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Aggregate structure, i.e., fractal dimension, has a coupled geometric and hydrodynamic impact on the aggregate collision frequencies. In this work, we evaluated different collision frequency kernel calculation schemes to simulate experimentally determined latex particle aggregation kinetics. Light scattering was used to simultaneously measure aggregate size and fractal dimension throughout the latex aggregation experiments. The intermediate collision scheme proposed by Veerepanneni and Wiesner (J. Colloid Interface Sci.177,45–57 (1996)) is in agreement with experimental aggregation kinetics if considered along with experimentally determined fractal dimension evolution. Aggregate restructuring was found to be an important mechanism in explaining aggregation kinetics.

A method based on static light scattering by fractal aggregates is introduced to extract structural information. In this study, we determine the scattered intensity by a fractal aggregate calculating the Structure and the Form factors noted, respectively, S(q) and F(q). We use the approximation of the mean field Mie scattering by fractal aggregates (R. Botet, P. Rannou, and M. Cabane, appl. opt.36, 8791, 1997). This approximation is validated by a comparison of the scattering and extinction cross sections values calculated using, on the one hand, Mie theory with a mean optical index n) and, on the other hand, the mean field approximation. Scattering and extinction cross sections values differ by about 5%. We show that the mean environment of primary scatterers characterized by the optical index nsmust be taken into account to interpret accurately the scattering pattern from fractal aggregates. Numerical simulations were done to evaluate the influence of the fractal dimension values (Df>2) and of the radius of gyration or the number of primary particles within the aggregates (N=50 to 250) on the scatterers' mean optical contrast (ns/n). This last parameter plays a major role in determining the Form factor F(q) which corresponds to the primary particles' scattering. In associating the mean optical index (n) to structural characteristics, this work provides a theoretical framework to be used to provide additional structural information from the scattering pattern of a fractal aggregate (cf. Part II).

Information on the size and structure of aggregates is critical in predicting the formation kinetics, settling velocities, and reactivity of particle aggregates. For some systems, however, accessing this information may be very difficult. Light scattering measurements are among the most useful techniques for accessing such information. In the case of large primary particles forming aggregates, the common Rayleigh approximation is not valid. Instead, Mie scattering must be used and multiple scattering must be accounted for. Moreover, size polydispersity and structure of aggregates are combined in the scattered intensity measurements. This work presents an experimental validation of a new theoretical approach for extracting information on both aggregate structure and size when multiple scattering cannot be neglected. The chemically controlled aggregation of 0.8-μm latex particles demonstrates the following: (1) Polydispersity effects prevent the interpretation of data to obtain structural information from the Structure factor S(q). (2) The calculated optical contrast decreasing during the aggregation can be correlated with the structural changes in the growing aggregates independently of size polydispersity. We have shown that a strict correlation can be obtained between the fractal dimension Dfand the scatterers' mean optical contrast calculated at large scattering angles. (3) The changes in the Form factor (F(q)) due to multiple scattering when particles are close together yield a predicted structure that is in agreement with expected fractal dimension values and therefore S(q) can be described in term of both structure and size polydispersity.

The structure of dimethyldioctadecylammonium-montmoril-Ionite is studied by nitrogen adsorption, methanol adsorption, and small angle X-ray scattering. It was shown that this material is an interstratified structure. The DDA molecules are arranged at different angles to the clay layers. In addition, there are some DDA molecules adsorbed on the external surfaces of the clay layers which prevent nitrogen molecules from entering the interlayer space, resulting in a very low surface area.

The fractal dimension of a particle aggregate can provide fundamental information on the structure and origin of the aggregate. The analysis of large chemically homogeneous fractal objects has been achieved, but reliable methods of estimating the fractal dimensions of large and chemically heterogeneous aggregates are needed. To this end, we used confocal scanning laser microscopy in which thin optical sections of aggregates were obtained in order to calculate their 2D and ultimately 3D fractal dimensions according to the Mandelbrot theory. Fractal dimensions of 2.08 ± 0.11 for a Brownian aggregation of latex particles and 2.25 ± 0.12 for shear aggregation were determined using the confocal technique. These values are within the ranges for universality classes predicted for such aggregates and observed by previous investigators. Thus, this method appears to provide reliable estimates of the fractal dimension with particular utility in the characterization of aggregates composed of larger particles or complex materials where the fractal dimension may not be accessible by light-scattering measurements. The confocal method is used to analyze flocs of activated sludge material as one example of the application of this method to more complex, large (up to 500 μm), and chemically heterogeneous flocs.

Fresh hydrous ferric oxides (HFO) are formed by precipitation of Fe3+solution or ferric polycations initially formed at very acidic pH at different neutralization ratios n= 2 and 2.5. At pH 6.5 the precipitates are particles with a positive surface charge. The IEP and the surface charge measured in NaCl electrolyte vary with n. But in all cases IEP or ZPSE are lower than 8.3. The adsorption of sodium dodecane sulfonate molecules at 20°C allows us to compare the different samples formed by precipitation from n= 0, n= 2, and n= 2.5 solutions and named "n= 0," "n= 2," and "n2.5." Using the two-dimensional adsorption on heterogeneous surfaces theory of Cases's group (Langmuir8, 1251 (1992)), it is possible to compare the different solids relatively to the affinity of surfactants for the surfaces. The energetic heterogeneity decreases in the following order, "n= 2" > "n= 2.5" > "n= 0." The adsorption isotherms present several plateaus. The evolution of ζ vs Ce mimics the evolution of Qa vs Ce. This indicates that the adsorption sites are mainly located on external surfaces as adsorption within micro- or mesopores would correspond to a constant zeta potential. The available specific surface area at pH 6.5 can be derived from the adsorption isotherms. The plateaus of the isotherms corresponding to ζ = 0 mV. The available specific surface area Scan then be calculated using the equation S=Qa· Na· A,where Qais the adsorbed amount (mol/g), Nais Avogadro's number, and Ais the molecular area in the hydrated crystal state (A= 20.8 Å2). The values of Sare 163, 134, and 139 m2/g for "n= 0," "n= 2," and "n= 2.5," respectively. DRIFT spectroscopy carried out on precipitates covered by various amounts of surfactants show that they are adsorbed on positively charge sites which are the = Fe - OH(H) singly coordinated sites located on edges of the double chain of βFeOOH-like particles. Continuous Ar gas adsorption technique on "n= 0," "n= 2," and "n= 2.5" freeze-dry samples shows that pore sizes of 6 Å are intercrystal pores present in βFeOOH solids and also that dry samples are microporous with a specific surface area of 300 m2/g. The large discrepancies between textural properties of HFO in water and in a dry state are certainly due to the possibility of HFO swelling in water.

The organoclays as dimethyldistearyl ammonium montmorillonite (DDA-Mt) are interstratified clays in which pure organic sheets and silicate layers coexist. The stacking disorder depends on the conformation of the DDA within the interlayer. This conformation depends on the quantity of sorbed vapor methanol. Immersion microcalorimetry of DDA-Mt in liquid methanol data shows endothermic reactions. The CH2/CH2bonds between two adjacent alkyl chains are disrupted atP/P0< 0.6 corresponding to two methanol molecules for one polar head. Beyond this value ΔHis constant.13C CP/MAS NMR data show, by correlation, that the mobility of the chains is strongly increased atP/P0> 0.6. Mobility and distance between alkyl chains vary in the same direction and correspond to an increase in the stacking order of the sheets within a particle.

Several assumptions are made when confocal scanning laser microscopy is used for the determination of the fractal dimension of aggregates. The purpose of this study is to experimentally show that one of these assumptions, which concerns the relation existing between the structure of an aggregate and that of its sections, is valid. A comparison between the structures of sections and reconstructed 3D edifices of latex aggregates shows that they are both directly related even in the case of relatively small aggregates.