Abstract
A smectic liquid-crystal phase formed by achiral banana-shaped molecules (CB2) is studied as one-dimensional piezoelectric crystals with fluidity of tilted-C2V anisotropy in the other two spatial dimensions. Variation of the elastic-piezoelectric free energy of the system predicts the existence of racemic (R), left-, and right-handed chiral (H) antiferroelectric equilibrium structures, a result in agreement with the observation by Link et al. [Science 278, 1924 (1997)]. The electric-field-induced ferroelectric state is shown to be a special C2 symmetry, which confirms the measurements by optical second harmonic generation in a CB2 by Macdonald et al. [Phys. Rev. Lett. 81, 4408 (1998)]. The hysteresis loop of switching polarization is also discussed, and the molecular tilt angle dependence of spontaneous polarization is obtained as a function of the elastic and the piezoelectric constants.
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