Viscosity coefficients Leslie

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... 

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... 

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. 

There exist a few works where Leslie viscosity coefficients or their linear combinations are determined in one experiment [65-69]. The principal approach to such an experiment is shown in Fig. 2.21. 

The total set of Leslie viscosity coefficients for nematic liquid crystal MBBA [28] and 5CB [32] are given in Table I (following the Introduction). 

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 two-dimensional model [66] of this domain structure shows that its threshold considerably depends on the value of the Leslie viscosity coefficient as and the dielectric anisotropy Ae. Unlike the Kapustin-Williams domains, this instability could also be observed for negative conductivity anisotropy. There remains only one specific point where the instability ceases to exist, namely, the conductivity isotropy point. Act = 0. 

A second requirement for this instability to occur is that the two Leslie viscosity coefficients tt2 and Oi are of opposite signs [276,312]. If the ratio between the two viscosities is positive, the director exhibits different dynamics it aligns with respect to the velocity at an angle 6I9 such that tan (6b) = a2/ 3- Note finally that, despite a complex microstructure, the classification in terms of flow-aligning and tumbling nematics, as defined for low molecular weight liquid-crystals, still applied to lyotropic systems. 

Theoretical treatments of liquid crystals such as nematics have proved a great challenge since the early models by Onsager and the influential theory of Maier and Saupe [34] mentioned before. Many people have worked on the problems involved and on the development of the continuum theory, the statistical mechanical approaches of the mean field theory and the role of repulsive, as well as attractive forces. The contributions of many theoreticians, physical scientists, and mathematicians over the years has been great - notably of de Gennes (for example, the Landau-de Gennes theory of phase transitions), McMillan (the nematic-smectic A transition), Leslie (viscosity coefficients, flow, and elasticity). Cotter (hard rod models), Luckhurst (extensions of the Maier-Saupe theory and the role of flexibility in real molecules), and Chandrasekhar, Madhusudana, and Shashidhar (pre-transitional effects and near-neighbor correlations), to mention but some. The devel-... 

Frank elastic constants and Leslie viscosity coefficients. Haller and Litster [41, 42] investigated the temperature dependence of the normalised scattering intensity and the scattering hnewidth as a function of temperature, finding that the latter was far more temperature sensitive. Many materials have been studied using this technique MBBA [43-45], di-butylazoxybenzene and p-methoxy-p -n-butylazoxybenzene [46-48], Schiffs bases [49-51 ], and the cyanobiphe-nyls [52, 53]. Typical data for the cyano-biphenyls are shown in Fig. 6. 

Frank Elastic and Ericksen Leslie Viscosity Coefficients... 

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. 

Here 1111 and are the longitudinal and transverse coefficients of the viscosity of a uniaxial anisotropic liquid which are correlated by linear correlations with the Miesowich and Ericksen-Leslie viscosity coefficients. In addition, these coefficients would be equal to Miesowich viscosities t j and 1)3 if there is an ideally oriented solution in the gap. However, it is practically impossible to obtain the ideal orientation in shear flow. 

The coefficients ai, ae are called the Leslie viscosity coefficients, or simply the Leslie viscosities. 

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