Dynamics of a model for nematic liquid crystalline polymers in planar shear flow

Liquid crystalline polymers (LCPs) have found a multitude of applications in the form of fibers, and applications that take advantage of the low thermal expansion coefficient and relatively low viscosity of LCPs such as small-scale precision molded parts. In spite of these successes, however, there are other potentially more important applications that have not been realized, among which the greatest loss is the inability to produce high-strength, lightweight engineering materials with mechanical properties that derive from the spontaneous ordering LCPs display in the liquid state. The difficulty lies in the fact that, although the spinning process used to produce fibers enhances this tendency for ordering, other forms of polymer processing, such as injection molding, involve either shear flows or combinations of shear and extensional flows. For LCPs that tumble in shear flows---which include all lyotropic and, apparently, many commercially interesting thermotropic LCPs---these flows seriously degrade or even destroy the orientational order.; The question, then, is whether the degradation of orientational order can be controlled sufficiently by some modification of the processing procedure (i.e., modest changes in the flow geometry). A necessary first step is to elucidate the structure-flow interaction and the dependence of the structural evolution on the flow type, and to develop a predictive capability that reproduces experimental observations. Accounting for the coupling between the microscopic structure and macroscopic stress using the molecular-based Doi-Marrucci-Greco (DMG) theory, we analyze two- and three-dimensional flows that occur in a planar shear cell. For the case of the two-dimensional calculations, we find that the DMG model exhibits dynamics in both qualitative and quantitative agreement with experimental observations reported for the so-called Ericksen number and Deborah number cascades. In addition to capturing textural transitions, which represent spatial variation of the molecular orientation, the model predicts the two common types of the orientational defects, known as disclinations, observed in LCP flows.; In our three-dimensional planar shear calculation we employ the DMG model to gain insight into the nature and dynamics of the complex, birefringent polydomain texture exhibited by LCPs and to provide a detailed description of the disclination loops typically observed in LCP shear flows. The model predicts a birefringent, striped texture in accordance with previous experimental and theoretical studies. Subsequent refinement of the texture is accompanied by the formation and development of disclination loops, which reside between within the polydomain texture and orient along the flow direction. These observations provide not only the first numerical investigation of coupled flow-structure problem with a full account of both viscoelasticity and gradient elasticity but also provide the first numerical confirmation of the reported loop disclination structure inferred from experimental data. Though often depicted as separate phenomena in the literature, we find an explicit coupling between the disclination structure and polydomain texture as predicted by the DMG theory.