Summary
The elastic deformations in nematic liquid crystals are analysed in one and two dimensions. The influence of the flexoelectric polarization on the elastic properties of the medium is studied. It is shown that for one-dimensional deformations, the presence of the flexoelectric polarization introduces a renormalization of the elastic constants. On the contrary in the bidimensional case, the effect of the flexoelectricity is not a simple renormalization of the elastic constants. The profiles of the electric potential and of the tilt angle are evaluated for the cases in which the substrate is an insulating or conducting material. The validity of the calculations is discussed by considering the value of Debye's screening length of the nematic liquid crystal.
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References
See,e.g.,A. A. Maradudin: inModern Problems of Surface Physics, ISCMP Varna '80, Bulgarian Academy of Sciences, Sofia (1981).
P. G. de Gennes:The Physics of Liquid Crystals (Clarendon Press, Oxford, 1974).
S. A. Pikin:Structural Transformations in Liquid Crystals (Gordon and Breach, New York, N.Y., 1991).
R. B. Meyer:Phys. Rev. Lett.,22, 918 (1969).
W. Helfrich:Z. Naturforsch. A,26, 833 (1971).
I. Dozov, Ph. Martinot-Lagarde andG. Durand:J. Phys. (Paris), Lett.,43, 365 (1982).
I. Dozov, Ph. Martinot-Lagarde andG. Durand:J. Phys. (Paris), Lett.,44, 817 (1983).
G. Barbero andA. Strigazzi:J. Appl. Phys.,58, 2544 (1985).
G. Durand:Mol. Cryst. Liq. Cryst.,113, 237 (1984).
A. Derzhanski, A. G. Petrov andM. D. Mitov:J. Phys. (Paris),39, 1294 (1978).
J. F. Palierne:Phys. Rev. Lett.,56, 1160 (1986).
K. Okano:Jpn. J. Appl. Phys.,25, L846 (1986).
A. L. Alexe-Ionescu andL. R. Evangelista:Local and non-local terms in the elastic energy for piezoelectric materials, to be published inMol. Mater. (1993).
A. L. Alexe-Ionescu andA. Th. Ionescu:Mol. Mater.,2, 245 (1993).
G. Barbero, N. V. Madhusudana andG. Durand:Z. Naturforsch. A,39, 1066 (1984).
G. Barbero andG. Durand:J. Phys. (Paris),47, 2129 (1986).
I. Dozov, G. Barbero, J. F. Palierne andG. Durand:Europhys. Lett.,1, 563 (1984).
R. Barberi, G. Barbero, Z. Gabbasova andA. K. Zvezdin:J. Phys. (Paris) II,3, 147 (1993).
H. J. Deuling:Solid State Commun.,14, 1073 (1974).
H. J. Deuling:Mol. Cryst. Liq. Cryst.,26, 281 (1974).
H. J. Deuling: inSolid State Physics, Suppl.14, edited byL. Liebert (Academic Press, New York, N.Y., 1976).
G. Barbero andG. Durand:Phys. Rev. A,35, 1294 (1987).
W. Helfrich:Mol. Cryst. Liq. Cryst.,26, 1 (1974).
A. L. Alexe-Ionescu:Int. J. Mod. Phys. B,7, 1131 (1993).
G. Barbero, I. Dozov, J. F. Palierne andG. Durand:Phys. Rev. Lett.,56, 2056 (1986).
L. Landau andE. I. Lifschitz:Electrodynamique des milieux continus (MIR, Moscow, 1974).
G. Barbero andR. Barberi:Elastic properties of nematic liquid crystals, inPhysics of Liquid Crystalline Materials, edited byI. C. Khoo andF. Simoni (Gordon and Breach, New York, N.Y., 1991), Chapt. VIII.
L. Elsgolts:Differential Equations and the Calculus of Variations (MIR, Moscow, 1977).
G. Barbero andG. Durand:J. Appl. Phys.,68, 5549 (1990).
V. Puskinov:Mathematics (MIR, Moscow, 1980).
L. R. Evangelista andG. Barbero:Phys. Rev. E (1993) to appear.
G. Barbero, A. N. Chuvyrov, A. P. Krekhov andO. Scaldin:J. Appl. Phys.,69, 6343 (1991).
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Alexe-Ionescu, A.L. One- and two-dimensional deformations in nematic liquid crystals: Influence of the flexoelectric polarization. Il Nuovo Cimento D 15, 1489–1506 (1993). https://doi.org/10.1007/BF02451941
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DOI: https://doi.org/10.1007/BF02451941