Modeling of titania nanoparticle accumulation at the open end of single-walled carbon nanotubes prior to TiO₂ encapsulation

Carbon nanotubes (CNTs) and titanium dioxide (TiO₂) are perhaps the most well-known nanoparticles. The encapsulation of TiO₂ into CNT could provide ideas for the development of targeted drug delivery systems. It is intuitively understood that due to particle size limitation, the relatively large size of TiO₂ prevents its encapsulation into CNT. However, it could be possible for TiO₂ to encapsulate when those two types of particles are still of comparable size. Motivated by experimental results, the aim of this paper is to utilize the Lennard-Jones (6-12) potential function and applied mathematical modeling tools to understand why TiO₂ nanoparticles aggregate at only one side of the carbon nanotube in order to be encapsulated into the tube (which is part of the main problem surrounding the encapsulation of TiO₂ nanoparticles into SWNT). The theoretical prediction suggests that TiO₂ particles are likely to cluster together since the energy level between two TiO₂ molecules and a carbon nanotube is lower than that between a TiO₂ molecule and a carbon nanotube. This work could be considered as one of the first step models to be used with the analytic approach before developing more complicate ones.