Shear nematics

Experiments demonstrate that at even higher Er, the rolls become unstable and irregular. Ultimately, defect lines called disclinations form in the flow direction. As the linear analysis concerns the behavior of infinitesimal disturbances, the growth of the instability and further bifurcations are inaccessible to such analyses. This motivated Feng, Tao, and Leal to carry out a direct numerical simulation of a sheared nematic. Using the LE theory, with the one-constant approximation, they predicted a cascade of instabilities illustrated in Fig. 3. Steady state rolls first appear at Er = 2368. The director twists toward the flow (z) direction at the center of the cells. With increasing Er, the secondary flow and the director twisting intensify. 

Fig. 3 Secondary flows in the x-y plane showing instabilities in a sheared nematic (A) velocity vectors showing steady roll cells at Er = 2602 (B) a snapshot of oscillating roll cells at Er = 4336 (C) cell splitting at Er = 2,611, and (D) ridges, indicated by arrows, break up to produce pairs of 1 defects marked by the ellipses. (From Ref. l)...

Manneville, P. Dubois-Violette, E. Shear flow instability in sheared nematic liquids theory steady simple shear flows. J. Phys. Paris 1976,37,285-296. 

Mather, P.T. Pearson, D.S. Larson, R.G. Flow patterns and disclination-density measurements in sheared nematic liquid crystals. II. Tumbling 8CB. Liq. Cryst. 1996, 20, 527-538. 

Tao, J. Feng, J.J. Effects of elastic anisotropy on the flow and orientation of sheared nematic liquid crystals. J. Rheol. 2003, 47 (4), 1051-1070. 

Fig. 4.3 a, b Homeotropic and schlieren textures of the nematic phase of 8CB containing 5 wt% 1 coated GNPs. c Sheared nematic texture near to the edge of the cover slip, d Focal-conic defect texture of the smectic A phase. Magnification xlOO [46], Copyright from Wiley-VCH 2011... 

Graziano and Mackley [36] reported a very extensive study on oscillatory sheared, nematic, longitudinal PLCs based on a series of random 50/50 copolyesters of chlorophenylene terephthalate and bis-phenoxyethane carboxylate. They observed a variety of textures in the polarized microscope and also noticed a pronounced difference between low and high molar mass samples. 

Shearing nematic surfactant solutions has revealed complex transient responses... 

Archer, L.A., Larson, R.G. (1995) A molecular theory of flow alignment and tumbling in sheared nematic liquid crystals. Journal of Chemical Physics, 103 (8), 3108-3111. 

AH distortions of the nematic phase may be decomposed into three basic curvatures of the director, as depicted in Figure 6. Liquid crystals are unusual fluids in that such elastic curvatures may be sustained. Molecules of a tme Hquid would immediately reorient to flow out of an imposed mechanical shear. The force constants characterizing these distortions are very weak, making the material exceedingly sensitive and easy to perturb. 

The selective redection of chiral nematic Hquid crystals has also been used to develop sensors for pressure, radiation (especially infrared), wind shear over surfaces, stmctural fatigue, and foreign chemical vapor (48). Other types of Hquid crystals have been used to make sensors to measure both electric and magnetic fields. 

Fig. 2.8.16 Director orientation, 0, as a function of shear rate for both flow aligning (solid squares) and tumbling (open squares 325 K, solid circles 328 K and open circles 333 K) nematic polymers. (From Siebert et al. [10].)...

Navard and Zachariades (125) examined the optical properties of shear deformed trifluoroacetox3q)ropyl cellulose and observed band phenomena identical to that for thermotropic nematic copolyesters. Steinmeier and Zugenmaier (107) demonstrated that the phenylacetate... 

Ratio of the shear stress, a, to the shear velocity gradient, y, for a nematic liquid crystal with a particular director orientation, denoted by /, under the action of an external field ... 

Note 1 The three Miesowicz coefficients (//i, 772, and 773) describe the shear flow of a nematic phase with three different director orientations, (see Fig. 31) namely 771 for the director parallel to the shear-flow axis 772 for the director parallel to the velocity gradient and 773 for the director perpendicular to the shear flow and to the velocity gradient. 

Fig. 31. Scheme of director alignment in the shear flow of velocity u of a nematic phase and... 

Alternating dark and bright bands observed, following shear, in a wide range of main-chain nematic and chiral nematic liquid-crystalline polymers. 

Actual calculations of w,E) for isotropic and nematic solutions will be described in Sects. 8 and 9 respectively. Furthermore, derived approximately for isotropic solutions in a steady shear flow in Sect. 8, but it will be neglected for nematic solutions in Sect. 9. 

With increasing flow rate, the orientational state in the nematic solution should change. Larson [154] solved numerically Eqs. (39) and (40b) with Vscf(a) given by Eq. (41) for a homogeneous system (T[f ] = 0) in the simple shear flow to obtain the time-dependent orientational distribution function f(a t) as a function of k. The non-steady orientational state in the nematic solution can be described in terms of the time-dependent (dynamic) scalar order parameter S[Pg.149]

Larson s results [154] are divided into the three shear rate regimes - tumbling, wagging, and steady-state - as explained below. He chose the strength of mean-field potential 2L2dc in Eq. (41) to be 10.67, which corresponds to the concentration cA of the nematic phase coexisting with the isotropic phase (in the second virial approximation), and expressed the shear rate in terms of T defined by... 

Tumbling regime At very low shear rates, the birefringence axis (or the director) of the nematic solution tumbles continuously up to a reduced shear rate T < 9.5. While the time for complete rotation stays approximately equal to that calculated from Eq. (85), the scalar order parameter S,dy) oscillates around its equilibrium value S. Maximum positive departures of S(dy) from S occur at 0 n/4 and — 3n/4, and maximum negative departures at 0 x — k/4 and — 5it/4, while the amplitude of oscillation increases with increasing T. 

From a DSC scan of the homopolymer of PHBA one can observe a major endotherm at 350 °C and a much smaller one at 445 °C (see Fig. 3) [29], The first transition has been examined by electron diffraction [27-30], X-ray diffraction [28] and proton and 13CNMR [30]. Additional insights have been provided by synthesizing much lower molecular weight samples which permit study of these transitions at appreciably lower temperatures [29]. These low molar mass homopolymers can also go into a nematic phase under a modest shear. 

With respect to the higher temperature transition at 445 °C, there are two conflicting views of this transition, namely that the phase above 445 °C is a smectic C and the other that it is nematic. Based on high temperature X-ray diffraction studies, Yoon et al. have concluded that it is a smectic C (see Fig. 4) [28], Thus, in Fig. 4, the disappearance of the 211 peak indicates that the nematic E structure is converting to a nematic C. In our work, using polarizing optical microscopy, we have observed a nematic texture for high molar mass specimens heated rapidly to 480 °C, sheared, and then quenched. In the case of a... 

Fig. 5a-b. Nematic texture of the homopolymer PHBA a DP 15, specimen quenched from 440 °C, no external shear applied b DP > 100, specimen quenched from above 480 °C, external shear was applied to increase the rate at which the fluid specimen sheared between the glass surface above... 

Fig. 8a,b. Nematic structure induced by moderate external shear in lower M samples a DP 15, specimen quenched from 300 °C b DP 39, specimen quenched from 330 °C... 

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