Measurement of Absolute Coagulation Rate Constants for Colloidal Particles: Comparison of Single and Multiparticle Light Scattering Techniques

Extraordinary Destabilization of Silica Nanocolloids by Filtration

After silica nanoparticles in solutions were filtered by a syringe filter with a much larger pore size than the particle diameter D_p, the filtrated effects on the rapid coagulation rate in 1 M KCl solution, the dynamic light scattering diameter, and the zeta potential at pH ∼ 6 were investigated by employing the particles of two different sizes: S particles (D_p ∼ 50 nm) of silica and latex and L particles (D_p ∼ 300 nm) of silica. It was found that the hydrodynamic diameters of silica particles became a little smaller and the absolute values of their zeta potentials decreased significantly by filtration, but that is not the case for latex particles. As for the rapid coagulation rate, the value of silica S particles increased more than 2 orders of magnitude by filtration, but no significant difference was found in the case of silica L and latex S particles. From these data, it was postulated that the gel-like layer was removed from the surface of silica S particles by filtration and the existence of the gel-like layer resulted into about 2 orders of magnitude reduction of the rapid coagulation rate. The extraordinary reduction of rapid coagulation of silica particles at D_p < 150 nm was successfully estimated by the revised Smoluchowski theory, which we call the Higashitani-Mori (HM) model. It was also found that the rapid coagulation rate of filtrated particles decreased slowly with a decreasing particle size at D_p < ca. 250 nm, which was also estimated properly by the HM model, neglecting the contribution of the redispersion of coagulated particles. Another finding in this study was that the gel-like layers were recovered with time even if they were removed by filtration, although the detailed mechanism of this recovering is not known at present and left as a future problem.

Holographic characterization and tracking of colloidal dimers in the effective-sphere approximation

An in-line hologram of a colloidal sphere can be analyzed with the Lorenz-Mie theory of light scattering to measure the sphere's three-dimensional position with nanometer-scale precision while also measuring its diameter and refractive index with part-per-thousand precision. Applying the same technique to aspherical or inhomogeneous particles yields measurements of the position, diameter and refractive index of an effective sphere that represents an average over the particle's geometry and composition. This effective-sphere interpretation has been applied successfully to porous, dimpled and coated spheres, as well as to fractal clusters of nanoparticles, all of whose inhomogeneities appear on length scales smaller than the wavelength of light. Here, we combine numerical and experimental studies to investigate effective-sphere characterization of symmetric dimers of micrometer-scale spheres, a class of aspherical objects that appear commonly in real-world dispersions. Our studies demonstrate that the effective-sphere interpretation usefully distinguishes small colloidal clusters in holographic characterization studies of monodisperse colloidal spheres. The effective-sphere estimate for a dimer's axial position closely follows the ground truth for its center of mass. Trends in the effective-sphere diameter and refractive index, furthermore, can be used to measure a dimer's three-dimensional orientation. When applied to colloidal dimers transported in a Poiseuille flow, the estimated orientation distribution is consistent with expectations for Brownian particles undergoing Jeffery orbits.

Sedimentation Kinetics of Magnetic Nanoparticle Clusters: Iron Oxide Nanospheres vs Nanorods

A detailed study of the sedimentation kinetics of iron oxide nanoparticle (IONP) clusters composed of nanospheres and nanorods is presented. Measurements were performed to determine the absorbance of an IONP suspension undergoing sedimentation over time by using a UV-vis spectrophotometer with simultaneous monitoring of the hydrodynamic diameter of the clusters formed with dynamic light scattering (DLS). Mathematical analysis based on Happel's spherical and cylindrical models was conducted to reveal the relationship between the settling velocity of the IONP clusters and their packing density. For the case of IONP clusters composed of rodlike particles, two distinctive phases of sedimentation were recorded, with the occurrence of rapid sedimentation at the beginning of the process (phase I) followed by a slower settling rate (phase II). In sedimentation phase II, even though the nanorod clusters had a hydrodynamic size of >500 nm, which was much larger than that of the nanosphere clusters (∼200 nm), their settling velocity of 0.0038 mm/min was still slower than that of the nanosphere clusters. Such observations were mainly a result of the packing density differences between the formed clusters; due to the end-to-end particle interactions of nanorods, the nanorod clusters were less tightly packed and more permeable. In addition to the mathematical analysis, quartz crystal microbalance with dissipation (QCM-D) was employed to measure the "softness" of the IONP clusters formed, and this physical property can be further related to their packing density. This study illustrated that for a rapidly aggregating system, such as magnetic IONPs, not only do the particle shape and size uniformity contribute to the physical properties of the particle clusters formed but also the nature of the aggregation, either end-to-end and/or side-to-side, should be carefully considered when designing a colloidally stable IONP suspension.

Aggregation of Colloidal Particles in the Presence of Hydrophobic Anions: Importance of Attractive Non-DLVO Forces

Aqueous suspensions of amidine latex (AL) and sulfate latex (SL) particles containing sodium tetraphenylborate and NaCl are studied with electrokinetic and time-resolved light-scattering techniques. In monovalent salt solutions, AL is positively charged, whereas SL is negatively charged. Electrophoretic mobility measurements demonstrate that adsorption of tetraphenylborate anions leads to a charge reversal of AL particles. At higher concentrations, both types of particles accumulate negative charge. For AL particles, the charge reversal leads to a narrow fast aggregation region and an intermediate regime of slow aggregation. For SL particles, the intermediate slow regime is also observed. These aspects can be explained with classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO). Another regime of fast aggregation is observed at intermediate concentrations, and the existence of this regime can be rationalized by an additional attractive non-DLVO force. We suspect that this additional force is caused by surface charge heterogeneities.

Effect of polymer coating composition on the aggregation rates of Ag nanoparticles in NaCl solutions and seawaters

The aggregation behaviour of polymer-coated silver nanoparticles (AgNPs) was characterized in NaCl solutions, and in two seawaters of different salinities and dissolved organic matter (DOM) contents. Representative organic coatings i.e. tannic acid (TA), alginic acid (ALG), two gum Arabic samples (GAL and GAH), branched polyethylenimine (BPEI), and non-ionic surfactants (reference material NM-300K) were selected to cover a wide range of zeta-potentials. The stability in NaCl solutions, as determined from the rate of variation in hydrodynamic size within a timeframe of one hour, followed the order BPEI≫NM-300K≈GAL≫ALG≈TA≫GAH. In the seawater samples the order was NM-300K≈GAL≫ALG>GAH>TA≈BPEI, and only TA, GAL and NM-300K batches behaved as expected from the NaCl experiments. Remarkably, the BPEI sample showed the largest aggregation rate in the seawater sample with the highest DOM concentration (277μM C). The GAH sample displayed a non-monotonic variation in aggregation rate with NaCl concentration, apparently due to concomitant precipitation of AgCl. The results indicate that non-electrostatic stabilization mechanisms and DOM-coating interactions are important for the prediction of stability and persistence of polymer-coated AgNPs in seawater.

Ionic Specificity in Rapid Coagulation of Silica Nanoparticles

The Smoluchowski theory has been widely accepted as the basic theory to estimate the rapid coagulation rate of colloidal particles in electrolyte solutions. However, because the size and specificity of molecules and ions are not taken into account, the theory is applicable only if the particle size is large enough to neglect the effects caused by the structured layers composed of water molecules, ions, and hydrated ions adsorbed on the colloidal surface. In the present study, the rapid coagulation rates of silica nanoparticles in concentrated chloride and potassium solutions were measured by using a low-angle light-scattering apparatus, and the dependence of the experimental value of rapid coagulation rate, K_E^R, on the particle diameter, D_p, and also on the Gibbs free energy of hydration of ions, ΔG_hyd, was investigated extensively. The following were found. (1) When the particle size was small enough, the value of K_E^R reduced exponentially not only with the decreasing particle size but also with the increasing value of (-ΔG_hyd) of cations (counterions) in the case of chloride solutions and with that of anions (coions) in the case of potassium solutions. (2) Silica nanoparticles of D_p ≲ 70 nm in 1 M KNO₃ and KSCN solutions did not coagulate at all, although they coagulated at D_p ≳ 100 nm as in the other potassium solutions. These unexpected phenomena were explained by the proposed mechanisms.

Continuum-based models and concepts for the transport of nanoparticles in saturated porous media: A state-of-the-science review

Environmental applications of nanoparticles (NP) increasingly result in widespread NP distribution within porous media where they are subject to various concurrent transport mechanisms including irreversible deposition, attachment/detachment (equilibrium or kinetic), agglomeration, physical straining, site-blocking, ripening, and size exclusion. Fundamental research in NP transport is typically conducted at small scale, and theoretical mechanistic modeling of particle transport in porous media faces challenges when considering the simultaneous effects of transport mechanisms. Continuum modeling approaches, in contrast, are scalable across various scales ranging from column experiments to aquifer. They have also been able to successfully describe the simultaneous occurrence of various transport mechanisms of NP in porous media such as blocking/straining or agglomeration/deposition/detachment. However, the diversity of model equations developed by different authors and the lack of effective approaches for their validation present obstacles to the successful robust application of these models for describing or predicting NP transport phenomena. This review aims to describe consistently all the important NP transport mechanisms along with their representative mathematical continuum models as found in the current scientific literature. Detailed characterizations of each transport phenomenon in regards to their manifestation in the column experiment outcomes, i.e., breakthrough curve (BTC) and residual concentration profile (RCP), are presented to facilitate future interpretations of BTCs and RCPs. The review highlights two NP transport mechanisms, agglomeration and size exclusion, which are potentially of great importance in controlling the fate and transport of NP in the subsurface media yet have been widely neglected in many existing modeling studies. A critical limitation of the continuum modeling approach is the number of parameters used upon application to larger scales and when a series of transport mechanisms are involved. We investigate the use of simplifying assumptions, such as the equilibrium assumption, in modeling the attachment/detachment mechanisms within a continuum modelling framework. While acknowledging criticisms about the use of this assumption for NP deposition on a mechanistic (process) basis, we found that its use as a description of dynamic deposition behavior in a continuum model yields broadly similar results to those arising from a kinetic model. Furthermore, we show that in two dimensional (2-D) continuum models the modeling efficiency based on the Akaike information criterion (AIC) is enhanced for equilibrium vs kinetic with no significant reduction in model performance. This is because fewer parameters are needed for the equilibrium model compared to the kinetic model. Two major transport regimes are identified in the transport of NP within porous media. The first regime is characterized by higher particle-surface attachment affinity than particle-particle attachment affinity, and operative transport mechanisms of physicochemical filtration, blocking, and physical retention. The second regime is characterized by the domination of particle-particle attachment tendency over particle-surface affinity. In this regime although physicochemical filtration as well as straining may still be operative, ripening is predominant together with agglomeration and further subsequent retention. In both regimes careful assessment of NP fate and transport is necessary since certain combinations of concurrent transport phenomena leading to large migration distances are possible in either case.

Orders of Magnitude Reduction of Rapid Coagulation Rate with Decreasing Size of Silica Nanoparticles

The modification of the classical Smoluchowski theory for the rapid coagulation rate of colloidal particles, which takes account of the effect of the squeezing flow between colliding particles, has been widely accepted because it predicts experimental results adequately. However, it is not clear whether the modified theory, in which the coagulation rate is independent of the particle size, is applicable even to nanoparticles in solutions. In the present study, the rapid coagulation rates of silica particles in various 2 M chloride and 1 M potassium solutions were measured by using a low-angle light-scattering apparatus, and the dependence of rapid coagulation rate on the particle diameter, D_p, was investigated extensively. It was clearly shown that the rapid coagulation rate of spherical silica particles reduces by the orders of magnitude with decreasing particle size at D_p ≤ 300 nm, whereas it coincides with the value predicted by the modified theory at D_p ≥ 300 nm. A possible mechanism is proposed, and an analytical equation, which predicts the dramatic reduction in the rapid coagulation rate with decreasing particle size, is derived.

Probing effects of polymer adsorption in colloidal particle suspensions by light scattering as relevant for the aquatic environment: An overview

Modification of particle surfaces by adsorption of polymers is a process that governs particle behavior in aqueous environmental systems. The present article briefly reviews the current understanding of the adsorption mechanisms and the properties of the resulting layers, and it discusses two environmentally relevant cases of particle modification by polymers. In particular, the discussion focuses on the usefulness of methods based on light scattering to probe such adsorbed layers together with the resulting properties of the particle suspensions, and it highlights advantages and disadvantages of these techniques. Measurement of the electrophoretic mobility allows to follow the development of the adsorption layer and to characterize the charge of the modified particles. At saturation, the surface charge is governed by the charge of the adsorbed film. Dynamic light scattering provides information on the film thickness and on the behavior of the modified suspensions. The charge and the structure of the adsorbed layer influence the stability of the particles, as well as the applicability of the classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO). This fundamental knowledge is presented in the light of environmental systems and its significance for applied systems is underlined. In particular, the article discusses two examples of environmental processes involving adsorption of polymers, namely, the modification of particles by natural adsorption of humic substances and the tailoring of surface properties of iron-based particles used to remediate contaminated aquifers.

Enzyme-functionalized gold-coated magnetite nanoparticles as novel hybrid nanomaterials: synthesis, purification and control of enzyme function by low-frequency magnetic field

The possibility of remotely inducing a defined effect on NPs by means of electromagnetic radiation appears attractive. From a practical point of view, this effect opens horizons for remote control of drug release systems, as well as modulation of biochemical functions in cells. Gold-coated magnetite nanoparticles are perfect candidates for such application. Herein, we have successfully synthesized core-shell NPs having magnetite cores and gold shells modified with various sulphur containing ligands and developed a new, simple and robust procedure for the purification of the resulting nanoparticles. The carboxylic groups displayed at the surface of the NPs were utilized for NP conjugation with a model enzyme (ChT). In the present study, we report the effect of the low-frequency AC magnetic field on the catalytic activity of the immobilized ChT. We show that the enzyme activity decreases upon exposure of the NPs to the field.

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.

Combining spatially resolved hydrochemical data with in-vitro nanoparticle stability testing: assessing environmental behavior of functionalized gold nanoparticles on a continental scale

Many engineered nanoparticles (ENPs) are functionalized with different types of surface coatings to suit specific applications. The functionalization affects the fate and behavior of these ENPs in aquatic environments. In this study, gold nanoparticles (GNPs) coated with either citrate or 11-mercaptoundecanoic acid (MUA) are used as examples of functionalized ENPs. A method has been developed to assess the colloidal stability of functionalized ENPs under complex hydrochemical conditions, using their aggregation rates as indicators. The spatial distributions of stream-water chemistry data from across Europe were combined with the results of in-vitro colloidal stability testing. Aggregation rates were extracted for each stream-water sample and stability maps for Europe were plotted. The tendency of the tested GNPs to be dispersed or aggregated is described for water bodies of the respective region. Natural organic matter was identified as the predominant factor controlling the stability of the GNPs tested. The properties of surface coatings also affect aggregation rates as a result of differences in their hydrochemical parameters. The developed method can be used as a template for a stability assessment, and the results of this study provide a basis for exposure modeling and precautionary decision making.

Quantitative interpretation of anomalous coagulation behavior of colloidal silica using a swellable polyelectrolyte gel model of electrical double layer

Electrolyte-induced coagulation of colloidal dispersions of silica has remained a puzzle for many decades, and it is widely considered anomalous from the viewpoint of traditional Gouy-Chapman theory of diffuse double layer and ζ-potential at ideal surfaces and of their electrostatic interaction (Derjaguin-Landau-Verwey-Overbeek, DLVO theory). It is suggested that this anomaly is caused by the fact that silica particles are covered with swellable gel layers. Theoretical stability ratios are calculated combining the attractive van der Waals and repulsive electrosteric interactions between core-shell (soft) model spheres with homogeneously distributed fixed charges in the shells and matched with the experimental ones measured for nonporous silica microspheres of different diameters (50, 150, and 320 nm) in an univalent electrolyte (KCl) of increasing concentration and pH (2.6, 4, 6, and 8). The variation in the shell thickness with the KCl concentration (mimicking the charged gel layer swelling) as the only adjustable parameter, deduced in such a way from data at pH 6 and 8, not only can explain the parallel experimental electrophoretic mobilities but also conforms itself to a scaling law derived from the thermodynamic theory of polyelectrolyte hydrogels. A resulting inapplicability of the DLVO theory and the ζ-potential concept for a quantitative predicting the coagulation kinetics of gel layer-covered colloids is discussed.

Poisson-Boltzmann description of interaction forces and aggregation rates involving charged colloidal particles in asymmetric electrolytes

Forces and aggregation rates involving spherical particles are studied numerically within the theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO) for asymmetric and mixed electrolytes. Thereby, the double layer interactions are treated at the Debye-Hückel (DH) and Poisson-Boltzmann (PB) levels. The DH model is applicable for weakly charged systems, and effects of ion valence enter only implicitly through the ionic strength. The PB model is necessary for more highly charged systems, and depends on the actual ionic composition. One finds that forces in asymmetric electrolytes at fixed ionic strength weaken when the valence of the counterions is increased or when the valence of the coions is decreased. In symmetric electrolytes, the effect of counterions is more important than the one of the coions. For weakly charged systems, the critical coagulation concentration (CCC) decreases with the square of the valence in symmetric electrolytes, while this decrease is weaker in asymmetric ones. With increasing charge density, the dependence of the CCC on the valence becomes stronger, but the classical Schulze-Hardy decrease with the sixths power of the valence is only recovered for unrealistically high charge densities. Mixtures of electrolytes are treated within the same framework, and one observes that already small amounts of multivalent ions affect the system considerably. An empirical mixing rule is proposed to describe the calculated CCCs.

Mechanistic heteroaggregation of gold nanoparticles in a wide range of solution chemistry

Heteroaggregation behavior of gold nanospheres (AuNS) in presence of pluronic acid (PA) modified single-walled carbon nanotubes (PA-SWNTs) was systematically studied for a wide range of mono- and divalent (NaCl and CaCl(2)) electrolyte conditions. Homoaggregation rates of AuNS were also determined to delineate heteroaggregation mechanisms. Time resolved dynamic light scattering (DLS) was employed to monitor aggregation. The homoaggregation of AuNS showed classical Derjaguin-Landau-Verwey-Overbeek (DLVO) type behavior with defined reaction limited (RLCA) and diffusion limited (DLCA) aggregation regimes. PA-SWNTs homoaggregation on the one hand showed no response with electrolyte increase. AuNS heteroaggregation rates on the other hand, showed regime dependent response. At low electrolyte or RLCA regime, AuNS heteroaggregation showed significantly slower rates, compared to its homoaggregation behavior; whereas enhanced heteroaggregation was observed for DLCA regime. The key mechanisms of heteroaggregation of AuNS are identified as obstruction to collision at RLCA regime and facilitating enhanced attachment at DLCA regime manifested by the presence of PA-SWNTs. Presence of Suwannee River humic acid (SRHA) showed aggregation enhancement for both homo- and hetero-systems, in presence of divalent Ca(2+) ions. Bridging between SRHA molecules is identified as the key mechanism for increased aggregation rate. The findings of this study are relevant particularly to coexistence of engineered nanomaterials. The strategy of using nonaggregating PA-SWNTs is a novel experimental strategy that can be adopted elsewhere to further the heteroaggregation studies for a wider set of particles and surface coatings.

Nanoemulsion stability: experimental evaluation of the flocculation rate from turbidity measurements

The coalescence of liquid drops induces a higher level of complexity compared to the classical studies about the aggregation of solid spheres. Yet, it is commonly believed that most findings on solid dispersions are directly applicable to liquid mixtures. Here, the state of the art in the evaluation of the flocculation rate of these two systems is reviewed. Special emphasis is made on the differences between suspensions and emulsions. In the case of suspensions, the stability ratio is commonly evaluated from the initial slope of the absorbance as a function of time under diffusive and reactive conditions. Puertas and de las Nieves (1997) developed a theoretical approach that allows the determination of the flocculation rate from the variation of the turbidity of a sample as a function of time. Here, suitable modifications of the experimental procedure and the referred theoretical approach are implemented in order to calculate the values of the stability ratio and the flocculation rate corresponding to a dodecane-in-water nanoemulsion stabilized with sodium dodecyl sulfate. Four analytical expressions of the turbidity are tested, basically differing in the optical cross section of the aggregates formed. The first two models consider the processes of: a) aggregation (as described by Smoluchowski) and b) the instantaneous coalescence upon flocculation. The other two models account for the simultaneous occurrence of flocculation and coalescence. The latter reproduce the temporal variation of the turbidity in all cases studied (380≤[NaCl]≤600 mM), providing a method of appraisal of the flocculation rate in nanoemulsions.

Influence of the degree of ionization and molecular mass of weak polyelectrolytes on charging and stability behavior of oppositely charged colloidal particles

Positively charged amidine latex particles are studied in the presence of poly(acrylic acid) (PAA) with different molecular masses under neutral and acidic conditions by electrophoresis and time-resolved dynamic light scattering. Under neutral conditions, where PAA is highly charged, the system is governed by the charge reversal induced by the quantitatively adsorbing polyelectrolyte and attractive patch-charge interactions. Under acidic conditions, where PAA is more weakly charged, the following two effects come into play. First, the lateral structure of the adsorbed layers becomes more homogeneous, which weakens the attractive patch-charge interactions. Second, polyelectrolyte adsorption is no longer quantitative and partitioning into the solution phase is observed, especially for PAA of low molecular mass.

Stability behavior of anionic spherical polyelectrolyte brushes in the presence of La(III) counterions

In this paper we discuss the stability behavior of spherical polyelectrolyte brushes (SPB) in the presence of trivalent lanthanum counterions. Stability behavior is measured through the rate of coagulation of the SPB as a function of the lanthanum concentration using simultaneous static and dynamic light scattering. As the counterion concentration increases, we observe coagulation of the SPB which in turn leads to a dramatic decrease in the stability of our particles. Since the rate of coagulation is dependent upon the balance between the repulsive interactions and the thermal energy of the diffusing particles (reaction-limited colloidal aggregation; RLCA), we then can relate the measured particle stability to the value of the repulsive potential in the RLCA regime. These "microsurface potential measurements" (MSPM) allow us to measure repulsive energies down to the order of k(B)T. From the repulsive energy of the particles we can then determine precise information about the net surface potential Ψ0 of the SPB as a function of the lanthanum counterion concentration. Moreover, we demonstrate that a simple mean-field model predicts the stability of the SPB in the presence of lanthanum counterions with high accuracy.

Electrostatic heteroaggregation regimes in colloidal suspensions

Despite of their importance for many industrial applications and the understanding of natural phenomena, heteroaggregation processes have not been in the focus of attention of the scientific community until quite recently. Still nowadays, their tremendously complex nature turns a detailed experimental and theoretical treatment of these processes into a difficult task. Hence, we have limited the scope of this review to electrostatic heteroaggregation arising in symmetric two-component systems, i.e., those with the same concentration of cationic and anionic particles. The short and long-time aggregation kinetics will be addressed not only from an experimental but also from a theoretical and simulation point of view at almost six orders of magnitude of electrolyte concentration. The different aggregation regimes will be identified and described in detail.

Polysilazane-induced aggregation of hydrophobic silver colloids

Adsorbing polymers such as polysilazanes induce irreversible coagulation of hydrophobic silver colloids in nonpolar solvents. This is accompanied by broadening of the surface plasmon resonance (SPR) peak. A method to analyze the coagulation kinetics based on von Smoluchowski's theory utilizing the SPR change is described. The approach allows evaluating extinction spectra of aggregates of small sizes. A model for polymer adsorption kinetics in combination with a modified bridging efficiency model explains the observed coagulation inhibition over time in terms of macromolecules adsorption, spreading, and mutual repulsion.

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.

Effects of heat treatment on the aggregation and charging of Stöber-type silica

Colloidal silica is known to be stable at high salt concentrations and low pH, where silica is basically uncharged. This observation is in qualitative disagreement with the theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO), which predicts rapid aggregation (or coagulation) under these conditions. This study reports a very different behaviour for Stöber-type silica heated at 800 degrees C, as these particles follow DLVO theory quantitatively. Unheated samples behave approximatively according to DLVO theory, but they show systematic deviations, in particular, featuring higher stability at low pH. The heat treatment also substantially modifies the charging properties, as heated particles show titratable surface charge densities in the range expected for the water-silica interface, while much higher charge densities are observed for the unheated samples. The electrophoretic mobilities, on the other hand, are hardly influenced by the heat treatment. We suspect that the suspension stability of the unheated particles is influenced by the presence of a hairy-layer of polysilicilic acid chains on the surface.

Formation and structure of stable aggregates in binary diffusion-limited cluster-cluster aggregation processes

Binary diffusion-limited cluster-cluster aggregation processes are studied as a function of the relative concentration of the two species. Both, short and long time behaviors are investigated by means of three-dimensional off-lattice Brownian Dynamics simulations. At short aggregation times, the validity of the Hogg-Healy-Fuerstenau approximation is shown. At long times, a single large cluster containing all initial particles is found to be formed when the relative concentration of the minority particles lies above a critical value. Below that value, stable aggregates remain in the system. These stable aggregates are composed by a few minority particles that are highly covered by majority ones. Our off-lattice simulations reveal a value of approximately 0.15 for the critical relative concentration. A qualitative explanation scheme for the formation and growth of the stable aggregates is developed. The simulations also explain the phenomenon of monomer discrimination that was observed recently in single cluster light scattering experiments.

Role of the secondary minimum on the flocculation rate of nondeformable droplets

The kinetic stability of suspensions is usually associated with a decrease in the flux of flocculating particles due to the action of a repulsive potential. However, previous calculations on bitumen drops suggest the possible occurrence of relatively fast aggregation rates in systems with large electrostatic barriers for primary minimum flocculation. This indicates a strong effect of the secondary minimum in the process of aggregation. Here, emulsion stability simulations (ESS) are used to study the aggregation behavior of 11 systems showing different depths of the secondary minimum and three particle sizes. Micron size drops (as those of Bitumen emulsions) usually exhibit deep secondary minima, which rarely occur between nanometer size particles. At high surfactant concentrations, these drops do not coalesce but can still show fast aggregation rates caused by irreversible secondary-minimum flocculation. On the other hand, the extent of coalescence in nanometer-size systems markedly depends on the height of the repulsive barrier. Furthermore, the secondary minimum of these smaller particles is usually shallow, causing reversible aggregation or no aggregation at all. In this article, the consequences of the referred behaviors on the magnitude of the stability ratio are discussed.

Aggregation and charging of colloidal silica particles: effect of particle size

We studied systematically aqueous suspensions of amorphous well-characterized silica particles by potentiometric titration, electrophoretic mobility, and time-resolved light scattering. Their charging behavior and aggregation rate constants were measured as a function of pH and ionic strength in KCl electrolytes for three types of particles of approximately 30, 50, and 80 nm in diameter. The charging behavior was consistent with the basic Stern model; the silica particles carry a negative charge, and its magnitude gradually increases with increasing pH and ionic strength. On the other hand, their early-stage aggregation (or coagulation) behavior is complex. The aggregation of the largest particles shows features resembling predictions of the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory. On one hand, the rate constant decreases sharply with increasing pH at low ionic strengths and attains fast aggregation conditions at high ionic strengths. On the other hand, we observe a characteristic slowing down of the aggregation at low pH and high ionic strengths. This feature becomes very pronounced for the medium and the small particles, leading to a complete stabilization at low pH for the latter. Stabilization is also observed at higher pH for the medium and the small particles. From these aggregation measurements we infer the existence of an additional repulsive force. Its origin is tentatively explained by postulating hairy layers of consisting of poly(silicilic acid) chains on the particle surface.

Calculation of flocculation and coalescence rates for concentrated dispersions using emulsion stability simulations

A simple procedure for the quantification of flocculation (k(f)) and coalescence (k(c)) rates from emulsion stability simulations (ESS) of concentrated systems is presented. It is based on a simple analytical equation, which results from the sum of well-known formulas for the separate processes of flocculation and coalescence. The expression contains k(f) and k(c) as fitting parameters and is found to reproduce the behavior predicted by ESS spanning a wide range of volume fractions (1 < phi < 30%) and surfactant concentrations (1.2 x10(-5) < C < 1.2 x 10(-4) M). This procedure allows interpretation of ESS data in terms of the referred kinetic rates. Furthermore, it could also provide an additional mean for the direct comparison of the simulation data with experimental results.

Absolute aggregation rate constants in aggregation of kaolinite measured by simultaneous static and dynamic light scattering

The aggregation rate was determined for the < 0.2 microm size fraction of kaolinite (KGa-2) using simultaneous static and dynamic light scattering at pH 9.5. It was found that method suggested by Holthoff et al. [Langmuir 1996, 12, 5541] is suitable for determination of the absolute aggregation rate constant of a clay dispersion without using the particle optical factors. The determined fast aggregation rate constant is k11,fast = (3.7 +/- 0.2) x 10(-18) m3 s(-1). Stability behavior of kaolinite colloids was studied as a function of concentration of sodium chloride by simultaneous static and dynamic scattering. The critical aggregation concentration was found to be 0.085 +/- 0.005 mol dm(-3). When calculating the relationship between the stability ratio and the electrolyte concentration using the DLVO theory, the best fit to the experimental data was achieved with a Hamaker constant of A = (4.7 +/- 0.2) x 10(-20) J.

Effect of dynamic surfactant adsorption on emulsion stability

The effect of dynamic surfactant adsorption on the stability of concentrated oil in water emulsions is studied. For this purpose, a modification of the standard Brownian dynamics algorithm (Ermak, D.; McCammon, J. A. J. Chem. Phys. 1978, 69, 1352) previously used to study the behavior of bitumen emulsions assuming instantaneous adsorption (Urbina-Villalba, G.; García-Sucre, M. Langmuir 2000, 16, 7975) was employed. In the present case, dynamic adsorption (DA) was accounted for through a time-dependent electrostatic repulsion between the drops, a function of the surfactant surface excess. The surface excess was allowed to evolve with time according to well-established analytical expressions which depend parametrically on the surfactant diffusion constant (Ds) and the total surfactant concentration (C). The investigation required appropriate incorporation of hydrodynamic interactions in concentrated systems. This was achieved through a novel methodology, which expresses the diffusion constant of each particle as a function of its local concentration and the shortest distance of separation between nearest neighbors. In model systems, the variation of the number of drops as a function of time was followed for different magnitudes of the apparent diffusion constant D(app) of the surfactant. For each of these values, the effect of C and the volume fraction of internal phase (phi) was considered. DA was found to influence emulsion stability appreciably at moderately high phi. In this case, the average collision time between drops is comparable to the time required for the occurrence of a substantial surfactant adsorption, but the interdrop separation is sufficiently large to prevent a considerable slowdown of particle movement due to hydrodynamic interactions.

Structure of peptide solutions: a light scattering and numerical study

We investigated the interactions between protein molecules in solution, in particular for low salt concentrations and thus strong electrostatic interactions where a treatment based on the second virial coefficient is not sufficient. Static and dynamic light scattering experiments on solutions containing the peptide human calcitonin (hCT) were combined with calculations based on the Ornstein-Zernike equation with the hypernetted chain (HNC) closure and computer simulations within the primitive electrolyte model. The simulation illustrates the distribution of proteins in solution and the formation of (transient) protein aggregates. It furthermore allows us to predict the physical stability of hCT solutions in dependence of ionic strength, pH and hCT concentration.

Cluster discrimination in electrostatic heteroaggregation processes

Electrostatic heteroaggregation processes arising in 1:1 mixtures of oppositely charged microspheres at low and very low electrolyte concentrations were investigated by means of single-cluster light scattering. Cluster discrimination, i.e., the fact that clusters differing by only one constituent particle behave quite differently, was found for monomers and dimers. This effect was recently predicted by Brownian dynamic simulations but, to the best of our knowledge, not yet confirmed by experiments. The experimental data were confronted with the simulations and a good qualitative and quantitative agreement was obtained. The origin of the cluster discrimination phenomenon could be related to the range of the attractive electrostatic interactions.

Average hydrodynamic correction for the Brownian dynamics calculation of flocculation rates in concentrated dispersions

In order to account for the hydrodynamic interaction (HI) between suspended particles in an average way, Honig et al. [J. Colloid Interface Sci. 36, 97 (1971)] and more recently Heyes [Mol. Phys. 87, 287 (1996)] proposed different analytical forms for the diffusion constant. While the formalism of Honig et al. strictly applies to a binary collision, the one from Heyes accounts for the dependence of the diffusion constant on the local concentration of particles. However, the analytical expression of the latter approach is more complex and depends on the particular characteristics of each system. Here we report a combined methodology, which incorporates the formula of Honig et al. at very short distances and a simple local volume-fraction correction at longer separations. As will be shown, the flocculation behavior calculated from Brownian dynamics simulations employing the present technique, is found to be similar to that of Batchelor's tensor [J. Fluid. Mech. 74, 1 (1976); 119, 379 (1982)]. However, it corrects the anomalous coalescence found in concentrated systems as a result of the overestimation of many-body HI.