Leslie viscosities predictions

The molecular theory of Doi [63,166] has been successfully applied to the description of many nonlinear rheological phenomena in PLCs. This theory assumes an un-textured monodomain and describes the molecular scale orientation of rigid rod molecules subject to the combined influence of hydrodynamic and Brownian torques, along with a potential of interaction (a Maier-Saupe potential is used) to account for the tendency for nematic alignment of the molecules. This theory is able to predict shear thinning viscosity, as well as predictions of the Leslie viscosity coefficients used in the LE theory. The original calculations by Doi for this model employed a preaveraging approximation that was later... 

Few other sets of viscosities exist for polymeric nematics. Yang and Shine (1993) obtained three of the Leslie viscosities for monodomains of poly(n-hexyl isocyanate) (PHIC) from rheological measurements in the presence of an electric field, and they obtained values reasonably consistent with the predictions of the Kuzuu-Doi expressions. From monodomains of the polyion PBZT, poly(l,4-phenylene-2,6-benzobisthiazole) in methane sulfonic acid, some of the Leslie-Ericksen parameters have been extracted via light-scattering and magnetic-field-reorientation studies (Berry 198S Srinivasarao and... 

On detailed analysis of the transient stress signatures, certain numerical discrepancies were noted [Gu et al., 1993 Gu and Jamieson, 1994a] between the experimental increments in Leslie viscosities 8as and Sas versus the Brochard prediction. Specifically, for the side-chain LCP, assuming an oblate conformation, the theory [Eiqs. (1.55)] predicts that both 8as and Sas should be positive, whereas we found [Gu et al., 1993 Gu and Jamieson, 1994a] that Sas < 0 and Sas > 0. Also, the magnitude and signs of these viscosity increments were found to be strictly inconsistent with... 

Finally, in addition to predictions for the increments in Miesowicz and Leslie viscosities, the Brochard theory predicts [Brochard, 1979] the increment Syi in the viscosity associated with the twist distortion of a nematic solvent on dissolution of a polymeric solute ... 

From slow-shear-rate solutions of the Smoluchowski equation, Eq. (11-3), with the Onsager potential, Semenov (1987) and Kuzuu and Doi (1983, 1984) computed the theoretical Leslie-Ericksen viscosities. They predicted that ai/a2 < 0 (i.e., tumbling behavior) for all concentrations in the nematic state. The ratio jai is directly related to the tumbling parameter X by X = (1 -h a3/a2)/(l — aj/aa). Note the tumbling parameter X is not to be confused with the persistence length Xp.) Thus, X < I whenever ai/a2 < 0. As discussed in Section 10.2.4.1, an approximate solution of Eq. (11-3) predicts that for long, thin, stiff molecules, X is related to the second and fourth moments Sa and S4 of the molecular orientational distribution function (Stepanov 1983 Kroger and Sellers 1995 Archer and Larson 1995) ... 

The first normal stress difference exhibits a linear dependency on the shear rate in the region of constant viscosity for the two solutions in Figure 2. This proportionality is predicted by the Doi theory (10) and the Leslie-Ericksen theory (111 although the basic assumption in these theories, i.e. a monodomain structure, is not satisfied. 

Meyer (1982) predicted that as the length of the chain approaches infinity, the Leslie coefficients ai and 2 should tend to —oo and a3 tends to oo, while 04,05 and 06 are of finite values. The Miesowicz viscosities r/a and rjb are finite while r/c tends to infinity because the velocity is perpendicular to the director and the shear flow. 

In addition to the Miesowicz viscosities, the Brochard model also enables one to predict how dissolution of a polymer in a nematic solvent will modily the Leslie... 

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