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Nematic twist-bend:the heliconical phase of nonchiral liquid crystals

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The (one-dimensional modulated) nematic twist-bend phase (NTB), a fifth member of the nematic family, formed through spontaneous chiral symmetry breaking in the isotropic and nematic phases of a large class of liquid crystalline systems of achiral molecules (bent-core-, dimeric-, trimeric, etc.) is one of the most spectacular recent discoveries in soft matter physics. It has become a major field of activity in liquid crystal research across the world [1]. Its unique property is a heliconical structure of nanoscale pitch , where the director rotates on the cone like in the smectic C*, but without long-range positional order of molecules.
Initially, the theoretical concept of this phase has been presented by R. B. Meyer [2]. Subsequently Dozov [3] suggested that the formation of the NTB phase can be facilitated by the shape of bent–core molecules. In 2014 Shamid et. al. [4,5] showed that polar order induced by bend flexopolarization in liquid crystals of bent-core molecules can be responsible for the stabilization of NTB and of the novel class of blue phases. Their analysis was consistent with predictions of the mesoscopic theory of flexopolarization that we introduced as early as in 1990 [6, pp. 3464-3467].
Here, within generalized Landau-deGennes theory and molecular simulations we present theoretical studies concerning stability of NTB relative to other homogeneous and inhomogeneous structures [6-9]. We use a systematic bifurcation and numerical analyses to identify absolutely stable one-dimensional modulated structures that can condense from the isotropic phase. In addition, the behavior of NTB subjected to an external field is discussed in detail. We show that by controlling field’s strength and sign of anisotropy of permittivity a web of new structures can be identified.
This work is supported by the Grant No. DEC -2013/11/B/ST3/04247 of the National Science Centre in Poland.
[1]For a recent review see A. Jákli, O. D. Lavrentovich, and J. V. Selinger, “Physics of liquid crystals of bent-shaped molecules”, Rev. Mod. Phys., 90, 045004 (2018).
[2]R. B. Meyer, “Structural Problems in Liquid Crystal Physics”, pp. 273-373 in Les Houches
Summer School in Theoretical Physics, 1973 (Gordon and Breach, New York, 1976); Phys. Rev. Lett. 22, 918 (1969).
[3]I. Dozov, “On the spontaneous symmetry breaking in the mesophases of achiral banana-shaped molecules”, Europhys. Lett. 56, 247 (2001).
[4]S. M. Shamid, S. Dhakal and J. V. Selinger, ‚“Statistical mechanics of bend flexoelectricity and the twist-bend phase in bent-core liquid crystals”, Phys. Rev. E 87 , 052503 (2013).
[5]S. M. Shamid, D. W. Allender and J. V. Selinger, “Predicting a Polar Analog of Chiral Blue Phases
in Liquid Crystals”, Phys. Rev. Lett. 113, 237801 (2014).
[6]L. Longa and H.-R. Trebin, “Spontaneous polarization in chiral biaxial liquid crystals”, Phys. Rev. A 42 , 3453 (1990).
[7]Longa L, Pajak G., “Modulated nematic structures induced by chirality and steric polarization”.
Phys Rev E. Rapid 93, 040701 (2016).
[8]Trojanowski K, Cieśla M, and Longa L., “Modulated nematic structures and chiral symmetry
breaking in 2D”, Liquid Crystals, DOI : 10.1080/02678292.2016.1261192 (2016).
[9] Pajak G., Longa L, Chrzanowska A., “Nematic twist—bend phase in an external field”,, PNAS , 115, E10303 –E10312 (2018).

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