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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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