A model for carbon nanotube-DNA hybrid using one-dimensional density of states

A model for a carbon nanotube (CNT)-DNA hybrid embedded in an electrolyte solution is developed. The DNA charges are smeared out uniformly onto a cylindrical surface covering the CNT and the response of the CNT to the DNA charges is captured using the one-dimensional density of states (1D DOS) proposed by Mintmire et al. Coupled with the Debye-Hückel equation for the electrolyte, the expressions for the electric potential of the hybrid are obtained for both metallic and semiconducting CNT cores. For the surface charge density of the cylinder corresponding to the physically measured wrapping angles of a single-stranded DNA around a CNT, the developed model predicts that the induced charges on a semiconducting CNT are about one order of magnitude smaller than the DNA charges, while the induced charges on a metallic CNT can be comparable in magnitude to the DNA charges. Because of this, the magnitude of the electric potential for a metallic CNT-DNA hybrid can be as much as approximately equal 30% smaller than that for a semiconducting one. This result can be used to explain the experiments on DNA-assisted CNT separation using ion exchange chromatography.