Viscosity measurements Miesowicz

The first viscosity measurements of nematic liquid crystals were performed with classical shear flow viscometers flow induces a change in orientation of the director, see EQN (4), so the effective viscosity measured is r o [54,55]. Since r o can be considered a relatively good approximation to the Miesowicz r i, conventional viscometers are still in use in conjunction with yi measurements [44,56,82,86]. However, for the purpose of measuring the viscosity anisotropy oldo instruments had to be modified and new ones developed. 

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 ... 

We shall now discuss the application of the Ericksen-Leslie theory to some practical problems in viscometry. Probably the first precise determination of the anisotropic viscosity of a nematic liquid crystal was by Miesowicz. He oriented the sample by applying a strong magnetic field and measured the viscosity coefficients in the following three geometries using an oscillating plate viscometer ... 

It is instructive to compare rheological behavior of isotropic molten polymer phases to the simplest LC phases, that is nematic ones. In an isotropic phase molecular orientations are completely random the flow process can only introduce some order. In a nematic PLC a certain degree of order (as measured by the parameter s, see Section 41.3.1) already exists. Therefore, a flow process can either enhance or reduce the existing order. This problem has been analyzed by Mamicci and Maffettone [80]. If instead of the order parameter we consider viscosity, then—as defined for MLCs already in 1946 by Miesowicz [81]—one has to distinguish three viscosities dependent on the direction parallel to the flow direction parallel to the gradient of viscosity and perpendicular to both directions just named. 

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. 

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 boMiesowicz viscosities. (Note, that in the literature a variety of alternative 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 ... 

Miesowicz distinguished three principal viscosity coefficients, 7/1,772 and 773, that could be independently measured experimentally by considering the orientation of the director n in relation to the flow velocity v. The three basic flow geometries considered by Miesowicz are depicted in Fig. 4.1 and allow the measurement of the viscosities ... 

---