Structure and Pattern Formation in Biological Liquid Crystals: Insights From Theory and Simulation of Self-Assembly and Self-Organization

Abstract

This review presents theory and simulation of liquid crystal phase ordering in biological fibrous materials, solutions, and composites in the presence of elastic fields, second phase inclusions, and transport phenomena, including complex shear-extensional flow and mass transfer. Liquid crystal self-assembly through phase ordering on elastic deformable membranes is first applied to characterize the mechanisms that control the structures in plant cell walls, highlighting how curvophobic and curvophilic effects introduce new structuring fields beyond hard-core repulsion. Then chiral nematic self-assembly is simulated in a mesophase containing fibrillar colloidal inclusions (liquid crystal-fibre composites) to demonstrate how the inclusion positional order generates defects and disclinations as shown in the plant cell wall. Coupling phase ordering to tuned transport phenomena is shown how and why it leads to self-organization such as paranematic states of dilute acidic aqueous collagen solutions. Further directed dehydration of well-organized paranematic collagen leads to defect free cholesteric films only when directed dehydration is synchronized with chirality formation. In addition, the ubiquitous surface nanowrinkling of cholesterics is captured with surface anchoring. In these four representative systems, the new mechanisms that enhance the well-known exclude volume interactions are identified quantified and validated with experimental data. Future directions to create new advanced multifunctional materials based on principles of self-assembly and self-organization are identified by leveraging the new couplings between material structure, geometry, and transport phenomena.

Geometry-structure models for liquid crystal interfaces, drops and membranes: wrinkling, shape selection and dissipative shape evolution

“…Surface pattern formation and instabilities in equilibrium or near equilibrium self-assembly are richly enhanced when considering self-organization under dissipative dynamics [84][85][86][87][88] as shown below. In the kinematics and dynamics section of this review paper, we focus on kinematics and dynamics of timedependent curvature changes in surfaces and membranes.…”

“…(1) Identifying the director orientation of a liquid crystals with the unit normal to a membrane leads to the membranology 84,101,102 model explored mainly in equilibrium scenarios but here we show how the methodology is augmented to dissipative process;…”