Smectics external fields

In the previous sections we have shown that the inclusion of the director of the underlying nematic order in the description of a smectic A like system leads to some important new features. In general, the behavior of the director under external fields differs from the behavior of the layer normal. In this chapter we have only discussed the effect of a velocity gradient, but the effects presented here seem to be of a more general nature and can also be applied to other fields. The key results of our theoretical treatment are a tilt of the director, which is proportional to the shear rate, and an undulation instability which sets in above a threshold value of the tilt angle (or equivalently the shear rate). 

The subject of liquid crystals has now grown to become an exciting interdisciplinary field of research with important practical applications. This book presents a systematic and self-contained treatment of the physics of the different types of thermotropic liquid crystals - the three classical types, nematic, cholesteric and smectic, composed of rod-shaped molecules, and the newly discovered discotic type composed of disc-shaped molecules. The coverage includes a description of the structures of these four main types and their polymorphic modifications, their thermodynamical, optical and mechanical properties and their behaviour under external fields. The basic principles underlying the major applications of liquid crystals in display technology (for example, the twisted and supertwisted nematic devices, the surface stabilized ferroelectric device, etc.) and in thermography are also discussed. 

Preceding the reports on elastomers, piezoelectricity in chiral smectic C phases of low-molar weight molecules or of polymers has usually been observed. The special property is that the system possesses macroscopic electrical polarization without an external field, so it is classified as ferroelectric. 

Rod-shaped vimses can form hquid crystalline phases, which can be controlled by factors like virus suspension concentration, ionic strength of solution, external fields, etc. For example, Ml 3 phages are found to randomly orientated in an isotropic concentration range but transform to nematic, cholesteric, and smectic phases with... 

Intensity fluctuations are also clearly visible. However, the practiced eye will notice that only disclinations of whole number rank are present in the preparation. Focal conic zones remain unchanged, up to some small details. But where only one colour was observed previously, we now often find two colours separated by a thin wall. All these observations are compatible with the simple idea that molecules are tilted relative to the plane of the layer, as shown in Fig. 9.11a. When there is no external field, the tilt direction remains indeterminate, just as we found for the directions of optical axes in nematic phases, which gave rise to their threadlike texture. However, the absence of disclinations of whole number rank is characteristic of a layered structure. The two colours can be understood as being due to occurrence of positive and negative tilts in thin preparations (see Fig. 9.11b). These arguments are corroborated by crystallographic studies. We have thus discovered a second type of layered liquid crystal, called the smectic C phase, or Sc- Note that this tilting does not preclude a liquid-type order within layers (a kind of 2-dimensional nematic phase). 

Tendencies to instability in nature have been interpreted in various ways in continuum theory. We recall that many substances exhibit several phase transitions as, for example, their temperature is increased. A material initially described as a rigid solid may pass through smectic and nematic liquid crystal phases prior to behaving like an isotropic liquid. In a liquid crystal polymer, the concentration of solvent sometimes has the role of temperature. In the liquid crystal phase, the orientation of the molecules in terms of the optical axis may contribute to the response of this "fluid" to external fields. It is sometimes called an internal variable". The traditional field equations for an isotropic liquid are replaced by a more elaborate collection derived on the basis of continuum theory, (Ericksen [10], Leslie, [16], Hissbrun [H]). 

Both cholesteric and smectic mesophases are layered. In the former case, the periodicity arises from a natural twist to the director field, and in the latter, from a center-of-mass correlation in one dimension. There are many types of smectic phases distinguished by their symmetry and order. The set of field-induced phenomena is quite different for these two materials, owing primarily to the very different layer compressibility. That is, the cholesteric pitch can be unwound by an external field, whereas the smectic layering is typically too strong to be altered significantly. However, because of the common layered structure, there are also strong similarities. 

Contrary to cholesterics and nematics, not much work has been done regarding the effects of external fields on smectics. The possibility of a Freedericksz transition in a smectic liquid crystal by an external dc magnetic field has been considered by Helfrich, Rapini, Hurault, and Meirovitch et The results show that all transitions... 

The model is qualitatively as follows. At high frequencies an electro-convective instability with a periodic velocity distribution in the plane of the layer appears in all samples (in the isotropic phase, in the planar and homeotropically oriented nematics, in cholesterics [111], in nematics with smectic order, and even in smectic A [77]), because of the nonuniform distribution of the space charge along the direction of the external field Ez)-... 

Electric field is also expected as an effective external field to drive finite and fast deformation in LCEs, because, as is well known for low molecular mass LCs (LMM-LCs), an electric field is capable of inducing fast rotation of the director toward the field direction [6]. This electrically driven director rotation results in a large and fast change in optical birefringence that is called the electro-optical (EO) effect. The EO effect is a key principle of LC displays. Electrically induced deformation of LCEs is also attractive when they are used for soft actuators a fast actuation is expected, and electric field is an easily controlled external variable. However, in general, it is difficult for LCEs in the neat state to exhibit finite deformation in response to the modest electric fields accessible in laboratories. Some chiral smectic elastomers in the neat state show finite deformation stemming from electroclinic effects [7,8], but that is beyond the scope of this article we focus on deformation by director rotation. 

The twisted ground state of chiral liquid crystals willingly accepts the additional deformations imposed by external fields, surface interactions, or by a tendency of molecules to form smectic layers, hexagonal order, or doubletwist arrangements. Very often such additional deformations result in topo-... 

The electroclinic effect is a result of the coupling between tilt and polarization. The polarization Pe, which is induced by an external field E in the smectic- phase of chiral molecules, consists of a part Po which is present in every dielectric (orientation and electronic polarization), and a part Pg which is due to the P-6 coupling and should show a similar behavior as the induced tilt angle 9. While it is difficult to separate Pg and Pq exactly, measurements of the total polarization in the smectic- phase and around the smectic- -smectic-C transition indicate at least qualitatively that Pg and 9 show very similar behavior [65]. 

External field distortions in SmC and chiral SmC phases have been investigated [38], but the large number of elastic terms in the free-energy, and the coupling between the permanent polarization and electric fields for chiral phases considerably complicates the description. In the chiral smectic C phase a simple helix unwinding Fr6ede-ricksz transition can be detected for the c director. This is similar to the chiral nematic-nematic transition described by Eq. (83), and the result is identical for the SmC phase. Indeed it appears that at least in interactions with magnetic fields in the plane of the layers, SmC and SmC phases behave as two dimensional nematics [39]. 

An internal/external field competition [33] may be at work in the SmCfg phase observed in an applied electric field [35] when the helix structure is suppressed by an applied electric field. However, while our understanding of the re-entrant mechanism behind the behavior illustrated by Fig. 10 is relatively complete [34], nonlinear theories of smectic phase transitions [36] have not yet accounted for the observed helielec-... 

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