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University of Malta, University of Sheffield, Uk |
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Mathematical Structures and Graph Spectra and fullerenes |
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Example of a core graph. White are vertices with a positive entry in a respective eigenvector, black corresponds to negative. |
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Graph Spectra and Fullerene Molecular Structure |
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This project is a joint effort by University of Malta and the department of Chemistry of University of Sheffield, UK. The aim is to understand the structure and composition of fullerenes and other carbon structures through spectra of adjacency matrices representing these molecules. We explore the mathematics behind the properties of new carbon molecular architectures, with potential for application in molecular chemistry, nanoscience, and the physics of molecular electronic devices. As a result of this collaboration which started in 2001, a number of papers have been published and we have since continued this promising line of research. Over the past two decades, the study of the chemistry and physics of carbon has undergone a revolution. Following on from the Nobel-Prize-winning discovery of the fullerenes, a stream of new and ever more exotic forms of carbon and carbon compounds has emerged: nanotubes (single and multi-walled), carbon onions, toroids, peapods, nanocones, nanohorns, chemically functionalised forms of all of these, and, most recently, the graphenes (portions of single layers of graphite). At a fundamental level, all these forms have produced new understanding of what had been thought to be a well established body of knowledge, organic chemistry, and many have potential for applications in a variety of areas of nanoscience. The mathematical connection with this burst of experimental activity is through graph theory, which turns out to be a good model of the qualitative features of carbon nanostructures. Questions such as the relative stability of fullerenes, patterns of addition of bulky ligands to fullerene cages, the division between insulating and conducting nanotubes, and even, it turns out, the electron-transport properties of graphene sheets are all answered by graph-theoretical reasoning. The importance of understanding exactly the mechanisms of the latter was emphasised in the recent UK Royal Society meeting on Carbon-Based Electronics (May 21-22, 2007), where many putative applications of graphene- and nanotube-based devices hinged on the electronic states in the conical regions around the K points of the Brillouin zone - or in plain chemical language, the frontier states with near-zero energy, those near to the nullspace. A joint attack on the graph-theoretical description of such states is therefore highly topical. |
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University of Malta |
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To contact us: |
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Tel: +356 23402357-6 E-mail: irene.sciriha-aquilina@um.edu.mt |
