Director viscosity measurement

The hydrodynamic equations of the classical nematic ( 3.1) are applicable to the N, phase as well. There are six viscosity coefficients (or Leslie coefficients) which reduce to five if one assumes Onsager s reciprocal relations. A direct estimate of an effective value of the viscosity of from a director relaxation measurement indicates that its magnitude is much higher than the corresponding value for the usual nematic. 

The first viscosity measurements of nematic liquid crystals were performed with classical shear flow viscometers flow induces a change in orientation of the director, see EQN (4), so the effective viscosity measured is r o [54,55]. Since r o can be considered a relatively good approximation to the Miesowicz r i, conventional viscometers are still in use in conjunction with yi measurements [44,56,82,86]. However, for the purpose of measuring the viscosity anisotropy oldo instruments had to be modified and new ones developed. 

Table 3.14 Transition temperatures (°C), elastic constants fk/y, k22 kjj, 10 N), dielectric anisotropy ( e), dielectric constant measured perpendicular to the molecular long axis (e ), birefringence ( n), refractive index measured perpendicular to the director (noJ, rotational viscosity (y. Poise) and bulk viscosity (r, Poise) for tr ns-l-(4-cyanophe-nyl)-4-pentylcyclohexane (41), iTSins-l-(4-cyanophenyl)-4-[(E)-pent-l-enyl]cyclohexane (74) andtra.ns-l-(4-cyanophenyl)-4-[(E)-pent-3-enyI]cyclohexane (78) extrapolated to 100% at 22°...

If the director is held in a fixed orientation by a magnetic field strong enough to resist the orienting effects of flow, then shear-rate-independent viscosities can be measured in a simple shearing flow. The three simplest of these, called the Miesowicz viscosities, are obtained in each of the three director orientations shown in Fig. 10-8. These viscosities can be related in a simple way to the or,- s, namely,... 

Figure 10.8 (a-c) The Miesowicz viscosities, and rjc are measured when the director is locked by a strong field in the orientations shown. (Adapted from Skarp et al., reprinted with permission from Mol. Cryst. Liq. Cryst. 60 215, Copyright 1980, Gordon and Breach Publishers.)... 

Figure 10.14 Measured shear viscosity n against strain y for 8CB at 36.6°C (3.2°C below Tni) and a shear rate of y — 16 seer, fit by Eqs. (10-29) and (10-31) of the Ericksen theory with the director confined to the deforraation plane. (From Gu and Jamieson, reprinted with permission from J. Rheol. 38 555, Copyright 1994, American Institute of Physics.)...

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. 

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. 

The new FC technique made possible extensive measurements of the self-diffusion constans Dg and Dj of liquid crystals, parallel ( ) and perpendicular (-L) to the director axis, with v ues as low as 10 m s . The most challenging requirements exist for nematic mesophases because their low viscosity facilitates flow in the nonequilibrium state and so necessitates the fast FC procedure to establish the magic angle rotation of the director... 

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. 

The coefficient y is rotational viscosity of the director similar to coefficient yi for nematics. In fact, it does not include a factor of sin cp and, in the same temperature range, can be considerably larger than the viscosity ytp for the Gold-stone mode. This may be illustrated by Fig. 13.10 the temperature dependence of viscosities y and have been measured for a chiral mixture that shows the nematic, smectic A and smectic C phases [15]. The pyroelectric and electrooptic techniques were the most appropriate, respectively, for the measurements of ya and ytp describing the viscous relaxation of the amplitude and phase of the SmC order parameter. The result of measurements clearly shows that y is much larger than y and, in fact, corresponds to nematic viscosity yj. 

Five independent viscosity parameters are required to describe the flow of nematics and cholesterics. The set of five may be chosen in various ways.9 one particularly simple set determines resistance to the motions shown in Fig. 4. The first three, riii U2 and ri3, are like the viscosity of ordinary isotropic liquids but depend on the relative direction of shear and director orientation. These three may be regarded as principal axis of a viscosity ellipsoid. The fourth, ni2 is a measure of deviation from true ellipticity, giving a difference in viscosity as directors lean toward or opposite the shear flow. The final viscosity, Yl determines resistance to pure rotation without flow. In some cases a fair approximation to twist cell behavior may be obtained ignoring flow and considering only Yl When numerical computations are undertaken, however, one might as well do the problem correctly and include the flow.11 12... 

The measured viscosity rj depends on the director orientation L with respect to the shear flow Vz z) and its gradient dvzfdx, Fig. 2.21((b)-(e)). In order to provide reliable experimental results only very low fiow rates must be used, which, together with the orienting influence of the... 

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