Nonvanishing of the layer compressional elastic constant at the smetic-A-to-nematic phase transition: A consequence of Landau-Peierls instability?

In four different compounds of the alkyl(oxy)cyanobiphenyl series, the elastic modulus B is found not to vanish at the nematic--smectic-A (Sm-A) phase transition, contrary to most theoretical expectations. The phase transition is marginal, as the Sm-A phase is a one-dimensional solid in three-dimensional space, and it seems that B cannot decrease below a limiting value (about 10⁷ dyn cm^-2 here) where the fluctuations of the layers due to the Landau-Peierls instability, which scale as B^-0.25, would destroy the Sm-A ordering.