Fractal Growth and Structure in Ceramic Science (original) (raw)
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Structure of Random Silicates: Polymers, Colloids, and Porous Solids*
Fractals in Physics, 1986
Small angle x-ray scatteri ng and light scattering are used to characterize structures grown by rando~ processes wit~in the ~i l ica s~stem. Dense coll oids. rough colloids . and branched polymer s are grown by polymeri zation in sol ution . Supermolecular structures are also studied including gel s. coll oi dal 1\qui ds . and aggregates.
Structure of Soluble Silicates
MRS Proceedings, 1984
Small angle x-ray scattering (SAXS) is the technique of choice for the determination of structure on the 10-1000A scale.
Fractal Aspects of Ceramic Synthesis
MRS Proceedings, 1986
ABSTRACTThe concept of fractal geometry is used to describe the structure of silica polymers, colloidal aggregates, and critical systems. We illustrate the interpretation of scattering curves (X-ray, neutron and light) for fractal systems, and review simple growth models which generate fractal structures. We describe the polymerization of silica under various conditions and demonstrate that, depending on chemical conditions, polymerization maps onto simple fractal growth processes. The key factors which control growth are monomer-cluster vs. cluster-cluster growth, and reaction-limited vs. diffusion-limited growth.
Large-Scale Morphology of Dispersed Layered Silicates
MRS Proceedings, 2004
ABSTRACTUltra small angle x-ray scattering is used to probe the morphology of highly dispersed montmorillonite (MMT) in water and polyamide-66. In water the scattered intensity, I(q) shows a q-2 dependence for q > 0.01 Å-1, where q is the magnitude of the scattering vector. This is as expected for a two dimensional sheet-like object. On larger scales (smaller q) mass-fractal character is evident up to the radius-of-gyration of the individual scattering entities. The scattering profile is interpreted using a semi-flexible sheet model in which flat, disk-like entities of radius = 80 Å (an areal persistence length) are fractally distributed on large scales with a mass fractal dimension of 2.65. These size scales correspond to a scattering entity comprised of one or a few crumpled sheets. No evidence of inter-particle correlations is found at concentrations below the gel point. In polyamide-66 loaded with organically modified MMT long-range fractal behavior is also observed but with ...
Polymers, Fractals, and Ceramic Materials
Science, 1989
Concepts borrowed from polymer science have been applied to tailor the properties of inorganic materials, especially those derived from amorphous precursors. Fractal geometry can be used to characterize macromolecular precursors and to relate their structures to kinetic growth processes. Within the silica system, for example, it is possible to manipulate the conditions of solution polymerization to yield a variety of macromolecules from branched chains to smooth colloidal particles.
LIGHT SCATTERING INVESTIGATION OF THE FRACTAL BEHAVIOUR OF SILICA GELS
Le Journal de Physique Colloques, 1989
RBsume -L'intensitB lumineuse diffusee par les gels de silice prBsente une dBpendance, en fonction du vecteur d'onde, caracteristique des objets fractals en masse. On peut ainsi determiner la longueur de correlation 6 au-delA de laquelle le matBriau est homogene et la dimension fractale D.
Small-angle x-ray scattering study of the fractal morphology of porous silicas
The Journal of Chemical Physics, 1989
Small-angle x-ray and neutron scattering measurements have shown that on a length scale smaller than the average pore diameter but larger than the diameters of atoms or small molecules, the pore surfaces in four commercial porous silica gels with average pore diameters ranging from approximately 200 to 2500 A are fractal and have a fractal dimension D = 2.15 ± 0.10. When these gels were manufactured, the nonequilibrium micropore structure ,,:as relaxed by thermal methods:, The scattering data indicate that in the gels with average pore dlameters of about 200 and 500 A, and perhaps also in the two gels with larger average pore diameters, the relaxation process leads to a pore structure nearly identical in form but on a larger scale than the structure in a gel with an average pore diameter of 60 A that was the material from which the other four gels were produced.
Small-angle-scattering determination of the microstructure of porous silica precursor bodies
Journal of Applied Crystallography, 1990
Small-angle X-ray and small-angle neutron scattering measurements were carried out on a series of porous silica precursor (unsintered) bodies with different starting chemistries. The samples were prepared from mixtures containing 10 to 30 wt% colloidal silica sol and 90 to 70 wt% potassium silicate. Particle-size distributions were derived from the data using a maximum-entropy technique. Scattering data from the porous silica samples are especially suitable for such an analysis because the colloidal particles and clusters and aggregates of these particles are verified in detail to be spherical, and the scattering instrument use for this study covered the entire range of sizes in this material and was very well calibrated. It was found that the lower the amount of colloidal silica, the broader the size distribution of the silica aggregates.
Journal of Colloid and Interface Science, 2000
The early stages of formation of Stöber silica particles have been investigated in situ during the hydrolysis and condensation of tetraethylorthosilicate under base-ammonia conditions in different alcoholic solvents. Time-resolved ultra-small-angle X-ray scattering by the entities produced in the solutions is used for structural characterization and monitoring of the growth kinetics of the particles. Our primary focus is to assess the polydispersity of the formed colloidal particles and its evolution as a function of time. We first applied a maximum entropy analysis of the scattering data to determine the size distribution and the time evolution of the size distribution of the colloidal particles. Second, we extended the cumulant method to analyze our earlier small-angle X-ray scattering data (H. Boukari, J. S. Lin, and M. T. Harris, J. Colloid Interface Sci. 194, 311, 1997; Chem. Mater. 9, 2376, 1997) and search for the presence of a distribution of fractal particles. The maximum entropy analysis indicates that there is a continuous nucleation of particles during the synthesis, and that this takes place within a relatively narrow size distribution. The cumulant analysis shows that, except at later times, the data are not adequate to confirm conclusively the presence of a distribution of fractal dimension at any time during the experiment. We discuss the impact of these results on growth kinetic models proposed for this system. C 2000 Academic Press