Aggregation Rate Constants Research Articles

Polystyrene Sulfate Latex Particles in the Presence of Poly(vinylamine): Absolute Aggregation Rate Constants and Charging Behavior

Absolute aggregation rate constants of anionic polystyrene sulfate latex particles were measured in the presence of cationic poly(vinylamine) by time-resolved simultaneous static and dynamic light scattering. The colloidal stability depends sensitively on the polymer dose, pH, and ionic strength. While the stability ratio is strongly dependent on the ionic strength, the electrophoretic mobility depends much more weakly on it, and therefore the latter measurements cannot be used as a reliable measure of the suspension stability. In the fast aggregation regime, the presence of the oppositely charged polyelectrolytes leads to an enhancement of the aggregation rate with respect to the one in the presence of an indifferent electrolyte. This acceleration probably originates from attractive electrostatic interactions between surface charge heterogeneities.

Tracer studies of high‐shear granulation: II. Population balance modeling

AbstractA population balance framework developed describes the tracer studies in Part I. A two internal coordinate population balance equation (PBE) links the evolution with time of granule‐size and tracer‐mass distributions to underlying rate processes. A new analytical PBE was developed for the tracer distribution and novel numerical techniques, including a new discretized population balance equation for breakage or grinding. Also developed is a general differential technique for extracting rate constants from measurements of particle‐size distributions. Granulation in a high‐shear mixer proceeds after nucleation, not studied here, with very high initial breakage rates but a relatively unchanging aggregation rate constant. The breakage function is bimodal on a mass basis and the selection rate decays exponentially over about 20 s. A heterogeneous strength hypothesis was used to account for this time dependence. Aggregation rates are the highest for interactions between small and large granules and may be quantitatively given by the Equipartition of kinetic energy kernel developed from the theory of collisions between gas molecules. The model can describe granule‐size and tracer‐mass distributions simultaneously with great accuracy. The need to replace time as a driving force variable in the kinetics for these systems is identified.

Aggregation and deposition kinetics of mobile colloidal particles in natural porous media

A novel method for assessing the deposition kinetics of colloidal particles in natural porous media is presented. The method is applied for studying the deposition kinetics of in situ mobilized colloidal particles in a non-calcareous soil in mixed electrolytes containing sodium and calcium as counter ions. Particle deposition rate constants were measured by combining deposition experiments in packed columns and aggregation measurements by dynamic light scattering. The relative deposition and aggregation rate constants follow very similar trends, featuring fast (favorable) and slow (unfavorable) regimes at high and low salt concentrations, respectively. These regimes are separated by the critical coagulation or deposition concentrations (CCC or CDC, respectively), which sensitively depend on the type of counterion. In systems containing a single electrolyte, the CCC and CDC follow the classical Schulze-Hardy rule. In mixed sodium–calcium electrolytes, a gradual transition of the CCC and CDC between the values obtained for the corresponding pure (single) electrolyte systems is observed. The present approach provides a facile route for assessing deposition rates of mobile colloidal particles in natural porous media.

Aggregation of Colloidal Particles in the Presence of Oppositely Charged Polyelectrolytes: Effect of Surface Charge Heterogeneities

We study the early stages of flocculation in suspensions of charged colloidal particles in the presence of oppositely charged polyelectrolytes. Absolute aggregation rate constants are determined by...

The balance of concurrent aggregation and deaggregation processes in platelets is linked to differential occupancy of ADP receptor subtypes

Deaggregation, the partial reversal of the initial aggregation of platelets is observed following low, but not higher, micromolar ADP concentrations. This study tested the hypothesis that deaggregation results from a balance between concurrent, opposing, aggregation and deaggregation processes which are ADP (adenosine 5'-diphosphate) receptor occupancy-dependent. Aggregation of human platelet-rich plasma (PRP) prepared in r-hirudin was assayed in a 96-well plate reader over 20 min by measurement of the optical density (OD) at 580 nm. Aggregation and the time to reach peak aggregation were directly proportional to ADP receptor occupancy. The magnitude and time course of the response to ADP were comparable to those previously reported with standard aggregometry. The rate constant of platelet deaggregation, as assessed by a fourcompartment kinetic model, was inversely proportional to agonist concentration. The ratio of the rate constants of aggregation and deaggregation was receptor occupancy-dependent and directly proportional to aggregation. Consequently, platelet aggregation was proportional, and deaggregation inversely proportional, to ADP receptor occupancy. We propose that the response of PRP to ADP and to 2-MeS-ADP (2-methylthioadenosinediphosphate), in vitro , consists of at least two active, concurrent processes, aggregation and deaggregation. Incremental occupancy of the P 2T ADP receptor subtype attenuates deaggregation and governs the balance between these two processes.

Aggregation during precipitation from solution: an experimental investigation using Poiseuille flow

Aggregation is an important crystal size enlargement mechanism during precipitation and the rate of aggregation is affected by the various process conditions such as solution composition and the hydrodynamics of the system. In this paper, an investigation of the effect of hydrodynamics as well as solution composition on the aggregation of calcium oxalate monohydrate crystals is reported using a novel Poiseuille Flow Crystalliser (PFC). The well-characterised hydrodynamics of the PFC allows the prediction of collision rates using Smoluchowski's theory and therefore the quantification of the efficiency of aggregation. At low shear rates, i.e. in the high-efficiency regime, it is found that the aggregation rate constant varies linearly with shear rate providing good validation for Smoluchowski's theory. Further, at increasing shear rates a maximum in the value of the aggregation rate constant is observed confirming the disruptive role of fluid shear rate in impeding aggregation. In the investigation of the effect of solution composition on aggregation, it is found that the aggregation rate constant increases with the growth rate, but is independent of the species ion ratio. Finally, we find that dimensionless strength is a powerful correlating variable in determining aggregation efficiency.

Colloidal aggregation under steric interactions: Simulation and experiments

The influence of steric interactions in the initial stages of aggregation kinetics in colloidal systems has been studied by simulation and experiments. A simulation model has been proposed to study the initial stages of aggregation under short range repulsive potentials. A polystyrene latex was used as model colloid and the steric interaction was provided by adsorption of a nonionic surfactant. Depending on the range or strength of the interactions, sensitive or insensitive systems to electrolyte concentration can be observed. At low κa, the long-range electrostatic repulsion dominates the system behavior, stabilizing the colloidal system. In conditions of screened electrostatic potential, particle collision is the result of a competition between van der Waals attraction and steric repulsion, leading to a decrease in the dimer formation constant as the range or strength of the steric interaction increases. The steric interaction energy has been included in the theoretical calculation of the aggregation rate constant by means of Fuchs’ stability factor. Good agreement between simulation, experimental, and theoretical calculations was obtained.

Influence of the Secondary Interaction Energy Minimum on the Early Stages of Colloidal Aggregation

The pair interaction energy of charged colloidal particles in electrolyte solutions can exhibit a large barrier as well as a pronounced secondary minimum. We discuss the effect of a secondary energy minimum on aggregation kinetics by modeling irreversible dimer formation as a two-step process in which charged colloidal particles in electrolyte solutions first aggregate reversibly into the secondary minimum before they can cross the energy barrier. In the classical regime of slow aggregation, the secondary minimum is seen to have a pronounced effect if either the ionic strength of the solution is high (e.g., 0.1 M for particles of 150-nm radius) or particles are large (≥350-nm radius for an ionic strength of 0.01 M). Under these conditions, our calculations predict a transient period of fast aggregation into the secondary minimum followed by slow primary aggregation. The aggregation in this second regime is found to take place at a lower rate than what would be expected in the absence of the secondary minimum or from an earlier linearized model for secondary aggregation. The crossover time between the two regimes strongly depends on the particle size but not on the particle concentration, which however determines the degree of aggregation reached within the fast regime. We also conclude that a previously observed severe discrepancy between measured and predicted aggregation rate constants for submicron particles is not due to the neglect of secondary aggregation in the theoretical treatment.

Charging and Aggregation Properties of Carboxyl Latex Particles: Experiments versus DLVO Theory

Carboxyl latex particles of two different sizes were used to study the early stages of aggregation in dilute colloidal suspensions. The charging behavior as a function of solution pH was characterized in acid−base titration and electrophoresis experiments at fixed ionic strength; absolute aggregation rate constants were measured by combined static and dynamic light scattering as a function of pH and ionic strength. Up to an ionic strength of 10 mM in a KCl solution, the classical DLVO theory of colloidal stability is seen to work quantitatively. At higher ionic strength, however, well-known discrepancies between theory and experiment are observed. An analysis of the theoretical pair interaction energy suggests that quantitative agreement can be achieved when the energy barrier for reaction-limited aggregation lies at surface separations of at least 1−2 nm. This result is consistent with recent measurements of colloidal forces and interaction energies, as well as with earlier aggregation and deposition stu...

Short-lived thorium isotopes ( [formula omitted], [formula omitted]) as indicators of POC export and particle cycling in the Ross Sea, Southern Ocean

Repeated measurements of depth profiles of 234 Th (dissolved, 1–70 and >70 μm particulate) at three stations (Orca, Minke, Sei) in the Ross Sea have been used to estimate the export of Th and particulate organic carbon (POC) from the euphotic zone. Sampling was carried out on three JGOFS cruises covering the period from October 1996 (austral early spring) to April 1997 (austral fall). Deficiencies of 234 Th relative to its parent 238 U in the upper 100 m are small during the early spring cruise, increase to maximum values during the summer, and decrease over the course of the fall. Application of a non-steady-state model to the 234 Th data shows that the flux of Th from the euphotic zone occurs principally during the summer cruise and in the interval between summer and fall. Station Minke in the southwestern Ross Sea appears to sustain significant 234 Th removal for a longer period than is evident at Orca or Sei. Particulate 234 Th activities and POC are greater in the 1–70 μm size fraction, except late in the summer cruise, when the >70 μm POC fraction exceeds that of the 1–70 μm fraction. The POC/ 234 Th ratio in the >70 μm fraction exceeds that in the 1–70 μm fraction, likely due in part to the greater availability of surface sites for Th adsorption in the latter. Particulate 234 Th fluxes are converted to POC fluxes by multiplying by the POC/ 234 Th ratio of the >70 μm fraction (assumed to be representative of sinking particles). POC fluxes calculated from a steady-state Th scavenging model range from 7 to 91 mmol C m −2 d −1 during late January–early February, with the greatest flux observed at station Minke late in the cruise. Fluxes estimated with a non-steady-state Th model are 85 mmol C m −2 d −1 at Minke (1/13–2/1/97) and 50 mmol C m −2 d −1 at Orca (1/19–2/1/97). The decline in POC inventories (0–100 m) is most rapid in the southern Ross Sea during the austral summer cruise ( Smith et al., 2000. The seasonal cycle of phytoplankton biomass and primary productivity in the Ross Sea, Antarctica. Deep-Sea Research II 47, 3119–3140. Gardner et al., 2000. Seasonal patterns of water column particulate organic carbon and fluxes in the Ross Sea, Antarctica. Deep-Sea Research II 47, 3423–3449), and the 234 Th -derived POC fluxes indicate that the sinking flux of POC is ∼30–50% of the POC decrease, depending on whether steady-state or non-steady-state Th fluxes are used. Rate constants for particle POC aggregation and disaggregation rates are calculated at station Orca by coupling particulate 234 Th data with 228 Th data on the same samples. Late in the early spring cruise, as well as during the summer cruise, POC aggregation rates are highest in near-surface waters and decrease with depth. POC disaggregation rates during the same time generally increase to a maximum and are low at depth (>200 m). Subsurface aggregation rates increase to high values late in the summer, while disaggregation rates decrease. This trend helps explain higher values of POC in the >70 m fraction relative to the 1–70 m fraction late in the summer cruise. Increases in disaggregation rate below 100 m transfer POC from the large to small size fraction and may attenuate the flux of POC sinking out of the euphotic zone.

Growth and aggregation rates for calcite and calcium oxalate monohydrate

AbstractSeeded batch experiments were conducted at low magma densities and moderate ionic strength to determine the growth and aggregation rate constants for calcite precipitation in a stirred vessel. The growth was found to be surface‐reaction‐limited, and the growth rates agreed broadly with other studies of calcite precipitation. Aggregation rates have rarely been presented for calcite. The aggregation rate constant studied here was directly proportional to the instantaneous growth rate and inversely proportional to the average shear rate in the vessel. The results were also compared with similar work carried out on calcium oxalate monohydrate. It was found that the relationship between the aggregation rate constant and stirrer speed was virtually identical in the two cases, despite almost an order of magnitude difference in the growth rate constants.

The Structure of Cold-Set Whey Protein Isolate Gels Prepared With Ca++

The mechanism(s) of Ca2+-induced cold gelation of whey protein isolate was investigated. Kinetic data revealed that the rate constant of aggregation (20 g/L protein, 3°C) progressively increased as [CaCl2] was raised from 10 mmol/L to a maximum of 30 mmol/L, and then declined as [CaCl2] was raised to 120 mmol/L. This could be explained as the combined effect of charge dispersion and Ca2+-bridging caused by increasing [CaCl2]. Young modulus increased as protein was raised from 60–100 g/L w/v at each of the calcium levels tested (5–150 mmol/L). The calculated fractal dimension of the gels increased from 2.3 to 2.6 as a function of increasing [CaCl2]. This was also observed by scanning and transmission electron micrographs.

Reversible Agglomeration: A Kinetic Model for the Peptization of Titania Nanocolloids

We formulate a model for the peptization of titania nanocolloids. The model assumes simultaneous agglomeration/deagglomeration with size-independent rate constants. It predicts that the evolution of the particle size exhibits first-order kinetics and that the final particle size scales as R ∼ C1/df, where C is the mass concentration of the colloid and df is the fractal dimension. These predictions are tested experimentally. We find that the model provides a quantitative and consistent description of the peptization process over a wide range of experimental variables and that it allows the determination of the aggregation and deaggregation rate constants from the time evolution of the average size.

Determination of erythrocyte aggregation

One of the most common health criteria – erythrocyte sedimentation rate (ESR) – is considered in the paper. It is shown that the simple model presented, based on the generalized Stokes formula, the blood volume conservation law, and the Smoluchowski theory of particles coagulation, makes it possible, on the basis of experimentally recorded sedimentation curves, to identify quantitatively the values of the essential physical parameters of the coupled processes of erythrocyte aggregation and sedimentation. The analytical solution of Smoluchowski equation is used to evaluate the sedimentation and aggregation rate constants. The problem of determining the erythrocyte aggregation rate (EAR) is transformed to a minimization task in which only the experimental results for ESR are needed. Experimentally ESR is measured accurately enough by using an equipment set up just for the purpose. This method of identification could be used as a diagnostic test in hematological laboratories.

Absolute Aggregation Rate Constants of Hematite Particles in Aqueous Suspensions: A Comparison of Two Different Surface Morphologies

Measurements of absolute aggregation rate constants were performed for two samples of well-characterized spheroidal hematite particles with rather different surface morphology. At high ionic strength, the system is in the fast aggregation regime with pH independent rate constants around (1–4) × 10−18m3/s. At low ionic strengths, the rate constant is a function of pH and goes through a flat maximum around the point of zero charge (PZC) where fast aggregation conditions are reached. With increasing pH the rate constants increase gradually below the PZC while they decrease very rapidly above the PZC. Above the PZC the rate constants are rather well predicted by the classical DLVO theory. Below the PZC, however, it is necessary to assume a distribution in the surface potentials with a coefficient of variation around 30% to account for the observed behavior. In spite of the pronounced differences in the surface roughness of both hematite samples, their aggregation rate constants are rather similar.

The aggregation of nitrogen and the formation of A centres in diamonds

Abstract Topographic infra-red spectroscopy has been used to investigate the inhomogeneity of the aggregation of nitrogen in {111} growth sectors of synthetic diamonds. The aggregation rate constant was established to be different even within the same {111} growth sector. In particular, changes in the growth temperature, most likely changing the impurity content, are shown to result in changes in the aggregation rate constant; namely an increase in the growth temperature, in diamonds grown with a Co catalyst is found to reduce the nitrogen aggregation rate constant, and vice versa. These results indicate that the presence of Co impurities in the {111} growth sector influences the aggregation rate. It is found that the aggregation process follows second order kinetics as first established by Chrenko et al. [Nature, London, 270 (1977) 141]. The activation energy of the aggregation process in {111} growth sectors is measured as 5.5 ± 0.7 eV. It is also found that increasing the applied pressure during the annealing process reduces the aggregation rate constant, such that there is a significant difference between annealing at ambient pressure and annealing at 10 GPa.

Suspension Flocculation by Polyelectrolytes: Experimental Verification of a Developed Mathematical Model

Using experimental data of AgI sol and poly(2-methyl-5-vinylpyridine) chloride, we show that there is good agreement between the developed mathematical model of suspension flocculation by polyelectrolytes and the experimental data. The rate constants of bridging and nonbridging aggregation of particles and of floc breakup, as well as their ratios, have been determined. It has been shown that the role of the nonbridging mechanism, as compared with that of the bridging one, diminishes when molecular mass of polyelectrolyte increases from 1.4 × 105to 9.3 × 105.

Kinetics of two-dimensional phase transition of amphiphilic monolayers at the air/water interface

A theoretical model is developed which describes the adsorption kinetics of the two-dimensional first-order phase transition in an adsorption layer. The theory includes a kinetic model of the phase transition in Langmuir and Gibbs monolayers, the adsorption from bulk solution, and the dissociation kinetics of bulk micelles. The theory describes well the experimental results of the adsorption kinetics of the amphiphile N-dodecyl-hydroxy-butyric acidamide dissolved in the aqueous bulk phase. The inflection point of dynamic surface pressure curves corresponds to the first-order phase transition in the adsorption layer. The rate constants for the 2D aggregation in the adsorption layer and the bulk micelle formation are calculated. The relaxation time of the 2D aggregation is approximately ten times lower than that of the association/dissociation of bulk micelles.

Orthokinetic Aggregation During Precipitation: A Computational Model for Calcium Oxalate Monohydrate

Smoluchowski's theory for orthokinetic coagulation of spheres is extended to aggregation during precipitation of calcium oxalate monohydrate. Physical models for hydrodynamics and deposition in a binary aggregation event are combined to determine the success of collisions with different orientations to the shear field. Consequently, an effciency terms introduced that represents the proportion of collisions resulting in aggregates. The model is used to investigate the effect of shear rate, crystal size and ion concentration on the aggregation rate constant, β agg . A maximum in β agg is observed with shear rate that corresponds to two opposing effects; increasing rate of collisions and increasing tensile stress between crystals. By contrast Smoluchowski's theory predicts direct proportionality. Compared with Smoluchowski's theory, β agg is relatively insensitive to crystal size. Finally, β agg is highly sensitive to solution ion concentration, an effect Smoluchowski's theory does not consider.

The Role of Solution Composition on Aggregation During Precipitation

Aggregation is an important size enlargement mechanism in various precipitating systems. Unlike the aggregation of colloidal particles in ionic solutions which has been extensively studied, aggregation during precipitation from supersaturated solutions is less well understood. In this paper experimental data from the batch precipitation of calcium oxalate monohydrate are used to show how the aggregation rate depends on solution composition. A discretized population balance method is used to extract the growth and aggregation rates from experimental particle size distributions collected at regular time intervals. It is found that for all the experimental conditions considered, the measured growth rate may be described by a kinetic equation which is second order in a relative supersaturation, regardless of the solution composition, that is the calcium to oxalate ion ratio. Further, it is demonstrated that the rate of aggregation exhibits a more complex dependence on solution composition than the growth rate. A model is then proposed based on the diffusion of solute ions to a cementing site, which despite a number of simplifying assumptions is able to explain the experimentally observed behaviour of the aggregation rate constant.