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

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.