The Nematic Viscosities

It is appropriate at this point to discuss some of the properties of the nematic viscosity coefficients in relation to basic experimental ideas and give some insight to their physical interpretation. It is also important to give the relationship between the notation used for the Lesfie viscosities and the notation used by other 

Miesowicz distinguished three principal viscosity coefficients, 7/1,772 and 773, that could be independently measured experimentally by considering the orientation of the director n in relation to the flow velocity v. The three basic flow geometries considered by Miesowicz are depicted in Fig. 4.1 and allow the measurement of the viscosities  

We have adopted the notation used by Miesowicz, but it should be pointed out that some workers occasionally use what is commonly called the Helfrich notation [124], 

Substituting equation (4.156)i into the viscous stress given by (4.86) then dehvers 

When elastic terms are neglected the shear stress relevant to Fig. 4.1 is the viscous force along the a -direction per unit area in a plane normal to the 2 -axis this is simply i3. The apparent viscosity t7(, 0) is defined in the usual way for such a geometry by (cf. de Gennes and Frost [110, p.211], who use the transpose of the viscous stress defined in this text) 

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Table D.3 on page 330 gives a collection of viscosities for the nematic phases of the materials MBBA, PAA and 5CB. (Note that the coefficient ai quoted in de Gennes and Prost [110, p.231] for MBBA near 25°C (based upon the work of Gawiller [97]) is positive, whereas a more recent report by Kneppe, Schneider and Sharma [155] has revealed ai to be negative.) For a brief introduction to the major experimental techniques used for evaluating the nematic viscosities the reader is referred to the review by Moscicki [205].

The slow modes tend to be dominant in light scattering experiments from which information on the nematic viscosities can be obtained, as we now proceed to demonstrate. 

These results were obtained by using the viscous dissipation inequality (6.207) to obtain quadratic forms analogous to those used to obtain the inequalities for the nematic viscosities at equations (4.91) to (4.95) in Section 4.2.3. Ebcpressions (6.241) to (6.246) are of the form xp > with x > 0 and p > 0. Since (a — =... 

The polyamides are soluble in high strength sulfuric acid or in mixtures of hexamethylphosphoramide, /V, /V- dim ethyl acetam i de and LiCl. In the latter, compHcated relationships exist between solvent composition and the temperature at which the Hquid crystal phase forms. The polyamide solutions show an abmpt decrease in viscosity which is characteristic of mesophase formation when a critical volume fraction of polymer ( ) is exceeded. The viscosity may decrease, however, in the Hquid crystal phase if the molecular ordering allows the rod-shaped entities to gHde past one another more easily despite the higher concentration. The Hquid crystal phase is optically anisotropic and the texture is nematic. The nematic texture can be transformed to a chiral nematic texture by adding chiral species as a dopant or incorporating a chiral unit in the main chain as a copolymer (30). 

If one follows the solution viscosity in concentrated sulfuric acid with increasing polymer concentration, then one observes first a rise, afterwards, however, an abrupt decrease (about 5 to 15%, depending on the type of polymers and the experimental conditions). This transition is identical with the transformation of an optical isotropic to an optical anisotropic liquid crystalline solution with nematic behavior. Such solutions in the state of rest are weakly clouded and become opalescent when they are stirred they show birefringence, i.e., they depolarize linear polarized light. The two phases, formed at the critical concentration, can be separated by centrifugation to an isotropic and an anisotropic phase. A high amount of anisotropic phase is desirable for the fiber properties. This can be obtained by variation of the molecular weight, the solvent, the temperature, and the polymer concentration. 

The equilibrium value of a in the nematic phase can be determined by minimizing AF. With Eq. (19) for AF from the scaled particle theory, S has been computed as a function of c, and the results are shown by the curves in Fig. 12. Here, the molecular parameters Lc and N were estimated from the viscosity average molecular weight Mv along with ML and q listed in Table 1, and d was chosen to be 1.40 nm (PBLG), 1.15 nm (PHIC), and 1.08 nm (PYPt), as in the comparison of the experimental phase boundary concentrations with the scaled particle theory (cf. Table 2). 

The discotic phases can show also a complex polymorphism. Nematic and cholesteric-like, low viscosity phases have been reported recently. In these, the director vector is perpendicular to the plane of alignment of the flat molecules56) in contrast to the normal nematics and cholesterics where it is parallel to the molecular axis. Most frequently, however, discotics form columnar arrangements as shown in Fig. 10. The order within the columns may change from liquid to quasi-crystalline. The columns are then packed in hexagonal or tetragonal coordination, but are free to slide in the direction parallel to their axes S7). The viscosity of these more ordered discotics is considerably higher than the nematic discotics. 

Monomeric l.c. s show in the polarizing microscope under crossed polarizers characteristic textures, owing to their optical anisotropy 51). Examining a nematic phase, which is sandwiched between untreated glass plates, typical interferences are observed, because of the variations of the optical axis with respect to the incident of light. The nematic polymers exhibit a similar bevahior. In Fig. 10a a typical picture of the texture of a polymer is shown. While for 1-l.c, s the texture can be observed immediately after preparation because of their low viscosity, in most cases the polymers samples... 

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],... 

The molecular theory of Doi [63,166] has been successfully applied to the description of many nonlinear rheological phenomena in PLCs. This theory assumes an un-textured monodomain and describes the molecular scale orientation of rigid rod molecules subject to the combined influence of hydrodynamic and Brownian torques, along with a potential of interaction (a Maier-Saupe potential is used) to account for the tendency for nematic alignment of the molecules. This theory is able to predict shear thinning viscosity, as well as predictions of the Leslie viscosity coefficients used in the LE theory. The original calculations by Doi for this model employed a preaveraging approximation that was later... 

We close this section by examining the status of applications of these methods to polymer monolayers. Initially, ISR was used to probe the 2D nematic state of phthalocyaninatopolysiloxane, descriptively called a hairy rod , dispersed in eicosanol [ 149], and subsequently applied to a set of poly(f-butyl methacrylate) in the semi-dilute regime and beyond [150]. In the semi-dilute regime, the surface viscosity is found to scale linearly with molecular weight, which is in good accord with the results of Sacchetti et al. [134]... 

Liquid crystals can display different degrees of long-range order, dependent on temperature, chemical composition, and the presence or absence of electric fields. In the nematic phase, the molecular axes point in a common direction, denoted by the director n but the molecular centers are otherwise arranged randomly. Because of the low degree of long-range order, nematic LCs have viscosities typical of ordinary liquids, and displays based on nematic LCs can operate at television frame rates. The most popular nematic-based display, the twisted nematic (TN), will be discussed in more detail below. 

The three elastic constants are the Frank elastic constants, called after Frank, who introduced them already in 1958. They originate from the deformation of the director field as shown in Fig. 15.52. A continuous small deformation of an oriented material can be distinguished into three basis distortions splay, twist and bend distortions They are required to describe the resistance offered by the nematic phase to orientational distortions. As an example, values for Miesowicz viscosities and Frank elastic constants are presented in Table 15.10. It should be mentioned that those material constants are not known for many LCs and LCPs. Nevertheless, they have to be substituted in specific rheological constitutive equations in order to describe the rheological peculiarities of LCPs. Accordingly, the viscosity and the dynamic moduli will be functions of the Miesowicz viscosities and/or the Frank elastic constants. Several theories have been presented that are more or less able to explain the rheological peculiarities. Well-known are the Leslie-Ericksen theory and the Larson-Doi theory. It is far beyond the scope of this book to go into detail of these theories. The reader is referred to, e.g. Aciemo and Collyer (General References, 1996). 

For a specific polymer, critical concentrations and temperatures depend on the solvent. In Fig. 15.42b the concentration condition has already been illustrated on the basis of solution viscosity. Much work has been reported on PpPTA in sulphuric acid and of PpPBA in dimethylacetamide/lithium chloride. Besides, Boerstoel (1998), Boerstoel et al. (2001) and Northolt et al. (2001) studied liquid crystalline solutions of cellulose in phosphoric acid. In Fig. 16.27 a simple example of the phase behaviour of PpPTA in sulphuric acid (see also Chap. 19) is shown (Dobb, 1985). In this figure it is indicated that a direct transition from mesophase to isotropic liquid may exist. This is not necessarily true, however, as it has been found that in some solutions the nematic mesophase and isotropic phase coexist in equilibrium (Collyer, 1996). Such behaviour was found by Aharoni (1980) for a 50/50 copolymer of //-hexyl and n-propylisocyanate in toluene and shown in Fig. 16.28. Clearing temperatures for PpPTA (Twaron or Kevlar , PIPD (or M5), PABI and cellulose in their respective solvents are illustrated in Fig. 16.29. The rigidity of the polymer chains increases in the order of cellulose, PpPTA, PIPD. The very rigid PIPD has a LC phase already at very low concentrations. Even cellulose, which, in principle, is able to freely rotate around the ether bond, forms a LC phase at relatively low concentrations. 

An important dimensionless relationship between viscosity and concentration was found by Papkov et al. (1974) and reproduced in Fig. 16.30, where the variation of viscosity with polymer concentration for different molecular weights, expressed as intrinsic viscosities, is shown (left). The reduced viscosity t]/if vs. the reduced concentration c/c is shown on the right. The viscosity of the solution jumps down rapidly above the critical concentration as the nematic mesophase forms. The dimensionless relationship is remarkable. The relationship between the viscosity at the maximum and the intrinsic viscosity (see inset) appears to be r/max = 5.5b/]1 5, where rj is expressed in Ns/m2 and [77] in m3/kg. 

The flow viscosity of a nematic phase also determines the spatial and temporal response of the director to an applied field. The bulk viscosity of a nematic phase depends on the direction of flow of each molecule with respect to the director, averaged out over the whole of the sample. Therefore, bulk viscosity is... 

Therefore, switch-off times are independent of the field strength and directly dependent on material parameters, such as viscosity coefficients and elastic constants, and the cell configuration. Therefore, they are often three or four orders of magnitude larger than the switch-on times. However, sophisticated addressing techniques can produce much shorter combined response times ( on + off The nematic director should be inclined, e.g. 1° pretilt,... 

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