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

Liquid crystalline self-assembly of mixtures of rod- and wedge-shaped MIDA boronates

Rod-like MIDA boronates form smectic mesophases, while wedge-shaped MIDA boronates self-assemble into columnar mesophases. However, the phase behavior of mixtures is less understood. In order to obtain further insight on the molecular self-assembly of MIDA boronate mixtures two series of binary mixtures of rod-like and wedge-shaped mesogens were prepared. The phase behavior was studied using differential scanning calorimetry (DSC), polarizing optical microscopy (POM) and X-ray diffraction (XRD). The study revealed a strong dependency of the mesophase structure on the mesogen composition. Usage of a less bulky columnar mesogen suppressed the formation of columnar mesophases in the mixture and led to a decrease in melting and clearing temperatures. The phase behavior is discussed in terms of the packing parameter model typically applied for lyotropic liquid crystals.

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.

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.

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.

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.

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

Using a geometry-based fundamental measure density functional theory, we calculate bulk fluid phase diagrams of colloidal mixtures of vanishingly thin hard circular platelets and hard spheres. We find isotropic-nematic phase separation, with strong broadening of the biphasic region, upon increasing the pressure. In mixtures with large size ratio of platelet and sphere diameters, there is also demixing between two nematic phases with differing platelet concentrations. We formulate a fundamental measure density functional for mixtures of colloidal platelets and freely overlapping spheres, which represent ideal polymers, and use it to obtain phase diagrams. We find that, for low platelet-polymer size ratio, in addition to isotropic-nematic and nematic-nematic phase coexistence, platelet-polymer mixtures also display isotropic-isotropic demixing. By contrast, we do not find isotropic-isotropic demixing in hard-core platelet-sphere mixtures for the size ratios considered.

Connectivity percolation in suspensions of hard platelets

We present a study on connectivity percolation in suspensions of hard platelets by means of Monte Carlo simulation. We interpret our results using a contact-volume argument based on an effective single-particle cell model. It is commonly assumed that the percolation threshold of anisotropic objects scales as their inverse aspect ratio. While this rule has been shown to hold for rodlike particles, we find that for hard platelike particles the percolation threshold is nonmonotonic in the aspect ratio. It exhibits a shallow minimum at intermediate aspect ratios and then saturates to a constant value. This effect is caused by the isotropic-nematic transition preempting the percolation transition. Hence the common strategy to use highly anisotropic, conductive particles as fillers in composite materials in order to produce conduction at low filler concentration is expected to fail for platelike fillers such as graphene and graphite nanoplatelets.

Deriving the Rosenfeld functional from the virial expansion

In this article we replace the semiheuristic derivation of the Rosenfeld functional of hard convex particles with the systematic calculation of Mayer clusters. It is shown that each cluster integral further decomposes into diagrams of intersection patterns that we classify by their loop number. This extends the virial expansion of the free energy by an expansion in the loop order, with the Rosenfeld functional as its leading contribution. Rosenfeld's weight functions then follow from the derivation of the intersection probability by generalizing the equation of Blaschke, Santalo, and Chern. It is found that the 0-loop order can be derived exactly and reproduces the Rosenfeld functional. We further discuss the influence of particle dimensions, topologies, and geometries on the mathematical structure of the calculation.

Phase behaviour of binary mixtures of diamagnetic colloidal platelets in an external magnetic field

Using fundamental measure density functional theory we investigate paranematic-nematic and nematic-nematic phase coexistence in binary mixtures of circular platelets with vanishing thicknesses. An external magnetic field induces uniaxial alignment and acts on the platelets with a strength that is taken to scale with the platelet area. At particle diameter ratio λ = 1.5 the system displays paranematic-nematic coexistence. For λ = 2, demixing into two nematic states with different compositions also occurs, between an upper critical point and a paranematic-nematic-nematic triple point. Increasing the field strength leads to shrinking of the coexistence regions. At high enough field strength a closed loop of immiscibility is induced and phase coexistence vanishes at a double critical point above which the system is homogeneously nematic. For λ = 2.5, besides paranematic-nematic coexistence, there is nematic-nematic coexistence which persists and hence does not end in a critical point. The partial orientational order parameters along the binodals vary strongly with composition and connect smoothly for each species when closed loops of immiscibility are present in the corresponding phase diagram.