Topologically and chemically unprecendented spherical-icosahedral capsules containing 20 pores and channels and a cavity, allow encapsulation of topologically and chemically unusual matter under confined conditions. This includes the generation and observation of unusual structures, e.g. of water with and without electrolytes and of other materials. Icosahedral water clusters can be generated - formally built up from Platonic and Archimedean solids showing the Golden Section - including the famous dodecahedron which stimulated Linus Pauling to new ideas. Furtheron, toplogically interesting tilings of the sphere due to the abundance of pores are possible.
To summarize: New interesting challenges for discrete geometry arise from recent progress in chemistry, and it is the intention of the workshop to focus these challenges jointly, from the point of view of chemistry and that of mathematics.
Structurally well defined metal-oxide based spherical porous nanocapsules/artificial cells allow unprecedented chemistry under confined conditions, e.g., encapsulation chemistry including related capsule-environment interactions. This includes studies of encapsulated nanomaterials (e.g. water with and without electrolytes), as well as of ion uptake-and-release equilibria through the pores and channels of the artificial membranes. In this respect some of Nature's pathways can be modelled, like cell response to stimuli as pore closing influences significantly encapsulates' structures. An interesting corresponding subject is coordination chemistry in capsules, allowing a new type of spectroscopic and magnetic studies while the capsules themselves can separate/position cations like a nano ion chromatograph. A special aspect refers to the possibility of getting more information about confined water structures.
Important related points are:(1) the size of the capsules and their pores can be tuned, while the latter can be opened and closed,(2) the internal cavity shell functionality can be tuned from hydrophilic to hydrophobic, and(3) the twenty(!) abundant pores have crown-ether functions allowing sphere-surface as well as super-supramolecular chemistry including in principle the study of allosteric effects.
This area shows revolutionary routes to different disciplines, such as materials science in several directions, physics (regarding confined matter properties), and even mathematics concerning the tiling problem of sphere surfaces.*
Highlighted, e.g. in: W. G. Klemperer, G. Westwood, "Traps for Cations", Nature Materials (News & Views) 2003, 2, 780. M. Gross, "Encapsulating Chemistry", Chemistry in Britain 2003, Aug. Issue, p. 18. G. Zosimo-Landolfo, "À la découverte de l'eau", Biofutur 2003, Feb. Issue, p.17. N. Hall, "Bringing Inorganic Chemistry to Life", Chemical Communications 2003, 803.
* According to the rather large hydrophilic capsule surface the interface water gets structured, which leads to a new type of assembly to vesicles and even to a new ion solute state. This holds especially in case of related wheel-shaped species with extremely hydrophilic surfaces (T. Liu, E. Diemann, H. Li, A. W. M. Dress, A. Müller, "Self-assembly in aqueous solution of wheel-shaped Mo154 oxide clusters into vesicles", Nature 2003, 426, 58; highlighted, e.g., in Materials Today ( "Rounding up nanoclusters - nanotechnology") 2004, Jan. Issue, p. 10).
Platonic and Archimedean solids has inspired mathematicians and philosophers for centuries. But nowadays, molecular chemists are able to synthesize nano-objects that mimic the topology of these fundamental structures. The different self-assembly strategies that have been used to produce polyhedral organic or inorganic nano-objects from molecules will be reviewed and analyzed in the context of the well-known Euler's rule.
Generally speaking, I would like to review some recent approaches to the mathematical description of crystal topologies and discuss what could and should be done in the near future.
