Innovative interdisciplinary research at the University of Southampton is exploring new applications of topology, a discipline of pure mathematics dedicated to the study of shape, to develop new materials with attractive and competitive optical properties.
Researchers from Physics and Astronomy have joined experts in Mathematical Sciences with an aim to revolutionise the design and manufacture of micro and nanostructured materials through a new project funded by the Leverhulme Trust.
The cutting-edge research will lead to a much clearer understanding of how materials self-assemble on the nanoscale and ultimately to a range of technical applications, starting with a new generation of wavelength selective optical components in devices such as lasers.
Professor Malgosia Kaczmarek, co-director of the Soft Photonic Systems Group who is leading the project, says: “Mathematics is very good at spotting underlying structures in very complex data. In particular, topology has been used to characterise the structure of neuron connections in the brain and to shed light on their function, or to classify the shape of human lungs which allows a deeper understanding of serious diseases.
“So far, topological methods in data analysis have been used for visualisation and classification; we are now taking them in an exciting new direction, namely to analyse and characterise the optical response to design new materials.”
The research builds upon the strong interdisciplinary ethos cultivated at the University of Southampton, and is a collaboration with Professor Jacek Brodzki and Dr Giampaolo D’Alessandro from Mathematical Sciences. This joint project provides a perfect environment to exploit the synchronicity between topological methods and rapid progress in the manufacture of novel materials.
“Creating truly visionary, new materials often requires unprecedented levels of control of architecture design and manufacture,” Giampaolo explains. “This poses significant challenges at the nanoscale, where the best that researchers can achieve is some approximate regularity. This does not, however, mean that the end material will not be functionally useful. An ant-hill is far less regular than a beehive, but ants still form extremely organised societies: an apparently disordered system may hide significant underlying order if looked at in the correct way.”
An important goal of the project is to demonstrate that it is possible to use new mathematical ideas to extract more from easy to fabricate self-assembled organic and hybrid systems. In order to test this idea the team will make use of the advanced fabrication and characterisation lab facilities available at the University.
“The ability to structure materials, especially on the nanoscale, offers the tantalising prospect of giving them incredible mechanical or optical properties,” Jacek says. “This has been recently demonstrated by passive cooling films developed at the University of Colorado that lower temperature by 10°C and the structured materials developed by many colleagues here at the University of Southampton.
“These materials are expensive to manufacture and hard to realise on a large scale. We aim to balance order with disorder by spotting any underlying pattern to the variability of partially disordered systems. Quantifying this balance can lead to simpler fabrication process, while maintaining reasonable reliability of the material properties.”
