Structure of polydispersed colloids characterised by light scattering and electron microscopy

The dynamics of growth and aggregation of colloidal silver iodide particles was followed by the static light scattering method. The particles were treated as spheres and they were stable in size in the defined time interval. This approach enabled the use of the Zimm plots in order to determine the radii of gyration and the radii of spherical particles. Stable AgI colloids, either positively or negatively charged, showed the usual Zimm diagrams, while the diagrams were untypical when the stability of the colloids decreased. The untypical Zimm diagrams showed 'curves' with envelopes and 'curves' with minima in the unstable domain and in the domain where the most rapid nucleation occurs, respectively. Satisfactory agreement of particle sizes within the limits of accuracy, determined using static--and dynamic light scattering data and of the values obtained from the electron microscopic images was shown. Fitting the theoretical and experimental data, P(theta) functions showed that the particle shapes approach the theoretical model for spheres and thin discs. The colloid stability of polydispersed aggregates was also explained using the second virial coefficient, its negative sign implying interaction of particles in the solution, its positive value indicating formation of new particles from the supernatant solution. In addition, the colloid stability can be characterised by the mass fractal dimension. For positive stable colloids, Dm = 2.70 +/- 0.26, it can be related to the reaction controlled processes, whereas for negative stable colloids, Dm = 1.97 +/- 0.19, it was attributed to the diffusion controlled processes.     

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.     

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.     

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.     

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.     

Relation between aggregation kinetics and the structure of kaolinite aggregates

Dynamic and static light scattering were applied to the determination of the stability ratio and fractal dimension of kaolinite (KGa-2) at different kaolinite or/and electrolyte concentrations at pH 9.5. Dynamic light scattering was used to measure the kinetics of early stage aggregation to determine the stability ratio, W, as well as the cluster sizes which determine the fractal regime. Static light scattering was used to measure the fractal dimension, D(f). Results show that the two classes of "universality" (Lin et al. Nature 1989, 339, 360) characterizing the diffusion- and reaction-limited regimes of cluster-cluster aggregation do apply to colloidal kaolinite as limit cases when W approximately 1 or W > 100, respectively. In the intermediate regime where 5 < W < 100, the growth of the aggregate radius showed a power-law behavior similar to diffusion-limited cluster aggregation. For the intermediate aggregation regime, a scaling relation between fractal dimension and stability ratio, reflecting a continuous increase in particle packing density in the aggregate as the sticking probability of particles was reduced, was demonstrated.     

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.     

Scattering structure factor of colloidal gels characterized by static light scattering, small-angle light scattering, and small-angle neutron scattering measurements

The scattering structure factor of a colloidal gel in a q range of 5 orders of magnitude has been determined by combining static light scattering, small-angle light scattering, and neutron scattering measurements. It exhibits simultaneously two types of structure information: a mass fractal scaling within the clusters that constitute the gel and a surface fractal scaling for length scales larger than that of the clusters. Such scattering behavior can be well interpreted by the pair-correlation function proposed in the literature to model an ideal structure constituted of mass fractal objects inside surface fractal objects.     

Characterization of Enzymatically Induced Aggregation of Casein Micelles in Natural Concentration by in Situ Static Light Scattering and Ultra Low Shear Viscosimetry

The aggregation of casein micelles in undiluted skim milk after the addition of chymosin was studied by static light scattering and ultra low shear viscometry. The static light scattering measurements were made with two different sample thicknesses, 72 and 16 μm. The scattering data were analyzed by indirect Fourier transformation and by the polydispersity inversion technique which led to pair distance distribution functions and size distribution function, respectively. The minimum scattering angle was 1 degrees, which allows for the determination of particle sizes up to a maximum diameter of 12 μm. The fractal dimension determined from double logarithmic plots of intensity versus scattering vector resulted in values between 1.9 and 2.0. The influence of multiple scattering was determined by comparison of the measurements with the different sample thicknesses. The measurements show no significant influence of multiple scattering when the transmission is above 0.85. Due to the very complex and porous structure of the casein aggregates the Rayleigh-Debye-Gans scattering theory has been used in the data analysis. Measurements with a new instrument using ultra low shear showed good agreement with theory. Copyright 1999 Academic Press.     

Investigations on the semi-batch precipitation of silica

The semi-batch precipitation process of silica from sodium silicate and sulphuric acid has been structured into a primary particle production stage, an aggregation process until the gel point is reached and finally a gel fragmentation and compaction process. The progress of aggregation was analyzed by photon correlation spectroscopy. The reaction limited aggregation kernel was found to be proportional to B'(t)(q(p - q))A/2, where A assumes the value of one. The quantity B'(t) varies between 3.4 x 10(-20) and 2.6 x 10(-20) 1/min and is only a weak function of time. The stability ratio W for the aggregation process decreases with increasing aggregate size. During the period after the gel point the gel fragmentates. The gel clusters have an initial fractal dimension of approximately 1.8 which rapidly increases to 2.4 and stays roughly constant until the end of the process. The specific surface area decreases from 480 to 300 m2/g. The primary particles have a uniform size of 22.7 nm.     

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.     

Characterisation of poly(N-isopropylacrylamide) by asymmetrical flow field-flow fractionation, dynamic light scattering, and size exclusion chromatography

Asymmetrical flow field-flow fractionation (AsFIFFF) was used to determine the hydrodynamic particle sizes, molar masses, and phase transition behaviour of various poly(N-isopropylacrylamide) (PNIPAM) samples synthesised by reversible addition--fragmentation chain transfer (RAFT) and conventional free radical polymerisation processes. The results were compared with corresponding data obtained by dynamic light scattering (DLS) and size exclusion chromatography (SEC). Agreement between the three methods was good except at higher molar masses, where the molar mass averages obtained by SEC were much lower than those obtained by AsFIFFF and light scattering. The aggregation of the polymers, which are thermally sensitive, was studied by DLS and AsFIFFF at various temperatures. In deionised water there was an abrupt change in the particle size due to phase separation at approximately equal to 32-35 degrees C. The critical temperatures determined by AsFIFFF were 3-5 degrees C higher than those obtained by DLS.     

Morphology of dry lignins and size and shape of dissolved kraft lignin particles by X-ray scattering

Lignin is a highly branched polymer consisting of phenylpropane units, and it is one of the ingredients of the supporting matrix in plant cell walls. The morphology of several lignins extracted from plant cell walls using different methods was studied by small-angle and ultra-small-angle X-ray scattering. A power-law type intensity was observed for the dry lignins, but on the basis of the power-law exponent the fractal approach often applied to lignins is not fully justified. However, the intensity of kraft lignin did show a power law with surface fractal dimension D(s) = 2.7 +/- 0.1. The specific surface area of the lignins ranged from about 0.5 to 60 m(2)/g with 20% relative accuracy. The radius of gyration was determined from small-angle X-ray scattering data for aqueous solutions of kraft lignin. The shape of the particles in NaCl and NaOH solutions was found to be elongated. The particles were about 1-3 nm thick, while the length (5-9 nm) depended on the solvent and on the lignin concentration. The size of these primary particles was approximately the same as the size of the pores in the fractal aggregates of the dry kraft lignin. Their size was determined to be about 3.5 nm.     

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.     

Experimental investigation of colloidal gel structures

We investigate experimentally the structural properties of colloidal gels, formed under both diffusion-limited and reaction-limited aggregation conditions, using light scattering measurements and compare the results with the literature Monte Carlo (MC) simulations. The scattering structure factors have been measured for the two classes of gels in the range of the particle volume fractions between 0.02 and 0.07. From these, the corresponding fractal dimension values have been estimated. These have been found to be in good agreement with those estimated from the structure factors computed from MC simulated gels. On the basis of our previous research (Lattuada et al. Langmuir 2003, 19, 6312), this confirms that the scattering structure factor of a gel provides erroneously a small fractal dimension value, which decreases as the particle volume fraction increases. Furthermore, it is observed that the average size of the fractal clusters is larger in real gels than in simulated gels.     

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   

Prediction of three-dimensional fractal dimensions using the two-dimensional properties of fractal aggregates

Fractal dimension analysis using an optical imaging analysis technique is a powerful tool in obtaining morphological information of particulate aggregates formed in coagulation processes. However, as image analysis uses two-dimensional projected images of the aggregates, it is only applicable to one and two-dimensional fractal analyses. In this study, three-dimensional fractal dimensions are estimated from image analysis by characterizing relationships between three-dimensional fractal dimensions (D(3)) and one (D(1)) and two-dimensional fractal dimensions (D(2) and D(pf)). The characterization of these fractal dimensions were achieved by creating populations of aggregates based on the pre-defined radius of gyration while varying the number of primary particles in an aggregate and three-dimensional fractal dimensions. Approximately 2000 simulated aggregates were grouped into 33 populations based on the radius of gyration of each aggregate class. Each population included from 15 to 115 aggregates and the number of primary particles in an aggregate varied from 10 to 1000. Characterization of the fractal dimensions demonstrated that the one-dimensional fractal dimensions could not be used to estimate two- and three-dimensional fractal dimensions. However, two-dimensional fractal dimensions obtained statistically, well-characterized relationships with aggregates of a three-dimensional fractal characterization. Three-dimensional fractal dimensions obtained in this study were compared with previously published experimental values where both two-dimensional fractal and three-dimensional fractal data were given. In the case of inorganic aggregates, when experimentally obtained three-dimensional fractal dimensions were 1.75, 1.86, 1.83+/-0.07, 2.24+/-0.22, and 1.72+/-0.13, computed three-dimensional fractal dimensions using two-dimensional fractal dimensions were 1.75, 1.76, 1.77+/-0.04, 2.11+/-0.09, and 1.76+/-0.03, respectively. However, when primary particles were biological colloids, experimentally obtained three-dimensional fractal dimensions were 1.99+/-0.08 and 2.14+/-0.04, and computed values were both 1.79+/-0.08. Analysis of the three-dimensional fractal dimensions with the imaging analysis technique was comparable to the conventional methods of both light scattering and electrical sensing when primary particles are inorganic colloids.     

Kinetics of gold nanoparticle aggregation: experiments and modeling

We investigate the aggregation kinetics of gold nanoparticles using both experimental techniques (i.e., quasi-elastic light scattering, UV-visible spectroscopy, and transmission electron microscopy) and mathematical modeling (i.e., constant-number Monte Carlo). Aggregation of gold nanoparticles is induced by replacing the surface citrate groups with benzyl mercaptan. We show that the experimental results can be well described by the model in which interparticle interactions are described by the classical DLVO theory. We find that final gold nanoparticle aggregates have a fractal structure with a mass fractal dimension of 2.1-2.2. Aggregation of approximately 11 initial gold nanoparticles appears to be responsible for the initial color change of suspension. This kinetic study can be used to predict the time required for the initial color change of a gold nanoparticle suspension and should provide insights into the design and optimization of colorimetric sensors that utilize aggregation of gold nanoparticles.     

Roles of nucleation, denucleation, coarsening, and aggregation kinetics in nanoparticle preparations and neurological disease

Kinetic models for nucleation, denucleation, Ostwald ripening (OR), and nanoparticle (NP) aggregation are presented and discussed from a physicochemical standpoint, in terms of their role in current NP preparations. Each of the four solid-state mechanisms discussed predict a distinct time dependence for the evolution of the mean particle radius over time. Additionally, they each predict visually different particle size distributions (PSDs) under limiting steady-state (time-independent) conditions. While nucleation and denucleation represent phase transformation mechanisms, OR and NP aggregation do not. Thus, when modeling solid-state kinetics relevant to NP processing, either the time evolution of the mean particle radius or the fractional conversion data should be fit using appropriate models (discussed herein), without confusing/combining the two classes of models. Experimental data taken from the recent literature are used to demonstrate the usefulness of the models in real-world applications. Specifically, the following examples are discussed: the preparation of bismuth NPs, the synthesis of copper indium sulfide nanocrystals, and the aggregation of neurological proteins. Because the last process is found to obey reaction-limited colloid aggregation (RLCA) kinetics, potential connections between protein aggregation rates, the onset of neurological disease, and population lifespan dynamics are suggested by drawing a parallel between RLCA kinetics and Gompertz kinetics. The physical chemistry underpinning NP aggregation is investigated, and a detailed definition of the rate constant of aggregation, k(a), is put forth that provides insight into the origin of the activation energy barrier of aggregation. For the two nanocrystal preparations investigated, the initial kinetics are found to be well-described by the author's dispersive kinetic model for nucleation-and-growth, while the late-stage NP size evolution is dominated by OR. At intermediate times, it is thought that the two mechanisms both contribute to the NP growth, resulting in PSD focusing as discussed in a previous work [Skrdla, P. J. J. Phys. Chem. C2012, 116, 214-225]. On the basis of these two mechanisms, a synthetic procedure for obtaining monodisperse NP PSDs, of small and/or systematically targeted mean sizes, is proposed.