Reaction-limited Aggregation Process Research Articles

Characterization of particles and their relation with residual aluminum in water treated with pulsating floc blanket clarifiers and conventional clariflocculators using PACl

Abstract A pulsating floc blanket clarifier (PFBC) employing cyclic contractions and rarefactions to a bed of densely concentrated suspension of flocculated particles in a fluidized state, was compared with conventional clariflocculator (CC) at pilot scale (8,000 L/day) in continuous mode of operation. For influent turbidity varied from 2 to 20 NTU, coagulation-flocculation behavior exhibited under the two fundamentally different treatment processes with PACl influenced inter-related performance parameters. The residual turbidity was found to be lower by 74%, flocs and fine colloids in suspension larger by 73 and 75% respectively, and the total and dissolved residual aluminum lower by 50 and 49% respectively on average for PFBC compared to CC. Particulate form comprised major fraction (≈72%) of total residual aluminum for both. PFBC abetted formation of a more consolidated floc structure, which rendered the shape, size and morphology such that the settling velocity was 50% to 410% higher than that of the CC flocs. Reaction-limited aggregation (RLA) process and inter-particle bridging were dominant and the resulting floc structure and its formation mechanism have been presented.

Kinetics of Network Formation and Heterogeneous Dynamics of an Egg White Gel Revealed by Coherent X-Ray Scattering

The kinetics of heat-induced gelation and the microscopic dynamics of a hen egg white gel are probed using x-ray photon correlation spectroscopy along with ultrasmall-angle x-ray scattering. The kinetics of structural growth reveals a reaction-limited aggregation process with a gel fractal dimension of ≈2 and an average network mesh size of ca. 400nm. The dynamics probed at these length scales reveals an exponential growth of the characteristic relaxation times followed by an intriguing steady state in combination with a compressed exponential correlation function and a temporal heterogeneity. The degree of heterogeneity increases with decreasing length scale. We discuss our results in the broader context of experiments and models describing attractive colloidal gels.

Influence of ionomer adsorption on agglomerate structures in high-solid catalyst inks

Because the agglomerate structures of carbon-black-supported platinum nanoparticles (Pt/C) in catalyst inks affect their productivity and performance, identifying the structural parameters that control the dispersion state and stability of Pt/C agglomerates is important. This study aimed to identify agglomerate structures of Pt/C in high-solidity catalyst inks by examining the rheological behavior, fractal dimension, and electrical conductivity of the inks. In inks containing 48–75% water, the amount of adsorbed ionomers decreased with decreasing water content, resulting in increases in the shear viscosity (η), storage modulus (G′), and electrical conductivity (Σ). The fractal dimension of the agglomerates (df) was 1.7–2.1, suggesting that Pt/C agglomerates form a rigid three-dimensional network via a diffusion-limited cluster aggregation process. Conversely, in inks containing 89% water, the amount of adsorbed ionomers increased, leading to the lowest values for η, G′, and Σ. The df value was 2.6, suggesting that Pt/C agglomerates formed a weak-link network via a reaction-limited cluster aggregation process, which was inhibited by the steric and electrostatic repulsion effects of the adsorbed ionomers. The results of this study demonstrate that agglomeration can be controlled through ionomer adsorption by Pt/C, leading to changes in the rheological behavior and stability of catalyst inks.

Recent Developments on the Elucidation of Colloidal Aspects of Asphaltenes and Their Relevance to Oilfield Problems

Asphaltenes constitute the heavy petroleum fraction responsible for deposition events that may lead to reduced oil production, therefore of great interest for flow assurance. These molecules self-assemble in solutions leading to formation of aggregates that eventually grow towards precipitation and blockages in reservoirs and pipelines. Based on the Yen-Mullins aggregation model, two complementary scenarios are involved in asphaltenes phase behavior: one called thermodynamic, in which interacting molecules and other species can be assumed to be in equilibrium, and a second one, involving interacting colloidal particles, both being described by different theoretical frameworks. For the first, molecular interactions can explain the experimental observations or theoretical models. For the second stage, colloidal forces such as those described by Derjaguin, Landau, Verwey and Overbeek (DLVO) theory, steric particle stabilization and diffusion or reaction limited aggregation processes might control the process. Our evaluation is that this second approach is underrepresented in the current literature. For this reason, this review focuses on describing evidences for the presence of colloidal particles in crude oils obtained with different experimental techniques, drawing attention to this important attribute and we raise a few questions that we believe must be addressed in order to better understand the contributions from colloidal aspects.

Flowing suspensions of carbon black with high electronic conductivity for flow applications: Comparison between carbons black and exhibition of specific aggregation of carbon particles

Flow batteries and flow capacitors are promising technologies to store and generate electrical power. However, to increase their energy performances, low viscosity, electronic conductive suspensions loaded with active material are required. Comparing the behavior of three types of carbon black particles in water suspensions, we show that compressed acetylene carbon black particles suspensions display a slow variation of viscosity and conductivity as a function of concentration. It allows reaching intermediate viscosity (1 Pa s for a shear rate of 10 s−1) with high electronic conductivity between 0.1 and 5 mS/cm. This behavior is very promising for flow applications. At small range, attractive van der Walls interactions between carbon aggregates dominate. However, at longer range, compressed acetylene carbon black particles are highly attractive in water. After shearing with emulsifier, fractal-like shape clusters are obtained through a diffusion limited aggregation process. These fractal clusters constitute the building blocks of a flexible connected network. By contrast, for the two other investigated carbons, an energy barrier has to be overcome to enable aggregation. The clusters are compact and result from a reaction limited aggregation process. For these two carbons, the conductivity and the viscosity vary abruptly at percolation which is not suitable for flow devices.

Scaling law, fractal analysis and rheological characteristics of physical gels cross-linked with sodium trimetaphosphate

The scaling behavior and fractal analysis of basil seed gum (BSG) cross-linked with sodium trimetaphosphate (STMP) have been investigated by rheological small amplitude oscillatory shear measurements. Storage modulus and critical strain (γo) of the gels exhibited power law relationships with BSG concentration. Based on the power-law exponent values, the fractal dimension (df) of gels was estimated using scaling models, revealed the weak-link regime of BSG. The df values lied well within the range of fractal dimension values (1.5–2.8) reported for protein gels. However, they slightly differed from df for diffusion-limited and reaction limited cluster-cluster aggregation processes. Stress sweep test was shown that STMP addition to BSG made a stronger gel than that of BSG lacking STMP. Mechanical spectrum of gels was also revealed that adding STMP can improve the elasticity of gels. BSG had a tan δ of >0.1, indicating paste-like weak gel, while tan δ of BSG-STMP has approached to 0.1 exhibited the character of a cross-linked network near to “true gel”. BSG-STMP was also recognized as a thermo-reversible physical gel, which gelation and thermal properties did not affect by STMP. Therefore, the scaling behavior can be applied for hydrocolloids gels to extract structural information through rheological measurements. Moreover, the rheological characteristics of BSG-STMP showed it can be used as a proper hydrogel in food and pharmaceutical applications.

Explaining the Non-Newtonian Character of Aggregating Monoclonal Antibody Solutions Using Small-Angle Neutron Scattering

A monoclonal antibody solution displays an increase in low shear rate viscosity upon aggregation after prolonged incubation at 40°C. The morphology and interactions leading to the formation of the aggregates responsible for this non-Newtonian character are resolved using small-angle neutron scattering. Our data show a weak repulsive barrier before proteins aggregate reversibly, unless a favorable contact with high binding energy occurs. Two types of aggregates were identified after incubation at 40°C: oligomers with radius of gyration ∼10 nm and fractal submicrometer particles formed by a slow reaction-limited aggregation process, consistent with monomers colliding many times before finding a favorable strong interaction site. Before incubation, these antibody solutions are Newtonian liquids with no increase in low shear rate viscosity and no upturn in scattering at low wavevector, whereas aggregated solutions under the same conditions have both of these features. These results demonstrate that fractal submicrometer particles are responsible for the increase in low shear rate viscosity and low wavevector upturn in scattered intensity of aggregated antibody solutions; both are removed from aggregated samples by filtering.

A Comparative Study of Urea-Induced Aggregation of Collapsed Poly(N-isopropylacrylamide) and Poly(N,N-diethylacrylamide) Chains in Aqueous Solutions

The urea-induced aggregation of poly(N-isopropylacrylamide) (PNIPAM) and poly(N,N-diethylacrylamide) (PDEAM) globules was studied by using a combination of static and dynamic light scattering. Our results have revealed that urea acting as a cross-linker via formation of two hydrogen bonds with the amide groups of PNIPAM and PDEAM in different globules causes the aggregation, and the aggregation of PNIPAM and PDEAM globules is a reaction-limited cluster-cluster aggregation (RLCA) process. The aggregates have a uniform sphere structure that may be due to the restructuring of the aggregates. The aggregation rate of PNIPAM globules is slower than that of PDEAM, which might mainly contribute to the reasons that the amides groups of PNIPAM have more chance to be inside the globules because of the formation of intra- and inter-hydrogen bonds and the smaller number density of the PNIPAM aggregates at the original time. When the aqueous urea solutions were cooled and reheated to 40 °C, the aggregation became faster than the first heating process, indicating that the urea molecules have replaced some water molecules binding to the amide groups at high temperature and some of the urea molecules remain interacting with the polymers even at the temperature lower than the cloud point temperature.

One-Step Index-Tunable Antireflection Coatings from Aggregated Silica Nanoparticles

We demonstrate a method for producing thickness- and refractive index-tunable antireflection coatings utilizing a one-step spin coating procedure with silica nanoparticle solutions. Aging nanoparticle solutions under controlled pH and temperature induces aggregation, allowing precise control of the porosity and refractive index of the spin-processed coating. Coating thickness measurements as a function of solution aging time and temperature allow for determination of the activation energy of the reaction-limited aggregation process. We demonstrate optimization of the antireflection effect for a single-layer silica nanoparticle coating on glass, and suggest that the aggregation method may be generalized to various other nanoparticle-based assemblies.

Morphological quantification of hierarchical geomaterials by X-ray nano-CT bridges the gap from nano to micro length scales

Morphological quantification of the complex structure of hierarchical geomaterials is of great relevance for Earth science and environmental engineering, among others. To date, methods that quantify the 3D morphology on length scales ranging from a few tens of nanometers to several hundred nanometers have had limited success. We demonstrate, for the first time, that it is possible to go beyond visualization and to extract quantitative morphological information from X-ray images in the aforementioned length scales. As examples, two different hierarchical geomaterials exhibiting complex porous structures ranging from nanometer to macroscopic scale are studied: a flocculated clay water suspension and two hydrated cement pastes. We show that from a single projection image it is possible to perform a direct computation of the ultra-small angle-scattering spectra. The predictions matched very well the experimental data obtained by the best ultra-small angle-scattering experimental setups as observed for the cement paste. In this context, we demonstrate that the structure of flocculated clay suspension exhibit two well-distinct regimes of aggregation, a dense mass fractal aggregation at short distance and a more open structure at large distance, which can be generated by a 3D reaction limited cluster-cluster aggregation process. For the first time, a high-resolution 3D image of fibrillar cement paste cluster was obtained from limited angle nanotomography.

The Mobility of Fractal Aggregates: A Review

A review of the experimental and theoretical literature describing the mobility of fractal aggregates over the previous three decades is presented. Aggregates are those formed via both diffusion and reaction limited cluster-cluster aggregation processes, DLCA and RLCA, which form aggregates with fractal dimensions and prefactors of ca. 1.78 and 1.3 and 2.1 and 0.94, respectively. Emphasis is placed on DLCA aggregates. The entire Knudsen number range from continuum to free molecular is reviewed. The review finds a simple and general consensus description of mobility for the entire range.

Island Nucleation and Growth Dynamics during Submonolayer Vapor Deposition Polymerization

The evolution of island formation during submonolayer growth of poly(chloro-p-xylylene) films on naturally grown silicon oxide substrates is investigated using atomic force microscopy (AFM), and analyzed within the framework of dynamic scaling theory. A transition of film growth mechanism from diffusion-limited aggregation to reaction-limited aggregation is dramatically displayed in an unprecedented progression of the island density distribution functions. As surface coverage increases, a conventional bell-shaped monomodal distribution in early growth regime (θ = 0.07) gradually changes to a monotonically decreasing function, approximately following a power-law. The marginal power-law scaling behavior of the island distribution functions, reminiscent of the behavior of colloid aggregation, strongly suggests that film growth by vapor deposition polymerization is a new type of surface growth governed by reaction-limited aggregation process in which the competition between diffusion and deposition does not define the typical time scale of film growth.

Structural and rheological evolution of silica nanoparticle gels

The gelation dynamics of a sol of colloidal silica of approximately 7 nm radius particles is studied using a combination of light scattering and rheometry. By changing the ionic strength (by addition of a salt solution resulting in different ultimate molarities) of the mixture, a stable sol can be destabilized, leading to aggregation and later gelation. The gel time tgel can be varied from hours to weeks, indicating a reaction-limited aggregation process. Static light scattering is used to extract the fractal dimension Df of the aggregates, which is found to be approximately 2. The evolution of cluster size is probed by dynamic light scattering, and follows an exponential growth. Rheometry is used to assess the gelation time and further development of the network strength after gelation. The elastic modulus (G′) is found to scale as G′ ∼ ϕ3.3, where ϕ is the silica particle volume fraction. It was observed that the gel time (after salt solution addition) depends on both the particle volume fraction and salt concentration, showing a divergence at low volume fraction or low salt concentration. For a single solid fraction, data for the cluster hydrodynamic radius, normalized by the single particle radius, from experiments with a wide range of gel times can be collapsed onto a master curve when the time after the salt addition, t, is scaled as t/tgel; a similar collapse of viscosity and the linear viscoelastic data after gelation can be obtained using the same scaling of time. Salt concentration affects the gel time but not the strength of the gel network, thus allowing very accurate prediction of network formation times and mechanical properties.

Kinetics of self-organization of polyampholyte nanoparticles in solutions

An appropriate composition of a binary solvent, water-ethanol, provides the necessary thermodynamic environment for the polyampholyte (gelatin) molecules to form self-assembled nano-clusters having fractal dimension, ≈ 2.6, in the bulk (3-D). The aggregation in the bulk of the solution appears to be an anomalous process and could be explained through Smoluchowski aggregation model. It gives a diffusion limited aggregation (DLA) type fractal dimension to the cluster in bulk, but shows extremely low polydispersity, which in fact is a signature of a slowly growing reaction limited cluster aggregation (RLA) process. Experimental results obtained from light scattering and electrophoresis experiments enable us to probe the kinetics of such growth processes.

Small-Angle Neutron Scattering Study of Natural Aquatic Nanocolloids

We examine the potential of small-angle neutron scattering (SANS) as a quantitative tool for studying nanostructure and length scales in natural freshwater aquatic colloidal dispersions (river water, river bed sediments, agricultural field drainage and slurry). Our results show that natural aquatic colloids are generally fractal with 3D network-type structures. None of these structures are consistent with diffusion-limited (DLCA) or reaction-limited (RLCA) particleparticle aggregation processes. The results also suggest three characteristic length scales: one ca. 3-10 nm, which we identify with "primary particle" sizes, another of ca. 20-50 nm suggestive of small aggregates, and the last ca. 50-200 nm which we postulate arises from transient networks of the aggregates. The role of organic matter in mediating colloid structure in aquatic dispersions was examined by neutron contrast variation and by measuring samples both before and after treatment with hydrogen peroxide. The results suggest that the aggregate network structure is mediated by organic matter.

A heuristic formula for turbulence-induced flocculation of cohesive sediment

This paper presents new measurements on the settling velocity of mud flocs in the Lower Sea Scheldt, Belgium, and compares the results with data obtained previously in the Tamar estuary, UK. The data show that the flocs are fairly compact with a fractal dimension of about 2.2, which is indicative for reaction limited aggregation processes, characteristic in dynamic aquatic systems with large tidal flow velocities and high SPM (suspended particulate matter) concentrations. The data also reveal a fairly small dependency of the settling velocity from SPM concentrations, consistently much smaller than earlier data published in literature. Furthermore, a simple explicit formulation is proposed for the settling velocity of cohesive sediment in estuaries and coastal seas. It is derived from an analytical solution of a Lagrangean flocculation model, which accounts for turbulence-induced aggregation and floc break-up. Also the effects of variations in SPM and of a limited residence time of the flocs in the turbulent water column are included. The model has been calibrated against data from settling velocity measurements carried out in the Tamar estuary. Values of the measured settling velocity vary between 0.5 and 5 mm s −1 at SPM-values between 0.05 and 8 g l −1. Using the tuned coefficients, the model describes the observations satisfactory, with an overall relative standard deviation of 30%. Also, the well-known and observed increase in settling velocity with turbulent shear stress at low stresses and the opposite trend at high stresses is described properly. Next, the model is applied to the new data obtained in the Lower Sea Scheldt estuary, again comparing favourably with overall relative standard deviations of 30–50%. It appeared that the coefficients of the model can be determined from independent measurements, but two of them have to be determined by trial and error, for which a simple procedure is proposed.

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.

Cluster-cluster aggregation controlled by the number of intercluster connections: kinetics of aggregation and cluster mass frequency.

The aggregation of colloids in the presence of hydrodynamic forces was investigated, employing a numerical model that took into account the masses of the individual clusters and the number of intercluster connections established when two clusters stuck together. The number of possible connections was determined by analyzing all the possible nonoverlapping configurations of stuck clusters. This operation was done for a couple of clusters of various masses, taking into account the assembly of clusters of even and uneven masses. The formulation of the constraints established a certain hierarchy in the sticking on a basis compatible with the irregular fracture model of Horwatt and co-workers. As a result, the permanent sticking of large clusters required the formation of a large number of connections, whereas that of small clusters might be realized even with a small number of connections. Thus, the aggregation started with the features of the standard reaction-limited process and this cluster growth became progressively inhibited as a result of the prevailing effects of the connection constraints. The cluster-mass frequency showed the emergence at least of a second population whose bell-shaped mass distribution was superimposed on the monotonically decreasing distribution resulting from the reaction-limited aggregation process. The results of the numerical study were confronted with those previously obtained in the aggregation of hydrated polystyrene latex particles dispersed in 1 M sodium chloride solution. The two striking features--the aggregate growth kinetics and the mass distribution function--were common to the computer-generated clusters and the latex aggregates.

Structure and cohesion of weakly agglomerated fractal systems

We investigated the cohesion of agglomerates formed by sticking together two fractal clusters with the assumption that this parameter can be measured by the number of connections that were established on sticking. In a first step, clusters of selected mass were generated by numerical simulation of the aggregation process on a cubic lattice using the usual algorithm of the diffusion- or reaction-limited aggregation process. Then, agglomerates of various configurations were formed by assembling two by two clusters of even or uneven masses. For each system, the average connection frequency and the total number of configurations were determined. This investigation provided agglomerate characteristics that were determined to be independent of the agglomerate mass (in the domain of large agglomerates) and only dependent of the conditions of the cluster formation. In a second step, aggregates were formed in experiments carried out under conditions of diffusion- or reaction-limited aggregation (as fixed by the electrolyte concentration) as well as under orthokinetic and perikinetic aggregation conditions for aggregates formed in the presence of a small amount of polyvinylpyridine. The fragmentation of all these aggregates was promoted by immersing aggregate samples in polyvinylpyridine solutions of high concentration. Whereas the rate of decrease of the average masses of the aggregates was found to depend on the aggregate mass or the characteristics of the fragmenting medium, the rate of fragmentation a( n) for aggregates of mass n might be expressed by the scaling law a( n)∝ n λ . The exponent λ was found to only depend of the experimental conditions of the aggregate formation. The comparison between results of the numerical and experimental investigations seems to indicate that the number of intra-agglomerate connections effectively control the rate of fragmentation and thus the aggregate cohesion.

Structural Evolution of an Interpolyelectrolyte Complex of Charged Dendrimers Interacting with Poly(l-glutamate)

The size and molecular mass of water-soluble interpolyelectrolyte complex (PEC) formed between poly(l-glutamate) and poly(amido amine) dendrimer in aqueous solution were estimated as a function of the decreasing pH from the turbidities (τ) and their wavelength dependence, by comparison with numerical τ calculations by applying the Rayleigh−Debye−Gans and Mie scattering theories. Close to the pKa of the peripheral amino groups of the dendrimer, PECs with densities comparable to that of fractal clusters from a reaction limited colloid aggregation process collapsed to dense particles with ∼1 μm diameter. At a pH close to the pKa of the amino groups in the interior of the dendrimer, systems with carboxylate excess over amino/ammonium groups formed compact particles, and ion pairing likely extended to the ammonium groups in the dendrimer interior. PECs with the highest polymer density were formed at the stoichiometric ratio: They appeared to be stable against dissociation at pH 3 in contrast to PECs formed wi...