Nematic viscosities

An anomalous increase of A, has been observe but the principal experimental difficulty in determining the critical exponent accurately is that the normal nematic viscosity (in the absence of correlations) is itself strongly temperature dependent and the anomalous part forms only a relatively small contribution. However, careful measurements have indicated a mean field behaviour. 

For the smectic A phase the permeation effect is even more important [16]. In fact, with the layers fixed at the walls of a capillary, a smectic may flow only as a whole, like a plug, without velocity gradients. Fig. 9.10b. The velocity is again given by equation Vp = kpV, where kp is the permeation coefficient depending on the smectic characteristic length given by Eq. (8.46), cmiventional nematic viscosity q and temperature ... 

The coefficient y is rotational viscosity of the director similar to coefficient yi for nematics. In fact, it does not include a factor of sin cp and, in the same temperature range, can be considerably larger than the viscosity ytp for the Gold-stone mode. This may be illustrated by Fig. 13.10 the temperature dependence of viscosities y and have been measured for a chiral mixture that shows the nematic, smectic A and smectic C phases [15]. The pyroelectric and electrooptic techniques were the most appropriate, respectively, for the measurements of ya and ytp describing the viscous relaxation of the amplitude and phase of the SmC order parameter. The result of measurements clearly shows that y is much larger than y and, in fact, corresponds to nematic viscosity yj. 

The index (prefers to the (p variable, and the index-free y corresponds to the nematic twist viscosity. Equation (304) means that the cone mode viscosity is lower than the standard nematic viscosity (y [Pg.1621]

Experimentally, J] was found to be in the order of nematic viscosity, with value depending on the shear rate and history, indicating the effect of defects on the flow properties. It was also found that IN/m, which is comparable to azz = B na/L) n-3N/m with n 3, where a is the layer thickness, and L is the width of the film ( 1 cm). Because > (Tq, tire effect of residual stress may explain the observations. We will see a bit later, however, that more subtle explanation of the existence of may be connected to the breakdown of the hydrod5mamics. Results obtained under periodic shears, however, show pure viscous behavior with no frequency dependence. This shows the importance of working with small amplitudes, which reduces the residual effects due to the thickness variations and of the nonlinear effects. 

Relationship between nematic viscosities and molecular structure... 

It is appropriate at this point to discuss some of the properties of the nematic viscosity coefficients in relation to basic experimental ideas and give some insight to their physical interpretation. It is also important to give the relationship between the notation used for the Lesfie viscosities and the notation used by other... 

Table D.3 on page 330 gives a collection of viscosities for the nematic phases of the materials MBBA, PAA and 5CB. (Note that the coefficient ai quoted in de Gennes and Prost [110, p.231] for MBBA near 25°C (based upon the work of Gawiller [97]) is positive, whereas a more recent report by Kneppe, Schneider and Sharma [155] has revealed ai to be negative.) For a brief introduction to the major experimental techniques used for evaluating the nematic viscosities the reader is referred to the review by Moscicki [205].

The slow modes tend to be dominant in light scattering experiments from which information on the nematic viscosities can be obtained, as we now proceed to demonstrate. 

These results were obtained by using the viscous dissipation inequality (6.207) to obtain quadratic forms analogous to those used to obtain the inequalities for the nematic viscosities at equations (4.91) to (4.95) in Section 4.2.3. Ebcpressions (6.241) to (6.246) are of the form xp > with x > 0 and p > 0. Since (a — =... 

The viscosities ti and rs often appear together in problems. Preliminary mathematical results indicate that it may be reasonable to assume T5 > ti for SmC materials, in which case the modulus sign may be omitted in equation (6.255), although acceptance of this inequality should perhaps await experimental confirmation see the elementary argument used to justify this inequality at equation (6.286) in Section 6.3.3. The reader is referred to Carlsson et al [36] for some speculative theoretical suggestions for various SmC viscosity values and restrictions, including some preliminary estimates based upon a comparison with nematic viscosities. It has also been suggested from physical considerations [36] that rs > 0. 

V.V. Belyaev, Relationship between nematic viscosities and molecular structure, Section 8.4 in Reference [68]. 

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