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.     

Finite-thickness-enhanced attractions for oppositely charged membranes and colloidal platelets

Within linearized Poisson-Boltzmann theory, we study the disjoining pressure of two oppositely charged parallel objects (membranes and colloidal platelets) in a 1:1 electrolyte, with a focus on the effects of their finite thickness. This extension of the standard Gouy-Chapman model from an interacting pair of double layers to a quartet (one on each side of the two interacting objects) is shown to enhance the regime of attractive interactions significantly, in particular, when the separation and the thickness are on the order of the Debye length of the solvent, provided the dielectric mismatch between objects and solvent is not too extreme. The enhancement of attractions occurs for objects with fixed charge as well as for those that exhibit charge regulation but not for those with a constant surface potential. The underlying mechanism for this enhancement for thin objects is the transfer of net ionic charge from the electrolyte in between to the other sides. For biological membranes in water, this effect is small; however, it is due to strong image charge effects.     

Lyotropic smectic B phase formed in suspensions of charged colloidal platelets

Here, we present the first observation of a smectic B (Sm(B)) phase in a system of charged colloidal gibbsite platelets suspended in dimethyl sulfoxide (DMSO). The use of DMSO, a polar aprotic solvent, leads to a long range of the electrostatic Coulomb repulsion between platelets. We believe this to be responsible for the formation of the layered liquid crystalline phase consisting of hexagonally ordered particles, that is, the Sm(B) phase. We support our finding by high-resolution X-ray scattering experiments, which additionally indicate a high degree of ordering in the Sm(B) phase.     

Columnar versus smectic order in systems of charged colloidal rods

We study the stability of inhomogeneous liquid crystalline states in systems of monodisperse, stiff, charged rods. By means of a bifurcation analysis applied to the Onsager free energy for charged rods in strongly nematic states, we investigate nematic-smectic and nematic-columnar instabilities as a function of the Debye screening length kappa(-1). While the nematic-smectic transition clearly preempts the nematic-columnar one in the regime of strong screening (i.e., small kappa(-1)) a marked stability of hexagonal columnar order is observed at larger screening lengths. The theoretical results are substantiated by Brownian dynamics computer simulation results based on the Yukawa site model. Our findings connect to experiments on tobacco mosaic virus rods, in particular, but might be relevant for soft rodlike mesogens in strong external directional fields in general.     

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.     

Screening of charged spheroidal colloidal particles

We study the effective screened electrostatic potential created by a spheroidal colloidal particle immersed in an electrolyte, within the mean field approximation, using Poisson-Boltzmann equation in its linear and nonlinear forms, and also beyond the mean field by means of Monte Carlo computer simulation. The anisotropic shape of the particle has a strong effect on the screened potential, even at large distances (compared to the Debye length) from it. To quantify this anisotropy effect, we focus our study on the dependence of the potential on the position of the observation point with respect with the orientation of the spheroidal particle. For several different boundary conditions (constant potential, or constant surface charge) we find that, at large distance, the potential is higher in the direction of the large axis of the spheroidal particle.     

Sedimentation of a charged colloidal sphere in a charged cavity

An analytical study is presented for the quasisteady sedimentation of a charged spherical particle located at the center of a charged spherical cavity. The overlap of the electric double layers is allowed, and the polarization (relaxation) effect in the double layers is considered. The electrokinetic equations that govern the ionic concentration distributions, electric potential profile, and fluid flow field in the electrolyte solution are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a symmetric electrolyte with the surface charge densities of the particle and cavity as the small perturbation parameters. An analytical expression for the settling velocity of the charged sphere is obtained from a balance among the gravitational, electrostatic, and hydrodynamic forces acting on it. Our results indicate that the presence of the particle charge reduces the magnitude of the sedimentation velocity of the particle in an uncharged cavity and the presence of the fixed charge at the cavity surface increases the magnitude of the sedimentation velocity of an uncharged particle in a charged cavity. For the case of a charged sphere settling in a charged cavity with equivalent surface charge densities, the net effect of the fixed charges will increase the sedimentation velocity of the particle. For the case of a charged sphere settling in a charged cavity with their surface charge densities in opposite signs, the net effect of the fixed charges in general reduces/increases the sedimentation velocity of the particle if the surface charge density of the particle has a greater/smaller magnitude than that of the cavity. The effect of the surface charge at the cavity wall on the sedimentation of a colloidal particle is found to increase with a decrease in the particle-to-cavity size ratio and can be significant in appropriate situations.     

Gravitational compression dynamics of charged colloidal crystals

We examine the compression of charged colloidal crystals under the influence of gravitational force by monitoring the spatiotemporal variations of Bragg diffraction from the crystal lattice. We use the dilute aqueous dispersions of colloidal silica particles (diameter=216 nm, charge number=733, a particle volume fraction φ=0.06) in the presence of 5-15 μM sodium chloride. The sedimentation profiles of the colloidal crystals along the crystal height are determined by in situ fiber optics reflection spectroscopy. The time evolutions of the sedimentation profiles are calculated by numerical simulations based on a phenomenological continuum model that explicitly incorporates the electrostatic interparticle interactions. The simulation results correctly describe the experiments at sufficiently high ionic strength.     

Growth of columnar hydrogel colloidal crystals in water-organic solvent mixture

A novel emulsion method has been demonstrated to grow columnar hydrogel colloidal crystals by mixing an aqueous suspension of poly-N-isopropylacrylamide-co-allylamine microgels with organic solvent, driven by the coalescence of micelles consisting of organic oil droplets coated by many microgels. This method leads to microgel colloidal crystals of several centimeters growing from the top to the bottom along the gravity direction. Both temperature and polymer concentration play critical roles for the formation of columnar crystals. A phase diagram has been determined, and it can be used as a guide to selectively grow different crystals, including columnar crystals and randomly oriented crystals, and enable the coexistence of columnar crystals and randomly oriented crystals.     

Gas-solid coexistence in highly charged colloidal suspensions

Aqueous suspensions of highly charged polystyrene particles with different volume fractions have been investigated for structural ordering and phase behavior using static light scattering (SLS) and confocal laser scanning microscope (CLSM). Under deionized conditions, suspensions of high-charge-density colloidal particles remained disordered whereas suspensions of relatively low charge density showed crystallization by exhibiting iridescence for the visible light. Though for the unaided eye crystallized suspensions appeared homogeneous, SLS measurements and CLSM observations have revealed their inhomogeneous nature in the form of the coexistence of voids with dense ordered regions. CLSM investigations on disordered suspensions showed their inhomogeneous nature in the form coexistence of voids with dense disordered (amorphous) regions. Our studies on highly charged colloids confirm the occurrence of gas-solid transition and are in accordance with predictions of Monte Carlo simulations using a pair-potential having a long-range attractive term [Mohanty, P. S.; Tata, B. V. R. J. Colloid Interface Sci. 2003, 264, 101]. On the basis of our experimental and simulation results, we argue that the reported reentrant disordered state [Yamanaka et al. Phys. Rev. Lett. 1998, 80, 5806 and Toyotama et al. Langmuir 2003, 19, 3236] in charged colloids observed at high charge densities is a gas-solid coexistence state.     

Depletion potentials induced by charged colloidal rods

We present direct depletion potential measurements for a single colloidal sphere close to a wall in suspensions of charged colloidal rods. In contrast to earlier studies of purely entropic systems (Helden et al. Phys. Rev. Lett. 2003, 90, 048301), here electrostatic interactions are important. These enhance the depletion attraction and lead to repulsive parts in the interaction potentials, indicating correlation effects between the rods.     

Diffusiophoresis of a moderately charged spherical colloidal particle

An analytic expression is obtained for the diffusiophoretic mobility of a charged spherical colloidal particle in a symmetrical electrolyte solution. The obtained expression, which is expressed in terms of exponential integrals, is correct to the third order of the particle zeta potential so that it is applicable for colloidal particles with low and moderate zeta potentials at arbitrary values of the electrical double-layer thickness. This is an improvement of the mobility formula derived by Keh and Wei, which is correct to the second order of the particle zeta potential. This correction, which is related to the electrophoresis component of diffusiophoresis, becomes more significant as the difference between the ionic drag coefficients of electrolyte cations and anions becomes larger and vanishes in the limit of thin or thick double layer. A simpler approximate mobility expression is further obtained that does not involve exponential integrals.     

The rheology and microstructure of charged colloidal suspensions

The effects of electric charge interation and particle correlations on suspension rheology are examined. A one-component fluid analysis using a Smoluchowski equation for the equilibrium structure is applied to charged suspensions of spherical colloids under shear. The frequency dependent modulus and viscosity, predicted as functions of particle and added salt concentrations, are compared with published rheological measurements on model suspensions. Recent improvements in the statistical mechanical theories for the equilibrium microstructure, its nonequilibrium deformation, and the bulk shear stresses are included. The direct electrostatic interaction is found to drive the divergence in the shear viscosity near the liquid-solid phase transition. Extensions of the theory predict the elastic modulus of binary mixtures of charged colloids. Estimates of the primary electroviscous effect, hydrodynamic interactions, and errors in the Yukawa limiting form for the potential and applications of asymptotic theories are presented. Predictions for the rheology based on effective hard-sphere models are found to be reasonable when using a parameter fit from the equilibrium phase behavior. Mean-field mode coupling theories predict larger relaxation times than calculated from the Smoluchowski equation (=SE). A study of binary mixing effects on elasticity shows non-ideal behavior. It is noted that equilibrium structural information can be used to resolve discrepancies between the theoretical predictions and the measured rheology.     

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 behaviour of binary mixtures of colloidal charged spheres

As a step towards the modelling of binary metal alloys we here report on the shape of the phase boundary of two deionized charged sphere colloidal suspensions as a function of mixing ratio and particle density. Their size ratios are r = 0.68 and r = 0.56. Both aqueous suspensions of polystyrene copolymer spheres crystallize in a body-centred cubic structure. Interesting differences in the shape of the phase boundary are observed. In the first case a peaked increase of crystal stability was observed for a mixing ratio of p = 0.2–0.3, which gives the fraction of small spheres. Also in the second case the stability of the crystalline phase is larger than expected for an ideal solid solution but over a more extended range of small p. In addition at p = 0.7–0.8 we find a pronounced suppression of crystallization and furthermore some indications of a precipitation of one species at p = 0.9. While the first phase diagram resembles that of a solid solution with possibly the onset of compound formation, the second more resembles a eutectic.     

Heteroaggregation in binary mixtures of oppositely charged colloidal particles

Heteroaggregation (or heterocoagulation) rate constants have been measured in mixtures of well-characterized colloidal particles of opposite charge with multiangle static and dynamic light scattering. This technique permits routine measurements of absolute heteroaggregation rate constants, also in the presence of homoaggregation. Particularly with multiangle dynamic light scattering, one is able to estimate absolute heteroaggregation rate constants accurately in the fast aggregation regime for the first time. Heteroaggregation rate constants have also been measured over a wide range of parameters, for example, ionic strength and different surface charge densities. Amidine latex particles, sulfate latex particles, and silica particles have been used for these experiments, and they were well characterized with respect to their charging and homoaggregation behavior. It was shown that heteroaggregation rate constants of oppositely charged particles increase slowly with decreasing ionic strength, and provided the surface charge is sufficiently large, the rate constant is largely independent of the surface charge. These trends can be well described with DLVO theory without adjustable parameters.     

Oppositely charged colloidal binary mixtures: a colloidal analog of the restricted primitive model

The equilibrium phase diagram of a colloidal system composed of 1:1 mixture of positive and negative particles with equal charge is studied by means of Monte Carlo simulations. The system is the colloidal analog of the restricted primitive model (RPM) for ionic fluids. A liquid-gas transition is found in the low-temperature-low-density region, similar to the liquid-gas transition in the RPM. The fluid-crystal transition is also studied, and the liquid phase is shown to be stable in a narrow range of temperatures. In the liquid, the pair distribution function shows alternating layers of particles with opposite sign of charge surrounding every particle. In the vapor phase, clusters of particles are observed, again in agreement with the RPM. However, a decreasing distribution of clusters is obtained, instead of the discrimination between charged and neutral clusters found in the RPM.