Bulk fluid phase behaviour of colloidal platelet-sphere and platelet-polymer mixtures

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.

Orientational ordering and layering of hard plates in narrow slitlike pores

We examine the ordering behavior of hard platelike particles in a very narrow, slitlike pore using the Parsons-Lee density functional theory and the restricted orientation approximation. We observe that the plates are orientationally ordered and align perpendicularly (face-on) to the walls at low densities, a first-order layering transition occurs between uniaxial nematic structures having n and n+1 layers at intermediate densities, and even a phase transition between a monolayer with parallel (edge-on) orientational order and n layers with a perpendicular one can be detected at high densities. In addition to this, the edge-on monolayer is usually biaxial nematic, and a uniaxial-biaxial nematic phase transition can be also seen at very high densities.

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.

Stratification in the dynamics of sedimenting colloidal platelet-sphere mixtures

The dynamics of sedimentation in a binary mixture of colloidal platelets-spheres is studied theoretically using the minimal energy model. Revisiting a sedimenting mixture of platelets, we find that nematic phase behaviors are formed, coupled with certain stratification structures in the mixed sediments, which has never been discussed before. Non-equilibrium sedimentation-diffusion equations involving excluded volume interactions between the colloids have been developed to show the occurrence of the stratified structures in the mixed platelet-sphere sediments. The model shows clearly how the nematic configuration occurs corresponding to the stratifications (the peak-like concentration profiles) over time. Both initial sphere concentration and size ratio are found to have great effects on these two coupled structural configurations, which has been illustrated in two state diagrams in detail. It is found that the stratification structure of sphere-on-top corresponds to the nematic bottom phase configuration for a small size ratio; meanwhile, the platelet-on-top structure occurs corresponding to the floating nematic phase configuration for a large size ratio. Interestingly, we can specify a moderate range of size ratio in which the mixture displays only the nematic phase configuration (either the nematic bottom phase or the floating nematic phase depending on the sphere loadings), while the mixed sediments are unstratified as a bulk.

Hybrid fillers of hexagonal and cubic boron nitride in epoxy composites for thermal management applications

In this study, the synergistic effect of hexagonal boron nitride (h-BN) with cubic boron nitride (c-BN) on enhancement of thermal conductivity of epoxy resin composites has been reported. The measured thermal conductivities of the epoxy composites filled with h-BN, c-BN and hybrid h-BN/c-BN compared with the theoretical predications of Agari's model strongly suggest that the combination of h-BN platelets and c-BN spherical particles with different sizes is beneficial to enhance the thermal conductivity of the polymer composites by preferentially forming 3D thermally conductive networks at low loading content. Furthermore, the small addition of gold nanoparticles enhances the thermal conductivity from 166% to 237%. The potential application of these composites for thermal management has been demonstrated by the surface temperature variations in real time during heating. The results demonstrate that such thermally conductive but electrically insulating polymer-based composites are highly desirable for thermal management applications.

The synergistic effect of h-BN/c-BN/EP on the enhancement of thermal conductivity of polymeric composites has been demonstrated.

Staged phase separation in the I-I-N tri-phase region of platelet-sphere mixtures

Mixtures of colloids with different sizes or shapes are ubiquitous in nature and extensively applied in industries. Phase transition pathways and kinetics in this model system should be investigated because of the difficulty in observing tri-phase coexistence in colloidal platelet-sphere mixtures. Similar to the polymer-sphere mixtures, the phase transition pathway has three main categories. Analytical results show a staged phase transition process in which the mixture first separates into one or two metastable phases, then further separates, and subsequently reaches tri-phase equilibrium. Unique to our system, and different from the gas-liquid-crystal coexistence in colloid-polymer mixtures, the platelet-sphere mixture reached a gas-liquid-liquid crystal (nematic) coexistence. Thus, the different phases are easy to distinguish using the birefringence of the liquid crystals. In addition, the volume fraction of the liquid crystal formation in the ZrP platelet suspensions is much lower than for the crystal formation in hard spheres.

Induced stabilization of columnar phases in binary mixtures of discotic liquid crystals

Three discotic liquid-crystalline binary mixtures, characterized by their extent of bidispersity in molecular thickness, were investigated with molecular dynamics simulations. Each equimolar mixture contained A-type (thin) and B-type (thick) discogens. The temperature-dependence of the orientational order parameter reveals that A-type liquid samples produce ordered phases more readily, with the (hexagonal) columnar phase being the most structured variant. Moderately and strongly bidisperse mixtures produce globally-segregated samples for temperatures corresponding to ordered phases; the weakly bidisperse mixture displays microheterogeneities. Ordered phases in the B-type liquid are induced partially by the presence of the A-type fluid. In the moderately bidisperse mixture, order is induced through orientational frustration: a mixed prenematic-like phase precedes global segregation to yield nematic and columnar mesophases upon further cooling. In the strongly bidisperse mixture, order is induced less efficiently through a paranematic-like mechanism: a highly-ordered A-type fluid imparts order to B-type discogens found at the interface of a fully-segregated sample. This ordering effect permeates into the disordered B-type domain until nematic and columnar phases emerge upon further cooling. At sufficiently low temperatures, all samples investigated exhibit the (hexagonal) columnar mesophase.

Observation of isotropic-isotropic demixing in colloidal platelet-sphere mixtures

Mixtures of colloids with different sizes and shapes are ubiquitous in nature and industry. The possible existence of isotropic-isotropic (I1-I2) demixing of platelets and spheres remains an open question. Here we present direct experimental evidence of I1-I2 demixing using platelets with a very small thickness-to-diameter ratio mixed with silica spheres at the size ratio q = R(sphere)/R(disk) = 0.0901 ± 0.0004. The platelets cause the isotropic-to-nematic phase transition at a very low volume fraction because of their highly anisometric shape. The presence of silica spheres in the suspension accelerates the phase transition and packs the nematic phase more densely via depletion interaction. Increasing the sphere volume fraction to 0.0014, a tri-phase region emerges. This direct observation of I1-I2 demixing seems to validate the free-volume scaled particle theory and indicates the need for refinement of the fundamental measure density functional theory.

Hard-body models of bulk liquid crystals

Hard models for particle interactions have played a crucial role in the understanding of the structure of condensed matter. In particular, they help to explain the formation of oriented phases in liquids made of anisotropic molecules or colloidal particles and continue to be of great interest in the formulation of theories for liquids in bulk, near interfaces and in biophysical environments. Hard models of anisotropic particles give rise to complex phase diagrams, including uniaxial and biaxial nematic phases, discotic phases and spatially ordered phases such as smectic, columnar or crystal. Also, their mixtures exhibit additional interesting behaviours where demixing competes with orientational order. Here we review the different models of hard particles used in the theory of bulk anisotropic liquids, leaving aside interfacial properties and discuss the associated theoretical approaches and computer simulations, focusing on applications in equilibrium situations. The latter include one-component bulk fluids, mixtures and polydisperse fluids, both in two and three dimensions, and emphasis is put on liquid-crystal phase transitions and complex phase behaviour in general.

Floating nematic phase in colloidal platelet-sphere mixtures

The phase behaviour of colloidal dispersions is interesting for fundamental reasons and for technological applications such as photonic crystals and electronic paper. Sedimentation, which in everyday life is relevant from blood analysis to the shelf life of paint, is a means to determine phase boundaries by observing distinct layers in samples that are in sedimentation-diffusion equilibrium. However, disentangling the effects due to interparticle interactions, which generate the bulk phase diagram, from those due to gravity is a complex task. Here we show that a line in the space of chemical potentials µ(i), where i labels the species, represents a sedimented sample and that each crossing of this sedimentation path with a binodal generates an interface under gravity. Complex phase stacks can result, such as the sandwich of a floating nematic layer between top and bottom isotropic phases that we observed in a mixture of silica spheres and gibbsite platelets.