Smectic spontaneous polarization, pitch

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

A variety of effects can occur in the TGB phases due to the influence of an electric field. The coupling between the director and the field may be due to the dielectric anisotropy Sa, or due to the dependence of the smectic tilt angle on the electric field (electroclinic effect), or due to the spontaneous polarization. In contrast to the typical behavior of smectic phases, a small electric field cannot only result in a reorientation of the director, but also in a reorientation of the smectic layers [138], Higher fields can cause a reorientation of the pitch axis, helical unwinding [139], [140], a shift of the wavelength of selective refiection [141], or field-induced phase transitions [103], [141]. 

In the TGBc phase, each smectic slab exhibits a spontaneous polarization which is perpendicular to the pitch axis and shows a helical structure. Consequently, helielectric behavior can be expected. Indeed, a helical unwinding from the TGBc phase to a uniformly oriented SmC phase was observed [103]. 

In the higher temperature Sm A phase of a chiral compound the molecular symmetry axes are normal to the smectic layers and the local point symmetry is 2/m. This does not allow for spontaneous polarization to occur. In the Sm C phase, on the other hand, the tilt of the long molecular axes with respect to the layer normal breaks the mirror plane symmetry and the spontaneous polarization is induced. Due to chirality of the molecules, the symmetry axis turns its direction on going from one smectic layer to another. This implies that the polarization shows a helicoidal order with a pitch distinctly larger than the layer thickness. The helix can be easily unwound by an external electric field normal to the... 

In the absence of any constraints, the direction of Ps rotates from one smectic layer to the next, with a period equal to the smectic C pitch, and so the average polarization for a sample would be zero. However, surface treatment or application of a field can cause the helix to untwist, resulting in a permanently polarized sample. The spontaneous polarization arises from a preferred alignment of molecular dipole components which are perpendicular to the molecular long axis, but it behaves differently from the ferroelectric and ferromagnetic polarization characterised for crystals. The liquid crystalline ferroelectric phases identified so far are improper ferroelectrics, since the spontaneous polarization results from a symmetry constraint, whereas in proper ferroelectrics the polarization results from dipole -dipole interactions. The Curie-Weiss law for proper ferroelectrics predicts a second order phase transition at the Curie temperature from the high temperature paraelectric state to a permanently polarized ferroelectric state ... 

The Clark-Lagerwall Effect. This effect is observed in thin surface-stabilized FLC (SSFLC) cells where the smectic layers are perpendicular to the substrates, the thickness is less than the helical pitch (delectric field of opposite polarity switches the direction of the spontaneous polarization between the UP and... 

On a macroscopic scale, the spontaneous polarization vector in the optically active phase spirals about an axis perpendicular to the smectic layers (Fig. 20), and sums to zero. This macroscopic cancellation of the polarization vectors can be avoided if the helical structure is unwound by surface forces, by an applied field, or by pitch compensation with an oppositely handed dopant. The surface stabilized ferroelectric liquid crystal display utilizes this structure and uses coupling between the electric field and the spontaneous polarization of the smectic C phase. The device uses a smectic C liquid crystal material in the so-called bookshelf structure shown in Fig. 21a. This device structure was fabricated by shearing thin (about 2 i,m) layers of liquid crystal in the... 

In other words, molecular design and the synthesis were carried to express various characteristics for the required purposes that depend on the specific application of the ferroelectric liquid crystal. For example, ferroelectric liquid crystals with large spontaneous polarization, a large tilt angle with small temperature dependence, a specific viscosity, a small rotational viscosity of the molecules along their long axis, a chiral smectic C phase over a wide temperature range, a characteristic anisotropy of the dielectric constant, a suitable phase sequence, a suitable helical pitch, photochemical stability, and so on have been newly synthesized [3-5]. 

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