Liquid Crystal Phase Transitions in Systems of Colloidal Platelets with Bimodal Shape Distribution

Phase Behavior and Rheological Properties of Size-Fractionated MXene (Ti3C2Tx) Dispersions

Understanding the dispersion behavior of MXenes is interesting from a fundamental colloid science perspective and critical to enabling the fluid-phase manufacturing of MXene devices with controlled microstructures and properties. However, the polydispersity, irregular shape, and charged surfaces of MXenes result in a complex phase behavior that is difficult to predict through theoretical calculations. As two-dimensional (2D) nanomaterials, MXenes can form lyotropic liquid crystal phases, gels, and aggregates. This work aims to elucidate the effects of MXene (Ti3C2Tx) sheet size on their phase behavior and associated rheological properties. Aqueous dispersions of large sheets with an average lateral dimension of 3.0 μm, small sheets with an average lateral dimension of 0.3 μm, and a bimodal mixture of the two sizes were investigated by using cross-polarized optical microscopy and rheology. At low concentrations, the large MXene dispersions exhibited lyotropic liquid crystal behavior and extended aligned textures, but increasing concentration resulted in the formation of dense flocs. Dispersions of small sheets formed small birefringent domains with increasing concentration but lacked long-range ordering. A bimodal mixture of these sizes enabled the formation of liquid crystalline phases with extended aligned textures with less floc formation. These results provide insights into using polydispersity to tune dispersion microstructure and rheological properties that can be applied to designing dispersions for fluid-phase manufacturing methods, such as direct ink writing.

Cellulose Nanocrystal Aqueous Colloidal Suspensions: Evidence of Density Inversion at the Isotropic-Liquid Crystal Phase Transition

The colloidal suspensions of aqueous cellulose nanocrystals (CNCs) are known to form liquid crystalline (LC) systems above certain critical concentrations. From an isotropic phase, tactoid formation, growth, and sedimentation have been determined as the genesis of a high-density cholesteric phase, which, after drying, originates solid iridescent films. Herein, the coexistence of a liquid crystal upper phase and an isotropic bottom phase in CNC aqueous suspensions at the isotropic-nematic phase separation is reported. Furthermore, isotropic spindle-like domains are observed in the low-density LC phase and high-density LC phases are also prepared. The CNCs isolated from the low- and high-density LC phases are found to have similar average lengths, diameters, and surface charges. The existence of an LC low-density phase is explained by the presence of air dissolved in the water present within the CNCs. The air dissolves out when the water solidifies into ice and remains within the CNCs. The self-adjustment of the cellulose chain conformation enables the entrapment of air within the CNCs and CNC buoyancy in aqueous suspensions.

Structure and rheology of soft hybrid systems of magnetic nanoparticles in liquid-crystalline matrices: results from particle-resolved computer simulations

Hybrid mixtures composed of magnetic nanoparticles (MNP) in liquid crystalline (LC) matrices are a fascinating class of soft materials with intriguing physical properties and a wide range of potential applications, e.g., as stimuli-responsive and adaptive materials. Already in the absence of an external stimulus, these systems can display various types of orientationally disordered and ordered phases, which are enriched by self-assembled structures formed by the MNPs. In the presence of external fields, one typically observes highly nonlinear macroscopic behavior. However, an understanding of the structure and dynamics of such systems on the particle level has, so far, remained elusive. In the present paper we review recent computer simulation studies targeting the structure, equilibrium dynamics and rheology of LC-MNP systems, in which the particle sizes of the two components are comparable. As a numerically tractable model system we consider mixtures of soft spherical or elongated particles with a permanent magnetic dipole moment and ellipsoidal non-magnetic particles interacting via a Gay-Berne potential. We address, first, equilibrium aspects such as structural organization and self-assembly (cluster formation) of the MNPs in dependence of the orientational state of the matrix, the role of the size ratio, the impact of an external magnetic field, and the translational and orientational diffusion of the two components. Second, we discuss the non-equilibrium dynamics of LC-MNP mixtures under planar shear flow, considering both, spherical and non-spherical MNPs. Our results contribute to a detailed understanding of these intriguing hybrid materials, and they may serve as a guide for future experiments.

Role of length polydispersity in the phase behavior of freely rotating hard-rectangle fluids

We use the density-functional formalism, in particular the scaled-particle theory, applied to a length-polydisperse hard-rectangle fluid to study its phase behavior as a function of the mean particle aspect ratio κ_{0} and polydispersity Δ_{0}. The numerical solutions of the coexistence equations are calculated by transforming the original problem with infinite degrees of freedoms to a finite set of equations for the amplitudes of the Fourier expansion of the moments of the density profiles. We divide the study into two parts. The first one is devoted to the calculation of the phase diagrams in the packing fraction η_{0}-κ_{0} plane for a fixed Δ_{0} and selecting parent distribution functions with exponential (the Schulz distribution) or Gaussian decays. In the second part we study the phase behavior in the η_{0}-Δ_{0} plane for fixed κ_{0} while Δ_{0} is changed. We characterize in detail the orientational ordering of particles and the fractionation of different species between the coexisting phases. Also we study the character (second vs first order) of the isotropic-nematic phase transition as a function of polydispersity. We particularly focus on the stability of the tetratic phase as a function of κ_{0} and Δ_{0}. The isotropic-nematic transition becomes strongly of first order when polydispersity is increased: The coexistence gap widens and the location of the tricritical point moves to higher values of κ_{0} while the tetratic phase is slightly destabilized with respect to the nematic one. The results obtained here can be tested in experiments on shaken monolayers of granular rods.

Polydispersity reduction of colloidal plates via size fractionation of the isotropic-nematic phase transition

Controlling the size polydispersity of colloidal particles is important for their phase transitions, resulting structures, and properties. In this study, a fractionation method was established to control the polydispersity of colloidal plates based on the isotropic-nematic (I-N) phase transition. The size ratio of nanoplates between the N phase and the I phase (D_N/D_I) was relatively large, whereas the size polydispersities in both the N phase and the I phase were smaller than that of the original sample before fractionation. The degree of fractionation was dependent on the time since the phase transition began and the polydispersity of the original sample. A long time resulted in a small D_N/D_I and a small degree of polydispersity reduction. The experimental data confirmed a quadratic scaling of D_N/D_I with polydispersity that was predicted by simulations. Large to small particles were segregated sequentially by sedimentation because of self-assembly and gravity. The polydispersity reduction based on the I-N phase transition can be utilized to select nanoplates with a certain size with improved size monodispersity.

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.

Multiphase coexistence and destabilization of liquid crystalline binary nanosheet colloids of titanate and clay

A plate-plate binary colloid system of photocatalytically active titanate and inert clay nanosheets shows macroscopically separated multiphase coexistence. Two liquid crystalline phases and one isotropic phase coexist at high titanate and low clay concentrations whereas the colloids are destabilized at high clay concentrations.

Fast synthesis and size control of gibbsite nanoplatelets, their pseudomorphic dehydroxylation, and efficient dye adsorption

In this paper, a simple and fast (4 days) procedure to synthesize colloidal gibbsite nanoplatelets (NPTs) from a single aluminum alkoxide (aluminum sec-butoxide) as precursor is presented. The introduction of a preheating step accelerated the precursor's hydrolysis/peptization and considerably shortened the overall reaction time while the acid concentration affected the uniformity of the platelets shape. This procedure was successfully exploited to rapidly produce gibbsite platelets of controllable sizes by combination with the seeded growth method. The use of a single alkoxide precursor induced high growth rates and allowed a fast control of the platelets size over a wide range (nano- to microscale after only three growth steps). No signs for size limitation were observed. The dehydroxylation sequence of the as-synthesized NPTs was systematically investigated. Thermally stable chi-alumina NPTs, pseudomorphs of the parent gibbsite platelets, with a micro/mesoporous structure and high specific surface area, were obtained. The synthesized gibbsite NPTs can efficiently adsorb Methyl Orange dye in wastewater treatment with removal efficiency up to 94.8%.

Interactions between spheroidal colloidal particles

Using Derjaguin's approximation, we have evaluated the interaction energy associated with van der Waals, electrostatic, depletion, and capillary forces between colloidal spheroids. If the interaction range between spheroids is distinctly smaller than the lengths of their principal axes, then simple pair potentials that depend on particle distance and orientation can be derived. Attractive interactions between adjacent spheroids favor their parallel alignment. Parallel spheroids can be arranged into a variety of densely packed configurations. All of these configurations turn out to have the same lattice energy. We discuss the implications of this degeneracy with respect to the stability of photonic crystals consisting of spheroids.

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

We studied, by means of polarized light microscopy, the shape and director field of nematic tactoids as a function of their size in dispersions of colloidal gibbsite platelets in polar and apolar solvents. Because of the homeotropic anchoring of the platelets to the interface, we found large tactoids to be spherical with a radial director field, whereas small tactoids turn out to have an oblate shape and a homogeneous director field, in accordance with theoretical predictions. The transition from a radial to a homogeneous director field seems to proceed via two different routes depending in our case on the solvent. In one route, the what presumably is a hedgehog point defect in the center of the tactoid transforms into a ring defect with a radius that presumably goes to infinity with decreasing drop size. In the other route, the hedgehog defect is displaced from the center to the edge of the tactoid, where it becomes virtual again going to infinity with decreasing drop size. Furthermore, quantitative analysis of the tactoid properties provides us with useful information on the ratio of the splay elastic constant and the anchoring strength and the ratio of the anchoring strength and the surface tension.

Experimental observation of fractionated crystallization in polydisperse platelike colloids

We have discovered that the long-term aging of the hexagonal columnar liquid-crystal phase of polydisperse gibbsite platelets leads to fractionated crystallization, that is, to the formation of coexisting columnar crystals with different periods. This process was revealed by microradian X-ray diffraction demonstrating the splitting of the Bragg intercolumnar reflections into sequences of sharper reflections. The fractionated crystallization was observed in a number of samples of sterically stabilized as well as charge-stabilized polydisperse gibbsite platelets.

Bulk phase behavior of binary hard platelet mixtures from density functional theory

We investigate isotropic-isotropic, isotropic-nematic, and nematic-nematic phase coexistence in binary mixtures of circular platelets with vanishing thickness, continuous rotational degrees of freedom, and radial size ratios lambda up to 5. A fundamental measure density functional theory, previously used for the one-component model, is presented and results are compared against those from Onsager theory as a benchmark. For lambda<or=1.7 the system displays isotropic-nematic phase coexistence with a widening of the biphasic region for increasing values of lambda . For size ratios lambda>or=2, we find that demixing into two nematic states becomes stable and an isotropic-nematic-nematic triple point can occur. Fundamental measure theory gives a smaller isotropic-nematic biphasic region than Onsager theory and locates the transition at lower densities. Furthermore, nematic-nematic demixing occurs over a larger range of compositions at a given value of lambda than found in Onsager theory. Both theories predict the same topologies of the phase diagrams. The partial nematic order parameters vary strongly with composition and indicate that the larger particles are more strongly ordered than the smaller particles.