Mathmatical Modeling: Why...
Small-molecule liquid crystal experiments have been successfully explained by Leslie–Ericksen–Frank continuum models. The LCPs, their macromolecular counterparts, exhibit much richer dynamics, more complex structure, and stronger feedback to hydrodynamics.
Decades of modeling and simulation have been devoted to an understanding of sheared nematic polymers and liquid crystals, motivated by applications to high-performance materials in film and mold geometries, as well as for fundamental interest in the shear-dominated hydrodynamics of anisotropic liquids. More emphasis has arisen recently in nematic polymer models and simulation because of their relevance to technological applications of nanocomposites where the nanoparticles are thin rod and platelet inclusions.
Defects lie at the center of liquid crystal and LCP phenomena, from statics where free energy minimization principles apply, to strongly non-equilibrium conditions where the only tools at present are computational. Open issues include defect genesis, spatial extent, number density, the nature of defect cores, the role of defects in Regions I, II, III of the shear-viscosity curve of Onogi and Asada (1980), and the dynamics and fate of defects during and upon cessation of shear.
Mathematical Modeling: How...