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The molecular interactions between a single-strand deoxyribonucleic acid (ssDNA) molecule and a carbon nanotube (CNT) are modelled to determine the suction force experienced by the DNA which is assumed to be located on the axis near the open end of a single-walled CNT (SWCNT). They determine the optimal nanotube radius for encapsulation, that is, the radius of the nanotube with the lowest interaction energy. The expression for the molecular interaction energy is derived from the 6-12 Lennard-Jones potential together with the continuum approach, which assumes that a discrete atomic structure can be replaced by a line or a surface with constant average atomic density. It was found that an ssDNA can be encapsulated inside a SWCNT with a radius larger than 8.2 Å, and it is shown that the optimal SWCNT needed to fully enclose the DNA molecule has a radius of 8.8 Å, which approximately corresponds to the chiral vector numbers (13,13). This means that if it is wished to encapsulate the ssDNA into a CNT, an ideal SWCNT to do this is (13, 13) which has the required radius of 8.8 Å.

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Nanotubes, such as those made of carbon, silicon, and boron nitride, have attracted tremendous interest in the research community and represent the starting point for the development of nanotechnology. In the current study, the use of nanotubes as a means of drug delivery and, more specifically, for cancer therapy, is investigated. Using traditional applied mathematical modelling, I derive explicit analytical expressions to understand the encapsulation behaviour of drug molecules into different types of single-walled nanotubes. The interaction energies between three anticancer drugs, namely, cisplatin, carboplatin, and doxorubicin, and the nanotubes are observed by adopting the Lennard–Jones potential function together with the continuum approach. This study is focused on determining a favourable size and an appropriate type of nanotube to encapsulate anticancer drugs. The results indicate that the drug molecules with a large size tend to be located inside a large nanotube and that encapsulation depends on the radius and type of the tube. For the three nanotubes used to encapsulate drugs, the results show that the nanotube radius must be at least 5.493 Å for cisplatin, 6.452 Å for carboplatin, and 10.208 Å for doxorubicin, and the appropriate type to encapsulate drugs is the boron nitride nanotube. There are some advantages to using different types of nanotubes as a means of drug delivery, such as improved chemical stability, reduced synthesis costs, and improved biocompatibility.