In a brief history of the discovery of antiferroelectricity in liquid crystals, the important role played by tristable switching, i.e. an electric field induced phase transition from antiferroelectric SCA* to ferroelectric SC*, has been emphasised and the antiferroelectric herringbone structure of SCA* has been presented. Then we have explained how to identify the subphases in the SC* region, e.g. SC,*, SC,*; the clarification of the subphase structures is essential for understanding antiferroelectricity in liquid crystals. After summarizing the evidence for the SCA* structure presented, we have suggested the pair formation of transverse dipole moments in adjacent smectic layers as the cause of its antiferroelectricity, showing that the smectic layer is much closer to the usual picture of molecules lying on equidistant planes; the packing entropy due to the sinusoidal density wave character stabilizes ferroelectric SC*. The competition between the interactions stabilizing SCA* and SC* is responsible for the occurrence of several varieties of ferrielectric and antiferroelectric subphases, which constitutes the Devil's staircase. We have further suggested that the essentials of the SC,* phase are its considerably reduced ability to form SCA* and SC*. At least when the spontaneous polarization is zero, SC,* is a smectic C-like phase with molecular tilting that is non-correlated on the visible wavelength scale When the spontaneous polarization is not zero, as suggested by Prost and Bruinsma recently, a novel type of Coulomb interaction between smectic layers due to the collective polarization fluctuations causes the antiferroelectricity in the high-temperature region of SC,*; the competition between this antiferroelectricity and the SC* ferroelectricity niay form another staircase, causing the complexity in SC;. Applications and some future problems have been described in the final section.

At least two antiferroelectric liquid crystalline phases were discovered in MHPOBC. These phases appear below the usual ferroelectric Sm C* phase. Because of the alternation of the molecular tilt directions as well as the dipole orientations in successive layers, the optic axis is along the layer normal. This strong stabilization along the layer normal brings about the so-called third stable state responsible for the tristable switching. The antiferroelectric structure was strongly supported by selective reflections in oblique incidence; a full-pitch band does not appear in the antiferroelectric phases, while it does appear in the ferroelectric phase.

It is proposed to apply the direct measurement of spontaneous polarization using triangular waves to ferroelectric liquid crystals. The use of the triangular waves allows us to easily subtract the background contribution due to the conductive and the capacitive current and to accurately determine the spontaneous polarization, since a bump due to the polarization realignment appears on a straight base line. Moreover, the experiment with pulsed triangular waves clearly reveals no existence of the threshold voltage for deforming the helix and some characteristic properties of the dynamic reaction of the helix to the field applied.

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The phase, designated as Sm CA *, which shows tristable switching was investigated in C8H17O–--COO–-COO*CH(CH3)C6H13 (MHPOBC) by means of thermal analyses, a miscibility test and microscope observation. The phase transition from Sm C* to Sm CA * is not observable by AC calorimetry but small peaks comparable to the Sm A-Sm C* transition are discernible in DSC. According to the miscibility test of racemic MHPOBC with a standard compound, this new phase was found to exist between Sm C* and Sm I* and not to be miscible with Sm Bhex. Therefore, the assignment of Sm CA * to one of the known phases is ruled out, which means that Sm CA * is a totally new phase. The difference between the pure enantiomer and the racemate is also pointed out.

A new switching process was observed in surface stabilized ferroelectric liquid crystals. The switching is associated with a third stable state in addition to the well-known bistable states. The appearance of the third state is characteristic of materials with a large spontaneous polarization and is caused by minimizing induced polarization charges. The switching between each bistable state and the third state exhibits a sharp dc-threshold and hysteresis, suggesting a possible application for a switching device.

By diminishing the energy barrier between SC; and SC*, antiferroelectricity has become thresholdless in a threecomponent mixture. It shows V-shaped switching, realizing attractive display characteristics: extremely wide viewing angle with very large contrast ratio, high speed response and ideal analogue grey scale with no hysteresis. A simplified model of the phase with this property is presented.

We have studied the frustration between ferro- and antiferro-electricity in chiral smectic C like liquid crystalline phases, which is not only fundamentally interesting but also very attractive from an application point of view. It causes temperature induced successive phase transitions as characterized by a devil's staircase and the thresholdless, hysteresis-free, V-shaped switching induced by an applied electric field. The devil's staircase indicates some type of interlayer ordering, while the V-shaped switching suggests considerably diminished tilting correlation. These two are apparently contradictory to each other, but result from the same cause, i.e. the frustration. We have first summarized experimental facts regarding subphases and successive phase transitions observed in many compounds and mixtures, which we believe are related to one another and result from the frustration. We have introduced several different theoretical explanations for these observed facts, and shown that only the axial next nearest neighbor Ising (ANNNI) model can explain almost all of the facts, provided that it is unified with the XY model appropriately. The unified model can make a comprehensive explanation in the most natural way based on the most probable molecular interactions. We have then emphasised that there are several modes regarding the V-shaped switching, because the system becomes so soft with respect to the tilting direction and sense that any additional external or internal force modifies the in-plane local director alignments. For the practically usable ones, we have emphasised the need for some type of randomization in the molecular alignment at the tip of the V and/or the switching process. In particular, the two dimensional (ideally, cylindrically symmetric) azimuthal angle distribution of local in-plane directors around the smectic layer normal is most attractive. Such a randomized state at the tip of the V is thermodynamically unique under a given condition imposed by interfaces. It stays stable even when the smectic layer structure, such as a chevron, changes with temperature. Finally, we have summarized the so-far reported compounds and mixtures for the V-shaped switching and introduced some prototypes of LCDs using them.