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Fluids with attitude

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The Mathematics of Liquid Crystals

This talk includes: an account of the early development of liquid crystal science (c1888-1940), a history of key mathematical ideas, a discussion of devices in liquid crystals, and finally a personal view of future perspectives.

Friedrich Reinitzer (1888, Prague) found that cholesteryl benzoate exhibited two fluid phases, one of which was cloudy. Otto Lehmann (Karlsruhe) studied similar compounds, which seemed both liquid and crystal, hence the term liquid crystal. In France Georges Friedel (1922) realised that liquid crystals were instead orientationally ordered fluids, inventing the terms nematic, smectic and cholesteric. The first (swarm) theory was due to Emil Bose (Danzig, 1908). More successful was the distinguished Swedish theoretical physicist Carl Wilhelm Oseen, who constructed a hydrostatic theory of liquid crystals (1922-44). Oseens theory explained Frederikss results from the USSR on threshold fields, but his Ph.D. student Adolf Anzelius was not able to build a consistent dynamical theory.

The first statistical mechanical theory was a mean field picture based on Curie-Weiss magnetism, due to Franois Grandjean (France, 1917). His work was ignored. The later 1958 Maier-Saupe theory is essentially identical. The liquid crystal order parameter is due to the Russian physicist Victor Tsvetkov in 1941.

Liquid crystal devices emerged in the USA in the 1960s. The TN cell was patented in 1970. There remains dispute over its discovery. Device development was accompanied by enormous theoretical and mathematical activity. The current hydrodynamic theory due to Ericksen and Leslie in 1966, and the Landau theory due to de Gennes in 1970, have been immensely influential. The importance of lcds has focussed mathematical interest in liquid crystals in recent years, but in the future these ideas may be even more important in understanding processes in living cells.

This talk is part of the Isaac Newton Institute Seminar Series series.

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