Six-fold director field configuration in amyloid nematic and cholesteric phases

Single-Step Control of Liquid-Liquid Crystalline Phase Separation by Depletion Gradients

Fine-tuning nucleation and growth of colloidal liquid crystalline (LC) droplets, also known as tactoids, is highly desirable in both fundamental science and technological applications. However, the tactoid structure results from the trade-off between thermodynamics and nonequilibrium kinetics effects, and controlling liquid-liquid crystalline phase separation (LLCPS) in these systems is still a work in progress. Here, a single-step strategy is introduced to obtain a rich palette of morphologies for tactoids formed via nucleation and growth within an initially isotropic phase exposed to a gradient of depletants. The simultaneous appearance is shown of rich LC structures along the depleting potential gradient, where the position of each LC structure is correlated with the magnitude of the depleting potential. Changing the size (nanoparticles) or the nature (polymers) of the depleting agent provides additional, precise control over the resulting LC structures through a size-selective mechanism, where the depletant may be found both within and outside the LC droplets. The use of depletion gradients from depletants of varying sizes and nature offers a powerful toolbox for manipulation, templating, imaging, and understanding heterogeneous colloidal LC structures.

Structural Colors from Amyloid-Based Liquid Crystals

The helical periodicity and layered structure in cholesteric liquid crystals (CLCs) may be tuned to generate structural color according to the Bragg's law of diffraction. A wide range of natural-based materials such as condensed DNA, collagen, chitin, cellulose, and chiral biopolymers exhibit cholesteric phases with left-handed helixes and ensued structural colors. Here, the possibility of using amyloid CLCs is reported to prepare films with iridescent color reflection and opposite handedness. Right-handed CLCs assembled by left-handed amyloid fibrils are dried into layered structures with variable pitch controlled by the addition of glucose. Circularly polarized light with the same handedness of amyloid CLCs helix is reflected in the Bragg regime. Varying the drying speed leads to the switching between films with a rainbow-like color gradient and large area uniform color. It is confirmed that the origin of the colors derives from the layered structures of the amyloid CLCs, given the negligeable birefringence of the films, calculated from optical rotatory dispersion. These findings provide a facile approach to constructing biosourced cholesteric materials and introduce an original class of proteinaceous materials for the generation of structural colors from right-handed circularly polarized light.

Self-assembly of cellulose nanocrystals confined to square capillaries

Biological systems exploit restricted degrees of freedom to drive self-assembly of nano- and microarchitectures. Simplified systems, such as colloidal nanoparticles that behave as lyotropic liquid crystalline mesophases in confined geometric spaces, may be used to mimic biological structures. Cellulose nanocrystals (CNCs) are colloidally stable nanoparticles that self-assemble into chiral nematic (ChN) liquid crystalline mesophases. To date, the self-assembly of ChN mesophases of CNCs has been studied under confinement conditions within curved surfaces or under drying conditions that impose curvatures that can be exploited to control ChN ordering; however, their self-assembly has not been investigated in geometries with square cross-sections under static conditions. Here, we show that because of surface anchoring on perpendicular surfaces, the ChN CNC phase is unable to bend with the 90° angle of the square capillary under increasing confinement. Instead, the ChN phase forms radial layers in the shape of concentric squircle shells. With increasing layer distance from the capillary wall, the squircles transition into concentric cylinder shells. In larger capillaries, the radial shell layers appear as a continuous spiral pattern that engulfs fragmented ChN pseudolayers, a defect to accommodate the cylindrical confinement of the mesophase. These results are useful for understanding the fundamentals of self-assembling systems and development of new technologies.

Nematic to Cholesteric Transformation in the Cellulose Nanocrystal Droplet Phase

Nucleation, growth, and transformation of chirality in nanomaterial systems is a growing research topic with broad interest in tunable and configurable chiroptical materials. Similar to other one-dimensional nanomaterials, cellulose nanocrystals (CNCs), which are nanorods of naturally abundant biopolymer cellulose, display chiral or cholesteric liquid crystal (LC) phases in the form of tactoids. However, the nucleation and growth of the cholesteric CNC tactoids to equilibrium chiral structures and their morphological transformations are yet to be critically assessed. We noticed that the onset of liquid crystal formation in CNC suspensions is characterized by the nucleation of a nematic tactoid that grows in volume and spontaneously transforms into a cholesteric tactoid. The cholesteric tactoids merge with the neighboring tactoids to form bulk cholesteric mesophases with various configurational palettes. We applied scaling laws from the energy functional theory and found suitable agreement with the morphological transformation of the tactoid droplets monitored for their fine structure and orientation by quantitative polarized light imaging.

LLPS vs. LLCPS: analogies and differences

We compare the process of Liquid-Liquid Phase Separation (LLPS) of flexible macromolecular solutions, with the Liquid-Liquid Crystalline Phase Separation (LLCPS) of semiflexible polymers and rigid filamentous colloids, which involves the formation of a liquid phase that possesses a directional alignment. Although the observed phase separation follows a similar dynamic path, namely nucleation and growth or spinodal decomposition separating two phases of dilute and concentrated compositions, the underlying physics that defines the theoretical framework of LLCPS is completely different from the one of LLPS. We review the main theories that describe the phase separation processes and relying on thermodynamics and dynamical arguments, we highlight the differences and analogies between these two phase separation phenomena, attempting to clarify the inner mechanisms that regulate those two processes. A particular focus is given to metastable phases, as these intermediate states represent a key element in understanding how phase separation works.

Evaporation-Driven Liquid-Liquid Crystalline Phase Separation in Droplets of Anisotropic Colloids

Drying a colloidal droplet involves complex physics that is often accompanied by evaporation-induced concentration gradients inside of the droplet, offering a platform for fundamental and technological opportunities, including self-assembly, thin film deposition, microfabrication, and DNA stretching. Here, we investigate the drying, liquid crystalline structures, and deposit patterns of colloidal liquid crystalline droplets undergoing liquid-liquid crystalline phase separation (LLCPS) during evaporation. We show that evaporation-induced progressive up-concentration inside the drying droplets makes it possible to cross, at different speeds, various thermodynamic stability states in solutions of amyloid fibril rigid filamentous colloids, thus allowing access to both metastable states, where phase separation occurs via nucleation and growth, as well as to unstable states, where phase separation occurs via the more elusive spinodal decomposition, leading to the formation of liquid crystalline microdroplets (or tactoids) of different shapes. We present the tactoids "phase diagram" as a function of the position within the droplet and elucidate their hydrodynamics. Furthermore, we demonstrate that the presence of the amyloid fibrils not only does not enhance the pinning behavior during droplet evaporation but also slightly suppresses it, thus minimizing the coffee-ring effect. We observed that microsize domains with cholesteric structure emerge in the drying droplet close to the droplet's initial edge, yet such domains are not connected to form a uniform cholesteric dried film. Finally, we demonstrate that a fully cholesteric dried layer can be generated from the drying droplets by regulating the kinetics of the evaporation process.

Amyloid Fibrils of Stefin B Show Anisotropic Properties

Human stefin B, a member of the cystatin family of cysteine protease inhibitors, tends to form amyloid fibrils under relatively mild conditions, which is why it is used as a model protein to study amyloid fibrillation. Here, we show for the first time that bundles of amyloid fibrils, i.e., helically twisted ribbons, formed by human stefin B exhibit birefringence. This physical property is commonly observed in amyloid fibrils when stained with Congo red. However, we show that the fibrils arrange in regular anisotropic arrays and no staining is required. They share this property with anisotropic protein crystals, structured protein arrays such as tubulin and myosin, and other anisotropic elongated materials, such as textile fibres and liquid crystals. In certain macroscopic arrangements of amyloid fibrils, not only birefringence is observed, but also enhanced emission of intrinsic fluorescence, implying a possibility to detect amyloid fibrils with no labels by using optical microscopy. In our case, no enhancement of intrinsic tyrosine fluorescence was observed at 303 nm; instead, an additional fluorescence emission peak appeared at 425 to 430 nm. We believe that both phenomena, birefringence and fluorescence emission in the deep blue, should be further explored with this and other amyloidogenic proteins. This may allow the development of label-free detection methods for amyloid fibrils of different origins.

Polymer induced liquid crystal phase behavior of cellulose nanocrystal dispersions

Cellulose nanocrystals (CNCs) are a promising bio-based material that has attracted significant attention in the fabrication of functional hybrid materials. The rod-like shape and negative surface charge of CNCs enable their rich colloidal behavior, such as a liquid crystalline phase and hydrogel formation that can be mediated by different additives. This study investigates the effect of depletion-induced attraction in the presence of non-absorbing polyethylene glycol (PEG) of different molecular weights in CNC aqueous dispersions, where the polymer molecules deplete the space around particles, apply osmotic pressure and drive the phase transition. Polarized light microscopy (PLM), rheology, small angle X-ray scattering (SAXS) and atomic force microscopy (AFM) are used to characterize the phase behavior over a time period of one month. In our results, pure CNC dispersion shows three typical liquid crystal shear rheology regimes and cholesteric self-assembly behavior. Tactoid nucleation, growth and coalescence are observed microscopically, and eventually the dispersion presents macroscopic phase separation. PEG with lower molecular weight induces weak attractive depletion forces. Tactoid growth is limited, and the whole system turns into a fully nematic phase macroscopically. With PEG of higher molecular weight, attractive depletion force becomes predominant, thus CNC self-assembly is inhibited and nematic hydrogel formation is triggered. Overall, we demonstrate that depletion induced attraction forces by the addition of PEG enable precise tuning of CNC self-assembly and phase behavior with controllable mechanical strength and optical activity. These findings deepen our fundamental understanding of cellulose nanocrystals and advance their application in colloidal systems and nanomaterials.

Shape and structural relaxation of colloidal tactoids

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.

Tactoids, consisting of micro-confined liquid crystalline colloids with self-selected shape, bear both fundamental and technological significance. The authors show that the shape relaxation of tactoids follows an exponential decay and develop a model to predict this out-of-the-equilibrium process.

Effect of electric fields on the director field and shape of nematic tactoids

Tactoids are spindle-shaped droplets of a uniaxial nematic phase suspended in the coexisting isotropic phase. They are found in dispersions of a wide variety of elongated colloidal particles, including actin, fd virus, carbon nanotubes, vanadium peroxide, and chitin nanocrystals. Recent experiments on tactoids of chitin nanocrystals in water show that electric fields can very strongly elongate tactoids even though the dielectric properties of the coexisting isotropic and nematic phases differ only subtly. We develop a model for partially bipolar tactoids, where the degree of bipolarness of the director field is free to adjust to optimize the sum of the elastic, surface, and Coulomb energies of the system. By means of a combination of a scaling analysis and a numerical study, we investigate the elongation and director field's behavior of the tactoids as a function of their size, the strength of the electric field, the surface tension, anchoring strength, the elastic constants, and the electric susceptibility anisotropy. We find that tactoids cannot elongate significantly due to an external electric field, unless the director field is bipolar or quasibipolar and somehow frozen in the field-free configuration. Presuming that this is the case, we find reasonable agreement with experimental data.

Liquid-liquid crystalline phase separation in biological filamentous colloids: nucleation, growth and order-order transitions of cholesteric tactoids

The process of liquid-liquid crystalline phase separation (LLCPS) in filamentous colloids is at the very core of multiple biological, physical and technological processes of broad significance. However, the complete theoretical understanding of the process is still missing. LLCPS involves the nucleation, growth and up-concentration of anisotropic droplets from a continuous isotropic phase, until a state of equilibrium is reached. Herein, by combining the thermodynamic extremum principle with the Onsager theory, we describe the nucleation and growth of liquid crystalline droplets, and the evolution of their size and concentration during phase separation, eventually leading to a multitude of order-order phase transitions. Furthermore, a decreasing pitch behaviour can be predicted using this combined theory during tactoid growth, already observed experimentally but not yet explained by present theories. The results of this study are compared with the experimental data of cholesteric pitch, observed in three different systems of biological chiral liquid crystals. These findings give an important framework for predicting the formation, growth and phase behaviour of biological filamentous colloids undergoing LLCPS, advancing our understanding of liquid-liquid phase separation and self-assembly mechanisms in biological systems, and provide a valuable rationale for developing nanomaterials and applications in nanotechnology.

Elastic constants of biological filamentous colloids: estimation and implications on nematic and cholesteric tactoid morphologies

Biological liquid crystals, originating from the self-assembly of biological filamentous colloids, such as cellulose and amyloid fibrils, show a complex lyotropic behaviour that is extremely difficult to predict and characterize. Here we analyse the liquid crystalline phases of amyloid fibrils, and sulfated and carboxylated cellulose nanocrystals and measure their Frank-Oseen elastic constants K1, K2 and K3 by four different approaches. The first two approaches are based on the benchmark of the predictions of: (i) a scaling form and (ii) a variational form of the Frank-Oseen energy functional with the experimental critical volumes at order-order liquid crystalline transitions of the tactoids. The third and the fourth methods imply: (iii) the direct scaling equations of elastic constants and (iv) a molecular theory predicting the elastic constants from the experimentally accessible contour length distributions of the filamentous colloids. These three biological systems exhibit diverse liquid crystalline behaviour, governed by the distinct elastic constants characterizing each colloid. Differences and similarities among the three systems are highlighted and interpreted based on the present analysis, providing a general framework to study dispersed liquid crystalline systems.

Flow-induced order-order transitions in amyloid fibril liquid crystalline tactoids

Liquid crystalline droplets, also known as tactoids, forming by nucleation and growth within the phase diagram region where isotropic and nematic phases coexist, challenge our understanding of liquid crystals under confinement due to anisotropic surface boundaries at vanishingly small interfacial tension, resulting in complex, non-spherical shapes. Little is known about their dynamical properties, since they are mostly studied under quiescent, quasi-equilibrium conditions. Here we show that different classes of amyloid based nematic and cholesteric tactoids undergo order–order transitions by flow-induced deformations of their shape. Tactoids align under extensional flow, undergoing extreme deformation into highly elongated prolate shapes, with the cholesteric pitch decreasing as an inverse power-law of the tactoids aspect ratio. Free energy functional theory and experimental measurements are combined to rationalize the critical elongation above which the director-field configuration of tactoids transforms from bipolar and uniaxial cholesteric to homogenous and to debate on the thermodynamic nature of these transitions.

Tactoids are liquid crystal droplets with nearly vanishing interfacial tension. Almohammadi et al. show using a microfluidic focusing device how to manipulate them gently enough to facilitate the study of amyloid liquid crystal phase transitions subject to non-equilibirum forcing and shape changes.

Relaxation dynamics in bio-colloidal cholesteric liquid crystals confined to cylindrical geometry

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.

Prolate and oblate chiral liquid crystal spheroids

Liquid crystals are known to exhibit intriguing textures and color patterns, with applications in display and optical technologies. This work focuses on chiral materials and examines the palette of morphologies that arises when microdroplets are deformed into nonspherical shapes in a controllable manner. Specifically, geometrical confinement and mechanical strain are used to manipulate orientational order, phase transitions, and topological defects that arise in chiral liquid crystal droplets. Inspired by processes encountered in nature, where insects and animals often rely on strain and temperature to alter the optical appearance of dispersed liquid crystalline elements, chiral droplets are dispersed in polymer films and deformation induced by uniaxial or biaxial stretching. Our measurements are interpreted by resorting to simulations of the corresponding systems, thereby providing an in-depth understanding of the morphologies that arise in these materials. The reported structures and assemblies offer potential for applications in smart coatings, smart fabrics, and wearable sensors.

Metal ions confinement defines the architecture of G-quartet, G-quadruplex fibrils and their assembly into nematic tactoids

G-quadruplex, assembled from a square array of guanine (G) molecules, is an important structure with crucial biological roles in vivo but also a versatile template for ordered functional materials. Although the understanding of G-quadruplex structures is the focus of numerous studies, little is known regarding the control of G-quartet stacking modes and the spontaneous orientation of G-quadruplex fibrils. Here, the effects of different metal ions and their concentrations on stacking modes of G-quartets are elucidated. Monovalent cations (typically K+) facilitate the formation of G-quadruplex hydrogels with both heteropolar and homopolar stacking modes, showing weak mechanical strength. In contrast, divalent metal ions (Ca2+, Sr2+, and Ba2+) at given concentrations can control G-quartet stacking modes and increase the mechanical rigidity of the resulting hydrogels through ionic bridge effects between divalent ions and borate. We show that for Ca2+ and Ba2+ at suitable concentrations, the assembly of G-quadruplexes results in the establishment of a mesoscopic chirality of the fibrils with a regular left-handed twist. Finally, we report the discovery of nematic tactoids self-assembled from G-quadruplex fibrils characterized by homeotropic fibril alignment with respect to the interface. We use the Frank-Oseen elastic energy and the Rapini-Papoular anisotropic surface energy to rationalize two different configurations of the tactoids. These results deepen our understanding of G-quadruplex structures and G-quadruplex fibrils, paving the way for their use in self-assembly and biomaterials.