In this thesis, we describe periodic 2D supramolecular networks using a simple polyomino model with nearest-neighbour interactions. In particular, we focus on design rules for ordered molecular tilings, describing how the realised molecular tiling depends on the parameters of the system, such as the interactions, molecular shape, temperature, and defects. A major component of our analysis is in keeping the interaction parameters free and exploring the polyomino system from the perspective of the space of interaction counts. The design principles and methods outlined in this thesis include several different themes, which give a complementary view on the properties of 2D supramolecular networks. Within the thesis we describe our algorithm for enumerating polyomino patterns and identifying their symmetries, making use of group theory methods that are specific for polyomino tilings. This information is used to analyse properties such as chirality, lowest energy states, degeneracy, and heat capacity curves, as depending on system parameters. The domino tilings are considered in terms of enumeration by periodicity, and in terms of the kinetically accessible subsets of configurations. The generalisation to polyominoes gives a wider sense in which many of the techniques can be used, showing similarities and some differences with the domino system. A probabilistic version of algorithm DLX is described and tested that allows us to gather sample statistics of domino configurations for larger unit cells. Finally, fixed defects are considered and their effect on the kinetically accessible domino subsets is elucidated.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:737682 |
| Date | January 2017 |
| Creators | Nicholls, Joel |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/98236/ |
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