Some Remarks on the Polymorphism of Smectics

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.