RESEARCH INTERESTS

Mathematical modeling in nanotechnology

In my PhD thesis, I studied three broadly mechanical issues for the nano-scaled materials.
Firstly, the Lennard-Jones potential function and the continuum approximation are undertaken to investigate the mechanical properties of nanostructures. In particular, the van der Waals interaction energy, the suction energy, the offset location and the oscillatory behavior are analytically determined.
The second area is the joining of nanostructures by invoking the variation principle. In this study, I considered both the carbon and boron nitride nanostructures where the essential mathematical ideas for combining boron nitride structures are quite different to those required for connecting the corresponding carbon structures. Initially, toroidal molecules are described, and the perpendicular joining structures for carbon nanotubes and flat graphene are examined.
The third area involves the elastic model of carbon nanotubes. Here, carbon nanotubes are assumed to be modeled as transversely isotropic linearly elastic materials. The equilibrium equations are derived and they can be shown to generalize those for isotropic materials. Further, wave-like deformations on the outer-most surface of the oscillating carbon nanotubes are investigated.

Another topic that I am currently studying involves the encapsulation of Titanium dioxide (TiO2) in the nano-containers. The particles of TiO2 have been suggested to be associated with the cell killing effect of UV light, and the TiO2 photocatalysis process has been widely use to kill tumor cells or cancer cells. However, in order to deliver TiO2 to the target cells, the particles might be in contract with some good cells. Therefore, the encapsulation of TiO2 into nanocapsules, such as C60 fullerenes and carbon nanotubes, is a design for the targeted drug delivery. This project will undertake the Lennard-Jones function to determine the position of TiO2 in the capsule, and also the relation between the amount of TiO2 and the size of nanocapsules.