Director alignment, shear viscosity

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]. 

During fabrication the orientation occurs on the surface, which depends on chemical nature of LC polyester. The molecular weight also affects surface orientation the short chains being rapidly oriented. The low viscosity of liquid crystals monomer/polymer as compared to isotropic fluid is due to their ready local alignment. The rheology is complex in nature. The viscosity in the anisotropic phase is much lower as compared to that at disordered isotropic state. In the anisotropic solution phase the director readily aligns in the shear direction and lower viscosity results. 

If the director is free to rotate there will be either a rotation to a stable orientation (flow alignment, see Fig. 6) or a continuous rotation (tumbling) under the influence of the shear gradient. Which case is observed depends on the signs of 2 and a. Because of thermodynamical arguments (see Sect. 8.1.9) the rotational viscosity coefficient must be positive. 

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-... 

The conditions for the first two viscosity coefficient ratios correspond to Eq. (100). A discussion of the stability of the various solutions is presented in the paper of Saupe [59]. Brand and Pleiner [61] as well as Leslie [62] discuss the flow alignment without the restriction that one director is perpendicular to the shear plane. 

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-... 

If n is mobile (no body forces present), then in cases (i) and (ii) above a viscous torque rotates n, and conversely rotation of n by body forces induces a flow. Two additi(Mial viscosity coefficients, yi and 72, which have no counterpart in isotropic liquids, are necessary to describe this situatitm. The first coefficient, yi, characterises the torque associated with rotation of n. The latter coefficient, j2, gives the contribution to the torque due to a shear velocity gradient in the nematic. The two coefficients also define the flow alignment of the director under stationary shear flow ... 

Straightforward evaluation of Yi from measurements of the torque exerted by a rotating director on the sample holder walls was pioneered by Tsvetkov in the late 1930s [8,9]. The alignment can be measured by optical methods, but it can also be found indirectly from measurements of the viscosity coefficient, tIo, in the simple shear flow experiment in the absence of a locking external field, when the director is aligned (and immobilised) by the flow. 

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