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Molecular field theory for biaxial smectic A liquid crystals

Presented by: 
T To [Southampton]
Wednesday 22nd May 2013 - 10:00 to 10:20
INI Seminar Room 1
Stable biaxial nematics (Nb) have been reported in a few experimental systems and the phases are often difficult to prove conclusively; however, stable biaxial smectic A phases (SmAb) have been found in a larger number of systems in which the evident is conclusive. To understand the stability difference between Nb and SmAb, we use a molecular field theory that combines Straley's theory [1] for biaxial nematics and McMillan's theory [2] for uniaxial smectic A phases. To simplify the calculation, we use alternatively the geometric mean [3] and the Sonnet-Virga-Durand [4] approximation to reduce the number of biaxiality parameters to one; in addition, we use the Kventsel-Luckhurst-Zewdie [5] approximation to decouple the orientational and translational distribution functions. Thus our simple theory has one biaxiality parameter and one smecticity parameter; together with three order parameters. The resulting phase diagrams showed that, for a large region of the para meter space, the presence of the smectic A phases disallowed Nb to form. On the other hand, SmAb is always stable at ground state for positive smecticity parameter. Thus this may explain why SmAb has been found more abundant than Nb.

[1] J. P. Straley, Phys. Rev. A 10, 1881 (1974). [2] W. L. McMillan, Phys. Rev. A 4, 1238 (1971). [3] G. R. Luckhurst, C. Zannoni, P. L. Nordio, and U. Segre, Mol. Phys. 30, 1345 (1975). [4] A. Sonnet, E. G. Virga, and G. E. Durand, Phys. Rev. E 67, 061701 (2003). [5] G. F. Kventsel, G. R. Luckhurst, and H. B. Zewdie, Mol. Phys. 56, 589 (1985).

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons