Some Remarks on the Polymorphism of Smectics

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Abstract
We discuss the nature of the order in the main smectic phases (A, C, and B) together with the related phase transitions. (1) The B phase may correspond to a plastic crystal, or to a system of weakly coupled solid layers: to discriminate between these two models, acoustical studies using shear waves appear to be most promising, (2) the transitions A  N, C  N, C  A (where N stands for nematic) may be of second order in certain cases, which will allow for a number of interesting experiments. The C  A transition should be very similar to the λ transition of helium, and some critical exponents which are not accessible in helium could be measured here. The N  A transition is similar to the onset of superconductivity in a metal. A bend (or twist) deformation tends to suppress the A phase just as a magnetic field destroys superconductivity. In the N phase the twist and bend elastic constants should show pretransitional anomalies. The C  N transition is more complex. A tentative calculation suggests that here all three elastic constants should show pretransitional anomalies.