Usual ferroelectric compounds undergo a paraelectric-to-ferroelectric phase transition when the susceptibility of the electric polarization density changes its sign. The temperature is the only thermodynamic field that governs the phase transition. Chiral tilted smectics may also present an improper ferroelectricity when there is a tilt angle between the average long axis direction and the layer normal. The tilt angle is the order parameter of the phase transition which is governed by the temperature. Although the electric susceptibility remains positive, a polarization proportional to the tilt appears due to their linear coupling allowed by the chiral symmetry. Further complications come in when the chirality increases, as new phases are encountered with the same tilt inside the layers but a distribution of the azimuthal direction which is periodic with a unit cell of two (SmC(A)*, three (SmC(Fi1)*, four (SmC(Fi2)* or more (SmC(alpha)* layers. In most of these phases, the layer normal is a symmetry axis so there is no macroscopic polarization except for the SmC(Fi1)* in which the average long axis is tilted so the phase is ferrielectric. By studying a particular compound with only a SmC(Fi2)* and a SmC(alpha)* phase, we show that we recover the uniformly tilted ferroelectric SmC* when applying an electric field. We are thus led to build field-temperature phase diagrams for this class of compounds by combining different experimental techniques described here.

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Chiral smectic liquid crystals exhibit a series of phases, including ferroelectric, antiferroelectric, and ferrielectric commensurate structures as well as an incommensurate Sm-Calpha* phase. We carried out an extension of the phenomenological model recently presented by Hamaneh and Taylor based on the distorted-clock model. The salient feature of this model is that it links the appearance of phases to a spontaneous microscopic twist: i.e., an increment alpha of the azimuthal angle from layer to layer. The balance between this twist and an orientational order parameter J gives the effective phase. We introduce a second orientational order parameter I , which physical meaning comes from the macroscopic polarization; the effect of an applied electric is also studied. We derive phase diagrams and correlate them to our experimental results under field showing the sequence of phases versus temperature and electric field in some compounds.