Related Experiment Video
Updated: May 27, 2026

Resonance Raman Spectroscopy of Extreme Nanowires and Other 1D Systems
Published on: April 28, 2016
Universal curves for the van der Waals interaction between single-walled carbon nanotubes
Evgeny G Pogorelov1, Alexander I Zhbanov, Yia-Chung Chang
1Research Center for Applied Sciences, Academia Sinica, 128, Section 2, Academia Road, Nankang, Taipei 115, Taiwan.
Abstract:
We report very simple and accurate algebraic expressions for the van der Waals (VDW) potentials and the forces between two parallel and crossed carbon nanotubes. The Lennard-Jones potential for two carbon atoms and the method of the smeared-out approximation suggested by Girifalco were used. It is found that the interaction between parallel and crossed tubes is described by two universal curves for parallel and crossed configurations that do not depend on the van der Waals constants, the angle between tubes, and the surface density of atoms and their nature but only on the dimensionless distance. The explicit functions for equilibrium VDW distances, well depths, and maximal attractive forces have been given. These results may be used as a guide for the analysis of experimental data to investigate the interaction between nanotubes of various natures.
More Related Videos
Related Concept Videos
Van der Waals Interactions
Van der Waals Equation
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
The Van der Waals Equation
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation
¹H NMR: Long-Range Coupling
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.

