Offset configurations for single- and double-strand DNA inside single-walled carbon nanotubes

Abstract

Nanotechnology is a rapidly expanding research area, and it is believed that the unique properties of molecules at the nano-scale will prove to be of substantial benefit to mankind, especially so in medicine and electronics. Here we use applied mathematical modelling exploiting the basic principles of mechanics and the 6–12 Lennard-Jones potential function together with the continuum approximation, which assumes that intermolecular interactions can be approximated by average atomic surface densities. We consider the equilibrium offset positions for both single-strand and double-strand DNA molecules inside a single-walled carbon nanotube, and we predict offset positions with reference to the cross-section of the carbon nanotube. For the double-strand DNA, the potential energy is determined for the general case for any helical phase angle ϕ, but we also consider a special case when ϕ = π, which leads to a substantial simplification in the analytical expression for the energy. As might be expected, our results confirm that the global minimum energy positions for a single-strand DNA molecule and a double-strand DNA molecule will lie off axis and they become closer to the tube wall as the radius of the tube increases.