Degree Name

Doctor of Philosophy


School of Mathematics and Applied Statistics


Nanostructures such as carbon and peptide nanotubes have attracted considerable interest in research in nanotechnology due to their remarkable properties and potential applications. A proper understanding of the intermolecular interactions between these nanostructures is crucial for the practical realization of novel nanodevices. In this thesis, we construct mathematical models to determine the interaction energy for these nanostructures. In particular, we consider the noncovalent interaction energies, which significantly contribute to the determination of molecular equilibrium configurations, and determine the mechanical properties of the nanostructure. Here, we employ the continuum approach which assumes that atoms are smeared over the entire surface of the non-bonded molecules providing an average atomic density. This thesis focuses on three specific areas relating to the applications of carbon nanotubes and peptide nanotubes; namely oscillators for nanothermometers; structural conformation of peptide nanotubes and bundles of peptide nanotubes and their applications as artificial ion channels.

There are many possible constructions of carbon nanotubes as nanodevices. In particular we are interested in nano-oscillators which are based on the relative sliding motion between nanotubes. In this thesis, we investigate the mechanics of carbon nanotube oscillators, both shuttle and telescopic configurations which can be used as nanothermometers. The shuttle configuration represents a short outer tube sliding on a fixed inner tube and the telescopic configuration represents an inner tube moving both in the region between the two outer tubes and in the tubes themselves. We investigate the acceptance condition and the suction energy for a semi-infinite inner tube and we determine the oscillatory frequency of a finite inner tube for the shuttle configuration. Factors concerning the optimum performance for both configurations, such as the length of the tube, the inter-wall spacing and the distance between tubes are addressed.

In recent years, peptide nanotubes have been studied extensively in many diverse fields, such as biology, chemistry, material science and medicine. In this thesis, we determine the interactions between two peptide rings through applied mathematical modelling as a first step towards understanding the formation of a complex structure of peptide nanotubes. We determine the energy which dominates the total interaction energy of the system, as well as the size of the cyclic peptide which affects the stacking interaction. Finally, we obtain the equilibrium structures for both parallel, tilted and offset configurations.

One outstanding potential application of peptide nanotubes, which is of particular interest is as an ion channel. Our model incorporates the interactions between D,L-Ala cyclopeptide nanotube and the various ions, the ion-water cluster and the C60 fullerene. We determine whether or not, these ions and molecules are energetically favourable to be encapsulated into the nanotube, and the ideal positions of the ions or molecule in the nanotube are also investigated.

Since peptide nanotubes can be found in the form of bundles, we propose mathematical models for the interaction between peptide nanotubes in a bundle and the interaction of an ion with the bundle. These models describe the stable configurations of peptide nanotube bundles and the encapsulation of an ion into the bundle. The study involving the encapsulation of ions or molecules into a peptide nanotube or a bundle of peptide nanotubes, has relevance for ion selectivity for ion filtration and desalination applications, and for drug delivery applications.

In summary, we present new mathematical models to predict and describe the intermolecular interactions for carbon nanotubes and peptide nanotubes. These theoretical investigations provide new important insights into understanding the complex physical structures of nanotubes and give overall guidelines for future investigations, as well as for the development of novel nanodevices.