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We report a computational model for amyloid fibrils and discuss its main features and ability to match different experimental morphological characteristics. The model captures the liquid crystalline and cholesteric behaviours in short and rigid amyloid fibrils and shows promising extendibility to more complex colloidal liquid crystals.

Facile geometric-structural response of liquid crystalline colloids to external fields enables many technological advances. However, the relaxation mechanisms for liquid crystalline colloids under mobile boundaries remain still unexplored. Here, by combining experiments, numerical simulations and theory, we describe the shape and structural relaxation of colloidal liquid crystalline micro-droplets, called tactoids, where amyloid fibrils and cellulose nanocrystals are used as model systems. We show that tactoids shape relaxation bears a universal single exponential decay signature and derive an analytic expression to predict this out of equilibrium process, which is governed by liquid crystalline anisotropic and isotropic contributions. The tactoids structural relaxation shows fundamentally different paths, with first- and second-order exponential decays, depending on the existence of splay/bend/twist orientation structures in the ground state. Our findings offer a comprehensive understanding on dynamic confinement effects in liquid crystalline colloidal systems and may set unexplored directions in the development of novel responsive materials., (© 2022. The Author(s).)

Para-nematic phases, induced by unwinding chiral helices, spontaneously relax to a chiral ground state through phase ordering dynamics that are of great interest and crucial for applications such as stimuli-responsive and biomimetic engineering. In this work, we characterize the cholesteric phase relaxation behaviors of β-lactoglobulin amyloid fibrils and cellulose nanocrystals confined into cylindrical capillaries, uncovering two different equilibration pathways. The integration of experimental measurements and theoretical predictions reveals the starkly distinct underlying mechanism behind the relaxation dynamics of β-lactoglobulin amyloid fibrils, characterized by slow equilibration achieved through consecutive sigmoidal-like steps, and of cellulose nanocrystals, characterized by fast equilibration obtained through smooth relaxation dynamics. Particularly, the specific relaxation behaviors are shown to emerge from the order parameter of the unwound cholesteric medium, which depends on chirality and elasticity. The experimental findings are supported by direct numerical simulations, allowing to establish hard-to-measure viscoelastic properties without applying magnetic or electric fields.

In this paper we focus on the structural determination of biological orthogonal plywoods, fiber-like composite analogues of liquid crystalline phases, where the fibrils of the building blocks show sharp 90° orientation jumps between fibers in adjacent domains. We present an original geometric and computational modelling that allows us to determine the fibrillary orientation in biological plywoods from periodic herringbone patterns commonly observed in cross-sections. Although herringbone patterns were long reported, the specific and quantitative relationships between herringbones and the orthogonal plywoods were absent or at best incomplete. Here we provide an efficient and new procedure to perform an inverse problem that connects two specific features of the herringbone patterns (aperture angle and wavelength) with the 3D morphology of the structure, whose accuracy and validity were ascertained through in silico simulations and also with real specimens ("Eremosphaera viridis"). This contribution extends significantly the better known characterization methods of 2D cross sections, such as the arced patterns observed in biological helicoidal plywoods, and with the present proposed methodology it adds another characterization tool for a variety of biological fibrous composites that form cornea-like tissues.

Membrane flexoelectricity is an electromechanical coupling process that describes membrane bending and membrane electrical polarization caused by bending under electric fields. In this paper we propose, formulate, and characterize a stress-sensor device for mechanically loaded solids, consisting of a soft flexoelectric thin membrane attached to the loaded deformed solid. Because the curvature of the deformed solid is transferred to the attached flexoelectric membrane, the electromechanical transduction of the latter produces a charge that is proportional to the stress of the solid. The model of the stress-sensor device is based on the integration of the thermodynamics of polarizable membranes with isotropic solid elasticity, leading to a transfer function that identifies the elastic, electromechanical, and geometrical parameters involved in electrical-signal generation. The model is applied to representative normal bending and then to more complex off-axis bending of elastic bars. In all cases, a common transfer function shows the generic material and its geometric contributions. The sensor sensitivity increases linearly with flexoelectricity and the membrane-solid interface, and the sensitivity decreases with increasing membrane thickness and Young's modulus of the solid. The theoretical results contribute to ongoing experimental efforts towards the development of anisotropic soft-matter-based stress-sensor devices through solid-membrane interactions and electromechanical transduction., (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Membrane flexoelectricity is an electromechanical coupling process that describes membrane electrical polarization due to bending and membrane bending under electric fields. In this paper we propose, formulate, and characterize a mechanical energy harvesting system consisting of a deformable soft flexoelectric thin membrane subjected to harmonic forcing from contacting bulk fluids. The key elements of the energy harvester are formulated and characterized, including (i) the mechanical-to-electrical energy conversion efficiency, (ii) the electromechanical shape equation connecting fluid forces with membrane curvature and electric displacement, and (iii) the electric power generation and efficiency. The energy conversion efficiency is cast as the ratio of flexoelectric coupling to the product of electric and bending elasticity. The device is described by a second-order curvature dynamics coupled to the electric displacement equation and as such results in mechanical power absorption with a resonant peak whose amplitude decreases with bending viscosity. The electric power generation is proportional to the conversion factor and the power efficiency decreases with frequency. Under high bending viscosity, the power efficiency increases with the conversion factor and under low viscosities it decreases with the conversion factor. The theoretical results presented contribute to the ongoing experimental efforts to develop mechanical energy harvesting from fluid flow energy through solid-fluid interactions and electromechanical transduction.

Theory and simulations of simultaneous chemical demixing and phase ordering are performed for a mixed order parameter system with an isotropic-isotropic (I-I) phase separation that is metastable with respect to an isotropic-nematic (I-N) phase-ordering transition. Under certain conditions, the disordered phase transforms into an ordered phase via the motion of a double front containing a metastable phase produced by I-I demixing, a thermodynamically driven mechanism not previously reported. Different kinetic regimes are found depending on the location of the initial conditions in the thermodynamic phase diagram and the ratio between diffusional and nematic phase-ordering mobilities. For a diffusional process, depending if the temperature is above or below the critical codissolution point, an inflection point or a phase separation takes place in the depletion layer. This phase separation leads to the formation of a second interface where the separation of the two metastable isotropic phases grows monotonically with time. The observed deviations from the typical Fickian concentration profiles are associated with strong positive deviations of the mixture from ideality due to couplings between concentration and nematic ordering. Although systems of interest include liquid-crystalline nanocomposites, this mechanism may apply to any mixture that can undergo an order-disorder transition and demix.

A review of thermodynamic, materials science, and rheological liquid crystal models is presented and applied to a wide range of biological liquid crystals, including helicoidal plywoods, biopolymer solutions, and in vivo liquid crystals. The distinguishing characteristics of liquid crystals (self-assembly, packing, defects, functionalities, processability) are discussed in relation to biological materials and the strong correspondence between different synthetic and biological materials is established. Biological polymer processing based on liquid crystalline precursors includes viscoelastic flow to form and shape fibers. Viscoelastic models for nematic and chiral nematics are reviewed and discussed in terms of key parameters that facilitate understanding and quantitative information from optical textures and rheometers. It is shown that viscoelastic modeling the silk spinning process using liquid crystal theories sheds light on textural transitions in the duct of spiders and silk worms as well as on tactoidal drops and interfacial structures. The range and consistency of the predictions demonstrates that the use of mesoscopic liquid crystal models is another tool to develop the science and biomimetic applications of mesogenic biological soft matter., (Copyright © 2011 Wiley Periodicals, Inc.)

A systematic analysis of defect textures in faceted nanoparticles with polygonal configurations embedded in a nematic matrix is performed using the Landau-de Gennes model, homeotropic strong anchoring in a square domain with uniform alignment in the outer boundaries. Defect and textures are analyzed as functions of temperature T, polygon size R, and polygon number N. For nematic nanocomposites, the texture satisfies a defect charge balance equation between bulk and surface (particle corner) charges. Upon decreasing the temperature, the central bulk defects split and together with other -1/2 bulk defects are absorbed by the nanoparticle's corners. Increasing the lattice size decreases confinement and eliminates bulk defects. Increasing the polygon number increases the central defect charge at high temperature and the number of surface defects at lower temperatures. The excess energy per particle is lower in even than in odd polygons, and it is minimized for a square particle arrangement. These discrete modeling results show for first time that, even under strong anchoring, defects are attached to particles as corner defects, leaving behind a low energy homogeneous orientation field that favors nanoparticle ordering in nematic matrices. These new insights are consistent with recent thermodynamic approaches to nematic nanocomposites that predict the existence of novel nematic/crystal phases and can be used to design nanocomposites with orientational and positional order.

A new defect-forming mechanism is predicted for liquid crystals undergoing an isotropic-to-nematic phase transition. A continuum theory characterizes how +1/2 defects (D<30 nm) evolve within and then shed from the interface (cross section approximately 100 nm) of a growing 5CB (4-n-4'-pentyl-4-cyanobiphenyl) nanodroplet (20 nm

Optical simulations of a liquid crystal biosensor device are performed using an integrated optical/textural model based on the equations of nematodynamics and two optical methods: the Berreman optical matrix method [J. Opt. Soc. Am. 62, 502 (1972)] and the discretization of the Maxwell equations based on the finite difference time domain (FDTD) method. Testing the two optical methods with liquid crystal films of different degrees of orientational heterogeneities demonstrates that only the FDTD method is suitable to model this device. Basic substrate-induced texturing process due to protein adsorption gives rise to an orientation correlation function that is nearly linear with the transmitted light intensity, providing a basis to calibrate the device. The sensitivity of transmitted light to film thickness, protein surface coverage, and wavelength is established. A crossover incident light wavelength close to lambda(co) approximately 500 nm is found, such that when lambda>lambda(co) thinner films are more sensitive to the amount of protein surface coverage, while for lambda

Optical images of textured liquid-crystal films containing various types of twist disclination loops are computed using an approximate matrix method and a direct numerical simulation based on the finite-difference time-domain (FDTD) method. The selected defects introduce large multidirectional spatial gradients in the optic axis, mimicking the orientation textures that arise in the construction and use of biosensors based on liquid-crystal vision. It is shown that under these experimentally relevant conditions, the matrix method fails to capture important signatures in the transmitted light intensity under crossed polarizers. The differences between the predictions by the two methods are analyzed with respect to gradients in the optic axis. We show that the FDTD method is a useful tool to perform computational optics of textured liquid-crystal films.

Background: Liquid crystal (LC) mesophases have an orientational and positional order that can be found in both synthetic and biological materials. These orders are maintained until some parameter, mainly the temperature or concentration, is changed, inducing a phase transition. Among these transitions, a special sequence of mesophases has been observed, in which priority is given to the direct smectic liquid crystal transition. The description of these transitions is carried out using the Landau–de Gennes (LdG) model, which correlates the free energy of the system with the orientational and positional order. Methodology: This work explored the direct isotropic-to-smectic A transition studying the free energy landscape constructed with the LdG model and its relation to three curve families: (I) level-set curves, steepest descent, and critical points; (II) lines of curvature (LOC) and geodesics, which are directly connected to the principal curvatures; and (III) the Casorati curvature and shape coefficient that describe the local surface geometries resemblance (sphere, cylinder, and saddle). Results: The experimental data on 12-cyanobiphenyl were used to study the three curve families. The presence of unstable nematic and metastable plastic crystal information was found to add information to the already developed smectic A phase diagram. The lines of curvature and geodesics were calculated and laid out on the energy landscape, which highlighted the energetic pathways connecting critical points. The Casorati curvature and shape coefficient were computed, and in addition to the previous family, they framed a geometric region that describes the phase transition zone. Conclusion and significance: A direct link between the energy landscape’s topological geometry, phase transitions, and relevant critical points was established. The shape coefficient delineates a stability zone in which the phase transition develops. The methodology significantly reduces the impact of unknown parametric data. Symmetry breaking with two order parameters (OPs) may lead to novel phase transformation kinetics and droplets with partially ordered surface structures. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the internal viscosity model developed by Professor Williams to semiflexible polymers, biofilaments, and worm‐like micelles, where molecular dissipation is generated by bending. Current models for viscoelasticity with internal viscosity in semiflexible polymers and filaments are based on generalizations of the worm‐like model, but they neglect potential electromechanical couplings such as flexoelectricity. In this paper, inspired by the early work of Professor Williams, we develop a model for worm‐like viscoelastic flexoelectric filaments based on the "line liquid crystal model". The electroelastic free energy and entropy production are formulated and used to derive the shape equation for these filaments undergoing thermal fluctuations. The resulting time relaxation spectrum is a useful tool to characterize experimentally viscoelastic material parameters. We show that flexoelectricity or polarization‐induced bending softens the filaments. The predicted time relaxation spectrum shows that at longer wavelength modes, the filament behaves like a rigid rod in a viscous solvent, but at shorter wavelengths, it reaches a plateau defined by the bending time scale. The key effect of flexoelectricity is to shift the entire spectrum to higher values, slowing down the response. The model itself is validated using the worm‐like chain and the viscoelasticity of liquid crystals, and the predictions are shown to be in qualitative consistency with the data. Since filament flexoelectricity is associated with 1D sensor‐actuator functionalities, the presented model has many potential novel applications in reduced geometries. [ABSTRACT FROM AUTHOR]

The extended Maier–Saupe model for binary mixtures of model carbonaceous mesophases (uniaxial discotic nematogens) under externally imposed flow, formulated in previous studies [M. Golmohammadi and A. D. Rey, Liquid Crystals 36, 75 (2009); M. Golmohammadi and A. D. Rey, Entropy 10, 183 (2008)], is used to characterize the effect of uniaxial extensional flow and concentration on phase behavior and structure of these mesogenic blends. The generic thermorheological phase diagram of the single-phase binary mixture, given in terms of temperature (T) and Deborah (De) number, shows the existence of four T-De transition lines that define regions that correspond to the following quadrupolar tensor order parameter structures: (i) oblate (⊥,∥), (ii) prolate (⊥,∥), (iii) scalene O(⊥,∥), and (iv) scalene P(⊥,∥), where the symbols (⊥,∥) indicate alignment of the tensor order ellipsoid with respect to the extension axis. It is found that with increasing T the dominant component of the mixture exhibits weak deviations from the well-known pure species response to uniaxial extensional flow (uniaxial ⊥nematic→biaxial nematic→uniaxial∥paranematic). In contrast, the slaved component shows a strong deviation from the pure species response. This deviation is dictated by the asymmetric viscoelastic coupling effects emanating from the dominant component. Changes in conformation (oblate<=>prolate) and orientation (⊥<=>∥) are effected through changes in pairs of eigenvalues of the quadrupolar tensor order parameter. The complexity of the structural sensitivity to temperature and extensional flow is a reflection of the dual lyotropic/thermotropic nature (amphotropic nature) of the mixture and their cooperation/competition. The analysis demonstrates that the simple structures (biaxial nematic and uniaxial paranematic) observed in pure discotic mesogens under uniaxial extensional flow are significantly enriched by the interaction of the lyotropic/thermotropic competition with the binary molecular architectures and with the quadrupolar nature of the flow. [ABSTRACT FROM AUTHOR]

The textures exhibited by nematic liquid crystals confined to cylindrical capillaries under homeotropic anchoring have been studied for nearly thirty years. One of the reasons behind this maintained interest is that the processing of many high-performance fibers including carbon fibers and spider silks involves these textures. Three of these textures, the planar radial with line defect, the planar polar with two line defects (PPLD), and the escape radial (ER), are relatively well understood. A third one, the escape radial with point defects presents, however, some unresolved issues and recent studies have questioned the real nature and dimensionality of the defects involved in this texture. It seems that the defects are not in the form of points but rather in the form of closed lines or rings. This paper presents a detailed study on the connection between point and ring defects in a cylindrical cavity using three-dimensional simulations based on the continuum Landau–de Gennes theory. The results show that true point defects cannot exist in cylindrical cavities and that the merging of two ringlike defects may lead to two qualitatively different stable textures, namely, the ER and PPLD textures. The various results are in qualitative agreement with recent molecular dynamic studies and with theoretical predictions based on experimental observations. The predictions provide new insights on the structural connections between synthetic and biological superfibers. [ABSTRACT FROM AUTHOR]

Nematic liquid crystals confined in a cylindrical capillary and subjected to strong homeotropic anchoring conditions is a long-studied fundamental problem that uniquely incorporates nonlinearity, topological stability, defects, and texture physics. The observed and predicted textures that continue to be investigated include escape radial, radial with a line defect, planar polar with two line defects, and periodic array of point defects. This paper presents theory and multiscale simulations of global and fine scale textures of nematic point defects, based on the Landau–de Gennes tensor order parameter equations. The aim of this paper is to further investigate the ringlike nature of point defect cores and its importance on texture transformation mechanisms and stability. The paper shows that the ringlike cores can be oriented either along the cylinder axis or along the radial direction. Axial rings can partially expand but are constrained by the capillary sidewalls. Radial rings can deform into elliptical structures whose major axis is along the capillary axis. The transformation between several families of textures under capillary confinement as well as their stability is discussed in terms of defect ring distortions. A unified view of nematic textures found in the cylindrical cavities is provided. [ABSTRACT FROM AUTHOR]

Optical simulations of a liquid crystal biosensor device are performed using an integrated optical/textural model based on the equations of nematodynamics and two optical methods: the Berreman optical matrix method [J. Opt. Soc. Am. 62, 502 (1972)] and the discretization of the Maxwell equations based on the finite difference time domain (FDTD) method. Testing the two optical methods with liquid crystal films of different degrees of orientational heterogeneities demonstrates that only the FDTD method is suitable to model this device. Basic substrate-induced texturing process due to protein adsorption gives rise to an orientation correlation function that is nearly linear with the transmitted light intensity, providing a basis to calibrate the device. The sensitivity of transmitted light to film thickness, protein surface coverage, and wavelength is established. A crossover incident light wavelength close to λco≈500 nm is found, such that when λ>λco thinner films are more sensitive to the amount of protein surface coverage, while for λ≤λco the reverse holds. In addition it is found that for all wavelengths the sensitivity increases with the amount of protein coverage. The integrated device model based on FDTD optical simulations in conjunction with the Landau-de Gennes nematodynamics model provides a rational basis for further progress in liquid crystal biosensor devices. [ABSTRACT FROM AUTHOR]

The early stages of liquid crystal phase ordering upon thermal quenches of isotropic phases into unstable and metastable temperature ranges is studied using two-dimensional (2D) computational solutions of the governing Landau-de Gennes (L-dG) equations for low molar mass nematic liquid crystals and analysis based on the corresponding interfacial nematodynamic model. The early phase ordering stage, for both unstable and metastable quenches of the isotropic phase, is shown to lead to highly textured nematic spherulites through a mechanism of interfacial defect nucleation. The underlying mechanisms of interface-driven texturing are elucidated using complementary 2D computational parametric studies of the bulk L-dG equation and analysis of the IN model. It is shown that for highly curved nanodomains and realistic elastic anisotropy, sharp interfacial transitions between uniaxial and biaxial states arise and are resolved by interfacial defect nucleation, which upon subsequent migration into the spherulite’s interior leads to strong texturing. This paper shows that texture formation in the early stages of phase ordering is interface driven, and due to low interface tension, elastic anisotropy, and large curvature. Interfacial defect shedding in highly curved, low tension, anisotropic interfaces is a significant defect nucleation mechanism that needs to be taken into account when considering texturing processes. [ABSTRACT FROM AUTHOR]

Computational modeling of texture formation in coupled phase separation-phase ordering processes in polymer/liquid crystal mixtures is performed using a unified model based on the nematic tensor order parameter and gradient orientation elasticity. The computational methods are able to resolve defect nucleation, defect-defect interactions, and defect-particle interactions, as well as global and local morphological features in the concentration and order parameter spatiotemporal behavior. Biphasic structures corresponding to polymer dispersed liquid crystals (PDLCs), crystalline filled nematic (CFNs), and random filled nematics (RFNs) are captured and analyzed using liquid crystal defect physics and structure factors. Under spinodal decomposition due to concentration fluctuations, the PDLC structure emerges, and the nucleation and repulsive interaction of defects within nematic droplets leads to bipolar nematic droplets. Under spinodal decomposition due to ordering fluctuations, the CFNs structure emerges, and the stable polymer droplet crystal is pinned by a lattice of topological defects. For intermediate cases, where the mixture is unstable to both concentration and nematic order fluctuations, the RFN structure emerges, and polymer droplets and fibrils are pinned by a defect network, whose density increases with the curvature of the polymer-liquid crystal interface. The simulations provide an information of the role of topological defects on phase separation-phase ordering processes in polymer-liquid crystal mixtures. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The Gibbs–Duhem equation for interfaces between nematic liquid crystals and isotropic fluids is formulated and shown to be a generic equation for soft anisotropic surfaces. The one-to-one correspondence between the nematic and crystalline surface Gibbs–Duhem equations is established. Consistency between the surface Gibbs–Duhem equation and the classical equations of interfacial nematostatics is shown. Using a phase space that takes into account thermodynamics, liquid crystalline order, and geometric variables, the generalized nematic surface Gibbs–Duhem equation reveals the presence of couplings between shape, adsorption, temperature, and average molecular orientation. Merging the thermodynamic analysis with nematostatics results in a model for morphactancy, that is, adsorption-induced interfacial shape selection. The specific roles of gradient bulk Frank elasticity, interfacial tension, and anchoring energy are elucidated by analyzing particular paths in the thermodynamic-geometric phase space. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The Cahn-Hoffman capillarity vector thermodynamics for curved anisotropic interfaces is adapted to soft liquid crystalline interfaces. The formalism is used to derive Herring's capillary pressure equation for anisotropic surfaces, where the role of anchoring energy of liquid crystals is made explicity. It is shown in detail that liquid crystal interfaces have three distinct contributions to capillary pressure: (i) area reduction, (ii) area rotation, and (iii) orientation curvature. General expressions representing these three mechanisms in terms of isotropic and anisotropic surface tensions are derived and used to analyze the Rayleigh capillary instability in thin fibers. It is shown that liquid crystal fibers and filaments are unstable to peristaltic and chiral surface ripple modes. The peristaltic mode leads to droplet formation, while chiral modes produce ripples in the curvature of the fiber. The role of liquid crystal orientation and anchoring energy on mode selection is elucidated and quantified. [ABSTRACT FROM AUTHOR]

This work presents an analysis that identifies the two prominent mechanisms that govern the helix uncoiling of sheared cholesteric liquid crystals. In the presence of free surface orientation helix uncoiling proceed by pitch expansion of traveling orientational waves, and in the presence of fixed surface orientation helix uncoiling proceeds via compression of elastic boundary layers. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A density functional theory (DFT) based multi-step simulation method is used to characterize the detailed molecular structure and inter/intra- molecular interactions of two benchmark liquid crystals (LC) 5CB, 8CB and a novel tri-biphenyl ring bent core LC material. The method uses hybrid DFT at the B3LYP/6-31G* level to obtain molecular structure and Raman data. These results are fed to a crystal packing simulation to find possible crystal structures. A pico-second quantum mechanics/molecular mechanics (QM/MM) simulation model is built for the selected structures with lower overall energy as well as optimal density. The stabilized crystal structures are then extended into a super cell, heated and simulated using a mixed force field and nano-second molecular dynamics (MD). The described simulation process sequence provides predictions of molecular Raman spectrum, LC density, isotropic depolarization ratio, ratio of differential polarizability, order parameters, molecular structures, and rotating Raman spectrum of the different mesophases. The Raman spectra, order parameters and depolarization ratios all agree well with existing experimental and previous simulation results. The study of the novel tri-biphenyl ring bent core LC system shows that the ratio of differential polarizability depends on intra-molecular interactions. The findings presented in this manuscript contribute to the on-going efforts to establish links between LC molecular structures and their properties, including optical behavior. A multi-step simulation method is used to characterize the order parameter, rotating Raman spectrum and X-ray data of two benchmark liquid crystals 5CB, 8CB and a novel tri-biphenyl ring bent core mesogen. The force field for molecular dynamic is constructed based on the quantum chemistry optimization. Simulations show the contribution to different Raman peaks from different molecular functional groups and how this can impact the accuracy of theoretical and experimental results. [ABSTRACT FROM AUTHOR]

A review of thermodynamic and flow liquid crystal models is presented and applied to a wide range of biological liquid crystals (BLCs), including helicoidal plywoods, biopolymer solutions andin vivoliquid crystals. The key characteristics of liquid crystals (self-assembly, packing, defects, functionalities, processability) are discussed in relation to biological materials and the strong correspondence between different synthetic and biological materials is discussed. Viscoelastic models for nematic and chiral nematics are reviewed and discussed in terms of key parameters that facilitate understanding and quantitative information from experimental measurements. The range and consistency of the predictions demonstrates that the use of mesoscopic liquid crystal models is an efficient tool to develop the science and biomimetic applications of mesogenic biological materials. [ABSTRACT FROM AUTHOR]

Liquid crystals (LCs) are synthetic and biological viscoelastic anisotropic soft matter materials that have a combination of fluidity of liquids and anisotropy of solids and find use in optical devices, sensor/actuators, lubrication and super-fibres. Mesogens are frequently mixed with colloidal and nanoparticles (NPs), other mesogens, isotropic solvents, thermoplastic polymers, cross-linkable monomers, among others. This comprehensive review presents recent progress in meso- and macro-scale thermodynamic modelling, highlighting (i) the novelties in spinodal and binodal lines in various phase diagrams, (ii) the growth laws under phase transitions and phase separation, (iii) the ubiquitous role of metastability and its manifestation in complex droplet interfaces, (iv) the various spinodal decompositions due to composition and order fluctuations, (v) the formation of novel material architectures such as colloidal crystals, (vi) the particle-rich phase behaviour in LC nanocomposites, (vii) the use of topological defects to absorb and organise NPs and (viii) the ability of faceted NPs to link into strings and organise into lattices. Emphasis is given to highlight dominant mechanisms and driving forces, and to link them to specific terms in the free energies of these complex mixtures. The novelties of incorporating mesophases into blends, solutions, dispersions and mixtures are revealed by using theory, modelling, computation and visualisation. [ABSTRACT FROM AUTHOR]

A new computational strategy is proposed to approximate, with a simple but accurate expression, the Maier-Saupe free energy for nematic order. Instead of the traditional approach of expanding the free energy with a truncated Taylor series, we employ a least-squares fitting to obtain the coefficients of a polynomial expression. Both methods are compared, and the fitting with at most five polynomial terms is shown to provide a satisfactory fitting, and to give much more accurate results than the traditional Taylor expansion. We perform the analysis in terms of the tensor order parameter, so the results are valid in uniaxial and biaxial states. [ABSTRACT FROM AUTHOR]

Biological liquid crystalline polymers are found in cellulosic, chitin, and DNA based natural materials. Chiral nematic liquid crystalline orientational order is observed frozen-in in the solid state in plant cell walls and is known as a liquid crystal analogue characterized by a helicoidal plywood architecture. The emergence of the plywood architecture by directed chiral nematic liquid crystalline self assembly has been postulated as the mechanism that leads to optimal cellulose fibril organization. In natural systems, tissue growth and development takes place in the presence of inclusions and secondary phases leaving behind characteristic defects and textures, which provide a unique testing ground for the validity of the liquid crystal self-assembly postulate. In this work, a mathematical model, based on the Landau-de Gennes theory of liquid crystals, is used to simulate defect textures arising in the domain of self assembly, due to presence of secondary phases representing plant cells, lumens and pit canals. It is shown that the obtained defect patterns observed in some plant cell walls are those expected from a truly liquid crystalline phase. The analysis reveals the nature and magnitude of the viscoelastic material parameters that lead to observed patterns in plant-based helicoids through directed self-assembly. In addition, the results provide new guidance to develop biomimetic plywoods for structural and functional applications. [ABSTRACT FROM AUTHOR]

Carbon fibers and composites derived from mesophase pitch exhibit ultrahigh stiffness and thermal conductivity due to a high degree of graphitic content, which is generated by the liquid crystalline state of the precursor and the molecular orientation that is developed during melt processing steps. To understand the flow and its effect on microstructure, this paper presents an integrated experimental and modeling approach for a synthetic discotic mesophase pitch (AR-HP). Careful control of shear rate and strain was exercised throughout the rheological studies. Wide-angle x-ray diffraction studies were conducted on carefully solidified rheological specimens to obtain azimuthal profiles for layer plane orientation. Cross-polarized microscopy was conducted in the reflected mode using a first-order red plate to examine the orientation in three orthogonal planes. Under the influence of steady shear, the microstructure of mesophase pitch became flow-aligned, which is similar to the fibrous structure reported in the literature. Transient stress response, however, displayed a nonmonotonic behavior. Microscopic observations indicate that the local maximum in the shear stress is likely caused by the deformation of the initial microstructure. To develop a better understanding of these complex flow dynamics, simulations based on the Landau–de Gennes nematodynamics adapted to discotic mesophases were performed, and a qualitative agreement between simulations and experiments was found. The experimentally obtained rheostructural results and the numerical simulations provide a systematic understanding of flow-microstructure relationships during transient and steady shear flow. [ABSTRACT FROM AUTHOR]

Abstract: This short communication presents a flow perturbation model for filament buckling that is typically observed under smectic A liquid crystal phase ordering from the isotropic phase. In the absence of flow, liquid crystal filaments buckle with a characteristic wave-length under the action of negative tension generated by the decrease in free energy that drives the growth process. This phenomenon is demonstrated numerically using simulations of a previously presented non-driven mesoscopic model. We then investigate how shear and extensional flow affect the filament buckling process. Using a linearized model, the filament shape dynamics are cast into a Cahn–Hilliard equation whose solutions are the buckling modes. The growth rate of the dominant mode is expressed in terms of the factorized product of the elastic contribution and the flow contribution. The flow Deborah number, D e, contributions to the growth of the dominant wave-vector are found to be , where + (−) denotes compression (extension), and where n =2 (1/2) for planar extensional (shear) flow. The model provides insights on how flow-generated stresses affect shape formation, an area of significant interest to biological form and growth. [Copyright &y& Elsevier]

This paper presents a computational study of defect nucleation associated with the kinetics of the isotropic-to-nematic phase ordering transition over heterogeneous substrates, as it occurs in new liquid crystal biosensor devices, based on the Landau-de Gennes model for rod-like thermotropic nematic liquid crystals. Two regimes are identified due to interfacial tension inequalities: (i) nematic surface film nucleation and growth normal to the heterogeneous substrate, and (ii) nematic surface droplet nucleation and growth. The former, known as wetting regime, leads to interfacial defect shedding at the moving nematic-isotropic interface. The latter droplet regime, involves a moving contact line, and exhibits two texturing mechanisms that also lead to interfacial defect shedding: (a) small and large contact angles of drops spreading over a heterogeneous substrate, and (b) small drops with large curvature growing over homogeneous patches of the substrate. The numerical results are consistent with qualitative defect nucleation models based on the kinematics of the isotropic-nematic interface and the substrate-nematic-isotropic contact line. The results extend current understanding of phase ordering over heterogeneous substrates by elucidating generic defect nucleation processes at moving interfaces and moving contact lines. [ABSTRACT FROM AUTHOR]

Abstract: De-mixing in polymer–nematic liquid crystal mixtures is simulated using a previous model that includes phase separation–phase ordering–texturing processes. It is shown that the activation of phase separation–phase ordering–texturing is associated with four internal length scales, whose relative magnitudes gives rise to three regimes of distinct morphological and textural features, as follows: (i) Phase separation and formation of few and large polymer droplets, leads to a defect lattice in the nematic matrix through the prevailing strong anchoring at the polymer–liquid crystal interface; (ii) When the number of polymer droplets increases and their size decreases, a random polymer droplet morphology emerges; due to weak anchoring conditions the nematic matrix is random and weakly oriented; (iii) When the droplet size is of the order of the nematic ordering length scale, phase ordering is frustrated and small droplet morphology emerges. This paper shows that coupling between phase separation–phase ordering–texturing processes lead to complex de-mixing morphologies with varying degrees of positional and orientational order, thus augmenting ways of controlling material architectures beyond the well-known droplet patterns in off-critical quenches of spinodal decomposition. [Copyright &y& Elsevier]

Static and dynamic linear analyses of axisymmetric capillary instabilities in textured nematic liquid crystalline fibres are performed using the equations of nemato-statics and inviscid nemato-dynamics. Three representative textures, viz. axial, onion, and radial, are analysed to show all possible effects of Frank gradient elasticity on the wavelength selection and growth rate of peristaltic modes driven by surface area reduction. It is found that Frank elasticity may tend to stabilize or destabilize the fibre, depending on the initial fibre texture. Axial textures tend to stabilize the fibre through the director splay-bend distortions driven by surface tilting. Onion textures are destabilized by decreasing azimuthal bend elastic energy caused by surface displacement. Radial textures exhibit a stabilizing tilt mechanism due to bend modes and a destabilizing displacement mechanism due to splay modes, but the former is predicted to be dominant. The static analysis provides good estimates of the instability thresholds while the transient energy balance provides information on the fastest growing modes. The static and dynamic results are compared and shown to be fully consistent. The couplings between splay and/or bend distortions, surface tilting, and surface displacement in nematic fibres are characterized and used to explain the deviations from the classical Rayleigh instability. [ABSTRACT FROM AUTHOR]

We re-examine the dynamics of uniaxial nematic liquid crystals using the polar fluid model. This modelling approach was investigated by Eringen, but his description of rotational elasticity is significantly less tractable than that proposed by Ossen and Frank who represented the microstructure by a unit vector, known as the director. In this paper we combine the Ossen–Frank elastic energy with the polar fluid model and establish the differences of the resulting polar nematic fluid model with the classical Eriksen–Leslie equations of nematodynamics. Although the polar fluid framework seems quite different from the Eriksen–Leslie model, the non-dissipative contributions in the final equations appear to be closely related, while the dissipative contributions differ slightly. [Copyright &y& Elsevier]

Mesophase pitches are multicomponent discotic nematic liquid crystals (DNLCs), whose characteristic molecular weight is intermediate between low molar mass and polymeric nematic liquid crystals. Flow modelling of these fluids is performed using a previously formulated mesoscopic viscoelastic rheological theory [J. Non-Newtonian Fluid Mech. 94 (2000) 87] that takes into account flow-induced texture transformations. A complete extra stress tensor equation is developed from first principles for liquid crystal materials under non-homogeneous arbitrary flow. This mesoscopic viscoelastic model has been adapted to describe the rheology of flow-aligning thermotropic DNLCs as models of mesophase pitches. We develop a fundamental understanding of the relations between rheology and flow of carbonaceous mesophases using theory and simulation by characterizing the steady and transient shear rheological material functions of flow-aligning DNLCs. Predictions for simple shear flow (under non-homogeneous conditions) for the apparent shear viscosity and first normal stress differences are presented. The predicted relations among rheological properties, shear-induced microstructure, processing conditions and material parameters of discotic mesophases are characterized and discussed. [Copyright &y& Elsevier]

Carbon fibres are spun from carbonaceous mesophases using standard melt spinning techniques. These melt spun carbon fibres exhibit a set of distinct cross-sectional textures. Two widely reported textures in literature are the planar radial (PR) and planar polar (PP). This work uses a mesoscopic model, based on the classical Landau-de Gennes theory of liquid crystals adapted to carbonaceous mesophases, to elucidate the principles that control the texture formation processes. The model is able to capture the microstructure and the formation of the PR and PP textures. A phase diagram for classical PR and PP textures has been constructed in terms of temperature and fibre radius, thus establishing the processing conditions and geometric factors that lead to the selection of these textures. The multipath formation process of the planar polar texture through defect splitting, direct planar polar formation, and defect annihilation has been thoroughly characterized. The results of this work provide new knowledge for optimization and control of mesophase carbon fibre textures. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of the role of orientation on the rheology of discotic nematic liquid crystals. The shear rheological properties exhibited by flow-aligning discotic mesophases are calculated by using a complete generalized nonlinear second-order tensor Landau-de Gennes model that takes into account short-range order elasticity, long-range elasticity, and viscous effects. A unified expression for the extra stress tensor is given. The second-order tensor Landau-de Gennes model was reduced to the uniaxial Leslie-Ericksen to obtain limiting rheological material functions valid at low and high shear rates. Analytical results are able to predict the material functions computed by the full Landau-de Gennes model for nonhomogeneous flow-aligning discotic nematic liquid crystals. Experimentally reported changes in the sign of the first normal stress differences with shear rate are captured by the model. A new Carreau-Yasuda liquid crystal model has been used to characterize the shear rheology for characteristic boundary conditions, and a viscosity power law exponent of 0.5 and a normal stress coefficient power law exponent of 0.44 have been obtained. [ABSTRACT FROM AUTHOR]

The Neumann and Young equations for three-phase nematic contact lines have been derived using the momentum balance equation and classical liquid crystal physics theories. The novel finding is the presence of bending forces, originating from the anchoring energy of nematic interfaces, and acting on the contact line. The classical Neumann triangle or tensile force balance becomes in the presence of a nematic phase the Neumann pentagon, involving the usual three tensile forces and two additional bending forces. The Young equation that describes the static contact angle of a fluid in contact with a rigid solid is again a tensile force balance along the solid, but for nematics it also involves an additional bending force. The effects of the bending forces on contact angles and wetting properties of nematic liquid crystals are thoroughly characterized. It is found that in terms of the spreading coefficient, bending forces enlarge the partial wetting window that exists between dewetting and spontaneous spreading. Bending forces also affect the behaviour of the contact angle, such that spreading occurs at contact angles greater than zero and dewetting at values greater than pi. Finally, the contact angle range in the partial wetting regime is always less than pi. [ABSTRACT FROM AUTHOR]

A two-dimensional model composed of a synthesis of the Leslie-Ericksen continuumtheory of nematics and the Euler-Lagrange equation for surface director motion is used to study the magnetic-induced director reorientation dynamics confined in spherical bipolar droplets with viscoelastic surfaces. The magnetic field is restricted to the droplet axis of symmetry direction. The numerical results indicate that the surface viscosity and anchoring strength must be taken into account to describe accurately director reorientation dynamics in droplets. In addition, the numerical results replicate frequently reported experimental observations on the performance of polymer dispersed liquid crystal films. These observations include the familiar exponential increase followed by saturation in light transmittance as the external applied field increases, and the exponential increase (decrease) followed by saturation as time increases in the on (off) state. Furthermore, this model is able to predict precisely the relationships between the rise and decay times and the external applied field strength, and the fact that the switching field strength is inversely proportional to droplet size. [ABSTRACT FROM AUTHOR]

Studies nematic Marangoni flow in liquid crystal interfaces using tangential stress balance equation of nematocapillarity. Effects of interfacial tension on fluid flow phenomena; Expression for the Marangoni force in a typical case that exhibits the features of the effect; Surface divergence of the surface stress tensor.

We present a theoretical analysis and linear scaling of two-wavelength surface nanostructures formed at the free surface of cholesteric liquid crystals (CLC). An anchoring model based on the capillary shape equation with the high order interaction of anisotropic interfacial tension is derived to elucidate the formation of the surface wrinkling. We showed that the main pattern-formation mechanism is originated due to the interaction between lower and higher order anchoring modes. A general phase diagram of the surface morphologies is presented in a parametric space of anchoring coefficients, and a set of anchoring modes and critical lines are defined to categorize the different types of surface patterns. To analyze the origin of surface reliefs, the correlation between surface energy and surface nano-wrinkles is investigated, and the symmetry and similarity between the energy and surface profile are identified. It is found that the surface wrinkling is driven by the director pressure and is annihilated by two induced capillary pressures. Linear approximation for the cases with sufficient small values of anchoring coefficients is used to realize the intrinsic properties and relations between the surface curvature and the capillary pressures. The contributions of capillary pressures on surface nano-wrinkling and the relations between the capillary vectors are also systematically investigated. These new findings establish a new approach for characterizing two-length scale surface wrinkling in CLCs, and can inspire the design of novel functional surface structures with the potential optical, friction, and thermal applications. [ABSTRACT FROM AUTHOR]

Biological plywoods are multifunctional fibrous composites materials, ubiquitous in nature. The chiral fibrous organization is found in chitin (insects), cellulosics (plants), and collagen I (cornea and bone of mammals) and is a solid analog of that of cholesteric liquid crystals. The surface and interfaces of plywoods are distinguished by hierarchical topographies and nanowrinkling. In this paper, we present a theory to model the emergence of these surfaces and interfaces using liquid crystal-based shape equations that directly connect material properties with geometric wrinkling. The model applies to liquid crystal precursors of the plywood solid analoges. We focus on wrinkling geometry, wrinkling mechanics, and the mechanogeometry relationships that underlie multifunctionality ubiquitous in biological surfaces. Scaling wrinkling laws that connect mechanical pressures and stresses to folding and bending are formulated and quantified. A synthesis of the connections between mechanics and geometry is achieved using the topology of stress curves and curvature of the wrinkles. Taken together the results show that anchoring is a versatile surface morphing mechanism with a rich surface bending stress field, two ingredients behind many potential multifunctionalities. [ABSTRACT FROM AUTHOR]