This paper presents an overview of liquid crystal (LC) models of phase diagrams, phase transitions, self-assembly, interfaces, defects, and rheology and their integrated applications to biological mesophase materials and processes. Biological liquid crystals, classified into analogues (helicoidal plywoods), biopolymer solutions (in vitro DNA, polypeptides, collagen solutions) and in vivo LCs (membranes, silk, DNA), are discussed in terms of molecular characteristics and the symmetry of the thermodynamic phases. The thermodynamics and self-assembly of biological liquid crystals (BLCs) are discussed in terms of the Doi-Maier-Saupe lyotropic model and its extensions to chiral phases, showing the role of excluded volume and chirality. The defect physics of BLCs is described using the Landau-de Gennes model of chiral and achiral nematostatics to identify (i) thermodynamic phases, and (ii) observed textures and defect lattices under confinement and flow. The rheology and flow properties of BLCs are described using the Leslie-Ericksen and the Landau-de Gennes models of nematodynamics. The applications of integrated thermodynamic/defect/rheology modeling to the experimental characterization of several BLCs, including collagen and DNA solutions, are shown to provide organizing principles and quantitative tools to establish the properties of these natural materials. The phase transitions, tactoidal spherulites, flow-birefringence in dilute solutions, and banded textures in sheared concentrated solutions of collagen show how the principles of LC physics operate in BLC materials. Drying and spreading drops of DNA solutions leading to the formation of nematic monodomain aligned along the contact line are shown to follow self-assembly structuring under the action of interfacial, bulk, and contact line torques. Finally modeling of spider and silkworm LC spinning is presented as an example of biological polymer processing, where a high performance fiber material is produced through a lyotropic LC protein solution. The concerted structuring action of capillary confinement, strong anchoring, and nematic flow leads to predictions in agreement with the reported textural transitions in the duct of spiders and silkworms. The quantitative description of BLC materials and processes using mesoscopic models provides another tool to develop the science and future biomimetic applications of these ubiquitous natural anisotropic soft materials.

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▪ Abstract  Recent progress in modeling and simulation of the flow of nematic liquid crystals is presented. The Leslie-Ericksen (LE) theory has been successful in elucidating the flow of low molar-mass nematics. The theoretical framework for the flow of polymeric nematic liquid crystals is still evolving; extensions of the Doi theory capture qualitative features of the flow of polymeric nematics in simple geometries, but these theories have not been shown to predict texture development in flow. Mesoscopic theories for textured materials based on spatial averaging capture only some qualitative features of nonrectilinear liquid-crystalline polymer flow. Interfacial effects in liquid-crystalline systems have begun to receive attention in the context of interfacial viscoelasticity and the dynamics of dispersed liquid-crystalline polymers in immiscible blends.

A model composed of a synthesis of the nonlinear Cahn−Hilliard and Flory−Huggins theories for spinodal decomposition (SD) and a second-order rate equation for the self-condensation of a trifunctional monomer is presented and used to analyze polymerization-induced phase separation (PIPS). The numerical results replicate frequently reported experimental observations on the PIPS of a binary monomer−solvent solution. These observations include a transient periodic concentration spatial profile with a wavelength that decreases with increasing rate constant. In addition, the time evolution of the maximum value of the structure factor exhibits an exponential growth during the early stage, but then slows down in the intermediate stage of SD. Computational analysis shows that, in the PIPS method, the wavelength of the phase-separated structure depends on the complex interaction between the competing polymerization and phase separation processes. The effects of these two competing processes on the characteristic time and length scales of the phase separation phenomena depend on the magnitudes of a scaled diffusion coefficient D for phase separation and a scaled rate constant K 1 for polymerization. As D increases, the dominant dimensionless wavenumber k m * also increases, but the phase separation lag time decreases. Similarly, as K 1 increases, k m * also increases, but the polymerization lag time decreases. On the basis of these two dimensionless parameters, the dominant wavelength selection mechanism in the PIPS process is identified, which enables the control of morphology during the PIPS phenomena.

SUMMARY:In this work a model, composed of the nonlinear Cahn-Hilliard and Flory-Huggins theories, is used to numerically simulate the phase separation and pattern formation phenomena of oligomer and polymer solutions when quenched into the unstable region of their binary phase diagrams. This model takes into account the initial thermal concentration fluctuations. In addition, zero mass flux and natural nonperiodic boundary conditions are enforced to better reflect experimental conditions. The model output is used to characterize the evolution and morphology of the phase separation process. The sensitivity of the time and length scales to processing conditions (initial condition c:) and properties (dimensionless diffusion coefficient D ) is elucidated. The results replicate frequently reported experimental observations on the morphology of spinodal decomposition (SD) in binary solutions: (1) critical quenches yield interconnected structures, and (2) off-critical quenches yield a droplet-type morphology. As D increases, the dominant dimensionless wavenumber k& increases as well, but the dimensionless transition time t: from the early stage to the intermediate stage decreases. In addition, f; is shortest when c8 is at the critical concentration, but increases to infinity when c: is at one of the two spinodal concentrations. These results are found when the solute degree of polymerization N, is in the range I 5 N2 5 100. When N2 > 100, however, a problem of numerical nonconvergence due to diverging relaxation rates occurs because of the very unsymrnetric nature of the phase diagram. A novel scaling procedure is introduced to explain the phase separation phenomena due to SD for any value of N2 during the time range explored in this study.

Membrane flexoelectricity is an electromechanical coupling effect between the membrane average curvature and macroscopic electric polarization. Flexolelectricity is a biological actuation mechanism involved in the functioning of hearing. This thesis uses theory and simulation to develop a fundamental understanding of flexolectricity of relevance to hearing processes by integrating membrane elasticity and flexolectricity with viscoelastic processes.

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