Phase behavior of colloidal hard tetragonal parallelepipeds (cuboids): a Monte Carlo simulation study

The impact of particle geometry on the phase behavior of hard colloidal tetragonal parallelepipeds (TPs) was studied by using Monte Carlo simulations in continuum space. TPs or "cuboids" of aspect ratios varying from 0.25 to 8 were simulated by approximating their shapes with multisite objects, i.e., via rigid clusters of hard spheres. Using equation of state curves, order parameters, radial distribution functions, particle distribution functions along three directions, and visual analysis of configurations, an approximate phase diagram for the TPs was mapped out as a function of aspect ratio (r) and volume fraction. For r > 3 and intermediate concentrations, the behavior of the TPs was similar to that of spherocylinders, exhibiting similar liquid crystalline mesophases (e.g., nematic and smectic phases). For r = 1, a cubatic phase occurs with orientational order along the three axes but with little translational order. For 1 < r < 4, the TPs exhibit a cubatic-like mesophase with a high degree of order along three axes where the major axes of the particles are not all aligned in the same direction. For r < 1, the TPs exhibit a smectic-like phase where the particles have rotational freedom in each layer but form stacks with tetratic order. The equation of state for perfect hard cubes (r = 1) was also simulated and found to be consistent with that of the rounded-edge r = 1 TPs, except for its lack of discontinuity at the cubatic-solid transition.     

Anomalous columnar order of charged colloidal platelets

Monte Carlo computer simulations are carried out for a model system of like-charged colloidal platelets in the isothermal-isobaric ensemble (NpT). The aim is to elucidate the role of electrostatic interactions on the structure of synthetic clay systems at high particle densities. Short-range repulsions between particles are described by a suitable hard-core model representing a discotic particle. This potential is supplemented with an electrostatic potential based on a Yukawa model for the screened Coulombic potential between infinitely thin disklike macro-ions. The particle aspect-ratio and electrostatic parameters were chosen to mimic an aqueous dispersion of thin, like-charged, rigid colloidal platelets at finite salt concentration. An examination of the fluid phase diagram reveals a marked shift in the isotropic-nematic transition compared to the hard cut-sphere reference system. Several statistical functions, such as the pair correlation function for the center-of-mass coordinates and structure factor, are obtained to characterize the structural organization of the platelets phases. At low salinity and high osmotic pressure we observe anomalous hexagonal columnar structures characterized by interpenetrating columns with a typical intercolumnar distance corresponding to about half of that of a regular columnar phase. Increasing the ionic strength leads to the formation of glassy, disordered structures consisting of compact clusters of platelets stacked into finite-sized columns. These so-called "nematic columnar" structures have been recently observed in systems of charge-stabilized gibbsite platelets. Our findings are corroborated by an analysis of the static structure factor from a simple density functional theory.     

Simulation of scattering and phase behavior around the isotropic-nematic transition of discotic particles

The detailed study of the isotropic-nematic phase transition in a system of discotic particles of aspect ratios L/D≤0.1 presented here is relevant to a broad range of colloidal suspensions of chemically modified clay particles. Using Monte Carlo simulation techniques the equation of state, radial distribution functions, structure factors and normalized scattering intensities are calculated for each phase. The results are interpreted and related to previously reported free energy calculations [Fartaria and Sweatman, Chem. Phys. Lett. 478 (2009) 150], suggesting a nearly continuous isotropic-nematic transition for lower aspect ratios. Given this behavior we examined the structural information for each phase to determine how experimental scattering data might be used to distinguish the two phases. The radial distribution functions in each phase depend strongly on aspect ratio, and for larger aspect ratios a dramatic increase in the local ordering of discotic particles (represented here as cut-spheres) is observed just before the phase transition. However, this nearest-neighbor ordering seen in g(r) around r/D=0.1 would hardly be discernible in experimental scattering data subject to usual statistical errors. The structure factors and scattering intensities were calculated for L/D=0.1, 0.04 and 0.01 for the isotropic and nematic phases at and away from the isotropic-nematic transition. While the isotropic-nematic phase transition can be detected from the height and shape of the first scattering peak around 7QD for larger aspect ratios, this feature becomes much less discriminatory with decreasing aspect ratio. Instead, scattering intensities at low scattering vector amplitudes (Q→0) can be used for detection of the phase transition at low aspect ratios. These results provide useful insight to guide interpretation of X-ray and light scattering measurements for colloidal dispersions of thin platelets undergoing isotropic-nematic transitions.     

Gravity-induced liquid crystal phase transitions of colloidal platelets

The influence of gravity on a suspension of sterically stabilized colloidal gibbsite platelets is studied. An initially isotropic-nematic biphasic sample of such a suspension develops a columnar phase on the bottom on prolonged standing. This phenomenon is described using a simple osmotic compression model. We performed Monte Carlo simulations of cut spheres with aspect ratio L/D=1/15 and took data from the literature to supply the equations of state required for the model. We find that the model describes the observed three-phase equilibrium quite well.     

Sedimentation and phase transitions of colloidal gibbsite platelets

We study the competition between sedimentation, gelation, and liquid crystal formation in suspensions of colloidal gibbsite platelets of five different sizes at three ionic strengths. For large particles (with diameters of 350, 420, and 570 nm) sedimentation is initially the most important factor determining the macroscopic behavior. Only after the main part of the sample has sedimented in an amorphous phase, phase separation takes place. For the smallest particles (diameter 210 and 270 nm), it is the other way around: fast (within one week) phase separation or gelation takes place, after which sedimentation determines the final macroscopic appearance. We distinguish six different scenarios within this two-fold scheme and interpret these on the basis of the previously obtained phase diagram of colloidal gibbsite platelets (van der Beek, D.; Lekkerkerker, H. N. W. Langmuir 2004, 20, 8582).     

Phase diagram of hard snowman-shaped particles

We present the phase diagram of hard snowman-shaped particles calculated using Monte Carlo simulations and free energy calculations. The snowman particles consist of two hard spheres rigidly attached at their surfaces. We find a rich phase behavior with isotropic, plastic crystal, and aperiodic crystal phases. The crystalline phases found to be stable for a given sphere diameter ratio correspond mostly to the close packed structures predicted for equimolar binary hard-sphere mixtures of the same diameter ratio. However, our results also show several crystal-crystal phase transitions, with structures with a higher degree of degeneracy found to be stable at lower densities, while those with the best packing are found to be stable at higher densities.     

Colloidal particles as elastic triads in nematic liquid crystals

ABSTRACT

In this short review we summarise already published results to manifest very important role of high order elastic terms in the formation of colloidal structures in nematic liquid crystals (NLC). We reveal that every colloidal particle in nematics can be effectively represented as a triad of nonzero elastic moments. Usually colloidal particles in NLCs are treated with their elastic dipole and/or quadrupole moments only. But we demonstrate that octupole, hexadecapole and even 64-pole moments play an important role as well and determine parameters of different 1D, 2D and even 3D colloidal crystals in NLCs. In general the triad of the first three nonzero elastic moments can describe almost all colloidal structures observed so far. Dipole particles should be considered as hard spheroids with a triad of the dipole, quadrupole and octupole moments. Quadrupole particles should be treated as hard spheres with a triad of quadrupole, hexadecapole and 64-pole elastic moments

PACS numbers: 61.30.Dk, 82.70.Dd, 64.70.M?     

Thermosensitive hard spheres

We demonstrate an extension of a UV-Vis spectroscopy method to determine the phase boundaries for thermosensitive colloids as an alternative to the time-consuming sedimentation method. The Bragg attenuation peak from colloidal crystallites was monitored during the quasi-equilibrium colloidal crystal melting. The melting and freezing boundaries of the coexistence region were determined via a blue shift of Bragg's peak and the disappearance of peak area. We confirm this method using poly(N-isopropylacrylamide) (PNIPAM) particles at different charge densities and temperatures far below the lower critical solution temperature. At low pH, the particles behave as thermosensitive hard spheres.     

Phase diagram of mixtures of hard colloidal spheres and discs: a free-volume scaled-particle approach

Phase diagrams of mixtures of colloidal hard spheres with hard discs are calculated by means of the free-volume theory. The free-volume fraction available to the discs is determined from scaled-particle theory. The calculations show that depletion induced phase separation should occur at low disc concentrations in systems now experimentally available. The gas-liquid equilibrium of the spheres becomes stable at comparable size ratios as with bimodal mixtures of spheres or mixtures of rods and spheres. Introducing finite thickness of the platelets gives rise to a significant lowering of the fluid branch of the binodal.     

Liquid crystal phases of charged colloidal platelets

The liquid crystal phase behavior of a suspension of charged gibbsite [Al(OH)3] platelets is investigated. By variation of the ionic strength, we are able to tune the effective thickness-to-diameter ratio of the platelets in suspension. This enables us to experimentally test the liquid crystal phase transition scenario that was first predicted a decade ago by computer simulations for hard platelets (Veerman, J. A. C.; Frenkel, D. Phys. Rev. A 1992, 45, 5632), that is, the isotropic (I) to nematic (N) and isotropic to columnar (C) phase transitions in one colloidal suspension. In addition to the shape-dependent thermodynamic driving force, the effect of gravity is important. For example, a biphasic (I-N) suspension becomes triphasic (I-N-C) on prolonged standing. This effect is described by a simple osmotic compression model.     

Correlative studies on the fabrication of poly(styrene-methyl-methacrylate-acrylic acid) colloidal crystal films

This research describes a one-step procedure for monodispersed poly(styrene-methyl-methacrylate-acrylic acid colloidal spheres [P(St-MMA-AA)] via soap-seeded emulsion polymerization. The effects ofreaction conditions such as temperature, stirring speed, initiation concentration, e.t.c. were examined. The results obtained showed that the spheres average particle diameter decreased with increase in initiator concentration, the reaction temperature and stirring speed and increased with an increase in monomer concentrations. The particles show stable mechanical properties within the transition and heating temperatures of 111.9?°C and 388?°C respectively. Zeta-potential values ranging from ?31.8?mV to ?36.5?mV which is indicative of stable dispersion of colloidal particles were obtained for all the prepared latexes. The assembled colloidal latex had periodic structures with mainly hexagonal three-dimensional structures with multi-facet arrangements. The latex also shows spherical shape of monodispersed core-shell particles.     

A universal approach to fabricate ordered colloidal crystals arrays based on electrostatic self-assembly

We present a novel and simple method to fabricate two-dimensional (2D) poly(styrene sulfate) (PSS, negatively charged) colloidal crystals on a positively charged substrate. Our strategy contains two separate steps: one is the three-dimensional (3D) assembly of PSS particles in ethanol, and the other is electrostatic adsorption in water. First, 3D assembly in ethanol phase eliminates electrostatic attractions between colloids and the substrate. As a result, high-quality colloidal crystals are easily generated, for electrostatic attractions are unfavorable for the movement of colloidal particles during convective self-assembly. Subsequently, top layers of colloidal spheres are washed away in the water phase, whereas well-packed PSS colloids that are in contact with the substrate are tightly linked due to electrostatic interactions, resulting in the formation of ordered arrays of 2D colloidal spheres. Cycling these processes leads to the layer-by-layer assembly of 3D colloidal crystals with controllable layers. In addition, this strategy can be extended to the fabrication of patterned 2D colloidal crystals on patterned polyelectrolyte surfaces, not only on planar substrates but also on nonplanar substrates. This straightforward method may open up new possibilities for practical use of colloidal crystals of excellent quality, various patterns, and controllable fashions.     

Anisotropic and hindered diffusion of colloidal particles in a closed cylinder

Video microscopy and particle tracking were used to measure the spatial dependence of the diffusion coefficient (D(α)) of colloidal particles in a closed cylindrical cavity. Both the height and radius of the cylinder were equal to 9.0 particle diameters. The number of trapped particles was varied between 1 and 16, which produced similar results. In the center of the cavity, D(α) turned out to be 0.75D(0) measured in bulk liquid. On approaching the cylindrical wall, a transition region of about 3 particle diameters wide was found in which the radial and azimuthal components of D(α) decrease to respective values of 0.1D(0) and 0.4D(0), indicating asymmetrical diffusion. Hydrodynamic simulations of local drag coefficients for hard spheres produced very good agreement with experimental results. These findings indicate that the hydrodynamic particle-wall interactions are dominant and that the complete 3D geometry of the confinement needs to be taken into account to predict the spatial dependence of diffusion accurately.     

Fast formation of opal-like columnar colloidal crystals

We demonstrate that highly polydisperse colloidal gibbsite platelets easily form an opal-like columnar crystal with striking iridescent Bragg reflections. The formation process can be accelerated by orders of magnitude under a centrifugation force of 900 g without arresting the system in a disordered glassy phase. Using transmission electron microscopy and small-angle X-ray scattering techniques, we find that the forced sedimentation is accompanied by particle size fractionation, leading to inversion of the iridescent colors. The relatively easy self-organization of the polydisperse colloidal particles into opal-like crystals may be explained on the basis of the observed particle fractionation and possibly also on hexatic-like ordering.     

Neutron scattering studies of K(3)H(SO(4))(2) and K(3)D(SO(4))(2): The particle-in-a-box model for the quantum phase transition

In the crystal of K(3)H(SO(4))(2) or K(3)D(SO(4))(2), dimers SO(4)???H???SO(4) or SO(4)???D???SO(4) are linked by strong centrosymmetric hydrogen or deuterium bonds whose O???O length is ≈2.50 A?. We address two open questions. (i) Are H or D sites split or not? (ii) Is there any structural counterpart to the phase transition observed for K(3)D(SO(4))(2) at T(c) ≈ 85.5 K, which does not exist for K(3)H(SO(4))(2)? Neutron diffraction by single-crystals at cryogenic or room temperature reveals no structural transition and no resolvable splitting of H or D sites. However, the width of the probability densities suggest unresolved splitting of the wavefunctions suggesting rigid entities H(L1∕2) -H(R1∕2) or D(L1∕2) -D(R1∕2) whose separation lengths are l(H) ≈ 0.16 A? or l(D) ≈ 0.25 A?. The vibrational eigenstates for the center of mass of H(L1∕2) -H(R1∕2) revealed by inelastic neutron scattering are amenable to a square-well and we suppose the same potential holds for D(L1∕2) -D(R1∕2). In order to explain dielectric and calorimetric measurements of mixed crystals K(3)D((1 - ρ))H(ρ)(SO(4))(2) (0 ≤ ρ ≤ 1), we replace the classical notion of order-disorder by the quantum notion of discernible (e.g., D(L1∕2) -D(R1∕2)) or indiscernible (e.g., H(L1∕2) -H(R1∕2)) components depending on the separation length of the split wavefunction. The discernible-indiscernible isostructural transition at finite temperatures is induced by a thermal pure quantum state or at 0 K by ρ.     

Several routes to the glassy states in the one component soft core system: revisited by molecular dynamics

Molecular dynamics simulations have been performed to study the glass transition for the soft core system with a pair potential φ(n)(r) = ε(σ∕r)(n) of n = 12. Using the compressibility factor, PV/Nk(B)T=P?(ρ*), its phase diagram can be represented as a function of a reduced density, ρ? = ρ(ε∕k(B)T)(3∕n), where ρ = Nσ(3)∕V. In the present work, NVE relaxations to the glassy or crystalline states starting from the unstable states in the phase diagram have been revisited in details and compared with other processes. Relaxation processes can be characterized by the time dependence of the dynamical compressibility factor (PV/Nk(B)T)(t)?(≡g(ρ(t)*)) on the phase diagram. In some cases, g(ρ(t)*) reached a crystal branch in the phase diagram; however, metastable states are found in many cases. With connecting points for the metastable states in the phase diagram, we can define a glass branch where the dynamics of particles are almost frozen. The structures observed there have common properties characterized as glasses. Although overlaps of glass forming process and nanocrystallization process are observed in some cases, these behaviors are distinguishable to each other by the characteristics of structures. There are several routes to the glass branch and we suggest that all of them are the glass transition.     

Cubatic liquid-crystalline behavior in a system of hard cuboids

The lyotropic phase behavior of cuboidal particles was investigated via Monte Carlo simulations. Hard cubes were approximated by suitably shaped clusters of hard spheres. Changes in concentration and structure of the system were monitored as a function of osmotic pressure P* (imposed in an isobaric ensemble). As expected, an isotropic phase prevailed at low concentrations (low P*) and a crystalline phase formed at high concentrations (high P*). A third distinct phase was also observed for an intermediate range of concentrations (approximately marked by breaks in the P* versus concentration curve). The structure of this mesophase was characterized both visually and analytically by calculating radial distribution functions and order parameters. It was found that such a mesophase exhibits orientational ordering along three axes (cubatic order) but significant translational disorder, thus having a structure clearly distinct from both isotropic and crystalline phases.     

Interfacial colloidal crystallization via tunable hydrogel depletants

We demonstrate an approach using temperature-dependent hydrogel depletants to thermoreversibly tune colloidal attraction and interfacial colloidal crystallization. Total internal reflection and video microscopy are used to measure temperature-dependent depletion potentials between approximately 2 microm silica colloids and surfaces as mediated by approximately 0.2 microm poly-N-isopropylacrylamide (PNIPAM) hydrogel particles. Measured depletion potentials are modeled using the Asakura-Oosawa theory while treating PNIPAM depletants as swellable hard spheres. Monte Carlo simulations using the measured potentials predict reversible, quasi-2D crystallization and melting at approximately 27 degrees C in quantitative agreement with video microscopy images of measured microstructures (i.e., radial distribution functions) over the temperature range of interest (20-29 degrees C). Additional measurements of short-time self-diffusivities display excellent agreement with predicted diffusivities by considering multibody hydrodynamic interactions and using a swellable hard sphere model for the PNIPAM solution viscosity. Our findings demonstrate the ability to quantitatively measure, model, and manipulate kT-scale depletion attraction and phase behavior as a means of formally engineering interfacial colloidal crystallization.     

Colloidal crystallization of thermo-sensitive gel spheres of poly (N-isopropyl acrylamide). Influence of degree of cross-linking of the gels

Morphology, phase diagram, and reflection spectroscopy of the colloidal crystals of thermo-sensitive gel spheres, poly (N-isopropylacrylamide) having degrees of cross-linking 10 and 2?mol.% (pNIPAm(200?C10) and pNIPAm(200?C2)) were studied. Giant colloidal single crystals formed at very low gel concentrations. Critical concentrations of melting increased as the degree of cross-linking decreased in the range from 10 to 0.5?mol.% and/or suspension temperature increased from 20 to 45?°C. The critical concentration decreased sharply as the suspensions were deionized with coexistence of the mixtures of cation- and anion-exchange resins. Density of a gel sphere (gel concentration in weight percent divided by that in volume percent) increased sharply as the degree of cross-linking and/or temperature increased. These results demonstrated that the colloidal crystallization takes place by the extended electrical double layers formed around the gel spheres in addition of the excluded-volume effect of the gels. Most of the researchers including the authors have believed that the crystallization of the gel spheres takes place by the excluded-volume effect. However, the present work clarified that the colloidal interfaces, which are inevitable for the formation of the electrical double layers, are formed firmly between the water phase and gel spheres, though the gel spheres contain a lot of water molecules in the sphere region.