Flexoelectric Blue Phases

Abstract

We describe the occurence and properties of liquid crystal phases showing two dimensional splay and bend distortions which are stabilised by flexoelectric interactions. These phases are characterised by regions of locally double splayed order separated by topological defects and are thus highly analogous to the blue phases of cholesteric liquid crystals. We present a mean field analysis based upon the Landau-de Gennes Q-tensor theory and construct a phase diagram for flexoelectric structures using analytic and numerical results. We stress the similarities and discrepancies between the cholesteric and flexoelectric cases. PACS numbers: 61.30.Gd, 64.70.Md, 61.30.Mp Elastic distortions in the nematic phase of liquid crystals can be categorised into three types: splay, twist and bend. Stable phases with two dimensional twist distortions have been well characterised and observed experimentally. Here we predict the occurence of structures with two dimensional splaybend distortions.When nematics are doped with chiral molecules they can show stable phases with a natural twist known as cholesterics, shown in Fig. 1(a). In general cholesteric phases comprise a one-dimensional helix. This is because topological constraints mean that it is not possible to construct a state with helical ordering in two dimensions without introducing defects, or disclination lines, into the structure. However local regions of double twist are possible. Fig. 2(a) shows a simple, two dimensional example of a director field where regions of double twist are separated by topological defects. If the free energy advantage of the double twist regions offsets the disadvantage of the disclinations phases of this type will be stable.Such states, the so-called blue phases of cholesteric liquid crystals, have indeed been observed [1]. The disclination structure is, however, more complicated than that of the simple example in Fig. 2(a). The disclinations form textures with cubic symmetry and the stable phases have space groups O 8− and O 2 . The blue phases are stable at the isotropic-cholesteric phase boundary as here the magnitude of the order is small and hence the free energy penalty associated with disclinations is low. They are stable only over a narrow temperature range ∼ 1 K, although recently this has been extended to ∼ 60 K by adding polymers or bimesogenic molecules [2,3].One might therefore ask whether analogous behaviour could be observed in a liquid crystal which shows splay and bend, rather than twist, distortions. In 1969 Meyer showed that the one dimensional splay-bend distortion of the director field, shown in Fig. 1(b), could result from flexoelectric coupling to an external field [4]. Here we extend these results to show that near the isotropic-nematic transition two dimensional splay-bend structures (e.g., Fig. 2(b)) can be stable.We shall term such phases flexoelectric blue phases. Similar director field configurations, but stabilised by a saddle splay term in the free energy, have been reported in [5]. The coupling of a liquid c...

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