Mamoru Yamashita

A novel property caused by frustration between ferroelectricity and antiferroelectricity and its application to liquid crystal displays-frustoelectricity and V-shaped switching

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 devils staircase and the thresholdless, hysteresis-free, V-shaped switching induced by an applied electric field. The devils 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.

Long Range Interactions and the Sense of Molecular Long Axis in Ferroelectric Smectics

The successive phase transitions in the ferro- and antiferro-electric smectics have been described by the Ising model with competing interactions. The additional pseudo-spins are introduced newly to represent the sense of the molecular long axis. By taking the sum over the whole states of these pseudo-spins in the partition function, not only the nearest neighbour parameter of the Ising model are renormalized but additional long range interactions and many-body forces are shown to be induced. The effective second nearest neighbour interaction is shown to be antiferroelectric kind and the third nearest neighbour one is ferroelectric in some cases. In the ferroelectric phase and main antiferroelectric one the sense of the molecules is arranged such that the ordering is absent even in the ordered region in agreement with the symmetry of these phases, while in the other intermediate phases this ordering is proved to exist because of the bias due to the stacking of layer-orders.

Mechanism to Stabilise the Ferrielectric Phase in Ferroelectric Smectics

A model with a freedom of molecular sense has been proposed recently for the purpose to certify the assumptions in the ANNNI model with the third nearest neighbour interaction for successive phase transitions in ferroelectric smectics. The phase diagram of that model at the absolute zero temperature and orderings of the sense of molecular long axis are examined to clarify the mechanism to stabilise the ferrielectric phase (SmC * γ ) and the intermediate antiferroelectric phase (AF) appearing in such phase transitions. These phases are shown to be stable in certain area on a parameter space, which coincides qualitatively with the results based on the ANNNI model and consequently justifies the minimal theory carried out previously in which negative definiteness of the second nearest neighbour interaction and the existence of the third nearest neighbour one (or, positiveness) are certified.

Surface-Stabilized Smectic A Phase in the Gay-Berne Model.

Constant temperature molecular dynamics simulations of the system of molecules with the Gay-Berne potential interacting with walls are carried out to study the effects of the walls on the positional and orientational smectic orders. The system is composed of molecules put into a space sandwiched by parallel walls with periodic boundary condition in the lateral directions, in which various types of conditions of the walls are tested. The system is shown to exhibit several phases, that is, isotropic, nematic, smectic and crystalline phases as the temperature decreases, in which two types of smectic phases, the surface-stabilized smectic A phase and the usual one observed at the bulk system, are found and also the phase transition between these is shown to occur. The degrees of the positional and orientational orders of the former are higher than those of the latter, which indicates that the walls work not only as the field of the directional anchoring but also as a symmetry breaking field inducing the smect...

On Antiferroelectric Smectics Exhibiting Successive Phase Transitions in the Electric Field

The phase diagram of the axial next nearest neighbour Ising model with the third nearest neighbour interaction in an electric filed is obtained to study the phase transitions occurring in antiferroelectric smectic liquid crystals. Under suitable conditions, the jumps of the order parameters are small, though the transitions are necessarily of the first order in the absence of the electric field. The instability line of the ferroelectric phase, showing instability of the uniform phase with respect to periodic perturbation is also tested. The phase diagrams strongly suggest that the structure of the intermediate ferrielectric phase FIH has the wave number 2/7, and are also consistent with the previous result on FIL.

Effect of Fluctuation of Tilt Angle on Pitch in Chiral Smectic C Liquid Crystal

An anomalous temperature dependence of pitch of the helicoidal Sm C * structure near the Sm C * -Sm A transition point is investigated and attributed to the fluctuation effect of tilt angle. The large fluctuation increases the number of turns in the helicoidal structure, and leads to such an anomalous behaviour near the transition point. The deviation of the electric field dependence of pitch from the prediction of the conventional theory in this temperature region is also interpreted as the effect of that fluctuation.

Global phase diagram of Maier-Saupe model and inhomogeneity due to walls

A global phase diagram of Maier–Saupe model for nematic–isotropic phase transition on the external field versus temperature plane is obtained, where due to non-polar property of the system two sets...

V-shaped switching due to frustoelectricity in antiferroelectric liquid crystals

Abstract We have reinforced the assertion that the devils staircase and the thresholdless, hysteresis free, V-shaped switching are two manifestations of the frustration between ferro-and antif-erro-electricity, emphasizing that the third nearest neighbor interaction parameter may become negative, i.e. J 3 < 0. Three important consequences are: (1) The subphase with q=1/6 becomes to exist stably even in the ground state. (2) A number of subphases emerge and may apparently look like a single subphase. (3) It is not easy to distinguish SC* from frustrated subphases with small q numbers. We have summarized compounds and mixtures for the Y-shaped switching that are described in Japanese Patent Gazettes open to public recently. The materials show an antiferroelectric, probably q=1/6, subphase or an apparently single subphase in a wide temperature range; some of them are characterized with novel chiral parts.

Maier-saupe nematic isotropic phase transition in the presence of an external field

The nematic-isotropic phase transition in an external field is studied in the frame of Maier-Saupe model, where a global phase diagram including both cases of positive and negative susceptibility anisotropic is obtained. In the extreme case of infinitely large negative anisotropy, the system is reduced to the classical XY model because the rotational degree of freedom is restricted to lie in the plane perpendicular to the field, in which the second order phase transition occurs. The crossover of the directional degree of freedom between 3-dimension and 2-dimension is depicted. On the other hand, the critical point appears at a certain strength of the positive anisotropy, beyond which the transition disappears. The theory can be applied to the phase transition of very thin systems with homeotropic and planar anchorings.

Surface-Induced Spatial Ordering in Nematic and Smectic Phases of Gay-Berne Model

Abstract By constant temperature molecular dynamics simulation of Gay-Berne model with walls, the formation of liquid crystalline orders is studied, where typical three types of walls are tested. The wall is shown to work as a symmetry breaking field both for smectic order and nematic short range order of position. In addition to the surface-stabilised smectic A phase, smectic C phases stabilised topologically by the periodic boundary condition are obtained. In case these phases coexist it takes quite long time to achieve a uniform state of thermal equilibrium.