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

Self-assembly in amphiphilic macromolecules with solvent exposed hydrophobic moieties

Self-assembly by amphiphilic molecules with solvent exposed hydrophobic groups are relevant in biomolecular systems as well as in technological applications. Here we study such self-assembly in these systems using a model system of spherical particles having charge at core but solvent repelling surface, using Monte-Carlo simulations and mean field treatment. We find that solvophobicity mediated attraction leads aggregation, while electrostatic repulsions control stability of finite clusters. The aggregation threshold relates the parameters of two interactions through an algebraic dependence. The study also qualitatively explains experimental observations on aggregation of misfolded proteins and can be useful guide to tune stability of nm sized self-assembly in systems with exposed hydrophobic groups.

Computer simulations of the restricted primitive model at very low temperature and density

The problem of successfully simulating ionic fluids at low temperature and low density states is well known in the simulation literature: using conventional methods, the system is not able to equilibrate rapidly due to the presence of strongly associated cation-anion pairs. In this paper we present a numerical method for speeding up computer simulations of the restricted primitive model (RPM) at low temperatures (around the critical temperature) and at very low densities (down to 10(-10)σ(-3), where σ is the ion diameter). Experimentally, this regime corresponds to typical concentrations of electrolytes in nonaqueous solvents. As far as we are aware, this is the first time that the RPM has been equilibrated at such extremely low concentrations. More generally, this method could be used to equilibrate other systems that form aggregates at low concentrations.

Poisson-Boltzmann cell model for heterogeneously charged colloids

We introduce the Poisson-Boltzmann cell model for spherical colloidal particles with a heterogeneous surface charge distribution. This model is obtained by generalizing existing cell models for mixtures of homogeneously charged colloidal spheres. Our model has similar features as Onsager's second-virial theory for liquid crystals, but it predicts no orientational ordering if there is no positional ordering. This implies that all phases of heterogeneously charged colloids that are liquidlike with respect to translational degrees of freedom are also isotropic with respect to particle orientation.

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.

Self-assembled colloidal crystals from ZrO2 nanoparticles

Ordered three-dimensional (3-D) assemblies of nanocrystalline zirconia were synthesized from aqueous suspensions of ZrO(2) nanoparticles without the need for hydrocarbon surfactants or solvents to control colloidal crystal growth. Nanoparticles were suspended in mild acid and subsequently titrated from low to neutral pH. The solubility was reduced as the surfaces were neutralized, promoting assembly of the nanoparticles into ordered monoliths. TEM measurements indicated the formation of three-dimensional, hexagonal faceted, micrometer-sized colloidal crystals composed of 4 nm diameter ZrO(2) nanoparticles. Lacking organic surfactants, the colloidal crystals were exceptionally robust and were sintered at high temperatures (300-500 degrees C) for further stability. Small-angle X-ray scattering (SAXS) measurements demonstrate that the samples become progressively more amorphous above 350 degrees C, although some ordered domains of nanoparticles persist. Additionally, the heat treatment dramatically increases the surface area of the colloidal crystals as water and residual organics are desorbed, revealing highly controlled interstitial spaces and pores.

Low temperature behavior and glass line in the symmetrical colloidal electrolyte

We report on the low temperature behavior of the colloidal electrolyte by means of molecular dynamics simulations, where the electrostatic interactions were modeled using effective screened interactions. As in previous works, we have found a region of gas-liquid coexistence located in the low T-low rho region. At temperatures much lower than the critical one, the system cannot reach equilibrium, that is, the gas-liquid transition is arrested. Two different mechanisms have been identified to cause arrest: crowding at intermediate T values, associated with the crossing point between the binodal and the glass line, and a gelationlike arrest at very low T. To test the latter, the dynamics of the colloidal electrolyte near this crossing point has been computed and compared to the universal predictions of the ideal mode-coupling theory. As in other glass-forming liquids, we found good agreement between this mean field theory and the dynamics of this complex system, although it fails just at the transition. Interestingly, in this region we found that the dynamics of this system is driven mainly by the steric interactions, showing all the typical properties of a repulsive colloidal glass. Finally, the isodiffusivity lines show that in this system with short-range attractions, there is no reentrant glass phenomenon as opposed to monocomponent attractive systems.

Stability of binary colloids: kinetic and structural aspects of heteroaggregation processes

This review reports on recent advances in our knowledge about the stability of binary colloids. We focus not only on experimental results but also discuss theoretical and simulation studies regarding kinetic and structural aspects of heteroaggregation processes arising in such systems. In the first part of this work, heteroaggregation of oppositely charged particles is reviewed. When the interactions are short ranged, binary diffusion-limited cluster-cluster aggregation takes place. In this case, the short time behavior of the system follows the Hogg, Healy and Fuerstenau (HHF) theory. At long times, however, stable aggregates may form and remain in the system. Furthermore, cluster discrimination is observed, clusters that differ only by one constituent particle were found to behave quite differently. When the range of the interactions is increased, the latter effects become more pronounced. The fractal dimension of heteroaggregates is, in general, smaller than the values reported for fast and slow homoaggregation processes. In some cases, even values close to unity were obtained. This means that heteroaggregates have an open branched structure that may approach a chain-like morphology. In the second part of this work, we briefly discuss similar effects arising in heteroaggregation phenomena due to differences in particle size and chemical composition. The third part of this review tackles recent developments in the field of equilibrium phase diagrams of binary colloids. In the last section, the relatively small number of papers about heteroaggregation processes in two-dimensional systems is also discussed.

Phase diagram of patchy colloids: towards empty liquids

We report theoretical and numerical evaluations of the phase diagram for patchy colloidal particles of new generation. We show that the reduction of the number of bonded nearest neighbors offers the possibility of generating liquid states (i.e., states with temperature T lower than the liquid-gas critical temperature) with a vanishing occupied packing fraction (phi), a case which can not be realized with spherically interacting particles. Theoretical results suggest that such reduction is accompanied by an increase of the region of stability of the liquid phase in the (T-phi) plane, possibly favoring the establishment of homogeneous disordered materials at small phi, i.e., stable equilibrium gels.

Gas-liquid phase separation in oppositely charged colloids: Stability and interfacial tension

We study the phase behavior and the interfacial tension of the screened Coulomb (Yukawa) restricted primitive model (YRPM) of oppositely charged hard spheres with diameter sigma using Monte Carlo simulations. We determine the gas-liquid and gas-solid phase transitions using free energy calculations and grand-canonical Monte Carlo simulations for varying inverse Debye screening length kappa. We find that the gas-liquid phase separation is stable for kappasigma<or=4, and that the critical temperature decreases upon increasing the screening of the interaction (decreasing the range of the interaction). In addition, we determine the gas-liquid interfacial tension using grand-canonical Monte Carlo simulations. The interfacial tension decreases upon increasing the range of the interaction. In particular, we find that simple scaling can be used to relate the interfacial tension of the YRPM to that of the restricted primitive model, where particles interact with bare Coulomb interactions.

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.

Phase behavior of mixtures of oppositely charged protein nanoparticles at asymmetric charge ratios

We present experimental and theoretical results for the phase behavior of mixtures of oppositely charged globular protein molecules in aqueous solutions containing monovalent salt. These colloidal mixtures are interesting model systems, on the one hand for electrolyte solutions ("colloidal ionic liquids"), and on the other for mixtures of oppositely charged (bio)macromolecules, colloids, micelles, etc., with the range of the electrostatic interactions (Debye length) easily tunable from much smaller to much larger than the particle size, simply by adding different amounts of monovalent salt. In this paper we investigate the phase behavior of such mixtures in the case that equally sized colloids have a large difference in charge magnitude. This is possible at any mixing ratio because small ions compensate any colloidal charge asymmetry. Our experimental system is based on lysozyme, a positively charged "hard" globular protein molecule, and succinylated lysozyme, a chemical modification of lysozyme which is negatively charged. By changing the solution pH we can adjust the ratio of charge between the two molecules. To describe phase separation into a dilute phase and a dense "complex" phase, a thermodynamic model is set up in which we combine the Carnahan-Starling-van der Waals equation of state with a heterogeneous Poisson-Boltzmann cell model and include the possibility that protein molecules adjust their charge when they move from one phase to the other (charge regulation). The theory uses the nonelectrostatic attraction strength as the only adjustable parameter and reasonably well reproduces the data in that complexation is only possible at intermediate , not too asymmetric mixing ratios, and low enough ionic strength and temperature.

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.

Phase behavior of mixtures of oppositely charged nanoparticles: heterogeneous Poisson-Boltzmann cell model applied to lysozyme and succinylated lysozyme

We study the phase behavior of mixtures of oppositely charged nanoparticles, both theoretically and experimentally. As an experimental model system we consider mixtures of lysozyme and lysozyme that has been chemically modified in such a way that its charge is nearly equal in magnitude but opposite in sign to that of unmodified lysozyme. We observe reversible macroscopic phase separation that is sensitive not only to protein concentration and ionic strength, but also to temperature. We introduce a heterogeneous Poisson-Boltzmann cell model that generally applies to mixtures of oppositely charged nanoparticles. To account for the phase behavior of our experimental model system, in addition to steric and electrostatic interactions, we need to include a temperature-dependent short-ranged interaction between the lysozyme molecules, the exact origin of which is unknown. The strength and temperature dependence of the short-ranged attraction is found to be of the same order of magnitude as that between unmodified lysozyme molecules. The presence of a rather strong short-ranged attraction in our model system precludes the formation of colloidal liquid phases (or complex coacervates) such as those typically found in mixtures of globular protein molecules and oppositely charged polyelectrolytes.

CuAu structure in the restricted primitive model and oppositely charged colloids

We study the phase behavior of oppositely charged equal-size hard spheres both theoretically and experimentally, using Monte Carlo simulations and confocal microscopy. In the simulations, two systems are considered: the restricted primitive model (RPM) and a system of screened Coulomb particles. We construct the phase diagrams of both systems by computer simulations and predict a novel solid phase that has the CuAu structure. In addition, the CuAu structure is observed experimentally in a system of oppositely charged colloids. The qualitative agreement between the RPM, the screened Coulomb system, and the experiments shows that colloids form a suitable model system to study phase behavior in ionic systems.

Ionic colloidal crystals of oppositely charged particles

Colloidal suspensions are widely used to study processes such as melting, freezing and glass transitions. This is because they display the same phase behaviour as atoms or molecules, with the nano- to micrometre size of the colloidal particles making it possible to observe them directly in real space. Another attractive feature is that different types of colloidal interactions, such as long-range repulsive, short-range attractive, hard-sphere-like and dipolar, can be realized and give rise to equilibrium phases. However, spherically symmetric, long-range attractions (that is, ionic interactions) have so far always resulted in irreversible colloidal aggregation. Here we show that the electrostatic interaction between oppositely charged particles can be tuned such that large ionic colloidal crystals form readily, with our theory and simulations confirming the stability of these structures. We find that in contrast to atomic systems, the stoichiometry of our colloidal crystals is not dictated by charge neutrality; this allows us to obtain a remarkable diversity of new binary structures. An external electric field melts the crystals, confirming that the constituent particles are indeed oppositely charged. Colloidal model systems can thus be used to study the phase behaviour of ionic species. We also expect that our approach to controlling opposite-charge interactions will facilitate the production of binary crystals of micrometre-sized particles, which could find use as advanced materials for photonic applications.

Monte Carlo simulations of oppositely charged macroions in solution

The structure and phase behavior of oppositely charged macroions in solution have been studied with Monte Carlo simulations using the primitive model where the macroions and small ions are described as charged hard spheres. Size and charge symmetric, size asymmetric, and charge asymmetric macroions at different electrostatic coupling strengths are considered, and the properties of the solutions have been examined using cluster size distribution functions, structure factors, and radial distribution functions. At increasing electrostatic coupling, the macroions form clusters and eventually the system displays a phase instability, in analogy to that of simple electrolyte solutions. The relation to the similar cluster formation and phase instability occurring in solutions containing oppositely charged polymers is also discussed.