Polymers Leslie viscosities

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. 

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... 

Using scattering and spectroscopy experiments, it has been shown that the physical quantities characterizing the wormlike micellar nematics such as the order parameter, Leslie viscosities ratio, or alignment angles can be determined. The main result of this section is the analogy between the wormlike micelles and the liquid-crystalline polymers, as far as their nematic states are concerned. Because these... 

The values of the rotational viscosity coefflcients obtained for polymers X in the nematic phase (10-10 Pa sec) [37, 40], for polymer vn in the reentrant nematic phase (=5 10 Pa-sec) [42], and finally, the values of the Leslie viscosity coefficients (03, for polymer I (=10 Pa-sec) [43] also indicate the participation of the main chains of the macromolecules in orientational motion. It is evident that the polymeric viscosity of LC melts of comb-shaped polymers also determines all of the basic kinetic features of the orientational processes in external fields. 

At low enough shear rates, polymeric nematics ought to obey the same Leslie-Ericksen continuum theory that describes so well the behavior of small-molecule nematics. The main difference is that polymers have a much higher molecular aspect ratio than do small molecules, which leads to greater inequalities in the the numerical values of the various viscosities and Frank constants and to much higher viscosities. 

The hydrodynamics of the liquid crystalline polymer is described by the Ericksen-Leslie theory but liquid crystalline polymers have their polymeric characteristics, such as the viscosity s dependence on the molecular length. 

The detail of the Doi theory can be refered to in the book by Doi and Edwards The Theory of Polymer Dynamics (1986) in which the Leslie coefficients are related to the order parameter and the isotropic viscosity fj as follows... 

As elaborated above, the Ericksen-Leslie theory takes into account only the first rank effect of the velocity gradient of liquid crystalline polymers. If the amplitude of the velocity gradient is high enough, these theories are no longer valid and the steady viscosity of liquid crystalline polymers... 

In addition to the Miesowicz viscosities, the Brochard model also enables one to predict how dissolution of a polymer in a nematic solvent will modily the Leslie... 

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-... 

S. Kazunori, G. C. Berry, Frank elastic constants and Leslie-Ericksen viscosity coefficients of nematic solutions of rodlike polymer. Mol. Cryst. Liq. Cryst. 1987,153,133-142. 

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