Ericksen Model Research Articles

Transient molecular orientation and rheology in flow aligning thermotropic liquid crystalline polymers

Quantitative measurements of molecular orientation and rheology are reported for various transient shear flows of a nematic semiflexible copolyether. Unlike the case of lyotropic liquid crystalline polymers (LCPs), whose structure and rheology in shear are dominated by director tumbling, this material exhibits flow aligning behavior. The observed behavior is quite similar to that seen in a copolyester that we have recently studied [Ugaz and Burghardt (1998)], suggesting that flow aligning dynamics may predominate in main-chain thermotropes that incorporate significant chain flexibility. Since the flow aligning regime has received little attention in previous attempts to model the rheology of textured, polydomain LCPs, we attempt to determine whether available models are capable of predicting the orientation and stress response of this class of LCP. We first examine the predictions of the polydomain Ericksen model, an adaptation of Ericksen’s transversely isotropic fluid model which accounts for the polydo...

Some mathematical issues in the modeling of flow phenomena of polymeric liquid crystals

We consider shear flow of polymeric liquid crystals for large and small values of the Ericksen number ℰ. The model consists of governing equations for the velocity field v, the pressure p, the director n, and the order parameter s. The constitutive functions for the Leslie coefficients, αi, derived from the molecular theory of Doi play a crucial role in the modeling. One of the goals of the analysis is to examine the role of s in describing singularities as well as in obtaining new regimes which cannot be predicted by the previous Leslie–Ericksen model. In particular, solutions are obtained that correspond to domain structures parallel to the flow. The domains are separated by singular lines across which the director experiences jumps of ±45°. Such flows correspond to regimes with large values of ℰ. Another type of configuration analyzed in the article corresponds to periodic stripes parallel to the flow and such that the optic fields vary along the direction perpendicular to the plane of shear. Such configurations occur in the limit of small ℰ.

Transient shear flow of nematic liquid crystals: Manifestations of director tumbling

Calculations of a variety of transient flow phenomena based on the Leslie–Ericksen model for nematic liquid crystals are presented. Emphasis is placed on the behavior of nematics subject to director tumbling. A wide range of complicated transient phenomena such as oscillatory responses are predicted when the Ericksen number is sufficiently high to cause significant rotation of the director at steady state. Particular attention is given to relaxation processes such as constrained elastic recoil and stress relaxation that arise from the interaction of the relaxing director profile with the viscous response of the nematic. These relaxation processes are dramatically different in tumbling and flow aligning systems, due to the saturation of the director profile at high Ericksen number for the flow aligning case. A qualitative physical model of a textured polymer liquid crystal is presented in which the dynamics on a local scale governed by the distance between defects are assumed to be similar to the macroscopic dynamics presented in these calculations. By assuming (i) director tumbling and (ii) the existence of a limiting Ericksen number in polymer systems, a wide range of published observations in lyotropic liquid crystalline polymer solutions may be qualitatively reproduced.