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Cox, Barry Chen, Michael Bowe, Patrick James School of Mathematical Sciences 2021 https://hdl.handle.net/2440/132531 Since their discovery in 1993, carbon nanotubes have been studied for their unique properties which make them an attractive option for many potential applications. Often such applications require the use of nanotubes with specific chiralities and therefore properties. Because of this, methods by which the structure of carbon nanotubes can be controlled during synthesis are desirable. Such methods may represent a significant decrease in the cost of producing carbon nanotubes for new technologies. In this thesis we develop a model for the growth and dewetting of graphene caps via chemical vapour deposition. This model will allow us to predict the conditions which favour the production of carbon nanotubes with a specific chirality. To model the growth of graphene caps wetted to a metallic catalyst particle, we use the calculus of variations to determine the optimal configuration of the system for various cap sizes. The growth of graphene caps is simulated by treating their surface area as a time-like variable. We use this model to predict when dewetting from the metallic catalyst particle becomes energetically favourable by comparing the optimal energies of the wetted and dewetted states. When dewetted, the structure of the graphene cap determines the structure of the resultant nanotube. Testing our model on three metallic catalysts we found that our model consistently predicted lower CNT diameters than those observed in experiments by other researchers. For iron carbide we predicted diameters of 6.5-7.1 A compared to 30 A in experiments, and for gold we predicted diameters of 7-9 A compared to 9-18 A in experiments. For nickel carbide our model predicted no CNT production despite it being a common catalyst material in CVD. Our model predicted that iron carbide catalyst particles would produce more metallic CNTs compared to gold, with 50% of CNTs produced using iron carbide predicted to be metallic compared to 33-46% of CNTs produced using gold. Due to the inaccuracy of our model when compared to experimental results, we recommend that future research focuses on improving the model. This could be achieved by reducing the amount or restrictiveness of our assumptions, or increasing the detail with which our model accounts for various factors of the cap growth and dewetting processes. Thesis (MPhil.) -- University of Adelaide, School of Mathematical Sciences, 2021 en Nanotubes mathematical modelling chemical vapour deposition Predictive Model of Cap Formation for Carbon Nanotube Synthesis via Chemical Vapour Deposition Thesis This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at: http://www.adelaide.edu.au/legalsopen.access