Chiral front propagation in liquid-crystalline materials: Formation of the planar monodomain twisted plywood architecture of biological fibrous composites

Abstract

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.

Modeling Textural Processes during Self-Assembly of Plant-Based Chiral-Nematic Liquid Crystals

“…The homogeneous (gradient) elastic effects are represented by power series of scalar invariants of tensor parameter Q (gradient of tensor order parameter Q ). In the absence of an external field, the total free energy density of the mesophase (f) can be given in the following dimensionless form [15,33,34,46]:…”

“…These computations elucidated the need for a constraining surface that can direct the chiral nematic helix in a direction normal to it, to form a defect free monodomain twisted plywood structure [34,35]. Recently, an integrated mechanical model describing nematic liquid crystalline self-assembly of rigid rods on an arbitrarily curved membrane has been presented and relative predictions of cellulose ordering and orientation in the plant cell wall are presented.…”

“…Previously a computationally implemented mathematical model based on the Landau-de Gennes theory has been employed to investigate the effect of constraining surfaces on the development of structure in a lyotropic chiral nematic liquid crystalline mesophase [34,35]. These computations elucidated the need for a constraining surface that can direct the chiral nematic helix in a direction normal to it, to form a defect free monodomain twisted plywood structure [34,35].…”

Liquid crystal models of biological materials and silk spinning

“…Amphiphiles self-assemble into lamellar, cubic, and bicontinuous phases. 16,18,19,23,27,35,36 Incorporation of rod and disc mesogens into flexible polymer form thermotropic liquid crystal polymers with architectures that include side-chain, main-chain, and cross-linked elastomers. 1,2,16,21,28,34 Highly synthetic rigid rod-like polymers such as polyamides (Kevlar) required strong solvents to form nematic phases.…”

“…Approximating the DMS homogeneous free energy f h with the LdG expansion leads to 2,16,20,27,35,36 :…”