Shear, director orientations

Fig. 2.8.16 Director orientation, 0, as a function of shear rate for both flow aligning (solid squares) and tumbling (open squares 325 K, solid circles 328 K and open circles 333 K) nematic polymers. (From Siebert et al. [10].)...

Ratio of the shear stress, a, to the shear velocity gradient, y, for a nematic liquid crystal with a particular director orientation, denoted by /, under the action of an external field ... 

Note 1 The three Miesowicz coefficients (//i, 772, and 773) describe the shear flow of a nematic phase with three different director orientations, (see Fig. 31) namely 771 for the director parallel to the shear-flow axis 772 for the director parallel to the velocity gradient and 773 for the director perpendicular to the shear flow and to the velocity gradient. 

Experiments by Muller et al. [17] on the lamellar phase of a lyotropic system (an LMW surfactant) under shear suggest that multilamellar vesicles develop via an intermediate state for which one finds a distribution of director orientations in the plane perpendicular to the flow direction. These results are compatible with an undulation instability of the type proposed here, since undulations lead to such a distribution of director orientations. Furthermore, Noirez [25] found in shear experiment on a smectic A liquid crystalline polymer in a cone-plate geometry that the layer thickness reduces slightly with increasing shear. This result is compatible with the model presented here as well. 

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,... 

As y is increased still further, the tumbling behavior of the director is replaced by a wagging motion wherein the director oscillates back and forth about the flow direction. The frequency of this wagging motion increases with further increases in y and after another transitional shear rate is exceeded, the wagging motion damps out and a steady-state is attained in both 5 and in the director orientation (Larson 1990). 

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... 

Experimentally, both small molecule liquid crystals and LCP s display all sorts of director orientation patterns at high shear rates, and the existence of these Is of obvious Importance to control of orientation In processing (see Page 656 of Reference 2 for some discussion and references). It is conjectured that these may correspond to instabilities of the solutions of L-E theory. If feasible, a study of these instabilities - classification of patterns, prediction of conditions for occurrence, etc. - would be useful to relate to experimental observations. 

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... 

As mentioned above, shear viscosities r/i, r/2) Vs could be measured in a viscosimeter of special construction, where shear rates are very low and a magnetic field is applied to keep the director orientation unchanged [65-69, 72, 92]. The viscosities rj are defined as the coefficients of proportionahty between the viscous stress cTxz and the velocity gradient for different geometries (Fig. 2.21)... 

Grabowski D, Schmidt C (1994) Simultaneous measurements of shear viscosity and director orientation of a side-chain liquid crystalline polymer by rheo-NMR. Macromolecules... 

In the fibers produced from lyotropic spinning dopes, there still appear to be limitations on the ultimate physical properties due to higher-order morphological defects (the periodic director-orientation distortions alluded to earlier) [115]. In this context, much experimental and theoretical work remains to be done to delineate those parameters that control disclination textures and director patterns created by complex shear fields encountered in processing LCPs. As is typically the case, there are natural systems wherein these difficulties appear to have been optimally minimized spiders spin nearly defect-free fibers from a mesomorphic form of silk [116]. Consequently, efforts to analyze the spinning process - the spinner draw-down geometry and its associated shear field - used by arachnids are under way. 

The shear viscosity coefficients tJi, t]2, and 773 can separately be determined in shear flow experiments with adequate director orientations [27]. 

For the determination of 7712 at least three experiments are necessary. Two for the determination of 77, and 772 and one experiment with a director orientation where the influence of 77j2 on the shear viscosity is maximal (0=90°, 0=45°). Then, 77,2 can be calculated according to... 

Viscous torques are exerted on the director of a liquid crystal during a rotation of the director and by a shear flow with a fixed director orientation. The density T] of the viscous torque is obtained by application of the Levi-Civita tensor... 

If a nematic liquid crystal with a fixed director orientation is sheared a torque according to Eq. (17) is exerted on the director... 

At high shear rates the director orientation in the bulk is dominated by flow alignment. The Influence of elastic torques is restricted to small boundary layers at the surfaces and regions where the velocity gradient changes sign. Therefore the apparent viscosity is close to the value for flow align-... 

At medium shear rates director orientation and velocity profde can only be obtained by numerical calculations. In the following the flow between parallel plates with a surface alignment parallel to the pressure gradient is calculated [37]. The orientation of the capillary is the same as in Fig. 10. The equation for linear momentum is ... 

An externally applied torque on the director can only be transmitted to the surfaces of a vessel without shear, if the director rotation is homogeneous throughout the sample as assumed in Sect. 8.1.2 for the rotational viscosity. Otherwise this transmission occurs partially by shear stresses. The resulting shear flow is called backflow. As there is usually a fixed director orientation at the surfaces of the sample container, a director rotation in the bulk of the sample by application of a routing magnetic field leads to an inhomogeneous rotation of the director and to a backflow [42]. 

The cholesteric liquid crystal is sheared between two parallel walls at z= T. Leslie [49] and Kini [50] have studied this case with different boundary conditions. Leslie assumes that the pitch of the helix remains constant at the walls whereas Kini assumes a fixed orientation of the director at the wall with an orientation which corresponds to that of the undistorted helix. Both boundary conditions are difficult to realize in an experiment. In spite of the different orientations at the walls the results of the calculations are qualitatively the same. In the bulk the director orientation is determined by elastic and viscous torques. Transverse flow in z-direction is excluded. 

The cholesteric liquid crystal is sheared between two parallel walls. It is assumed that the walls do not influence the director orientation (weak anchoring) and that the flow velocity is parallel to the movement of... 

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