Ferrielectricity in smectic-C^{*} dechiralization-line lattices

Recent experiments probing a new ferroelectric liquid crystal (CLF08) confined in cells with planar alignment have shown dielectric and optic anomalies suggesting the onset of ferrielectric ordering within the surface lattice of dechiralization lines. We present a phenomenological theory describing the corresponding phase transition sequence SmA→SmC^{*}→Ferri. Phase diagrams and thermodynamic, dielectric, and optic properties are worked out and compared with experiments. The anomalies are related to the predicted tristability of the experimental cells under applied electric field. The order parameters of Landau theory are reinterpreted in terms of line positions, allowing description of the entrance and exit line behavior, and yielding the prediction and identification of new limit phases within a nonconventional Landau approach.