Flow-aligning behavior

Clearly flow aligning behavior of the director is present and do increases linearly with the tilt angle, do. Above a threshold in the Spain rate, y 0.011, undulations in vorticity direction set in. In Fig. 14 the results of simulations for y 0.015 are shown. In Fig. 15 we have plotted the undulation amplitude obtained as a function of the shear rate. The dashed line indicates a square root behavior corresponding to a forward bifurcation near the onset of undulations. This is, indeed, what is expected, when a weakly nonlinear analysis based on the underlying macroscopic equations is performed [54], In Fig. 16 we have plotted an example for the dynamic behavior obtained from molecular dynamics simulations. It shows the time evolution after a step-type start for two shear rates below the onset of undulations. The two solid lines correspond to a fit to the data using the solutions of the averaged linearized form of (27). The shear approaches its stationary value for small tilt angle (implied by the use of the linearized equation) with a characteristic time scale t = fi/Bi. 

An interesting similarity of what we discussed here appears if one deals with mixtures of rodlike and disklike micelles. These systems could behave very similarly to a truly biaxial nematic, but show interesting differences to them. Whereas for the usual orthorhombic biaxial nematics both directors are perpendicular to each other by construction, in mixtures there is no need to impose this restriction. Pleiner and Brand [70] investigated how mixtures are influenced by an external field (magnetic field or shear flow) and found that the angle between the two directors exhibits a flow aligning behavior similar to the one studied in [42,43],... 

It seems that the majority of thermotropic LCPs exhibit flow-aligning behavior. Thus, to describe the experimental observations for these polymers, the general viscoelastic nematodynamic theory [16,17] is used in our simulations with aligning assumption. 

Flow Aligning Behavior of Thermotropic Main-Chain LCPs... 

Fig. 9 Critical values as functions of the flow alignment parameter X for various viscosities (a, b) and compressibilities (c, d). In the upper row we plot this dependence for a set of (isotropic) viscosities ranging from v, = 1 (thick solid line,) down to V = 10 3 (thick dashed line,). The lower row illustrates the behavior for varying layer compressibility Bo with Bo 3 f°r the thick solid curve and Bo = 100 for the thick dashed curve. In all plots the thin solid lines give the behavior for some intermediate values. For an interpretation of this behavior see the text...

Out of the five viscosities, only two (V2 and V3) show a significant influence on the critical values. In Fig. 8 we present the dependence of 9C and qc on an assumed isotropic viscosity (upper row) and on these two viscosity coefficients (middle and lower row). Since the flow alignment parameter X has a remarkable influence on these curves we have chosen four different values of X in this figure, namely X = 0.7, X = 1.1, X = 2, and X = 3.5. The curves for X < 1 and X > 3 for an isotropic viscosity tensor are very similar to the corresponding curves where only V2 is varied. In this parameter range the coefficient V2 dominates the behavior. Note that the influence of V3 on the critical values is already much smaller than that of V2. We left out the equivalent graphs for the other viscosity coefficients, because they have almost no effect on the critical values. For further comments on the influence of an anisotropic viscosity tensor see also Sect. 3.4. 

All the parameters we have discussed up to now caused variations in the critical values that did not select specific values of the considered parameter. In this aspect the situation is completely different in the case of the flow alignment parameter X. As shown in Fig. 9 there is a clear change in behavior for X 1 and X 3. The... 

The rheological and flow properties of ordered block copolymers are extraordinarily complex these materials are well-deserving of the apellation complex fluids. Like the liquid-crystalline polymers described in Chapter 11, block copolymers combine the complexities of small-molecule liquid crystals with those of polymeric liquids. Hence, at low frequencies or shear rates, the rheology and flow-alignment characteristics of block copolymers are in some respects similar to those of small-molecule liquid crystals, while at high shear rates or frequencies, polymeric modes of behavior are more important. 

As shown in Fig. 9, the stress relaxation curves of all AEC/AA solutions collapse into one curve when the solutions were presheared with the same rate. Because the stress relaxation is at the molecular level and the chiro-optical properties reflect the suprastructural level, it is expected that the lyotropic solutions with different chiro-optical properties have the same stress relaxation behavior in both the tumbling and flow-align regions. 

A stable flow alignment, at small shear rates, exists for Aeq l only. For Aeq < 1 tumbling and an even more complex time dependent behavior of the orientation occur. The quantity Aeq - 1 can change sign as function of the variable cf. Fig. 4. For Aeq < 1 and in the limit of small shear rates 7, the Jeffrey tumbling period [18] is related to the Ericksen-Leslie tumbling parameter Agq by... 

Survey. Next, results are presented for the time-averaged rheological behavior and the time averaged alignment in the nematic phase at a state point where no stable flow alignment is possible. In particular, the temperature = 0 and the parameters Ak = 1.25 and k = 0 are chosen. In Fig. 8 the shear stress and the viscosity are displayed as functions... 

Between the tumbling region and the flow-aligning region, a transient region, characterized by the oscillatory behavior of the director, can be observed. As shear rate increases, the amplitude of the oscillations decreases towards zero, determining a flowaligning type of behavior. 

Pursuant to this, small angle neutron scattering and iheology have been used to investigate the flow and alignment behavior of two veiy similar LCP solutions. The solutions are poly( y-benzyl L-glutamate) in deuterated m-cresol (DMC) and... 

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