PATTERN-FORMATION AND NONLINEAR PHENOMENA IN STRETCHED DISCOTIC LIQUID-CRYSTAL FIBERS

This paper presents a non-linear numerical and bifurcation analysis of pattern formation phenomena in a discotic nematic liquid crystal conf ined to annular cylindrical cavities and subjected to extensional defo rmations. The results are of direct relevance to understanding the ind ustrial melt spinning of mesophase carbon fibres, using discotic nemat ic liquid crystals precursor materials. Three types of orientation pat terns are identified in this study: spatially constant (radial), monot onic (pinwheel), and oscillatory (zigzag). Numerical and closed form a nalytical results predicting continuous transformations between the ra dial, pinwheel, zigzag radial orientation modes are presented. The bif urcation analysis provides a direct characterization of the parametric dependence and the transitions between these three basic patterns, an d provides a complete understanding of the multistability phenomena th at is present in the oscillatory orientation patterns. In general it i s found that small fibres of nearly elastically isotropic discotic nem atic liquid crystals tend to adopt the classical ideal radial texture, while larger fibres with anisotropic elastic moduli tend to yield the zigzag texture. Fixed arbitrary surface orientation of intermediate s ize and anisotropy tend to adopt the pinwheel texture. The theoretical results are able to explain the main features and mechanisms that lea d to the commonly observed cross-section textures of industrially spun mesophase carbon fibres.