Tracking three-phase coexistences in binary mixtures of hard plates and spheres

Multiphase Coexistence in Binary Hard Colloidal Mixtures: Predictions from a Simple Algebraic Theory

A general theoretical framework is proposed to quantify the thermodynamic properties of multicomponent hard colloidal mixtures. This framework is used to predict the phase behavior of mixtures of rods with spheres and rods with plates taking into account (liquid) crystal phases of both components. We demonstrate a rich and complex range of phase behaviors featuring a large variety of different multiphase coexistence regions, including two five-phase coexistence regions for hard rod/sphere mixtures, and even a six-phase equilibrium for hard rod/plate dispersions. The various multiphase coexistences featured in a particular mixture are in line with a recently proposed generalized phase rule and can be tuned through subtle variations of the particle shape and size ratio. Our approach qualitatively accounts for certain multiphase equilibria observed in rod/plate mixtures of clay colloids and will be a useful guide in tuning the phase behavior of shape-disperse mixtures in general.

Enhancement in the diffusivity of Brownian spheroids in the presence of spheres

In the present paper, we have extended the simulation technique Brownian cluster dynamics (BCD) to analyze the dynamics of the binary mixture of hard ellipsoids and spheres. The shape dependent diffusional properties have been incorporated into BCD using Perrin's factor and compared with analytical results of a one-component ellipsoidal system. We have investigated pathways to enhance the diffusivity of spheroids in the binary mixture by manipulating the phase behavior of the system through varying the fraction of spheres in the binary mixture. We show that at low volume fraction the spherical particles have a higher diffusion coefficient than the ellipsoids due to the higher friction coefficient. However, at a higher volume fraction, we show that the diffusion coefficient of the ellipsoids increases irrespective of the aspect ratio due to the anisotropic shape.

Second-virial theory for shape-persistent living polymers templated by disks

Living polymers composed of noncovalently bonded building blocks with weak backbone flexibility may self-assemble into thermoresponsive lyotropic liquid crystals. We demonstrate that the reversible polymer assembly and phase behavior can be controlled by the addition of (nonadsorbing) rigid colloidal disks which act as an entropic reorienting "template" onto the supramolecular polymers. Using a particle-based second-virial theory that correlates the various entropies associated with the polymers and disks, we demonstrate that small fractions of discotic additives promote the formation of a polymer nematic phase. At larger disk concentrations, however, the phase is disrupted by collective disk alignment in favor of a discotic nematic fluid in which the polymers are dispersed antinematically. We show that the antinematic arrangement of the polymers generates a nonexponential molecular-weight distribution and stimulates the formation of oligomeric species. At sufficient concentrations the disks facilitate a liquid-liquid phase separation which can be brought into simultaneously coexistence with the two fractionated nematic phases, providing evidence for a four-fluid coexistence in reversible shape-dissimilar hard-core mixtures without cohesive interparticle forces. We stipulate the conditions under which such a phenomenon could be found in experiment.

Electrically Induced Alignment of Semiconductor Nanosheets in Niobate-Clay Binary Nanosheet Colloids toward Significantly Enhanced Photocatalysis

Aqueous binary colloids of niobate and clay nanosheets, prepared by the exfoliation of their mother layered crystals, are unique colloidal systems characterized by the separation of niobate and clay nanosheet phases, where niobate nanosheets form liquid crystalline domains with the size of several tens of micrometers among isotropically dispersed clay nanosheets. The binary colloids show unusual photocatalytic reactions because of the spatial separation of photocatalytically active niobate and photochemically inert clay nanosheets. The present study shows structural conversion of the binary colloids with an external electric field, resulting in the onsite alignment of colloidal nanosheets to improve the photocatalytic performance of the system. The colloidal structure is reshaped by the growth of liquid crystalline domains of photocatalytic niobate nanosheets and by their electric alignment. Niobate nanosheets are assembled by the domain growth process and then aligned by AC voltage, although clay nanosheets do not respond to the electric field. Photocatalytic decomposition of the cationic rhodamine 6G dye, which is selectively adsorbed on clay nanosheets, is examined for the niobate-clay binary nanosheet colloids with or without domain growth and electric field. The fastest decomposition is observed for the electrically aligned colloid without the domain growth, whereas the sample with the domain growth and without the electric alignment shows the slowest decomposition. The results demonstrate the improvement of the photocatalytic performance by changing the colloidal structure, even though the sample composition is the same.

From n-layer planar ordering to the monolayer homeotropic structure of confined hard rods: The effect of shape anisotropy and wall-to-wall separation

Using the Parsons-Lee theory, we examined the effect of shape anisotropy and the wall-to-wall separation (H) on the phase behavior of the hard parallelepiped rods with dimensions L, D, and D (L>D) in such narrow slitlike pores which only one homeotropic layer can form. The phase structures, including biaxiality, planar nematic layering transition as well as planar to homeotropic, were studied for some separations in the range 2.5D≤H≤10.0D for H-D≤L<H.

Self-assembly and entropic effects in pear-shaped colloid systems. II. Depletion attraction of pear-shaped particles in a hard-sphere solvent

We consider depletion effects of a pear-shaped colloidal particle in a hard-sphere solvent for two different model realizations of the pear-shaped colloidal particle. The two models are the pear hard Gaussian overlap (PHGO) particles and the hard pears of revolution (HPR). The motivation for this study is to provide a microscopic understanding for the substantially different mesoscopic self-assembly properties of these pear-shaped colloids, in dense suspensions, that have been reported in the previous studies. This is done by determining their differing depletion attractions via Monte Carlo simulations of PHGO and HPR particles in a pool of hard spheres and comparing them with excluded volume calculations of numerically obtained ideal configurations on the microscopic level. While the HPR model behaves as predicted by the analysis of excluded volumes, the PHGO model showcases a preference for splay between neighboring particles, which can be attributed to the special non-additive characteristics of the PHGO contact function. Lastly, we propose a potentially experimentally realizable pear-shaped particle model, the non-additive hard pear of revolution model, which is based on the HPR model but also features non-additive traits similar to those of PHGO particles to mimic their depletion behavior.

Self-assembly and entropic effects in pear-shaped colloid systems. I. Shape sensitivity of bilayer phases in colloidal pear-shaped particle systems

The role of particle shape in self-assembly processes is a double-edged sword. On the one hand, particle shape and particle elongation are often considered the most fundamental determinants of soft matter structure formation. On the other hand, structure formation is often highly sensitive to details of shape. Here, we address the question of particle shape sensitivity for the self-assembly of hard pear-shaped particles by studying two models for this system: (a) the pear hard Gaussian overlap (PHGO) and (b) the hard pears of revolution (HPR) model. Hard pear-shaped particles, given by the PHGO model, are known to form a bicontinuous gyroid phase spontaneously. However, this model does not replicate an additive object perfectly and, hence, varies slightly in shape from a "true" pear-shape. Therefore, we investigate in the first part of this series the stability of the gyroid phase in pear-shaped particle systems. We show, based on the HPR phase diagram, that the gyroid phase does not form in pears with such a "true" hard pear-shaped potential. Moreover, we acquire first indications from the HPR and PHGO pair-correlation functions that the formation of the gyroid is probably attributed to the small non-additive properties of the PHGO potential.

Mesoscopic Architectures Made of Electrically Charged Binary Colloidal Nanosheets in Aqueous System

Inorganic layered materials can be converted to colloidal liquid crystals through exfoliation into inorganic nanosheets, and binary nanosheet colloids exhibit rich phase behavior characterized by multiphase coexistence. In particular, niobate-clay binary nanosheet colloids are characterized by phase separation at a mesoscopic (∼several tens of micrometers) scale whereas they are apparently homogeneous at a macroscopic scale. Although the mesoscopic structure of the niobate-clay binary colloid is advantageous to realize unusual photochemical functions, the structure itself has not been clearly demonstrated in real space. The present study investigated the structure of niobate-clay binary nanosheet colloids in detail. Four clay nanosheets (hectorite, saponite, fluorohectorite, and tetrasilisic mica) with different lateral sizes were compared. Small-angle X-ray scattering (SAXS) indicated lamellar ordering of niobate nanosheets in the binary colloid. The basal spacing of the lamellar phase was reduced by increasing the concentration of clay nanosheets, indicating the compression of the liquid crystalline niobate phase by the isotropic clay phase. Scattering and fluorescence microscope observations using confocal laser scanning microscopy (CLSM) demonstrated the phase separation of niobate and clay nanosheets in real space. Niobate nanosheets assembled into domains of several tens of micrometers whereas clay nanosheets were located in voids between the niobate domains. The results clearly confirmed the spatial separation of two nanosheets and the phase separation at a mesoscopic scale. Distribution of clay nanosheets is dependent on the employed clay nanosheets; the nanosheets with large lateral length are more localized or assembled. This is in harmony with larger basal spacings of niobate lamellar phase for large clay particles. Although three-dimensional compression of the niobate phase by the coexisting clay phase was observed at low clay concentrations, the basal spacing of niobate phase was almost constant irrespective of niobate concentrations at high clay concentrations, which was ascribed to competition of compression by clay phase and restoring of the niobate phase.

Defect-mediated colloidal interactions in a nematic-phase discotic solvent

Interactions between colloidal inclusions dispersed in a nematic discotic liquid-crystalline solvent were investigated for different solute-solvent coupling conditions. The solvent was treated at the level of Gay-Berne discogens. Colloidal inclusions were coupled to the solvent with a generalized sphere-ellipsoid interaction potential. Energy strengths were varied to promote either homeotropic or planar mesogenic anchoring. Colloid-colloid interactions were modeled using a soft, excluded-volume contribution. Single-colloid and colloid-pair samples were evolved with Molecular Dynamics simulations. Equilibrium trajectories were used to characterize structural and dynamical properties of topological defects arising in the mesomorphic phase due to colloidal inclusions. Boojums were observed with planar anchoring, whereas Saturn rings were obtained with homeotropic anchoring. The manner in which these topological defects drive colloidal interactions was assessed through a free energy analysis, taking into account the relative orientation between a colloidal dyad and the nematic-field director. The dynamical behavior of defects was qualitatively surveyed from equilibrium trajectories borne from computer simulations.

Entropic patchiness drives multi-phase coexistence in discotic colloid-depletant mixtures

Entropy-driven equilibrium phase behaviour of hard particle dispersions can be understood from excluded volume arguments only. While monodisperse hard spheres only exhibit a fluid-solid phase transition, anisotropic hard particles such as rods, discs, cuboids or boards exhibit various multi-phase equilibria. Ordering of such anisotropic particles increases the free volume entropy by reducing the excluded volume between them. The addition of depletants gives rise to an entropic patchiness represented by orientation-dependent attractions resulting in non-trivial phase behaviour. We show that free volume theory is a simple, generic and tractable framework that enables to incorporate these effects and rationalise various experimental findings. Plate-shaped particles constitute the main building blocks of clays, asphaltenes and chromonic liquid crystals that find widespread use in the food, cosmetics and oil industry. We demonstrate that mixtures of platelets and ideal depletants exhibit a strikingly rich phase behaviour containing several types of three-phase coexistence areas and even a quadruple region with four coexisting phases.