Director tumbling

On the other hand, if X is smaller than unity, the latter dominates, so that the director tumbles continuously without any steady-state orientation. The period P per rotation is given by... 

W. R. Burghardt and G. G. Fuller, Role of director tumbling in the rheology of polymer liquid crystal solutions, Macromolecules, 24, 2546 (1991). 

Doi molecular theory adds a probability density function of molecular orientation to model rigid rodlike polymer molecules. This model is capable of describing the local molecular orientation distribution and nonlinear viscoelastic phenomena. Doi theory successfully predicts director tumbling in the linear regime and two sign changes in the first normal stress difference,as will be discussed later. However, because this theory assumes a uniform spatial structure, it is unable to describe textured LCPs. 

Larson and Doi introduced a mesoscopic polydomain model based on LE theory. This model includes a domain orientation distribution function and incorporates director tumbling, distortional elasticity, and texture size. Larson-Doi model can qualitatively predict the steady flow behavior and transient behavior. However, discrepancies between the theoretical predictions and the experiments of model systems were observed, especially when the shear history includes rest periods. ° This model is restricted to low shear rates without perturbing the molecular orientation distribution function in each domain.f ... 

The negative Ni is the result of the coupling of molecular tumbling under flow and the local molecular-orientation distribution. At low shear rates, the director tumbles with the flow and Ni will be positive. At intermediate shear rates, nonlinear viscoelastic effects are important. The director tumbling competes with the steady director alignment along... 

If n is restricted to the y-z plane during the shear, a steady windup solution obtains for low shear rates, with n rotating the most at the center and less toward the walls. This windup picture becomes unstable at a critical shear rate, where the director tumbles discon-tinuously to a new solution with reduced elastic energy. The critical Er depends on material parameters, and falls roughly between 10 and 100. Mathematically, this instability is represented by the existence of multiple in-plane solutions at certain ranges of the shear rate. An example is shown in Fig. 2. 

For Eqs. (15)-(17) to be a self-contained rheological theory, the fourth-order moment Q has to be related to the second-moment 5 by a closure approximation. Such a closed theory describes the LCP orientation by the second-rank tensor S, and the director can be identified as the eigenvector for the largest eigenvalue. Doi ° introduced a decoupling approximation 5 Q = S.SS, which turns out to be unsatisfactory as it artificially suppresses director tumbling.More sophisticated closure models have since appeared, and their impact on the theory s prediction has been... 

The Ericksen-Leslie theory is valid for the polymeric liquid crystals if the velocity gradient is small. The theory was applied to examine the director tumbling in liquid crystals and the associated effects. It is concluded... 

It has been suggested that in the phase, the disc-like shape of the molecule may have a significant effect on p and 3. The stable orientation of the director under planar shear will now be as shown in fig. 6.5.2(0). Thus it can be argued that both p and p should be positive, and the flow alignment angle 0o should lie between —45 and —90°. It then follows that when p < 0, the director tumbles and the flow becomes... 

As a test of the revised theory, further experiments were conducted [Zhao et al., 2005] on nematic solutions of a SCLCP. ER measurements indicated, via application of the Brochard hydrodynamic model, a slightly prolate conformation, R /R = 1.17 0.02, consistent with small-angle neutron scattering measurements, which indicated, that= 1.12 0.06. Observations of the shear stress transient response of a homeotropic monodomain indicated that at a concentration between 0.01 and 0.02 g/mL, the solution exhibited a transition from director-aligning to director-tumbling behavior. The latter result is inconsistent with the original Brochard model [see Eq. (1.94)], which predicts such a transition (i.e., Sas > 0) only for a polymer with an oblate shape but agrees with the modified theory [Eq. (1.96)]. 

Gu, D., Jamieson, A. M., and Wang, S. Q., Rheological characterization of director tumbling induced in a flow-aligning nematic solvent by dissolution of a side-chain liquid crystal polymer, J. RheoL, 37, 985-1001 (1993). 

Director tumbling is predicted from molecular theories of rigid rod systems subject to shear flow and depends critically on the characteristics of the microscopic order parameters S2 and S4. The equation below shows the relationship for the tumbling parameter, p, proposed by Larson (20). 

Director Tumbling A number of researchers (Carlsson 1984 Kuzuu and Doi 1984 Pieranski and Guyon 1974 Semenov 1983) have investigated, with the aid of the Ericksen-Leslie theory, shear flow of nematic liquid crystals and found that instability... 

What is unclear at the present time is the explanation as to why the theories based on a rheological model, which predict director tumbling and wagging, also predict the transient rheological responses in a+(r, y ) and (r, y ) that resemble so much the... 

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