Kinetics of salt-induced aggregation in polystyrene lattices studied by quasielastic light scattering

Dependence of fractal dimension of DLCA clusters on size of primary particles

It is well known that clusters generated from colloidal aggregation driven by Brownian motion are typical fractal objects with the fractal dimension in the range of 1.75-1.85 under the diffusion-limited cluster aggregation (DLCA) conditions. In this work, we review and analyze the values of the fractal dimension for DLCA clusters experimentally determined in the literature. It is found that the value of the fractal dimension decreases significantly as the primary particle radius increases. Then, we have properly designed the DLCA experiments, using different radii of the primary particles, and determined the fractal dimensions of the generated clusters. Our results have well confirmed that the fractal dimension indeed decreases as the particle radius increases. To explore the mechanism leading to such dependence, we have performed intense computations through the full T-Matrix theory, and we conclude that this is not related to the effect of the intra-cluster multiple scattering on the slope of the scattering structure factor. The large fractal dimensions of the clusters generated by very small nanoparticles could be explained by thermal restructuring due to their low bonding energies, but no clear explanation can be given for the small fractal dimensions of the clusters made of large particles.

Study of colloidal particle Brownian aggregation by low-coherence fiber optic dynamic light scattering

The aggregation kinetics of particles in dense polystyrene latex suspensions is studied by low-coherence fiber optic dynamic light scattering. Low-coherence fiber optic dynamic light scattering is used to measure the hydrodynamic radius of the aggregates. The aggregation kinetics data obtained can be fitted into a single exponential function, which is the characteristic of slow aggregation. It is found that the aggregation rate of particles increased with higher electrolyte levels and with larger particle concentrations. The experimental results can be explained by use of the Derjaruin-Landau-Verwey-Overbeer (DLVO) theory.

Effect of surface properties of elastomer colloids on their coalescence and aggregation kinetics

We study the aggregation kinetics of two elastomer colloids with similar bulk polymer properties but with different surface charge groups in order to understand the role of the surface properties in particle coalescence during aggregation. It is confirmed that clusters of the elastomer particles stabilized purely by ionic surfactants coalesce in both reaction-limited and diffusion-limited aggregation (RLCA and DLCA) regimes and that the coalescence is independent of the coagulant type. On the other hand, clusters formed by elastomer particles stabilized by charged polymer end groups, which are fixed on the particle surface, are fractal objects with a fractal dimension of 1.7 in the DLCA and 2.1 in the RLCA regime. This indicates insignificant cluster coalescence during aggregation, most likely due to a hindrance effect of the fixed charges.

Monitoring particle aggregation processes

A wide range of test methods for monitoring particle aggregation processes is reviewed. These include techniques for measuring aggregation rates in fundamental studies and those which are useful in the monitoring and control of practical coagulation/flocculation processes. Most emphasis is on optical methods, including light transmission (turbidity) and light scattering measurements and the fundamentals of these phenomena are briefly introduced. It is shown that in some cases, absolute aggregation rates can be derived. However, even when only relative rates can be obtained, these can still be very useful, for instance in defining optimum flocculation conditions. Some of the methods available for investigating properties of aggregates (flocs), such as size, strength and fractal dimension are also discussed, along with some related properties such as sedimentation rate and filterability of flocculated suspensions.

Aggregate restructuring by polymer solvency effects

This study investigates the aggregation in cyclohexane of silica particles initially stabilized by grafted polystyrene and destabilized by temperature reduction. It complements an earlier study by Zhu and Napper (P.W. Zhu, D.H. Napper, Phys. Rev. E 50 (1994) 1360) in which the aggregation of polystyrene latex particles with tethered poly(N-isopropyl acrylamide) (PNIPAM) in water was investigated. Their dynamic light scattering results showed that both the rate of aggregation and the aggregate fractal dimension increased with a sufficient decrease in the PNIPAM adlayer solvency, achieved by means of either salt (NaNO3) addition or temperature rise. This result stands in contrast to those obtained when an electrostatically stabilized colloid is destabilized, i.e., that the more rapidly aggregates are formed, the lower the resulting fractal dimension. The authors explained their results in terms of the effects of both salt effects and increased temperature on the extent of the hydrophobic interactions between the adlayer-covered surfaces in the water. The present study examines a sterically-stabilized colloid in a nonaqueous solvent, where neither salt effects nor hydrophobic effects play a role. Temperature is decreased to bring the system from better-than-theta-conditions to worse-than-theta-conditions. Power-law aggregation kinetics are observed at 15.7 degrees C by dynamic light scattering. The particles first undergo reduced rate aggregation, producing low-fractal-dimension aggregates, which after some time, restructure into more compact aged clusters. The fractal dimension of these aged clusters increases with increasing initial aggregation rate, consistent with results seen by Zhu and Napper, but without the presence of hydrophobic effects. The ability of the polymer-grafted particles to rearrange suggests aggregation into a secondary minimum, with the ability to slide over one another to achieve a more energetically favorable, denser configuration. The reversible nature of the aggregation is verified by additional experiments gradually bringing the system from worse-than-theta-conditions back to better-than-theta-conditions, with an attendant decrease in aggregate fractal dimension, and ultimately full redispersion.

Time evolution of the formation of different size cationic liposome-polyelectrolyte complexes

We report on the time evolution of the aggregation behaviour of cationic liposome-polyelectrolyte complexes studied by means of dynamic light scattering technique. Pure dioleoyltrimethilammoniumpropane (DOTAP) and mixed DOTAP-dipalmitoylphosphatidylcholine (DPPC) liposomes in polyacrylate sodium salt aqueous solutions in a wide concentration range have been investigated and the size and size distributions of the resulting aggregates evaluated from the intensity autocorrelation function of the scattered light. Under appropriate conditions, we found two discrete aggregation regimes, resulting in two different structural arrangements, whose time evolution depends on the charge ratio and the polyelectrolyte molecular weight. A first small component of average size in the 100-500 range nm coexists with a larger component, whose typical size increases with time, up to some micrometers. The cluster growth from a single liposome, 70 nm in diameter, to the formation of polymer-coated liposome aggregates has been briefly discussed in the light of steric stabilization of colloids. Moreover, it has been found that the kinetics of aggregation of the larger, time-dependent, component follows a dynamical scaling within the diffusion-limited cluster aggregation (DLCA) regime. The understanding of structures resulting from interactions between polyelectrolytes with oppositely charged liposomes may help towards formulation of "lipoplexes" (cationic lipid-DNA complexes) to use as non-viral gene carriers.

Clustering under short-range finite interactions

In this paper the aggregation of surface modified colloidal particles is presented, paying special attention to the cluster structure and growth. The surface was modified by adsorbing bovine serum albumin (BSA). The interaction potential develops a minimum of restricted depth, weakening the clusters which subsequently restructure and form more compact morphologies. This minimum is responsible for the reversibility of the aggregation processes (this is an important difference between diffusion-limited cluster aggregation and reaction-limited cluster aggregation). The energy minimum is associated with the presence of a steric term in the energy balance, which depends on the size of the adsorbed molecules. BSA molecules with different sizes were employed to test this point. In addition, the short-range interaction seems not to affect significantly the paths of approximating particles, since the aggregation of the clusters at long times is independent of the size of these particles. The long-time kinetics was interpreted in the frame of dynamic scaling concepts. A kinetics model, including surface-surface, protein-surface, and protein-protein aggregation, is used to determine the dominant mechanism controlling the aggregation.

On techniques for the measurement of the mass fractal dimension of aggregates

A review is presented of a number of techniques available for the characterisation of the structure of aggregates formed from suspensions of sub-micron particles. Amongst the experimental techniques that have been commonly used are scattering (light, X-ray or neutron), settling and imaging and these are the focus of this work. The theoretical basis for the application of fractal geometry to characterisation of flocs and aggregates is followed by a discussion of the strengths and limitations of the above techniques. Of the scattering techniques available, light scattering provides the greatest potential for use as a tool for structure characterisation even though interpretation of the scattered intensity pattern is complicated by the strong interaction of light and matter. Restructuring further complicates the analysis. Although settling has long been used to characterise particle behaviour, the absence of an accurate permeability model limits the technique as a means of determining the porosity of fractal aggregates. However, it can be argued that the determination of fractal dimension is relatively unaffected. The strength of image analysis lies in its ability to provide a great deal of information about particle morphology and the weaknesses lie in the difficulties with image processing and sample size as this is a particle counting technique. There are very few papers which compare the fractal dimension measured by more than one technique. Light scattering potentially provides a useful tool for checking settling results. However, further work is required to develop proper models for aggregate permeability and flow-through effects.

A Light Scattering Study of the Transition Region between Diffusion- and Reaction-Limited Cluster Aggregation

Two limiting regimes for colloidal particle aggregation are well described in the literature: diffusion-limited cluster aggregation and reaction-limited cluster aggregation. Between these two limiting regimes, a vast transition region is expected. In this paper, the transition region is studied by means of static and dynamic light scattering. Therefore, a system of latex particles is aggregated at different electrolyte concentrations. The time dependence of the average diffusion coefficient is fitted considering the Brownian kernel and the kernel proposed by Schmitt et al. [Phys. Rev. E 62, 8335 (2000)]. The first fits the experimental data only at high electrolyte concentrations while the latter, which considers multiple cluster-cluster contacts, is found to fit the complete set of experimental data. Copyright 2001 Academic Press.

Electrical Double-Layer Effects on the Brownian Diffusivity and Aggregation Rate of Laponite Clay Particles

Dynamic light scattering was used to study the Brownian translational diffusion and rate of Brownian aggregation of Laponite (RD) clay particles at low (millimolar) electrolyte concentrations. Laponite is a manufactured clay consisting of monodisperse disk-shaped particles with a 30-nm diameter and a 1-nm thickness. The stability ratio, defined as the ratio of the coagulation rate for Brownian spheres with no particle interactions to the observed coagulation rate, was quite large O(10(5)), suggesting that there was a large potential energy barrier to Brownian aggregation. The apparent potential energy barrier for face-edge aggregation was rationalized on the basis of a calculation of the electrostatic interactions between two disks with negative face charges and positive rim charges. The aggregation rate increased with increasing electrolyte concentration owing to the screening of the electrostatic repulsion associated with the net charge on the particle. The rate decreased with increasing pH because of the decreasing positive charge on the rim. The translational diffusivity of the individual particles before the onset of aggregation exhibited a strong dependence on the electrolyte concentration and was as much as 50% smaller than the diffusivity for an uncharged disk. This effect is attributed to the added drag resulting from the electroviscous effects in the deformed double layer. The electroviscous effect on the diffusion of the disk-like particles is much stronger than that on rods and spheres. Copyright 2001 Academic Press.

Kinetic Theories for the Coagulation and Sedimentation of Particles

The coagulation and sedimentation of particles is central to many environmental and industrial processes. Kinetic descriptions of this process can be divided into two approaches. Population balance equation (PBE) theory accounts for mass transfer between particle size classes by coagulation and loss of particle mass by sedimentation. Its practical application is limited by the fact that the rate constants, or kernels, for coagulation between all combinations of cluster sizes are unknown, and only a few solutions are available for simplified forms of the coagulation kernel. A second approach involves the use of simple rate expressions for the loss of particle mass with time, where the order of the reaction is determined by the mathematical properties of the coagulation kernel and the sedimentation term. Two different theories (similarity theory, ST, and the quasi-steady-state hypothesis, QSSH) give conflicting estimates for the order of the reaction. In this paper, we derive a PBE solution for the choice of a constant kernel and a particle removal rate that increases linearly with cluster volume. The kinetics of mass removal predicted by this solution are then compared directly to generalized forms of ST and QSSH which we also derive. We find that the PBE solution does not rigorously conform to either ST or QSSH, although the predictions of ST may be close enough for practical applications. This paper presents the first rigorous comparison of PBE, ST, and QSSH descriptions of particle coagulation and sedimentation. Copyright 2001 Academic Press.

Charge heteroaggregation between hard and soft particles

In this paper, the heteroaggregation of opposite sign hard and soft colloidal particles has been studied by static and dynamic light scattering. The structure of the aggregates, as well as the aggregation kinetics, have been investigated. At low electrolyte concentration, where both long-range electrostatic repulsive and attractive forces are present, the aggregates were found to be more open than expected for diffusion-limited cluster aggregation (DLCA). However, the aggregate size time evolution is characteristic of diffusion-controlled processes. At high electrolyte concentration, where DLCA would be expected, very compacted clusters were found, as well as very rapid aggregation, leading to high polydispersity. These latter findings are interpreted in terms of the differences in the homoaggregation speeds for the hard and soft particles.

Dielectric Spectroscopic and Molecular Simulation Evidence for Aggregation of Surfactant-stabilized Calcium Carbonate Nanocolloids in Organic Media

Dielectric spectroscopy carried out on overbased phenate micelle particles of nominal diameter approximately 2 nm containing calcium carbonate cores in hydrophobic liquids indicates that the micelles are strongly aggregated. Mean cluster sizes in excess of approximately 10(3) individual micelles are typically found in toluene. The level of association is a little higher in dodecane which is chemically closer to engine oil, the usual solvent for these systems. The mean aggregate size increases dramatically with concentration above an effective solids volume fraction of approximately 0.1 on treating the micelles as spheres. Aggregate size also depends on the level of overbasing, with lower levels of overbasing giving more micelles in the cluster. Molecular dynamics simulations of individual micelle particles reveal them to have large dipole moments originating mainly from the amorphous carbonate cores. Dipoles of magnitude approximately 20D are typical for a range of different surfactant types used in the model. The magnitude of the dipole depends somewhat on the chemical composition of the stabilizing surfactant shell. Monte Carlo simulations of two phenate nanocolloids taking into account all atom and charge pair interactions show these particles to have a strong short-range coulombic attraction of typically -25kBT at T = 298 K in the favored "side-by-side" relative arrangement. This attraction could be responsible for the strong level of association inferred from the dielectric spectroscopy experiments. Copyright 1999 Academic Press.

Flocculation of Hematite with Polyacrylic Acid: Fractal Structures in the Reaction- and Diffusion-Limited Aggregation Regimes

The structure of hematite aggregates in the presence of fairly monodisperse polyacrylic acid (PAA) with two different molecular weights (Mw = 1.36 x 10(6), Mw/Mn = 1.53; Mw = 3.69 x 10(4), Mw/Mn = 1.60) was studied using static light scattering (SLS). The fractal dimensions were calculated from the scattering exponents, after taking into account the finite size of aggregates, using exponential and Gaussian cutoff functions. Three flocculation regimes, namely, pre-DLA, DLA (diffusion-limited aggregation), and post-DLA, were defined based on the polymer concentration. In the DLA regime, fractal dimension values, Df = 1.84 +/- 0.02 and 1.73 +/- 0.02, were obtained using exponential and Gaussian cutoff functions, respectively. A fractal dimension of approximately 2.0 was found, as expected, in the pre-DLA regime (at PAA concentrations lower than the optimal dosage for a DLA regime) where the flocculation rate was reaction limited. In contrast, in the post-DLA regime, the flocculation was slow but the structure of aggregates was as tenuous as in the DLA regime with a fractal dimension Df approximately 1.8. Moreover, for all three regimes, the Df values were independent of the molecular weights of PAA. The lower fractal dimension in post-DLA was probably due to the increased concentration of polymer chains between adjacent particles in aggregates. The steric hindrance favored tip-to-tip aggregation, leading to a more tenuous structure. Copyright 1998 Academic Press.

Cluster Morphology of Protein-Coated Polymer Colloids

We report measurements on the aggregation processes in a colloidal suspension of polystyrene particles covered with F(ab')2 (immunoglobulin IgG fragment) performed by static and dynamic light scattering. In order to study the cluster morphology of aggregates, the fractal dimension is obtained from the dependence of the scattered intensity on the scattering wave number. The stability domains of bare and protein-coated polystyrene particles were examined by plotting the stability ratio as a function of electrolyte concentration. The stability results have been explained using a modified Derjaguin-Landau-Verwey-Overbeek theory to describe the interparticle interaction. The observed change in the fractal dimension can be explained by the existence of a minimum separation distance between coagulated particles (restructuring). This minimum distance is attributed to the layer of hydrated ions and water molecules adsorbed on the particle surface. Our results are in agreement with the reversible-growth model of W. Y. Shih, I. A. Aksay, and R. Kikuchi (Phys. Rev. A. 36, 5015 (1987)) and they were supported by transmission electron microscopy observation. Copyright 1998 Academic Press.

A Study of Colloidal Particle Brownian Aggregation by Light Scattering Techniques

Aggregation kinetics and aggregate structure are studied for monodisperse polystyrene latex particles of diameter 60 and 140 nm. The experimental part consists of measurements over a rather broad range of electrolyte concentrations (0.1 to 0.8 M NaCl) and for particle volume fractions 10(-6) to 10(-5), using dynamic and static light scattering techniques. The aggregation kinetics data obtained can be fitted into a single curve with a proper scaling of time and size for both particle sizes. For relatively long times, we observe power-law type kinetics, characteristic of diffusion limited aggregation (DLA). Fractal dimensions in all cases are close to 1.7 (as expected for DLA). The light scattering behavior of aggregates of arbitrary size is also studied numerically by employing computer simulations, and existing models (Lin et al., 1990. J. Colloid Interface Sci. 137, 263) are tested and improved for certain conditions (large angles and/or large particles). The shape of the experimental kinetics curves is successfully described with numerical simulations, further suggesting that (under the conditions tested) DLA aggregation prevails for short times as well. Copyright 1997 Academic Press. Copyright 1997Academic Press

Inversion of light scattering data from fractals by the Chahine iterative algorithm

We used the nonlinear Chahine iterative inversion scheme to analyze size distributions of fractal objects and we tested its usefulness by computer simulations. The data to be inverted are elastic light scattering measurements at a number of angles. We chose the fractal dimension of the objects equal to 1.75 to duplicate colloid aggregates growing in the diffusion limited aggregation mode. Even in the presence of a realistic level of noise, the method offers good estimates of the average radius and of the spread of the distribution.