Ion selectivity using membranes comprising functionalized carbon nanotubes

In this paper, we use applied mathematical modelling to investigate the transportation of ions inside functionalized carbon nanotubes, and in particular the transport of sodium and chloride ions. This problem is important for future ion transport and detection, and also arises in ion diffusion inside complex biological channels. Some important future applications of the system for a solvent are ultra-sensitive biosensors and electrolytes for alkaline fuel cells. We model the interactions between the ions and the nanotube by the Lennard-Jones potential and the interactions between the ions and the functional group by the Coulomb potential, while the atomic interactions between the ions is modeled by both the Lennard-Jones and Coulomb potentials. We further assume that the carbon atoms, the charge of the functional group, and the ions are all evenly distributed on the surface of the nanotube, the entry of the nanotube and the envisaged ionic surface, respectively, so that we may use the continuous approximation to calculate the corresponding potential energies. For nanotubes located in salt water, the molecular effects arising from the bulk solution can be extracted from MD simulation studies. Assuming that the solvent is absent, we first determine the acceptance radii for the sodium or chloride ion entering the nanotube, both with and without a functional group, and we then determine the equilibrium positions of two identical ions inside the nanotube. Finally, the transportation time of an intruding ion through the nanotube is deduced from the total axial force. In the presence of a solvent, the molecular effects arising from the bulk solution are examined and we establish that the presence of a solvent stabilizes the selectivity of the ions.