Experimental phase diagram of symmetric binary colloidal mixtures with opposite charges

The phase behavior of equimolar mixtures of oppositely charged colloidal systems with similar absolute charges is studied experimentally as a function of the salt concentration in the system and the colloid volume fraction. As the salt concentration increases, fluids of irreversible clusters, gels, liquid-gas coexistence, and finally, homogeneous fluids, are observed. Previous simulations of similar mixtures of Derjaguin-Landau-Verwey-Overbeek (DLVO) particles indeed showed the transition from homogeneous fluids to liquid-gas separation, but also predicted a reentrant fluid phase at low salt concentrations, which is not found in the experiments. Possibly, the fluid of clusters could be caused by a nonergodicity transition responsible for the gel phase in the reentrant fluid phase. Liquid-gas separation takes a delay time after the sample is prepared, whereas gels collapse from the beginning. The density of the liquid in coexistence with a vapor phase depends linearly on the overall colloid density of the system. The vapor, on the other hand, is comprised of equilibrium clusters, as expected from the simulations.     

Liquid-gas separation in colloidal electrolytes

The liquid-gas transition of an electroneutral mixture of oppositely charged colloids, studied by Monte Carlo simulations, is found in the low-temperature-low-density region. The critical temperature shows a nonmonotonous behavior as a function of the interaction range, kappa(-1), with a maximum at kappasigma approximately 10, implying an island of coexistence in the kappa-rho plane. The system is arranged in such a way that each particle is surrounded by shells of particles with alternating charge. In contrast with the electrolyte primitive model, both neutral and charged clusters are obtained in the vapor phase.     

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.     

Linking phase behavior and reversible colloidal aggregation at low concentrations: simulations and stochastic mean field theory

We have studied the link between the kinetics of clustering and the phase behavior of dilute colloids with short range attractions of moderate strength. This was done by means of computer simulations and a theoretical kinetic model originally developed to deal with reversible colloidal aggregation. Three different regions of the phase diagram were accessed. For weak attractions, a gas phase of small clusters in equilibrium forms in the system. For intermediate attractions, the system undergoes liquid-gas separation, which is signatured by the formation of a few large droplike aggregates, a gas phase of small clusters, and an overall kinetics where a few seeds succeed in explosively growing at long times, after a lag time. Finally, for very strong attractions, fractal unbreakable clusters form and grow following DLCA-like (diffusion limited cluster aggregation) kinetics; liquid-gas separation is prevented by the strength of the bonds, which do not allow restructuration. Good qualitative and quantitative agreement is found between the dynamic simulations and the kinetic model in all the three regions.     

Phase Transitions of the Liquid–Liquid Type and a Change in the Particle Charge in Colloidal Solutions

The thermodynamic properties are studied for the solutions of charged colloidal particles with ionizable surface groups. The microscopic mechanism of microion binding at surface groups is considered. The free energy of the system in the parameter range where the usual theory of such solutions is inadequate (a range of practical interest) is calculated using the method of the thermodynamic perturbation theory. The first-order phase transition of the liquid–liquid type is shown to be possible; in this phase transition, a phase with a high concentration of colloidal particles that have a higher charge coexists with a phase with a lower concentration of particles that have a lower charge.     

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.     

Light-regulated electrostatic interactions in colloidal suspensions

The net charge of a colloidal particle was controlled using light and a new photocleavable self-assembled monolayer (SAM). The SAM contained a terminal ammonium group and a centrally located carboxylic acid group that was masked with an ortho-nitrobenzyl functionality. Once exposed to UV light, the 2-nitrobenzyl group was cleaved, therefore transforming the colloidal particle from a net positive (silica-SAM-NH3+) to a net negative (silica-SAM-COO-) charge. By varying the UV exposure time, their zeta potential could be tailored between +26 and -60 mV at neutral pH. To demonstrate a photoinduced gel-to-fluid phase transition, a binary colloidal suspension composed of silica-SAM-NH3+ and negatively charged, rhodamine-labeled silica particles was mixed to form a gel. Exposure to UV light rendered all of the particles negative and therefore converted the system into a colloidal fluid that settles to form a dense sediment.     

Phase transitions in two-dimensional colloidal particles at oil/water interfaces

Enhanced digital video microscopy is applied to study the equilibrium structure of a two-dimensional charged sulfate-polystyrene particle (2 mum in diameter) monolayer at decane/water interfaces. When the surface density is decreased, a sequential phase transition, pure solid phase-->pure hexatic phase-->liquid-hexatic-coexisting phase-->pure liquid phase, is observed. In addition, the transition between liquid and hexatic phases is first order, while the solid-hexatic phase transition is second order. The temperature effect on this two-dimensional melting transition is discussed by performing the experiments at three different temperatures. The Voronoi [J. Reine Angew. Math. 134, 198 (1908)] construction is applied to analyze the defect structure in the two-dimensional particle monolayer. The pair interaction potential of the two-dimensional colloidal particles is found to be a very long range repulsion and to decay with distance to the power of -3.     

Effect of charge asymmetry and charge screening on structure of superlattices formed by oppositely charged colloidal particles

Colloidal suspensions made up of oppositely charged particles have been shown to self-assemble into substitutionally ordered superlattices. For a given colloidal suspension, the structure of the superlattice formed from self-assembly depends on its composition, charges on the particles, and charge screening. In this study we have computed the pressure-composition phase diagrams of colloidal suspensions made up of binary mixtures of equal sized and oppositely charged particles interacting via hard core Yukawa potential for varying values of charge screening and charge asymmetry. The systems are studied under conditions where the thermal energy is equal or greater in magnitude to the contact energy of the particles and the Debye screening length is smaller than the size of the particles. Our studies show that charge asymmetry has a significant effect on the ability of colloidal suspensions to form substitutionally ordered superlattices. Slight deviations of the charges from the stoichiometric ratio are found to drastically reduce the thermodynamic stability of substitutionally ordered superlattices. These studies also show that for equal-sized particles, there is an optimum amount of charge screening that favors the formation of substitutionally ordered superlattices.     

Effect of quenched size polydispersity on the fluid-solid transition in charged colloidal suspensions

We study the effect of quenched size polydispersity on the phase behavior of charged colloidal suspensions using free-energy calculations in Monte Carlo simulations. The colloids are assumed to interact with a hard-core repulsive Yukawa (screened-Coulomb) interaction with constant surface potential, so that the particles are polydisperse both in size and charge. In addition, we take the size distribution to be fixed in both the fluid and crystal phase (no size fractionation is allowed). We study the fluid-solid transition for various screening lengths and surface potentials, finding that upon increasing the size polydispersity the freezing transition shifts toward higher packing fractions and the density discontinuity between the two coexisting phases diminishes. Our results provide support for a terminal polydispersity above which the freezing transition disappears.     

Recent study on counterion-mediated attraction between colloidal particles

Recent experimental results were reviewed. The 1D- and 2D-USAXS studies gave higher orders of Bragg diffraction for single crystals of colloidal silica particles, allowing more accurate determinations of the lattice constant, lattice symmetry, and direction. The closest interparticle spacing thus determined was confirmed to be smaller than the average spacing. The most closely packed planes ((110) planes for bcc) of negatively charged particles were found to be parallel to the likewise negatively charged capillary surface, inconsistently with the accepted double layer interaction theory but consistently with a recent experimental finding of positive adsorption. Shaking caused disruption of the single crystals but newly formed microcrystals retained the lattice constant and the preference of the (110) planes. The liquid-solid-liquid transition, a re-entrant phase transition, was found for silica particles and latex particles at given particle volume fraction and salt concentration, when the charge density of particles was varied. It was demonstrated that the purely repulsive Yukawa potential and the concept of renormalized charge cannot account for the re-entrant behavior. The Monte-Carlo simulation using the Sogami potential, which contains short-range repulsion and long-range attraction, was found to account for the fcc–bcc transition, which was earlier claimed to be explainable only by the Yukawa potential. Furthermore, the homogeneous-inhomogeneous phase transition and void formation could be accounted for by the simulation using the Sogami potential; the Yukawa potential could not reproduce the experiments. Attention was drawn to the experimental conditions in direct measurements of interparticle forces; only short interparticle distance and low charge density particles were covered, which make it practically impossible to detect the long-range counterion-mediated attraction. It is hoped that, by technical improvements, these shortcomings may be made up and quantitative argument become possible on the attraction.     

Phase behavior of lipid-based lyotropic liquid crystals in presence of colloidal nanoparticles

We have investigated the microstructure and phase behavior of monoglyceride-based lyotropic liquid crystals in the presence of hydrophilic silica colloidal particles of size comparable to or slightly exceeding the repeat units of the different liquid crystalline phases. Using small angle X-ray scattering (SAXS) and differential scanning calorimetry (DSC), we compare the structural properties of the neat mesophases with those of the systems containing silica colloidal particles. It is found that the colloidal particles always macrophase separate in inverse bicontinuous cubic phases of gyroid (Ia3d) and double diamond (Pn3m) symmetries. SAXS data for the inverse columnar hexagonal phase (H(II)) and lamellar phase (L(α)) suggest that a low volume fraction of the nanoparticles can be accommodated within the mesophases, but that at concentrations above a given threshold, the particles do macrophase separate also in these systems. The behavior is interpreted in terms of the enthalpic and entropic interactions of the nanoparticles with the lamellar and hexagonal phases, and we propose that, in the low concentration limit, the nanoparticles are acting as point defects within the mesophases and, upon further increase in concentration, initiate nucleation of nanoparticles clusters, leading to a macroscopic phase separation.     

Homogeneous and heterogeneous binary colloidal clusters formed by evaporation-induced self-assembly inside droplets

In this paper, we report the preparation of binary clusters of colloidal particles with different sizes or species into complex structures using oil-in-water emulsion droplets as confining geometries. First, polystyrene or silica particles with bimodal size distribution were packed densely by evaporation-induced self-assembly inside oil-in-water emulsion droplets. The configurations of larger particles inside the droplets minimize the second moment of the particle locations for the ratio of large to small particle sizes less than 3. Also, the configurations of bimodal clusters were predicted by using a surface evolver simulation, and the simulation predictions were compared with the experimental results. In addition, heterogeneous colloidal clusters were produced by emulsifying the binary mixture suspension of polystyrene and silica particles in aqueous medium followed by evaporating the oil phase. A density gradient centrifugation was applied to fractionate the asymmetric binary dimers comprised of PS and silica microspheres.     

Monte Carlo computer simulations and electron microscopy of colloidal cluster formation via emulsion droplet evaporation

We consider a theoretical model for a binary mixture of colloidal particles and spherical emulsion droplets. The hard sphere colloids interact via additional short-ranged attraction and long-ranged repulsion. The droplet-colloid interaction is an attractive well at the droplet surface, which induces the Pickering effect. The droplet-droplet interaction is a hard-core interaction. The droplets shrink in time, which models the evaporation of the dispersed (oil) phase, and we use Monte Carlo simulations for the dynamics. In the experiments, polystyrene particles were assembled using toluene droplets as templates. The arrangement of the particles on the surface of the droplets was analyzed with cryogenic field emission scanning electron microscopy. Before evaporation of the oil, the particle distribution on the droplet surface was found to be disordered in experiments, and the simulations reproduce this effect. After complete evaporation, ordered colloidal clusters are formed that are stable against thermal fluctuations. Both in the simulations and with field emission scanning electron microscopy, we find stable packings that range from doublets, triplets, and tetrahedra to complex polyhedra of colloids. The simulated cluster structures and size distribution agree well with the experimental results. We also simulate hierarchical assembly in a mixture of tetrahedral clusters and droplets, and find supercluster structures with morphologies that are more complex than those of clusters of single particles.     

Effect of a surface charge on the halfwidth and peak position of cluster plasmons in colloidal metal particles

The optical response of colloidal particles depends on a variety of properties of the cluster, e.g., shape, size, size distribution and particle material. Since particles often are charged, also the surface charge may be a parameter which influences their optical properties. In this paper the effect of a surface charge on optical properties of spherical colloidal particles is studied and its magnitude is estimated by extended computations for silver clusters with surface plasmon in aqueous suspension. Two models are presented and discussed. The first model is based on the electrodynamic solution by Bohren and Hunt (Can. J. Phys. 55, 1930 (1977)), where a surface conductivity _S for a free surface charge yield an additional contribution _S to the dielectric constant of the particle material. In the second model, the surface charge contributes to the number density of free electrons in the cluster. Both models lead to a shift of the cluster plasmon peak, while an increase of the plasmon halfwidth could not be derived. The effect is quite small and limited on very small clusters.PACS 61.46+w 73.20.Mf 78.20.Dj     

Theoretical studies of the early stage coagulation kinetics for a charged colloidal dispersion

We study the early stage coagulation kinetics for a charged colloidal dispersion which is here modeled by an effective two-body colloid-colloid potential. The colloidal system was physically prepared by choosing sets of colloidal parameters varying in particular the Hamaker constant and the particle's size. The kinetics of coagulation process was driven by the addition of an indifferent electrolyte and assumed to proceed in two quasi-steady steps. In the first step, colloidal particles are destabilized by the presence of a second potential minimum to diffuse from a bulk-stabilized liquid phase to a flocculated phase. In the second step, we assume that different entities are found in the second potential minimum. The entities comprise secondary dimers, secondary dimers undergoing redispersion, and monomers still in singlet states. If, under favorable condition, this kind of interaction-driven diffusive motion continues, a fraction of the secondary dimers will be induced to undergo primary dimers formation in the first deep minimum. Whether or not the latter process occurs is determined either energetically by the potential barrier falling below a prescribed value, say of 15k(B)T, or/and the second potential minimum becoming negligibly small (with a magnitude coagulation transition and would throw a fresh light on the use of both the energy and the kinetic criteria for understanding the colloidal stability such as those observed in the liquid-liquid coexistence.     

Two-dimensional Monte Carlo simulations of a polydisperse colloidal dispersion composed of ferromagnetic particles for the case of no external magnetic field

We have investigated the aggregation phenomena in a polydisperse colloidal dispersion composed of ferromagnetic particles by means of the cluster-moving Monte Carlo method. The results have been compared with those for a monodisperse system. The internal structures of aggregates have been analyzed in terms of the radial distribution function in order to clarify the quantitative differences in the internal structures of clusters. In addition, the cluster size distribution and angular distribution function have been investigated. The results obtained in the present study are summarized as follows. In a monodisperse system, open necklacelike clusters are formed and they extend with increasing strength of the magnetic particle-particle interaction. In a polydisperse system with a small standard deviation in the particle size distribution, sigma=0.2, larger necklacelike clusters are formed and some looplike clusters can also be observed. In a polydisperse system with a larger standard deviation, sigma=0.35, clumplike clusters are formed for a weak magnetic particle-particle interaction. For a stronger magnetic interaction, larger size clusters that exhibit a complicated network structure are formed. These complicated cluster formations found in a polydisperse system are mainly due to the effect of the presence of larger particles.     

Two-dimensional colloidal crystal in nonlinear Poisson-Boltzmann model

A two-dimensional hexagonal colloidal crystal of charged particles obeying the general nonlinear Poisson-Boltzmann equation is studied by the numerical method. Force constants and pressure in a system, as well as elastic constants of a crystal, are calculated on the basis of the solutions of the equation. Calculation procedures are described briefly and numerical data are reported. The effect of nonlinearity of charge distribution on the manifestation of many-body interactions and on the validity of the approximation of interaction of the nearest neighbors is considered.     

Cationic gel-phase liposomes with "decorated" anionic SPIO nanoparticles: morphology, colloidal, and bilayer properties

The assembly and complexation of oppositely charged colloids are important phenomena in many natural and synthetic processes. Liposome-nanoparticle assemblies (LNAs) represent an interesting hybrid system that combines "soft" and "hard" colloidal materials. This work describes the formation and characterization of gel-phase LNAs formed by the binding of anionic superparamagnetic iron oxide (SPIO) nanoparticles to cationic dipalmitoylphosphatidylcholine (DPPC)/dipalmitoyltrimethylammonium propane (DPTAP) liposomes. Particles were examined with hydrodynamic diameters below (16 nm) and above (30 nm) the cutoff reported for supported lipid bilayer formation. LNA formation with 16 nm particles was entropically driven and particles bound individually to yield "decorated" structures. In this case, increasing nanoparticle concentration yielded colloidal LNA aggregates and eventual charge inversion. In contrast, LNA formation with 30 nm particles was enthalpically driven, and the nanoparticles aggregated at the bilayer interface. These aggregates led to significant LNA aggregation and large bilayer sheets due to liposome rupture despite minimal charge screening of the liposome surface. In this case SLBs were present, but these structures were not dominant. Differences in LNA structure were also revealed through the lipid phase transition behavior. This work infers size-dependent nanoparticle binding and LNA formation mechanisms that can be used to tailor colloidal and bilayer properties. Analogies are made to polyelectrolyte patch charge heterogeneities and DNA complexation with cationic liposomes.     

Particle Monte Carlo simulation of string-like colloidal assembly in two and three dimensions

We simulate structural phase behavior of polymer-grafted colloidal particles by molecular Monte Carlo technique. The interparticle potential, which has a finite repulsive square-step outside a rigid core of the colloid, was previously confirmed via numerical self-consistent field calculation. This model potential is purely repulsive. We simulate these model colloids in the canonical ensemble in two and three dimensions and find that these particles containing no interparticle attraction self-assemble and align in a string-like assembly, at low temperature and high density. This string-like colloidal assembly is related to percolation phenomena. Analyzing the cluster size distribution and the average string length, we build phase diagrams and discover that the average string length diverges around the region where the melting transition line and the percolation transition line cross. This result is similar to Ising spin systems, in which the percolation transition line and the order-disorder line meet at a critical point.