Critical behavior of chiral smectic liquid crystals

The phase transitions from the smectic - A phase to the ferroelectric smect ic - C*, the antiferroelectric smectic - C*(A) and the incommensurate smect ic - C*(alpha) phase are of the three dimensional (3D) XY universality clas s, where the soft mode condenses either at the edge, at the boundary or at a general point of the smectic Brillouin zone. High-resolution optical pola rimetry and linear electro-optic response have been used to determine the t emperature dependence of the order parameter in the antiferroelectric liqui d crystals MHPOBC, MHP8CBC, EHPOBC, MHP10CBC and 10OTBBB1M7. The conclusion s are: (i) In the smectic- A phase antiferroelectric liquid crystals exhibi t unusually large tilt fluctuations. (ii) In most antiferroelectric liquid crystals, the critical exponents for tilt fluctuations are neither pure 3D XY nor Gaussian, but somewhat in between (iii) The "reconstructive" phase t ransitions between incommensurate, ferro-, ferri- and antiferroelectric pha ses are of first order. (iv) The discrete "clock" Landau model explains wel l the observed discontinuities. (v) The results of the resonant X-ray scatt ering experiment and optical polarimetry on 3 and 4-layer "clock" smectic p hases are inconsistent.