Viscosity measurements Leslie

Sometimes the volume viscosity, t/v, of a nematic liquid crystal is measured, which is close to the Leslie viscosities combination t]2 [14]. There is no theoretical explanation of the viscosity behavior of different liquid crystal substances and their mixtures. Also, there exist only a few works where the viscosity measurements are related to the corresponding molecular structure [28]. However, new liquid crystal, low-viscosity, materials are being successfully developed. To make these materials, the following phenomenological rules should be remembered [14] ... 

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.-----------------------------... 

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. 

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... 

We shall now discuss the application of the Ericksen-Leslie theory to some practical problems in viscometry. Probably the first precise determination of the anisotropic viscosity of a nematic liquid crystal was by Miesowicz. He oriented the sample by applying a strong magnetic field and measured the viscosity coefficients in the following three geometries using an oscillating plate viscometer ... 

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. 

Experimentally it is not easy to measure all of the Leslie coefficients. What is often measured is the Miesoviez viscosity defined by... 

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. 

New viscosity coefficients pj and A, are related to Leslie coefficients. In particular, po = 0 4 (viscosity of an isotropic liquid). Viscosimetry of SmA liquid crystals is difficult. For instance, in geometry (a), the upper and lower plates should be parallel with a great accuracy (few nanometers) otherwise defects appear. However, for several compounds the correspondent viscosities have been measured. In geometry (b) there was found a shear rate threshold above the threshold the isotropic behaviour (04) was observed. At lower rates, defects control a flow. 

The usual methods of determining the Leslie viscosity coefficients with magnetic field orientations, etc., are difficult to do with LCP s. The high viscosities make the time required excessively long for thermotropic LCP s with high transition temperatures. Devising new ways to measure these coefficients, preferably from flow experiments, possibly from flow stability measurements, would be useful to characterize these materials. 

Several methods have been developed to evaluate the Leslie viscosity coefficients described in detail in [18, 28, 31]. These methods include the inelastic scattering of light [60, 93], pulse [94], and rotating [95] magnetic fields, attenuation of the ultrasound shear wave [96], etc. The results obtained by different methods for such important coefficients as rotational viscosity agree fairly well with each other [78], Fig. 2.25. The simplest and most useful methods for measuring 71-values are based on the dynamics... 

The six Leslie coefficients can not be measured directly. They can only be determined with the aid of several experimental methods which ususally lead to combinations of these coefficients. Taking into account the Parodi equation, the six coefficients can be obtained from five linear independent viscosity coefficients. Thus, the four viscosity coefficients rji, rj2 and t/j2 and the rotational viscosity coefficient /] give a, = r)i2... 

An alternative to reorientation of the sample or the magnetic field is the application of shear during the NMR measurement [130-134]. For liquid-crystalline samples with high viscosity, such as liquid crystal polymers, the steady-state director orientation is governed by the competition between magnetic and hydrodynamic torques. Deuteron NMR can be used to measure the director orientation as a function of the applied shear rate and to determine two Leslie coefficients, and aj, of nematic polymers [131,134]. With this experiment, flow-aligning and tumbling nematics can be discriminated. Simultaneous measurement of the apparent shear viscosity as a function of the shear rate makes it possible to determine two more independent viscosity parameters [131, 134]. 

Figure 11 demonstrates the application of deuteron NMR spectroscopy on sheared samples with the simultaneous measurement of the viscosity to two different nematic polymer systems. The different behavior of these systems is apparent from the data one system is flow-aligning, the other system is tumbling. The Leslie eoefficients and 3 obtained for the shear-aligning system are both negative, whereas and 3>0 for the tumbling system. Deuteron NMR has also been employed to study the director orientation of lyotropic lamel-... 

There are other reports on the study of pretransitional dynamics in polymeric and lyotropic nematics. Quantitative measurements of ratios of Frank elastic constants and Leslie viscosities in the pretransitional range of poly-y-benzyl-glutamate polymeric nematic are reported by Taratuta et al. [85]. McClymer and Keyes [86-88] report light scattering studies of pretransitional dynamics of potassium laurate-decanol-D20 system. An interesting study of a magnetic-field induced I N phase transition in a colloidal suspension is reported by Tang and Fraden [89]. 

The static theory discussed in the previous section describes the equilibrium situation in chiral nematics very well - in general, theory and experiment are in good accord. The dynamic situation is less clear. On the molecular scale, the chiral nematic and nematic phases are identical the question then becomes, how does the macroscopic twist or helicity modify the vector stress tensor of the achiral nematic phase defined by the so-called [109] Leslie friction coefficients a -a T Experimentally, viscosity coefficients that are then related to the Leslie coefficients are measured in a way that depends specifically on the experiment being used to determine them. The starting point for discussion of dynamic properties is to use classical mechanics to describe the time dependencies of the director field n (r, t), the velocity field v (r, t), and their interdependency. Excellent reviews of this, for achiral nematics, are to be found in [59,109,... 

Although experimentally the pitch dependence is difficult to measure, the temperature dependence of the apparent viscosity indeed was foimd to show oscillating behavior, which is due to the temperature dependence of the pitch. Details of the Leslie and other theories and of the relevant experiments are discussed in the book of Chandrasekhar. ... 

In examining three different variants of the position of 71 relative to the directions of the velocity v and velocity gradient y, it is possible to distinguish and experimentally measure viscosity coefficients T i, Ti2. and TI3, which are correlated with the Leslie-Ericksen coefficients [50, p. 200] by the relations... 

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... 

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