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Lebwohl-Lasher models of liquid crystals: from quadrupolar to spontaneously induced chiral order

Presented by: 
L Longa Uniwersytet Jagiellonski
Wednesday 20th March 2013 - 14:00 to 14:50
INI Seminar Room 1
In 1972 P. A. Lebwohl and Q. Lasher (LL) (PRA 6, 426 (1972)) have carried out standard Monte Carlo simulations on the lattice version of the Maier-Saupe (MS) model to test predictions of the MS mean-field calculations. Preserving uniaxial symmetry ($D_{\infty h}$)for nematics they assumed liquid crystalline molecules to occupy the sites of a three dimensional cubic lattice subjected to periodic boundary conditions. Pair interaction potential, limited to nearest-neighbor molecules, was given by the second Legendre polynomial of the relative angle between the molecular long axes. The simulations showed that the LL lattice model undergoes a weak first-order phase transition between isotropic and uniaxial nematic order, in qualitative agreement with MS predictions. Since the model has proved to correctly account for the essential symmetry of liquid crystalline orientational order a large amount of work has been and is currently devoted to generalizations of the LL model to more complex situations. They involve, without trying to be exhaustive, (a) investigation of the nematic ordering in confined geometries, subject to different surface anchoring fields, (b) effect of an external field on the isotropic - nematic phase transition(s), (c) simulations of electro-optical devices, (d) simulation of chiral liquid crystal phases, (e) orientational properties of elastomers and (f) physics of two-dimensional systems.

In this talk, after a brief review of properties and generalizations of the LL model, I will concentrate on simple versions of this model that can be useful in investigating spontaneous formation of macroscopic chiral domains of opposite handednesses observed in bent-core, dimer and ferrocene mesogens. More specifically, I will discuss properties of the LL model with quadrupolar and octupolar pair-interactions. The model will be shown to generate long-range biaxial order along with ambidextrous twist deformations. A possibility of generating nonzero splay and bent configurations will also be discussed. The class of LL models is generic in the sense that only symmetry allowed terms are retained in the interaction potential. Hence, orientational structures identified not only characterize nematic-like states but can also coexist with a long-range positional order, characteristic of smectic, columnar or crystalline phases.

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