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The elasticity is known as Frank elasticity and the elastic modes are splay, bend, and twist ( Barbero and Evangelista, 2000). Since the uniaxial N phase has no positional order ( P 0), anisotropic viscosity is possible and since orientation gradients due to spatial gradients of n (∇ n ≠ 0) store energy, these materials are also elastic. In the uniaxial nematic phase ( Donald et al., 2006), the characterizing non-conserved order parameter (NCOP) is a symmetric traceless uniaxial tensor Q = S ( nn − I/3), where S controls fast time scales and short nano-length scales, and n is the slow variable associated with micron range length scales and unique direction of material property anisotropy (transverse isotropy) ( Tsuji and Rey, 1997 Liu and Calderer, 2000 Rey, 2009).

The simplest phase ordering transition is the isotropic-to-nematic N transition, predicted by the Onsager model ( Lekkerkerker and Vroege, 1993 Selinger, 2016), where the isotropic I phase undergoes an orientational ordering transition characterized by the emergence of molecular or fibrillar alignment (non-zero scalar order parameter S) along an anisotropic axis or director n this vector is of unit length ( n ⋅ n = 1) ( Donald et al., 2006). Rod-like lyotropic polymer and colloidal liquid crystals are viscoelastic multifunctional materials that undergo phase ordering transitions with increasing concentration mainly due to hardcore excluded volume interactions, giving rise to mesophases with intermediate degrees of orientational and positional order ( Tsuji and Rey, 1997 Lhuillier and Rey, 2004 Donald et al., 2006 Mottram and Newton, 2014 Zhao et al., 2017).

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. In these four representative systems, the new mechanisms that enhance the well-known exclude volume interactions are identified quantified and validated with experimental data. In addition, the ubiquitous surface nanowrinkling of cholesterics is captured with surface anchoring.

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Further directed dehydration of well-organized paranematic collagen leads to defect free cholesteric films only when directed dehydration is synchronized with chirality formation. 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. 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. 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.

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.

2HydrateTech, Department of Chemical Engineering, McGill University, Montréal, QC, Canada.

1Materials Modeling Research Group (MMRG), Department of Chemical Engineering, McGill University, Montréal, QC, Canada.

Ziheng Wang 1,2, Phillip Servio 2 and Alejandro D.

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