Ordering effects in thin smectic-C*films: An x-ray-reflectivity study

The x-ray-reflectivity technique is used to study the smectic order and the smectic-A (Sm-A) to smectic-${\mathit{C}}^{\mathrm{*}}$ (Sm-${\mathit{C}}^{\mathrm{*}}$) phase transition in thin and ultrathin films (150–600 Å) of the chiral ferroelectric liquid-crystal mixture ZLI-3654 (produced by Merck). The films, which are spin cast on various substrates [very smooth (float) glass, Si wafer, polymer-coated glass, etc.], order spontaneously with smectic layering parallel to the substrate surface; the film alignment is induced by anchoring forces at the film-air interface. The reflectivity profiles could be well described by a sinusoidal density modulation perpendicular to the film. We demonstrate that it is possible to extract the molecular tilt angle α in ferroelectric liquid crystals from x-ray-reflectivity measurements of thin films. The Sm-A–Sm-${\mathit{C}}^{\mathrm{*}}$ phase-transition temperature and the temperature dependence of the tilt angle in the smectic-${\mathit{C}}^{\mathrm{*}}$ phase are almost independent of the film thickness (down to ∼200 Å) and are similar to those in the bulk. In all cases the dependence of the tilt angle α(T) can be described by a power law: α∼${\mathit{t}}^{\gamma }$ (t=1-T/${\mathit{T}}_{\mathit{c}}$), where γ=0.31±0.04, in agreement with the de Gennes predicted superfluid helium analogy [Acad. Sci. Paris Ser. B 274, 785 (1972)]. In a film of about 200-Å thickness we observed a smectic layer spacing which is much larger than in thick films.