”

“…The analysis is possible to carry out for nonisotropic external-field susceptibilities, 40,41 but for an interpretation of our vdW-DF calculations of CNT interactions, it is sufficient to consider isotropic susceptibilities ␣ eff . We focus on the interaction regime where effects of the CNT morphology dominate the variation in E c nl Ϸ E vdW with distance.…”

Symmetry Based Fundamentals of Carbon Nanotubes

“…also thin SWNTs or inorganic tubes may be considered); possible deficiencies of the semiempirical foundation are at least compensated for to some extent controllable parameters (enabling to fit the experiments), and complete symmetry implementation (due to application of the DF potential through the tight-binding calculations). However, currently all DF methods fail to describe correctly Van der Waals systems; therefore, these methods are not reliable for multi-wall carbon nanotubes, despite some recent attempts to overcome this difficulty [29].…”