Abstract
One of the most remarkable properties of smectics is the wide variety of possible equilibrium structures. In this paper, based on the Landau theory of the phase transitions, the transitions between ferroelectric and antiferroelectric phases and the structure formed by smectic layers with different azimuthal and polar orientations of the molecules were calculated. This unique structure has been predicted [P.V. Dolganov et al., JETP Lett. 76, 498 (2002)] using the minimization of the free energy with respect to the phase and modulus of the two-component order parameter, but never before detected. Recently, a nonresonant Bragg reflection, consistent with the predictions of the model, was found [P. Fernandes et al., Eur. Phys. J. E 20, 81 (2006)] in the ferrielectric smectic C* FI1(SmC* FI1) phase. In the three-layer ferrielectric structure with a macroscopic helical pitch, the modulus of the order parameter is larger in anticlinic-like layers and smaller in layers with mixed ordering. The values of the interlayer interactions were determined for smectic liquid-crystalline materials forming different polar structures.
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A possible mechanism for the coupling between the tilt and the polarization p is the following. In an environment with mirror symmetry (SmA phase) at any particular moment, the molecules have with equal probability left-or right-handed conformations, i.e., the molecules on average are nonchiral. The collective molecular tilt breaks the mirror symmetry, so that left-and righthanded conformations are no longer equiprobable. To describe chiral, tilted, and polar smectics from the macroscopic symmetry point of view, one has to introduce three order parameters χ, ξ, and p, respectively. Note that these order parameters are not independent, and condensation of any pair of them, inevitably induces the nonzero value for the third one. This fact leads to the presence of the specific third order term (the product of these order parameters). In principle, one can include the dipole smectic layer polarization as a secondary order parameter in our model, and polar orientational order parameter configurations also imply electrical polarity. The nonuniform orientational deformations in such a case should produce space charges and long range Coulomb interaction. In reality, however, the molecules involved may have large steric anisotropy, without a large electric dipole moment. Moreover, ionic impurities can screen the Coulomb interaction. Thus, we disregard electrostatics in this paper.
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Dolganov, P.V., Zhilin, V.M., Dolganov, V.K. et al. Ferrielectric smectic phase with a layer-by-layer change of the two-component order parameter. Jetp Lett. 87, 253–257 (2008). https://doi.org/10.1134/S0021364008050068
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DOI: https://doi.org/10.1134/S0021364008050068