Correlations and x-ray scattering in polar smectic-A1 phases

The model introduced by Prost to describe polar liquid crystals with competition between two different layer spacings in smectic-A phases is used to calculate the x-ray scattering intensity I(q) in the monolayer (A1) phase. I( q) can respectively exhibit a single spot, single ring, double ring, or double spot pattern in the vicinity of the bi-layer wavenumber q 0 as the A2, A, C or incommensurate phases are approached. There may also be a double-spot-single-ring pattern when there is competition between the incommensurate and A phases. These idealized patterns may be masked by non-critical fluctuations if first order transitions prevent a close approach to the limit of stability of the A1 phase.