The production of intricate structures at the nanoscale has gone from fantasy to reality in just a few decades. This rapid speed of development in experimental techniques has left a large gap for mathematicians to fi􏰀ll, whether by optimising existing methods or developing predictive tools to lower to cost (both time and money) of experimentation and fabrication. In this seminar I will begin with a background and review including discussing carbon materials and polycyclic aromatic hydrocarbons and their uses; the Lennard-Jones potential and its use as an interatomic potential function to model van der Waals forces and why this potential is relevant to carbon materials; the continuum approximation of the Lennard-Jones potential and its usefulness when modelling intermolecular potentials and lastly an overview of molecular dynamics simulations.

I will then present my preliminary results which begins with a motivating problem of modelling a stack of coronene molecules encapsulated within a single walled carbon nanotube. I will then discuss how we model the system through picking appropriate surfaces and then solving integrals derived from the smaller coronene-coronene and coronene-nanotube interactions, which we then use to build up an analytic expression for the entire system.

Next I will consider the research I will undergo in the near future which includes investigating nonconstant attractive and repulsive coefficients within the Lennard-Jones potential, analysing carbon nanomaterials and other nanostructures use for gas storage, and brie􏰁fly touch on modelling carbon capture.

Lastly I will go over my research plan including manuscripts I have submitted and aim to submit, conferences and events I have attended and will attend in the coming year, and fi􏰀nally a rough timeframe for the completion of my thesis.