The textures exhibited by nematic liquid crystals confined to cylindrical capillaries under homeotropic anchoring have been studied for nearly thirty years. One of the reasons behind this maintained interest is that the processing of many high-performance fibers including carbon fibers and spider silks involves these textures. Three of these textures, the planar radial with line defect, the planar polar with two line defects (PPLD), and the escape radial (ER), are relatively well understood. A third one, the escape radial with point defects presents, however, some unresolved issues and recent studies have questioned the real nature and dimensionality of the defects involved in this texture. It seems that the defects are not in the form of points but rather in the form of closed lines or rings. This paper presents a detailed study on the connection between point and ring defects in a cylindrical cavity using three-dimensional simulations based on the continuum Landau-de Gennes theory. The results show that true point defects cannot exist in cylindrical cavities and that the merging of two ringlike defects may lead to two qualitatively different stable textures, namely, the ER and PPLD textures. The various results are in qualitative agreement with recent molecular dynamic studies and with theoretical predictions based on experimental observations. The predictions provide new insights on the structural connections between synthetic and biological superfibers.

Many natural composites exhibit an architecture known as twisted plywood which imparts to them a superior set of physical properties. The origin of this structure is complex and not yet understood. However, it is thought to involve a lyotropic chiral nematic liquid-crystalline mesophase. Indeed, striking structural similarities have been observed and reported between biological fibrous composites and ordered fluids. In this work, a mathematical model based on the Landau-de Gennes theory has been developed to investigate the role played by constraining surfaces in the structural development of a composite material that experiences a liquid-crystalline state during the early steps of its morphogenesis. The goal of this study is to verify the need for an initial constraining surface in the formation of monodomain twisted plywoods as hypothesized by Neville (Tissue & Cell 20, 133 (1988); Biology of Fibrous Composites (Cambridge University Press, 1993)). The numerical simulations qualitatively confirm this theory and highlight the important role that modelling of liquid-crystalline self-assembly plays in the study of tissue morphogenesis.

Biological fibrous composites commonly exhibit an architecture known as twisted plywood, which is similar to that of the cholesteric liquid-crystalline mesophases. The explanation for the structural similarity is that biological fibrous composites adopt a lyotropic cholesteric liquid-crystalline phase during their formation process. In this work, a mathematical model based on the Landau-de Gennes theory of liquid crystals has been developed to reproduce the process by which long chiral fibrous molecules form the twisted plywood structures observed in biological composites. The dynamics of the process was then further investigated by analytically solving a simplified version of the governing equations. Results obtained from the model are in good qualitative agreement with the theory of Neville [Biology of Fibrous Composites (Cambridge University Press, Cambridge, England, 1993)] who hypothesized the necessity of a constraining layer to lock the direction of the helical axis of the plywood in order to create a monodomain structure. Computational results indicate that the plywood architecture is obtained by a chiral front propagation process with a fully relaxed wake. The effects of chirality and concentration on the formation process kinetics are characterized.

Nematic liquid crystals confined in a cylindrical capillary and subjected to strong homeotropic anchoring conditions is a long-studied fundamental problem that uniquely incorporates nonlinearity, topological stability, defects, and texture physics. The observed and predicted textures that continue to be investigated include escape radial, radial with a line defect, planar polar with two line defects, and periodic array of point defects. This paper presents theory and multiscale simulations of global and fine scale textures of nematic point defects, based on the Landau-de Gennes tensor order parameter equations. The aim of this paper is to further investigate the ringlike nature of point defect cores and its importance on texture transformation mechanisms and stability. The paper shows that the ringlike cores can be oriented either along the cylinder axis or along the radial direction. Axial rings can partially expand but are constrained by the capillary sidewalls. Radial rings can deform into elliptical structures whose major axis is along the capillary axis. The transformation between several families of textures under capillary confinement as well as their stability is discussed in terms of defect ring distortions. A unified view of nematic textures found in the cylindrical cavities is provided.

We study Bloch wall defects formed by quenching nematic thin films from planar anchoring to homeotropic anchoring through a temperature-driven anchoring transition. The director profiles of the walls are directly visualized using fluorescence confocal polarizing microscopy, and shown to agree well with the simulation based on the Frank elasticity theory. A pure twist wall exists if the ratio of sample thickness to surface extrapolation length p is smaller than or close to 1; while a diffuse Bloch wall is obtained if p is much greater than 1.