Miesowicz viscosity

The five viscosities are the Miesowicz viscosities, called after Miesowicz, who introduced them already in 1946. The background of the first three viscosities is shown in Fig. 15.51 (Jadzyn and Czechowski, 2001) rji where the director is perpendicular to the direction of flow r]Z where the director is perpendicular to the velocity gradient and r 3 where the director is perpendicular to both the flow direction and the... 

The three elastic constants are the Frank elastic constants, called after Frank, who introduced them already in 1958. They originate from the deformation of the director field as shown in Fig. 15.52. A continuous small deformation of an oriented material can be distinguished into three basis distortions splay, twist and bend distortions They are required to describe the resistance offered by the nematic phase to orientational distortions. As an example, values for Miesowicz viscosities and Frank elastic constants are presented in Table 15.10. It should be mentioned that those material constants are not known for many LCs and LCPs. Nevertheless, they have to be substituted in specific rheological constitutive equations in order to describe the rheological peculiarities of LCPs. Accordingly, the viscosity and the dynamic moduli will be functions of the Miesowicz viscosities and/or the Frank elastic constants. Several theories have been presented that are more or less able to explain the rheological peculiarities. Well-known are the Leslie-Ericksen theory and the Larson-Doi theory. It is far beyond the scope of this book to go into detail of these theories. The reader is referred to, e.g. Aciemo and Collyer (General References, 1996). 

TABLE 15.10 Some values for the Miesowicz viscosities and Frank elastic constants... 

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 10-9a 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.-----------------------------... 

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.)... 

Taking R(p) 1, this leaves only one temperature-independent constant, ao/rj, left to be obtained by fitting the viscosities in the nematic state below Tni. Since ao is an orientation-independent contribution, the ratios of the Miesowicz viscosities r)c -r)b - a deviate less from unity as ao//y is increased. A value aQ/rj = 0.6 fits the Miesowicz viscosities of MBBA reasonably well the predictions of the theory with ao/// = 0.6 are given by the lines in Fig. 10-9a. Measurements of the Miesowicz viscosities for other liquid crystals are similar enough to those of MBBA that this theory with ao/rj = 0.6 is likely to work equally well... 

Problem 10.8 You are measuring the elasticities and viscosities of a room-temperature nematic at reduced temperatures and you find that below about 10°C the twist and bend constants K2 and become very large, while the splay constant Ki retains a modest value. Also, the Miesowicz viscosity t], becomes enormous while r) goes up only modestly. What could explain this behavior ... 

Comparison of the Miesowicz viscosities of prolate (p) and oblate (o) nematic liquid crystals. The entries for zero field have been obtained by using the Green-Kulw relation (4.4)-(4.6). The entries for finite field have been obtained by applying the SLLOD equations (3.9). Note that the EMD GK estimates and the NEMD estimates agree within the statistical error. 

Apart from these works referred to here, the viscosities of the original Gay-Beme fluid [5] with attractive interactions have been evaluated. Smondyrev et. al. [33] used the Forster fluctuation relations to calculate the Miesowicz viscosities as a function of the temperature. The results were confirmed by Cozzini et. al. [34] who used the fluctuation relations derived in [24]. 

Fig. 8 The Miesowicz viscosities, 77j (diamonds), 772 (squares) and 773 (squares) as a function of temperature for a version of the Gay-Beme fluid that forms both nematic and smectic A phases. The N - transition takes place at kgT/e=. 0. Note that 77, is undefined at the N — transition point and in the smectic phase.

Figure 4.8 The corresponding shear and rotational flow profiles for the anisotropic Miesowicz viscosity terms 7, 72. and r/j [26], and the rotational viscosity relative to an isolated liquid crystal molecule. In the design of TN LCD y, is of predominant importance, because it is proportional to the switching time of the display [27].

In analog to the approach used by Odijk when dealing with elastic constants, Lee (1988) took the orientation distribution function approximately as Gaussian. When the system is highly ordered, the asymptotic expression can be deduced for viscosities of liquid crystalline polymers, e.g., the Miesowicz viscosities (in the unit of fj) are expressed by... 

Meyer (1982) predicted that as the length of the chain approaches infinity, the Leslie coefficients ai and 2 should tend to —oo and a3 tends to oo, while 04,05 and 06 are of finite values. The Miesowicz viscosities r/a and rjb are finite while r/c tends to infinity because the velocity is perpendicular to the director and the shear flow. 

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 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 ... 

Using constraint director dynamics, McWhirter and Patey [206] also determine the shear and twist viscosities describing the coupling between the pressure and shear rate tensors and the Miesowicz viscosities (linear combinations of the former) and show that the latter are qualitatively similar to those of a ferroelectric tetragonal 1 lattice in accord with the fact that the short-range spatial correlations in the ferroelectric liquid state are similar to those of the tetragonal lattice structure [102]. 

Usual geometry to measure the Miesowicz viscosities. The film thickness is typically in the range of 20-100 pm, and the strength of the magnetic field is in the range of 0.5-1 T. 

Viscosity coefficients measured in these geometries when n is immobilised by boalternative notations are common in particular the definitions of r i and r 2 are frequently interchanged.) If the orientation of n is fixed in an arbitrary direction with respect to v and Vv, then the effective viscosity coefficient is given by a linear combination of the Miesowicz viscosities, and another viscosity constant Tju, which cannot be visualised in a pure shear-flow ... 

Apart from basic viscosity experiments, there is an increasing number of contemporary methods monitoring the director field modulations, i.e. the splay, twist and bend deformations [19]. Flows related to these deformations are characterised by viscosity coefficients rispiay, r tvrist> and ribeod respectively. These viscosities can be conveniently expressed via combinations of the Miesowicz viscosity coefficients and/or the Leslie parameters [20,21,26] ... 

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