Pattern formation and non-linear phenomena in stretched discotic liquid crystal fibres

Abstract

This paper presents a non-linear numerical and bifurcation analysis of pattern formation phenomena in a discotic nematic liquid crystal confined to annular cylindrical cavities and subjected to extensional deformations. The results are of direct relevance to understanding the industrial melt spinning of mesophase carbon fibres, using discotic nematic liquid crystals precursor materials. Three types of orientation patterns are identified in this study: spatially constant (radial), monotonic (pinwheel), and oscillatory (zigzag). Numerical and closed form analytical results predicting continuous transformations between the radial, pinwheel, zigzag radial orientation modes are presented. The bifurcation analysis provides a direct characterization of the parametric dependence and the transitions between these three basic patterns, and provides a complete understanding of the multistability phenomena that is present in the oscillatory orientation patterns. In general it is found that small fibres of nearly elastically isotropic discotic nematic 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 size and anisotropy tend to adopt the pinwheel texture. The theoretical results are able to explain the main features and mechanisms that lead to the commonly observed cross-section textures of industrially spun mesophase carbon fibres.