Effects of colloid polydispersity on the phase behavior of colloid-polymer mixtures

We study theoretically the equilibrium phase behavior of a mixture of polydisperse hard-sphere colloids and monodisperse polymers, modeled using the Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)] within the free volume approximation of H. N. W. Lekkerkerker, W. C. K. Poon, P. N. Pusey, A. Stroobants, and P. B. Warren [Europhys. Lett. 20, 559 (1992)]. We compute full phase diagrams in the plane of colloid and polymer volume fractions, using the moment free energy method. The intricate features of phase separation in pure polydisperse colloids combine with the appearance of polymer-induced gas-liquid coexistence to give a rich variety of phase diagram topologies as the polymer-colloid size ratio xi and the colloid polydispersity delta are varied. Quantitatively, we find that polydispersity disfavors fluid-solid against gas-liquid separation, causing a substantial lowering of the threshold value xi(c) above which stable two-phase gas-liquid coexistence appears. Phase splits involving two or more solids can occur already at low colloid concentration, where they may be kinetically accessible. We also analyze the strength of colloidal size fractionation. When a solid phase separates from a fluid, its polydispersity is reduced most strongly if the phase separation takes place at low colloid concentration and high polymer concentration, in agreement with experimental observations. For fractionation in gas-liquid coexistence we likewise find good agreement with experiment, as well as with perturbative theories for near-monodisperse systems.     

Transport of kaolinite colloids through quartz sand: influence of humic acid, Ca(2+), and trace metals

To evaluate the risk of contaminant transport by mobile colloids, it seems essential to understand how colloids and associated pollutants behave during their migration through uncontaminated soil or groundwater. In this study, we investigated at pH 4 the influence of flow velocity, humic acid, solution Ca(2+) concentrations, and trace metals (Pb(2+), Cu(2+)) on the transport and deposition of kaolinite particles through a pure crystalline quartz sand as porous medium. A short-pulse chromatographic technique was used to measure colloid deposition. Adsorption of humic acid to the kaolinite increase its negative surface charge and then decrease colloid deposition. Experiments with different flow rates showed that humic-coated kaolinite colloid deposition followed a first-order kinetic rate law. The deposition rate coefficients of humic-coated kaolinite colloids increase with increasing Ca(2+) concentration in the suspension. The effect of trace metals on the mobility is studied by injecting two suspensions with different concentrations of Pb(2+) and Cu(2+). At very low cation concentration, the fraction of colloids retained is low and roughly independent of the nature of divalent cations. At high concentration, the deposition is higher and depends on the affinity of divalent cations toward humic-coated kaolinite colloids.     

Phase behavior of charge stablized colloid dispersion with added water soluble polymers

Demixing and colloidal crystallization in the mixture of charge stabilized colloidal poly(methyl methacrylate) particles and soluble poly(ethylene oxide) were investigated by means of synchrotron small-angle X-ray scattering (SAXS) technique. Phase diagram of the mixture was obtained based on visual inspection and SAXS results. The phase behavior is determined as a function of the concentration of the polymer as well as the volume fraction of the colloidal particles. The system shows a one phase region when the concentration of the polymer is low, whereas a two-phase region is present when the concentration of the polymer is larger than a critical concentration at certain volume fraction of the colloids. Interestingly, a face centered cubic colloidal crystalline structure was formed under certain conditions, which has been rarely observed in experiments of colloid-polymer mixtures with competing interactions.     

Liquid crystalline nanosheet colloids with controlled particle size obtained by exfoliating single crystal of layered niobate k(4)nb(6)o(17)

Colloidally dispersed niobate nanosheets with the thickness of 1.8 nm and controlled mean lateral sizes of 0.15-7.8 mum were prepared and their liquid crystallinity was examined. The nanosheet colloids with different lateral sizes were obtained by exfoliation of single crystals of layered niobate K4Nb6O17 and subsequent ultrasonication. Naked-eye and microscope observations of the nanosheet colloids between crossed polarizers revealed liquid crystallinity of the sols characterized by birefringence as functions of the lateral sizes and concentration of the nanosheets. The nanosheet colloids with smaller lateral sizes (0.15-1.9 mum) varied from isotropic to biphasic (isotropic + liquid crystalline), and finally to fully liquid crystalline states as the colloid concentration increased. The phase transition concentrations (from isotropic to biphasic and biphasic to liquid crystalline) decreased with increasing aspect ratio (lateral-to-thickness ratio) of the nanosheets, almost in accordance with the prediction by Onsager theory, indicating that the liquid crystallinity is explained basically by excluded-volume effect between the nanosheets. On the other hand, the colloids with larger lateral sizes (6.2 and 7.8 mum) stably kept liquid crystalline state even at very low concentration (5.1 x 10-6 in volume fraction), which was much lower than that expected from the theory.     

Shape- and phase-controlled synthesis of monodisperse, single-crystalline ternary chalcogenide colloids through a convenient solution synthesis strategy

Colloidal, monodisperse, single-crystalline pyramidal CuInS2 and rectangular AgInS2 nanocrystals were successfully synthesized through a convenient and improved solvothermal process that uses hexadecylamine as a capping reagent. The crystal phase, morphology, crystal lattice, and chemical composition of the as-prepared products were characterized by using X-ray diffraction, transmission electron microscopy (TEM), high-resolution TEM, and energy dispersive X-ray spectroscopy. Results revealed that the as-synthesized CuInS2 colloid is in the tetragonal phase (size: 13-17 nm) and the AgInS2 in the orthorhombic structure (size: 17+/-0.5 nm). A possible shape evolution and crystal growth mechanism has been suggested for the formation of pyramidal CuInS2 and rectangular AgInS2 colloids. Control experiments indicated that the morphology- and/or phase-change of CuInS2 and orthorhombic AgInS2 colloids are temperature- and/or time-dependent. CuInS2 colloids absorb well in the range of visible light at room-temperature, indicating its potential application as a solar absorber. Two photoluminescence (PL) subbands at 1.938 and 2.384 eV in the PL spectra of CuInS2 colloids revealed that the recombination of the closest and the second closest donor-acceptor pairs within the CuInS2 lattice, in which the donor defect (Cui) occupies an interstitial position and the acceptor defect (VIn) resides at an adjacent cation site. In addition, the synthesis strategy developed in this study is convenient and inexpensive, and could also be used as a general process for the synthesis of other pure or doped ternary chalcogenides that require a controlled size (or shape). This process could be extended to the synthesis of other functional nanomaterials.     

Phase diagrams of colloidal spheres with a constant zeta-potential

We study suspensions of colloidal spheres with a constant zeta-potential within Poisson-Boltzmann theory, quantifying the discharging of the spheres with increasing colloid density and decreasing salt concentration. We use the calculated renormalized charge of the colloids to determine their pairwise effective screened-Coulomb repulsions. Bulk phase diagrams in the colloid concentration-salt concentration representation follow, for various zeta-potentials, by a mapping onto published fits of phase boundaries of point-Yukawa systems. Although the resulting phase diagrams do feature face-centered cubic and body-centered cubic phases, they are dominated by the (re-entrant) fluid phase due to the colloidal discharging with increasing colloid concentration and decreasing salt concentration.     

Melting line of charged colloids from primitive model simulations

We develop an efficient simulation method to study suspensions of charged spherical colloids using the primitive model. In this model, the colloids and the co- and counterions are represented by charged hard spheres, whereas the solvent is treated as a dielectric continuum. In order to speed up the simulations, we restrict the positions of the particles to a cubic lattice, which allows precalculation of the Coulombic interactions at the beginning of the simulation. Moreover, we use multiparticle cluster moves that make the Monte Carlo sampling more efficient. The simulations are performed in the semigrand canonical ensemble, where the chemical potential of the salt is fixed. Employing our method, we study a system consisting of colloids carrying a charge of 80 elementary charges and monovalent co- and counterions. At the colloid densities of our interest, we show that lattice effects are negligible for sufficiently fine lattices. We determine the fluid-solid melting line in a packing fraction eta-inverse screening length kappa plane and compare it with the melting line of charged colloids predicted by the Yukawa potential of the Derjaguin-Landau-Verwey-Overbeek theory. We find qualitative agreement with the Yukawa results, and we do not find any effects of many-body interactions. We discuss the difficulties involved in the mapping between the primitive model and the Yukawa model at high colloid packing fractions (eta>0.2).     

Influence of poly(ethylene oxide) brushes on the rheological properties of MgO colloidal suspensions in water

A combined experimental and multiscale simulation study of the influence of polymer brush modification on interactions of colloidal particles and rheological properties of dense colloidal suspensions has been conducted. Our colloidal suspension is comprised of polydisperse MgO colloidal particles modified with poly(ethylene oxide) (PEO) brushes in water. The shear stress as a function of shear rate was determined experimentally and from multiscale simulations for a suspension of 0.48 volume fraction colloids at room temperature for both bare and PEO-modified MgO colloids. Bare MgO particles exhibited strong shear thinning behavior and a yield stress on the order of several Pascals in both experiments and simulations. In contrast, simulations of PEO-modified colloids revealed no significant yielding or shear thinning and viscosity only a few times larger than solvent viscosity. This behavior is inconsistent with results obtained from experiments where modification of colloids with PEO brushes formed by adsorption of PEO-based comb-branched chains resulted in relatively little change in suspension rheology compared to bare colloids over the range of concentration of comb-branch additives investigated. We attribute this discrepancy in rheological properties between simulation and experiment for PEO-modified colloidal suspensions to heterogeneous adsorption of the comb-branch polymers.     

Complete phase behavior of the symmetrical colloidal electrolyte

We computed the complete phase diagram of the symmetrical colloidal electrolyte by means of Monte Carlo simulations. Thermodynamic integration, together with the Einstein-crystal method, and Gibbs-Duhem integration were used to calculate the equilibrium phase behavior. The system was modeled via the linear screening theory, where the electrostatic interactions are screened by the presence of salt in the medium, characterized by the inverse Debye length, kappa (in this work kappasigma=6). Our results show that at high temperature, the hard-sphere picture is recovered, i.e., the liquid crystallizes into a fcc crystal that does not exhibit charge ordering. In the low temperature region, the liquid freezes into a CsCl structure because charge correlations enhance the pairing between oppositely charged colloids, making the liquid-gas transition metastable with respect to crystallization. Upon increasing density, the CsCl solid transforms into a CuAu-like crystal and this one, in turn, transforms into a tetragonal ordered crystal near close packing. Finally, we have studied the ordered-disordered transitions finding three triple points where the phases in coexistence are liquid-CsCl-disordered fcc, CsCl-CuAu-disordered fcc, and CuAu-tetragonal-disordered fcc.     

Phase stability of colloidal spheres mixed with supramolecular rod-like polymers

Mixtures of colloids and supramolecular polymers exhibit stimuli-responsive phase behavior. In previous work (Peters and Tuinier, Physica A 510, 233 [2018]) the polymers were treated as fully flexible chains, while in experimental systems supramolecular polymers may have a certain degree of stiffness. Here we predict that for stiff rod-like supramolecular polymers phase separation can occur at much lower polymer concentrations than for flexible supramolecular polymers. Additionally, it is demonstrated that colloid–polymer interactions can significantly influence the equilibrium polymer size distribution, however this does not strongly affect the phase behavior of the mixture. At the low polymer concentrations at which the system already gets unstable, the effect of excluded volume interactions between polymers chains themselves is small. Finally, for an experimental system it is predicted that a variety of re-entrant phase transitions may be observed within a realistic temperature range as illustrated by a specific example.     

Effect of charge inhomogeneity and mobility on colloid aggregation

The aggregation of inhomogeneously charged colloids with the same average charge is analyzed using Monte Carlo simulations. We find aggregation of colloids for sizes in the range 10-200 nm, which is similar to the range in which aggregation is observed in several experiments. The attraction arises from the strongly correlated electrostatic interactions associated with the increase in the counterion density in the region between the particles; this effect is enhanced by the discreteness and mobility of the surface charges. Larger colloids attract more strongly when their surface charges are discrete. We study the aggregation as functions of the surface charge density, counterion valence, and volume fraction.     

Gold nanoparticles decorated with oligo(ethylene glycol) thiols: protein resistance and colloidal stability

The interactions between proteins and gold colloids functionalized with protein-resistant oligo(ethylene glycol) (OEG) thiol, HS(CH2)11(OCH2CH2)6OMe (EG6OMe), in aqueous solution have been studied by small-angle X-ray scattering (SAXS) and UV-vis spectroscopy. The mean size, 2R, and the size distribution of the decorated gold colloids have been characterized by SAXS. The monolayer-protected gold colloids have no correlations due to the low volume fraction in solution and are stable in a wide range of temperatures (5-70 degrees C), pH (1.3-12.4), and ionic strength (0-1.0 M). In contrast, protein (bovine serum albumin) solutions with concentrations in the range of 60-200 mg/mL (4.6-14.5 vol %) show a pronounced correlation peak in SAXS, which results from the repulsive electrostatic interaction between charged proteins. These protein interactions show significant dependence on ionic strength, as would be expected for an electrostatic interaction (Zhang et al. J. Phys. Chem. B 2007, 111, 251). For a mixture of proteins and gold colloids, the protein-protein interaction changes little upon mixing with OEG-decorated gold colloids. In contrast, the colloid-colloid interaction is found to be strongly dependent on the protein concentration and the size of the colloid itself. Adding protein to a colloidal solution results in an attractive depletion interaction between functionalized gold colloids, and above a critical protein concentration, c*, the colloids form aggregates and flocculate. Adding salt to such mixtures enhances the depletion effect and decreases the critical protein concentration. The aggregation is a reversible process (i.e., diluting the solution leads to dissolution of aggregates). The results also indicate that the charge of the OEG self-assembled monolayer at a curved interface has a rather limited effect on the colloidal stabilization and the repulsive interaction with proteins.     

Interaction between colloids with grafted diblock polyampholytes

The interaction between composite colloidal particles composed of a spherical core and grafted AB-diblock polyampholytes (diblock copolymers with oppositely charged blocks) are investigated by using a coarse-grained model solved with Monte Carlo simulations. The B block is end-grafted onto the core of the colloid and its linear charge density is varied, whereas the linear charge density of the A block is fixed. The brush structure of a single colloid, the mean force between two colloids, and the structure of solutions of such colloids have been determined for different linear charge densities of the B blocks and block lengths. Many features of the present system are controlled by the charge of the B blocks. In the limit of uncharged B blocks, (i) the grafted chains are stretched and form an extended polyelectrolyte brush, (ii) a strong repulsive force is operating between two colloids, (iii) and the solution is thermodynamic stable and displays strong spatial correlation among the colloids. In the limit where the charges of the two types of blocks exactly compensate each other, (i) the chains are collapsed and form a polyelectrolyte complex surrounding the cores, (ii) an attractive force appears between two colloids, and (iii) strong colloid clustering appears in the solution. These features become more pronounced as the length of the polymer blocks is increased, and a phase instability occurs at sufficiently long chains. A comparison with properties for other related colloidal particles is also provided.     

Electrostatics and aggregation: how charge can turn a crystal into a gel

The crystallization of proteins or colloids is often hindered by the appearance of aggregates of low fractal dimension called gels. Here we study the effect of electrostatics upon crystal and gel formation using an analytic model of hard spheres bearing point charges and short range attractive interactions. We find that the chief electrostatic free energy cost of forming assemblies comes from the entropic loss of counterions that render assemblies charge-neutral. Because there exists more accessible volume for these counterions around an open gel than a dense crystal, there exists an electrostatic entropic driving force favoring the gel over the crystal. This driving force increases with increasing sphere charge, but can be counteracted by increasing counterion concentration. We show that these effects cannot be fully captured by pairwise-additive macroion interactions of the kind often used in simulations, and we show where on the phase diagram to go in order to suppress gel formation.     

Electrophoresis of concentrated colloidal dispersions in low-polar solvents

We present a method to accurately measure the electrophoretic mobility of spherical colloids at high volume fractions in real space using confocal laser scanning microscopy (CLSM) and particle tracking. We show that for polymethylmethacrylate (PMMA) particles in a low-polar, density- and refractive-index-matched mixture of cyclohexylbromide and cis-decahydronaphthalene, the electrophoretic mobility decreases nonlinearly with increasing volume fraction. From the electrophoretic mobilities, we calculate the ζ-potential and the particle charge with and without correcting for volume fraction effects. For both cases, we find a decreasing particle charge as a function of volume fraction. This is in accordance with the fact that the charges originate from chemical equilibria that represent so-called weak association and/or dissociation reactions. Finally, as our methodology also provides data on particle self-diffusion in the presence of an electric field, we also analyze the diffusion at different volume fractions and identify a nonlinear decreasing trend for increasing volume fraction.     

Gel formation and aging in weakly attractive nanocolloid suspensions at intermediate concentrations

We report x-ray photon correlation spectroscopy (XPCS) and rheometry experiments to study the temporal evolution of gel formation and aging in suspensions of silica nanocolloids possessing a tunable short-range attraction. The colloid volume fractions, φ = 0.20 and 0.43, are below the glass regime at high concentration and above the fractal regime at low concentration. Following a sudden initiation of the interparticle attraction, the suspensions display a protracted latency period in which they remain fluid before acquiring a measurable elastic shear modulus. The duration of the latency period and the subsequent rate of increase of the modulus vary strongly with the strength of the attraction. The XPCS results indicate dynamic heterogeneity among the colloids during this gel formation in which a growing fraction of the particles become localized. The temporal evolution of this localization correlates with that of the rheology. In particular, the time scale over which the fraction of localized particles increases tracks the duration of the latency period. Also, at φ = 0.20 the localization length characterizing the motion of the localized fraction scales onto the shear modulus with no free parameters as predicted by a self-consistent theory based on mode coupling [K. S. Schweizer and G. Yatsenko, J. Chem. Phys. 127, 164505 (2007)], while deviations from the predicted scaling at φ = 0.43 are observed near the gel point. The XPCS results also reveal slow, hyperdiffusive motion of the colloids in the newly formed gels that is attributed to strain from the relaxation of internal stress. While some features of this motion correlate with the evolving rheology, others appear decoupled from the macroscopic mechanical behavior.     

Detachment of colloids from a solid surface by a moving air-water interface

Colloid attachment to liquid–gas interfaces is an important process used in industrial applications to separate suspended colloids from the fluid phase. Moving gas bubbles can also be used to remove colloidal dust from surfaces. Similarly, moving liquid–gas interfaces lead to colloid mobilization in the natural subsurface environment, such as in soils and sediments. The objective of this study was to quantify the effect of moving air–water interfaces on the detachment of colloids deposited on an air-dried glass surface, as a function of colloidal properties and interface velocity. We selected four types of polystyrene colloids (positive and negative surface charge, hydrophilic and hydrophobic). The colloids were deposited on clean microscope glass slides using a flow-through deposition chamber. Air–water interfaces were passed over the colloid-deposited glass slides, and we varied the number of passages and the interface velocity. The amounts of colloids deposited on the glass slides were visualized using confocal laser scanning microscopy and quantified by image analysis. Our results showed that colloids attached under unfavorable conditions were removed in significantly greater amounts than those attached under favorable conditions. Hydrophobic colloids were detached more than hydrophilic colloids. The effect of the air–water interface on colloid removal was most pronounced for the first two passages of the air–water interface. Subsequent passages of air–water interfaces over the colloid-deposited glass slides did not cause significant additional colloid removal. Increasing interface velocity led to decreased colloid removal. The force balances, calculated from theory, supported the experimental findings, and highlight the dominance of detachment forces (surface tension forces) over the attachment forces (DLVO forces).     

Size-selective electrochemical preparation of surfactant-stabilized Pd-, Ni- and Pt/Pd colloids

A detailed study concerning the size-selective electrochemical preparation of R4N+Br- -stabilized palladium colloids is presented. Such colloids are readily accessible using a simple electrolysis cell in which the sacrificial anode is a commercially available Pd sheet, the surfactant serving as the electrolyte and stabilizer. It is shown that such parameters as solvent polarity, current density, charge flow, distance between electrodes and temperature can be used to control the size of the Pd nanoparticles in the range 1.2-5 nm. Characterization of the Pd colloids has been performed using transmission electron microscopy (TEM), small angle X-ray scattering (SAXS) and X-ray powder diffractometry (XRD) evaluated by Debye-function-analysis (DFA). Possible mechanisms of particle growth are discussed. Experiments directed towards the size-selective electrochemical fabrication of (n-C6H13)4N+Br- -stabilized nickel colloids are likewise described. Finally, a new strategy for preparing bimetallic colloids (e.g., Pt/Pd nanoparticles) electrochemically is presented, based on the use of a preformed colloid (e.g., (n-C8H17)4N+Br- -stabilized Pt particles) and a sacrificial anode (e.g., Pd sheet).     

Particle size dependence of electro-optical switching in ZrP nano colloid

Aqueous colloid of 2-dimensional (2D) α-ZrP nanoparticles can serve as an excellent material for Kerr devices. We investigate the influence of the particle size on the electro-optical switching for isotropic and biphasic α-ZrP colloids that exhibit stable Kerr effect. Smaller sized α-ZrP colloid has wider range of isotropic and biphasic phases, but since the anisotropic polarizability is approximately proportional to square diameter of particles, the larger sized α-ZrP colloid has higher birefringence at a given concentration. The dynamic response time is also dramatically influenced by the particle size. Smaller sized particle has lower viscosity, and the fall time monotonically increases with increasing particle size. However, the rise time has the minimum at around 0.6 μm owing to the competitive contributions of the anisotropic polarizability and the rotational viscosity. Thus, the particle size in α-ZrP colloid is an important factor to determine the electro-optical performance of a Kerr device based on 2D α-ZrP colloids. These findings will be important in developing electro-optical devices using lyotropic liquid crystal colloids.     

Nonspherical ZnS colloidal building blocks for three-dimensional photonic crystals

The asymmetry introduced by a complex or nonspherical basis promotes photonic band gap formation in three-dimensional photonic crystals. However, relatively few techniques have been demonstrated to produce uniform nonspherical colloids for use as photonic crystal bases. Here we expand the menu of basis types with high refractive index by preparing nonspherical zinc sulfide colloids of uniform size and shape. Dimers, trimers, and planar tetramers were precipitated from aqueous solution by the thermal decomposition of thioacetamide in the presence of zinc nitrate, manganese nitrate, and nitric acid. The well-defined morphological types were obtained from suspensions aged for 4-6 h at 26-32 degrees C and then for 20-35 min at 85 degrees C. Stereological techniques were used to analyze SEM images and determine the percentage of each particle class. For example, the quantitative characterization of a particle population prepared at 29 degrees C for 6 h and 85 degrees C for 22 min had the composition 59+/-3% spheres, 31+/-2% dimers, 7+/-1% trimers, 0.4+/-0.2% tetramers, and 2.5+/-0.8% complex clusters (encompasses all other varieties of shape). X-ray diffraction and X-ray photoelectron spectroscopy confirmed the zinc blend crystal structure and the stoichiometric composition of the particles. The refractive index was estimated as 2.25 (413 nm) -2.09 (709 nm) by fitting experimental absorption spectra to curves derived from Mie scattering calculations. This indicated an average porosity approximately 24%. Such colloids offer the potential to form diamond-like lattices with large, stable photonic band gaps.