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Weak anchoring effects in smectic-$$A$$ Fréedericksz transitions. (English) Zbl 1422.74043
Summary: In smectic-$$A$$ (SmA) liquid crystals, rod-like molecules are organized into layers with their optical axis oriented along the normal to these layers. When subject to an external field and for a certain critical threshold, these layers can buckle into a new different configuration. Here, we consider SmA liquid crystals which are confined between two parallel plates aligned in the so-called bookshelf geometry and subject to an external magnetic field. By assuming that instability is induced by a uniform field, we investigate the influence of the anchoring strength on the critical threshold field and on the layers shape by a perturbative analysis to the equilibrium equations. Main differences with respect to the standard Fréedericksz transition of nematics are highlighted. The behavior of this threshold effect suggests a new way to measure geometrical and constitutive parameters of a SmA sample.
##### MSC:
 74G60 Bifurcation and buckling 76A15 Liquid crystals
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##### References:
 [1] Aursand, P.; Napoli, G.; Ridder, J., On the dynamics of the weak Freedericksz transition for nematic liquid crystals, Commun. Comput. Phys., 20, 1359-1380, (2016) · Zbl 1373.76010 [2] Bevilacqua, G.; Napoli, G., Reexamination of the Helfrich-Hurault effect in smectic-$$a$$ liquid crystals, Phys. Rev. E, 72, 041708, (2005) [3] Bevilacqua, G.; Napoli, G., Parity of the weak Fréedericksz transition, Eur. Phys. J. E, 35, 133, (2012) [4] Clark, NA; Meyer, RB, Strain-induced instability of monodomain smectic $$a$$ and cholesteric liquid crystals, Appl. Phys. Lett., 22, 493-494, (1973) [5] Vita, R.; Stewart, IW, Influence of weak anchoring upon the alignment of smectic a liquid crystals with surface pretilt, J. Phys. Condens. Matter, 20, 335101, (2008) [6] de Gennes, P., Prost, J.: The Physics of Liquid Crystals, 2nd edn. Clarendon Press, Oxford (1993) [7] Pascalis, R., Mechanically induced Helfrich-Hurault effect in a confined lamellar system with finite surface anchoring, Phys. Rev. E, 100, 012705, (2019) [8] Deuling, H., Deformation of nematic liquid crystals in an electric field, Mol. Cryst. Liq. Cryst., 19, 123, (1972) [9] Elias, F.; Flament, C.; Bacri, JC; Neveau, S., Macro-organized patterns in ferrofluid layer: experimental studies, J. Phys. I, 7, 711, (1997) [10] Elston, SJ, Smectic-A Fréedericksz transition, Phy. Rev. E, 58, r1215-r1217, (1998) [11] García-Cervera, CJ; Joo, S., Analytic description of layer undulations in smectic a liquid crystals, Arch. Ration. Mech. Anal., 203, 1-43, (2012) · Zbl 1318.76002 [12] Helfrich, W., Deformation of cholesteric liquid crystals with low threshold voltage, Appl. Phys. Lett., 17, 531-532, (1970) [13] Hurault, J., Static distortions of a cholesteric planar structure induced by magnet ic or ac electric fields, J. Chem. Phys., 59, 2068-2075, (1973) [14] Ishikawa, T.; Lavrentovich, OD, Undulations in a confined lamellar system with surface anchoring, Phys. Rev. E, 63, 030501, (2001) [15] Kedney, PJ; Stewart, IW, The onset of layer deformations in non-chiral smectic C liquid crystals, ZAMP, 45, 882-898, (1994) · Zbl 0820.76009 [16] Mirantsev, LV, Dynamics of Helfrich-Hurault deformations in smectic-A liquid crystals, Eur. Phys. J. E, 38, 104, (2015) [17] Napoli, G., Weak anchoring effects in electrically driven Freedericksz transitions, J. Phys. A Math. Gen., 39, 11-31, (2005) · Zbl 1083.76006 [18] Napoli, G., On smectic-A liquid crystals in an electrostatic field, IMA J. Appl. Math., 71, 34-46, (2006) · Zbl 1117.82328 [19] Napoli, G.; Nobili, A., Mechanically induced Helfrich-Hurault effect in lamellar systems, Phys. Rev. E, 80, 031710, (2009) [20] Napoli, G.; Turzi, S., On the determination of nontrivial equilibrium configurations close to a bifurcation point, Comput. Math. Appl., 55, 299-306, (2008) · Zbl 1140.49031 [21] Onuki, A.; Fukuda, JI, Electric field effects and form birefringence in diblock copolymers, Macromolecules, 28, 8788, (1996) [22] Poursamad, JB; Hallaji, T., Freedericksz transition in smectic-A liquid crystals doped by ferroelectric nanoparticles, Phys. B Condens. Matter, 504, 112-115, (2017) [23] Rapini, A., Papoular., M.: Distortion d’une lamelle nématique sous champ magnétique. conditions d’angrage aux paroix. J. Phys. Colloque C4, p. 54 (1969) [24] Ribotta, R.; Durand, G., Mechanical instabilities of smectic-A liquid crystals under dilatative or compressive stresses, J. Phys., 38, 179-203, (1977) [25] Santangelo, CD; Kamien, RD, Curvature and topology in smectic-A liquid crystals, Proc. R. Soc. A Math. Phys. Eng. Sci., 461, 2911-2921, (2005) · Zbl 1186.82091 [26] Senyuk, BI; Smalyukh, II; Lavrentovich, OD, Undulations of lamellar liquid crystals in cells with finite surface anchoring near and well above the threshold, Phys. Rev. E, 74, 011712, (2006) [27] Seul, M.; Wolfe, R., Evolution of disorder in magnetic stripe domains. I. Transverse instabilities and disclination unbinding in lamellar patterns, Phys. Rev. A, 46, 7519-7533, (1992) [28] Shalaginov, AN; Hazelwood, LD; Sluckin, TJ, Dynamics of chevron structure formation, Phys. Rev. E, 58, 7455-7464, (1998) [29] Siemianowski, S.; Brimicombe, P.; Jaradat, S.; Thompson, P.; Bras, W.; Gleeson, H., Reorientation mechanisms in smectic a liquid crystals, Liq. Cryst., 39, 1261-1275, (2012) [30] Singer, SJ, Layer buckling in smectic-A liquid crystals and two-dimensional stripe phases, Phys. Rev. E, 48, 2796-2804, (1993) [31] Stewart, IW, Layer undulations in finite samples of smectic-A liquid crystals subjected to uniform pressure and magnetic fields, Phys. Rev. E, 58, 5926-5933, (1998) [32] Virga, E.G.: Variational Theories for Liquid Crystals. Chapman & Hall, London (1993) · Zbl 0814.49002 [33] Weinan, E., Nonlinear continuum theory of smectic-A liquid crystals, Arch. Ration. Mech. Anal., 137, 159-175, (1997) · Zbl 0891.76009
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