Nematic viscosities restrictions

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. 

The zero shear viscosity of flexible linear polymers varies experimentally with and theoretically with [20]. Due to the highly restricted rotational diffusion, the viscosity of TLCPs is much more sensitive to the molecular weight than that of ordinary thermoplastics as discussed in section 3. Doi and Edwards predicted that the viscosity of rod-like polymers in semi-dilute solutions scales with A/ [see Equation (12)] [2]. Such a high power dependence of viscosity on the molecular weight has been experimentally observed both for lyotropic LCPs [14,15] and for TLCPs [16-18]. The experimental values of the exponent range from 4 to 7 depending on the chemical structure, the chain stiffness, and the domain or defect structure of the liquid crystalline solution or melt. The anisotropicity of the liquid seems to have little effect on the exponent. A slightly smaller exponent for the nematic phase than for the isotropic phase (6 in the nematic phase versus 6.5 in the isotropic... 

Finally, restricted 7-motion within an apex angle 0o [Eq. (7.80)] has been employed to interpret [7.11] spectral densities of aromatic deuterons in the nematic and smectic A phases of 50.7-d4. Assuming that a-, and 7-motion are completely uncorrelated, and neglecting the -motion [i.e., set / (0) = /3 t)], the spectral densities were evaluated by describing the a-motion by a simplified model of uniaxial free rotational diffusion about the director and the 7-motion by the reduced correlated functions given in Eq. (7.80). It remains to be examined whether the anisotropic viscosity model in conjunction with restricted 7-motion [i.e., Eq. (7.82)] would be better in interpreting spectral densities of motion in various smectic phases. Also, there is still no convincing NMR evidence for biased 7-motion in nematic or smectic A phases. 

Theory and intuition show that at a transition from a nematic to a smectic A phase, where the mobility is restricted to two dimensions, the viscosity coefficient 772 > which is coupled with a movement in the forbidden dimension, will diverge. The divergence can be described by the expression [52-54]... 

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