Suction Energy for Double-Stranded DNA Inside Single-Walled Carbon Nanotubes

Abstract

Summary Deoxyribonucleic acid (DNA) and carbon nanotubes (CNTs) constitute hybrid materials with the potential to provide new components with many applications in various technology areas, such as molecular electronics, field devices and medical applications. Using classical applied mathematical modelling, we investigate the suction force experienced by a double-stranded DNA (dsDNA) molecule which is assumed to be located on the axis near an open end of a semi-infinite single-walled CNT. We employ both the 6-12 Lennard-Jones potential and the continuum approximation, which assumes that a discrete atomic structure can be replaced by a surface with constant average atomic density. While most research in the area is dominated by molecular dynamics simulations, here we use elementary mechanical principles and classical applied mathematical modelling techniques to formulate explicit analytical criteria and ideal model behaviour. We observe that the suction behaviour depends on the radius of the CNT, and we predict that it is less likely for a dsDNA molecule to be accepted into the CNT when the value of the tube radius is ${<}12.9$ Å. The dsDNA molecule will be accepted into the CNT for radii lager than 13 Å, and we show that the optimal single-walled CNT necessary to fully enclose the DNA molecule has a radius of 13.56 Å, which approximately corresponds to the chiral vector numbers (20, 20). This means that the ideal single-walled CNT to be used to encapsulate a dsDNA is (20, 20) which has the required radius of 13.56 Å.