The Aggregation Kinetics of Colloidal Particles of Basic Yttrium Carbonate

Studyofthegrowthprocessofcolloidalparticlesofnonequilibriumandirreversibilityisanactiveareaofresearch.Therecognitionofcolloidalaggregatesasfractalobjectshasinspiredalargenumberofexperimentalandtheoreticalstudiesonthestructuralandkineticaspectsofaggregationprocesses"'.Morerecently,kineticsofhematiteaggregationbypolyacrylicacidhavebeenstudiedbyzhangandBume3.Theprimaryhematiteparticleswerequiteuniformandfairlyspherical.Inthispaper,wewillreportthesizeevolutionoffractalaggregatesofinitiallypolydis…     

Salt-induced fast aggregation of nano-emulsions: structural and kinetic scaling

Salt-induced fast aggregation of oil-in-water nano-emulsions stabilized by the anionic surfactant sodium dodecyl sulfate was analyzed by employing dynamic and static light scattering techniques. Nano-emulsions with different ratios of dodecane/hexadecane were studied. The time evolution of the average size of all nano-emulsions collapsed in the same curve despite differences in the composition of the oil phase. A power law growing and a value of the homogeneity parameter similar to that typically found in model solid particle systems in diffusive aggregation regime were found. A value of 2.4 was estimated for the effective fractal dimension both from the scaling of scattered intensity with scattering wave vector modulus and from the kinetic scaling. This result indicates that the aggregates are more compact structures compared with model solid systems. It can be explained as a result of the effect of polydispersity in the primary droplet size and the coalescence events that occur inside the aggregates.     

Measurement of Fractal Aggregates of Polydisperse Particles Using Small-Angle Light Scattering

The effect of primary particle polydispersity on the structure of fractal aggregates has been investigated through the salt-induced, diffusion-limited aggregation of mixtures of hematite. The fractal dimension was determined experimentally using three independent methods: q dependence of static light scattering, kinetic scaling, and correlation of aggregate mass and linear size both determined from Guinier scattering. The fractal dimensions D(f) obtained were 1.75+/-0.03, 1.76+/-0.03, and 1.70+/-0.05, respectively. The use of a previously derived fractal mean particle size was validated in allowing data collapse to master curves for the aggregation kinetics data. The fractal mean particle size is shown to have general utility by taking a number weighting to describe polydisperse aggregation kinetics and a mass weighting to describe small q scattering behavior. Copyright 2000 Academic Press.     

Further insights into the universality of colloidal aggregation

Dynamic light scattering (DLS) performed at various scattering wave vectors provides detailed information about the aggregation kinetics and the cluster mass distribution (CMD) in colloidal dispersions. Detailed modeling of the aggregation kinetics with population balance equations requires a quantitative connection between the CMD and measurable quantities such as the angle dependent hydrodynamic radii obtained by DLS. For this purpose we evaluate and compare various models for the structure factor of fractal aggregates. Additionally, we introduce a simple scattering model that accounts for the contribution of internal cluster dynamics of fractal clusters to the first cumulant of the dynamic structure factor. We show that this contribution allows to quantitatively describe previously measured experimental data on the scattering wave vector dependence of the hydrodynamic radius in diffusion limited cluster-cluster aggregation (DLCA), which was shown to exhibit some kind of universality behavior (master curve). Using the same scattering model, we analyze a similar set of experimental data but in reaction limited cluster-cluster aggregation (RLCA). We find that in this case the crossover from RLCA to DLCA and gravitational settling both have a significant influence on the CMD and consequently on the scattering wave vector dependent DLS data. Only when accounting for both these effects they temporarily compensate each other and a satisfactory representation of the aggregation master curve is possible for the RLCA data at longer times. Indeed, we find that either crossover from RLCA to DLCA or gravitational settling, when present individually, causes the loss of a master curve for aggregation.     

Phase separation kinetics of polyelectrolyte solutions

The kinetics of phase separation of aqueous solutions of sodium-poly(styrene sulfonate) (NaPSS) containing barium chloride (BaCl(2)) is studied by static and dynamic light scattering. We report a novel mechanism of phase separation, where an enrichment of polymer aggregates of well-defined size occurs in the very early stage of nucleation, which is then followed by a growth process in the formation of the new phase. In the latter stage, the polymer aggregates formed in the early stage act as the templating nuclei. Even in the homogeneous phase at higher temperatures above the upper critical phase boundary, polymer aggregates are present in agreement with previously reported results. Upon rapidly cooling the system below the phase boundary, the number concentration of the aggregates increases first by maintaining their size to be relatively monodisperse, before the growth process takes over at later times. The size and fractal dimension of aggregates in the homogeneous phase and the early nucleation stage of phase separation and the dependence of nucleation time and growth rate on quench depth and salt concentration are determined. The hydrodynamic radius (R(H)) of the unaggregated chains is of the order of 1-10 nm depending on the molecular weight of NaPSS, while R(H) of aggregates is of the order of 100 nm independent of the molecular weight of NaPSS. Unaggregated chains follow good solution behavior with a fractal dimension of 5/3 while the fractal dimension of aggregates is larger than 3.5 suggesting the branched nature of aggregates. Nucleation time is sensitive to quench depth and salt concentration. Increasing a quench depth or increasing BaCl(2) concentration shortens the nucleation time. After the nucleation time, during the growth period, the size of aggregates grows linearly with time, with growth rate being higher for deeper quench depths and higher BaCl(2) concentrations. The mechanism of phase separation of aqueous solutions of NaPSS and BaCl(2) is seen to proceed by utilizing the already-existing aggregates to nucleate the new phase, in marked contrast to hitherto known results on phase separation in uncharged polymer systems.     

Fractal structure of asphaltene aggregates

A photographic technique coupled with image analysis was used to measure the size and fractal dimension of asphaltene aggregates formed in toluene-heptane solvent mixtures. First, asphaltene aggregates were examined in a Couette device and the fractal-like aggregate structures were quantified using boundary fractal dimension. The evolution of the floc structure with time was monitored. The relative rates of shear-induced aggregation and fragmentation/restructuring determine the steady-state floc structure. The average floc structure became more compact or more organized as the floc size distribution attained steady state. Moreover, the higher the shear rate is, the more compact the floc structure is at steady state. Second, the fractal dimensions of asphaltene aggregates were also determined in a free-settling test. The experimentally determined terminal settling velocities and characteristic lengths of the aggregates were utilized to estimate the 2D and 3D fractal dimensions. The size-density fractal dimension (D(3)) of the asphaltene aggregates was estimated to be in the range from 1.06 to 1.41. This relatively low fractal dimension suggests that the asphaltene aggregates are highly porous and very tenuous. The aggregates have a structure with extremely low space-filling capacity.     

Influence of natural organic matter and ionic composition on the kinetics and structure of hematite colloid aggregation: implications to iron depletion in estuaries

The stability and aggregation behavior of iron oxide colloids in natural waters play an important role in controlling the fate, transport, and bioavailability of trace metals. Time-resolved dynamic light scattering experiments were carried out in a study of the aggregation kinetics and aggregate structure of natural organic matter (NOM) coated hematite colloids and bare hematite colloids. The aggregation behavior was examined over a range of solution chemistries, by adjusting the concentration of the supporting electrolyte-NaCl, CaCl2, or simulated seawater. With the solution pH adjusted so that NOM-coated and bare hematite colloids were at the same zeta potential, we observed a significant difference in colloid stability which results from the stability imparted to the colloids by the adsorbed NOM macromolecules. This enhanced stability of NOM-coated hematite colloids was not observed with CaCl2. Aggregate form expressed as fractal dimension was determined for both NOM-coated and bare hematite aggregates in both NaCl and CaCl2. The fractal dimensions of aggregates formed in the diffusion-limited regime indicate slightly more loosely packed aggregates for bare hematite than theory predicts. For NOM-coated hematite, a small decrease in fractal dimension was observed when the solution composition changed from NaCl to CaCl2. For systems in the reaction-limited regime, the measured fractal dimensions agreed with those in the literature. Colloid aggregation was also studied in synthetic seawater, a mixed cation system to simulate estuarine mixing. Those results describe the important phenomena of iron oxide aggregation and sedimentation in estuaries. When compared to field data from the Mullica Estuary, U.S.A., it is shown that collision efficiency is a good predictor of the iron removal in this natural system.     

Investigation of Asphaltene Aggregate Size Distribution Under Aggregation and Breakage Phenomena Using Monte Carlo Simulation

In this article, the aggregation and breakage processes are simulated through Monte Carlo method for asphaltene aggregates under shear-induced petroleum mixtures. The simulation results are verified by the aggregate size distributions of two types of asphaltenes having different fractal dimensions extracted from Iranian crude oil types. The obtained aggregate size distributions are affected by shear rate, toluene to heptane ratios and the oil type. The dynamic evolution of asphaltene aggregates shows an ascendant trend with time until they reach a maximum average diameter and then descent to a steady-state size. The asphaltene fractal dimension affects the aggregation process.     

Scaling of the kinetics of slow aggregation and gel formation for a fluorinated polymer colloid

The aggregation and gelation kinetics in moderately concentrated (0.004 相似文献   

The effect of inhomogeneous stickiness on polymer aggregation

The aggregation of polymers is important in the formation of marine aggregates and the vertical transport of material in the ocean. A polymer may be inhomogeneous along its length, with associating groups at some points along its length where bonds are more likely to form. In this paper we investigate the effects of inhomogeneous 'stickiness' along the polymer length. We describe the results of three-dimensional off-lattice simulations of polymer-polymer aggregation for four different types of polymer: polymers which are sticky along their entire length, polymers which are sticky at the ends only and two types of polymer which are slightly sticky along their entire length. We examine the mean radius of gyration and the fractal dimension of the resulting aggregates and the dynamics of aggregation. The slightly sticky polymers and the polymers which are sticky only at the ends form aggregates with a higher fractal dimension than the polymers which are sticky along their entire length. However, the mean radius of gyration of the aggregates formed by polymers which are sticky only at the ends is significantly larger than that of the aggregates formed from slightly sticky polymers. The aggregation dynamics are also different for the polymers which are sticky only at the ends compared to the slightly sticky polymers. A single 'stickiness value' is therefore likely to be inadequate to describe a polymer. We also examine the effect of polymer rigidity; it seems that the effect of inhomogeneous stickiness is greater for almost-straight polymers than for coiled chains.     

Destabilization of polystyrene latex particles induced by adsorption of polyvinylamine: mass, size and structure characteristics of the growing aggregates

The obviously visible aggregation of suspended colloidal particles resulting from the addition of polyvinylamine to the aqueous dispersion of polystyrene latex particles bearing surface sulfate groups set in with a delay of 24 h. The aggregation mechanisms and the fractal dimension of the aggregates were derived from the variations with time of the weight and number averaged masses of the aggregates as well as of the weight averaged harmonic mean diameter of the size distribution. Since the establishment of starved layers was determined to be relatively fast and to leave the liquid phase free of polymer, the delay for the obvious destabilization was attributed to the reconformation of adsorbed macromolecules that was expected to be extremely slow. This reconformation promoted the emergence of the diffusion-limited aggregation process that accompanies the permanent reaction-limited aggregation process. The fractal dimension of the latex particles/polyvinylamine aggregates was determined to be 2.12.     

Light-scattering study of the aggregation of syndiotactic poly(methyl methacrylate) in solution.

Syndiotactic poly(methyl methacrylate (s-PMMA) may undergo aggregation in n-butyl chloride (n-BuCl) at temperatures below the theta temperature. The aggregation behavior of the s-PMMA with weight-average molecular weight M(w) =6.06 x 10(5) g mol(-1) was studied by a combination of static and dynamic laser-light-scattering experiments. A solution of concentration 1.12 x 10(-4) g mL(-1) was quenched from 50 degrees C (above the theta temperature in n-BuCl, 35 degrees C to 12 degrees C, and the aggregation process was measured over 60 h. The time dependence of M(w) the root-mean-square z-average radius of gyration < R(g) >, and the average hydrodynamic radius were used to monitor the growth of the aggregates, with the result M(w) approximately < R(g) > d(f) (where d(f) = 1.98 +/- 0.02), which implies the formation of a fractal aggregate. The observed fractal dimension, d(f), is close to that expected for a reaction-limited cluster aggregation for which d(f) = 2.1. In addition, atomic force microscopy was used to image the aggregates.     

Colloidal Fouling of Ultrafiltration Membranes: Impact of Aggregate Structure and Size

A close coupling between the structure and size of hematite flocs formed in suspension and the permeability of the cake that accumulates on ultrafiltration membranes is observed. Specific resistances of cakes formed from flocs generated under diffusion-limited aggregation conditions are at least an order of magnitude lower than those of cakes formed from flocs generated under reaction-limited aggregation conditions. Similar effects are observed whether the aggregation regime is controlled by salt concentration, pH, or added organic anions. This dramatic difference in cake resistance is considered to arise from the size and fractal properties of the hematite assemblages. The ease of fluid flow through these assemblages will be influenced both by the fractal dimension of the aggregates and by their size relative to primary particle size (since, for fractal aggregates, porosity increases as the size of the aggregate increases). The size and strength of aggregates are also important determinants of the relative effects of permeation drag, shear-induced diffusion, and inertial lift and result, in the studies reported here, in relatively similar rates of particle deposition for both rapidly and slowly formed aggregates. The results presented here suggest that control of cake permeability (and mass) via control of aggregate size and structure is an area with scope for further development though the nature and extent of compaction effects in modifying the fractal properties of aggregates generated in suspension requires attention. Copyright 1999 Academic Press.     

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.     

Aggregation behavior of latex particles in shear flow confined between two parallel plates

In this study, the aggregation and breakup behaviors of latex particles in shear flow confined between two parallel plates were investigated using an in situ observation apparatus with a laser scanning confocal microscope. To investigate the effects of shear rate and the gap width between two parallel plates on the size and structure of the aggregates in the steady state, the distributions of the projected cross-sectional area and perimeter-based fractal dimension of the aggregates were measured. As a result, the average size of the aggregates decreases as shear rate increases and the gap width decreases due to the hydrodynamic effect acting on the aggregates. The size distributions of the aggregates become narrow as the gap width decreases. In addition, the fractal dimension, that is, the structure of the aggregates, was almost independent of shear rate and the gap width and approximately 1.2, which suggests that the aggregates are relatively compact.     

Deposition of spherical particles onto cylindrical solid surfaces. I. Numerical simulations

The permeability of fractal porous aggregates with realistic three-dimensional structure is investigated theoretically using model aggregates composed of identical spherical primary particles. Synthetic aggregates are generated by several techniques, including a lattice-based method, simulation of aggregation by differential settling and turbulent shear, and the specification of simple cubic structures, resulting in aggregates characterized by the number of primary particles, solid fraction, characteristic radius, and fractal dimension. Stokesian dynamics is used to determine the total hydrodynamic force on and the distribution of velocity within an aggregate exposed to a uniform flow. The aggregate permeability is calculated by comparing these values with the total force and velocity distribution calculated from the Brinkman equation applied locally and to the entire aggregate using permeability expressions from the literature. The relationship between the aggregate permeability and solid fraction is found to be best predicted by permeability expressions based on cylindrical rather than spherical geometrical elements, the latter tending to underestimate the aggregate permeability significantly. The permeability expressions of Jackson and James or Davies provide good estimates of the force on and flow through porous aggregates of known structure. These relationships are used to identify a number of general characteristics of fractal aggregates.     

Mathematical modeling of polymer-induced flocculation by charge neutralization

A detailed mathematical model for flocculation of colloidal suspensions in presence of salts and polymers is described and validated. In former case, the classical DLVO theory, which accounts for relevant variables such as pH and salt concentration, is incorporated into a geometrically sectioned discrete population balance model. For processes involving polymers, flocculation via simple charge neutralization is modeled using a modified DLVO theory in which the effect of adsorbed polymer layers on van der Waals attraction is included. The fractal dimension of aggregates is obtained by dynamic scaling of experimental data for time evolution of mean aggregate size. The particle surface potential is assumed to be approximately equal to the zeta potential. The model predictions are in close agreement with experimental results for flocculation of colloidal hematite suspensions in the presence of KCl and polyacrylic acid at different concentrations. In particular, given values of model parameters, e.g., Hamaker constant, fractal dimension, surface potential, and thickness of adsorbed polymer layer, the model can realistically describe the kinetics of flocculation by a simple charge neutralization mechanism and track the evolution of floc size distribution. Representative examples of sensitivity of the flocculation model to perturbations in surface potential and fractal dimension and to modification in the DLVO theory for polymer-coated particles are included.     

Analysis of the structure of very large bacterial aggregates by small-angle multiple light scattering and confocal image analysis

This work aims at developing a more accurate measurement of the physical parameters of fractal dimension and the size distribution of large fractal aggregates by small-angle light scattering. The theory of multiple scattering has been of particular interest in the case of fractal aggregates for which Rayleigh theory is no longer valid. The introduction of multiple scattering theory into the interpretation of scattering by large bacterial aggregates has been used to calculate the fractal dimension and size distribution. The fractal dimension is calculated from the form factor F(q) at large scattering angles. At large angles the fractal dimension can also be computed by considering only the influence of the very local environment on the optical contrast around a subunit. The fractal dimensions of E. coli strains flocculated with two different cationic polymers have been computed by two techniques: static light scattering and confocal image analysis. The fractal dimensions calculated with both techniques at different flocculation times are very similar: between 1.90 and 2.19. The comparison between two completely independent techniques confirms the theoretical approach of multiple scattering of large flocs using the Mie theory. Size distributions have been calculated from light-scattering data taking into account the linear independence of the structure factor S(q) relative to each size class and using the fractal dimension measured from F(q) in the large-angle range or from confocal image analysis. The results are very different from calculations made using hard-sphere particle models. The size distribution is displaced toward the larger sizes when multiple scattering is considered. Using this new approach to the analysis of very large fractal aggregates by static light multiple scattering, the fractal dimension and size distribution can be calculated using two independent parts of the scattering curve.