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Materials 2009, 2(2), 674-698; doi:10.3390/ma2020674

Role of Lifshitz Invariants in Liquid Crystals

Dipartimento di Fisica, Politecnico di Torino, Duca degli Abruzzi 24, Torino, Italy
Received: 5 May 2009 / Revised: 12 June 2009 / Accepted: 16 June 2009 / Published: 16 June 2009
(This article belongs to the Special Issue Liquid Crystals)
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The interaction between an external action and the order parameter, via a dependence described by a so-called Lifshitz invariant, is very important to determine the final configuration of liquid crystal cells. The external action can be an electric field applied to the bulk or the confinement due to free surfaces or cell walls. The Lifshitz invariant includes the order parameter in the form of an elastic strain. This coupling between elastic strains and fields, inserted in a Landau-Ginzburg formalism, is well known and gives rise to striction effects causing undulations in the director configuration. We want to discuss here the role of Lifshitz coupling terms, following an approach similar to that introduced by Dzyaloshinskii for magnetic materials. Case studies on nematics in planar and cylindrical cells are also proposed.
Keywords: liquid crystals; nematics; confined nematics liquid crystals; nematics; confined nematics
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Sparavigna, A. Role of Lifshitz Invariants in Liquid Crystals. Materials 2009, 2, 674-698.

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