Tactoids of plate-like particles: size, shape, and director field

Influence of buffer on colloidal stability, microstructure, and rheology of cellulose nanocrystals in hyaluronic acid suspensions

Hyaluronic acid (HA) is a natural biopolymer found in various human tissues, while cellulose nanocrystals (CNCs) extracted from pulp fibers have unique rheological properties and biocompatibility. Due to the superior biomechanical properties of CNC and HA, a CNC-based HA suspension may be useful in biomedical applications. While buffers are an essential constituent of any suspension used for biomedical applications to maintain the desired pH level, they can significantly affect the properties of the suspension, including colloidal stability, microstructure, and rheological characteristics. To our knowledge, this is the first study analyzing the influence of buffer solutions on the suspension characteristics of HA/CNC systems, integrating both theoretical and experimental approaches. The results revealed an alignment between predictions of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory and results from experiments characterizing a buffer-specific trend in colloidal stability. Suspensions with a higher energy barrier showed higher colloidal stability, with a lower tendency for phase separation and agglomerate formations. The microstructural analysis of CNC tactoids in the suspension revealed the existence of the hedgehog defect when dispersed in different buffer solutions. The defect is predicted to be caused by the pH-dependent protonation and deprotonation of HA. Furthermore, steady shear viscometry showed a microstructural-dependent shear viscosity trend, which, in turn, depends on the buffer solution. The study provides novel insights into the microstructural and bulk properties of HA and CNC suspensions in various buffer solutions. The results highlight the importance of solvent choice in tailoring the properties of the suspension for specific biomedical applications. These findings may be helpful in formulating HA and CNC suspensions for different biomedical applications, including drug delivery systems and viscosupplement injections.

Geometric method to determine planar anchoring strength for chromonics

Chromonic nematics are lyotropic liquid crystals that have already been known for half a century, but have only recently raised interest for their potential applications in life sciences. Determining elastic constants and anchoring strengths for rigid substrates has thus become a priority in the characterization of these materials. Here we present a method to determine chromonics' planar anchoring strength. We call it geometric as it is based on recognition and fitting of the stable equilibrium shapes of droplets surrounded by the isotropic phase in a thin cell with plates enforcing parallel alignments of the nematic director. We apply our method to shapes observed in experiments; they resemble elongated rods with round ends, which are called bâtonnets. Our theory also predicts other droplets' equilibrium shapes, which are either slender and round, called discoids, or slender and pointed, called tactoids. In particular, sufficiently small droplets are expected to display shape bistability, with two equilibrium shapes, one tactoid and one discoid, exchanging roles as stable and metastable shapes upon varying their common area.

Subtle Molecular Changes Largely Modulate Chiral Helical Assemblies of Achiral Conjugated Polymers by Tuning Solution-State Aggregation

Understanding the solution-state aggregate structure and the consequent hierarchical assembly of conjugated polymers is crucial for controlling multiscale morphologies during solid thin-film deposition and the resultant electronic properties. However, it remains challenging to comprehend detailed solution aggregate structures of conjugated polymers, let alone their chiral assembly due to the complex aggregation behavior. Herein, we present solution-state aggregate structures and their impact on hierarchical chiral helical assembly using an achiral diketopyrrolopyrrole-quaterthiophene (DPP-T4) copolymer and its two close structural analogues wherein the bithiophene is functionalized with methyl groups (DPP-T2M2) or fluorine atoms (DPP-T2F2). Combining in-depth small-angle X-ray scattering analysis with various microscopic solution imaging techniques, we find distinct aggregate in each DPP solution: (i) semicrystalline 1D fiber aggregates of DPP-T2F2 with a strongly bound internal structure, (ii) semicrystalline 1D fiber aggregates of DPP-T2M2 with a weakly bound internal structure, and (iii) highly crystalline 2D sheet aggregates of DPP-T4. These nanoscopic aggregates develop into lyotropic chiral helical liquid crystal (LC) mesophases at high solution concentrations. Intriguingly, the dimensionality of solution aggregates largely modulates hierarchical chiral helical pitches across nanoscopic to micrometer scales, with the more rigid 2D sheet aggregate of DPP-T4 creating much larger pitch length than the more flexible 1D fiber aggregates. Combining relatively small helical pitch with long-range order, the striped twist-bent mesophase of DPP-T2F2 composed of highly ordered, more rigid 1D fiber aggregate exhibits an anisotropic dissymmetry factor (g-factor) as high as 0.09. This study can be a prominent addition to our knowledge on a solution-state hierarchical assembly of conjugated polymers and, in particular, chiral helical assembly of achiral organic semiconductors that can catalyze an emerging field of chiral (opto)electronics.

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.

Dynamic light scattering analysis of size-selected graphene oxide 2D colloids fractioned via liquid crystal phase separation

Exfoliated platelets of graphene oxide (GO) can be considered as polydisperse 2D colloids that form nematic colloidal liquid crystal phases in aqueous suspension even at very low concentrations thanks to their extremely high aspect ratios. However, with the rapidly emerging scientific interest in these GO-based liquid crystals, it became clear that the precise analysis and control of the GO sheet size distribution is essential, both for their scientific understanding and for potential applications, e.g., in optoelectronic devices, nanocomposites, or catalysis. In this work, we show that the mean effective (hydrodynamic) GO platelet width can be determined from the translational diffusion coefficient with depolarized dynamic light scattering by using a model for circular, infinitely thin disks. We further studied the phase separation process of biphasic isotropic-nematic GO dispersions and developed a simple fractionation protocol, which can be used to prepare relatively monodisperse fractions of GO sheets with widths ranging from 2.0-12.4 μm. Overall, we expect that the combined application of these relatively simple fractionation and analysis methods will advance the fabrication of well-defined and size-selected GO-based systems.

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.

Nematic tactoid population

Tactoids are pointed, spindlelike droplets of nematic liquid crystal in an isotropic fluid. They have long been observed in inorganic and organic nematics, in thermotropic phases as well as lyotropic colloidal aggregates. The variational problem of determining the optimal shape of a nematic droplet is formidable and has only been attacked in selected classes of shapes and director fields. Here, by considering a special class of admissible solutions for a bipolar droplet, we study the prevalence in the population of all equilibrium shapes of each of the three that may be optimal (tactoids primarily among them). We show how the prevalence of a shape is affected by a dimensionless measure α of the drop's volume and the ratios k_{24} and k_{3} of the saddle-splay constant K_{24} and the bending constant K_{33} of the material to the splay constant K_{11}. Tactoids, in particular, prevail for α⪅16.2+0.3k_{3}-(14.9-0.1k_{3})k_{24}. Our class of shapes (and director fields) is sufficiently different from those employed so far to unveil a rather different role of K_{24}.

Spontaneous Creation of Anisotropic Polymer Crystals with Orientation-Sensitive Birefringence in Liquid Drops

It remains a grand challenge to prepare anisotropic crystal superstructures with sensitive optical properties in polymer science and materials field. This study demonstrates that semicrystalline polymers develop into anisotropic hollow spherulitic crystals spontaneously at interfaces of liquid drops. In contrast to conventional spherulites with centrosymmetric optics and grain boundaries, these anisotropic spherulitic crystals have vanished boundary defects, tunable aspect ratios, and noncentrosymmetric, orientation-sensitive birefringence. The experimental finding is elaborated in poly(l-lactic acid) crystals and is further verified in a broad class of semicrystalline polymers, irrespective of molecular chirality, chemical constitution, or interfacial modification. The facile methods and general mechanism revealed in this study shed light on developing new types of optical microdevices and synthesis of anisotropic semicrystalline particles from liquid emulsions.

Liquid crystalline tactoids: ordered structure, defective coalescence and evolution in confined geometries

Tactoids are liquid crystalline microdroplets that spontaneously nucleate from isotropic dispersions, and transform into macroscopic anisotropic phases. These intermediate structures have been found in a range of molecular, polymeric and colloidal liquid crystals. Typically only studied by polarized optical microscopy, these ordered but easily deformable microdroplets are now emerging as interesting components for structural investigations and developing new materials. In this review, we highlight the structure, property and transformation of tactoids in different compositions, but especially cellulose nanocrystals. We have selected references that illustrate the diversity and most exciting developments in tactoid research, while capturing the historical development of this field.This article is part of a discussion meeting issue 'New horizons for cellulose nanotechnology'.

Nanodrops of Discotic Liquid Crystals: A Monte Carlo Study

We study the morphologies of nematic nanodrops in a vapor of a discotic nematogen by Monte Carlo simulations. The fluid interactions are modeled by a Gay-Berne model with molecular elongations of κ = 0.3 and 0.5 and different values of the energy anisotropy parameter κ' in the range of temperature T in which the nematic coexists with a vapor phase. We considered nanodrops of N = 4000 and 32 000 particles. For κ > κ', we observe that nanodrops are quite spherical (even for N = 4000 nanodrops), with a homogeneous director field for κ = 0.3 and a bipolar nematic configuration with tangential anchoring for κ = 0.5. By increasing the value of κ', nanodrops change from spherical to lens-shaped for κ = 0.3, and for κ = 0.5, spherical nanodrops with homeotropic anchoring and a disclination ring located on its equatorial plane are observed. Although no radial nanodrops are observed, isotropic liquid nanodrops with a paranematic shell and radial texture are observed for temperatures slightly above the vapor-isotropic-nematic triple point when the vapor-isotropic interface is completely wet by the nematic phase.

Liquid crystalline behavior of graphene oxide in the formation and deformation of tough nanocomposite hydrogels

In this paper, we report the formation and transformation of graphene oxide (GO) liquid crystalline (LC) structures in the synthesis and deformation of tough GO nanocomposite hydrogels. GO aqueous dispersions form a nematic LC phase, while the addition of poly(N-vinylpyrrolidone) (PVP) and acrylamide (AAm), which are capable of forming hydrogen bonding with GO nanosheets, shifts the isotropic/nematic transition to a lower volume fraction of GO and enhances the formation of nematic droplets. During the gelation process, a phase separation of the polymers and GO nanosheets is accompanied by the directional assembly of GO nanosheets, forming large LC tactoids with a radial GO configuration. The shape of the large tactoids evolves from a sphere to a toroid as the tactoids increase in size. Interestingly, during cyclic uniaxial tensile deformation a reversible LC transition is observed in the very tough hydrogels. The isolated birefringent domains and the LC domains in the tactoids in the gels are highly oriented under a high tensile strain.

Colloidal liquid crystals in rectangular confinement: theory and experiment

We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional Oseen-Frank framework, with strong tangent anchoring, and obtain explicit analytical expressions for the director fields and energies of the 'diagonal' and 'rotated' solutions reported in the literature. These expressions separate the leading-order defect energies from the bulk distortion energy for both families of solutions. The continuum Oseen-Frank study is complemented by a microscopic mean-field approach. We numerically minimize the mean-field functional, including the effects of weak anchoring, variable order and random initial conditions. In particular, these simulations suggest the existence of higher-energy metastable states with internal defects. We compare our theoretical results to experimental director profiles, obtained using two types of filamentous virus particles, wild-type fd-virus and a modified stiffer variant (Y21M), which display nematic ordering in rectangular chambers, as found by confocal scanning laser microscopy. We combine our analytical energy expressions with experimentally recorded frequencies of the different equilibrium states to obtain explicit estimates for the extrapolation length, defined to be the ratio of the nematic elastic constant to the anchoring coefficient, of the fd-virus.

Formation of liquid crystalline phases in aqueous suspensions of platelet-like tripalmitin nanoparticles

Suspensions of platelet-like shaped tripalmitin nanocrystals stabilized by the pure lecithin DLPC and the lecithin blend S100, respectively, have been studied by small-angle x-ray scattering (SAXS) and optical observation of their birefringence at different tripalmitin (PPP) concentrations φ(PPP). It could be demonstrated that the platelets of these potential drug delivery systems start to form a liquid crystalline phase already at pharmaceutically relevant concentrations φ(PPP) of less than 10 wt. %. The details of this liquid crystalline phase are described here for the first time. As in a previous study [A. Illing et al., Pharm. Res. 21, 592 (2004)] some platelets are found to self-assemble into lamellar stacks above a critical tripalmitin concentration φ(PPP)(st) of 4 wt. %. In this study another critical concentration φ(PPP)(lc) ≈ 7 wt. % for DLPC and φ(PPP)(lc) ≈ 9 wt. % for S100 stabilized dispersions, respectively, has been observed. φ(PPP)(lc) describes the transition from a phase of randomly oriented stacked lamellae and remaining non-assembled individual platelets to a phase in which the stacks and non-assembled platelets exhibit an overall preferred orientation. A careful analysis of the experimental data indicates that for concentrations above φ(PPP)(lc) the stacked lamellae start to coalesce to rather small liquid crystalline domains of nematically ordered stacks. These liquid crystalline domains can be individually very differently oriented but possess an overall preferred orientation over macroscopic length scales which becomes successively more expressed when further increasing φ(PPP). The lower critical concentration for the formation of liquid crystalline domains of the DLPC-stabilized suspension compared to φ(PPP)(lc) of the S100-stabilized suspension can be explained by a larger aspect ratio of the corresponding tripalmitin platelets. A geometrical model based on the excluded volumes of individual platelets and stacked lamellae has been developed and successfully applied to reproduce the critical volume fractions for both, the onset of stack formation and the appearance of the liquid crystalline phase.

Morphogenesis of defects and tactoids during isotropic-nematic phase transition in self-assembled lyotropic chromonic liquid crystals

We explore the structure of nuclei and topological defects in the first-order phase transition between the nematic (N) and isotropic (I) phases in lyotropic chromonic liquid crystals (LCLCs). The LCLCs are formed by self-assembled molecular aggregates of various lengths and show a broad biphasic region. The defects emerge as a result of two mechanisms: (1) surface-anisotropy that endows each N nucleus ('tactoid') with topological defects thanks to preferential (tangential) orientation of the director at the closed I-N interface, and (2) Kibble mechanism with defects forming when differently oriented N tactoids merge with each other. Different scenarios of phase transition involve positive (N-in-I) and negative (I-in-N) tactoids with nontrivial topology of the director field and also multiply connected tactoid-in-tactoid configurations. The closed I-N interface limiting a tactoid shows a certain number of cusps; the lips of the interface on the opposite sides of the cusp make an angle different from π. The N side of each cusp contains a point defect-boojum. The number of cusps shows how many times the director becomes perpendicular to the I-N interface when one circumnavigates the closed boundary of the tactoid. We derive conservation laws that connect the number of cusps c to the topological strength m of defects in the N part of the simply connected and multiply connected tactoids. We demonstrate how the elastic anisotropy of the N phase results in non-circular shape of the disclination cores. A generalized Wulff construction is used to derive the shape of I and N tactoids as a function of I-N interfacial tension anisotropy in the approximation of frozen director field of various topological charges m. The complex shapes and structures of tactoids and topological defects demonstrate an important role of surface anisotropy in morphogenesis of phase transitions in liquid crystals.

Texture and shape of two-dimensional domains of nematic liquid crystals

We present a generalized approach to compute the shape and internal structure of two-dimensional nematic domains. By using conformal mappings, we are able to compute the director field for a given domain shape that we choose from a rich class, which includes drops with large and small aspect ratios and sharp domain tips as well as smooth ones. Results are assembled in a phase diagram that for given domain size, surface tension, anchoring strength, and elastic constant shows the transitions from a homogeneous to a bipolar director field, from circular to elongated droplets, and from sharp to smooth domain tips. We find a previously unaccounted for regime, where the drop is nearly circular, the director field bipolar, and the tip rounded. We also find that bicircular director fields, with foci that lie outside the domain, provide a remarkably accurate description of the optimal director field for a large range of values of the various shape parameters.

Emulsion of aqueous-based nonspherical droplets in aqueous solutions by single-chain surfactants: templated assembly by nonamphiphilic lyotropic liquid crystals in water

Single-chain surfactants usually emulsify and stabilize oily substances into droplets in an aqueous solution. Here, we report a coassembly system, in which single types of anionic or non-ionic surfactants emulsify a class of water-soluble nonamphiphilic organic salts with fused aromatic rings in aqueous solutions. The nonamphiphilic organic salts are in turn promoted to form droplets of water-based liquid crystals (chromonic liquid crystals) encapsulated by single-chain surfactants. The droplets, stabilized against coalescence by encapsulated in a layer (or layers) of single chain surfactants, are of both nonspherical tactoid (elongated ellipsoid with pointy ends) and spherical shapes. The tactoids have an average long axis of ∼9 μm and a short axis of ∼3.5 μm with the liquid crystal aligning parallel to the droplet surface. The spherical droplets are 5-10 μm in diameter and have the liquid crystal aligning perpendicular to the droplet surface and a point defect in the center. Cationic and zwitterionic surfactants studied in this work did not promote the organic salt to form droplets. These results illustrate the complex interplay of self-association and thermodynamic incompatibility of molecules in water, which can cause new assembly behavior, including potential formation of vesicles or other assemblies, from surfactants that usually form only micelles. These unprecedented tactoidal shaped droplets also provide potential for the fabrication of new soft organic microcapsules.

Self-assembly of 2D membranes from mixtures of hard rods and depleting polymers()

We combine simulations and experiments to elucidate the molecular forces leading to the assembly of two dimensional membrane-like structures composed of a one rod-length thick monolayer of aligned rods from an immiscible suspension of hard rods and depleting polymers. Computer simulations predict that monolayer membranes are thermodynamically stable above a critical rod aspect ratio and below a critical depletion interaction length scale. Outside of these conditions alternative structures such as stacked smectic columns or nematic droplets are thermodynamically stable. These predictions are confirmed by subsequent experiments using a model system of virus rod-like molecules and non-adsorbing polymer. Our work demonstrates that collective molecular protrusion fluctuations alone are sufficient to stabilize membranes composed of homogenous rods with simple excluded volume interactions.

Theoretical calculation of the phase behavior of colloidal membranes

We formulate a density functional theory that describes the phase behavior of hard rods and depleting polymers, as realized in recent experiments on suspensions of fd virus and nonadsorbing polymer. The theory predicts the relative stability of nematic droplets, stacked smectic columns, and a recently discovered phase of isolated monolayers of rods, or colloidal membranes. We find that a minimum rod aspect ratio is required for stability of colloidal membranes and that collective protrusion undulations are the dominant effect that stabilizes this phase. The theoretical predictions are shown to be qualitatively consistent with experimental and computational results.

Magnetic-field-induced nematic-nematic phase separation and droplet formation in colloidal goethite

We demonstrate the suitability of polarization microscopy to study the recently discovered (parallel) nematic-(perpendicular) nematic phase separation. This novel type of phase transition is induced by applying an external magnetic field to a nematic liquid crystal of boardlike colloidal goethite and is due to an interplay between the intrinsic magnetic properties of goethite and the collective effect of liquid crystal formation. It is shown that the intense ochre colour of goethite does not preclude the use of polarization microscopy and interference colours, and that dichroism can give valuable qualitative information on the nature of the phases, their anchoring and their sedimentation and order parameter profiles. We also apply these techniques to study 'nematic-nematic tactoids': nematic droplets sedimenting within a nematic medium with mutually perpendicular orientations.

Chiral symmetry breaking by spatial confinement in tactoidal droplets of lyotropic chromonic liquid crystals

In many colloidal systems, an orientationally ordered nematic (N) phase emerges from the isotropic (I) melt in the form of spindle-like birefringent tactoids. In cases studied so far, the tactoids always reveal a mirror-symmetric nonchiral structure, sometimes even when the building units are chiral. We report on chiral symmetry breaking in the nematic tactoids formed in molecularly nonchiral polymer-crowded aqueous solutions of low-molecular weight disodium cromoglycate. The parity is broken by twisted packing of self-assembled molecular aggregates within the tactoids as manifested by the observed optical activity. Fluorescent confocal microscopy reveals that the chiral N tactoids are located at the boundaries of cells. We explain the chirality induction as a replacement of energetically costly splay packing of the aggregates within the curved bipolar tactoidal shape with twisted packing. The effect represents a simple pathway of macroscopic chirality induction in an organic system with no molecular chirality, as the only requirements are orientational order and curved shape of confinement.