Smectic Viscosities

The viscous properties of a smectic A are characterized by the same five independent viscosities that characterize the nematic. As we shall see, however, the elastic properties of the smectic are very different from those of a nematic, and some flows permitted to the nematic are effectively blocked for the smectic. For smectic C, for which the director is tilted with respect to the layers, there are some 20 viscosities needed to characterize the viscous properties (Leslie 1993). Formulas for these, derived using a method analogous to that used for nematics by Kuzuu and Doi (1983, 1984) can be found in Osipov et al. (1995). The smectic phase for which rheological properties are most commonly measured is smectic A, however, and hereafter we will limit our discussion to it. 

In the b orientation in Fig. 10-28b, uniform shear tends to rotate the layers and change their spacing. Since the layer spacing is a solid-like property of the smectic phase, shearing in this orientation should produce a solid-like material response, at least for shearing stresses 

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Measurements for smectic viscosities are presently rather scarce in the literature although some early measurements, interpreted via dynamic equations similar to those for nematics, have been made by some workers such as Galerne, Martinand, Durand and Veyssie [100], among others see pages 300 and 301 below. Nevertheless, theoretical information about the smectic viscosities can be gained by further... 

It should also be remarked that Osipov, Sluckin and Terentjev [216] have applied a statistical approach for deriving elementary properties of the smectic viscosities. Their results coincide with the above expressions in equations (6.223) to (6.226) for small 6. Additionally, they give physical reasons for further approximations in elementary calculations, concluding that the viscosities A3, Ae, and T4, although not identically zero, may be set to zero in very basic and simple problems for the SmC phase because they expect these four viscosities to be much smaller than the remaining sixteen. These authors also note that there are four viscosity coefficients which may be considered as rotational viscosities. These particular viscosities are the ones which appear exclusively in the skew-symmetric contribution to the viscous stress namely. 

For other relevant combinations of the smectic viscosities which arise naturally, the reader should consult the article by Schneider and Kneppe [247]. These authors have identified and discussed, in relation to a general viscosity function, possibly relevant experimental combinations and have also suggested possible experiments for their measurement. 

Many inequalities involving the smectic viscosities can be derived using the viscous dissipation inequality (6.207). For example, elementary consideration of some basic flow alignments has shown that... 

Galerne, Martinand, Durand and Veyssie [100] have measured some of the smectic viscosities for the SmC liquid crystal DOBCP at 103°C. Prom the experimental data, Leslie and Gill [178] deduced that, in the context of light scattering, in terms... 

Tbe purpose of tbe bydroxyl group is to acbieve some hydrogen bonding with the nearby carbonyl group and therefore hinder the motion of the chiral center. Another way to achieve the chiral smectic Cphase is to add a chiral dopant to a smectic Chquid crystal. In order to achieve a material with fast switching times, a chiral compound with high spontaneous polarization is sometimes added to a mixture of low viscosity achiral smectic C compounds. These dopants sometimes possess Hquid crystal phases in pure form and sometimes do not. 

The viscosity of thermotropic liquid crystals increases following the sequenee nematic< smectic A < smectic C. 

It can be safely predicted that applications of liquid crystals will expand in the future to more and more sophisticated areas of electronics. Potential applications of ferroelectric liquid crystals (e.g. fast shutters, complex multiplexed displays) are particularly exciting. The only LC that can show ferroelectric property is the chiral smectic C. Viable ferroelectric displays have however not yet materialized. Antifer-roelectric phases may also have good potential in display applications. Supertwisted nematic displays of twist artgles of around 240° and materials with low viscosity which respond relatively fast, have found considerable application. Another development is the polymer dispersed liquid crystal display in which small nematic droplets ( 2 gm in diameter) are formed in a polymer matrix. Liquid crystalline elastomers with novel physical properties would have many applications. 

Polarized light is the must powerful tool for investigating liquid crystals, all of which exhibit characteristic optical properties. A smectic liquid crystal transmits light more slow ly perpendicular to the layers than parallel to them. Such substances are said to be optically positive. Nematic liquid crystals are also optically positive, bui their action is less definite than that of smectic liquid crystals. However, the application of a magnetic field to nematic liquid crystals lines up their molecules, changing their optical properties and even their viscosity. 

The rheological behaviour of thermotropic polymers is complex and not yet well understood. It is undoubtedly complicated in some cases by smectic phase formation and by variation in crystallinity arising from differences in thermal history. Such variations in crystallinity may be associated either with the rates of the physical processes of formation or destruction of crystallites, or with chemical redistribution of repeating units to produce non-random sequences. Since both shear history and thermal history affect the measured values of viscosity, and frequently neither is adequately defined, comparison of results between workers and between polymers is at present hazardous. 

As in the case of low-molecular liquid crystals the majority of information about the structure of LC polymers is obtained from their optical textures and X-ray diffraction data. Because of high viscosity of polymer melts, which results in retardation of all structural and relaxation processes it is quite difficult to obtain characteristic textures for LC polymers. As is noted by the majority of investigators smectic LC polymers form strongly birefringent films as well from solutions, as from melts11 27-... 

Analysis of flow curves of these polymers has shown that for a nematic polymer XII in a LC state steady flow is observed in a broad temperature interval up to the glass transition temperature. A smectic polymer XI flows only in a very narrow temperature interval (118-121 °C) close to the Tcl. The difference in rheological behaviour of these polymers is most nearly disclosed when considering temperature dependences of their melt viscosities at various shear rates (Fig. 20). 

For a nematic polymer in a transition region from LC to isotropic state, maximal viscosity is observed at low shear rates j. For a smectic polymer in the same temperature range only a break in the curve is observed on a lgq — 1/T plot. This difference is apparently determined by the same reasons that control the difference in rheological behaviour of low-molecular nematics and smectics 126). A polymeric character of liquid crystals is revealed in higher values of the activation energy (Ef) of viscous flow in a mesophase, e.g., Ef for a smectic polymer is 103 kJ/mole, for a nematic polymer3 80-140kJ/mole. 

Nakata M, Shao RF, Maclennan JE, Weissflog W, Clark NA (2006) Electric-field-induced chirality flipping in smectic liquid crystals the role of anisotropic viscosity. Phys Rev Lett 96 067802-1-067802-4... 

The phase transition temperatures of compounds 7a and 7b are summarized in Table 2. Compound 7a shows a highly viscous smectic (denoted as Sml) phase, smectic (denoted as Sm2 and Sm3) phases with lower viscosity, and an SmA phase. On the other hand, compound 7b shows a highly viscous smectic (denoted as Sm4) phase and a nematic phase. 

As mentioned in Sect. 2.1, we consider a shear induced smectic C like situation (but with a small tilt angle, i.e., a weak biaxiality). We neglect this weak biaxiality in the viscosity tensor and use it in the uniaxial formulation given above (with the director h as the preferred direction). This assumption is justified by the fact that the results presented in this chapter do not change significantly if we use p instead of h in the viscosity tensor. 

To extract concrete predictions for experimental parameters from our calculations is a non-trivial task, because neither the energetic constant B nor the rotational viscosity yi are used for the hydrodynamic description of the smectic A phase (but play an important role in our model). Therefore, we rely here on measurements in the vicinity of the nematic-smectic A phase transition. Measurements on LMW liquid crystals made by Litster [33] in the vicinity of the nematic-smectic A transition indicate that B is approximately one order of magnitude less than Bo. As for j we could not find any measurements which would allow an estimate of its value in the smectic A phase. In the nematic phase y increases drastically towards the nematic-smectic A transition (see, e.g., [51]). Numerical simulations on a molecular scale are also a promising approach to determine these constants [52],... 

In Fig. 8 we have illustrated that a small viscosity coefficient V2 facilitates the onset of undulations. In this section we will have a closer look at the effect of an anisotropic viscosity tensor and ask whether undulations can be caused only due to viscosity effects without any coupling to the director field (i.e., we consider standard smectic A hydrodynamics in this section). 

Consequently, a parallel alignment of smectic layers is linearly stable against undulations even if the perpendicular alignment might be more preferable due to some thermodynamic considerations. As we have shown in Fig. 8, this rigorous result of standard smectic A hydrodynamics is weakened in our extended formulation of smectic A hydrodynamics. When the director can show independent dynamics, an appropriate anisotropy of the viscosity tensor can indeed reduce the threshold values of an undulation instability. 

From now on, the permeation in (16) is neglected as it is several orders of magnitude smaller than the advection due to the radial component of the velocity vr (now playing the role of vz in the planar case). As far as the velocity perturbation is concerned, our aim is to describe its principal effect-the radial motion of smectic layers, i.e., instead of diffusion (permeation) we now have advective transport. In this spirit we make several simplifications to keep the model tractable. The backflow-flow generation due to director reorientation-is neglected, as well as the effect of anisotropic viscosity (third and fourth line of (19)). Thereby (19) is reduced to the Navier-Stokes equation for the velocity perturbation, which upon linearization takes the form... 

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