Mathematical Modeling on Ultra-Filtration Using Functionalized Carbon Nanotubes

Abstract

Numerous computational simulations have been performed for the study of the ultra-filtration using carbon nanotubes. However, most carbon nanotubes have dangling bonds at nanotube rims, which severely compromise the validity of such computational simulations. In this paper, we use applied mathematical modeling and the continuous approximation to investigate the acceptance conditions for the water and ions permeating through the functionalized carbon nanotube, and in particular the sodium and chloride ions. Such problem is important for future ion transport and detection. For the nanotube of radius 3.8 Å, while the presence of a tiny positive charge at the nanotube rim will prevent water from entering the nanotube, the presence of a negative charge at the nanotube rim will always enhance the water absorption. With a proper tuning of the total charge at the nanotube entry, we can selectively sieve the sodium or chloride ions. The mathematical framework presented here possesses the merit of delivering deductive and rapid results.