One-dimensional translational order — Smectic A and phases

As the temperature is further cooled, the molecules begin to segregate into planes giving rise to a smectic A or smectic C phase. In addition to the orientational order that the nematic phase shows, the smectic A and C phases exhibit a one-dimensional translational order, and can therefore form layered structures. There is a liquid-like motion of the rods in each layer and no correlation of the molecular positions from one layer to the next. In each layer, the mass centers of the molecules are randomly distributed as 

In the smectic A phase, molecules tend to be perpendicular to the smectic layers. The layer thickness d is roughly the same as the molecular length l. The thickness of the layers in the case of liquid crystalline polymers is about the order of the monomer s length. But in the smectic C phase, the molecules in the layers are parallel and tilted in arrangement with respect to the normal of the layers by a tilt angle 0. The layer thickness of the smectic C phase is d = l cos 6. The ordering of the smectic A and C phases are both higher than the nematic phase so that they appear at a lower temperature than the nematics do. The smectic A phase appears first as the temperature decreases if a compound shows both the smectic A and C phases. 

The positional correlation in the smectic A phase can be described as a sinusoidal modulation of the average mass density 

The thermal fluctuations destroy the ideal long-range periodic order of the smectic phase and there are power-law singularities rather than the 

The local symmetry of smectic A phase is the same as that of the nematics, be., its point group is D h, while the symmetry of the smectic C phase is ( b/, (a ( 2 symmetry axis plus a reflection plane perpendicular to the axis). In addition, both smectic phases exhibit a one-dimension translational order. Owing to the difference in symmetry, the smectic phases show different optical properties. The smectic A phase is optically uniaxial, but the smectic C phase is optically biaxial. 

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