Simulations of latex particles immersed in dendrimer solutions

Nanoplatelet interactions in the presence of multivalent ions: The effect of overcharging and stability

HYPOTHESIS

The stability of colloidal dispersions in the presence of multivalent ions depends strongly on the electrostatic interactions between the suspended particles. Of particular interest are colloidal particles having dimensions in the nanometric range and with an anisotropic shape due to its high surface area per unit mass, for example clay, which has the key characteristic of a negatively charged surface, surrounded by an oppositely charged rim.

EXPERIMENTS

In this study, we investigate the interactions in nanoplatelet dispersions for the model system of Laponite® clay with addition of mono- and multivalent salt. Molecular dynamics simulations with enhanced umbrella sampling have been utilised in combination with the experimental techniques of zeta-potential measurements, dynamic light scattering, and transmission electron microscopy.

FINDINGS

It was observed that tactoid formation and tactoidal dissolution due to overcharging occur upon the addition of trivalent salt. The overcharging effect was captured from calculated potential of mean force and confirmed from the zeta-potential, which changed sign from negative to positive when increasing the stoichiometric charge-ratio between the positive salt ions and the clay. Consequently, the gained information could provide useful physical insight of nanoplatelet interactions in the presence of multivalent ions.

Modeling the assembly of oppositely charged lock- and key-colloids

The interaction of oppositely charged lock- and key-colloids is investigated using computer simulations. We show that indented spheres, i.e., lock-particles, can be specifically assembled with spherical key-particles using solely electrostatic interactions in addition to a hard overlap potential. An analytic description of the entropic and energetic contributions is derived and supported by simulations and explicit energy calculations, respectively. The analytic expression of the electrostatic contribution is further employed to build up a schematic model allowing for efficient large-scale Monte Carlo simulations. The influence of the charge/ionic strength, the degree of indentation, and the size/number ratio is discussed by analyzing the specific and unspecific associations from the simulations. Herein, both particle design and mixing conditions lead to the formation of stable specific clusters analogous to colloidal molecules whose valence is defined by the number of lock-particles associated with a key-particle. In addition, the approach is extended to the encapsulation of an excess of small key-particles in largely indented lock-particles. These two examples exemplify that highly specific pairwise interactions can be implemented by using solely oppositely charged particles with complementary geometries, which opens the road for a rational design of complex hierarchical self-assemblies of complementary building blocks.

Polyelectrolyte adsorption, interparticle forces, and colloidal aggregation

This review summarizes the current understanding of adsorption of polyelectrolytes to oppositely charged solid substrates, the resulting interaction forces between such substrates, and consequences for colloidal particle aggregation. The following conclusions can be reached based on experimental findings. Polyelectrolytes adsorb to oppositely charged solid substrates irreversibly up to saturation, whereby loose and thin monolayers are formed. The adsorbed polyelectrolytes normally carry a substantial amount of charge, which leads to a charge reversal. Frequently, the adsorbed films are laterally heterogeneous. With increasing salt levels, the adsorbed mass increases leading to thicker and more homogeneous films. Interaction forces between surfaces coated with saturated polyelectrolyte layers are governed at low salt levels by repulsive electric double layer interactions, and particle suspensions are stable under these conditions. At appropriately high salt levels, the forces become attractive, principally due to van der Waals interactions, but eventually also through other forces, and suspensions become unstable. This situation can be rationalized with the classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO). Due to the irreversible nature of the adsorption process, stable unsaturated layers form in colloidal particle suspensions at lower polyelectrolyte doses. An unsaturated polyelectrolyte layer can neutralize the overall particle surface charge. Away from the charge reversal point, electric double layer forces are dominant and particle suspensions are stable. As the charge reversal point is approached, attractive van der Waals forces become important, and particle suspensions become unstable. This behaviour is again in line with the DLVO theory, which may even apply quantitatively, provided the polyelectrolyte films are sufficiently laterally homogeneous. For heterogeneous films, additional attractive patch-charge interactions may become important. Depletion interactions may also lead to attractive forces and suspension destabilization, but such interactions become important only at high polyelectrolyte concentrations.

Coalescence of repelling colloidal droplets: a route to monodisperse populations

Populations of droplets or particles dispersed in a liquid may evolve through Brownian collisions, aggregation, and coalescence. We have found a set of conditions under which these populations evolve spontaneously toward a narrow size distribution. The experimental system consists of poly(methyl methacrylate) (PMMA) nanodroplets dispersed in a solvent (acetone) + nonsolvent (water) mixture. These droplets carry electrical charges, located on the ionic end groups of the macromolecules. We used time-resolved small angle X-ray scattering to determine their size distribution. We find that the droplets grow through coalescence events: the average radius (R) increases logarithmically with elapsed time while the relative width σR/(R) of the distribution decreases as the inverse square root of (R). We interpret this evolution as resulting from coalescence events that are hindered by ionic repulsions between droplets. We generalize this evolution through a simulation of the Smoluchowski kinetic equation, with a kernel that takes into account the interactions between droplets. In the case of vanishing or attractive interactions, all droplet encounters lead to coalescence. The corresponding kernel leads to the well-known "self-preserving" particle distribution of the coalescence process, where σR/(R) increases to a plateau value. However, for droplets that interact through long-range ionic repulsions, "large + small" droplet encounters are more successful at coalescence than "large + large" encounters. We show that the corresponding kernel leads to a particular scaling of the droplet-size distribution-known as the "second-scaling law" in the theory of critical phenomena, where σR/(R) decreases as 1/√(R) and becomes independent of the initial distribution. We argue that this scaling explains the narrow size distributions of colloidal dispersions that have been synthesized through aggregation processes.

Investigating forces between charged particles in the presence of oppositely charged polyelectrolytes with the multi-particle colloidal probe technique

Direct force measurements are used to obtain a comprehensive picture of interaction forces acting between charged colloidal particles in the presence of oppositely charged polyelectrolytes. These measurements are achieved by the multi-particle colloidal probe technique based on the atomic force microscope (AFM). This novel extension of the classical colloidal probe technique offers three main advantages. First, the technique works in a colloidal suspension with a huge internal surface area of several square meters, which simplifies the precise dosing of the small amounts of the polyelectrolytes needed and makes this approach less sensitive to impurities. Second, the particles are attached in-situ within the fluid cell, which avoids the formation of nanobubbles on the latex particles used. Third, forces between two similar particles from the same batch are being measured, which allows an unambiguous determination of the surface potential due to the symmetry of the system. Based on such direct force measurements involving positively and negatively charged latex particles and different polyelectrolytes, we find the following forces to be relevant. Repulsive electrostatic double-layer forces and attractive van der Waals forces as described by the theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO) are both important in these systems, whereby the electrostatic forces dominate away from the isoelectric point (IEP), while at this point they vanish. Additional non-DLVO attractive forces are operational, and they have been identified to originate from the electrostatic interactions between the patch-charge heterogeneities of the adsorbed polyelectrolyte films. Highly charged polyelectrolytes induce strong patch-charge attractions, which become especially important at low ionic strengths and high molecular mass. More weakly charged polyelectrolytes seem to form more homogeneous films, whereby patch-charge attractions may become negligible. Individual bridging events could be only rarely identified from the retraction part of the force profiles, and therefore we conclude that bridging forces are unimportant in these systems.

Polyelectrolyte mediated interactions in colloidal dispersions: hierarchical screening, simulations, and a new classical density functional theory

The pair interaction between two charged colloidal particles, in the presence of a polyelectrolyte as well as simple salt, is analyzed theoretically. Of particular interest is the way in which such a combination of salts can be used to induce a strong, long-range attraction, with at most a minor free energy barrier. We show that the nature of the simple salt is highly relevant, i.e., 2:1, 1:1, and 1:2 salts generate quite different particle interaction free energies at the same overall ionic strength. We adopt several different theoretical levels of description. Defining simulations at the primitive model level with explicit simple salt as our reference, we invoke stepwise coarse-graining with careful evaluations of each approximation. Representing monovalent simple ions by the ionic screening they generate is one such simplification. In order to proceed further, with additional computational savings, we also develop a correlation-corrected classical density functional theory. We analyze the performance of this theory with explicit spherical particles as well as in a flat surface geometry, utilizing Derjaguin's approximation. The calculations are particularly fast in the latter case, facilitating computational savings of many (typically 5-7) orders of magnitude, compared to corresponding simulations with explicit salt. Yet, the predictions are remarkably accurate, and considering the crudeness of the model itself, the density functional theory is a very attractive alternative to simulations.

Long-ranged attractive forces induced by adsorbed dendrimers: direct force measurements and computer simulations

Interaction forces between charged interfaces in the presence of oppositely charged dendrimers are studied by experiment and simulation. The experiments involve direct force measurements with an atomic force microscope (AFM) between two negatively charged colloidal particles in the presence of adsorbed, positively charged globular dendrimers. The simulations are carried out by treating the macroions explicitly, while the small salt ions are treated implicitly through the Debye-Huckel approximation. The system undergoes overcharging, and at the isoelectric point long-ranged attractive electrostatic forces are present. The range of the attraction is on the order of half the Debye length at high salt concentration, but it becomes smaller at low salt concentration. Away from the isoelectric point, repulsive electrostatic forces are observed due to diffuse layer overlap. A semiquantitative agreement between experiment and simulation is obtained, despite the fact that the simple theoretical model does not involve any adjustable parameters. This study provides for the first time detailed comparison between experimental and simulation data of interaction forces between colloidal particles in the presence of multivalent macroions and monovalent salt ions.