Degree Name

Doctor of Philosophy (PhD)


School of Mathematics and Applied Statistics - Faculty of Informatics


The advent of nanotechnology has been the catalyst for considerable advances in industries such as electronics and medicine. The unique physical properties ob- served at the nanoscale has driven numerous investigations into their properties and potential applications. This thesis investigates three aspects of nanotechnology, in particular an alternative formulation for determining the intermolecular force be- tween interacting molecules, nanostructures as nano-oscillators, and nanotubes for applications in nanomedicine. The intermolecular forces between two interacting nanostructures are typically obtained by either summing over all the individual atomic interactions in the dis- crete atom-atom formulation or by using a continuum approach, for which the atoms are assumed to be uniformly distributed over the surface of each molecule. The con- tinuum approach enables highly complicated molecular interactions to be modelled in much less time than the equivalent discrete atom-atom formulation, which can be extremely time consuming. However, a constraint on the continuum approach is that it is mostly applicable to highly symmetrical structures. Motivated by the recent advances in nanotechnology for drug delivery, a hybrid discrete-continuum formu- lation is proposed in this thesis, for which only one of the interacting molecules is discretized and the other is considered to be continuous. The hybrid formulation enables non-regular shaped molecules, such as drugs, to be modelled and this is particularly useful for drug delivery systems which employ carbon nanotubes as car- riers. In a limited comparison the hybrid formulation is shown to compare well to both the discrete atom-atom and continuum formulations. The discovery of carbon nanostructures, such as carbon nanotubes, has gener- ated considerable interest for potential nanomechanical and nanomedical applica- tions. One such device is the high frequency nanoscale oscillator or `gigahertz oscil- lator'. Following the concept of these gigahertz oscillators and the recent discovery of toroidal carbon nanotubes or `nanotori', this thesis examines the mechanics of three nano-oscillators constructed from nanotori. In particular, this thesis investi- gates the C60-nanotorus orbiter which comprises a C60 fullerene orbiting around the inside of a nanotorus. Following this, the nanotorus-nanotube oscillator is examined which comprises a carbon nanotorus which is sucked by van der Waals forces onto the carbon nanotube, and subsequently oscillates along the nanotube axis. Finally, the carbon nanotorus-nanosector orbiter is investigated, in which a small sector of nanotorus orbits around the inside of a second seamless nanotorus of larger radius. These nanotori-based oscillators or orbiters are yet to be constructed and the pur- pose is to assess their feasibility by examining the dominant mechanics. One of the most exciting applications of nanotechnology is the proposed use in drug delivery, and in particular the targeted delivery of drugs using nanotubes. This means of targeted delivery would have significant implications for the future treatment of patients, particularly those suffering from cancer. Understanding the encapsulation and expulsion of drug molecules from nanocarriers is vital for the de- velopment of nanoscale drug delivery. This thesis examines theoretically the loading of molecular cargo into single-walled nanotubes, and the mechanics of a proposed nanosyringe which could be used to directly deliver drugs to cells. In particular, this thesis investigates the suction and acceptance of the anticancer drug molecules cisplatin, paclitaxel and doxorubicin into a carbon nanotube, and the effect on the encapsulation behaviour of alternative nanotube materials, which may be more bio- compatible. In particular, the materials boron nitride, silicon and boron carbide are investigated and compared to the corresponding analysis for the carbon nanotube. Finally, an alternative drug delivery mechanism is investigated, namely a proposed nanosyringe constructed from a double-walled carbon nanotube. For each of these nanomedical applications specific nanotube radii are determined for acceptance and maximum drug uptake, and some overall design guidelines are provided. In summary, the original contributions contained in this thesis are: the develop- ment of the hybrid discrete-continuous method; the concepts of the C60-nanotorus, nanotorus-nanotube and nanotorus-nanosector oscillators; the first mathematical examination for the encapsulation of drug molecules into nanotubes; and the con- cept of a double-walled carbon nanosyringe. These nanomechanical and nanomed- ical applications of nanostructures present exciting possibilities, but there are many practical challenges that need to be overcome before these nanodevices can be real- ized. However, this thesis presents a theoretical study which might facilitate their future development.

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