Growth of Fractal Aggregates in the Intermediate Regime of Particle Accommodation

The growth dynamics of fractal aggregates was studied within the framework of continuum model in the self-consistent mean field approximation. The regime that is intermediate between the diffusion-limited aggregation and reaction-limited aggregation was considered. The dependence of aggregate fractal dimension on the attachment probability of particles during their collisions with an aggregate was obtained. In the limiting cases, the values of fractal dimension coincide with those determined earlier. The domain of the values of attachment probability was revealed where several regions characterized by their own values of fractal dimension were specified in the structure of growing cluster. Physical nature of the emergence of various regions in the aggregate structure was discussed.     

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.     

Self‐assembled supramolecular microgels: Fractal structure and aggregation mechanism

Multifunctional molecules were designed to produce microgels with specific structures. Both static light scattering and dynamic light scattering were employed to determine the fractal dimension of the microgels. The protein, avidin, was strongly bound to four biotin moieties. Biotin was attached covalently to specifically engineered peptide nucleic acid (PNA) oligomers. Three designed DNA oligomers self‐assembled to produce a trifunctional three‐way junction (TWJ) with single‐stranded ends that were complementary to the PNA sequence. The sizes of the supramolecular aggregates were characterized by dynamic light scattering. The fractal dimension was obtained from the angular dependence of the scattered intensity when the microgels were large enough. When the microgels were formed via cooling from a temperature above the melting point of the PNA–DNA helices, reversible structures with a fractal dimension of approximately 1.86 were formed, which is consistent with a cluster–cluster aggregation mechanism. When the microgels were formed by the slow addition of biotinylated PNA bound to the TWJ to a solution of avidin at room temperature, the observed fractal dimension approached 2.6, which is consistent with a point–cluster aggregation mechanism. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3037–3046, 2003     

Evidence of Shear Rate Dependence on Restructuring and Breakup of Latex Aggregates

Small-angle static light scattering has been used to probe the evolution of aggregate size and structure in the shear-induced aggregation of latex particles. The size of aggregates obtained from the particle-sizing instrument (Coulter LS230) was compared with the size of those obtained with another approach utilizing the Guinier equation on the scattering data. Comparison of the two methods for studying the effects of mixing on the evolution of the aggregate size with time revealed similar trends. The aggregate structures were quantified in terms of their fractal dimensions on the grounds of the validity of Rayleigh-Gans-Debye scattering theory for the fractal aggregates. Analysis of the scattering patterns of aggregates verified that restructuring of the aggregates occurred as the aggregates were exposed to certain shear environments, resulting in a scale-dependent structure that could not be quantified by a fractal dimension. The effect of restructuring on aggregate size was particularly noticeable when the aggregates were exposed to average shear rates of 40 to 80 s(-1), whereas no significant restructuring occurred at lower shear rates. At 100 s(-1), the fragmentation of aggregates appeared to be more significant than aggregate compac-tion. Copyright 2001 Academic Press.     

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.     

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.     

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   

Characterizing dispersion and fragmentation of fractal, pyrogenic silica nanoagglomerates by small-angle X-ray scattering

Typical characterization of nanoparticle dispersion and compounding processes by dynamic light scattering (DLS) and TEM lack quantitative information on fractal structure, aggregation number, and specific surface area. In this work a synchrotron ultra-small-angle X-ray scattering (USAXS) investigation on diffusion flame and 'Aerosil' silica powders, as well as on their desagglomeration by high-pressure liquid dispersion (200-1400 bar) is presented. Primary particle size, polydispersity, and specific surface area are measured for powders, stirred-in dispersions, and after high-pressure processing with identical results, showing the in-situ applicability of USAXS. These parameters, as well as the hard aggregate mass fractal dimension, with typically Df = 2.15 representing reaction-limited cluster aggregation, are determined by synthesis process conditions. They are unchanged even at the highest hydrodynamic stresses; thus, neither comminution nor agglomerate restructuring nor re-agglomeration occurs. Fragmentation reflects in decreasing radii of gyration, which are compared to mobility equivalent radii from DLS in agreement with theory.     

Heteroflocculation of binary latex dispersions of similar chemistry but varying size

The stability of dilute bimodal (diameter:100 and 200 nm) model latex dispersions is studied as a function of electrolyte concentration and particle number fraction by measuring perikinetic aggregation with dynamic light scattering. A formally correct expression for the effective, doublet stability ratio of a bimodal system is derived that accounts for the difference in the particle size and hence, extends the derivation by Hogg and co-workers [Trans. Faraday Soc. 62 (1966) 1638]. Including the particle size ratio predicts slightly lower stability ratios for polydisperse but chemically similar systems. Stability ratios for binary mixtures of model colloidal latices are extracted from aggregation measurements in the fractal aggregation regime and are compared to predictions based on DLVO calculations of the potential. The results suggest that the composition of the aggregates is dependent on the relative stability of the two components (and consequently, on electrolyte concentration) and is richer in the least stable component.     

Characterization of aggregate structures of phospholipid in the process of vesicle solubilization with sodium cholate using laser light scattering method

The aggregate structures formed during vesicle solubilization by sodium cholate, and their properties, were characterized by static laser light scattering (SLS) and electrophoretic light scattering (ELS) methods. The change in dissymmetry value Z₄₅ was observed by examining the regions of vesicles and micelles. The angular light scattering intensity data could be fitted with a modified shell model for the vesicles and a hollow cylinder model for the mixed micelles. In the case of the vesicles, the scattering curves were fitted with a spherical shell model by introducing the interparticle scattering factor S(q) and taking into account the intervesicle positional correlations, which is a function of the fractal dimension (D) and the interparticle correlation length (L). On the basis of the physical meanings of the fractal dimension and interparticle correlation length, the molecular packings of the membrane and the repulsive interaction between the vesicles were analyzed. Furthermore, using electrophoretic light scattering (ELS) the zeta potentials on the mixed vesicles were found to increase with the molar ratio (Re) of sodium cholate to egg yolk phosphatidylcholine (EggPC) in the membrane. It is suggested that the electrostatic properties of the vesicles result in repulsive interaction which is responsible for no fusion of the mixed vesicles. In addition, in the transition from vesicles to micelles, a cylinder-like micelle appeared as an intermediate structure.     

Fractal behavior of functionalized fullerene aggregates. I. Aggregation of two-handed tetraaminofullerene with DNA

In tris-buffered saline (TBS) with a trace of dimethylformamide (DMF), the homoaggregation process of a functionalized fullerene, the two-handed tetraaminofullerene (TH), and the heteroaggregation process (complex formation) of TH with DNA (pGL3-control plasmid) were studied dynamically by using a combination of static and dynamic laser light scattering measurements. Fractal behavior was investigated in the aggregation process of both TH homoaggregates and TH-DNA heteroaggregates. The stability of aggregates in solution depends on the molar concentration ratio R(M), defined as the molar ratio of moles of TH to moles of the DNA base pair. Higher R(M) values resulted in lower aggregate stability. The transition of the fractal dimension (Df) in TH homoaggregation by rapidly mixing 3.78 microM TH with an equal volume of the blank buffer was found to vary from a value of 1.46 to 2.02. Dynamic light scattering results revealed that, in the aggregation process, the change in the size distribution of aggregates with time could be related to a Df transition. In the Df transition region, the size distribution of homoaggregates displayed a drastic change from a single-mode distribution to a bimodal distribution, which clearly suggested a restructuring process with the formation of large aggregates. When the aggregation process finally reached equilibrium, Df = 2.02, the size of the homoaggregates had a single mode but a broad distribution. However, TH-DNA heteroaggregation showed a Df transition from 1.58 to 1.7, but over a shorter time range of less than 5 min. Then, the Df value fluctuated in the range of 1.7 and finally reached an equilibrium value of Df approximately 1.78, which was independent of molar concentration. There are two main action forces involved in the heteroaggregation process: van der Waals forces and attractive electrostatic forces, with the latter one being stronger and faster than that of the former. Therefore, a two-step action could occur in the heteroaggregation process. In the beginning of mixing, the attractive electrostatic forces dictated the aggregation process, and then van der Waals forces also got involved in the entire aggregation process. By using an initial concentration of 3.78 microM each and R(M) = 1, TH-DNA heteroaggregates showed more stable solution behavior than the homoaggregates. The lower Df value of the heteroaggregates could be related to a looser compact structure. Results from scanning electron microscopy (SEM) also disclosed the different textures between TH homoaggregates and TH-DNA heteroaggregates; the former had a more dense packing than the latter one.     

A simple model for the structure of fractal aggregates

Structural properties of small aggregates containing up to 100 particles have been studied through detailed Monte Carlo cluster-cluster aggregation simulations in both diffusion-limited and reaction-limited conditions. First, the radius of gyration, the radius of the smallest sphere encompassing the cluster, and the particle-particle correlation function, g(r), have been computed based on the positions of all the particles in the cluster, and their fractal scaling has been analyzed. Then, an empirical model has been developed to simulate the g(r) function for aggregates of any size and used to determine the corresponding structural properties and scattering structure factors. Finally, in order to illustrate the application of the structural properties thus computed, two experiments on diffusion-limited aggregation have been performed, and the average scattering structure factors have been measured as a function of time using a small-angle light-scattering device. The obtained average scattering structure factors have been simulated using the Smoluchowski population balance equations, using the single aggregate structural properties and scattering structure factor predicted by the developed empirical g(r) model.     

Estimation of the dynamic size of fractal aggregates

A model is presented for an aggregation act occurring between two aggregates of any mass and fractal dimension. The kinetics of aggregation is also analyzed, as well as some previous works concerning the structure of fractal aggregates. As a result, a generalized curve is derived describing the normalized dynamic radius of clusters of spherical character as dependent on both the aggregate fractal dimension and the space dimension. It is shown how the curve may be utilized to determine the dynamic size of anisotropic aggregates. The obtained dependence can be used to estimate the dynamic size of fractal aggregates, to evaluate the prefactor in mass–radius relation and to model the aggregation kinetics.     

Detailed model of the aggregation event between two fractal clusters

A model has been developed for describing the aggregation process of two fractal clusters under quiescent conditions. The model uses the approach originally proposed by Smoluchowski for the diffusion-limited aggregation of two spherical particles but accounts for the possibility of interpenetration between the fractal clusters. It is assumed that when a cluster diffuses toward a reference cluster their center-to-center distance can be smaller than the sum of their radii, and their aggregation process is modeled using a diffusion-reaction equation. The reactivity of the clusters is assumed to depend on the reactivity and number of their particles involved in the aggregation event. The model can be applied to evaluate the aggregation rate constant as a function of the prevailing operating conditions by simply changing the value of the particle stability ratio, without any a priori specification of a diffusion-limited cluster aggregation, reaction-limited cluster aggregation, or transition regime. Furthermore, the model allows one to estimate the structure properties of the formed cluster after the aggregation, based on the computed distance between the aggregating clusters in the final cluster.     

Structures of DNA-linked nanoparticle aggregates

The room-temperature structure of DNA-linked gold nanoparticle aggregates is investigated using a combination of experiment and theory. The experiments involve extinction spectroscopy measurements and dynamic light scattering measurements of aggregates made using 60 and 80 nm gold particles and 30 base-pair DNA. The theoretical studies use calculated spectra for models of the aggregate structures to determine which structure matches the observations. These models include diffusion-limited cluster-cluster aggregation (DLCA), reaction-limited cluster-cluster aggregation (RLCA), and compact (nonfractal) cluster aggregation. The diameter of the nanoparticles used in the experiments is larger than has been considered previously, and this provides greater sensitivity of spectra to aggregate structure. We show that the best match between experiment and theory occurs for the RLCA fractal structures. This indicates that DNA hybridization takes place under irreversible conditions in the room-temperature aggregation. Some possible structural variations which might influence the result are considered, including the edge-to-edge distance between nanoparticles, variation in the diameter of the nanoparticles, underlying lattice structures of on-lattice compact clusters, and positional disorders in the lattice structures. We find that these variations do not change the conclusion that the room-temperature structure of the aggregates is fractal. We also examine the variation in extinction at 260 nm as temperature is increased, showing that the decrease in extinction at temperatures below the melting temperature is related to a morphological change from fractal toward compact structures.     

Scattering Behavior of Restructured Aggregates: A Simulation Study

Simulations of diffusion-limited cluster-cluster aggregation (DLCA) with no restructuring, full restructuring, and partial restructuring have been performed. The scattering patterns produced from these aggregates have been simulated using the Rayleigh-Gans-Debye approximation. Pure DLCA aggregates produced a scattering pattern with the slope of the fractal region being about -1.8. In contrast, the slope of the fractal region of the scattering pattern for fully restructured aggregates was about -2.1, indicating an increase in fractal dimension. Partial restructuring at large length scales produced an upward turn in the scattering pattern at low qr(o), while at high qr(o) the fractal section of the pure DLCA aggregate was retained. This last result was expected and is consistent with the results and postulations of several other workers. This simulation shows that the type of scattering pattern often obtained from orthokinetic or sheared aggregation can be produced by restructuring of aggregates at large length scales. Copyright 2001 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.     

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.     

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

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