Viscous nematics

New mathematical techniques [22] revealed the structure of the theory and were helpful in several derivations to present the theory in a simple form. The assumption of small transient (elastic) strains and transient relative rotations, employed in the theory, seems to be appropriate for most LCPs, which usually display a small macromolecular flexibility. This assumption has been used in Ref [23] to simplify the theory to symmetric type of anisotropic fluid mechanical constitutive equations for describing the molecular elasticity effects in flows of LCPs. Along with viscoelastic and nematic kinematics, the theory nontrivially combines the de Gennes general form of weakly elastic thermodynamic potential and LEP dissipative type of constitutive equations for viscous nematic liquids, while ignoring inertia effects and the Frank elasticity in liquid crystalline polymers. It should be mentioned that this theory is suitable only for monodomain molecular nematics. Nevertheless, effects of Frank (orientation) elasticity could also be included in the viscoelastic nematody-namic theory to describe the multidomain effects in flows of LCPs near equilibrium. 

Continuum theory has also been applied to analyse tire dynamics of flow of nematics [77, 80, 81 and 82]. The equations provide tire time-dependent velocity, director and pressure fields. These can be detennined from equations for tire fluid acceleration (in tenns of tire total stress tensor split into reversible and viscous parts), tire rate of change of director in tenns of tire velocity gradients and tire molecular field and tire incompressibility condition [20]. 

Chiral nematic Hquid crystals are sometimes referred to as spontaneously twisted nematics, and hence a special case of the nematic phase. The essential requirement for the chiral nematic stmcture is a chiral center that acts to bias the director of the Hquid crystal with a spontaneous cumulative twist. An ordinary nematic Hquid crystal can be converted into a chiral nematic by adding an optically active compound (4). In many cases the inverse of the pitch is directiy proportional to the molar concentration of the optically active compound. Racemic mixtures (1 1 mixtures of both isomers) of optically active mesogens form nematic rather than chiral nematic phases. Because of their twist encumbrance, chiral nematic Hquid crystals generally are more viscous than nematics (6). 

They have been prepared with several anions,332-335 the tetrafluoroborate salt exhibits SA and Sc phases332,333 but the triflate shows a nematic phase 334 One of the problems in studying these complexes was the very high temperatures at which the phases existed and the fact that decomposition was often observed in the upper reaches of the SA phases. Reduction of these temperatures was achieved by changing the small anions for dodecyl sulfate that also make that more materials exhibit nematic SA and Sc phases, and another more viscous phase appeared, named cubic phase So- With the anion octyl sulfate336 the crystal structure of one of the complex with 4-metoxystilbazole could be achieved (20), with this anion the cubic phase was not present. 

Here a is the elastic stress which arises from the change in the (dynamic) free energy in the macroscopic flow, while o(V) and a(S) are the viscous stresses produced by the polymer-solvent friction and the solvent-solvent friction, respectively. In concentrated isotropic polymer solutions, the elastic stress overwhelms the viscous stresses, so the latter are often neglected. However, it should be noticed that the viscous stresses may become significant in more dilute solutions as well as in nematic solutions where the elastic stress diminishes. 

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. 

Theoretical analysis indicates that occurrence of such convective instabilities depends on anisotropy of electrical conductivity and dielectric properties in the initial aligned nematic material. That is, conductivity parallel to the direction of alignment must differ from conductivity perpendicular to this direction. Calculation of the stability condition requires knowledge not only of these anisotropic electrical properties but also of anisotropic elastic and viscous properties which oppose disruption of the alignment and flow. 

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. 

Above 110 °C, this arrangement becomes mobile, and a smectic C liquid-crystalline phase is entered. Samples cooled down from the isotropic melt (140 °C) show Schlieren and banded textures when viewed under crossed polarizers (Figure 8). These textures look similar to nematic Schlieren textures, but from the X-ray diffraction data it is clear that 12c forms a homeotropically oriented smectic C phase. In a nematic phase, the small-angle diffraction peak would be absent, and a broad scattering feature, a nematic streak , would be observed. Polymer 12c was the first example of a PPE derivative for which three states of matter, i.e. crystalline, thermotropic liquid crystalline, and a highly viscous isotropic liquid, were accessible [46]. 

The big difference between normal isotropic liquids and nematic liquids is the effect of anisotropy on the viscous and elastic properties of the material. Liquid crystals of low molecular weight can be Newtonian anisotropic fluids, whereas liquid crystalline polymers can be rate and strain dependent anisotropic non-Newtonian fluids. The anisotropy gives rise to 5 viscosities and 3 elastic constants. In addition, the effective flow properties are determined by the flow dependent and history dependent texture. This all makes the rheology of LCPs extremely complicated. 

Aromatic liquid crystals, such as compounds 106-109 collated in Table 3.10, have been investigated to a much lesser extent since they were perceived to be intrinsically more viscous than the analogous cyclohexane derivatives. This is indeed often the case. It was hoped that the incorporation of a fluorine atom in a lateral position of a polar compound, such as the ester (106), would create a nematic material, such as the esters (107 and 108), of positive dielectric anisotropy and low ratio of and Ae/sj.. Although this was partially... 

In a flowing nematic, the viscous and distortional stresses must satisfy the balance of linear... 

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