Leslie viscosity

We have omitted discussing such interesting properties of liquid-crystal solutions as the Frank elastic constants, the Leslie viscosity coefficients, cholesteric pitch, textured structure (or defects), and rheo-optics. Some of them are reviewed in recent literature [8,167], but the level of their experimental and theoretical studies still remains largely qualitative. 

The ratio of elastic constants Ku, calculated for the S-effect according to the equation (4) appeared to be (Kn (polymer XIV)/Kn (polymer XIII)) x 1 100 and (Ku (polymer XVI)/Kn (polymer XV)) x 1 36. Yet, as we have just indicated, taking into account molecular masses of the LC polymers and reducing k, values for various polymers to equal values of DP one may come to substantially different values for ratios of constants presented. It is necessary to note that up to date no quantitative data on the determination of elastic constants of LC polymers has been published (excluding the preliminary results on Leslie viscosity coefficients for LC comb-like polymer127)). Thus, one of the important tasks today is the investigation of elastic and visco-elastic properties of LC polymers and their quantitative description. 

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... 

Figure 10.7 (a-c) The Leslie viscosities 0 3 and o 2 determine the direction and rate of rotation of the director (represented by the cylinders) in the orientations shown, For negative values of 3 and 2 (the usual signs for rod-like nematics), the rotation directions are shown by the arrows. The viscosity ua, determines the viscosity of the liquid when the director is in the vorticity direction. (Adapted from Skarp et al., reprinted with permission from Mol. Cryst. Liq. Cryst. 60 215, Copyright 1980, Gordon and Breach Publishers.)... 

Figure 10-9a shows measured values of these three viscosities as functions of temperature for MBBA (Kneppe et al. 1981, 1982). Of course, at temperatures for which MBBA is isotropic, all three viscosities are equal. From the three Miesowicz viscosities (the j s) in Fig. 10-9a, along with the three Leslie viscosities in Fig. 10-9b, the complete set of six Leslie viscosities can be extracted, de Gennes and Frost (1993) give a description of the experimental methods used to measure these viscosities.-----------------------------... 

In Eqs. (10-20), the six Leslie viscosities are given in terms of the characteristic viscosities 1 and ao (described below), the tumbling parameter k, the second and fourth moments... 

Very few data exist for the viscosities or Frank constants of discotic nematics—that is, nematics composed of disc-Uke particles or molecules (Chandrasekhar 1992). One can estimate values of the Leslie viscosities from the Kuzuu-Doi equations (10-20) by setting the aspect ratio p equal to the ratio of the thickness to the diameter of the particles thus /j — 0 for highly anisotropic disks. This implies that R(p) —1, and Eq. (10-20b) implies that the viscosity o 2 is large and positive for discoidal nematics, while it is negative for ordinary nematics composed of prolate molecules or particles. If, as expected, is much smaller in magnitude than 0 2. the director (which is orthogonal to the disks) will tend... 

Here is a typical Leslie viscosity, AT is a Frank constant, V is a flow velocity, /i is a length scale of the flow geometry, such as the tube diameter in Poiseuille flow, and ftn is the average shear rate. The Ericksen number is the ratio of the flow-induced viscous stress 6Ye.fi = /h to the Frank stress K/h. The appropriate Leslie viscosity or Frank constant... 

Because of the difficulty with which polymeric nematic monodomains are prepared, there are few measurements of Leslie viscosities and Frank constants for LCPs reported in the literature. The most complete data sets are for PBG solutions, reported by Lee and Meyer (1990), who dissolved the polymer in a mixed solvent of 18% dioxane and 82% dichloromethane with a few percent added dimethylformamide. Some of these data, measured by light scattering and by the response of the nematic director to an applied magnetic field, are shown in Figs. 11-19 and 11-20 and in Table 11-1. While the twist constant has a value of around K2 0.6 x 10 dyn, which is believed to be roughly independent of concentration and molecular weight, the splay and bend constants ATj and K3 are sensitive to concentration and molecular weight. 

Formulas for the Leslie viscosities, in turn, were derived from the Smoluchowski equation for hard rods by Kuzuu and Doi (1983,1984 Semenov 1987), and are given in Eqs. (10-20) with ao = 0- These formulas require as inputs values of 2,54, k, and Dr, which are functions of polymer concentration C. Reasonably reliable analytic functions for these dependencies were obtained by Kuzuu and Doi using a perturbation expansion for large order parameter, yielding... 

Here rj = v IcbT/ 0D is the viscosity of the (hypothetical) isotropic phase at C. The viscous stress, 10(v/v )7j jSyD (uuuu), contributes to the Leslie viscosities, as follows (Larson 1996) --------------------------------------------------------------------... 

Few other sets of viscosities exist for polymeric nematics. Yang and Shine (1993) obtained three of the Leslie viscosities for monodomains of poly(n-hexyl isocyanate) (PHIC) from rheological measurements in the presence of an electric field, and they obtained values reasonably consistent with the predictions of the Kuzuu-Doi expressions. From monodomains of the polyion PBZT, poly(l,4-phenylene-2,6-benzobisthiazole) in methane sulfonic acid, some of the Leslie-Ericksen parameters have been extracted via light-scattering and magnetic-field-reorientation studies (Berry 198S Srinivasarao and... 

Carlsson, T. Theoretical investigation of the shear flow of nematic liquid crystals with the Leslie viscosity as > 0 hydrodynamic analogue of first order phase transition. Mol. Cryst. Liq. Cryst. 1984, 104, 307-334. 

Table 2. Selected rotational viscosities and Leslie viscosities ui of the liquid crystalline n-alkyl-cyanobiphenyl series (nCB, n 5-8) obtained by FC flow experiments at di rent temperatures 6kT=Tc T relative to the nematic-to-isotropic transition temperature Tq (clearing point). Within the large error estimations of 10% for yj and 2, 100% for (04 + 05), 300% for 03, and 400% for oi, the results are essentially consistent with data reported in the literature. ...

On detailed analysis of the transient stress signatures, certain numerical discrepancies were noted [Gu et al., 1993 Gu and Jamieson, 1994a] between the experimental increments in Leslie viscosities 8as and Sas versus the Brochard prediction. Specifically, for the side-chain LCP, assuming an oblate conformation, the theory [Eiqs. (1.55)] predicts that both 8as and Sas should be positive, whereas we found [Gu et al., 1993 Gu and Jamieson, 1994a] that Sas < 0 and Sas > 0. Also, the magnitude and signs of these viscosity increments were found to be strictly inconsistent with... 

Finally, in addition to predictions for the increments in Miesowicz and Leslie viscosities, the Brochard theory predicts [Brochard, 1979] the increment Syi in the viscosity associated with the twist distortion of a nematic solvent on dissolution of a polymeric solute ... 

An explanation for these various discrepancies was suggested [Yao and Jamieson, 1998], based on the notion that when the nematic director of the solvent is allowed to rotate, one must take account of the coupling between the solvent director and the LCP director. This induces an additional viscous dissipation mechanism which contributes to the Leslie viscosities and the twist viscosity, but not to the Miesowicz viscosities ... 

With the Miesowicz technique one can measure three combinations of the Leslie viscosity coefficients from Eqs. (9.25) to (9.27). On account of the Parodi relationship, to find all five coefficients, one needs, at least, two additional measurements. In particular, the ratio of coefficients a3/a2 can be measured by observation of the director field distortion due to capillary flow of a nematic. The last combination yi = as — as can be found from the dynamics of director relaxation. 

Chapter 6 heralds the second part of the book and introduces the reader to anisotropy of the magnetic and electric properties of mesophases. Following in Chapter 7 there is a focus on the anisotropy of transport properties, especially of electrical cOTiductivity. Without these two chapters (Chapters 6 and 7), it would be impossible to discuss electro-optical properties in the third section of the book. Further, Chapters 7 and 8 deal with the anisotropy of the properties of elasticity and viscosity. Chapter 8 is more difficult than the others, and in order to present the theoretical results as clearly as possible, the focus is on the experimental methods for the determinatimi of Leslie viscosity coefficients from the viscous stress tensor of the nematic phase. Chapter 9 terminates the discussion of the anisotropy of... 

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