My research spans a variety of disciplines, but is directed to the single goal: understanding the role of curvature in condensed atomic and molecular materials. These materials include:
lyotropic liquid crystals (made up of soaps/detergents/lipids and water)
biominerals, especially mineralisation of calcite in sea-urchin shells (image at left)
zeolites (eg. Linde type A, on left, click here for more)
mesoporous inorganics, including clays
chiral thermotropic liquid crystals
novel carbon polymorphs, including buckytubes and hypothetical schwarzites
My own work is largely theoretical, but I prefer to work closely with experimentalists. I do some experiments myself (mainly small-angle X-ray scattering studies and related calorimetry and optical microscopy work); students and postdocs. tend to be experimentalists to keep my feet somewhere approaching terra firma. To that end we have access to a range of equipment, both within the dept. and on campus:
This materials work is underpinned by fundamental theoretical work, devoted principally to investigations of hyperbolic surfaces, and their role in describing structure and properties of both crystalline and liquid crystalline materials, at a variety of length scales, from a few Ångströms (zeolites, other covalent frameworks), to the meso-scale (10-100Å), found in lyotropic liquid crystals and, in some inorganic materials, such as novel hypothetical carbon polymorphs ("schwarzites"), clays and alumino-silicates (imogolite, allophane, etc.), and up to the micron scale in blue phases of thermotropic liquid crystals and some sea-urchin skeletons.
The study of hyperbolic surfaces involves techniques from differential geometry and topology, and is largely devoted to triply periodic minimal surfaces. These periodic examples arise naturally if the surface is constrained to have nearly constant (negative Gaussian) curvature and to be intersection-free. Simpler examples have asymptotically flat "ends", or eventually fold through themselves (as in the example of the generalised Enneper minimal surface, shown above).
Exact parametrisation techniques have been developed to allow computations of the lower genus surfaces, including cubic, rhombohedral, tetragonal, etc., examples.
To date, the simplest triply periodic minimal surfaces have been seen in condensed materials. These are the famous P (top left), D (bottom left)and G(yroid) surfaces. It is my suspicion that a larger variety of structures will be uncovered, particularly those of genus three and rhombohedral and tetragonal symmetry, given more accurate structural probes.
An emerging area of interest is that of a two-dimensional hyperbolic description of three-dimensional networks, such as the covalent frameworks of silicates. A few images of examples, generated by Stuart Ramsden at the ANU Vizlab, can be found elsewhere. That description is appealing, as it offers simple relations between the ring sizes in the net, and its three-dimensional density. This approach may also offer some useful insights into coordination sequences of nets, which are a useful fingerprint of a net topology, and exhibit curious polynomial relations.
This work is done in collaboration with a number of people in Applied Mathematics, especially Rob Corkery and Fiona Meldrum, and groups in Japan (Kyoto, Hashimoto group), Sweden (Lund, Andrew Fogden; Malmö, Zoltan Blum), the U.S. (Arizona, Michael O'Keeffe) and looser links elsewhere. If you have any queries about my work, please contact me. I can be accessed from this page via email.
updated March, 1998.