Interparticle interactions and direct imaging of colloidal phases assembled from microsphere-nanoparticle mixtures

Structural correlations in highly asymmetric binary charged colloidal mixtures

We explore structural correlations of strongly asymmetric mixtures of binary charged colloids within the primitive model of electrolytes considering large charge and size ratios of 10 and higher. Using computer simulations with explicit microions, we obtain the partial pair correlation functions between the like-charged colloidal macroions. Interestingly the big-small correlation peak amplitude is smaller than that of the big-big and small-small macroion correlation peaks, which is unfamiliar for additive repulsive interactions. Extracting optimal effective microion-averaged pair interactions between the macroions, we find that on top of non-additive Yukawa-like repulsions an additional shifted Gaussian attractive potential between the small macroions is needed to accurately reproduce their correct pair correlations. For small Coulomb couplings, the behavior is reproduced in a coarse-grained theory with microion-averaged effective interactions between the macroions. However, the accuracy of the theory deteriorates with increasing Coulomb coupling. We emphasize the relevance of entropic interactions exerted by the microions on the macroions. Our results are experimentally verifiable in binary mixtures of micron-sized colloids and like-charge nanoparticles.

Charge-Regulated Interactions: The Case of a Nanoparticle and a Sphere of Arbitrary Dielectric Constants

Surfaces of objects immersed in liquid develop an electric charge density that depends on the types and concentrations of dissolved ions. The strength and spatial distribution of this charge density controls a myriad of processes, from biological to industrial processes. In addition, the lack of a full understanding of the charge density precludes a complete foundational interpretation of liquid-mediated many-body interactions. This understanding is especially obscured by charge regulation, whereby the charge on an object hinges, in addition, on the charges and locations of all other charged objects in the liquid. Here, we present a rigorous mathematical approach based on the Poisson-Boltzmann Equation, with field-dependent boundary conditions, and apply it to obtain the liquid-mediated interaction energy between a charged dielectric sphere and a charged particle. The framework that we develop in this article should be of use beyond the limits of the example application considered here: it should be useful as a conceptual and technical starting point to obtain charge-regulated many-body interactions in liquids.

Effective electrostatic interactions in colloid-nanoparticle mixtures

Interparticle interactions and bulk properties of colloidal suspensions can be substantially modified by the addition of nanoparticles. Extreme asymmetries in size and charge between colloidal particles and nanoparticles present severe computational challenges to molecular-scale modeling of such complex systems. We present a statistical mechanical theory of effective electrostatic interactions that can greatly ease large-scale modeling of charged colloid-nanoparticle mixtures. By applying a sequential coarse-graining procedure, we show that a multicomponent mixture of charged colloids, nanoparticles, counterions, and coions can be mapped first onto a binary mixture of colloids and nanoparticles and then onto a one-component model of colloids alone. In a linear-response approximation, the one-component model is governed by a single effective pair potential and a one-body volume energy, whose parameters depend nontrivially on nanoparticle size, charge, and concentration. To test the theory, we perform molecular dynamics simulations of the two-component and one-component models and compute structural properties. For moderate electrostatic couplings, colloid-colloid radial distribution functions and static structure factors agree closely between the two models, validating the sequential coarse-graining approach. Nanoparticles of sufficient charge and concentration enhance screening of electrostatic interactions, weakening correlations between charged colloids and destabilizing suspensions, consistent with experiments.

Assembly of colloidal silica crystals inside double emulsion drops

We investigated the assembly of colloidal silica crystals inside double emulsion drops generated in microcapillary microfluidic devices. The double emulsions are composed of an aqueous suspension of monodisperse silica particles in the inner drop surrounded by a PDMS oil drop that acts as a semipermeable membrane for the diffusion of water into or out of the inner drop in the presence of an osmotic gradient. Imposing a high osmotic pressure in the continuous phase induces water diffusion out of the inner drop, increasing the silica volume fraction (φ(silica)) and leading to the formation of a spherical colloidal silica crystal. Silica suspensions with no salt or low salt concentration (<10(-3) M) formed colloidal crystals with φ(silica) up to 0.68. Monodisperse spherical colloidal silica crystals with sizes ranging from 16 to 133 μm were generated by varying the device geometry, flow-rate ratios, and initial silica fraction. At salt concentrations > 10(-3) M, the electrostatic repulsion is reduced, and crystallization is suppressed. Crystals were preserved in a hydrogel matrix or inside a silicone rubber shell. This study demonstrates a robust path for controlled colloidal assembly inside double emulsion drops.

Asymmetric charge renormalization for nanoparticles in aqueous media

The effective renormalized charge of nanoparticles in an aqueous electrolyte is essential to determine their solubility. By using a molecular model for the supporting aqueous electrolyte, we find that the effective renormalized charge of the nanoparticles is strongly dependent on the sign of the bare charge. Negatively charged nanoparticles have a lower effective renormalized charge than positively charged nanoparticles. The degree of asymmetry is a nonmonotonic function of the bare charge of the nanoparticle. We show that the effect is due to the asymmetric charge distribution of the water molecules, which we model using a simple three-site molecular structure of point charges.

Size ratio effects on interparticle interactions and phase behavior of microsphere-nanoparticle mixtures

We investigate the interparticle interactions and phase behavior of microsphere-nanoparticle mixtures of high charge asymmetry and varying size ratio. In the absence of nanoparticles, negligibly charged microspheres flocculate as a result of van der Waals interactions. Upon addition of a lower critical nanoparticle volume fraction, the microspheres are stabilized by the formation of nanoparticle halos around each microsphere. , A weak attraction between the two species leads to a pronounced enhancement of the effective nanoparticle concentration near the microsphere surface relative to the bulk solution. Above an upper critical nanoparticle volume fraction, the microspheres undergo reentrant gelation. Binary mixtures, in which the effective nanoparticle size is reduced at a fixed microsphere diameter, exhibit a narrow window of stability that ultimately disappears with increasing ionic strength. By contrast, binary mixtures of varying microsphere diameter are stabilized at similar nanoparticle volume fractions and exhibit a broader window of stability with decreasing size ratio. This unexpected observation may arise from the reduced attraction between smaller microspheres because negligible differences in nanoparticle halo formation are observed in these mixtures.

Phase diagram for stimulus-responsive materials containing dipolar colloidal particles

Dipolar colloidal particles self-assemble into a rich variety of microstructures ranging from co-crystals of unusual symmetry, to open networks (gels) of cross-linked chains of particles. We use molecular dynamics computer simulation to explore the self-assembly, structure, crystallization and/or gelation of systems of colloid particles with permanent dipole moments immersed in a high-dielectric solvent. Particle-particle interactions are modeled with a discontinuous potential. The phase diagram in the temperature-packing fraction plane is calculated. Several types of phases are found in our simulations: ordered phases including face-centered-cubic, hexagonal-close-packed, and body-centered-tetragonal at high packing fractions, and fluid, string-fluid, and gel phases at low packing fractions. The very low volume fraction gel phases and the well-ordered crystal phases are promising for advanced materials applications.

Sedimentation in nano-colloidal dispersions: effects of collective interactions and particle charge

This is a review paper summarizing the progress of the development of colloidal sedimentation models for monodisperse, bidisperse, and polydisperse nanoparticle dispersions. This topic is of considerable interest because the sedimentation behavior of nanoparticles plays an important role in many practical systems, such as industrial coatings, optical products, ceramics, paints, dyes, and cosmetics. The limitations of various models are discussed. Multi-particle systems are highlighted, with a focus on the collective thermodynamic interactions resulting in the attractive depletion and repulsive structural forces. The effects of the particle concentration, particle charge, polydispersity in size, and electrolyte concentration on the sedimentation process are briefly summarized. Our contributions to this subject are reviewed.

Effects of organic ligands, electrostatic and magnetic interactions in formation of colloidal and interfacial inorganic nanostructures

This paper discusses effects of organic ligands, electrostatic and magnetic interactions involved in morphological control of chemically synthesized inorganic nanostructures including colloid and planar systems. The special attention was concentrated on noble metal (gold and palladium) nanoparticles and nanostructures formed at the gas-liquid interface. The analysis of experimental data showed that electrostatic and ligand-related interactions influence very strongly on the metal nanostructure morphology. The hydrophobicity of ligand, charge and binding affinity to inorganic phase are important factors influencing the morphology of inorganic nanostructures formed in a layer at the gas/liquid interface by the interfacial synthesis method. The important point of this method is the quasi two-dimensional character of reaction area and possibilities to realize ultimately thin and anisotropic dynamic monomolecular reaction system with two-dimensional diffusion and interactions of precursors, intermediates and ligands resulting in planar growth and organization of inorganic nanoparticles and nanostructures in the plain of Langmuir monolayer. The morphology of resulting inorganic nanostructures can be controlled efficiently by variations of growth conditions via changes in state and composition of interfacial planar reaction media with the same precursor, and by variations of composition of adjacent bulk phases. The extreme anisotropy and heterogeneity of two-dimensional interfacial reaction system allows creating conditions when growing inorganic particles floating on the aqueous phase surface interact selectively with hydrophobic water-insoluble ligands in interfacial monolayer or with hydrophilic bulk-phase ligands, or at the same time with ligands of different nature present in monolayer and in aqueous phase. The spatial anisotropy of interfacial reaction system and non-homogeneity of ligand binding to inorganic phase gives possibilities for growth of integrated anisotropic nanostructures with unique morphologies, in particularly those characterized by very high surface/volume ratio, high effective perimeter, and labyrinth-like structure. In a case of magnetic nanoparticles dispersed in colloids specific magnetic dipolar interactions can result in formation of chains, rings and more complex nanoparticulate structures or separated highly anisotropic nanoparticles. Theoretical considerations indicate to the importance of system dimensionality in relation to the energy balance which determines specific features of structure organization in planar charged metallic and magnetic nanostructures. For example, a requirement of Coulomb energy minimum, the possibility of free electron redistribution and strengthened attractive interactions between particles in metallic nanostructures can explain formation of very branchy systems with extremely high "effective perimeter". The obtained experimental and literature data show that system dimensionality, organic ligand nature along with electrostatic and magnetic interactions are most important factors of morphological control of chemically synthesized inorganic nanomaterials. The understanding and appropriate exploitation of these factors can be useful for further developments of efficient nanofabrication techniques based on colloidal and interfacial synthetic methods.

Simulation of phase transitions in highly asymmetric fluid mixtures

We present a novel method for the accurate numerical determination of the phase behavior of fluid mixtures having large particle-size asymmetries. By incorporating the recently developed geometric cluster algorithm within a restricted Gibbs ensemble, we are able to probe directly the density and concentration fluctuations that drive phase transitions, but that are inaccessible to conventional simulation algorithms. We develop a finite-size scaling theory that relates these density fluctuations to those of the grand-canonical ensemble, thereby enabling accurate location of critical points and coexistence curves of multicomponent fluids. Several illustrative examples are presented.

Effective interactions in mixtures of silica microspheres and polystyrene nanoparticles

We investigate the effect of small concentrations of highly charged nanoparticles on the stability of uncharged colloidal microspheres using large-scale simulations. Employing pair potentials that accurately represent mixtures of silica microspheres and polystyrene nanoparticles as studied experimentally, we are able to demonstrate that nanoparticle-induced stabilization can arise from a relatively weak van der Waals attraction between the colloids and nanoparticles. This demonstrates that the nanoparticle haloing mechanism for colloidal stabilization is of considerable generality and potentially can be applied to large classes of systems. The range of optimal nanoparticle concentrations can be tuned by controlling the attraction between colloids and nanoparticles.

Colloidal stabilization via nanoparticle halo formation

We present a detailed numerical study of effective interactions between micrometer-sized silica spheres, induced by highly charged zirconia nanoparticles. It is demonstrated that the effective interactions are consistent with a recently discovered mechanism for colloidal stabilization. In accordance with the experimental observations, small nanoparticle concentrations induce an effective repulsion that counteracts the intrinsic van der Waals attraction between the colloids and thus stabilizes the suspension. At higher nanoparticle concentrations an attractive potential is recovered, resulting in reentrant gelation. Monte Carlo simulations of this highly size-asymmetric mixture are made possible by means of a geometric cluster Monte Carlo algorithm. A comparison is made to results obtained from the Ornstein-Zernike equations with the hypernetted-chain closure.