A SAXS study of the nanostructural characteristics of TEOS-derived sonogels upon heat treatment up to 1100 degrees C

Xerogels obtained from the acid-catalyzed and ultrasound stimulated hydrolysis of TEOS were submitted to heat treatment at temperatures ranging from 60 to 1100 degreesC and studied by small-angle X-ray scattering (SAXS). The SAXS intensity as a function of the modulus of the scattering vector q was obtained in the range from q(0) = 0.19 to q(m) = 4.4 nm(-1). At 60 degreesC the xerogels exhibit an apparent surface fractal structure with a fractal dimension D-s similar to 2.5 in a length scale ranging from 1/q(1) similar to 1 to 1/q(m) similar to 0.22 nm. This structure becomes extremely rough at 120 degreesC (D-s similar to 3) and at 150 degreesC, it apparently converts to a mass fractal with a fractal dimension D similar to 2.4. This may mean an emptying of the pores with preservation of a share of the original mass fractal structure of the wet aged gel, for it had presented a mass fractal dimension D similar to 2.2. A well characterized porous structure formed by 2.0 nm mean size pores with smooth surface of about 380 m(2)/g is formed at 300 degreesC and remains stable until approximately 800 degreesC. At 900 degreesC the SAXS intensity vanishes indicating the disappearance of the pores in the probed length scale. The elimination of the nanopores occurs by a mechanism in which the number of pores diminishes keeping constant their mean size. The xerogels exhibit a foaming phenomenon above 900 degreesC and scatter following Porod's law as does a surface formed by a coarse structure. (C) 2002 Elsevier B.V. B.V. All rights reserved.

SAXS study of gelation, aging and drying of silica-polypropyleneglycol hybrid materials

New silica-polypropyleneglycol ormosils (organically modified silicates) with covalent bends between the organic (polymer) and inorganic (silica) phases have been prepared by the sol-gel process. Their structural evolution during sol formation, sol-gel transition, gel aging and drying has been studied in situ by small-angle X-ray scattering (SAXS). The experimental SAXS curves corresponding to sols and gels exhibit features expected from fractal objects. Clusters of size around 55 Angstrom with an initial fractal dimension D = 2.4 are formed in the sol. They are constituted of small primary silica particles chemically crosslinked at the end of the polymer chains. A strong liquid-like spatial correlation between the silica particles develops during drying due to the shrinkage of the polymeric network induced by water and ethanol evaporation. The continuous increase in SAXS intensity during drying, while the interparticle distance remains constant, is a consequence of the progressive growth of the dry fraction of the total volume. After drying, the gel structure consists of a rather compact arrangement of silica particles embedded in the polypropyleneglycol matrix.

Structure and luminescence of Eu3+-doped class I siloxane-poly(ethylene glycol) hybrids

Transparent, flexible, and luminescent EU3+-doped siloxane-poly(ethylene glycol) (PEG) nanocomposites have been obtained by the sol-gel process. The inorganic (siloxane) and organic PEG phases are usually linked by weak bonds (hydrogen bonds or van der Waals forces), and small-angle X-ray scattering (SAXS) measurements suggest that the structure of these materials consists of fractal siloxane aggregates embedded in the PEG matrix. For low Eu3+ contents, n = 300 and n = 80, the aggregates are small and isolated and their fractal dimensions are 2.1 and 1.7, respectively. These values are close to those expected for gelation mechanisms consisting of reaction-limited cluster-cluster aggregation (RLCCA) and diffusion-limited cluster-cluster aggregation (DLCCA). For high Eu3+ content, SAYS results are consistent with a two-level structure: a primary level of siloxane aggregates and a second level, much larger, formed by the coalescence of the primary ones. The observed increase in the glass transition temperature for increasing Eu3+ content is consistent with the structural model derived from SAXS measurements. Extended X-ray absorption fine structure (EXAFS) and luminescence spectroscopy measurements indicate that under the experimental conditions utilized here Eu3+ ions do not strongly interact with the polymeric phase.

DYNAMICAL SCALING IN FRAGMENTATION

The dynamics of a fragmentation model is examined from the point of view of numerical simulation and rate equations. The model includes effects of temperature. The number n (s,t) of fragments of size s at time t is obtained and is found to obey the scaling form n(s,t) approximately s(-tau)t(omegasgamma e(-rhot) f(s/t(z)) where f(x) is a crossover function satisfying f(x) congruent-to 1 for x much less than and f(x) much less than 1 for x much greater than 1. The dependence of the critical exponents tau, omega, gamma and z on space dimensionality d is studied from d = 1 to 5. The result of the dynamics on fractal and nonfractal objects as well as on square and triangular lattices is also examined.

A SAXS study of kinetics of aggregation of TEOS-derived sonogels at different temperatures

The kinetics of aggregation of tetraethoxysilane (TEOS)-derived silica sols, produced by acid-catalyzed and ultrasound-stimulated hydrolysis, were studied by 'in situ' measurements of small-angle X-ray scattering (SAXS) at the temperatures 40 degreesC, 60 degreesC and 70 degreesC. The results were analyzed in terms of the evolution with time (t) of the SAXS intensity probing the mass fractal characteristics of the system, the average radius of gyration (Rc,) of the clusters and the number of primary particles per cluster. The aggregation process yields mass fractal structures which exhibit a scattering exponent (alpha) practically equal to 2, in the probed length scale range (5.3 nm < 1/q < 0.22 nm), beneath and even far beyond the gel point. This suggests that a is a direct measure of the real mass fractal dimension (D) of the structure. The precursor sol (pH = 2) exhibits I nm mean sized clusters with mass fractal dimension D similar to 1.9. Increasing the pH to 4.5, the cluster mean size and the number of primary particles per cluster increase but the system keeps a more opened structure (D similar to 1.4). In the first aggregation stages, D increases up to similar to2 by incorporating primary particles to the clusters without changing their mean size. From this stage, the aggregation progresses following a thermally activated scaling law well described by R-G similar tot(1/D) in all cases. This is indicative of a diffusion-controlled cluster-cluster aggregation process. The activation energy of the process was found to be 91.7 kJ/mol. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Gelation of siloxane-poly(oxypropylene) composites

The viscoelastic properties of siloxane-poly(oxypropylene) (PPO) nanocomposites prepared by the sol-gel process has been analyzed during gelation by dynamic rheological measurements. The changes of storage and loss moduli, complex viscosity and phase angle has been measured as a function of time showing the newtonian viscosity of the sol in the initial step of gelation, and its progressive transformation to a viscoelastic gel. The rheologic properties have been correlated to mass fractal, nearly linear growth models and percolation theory. This study, completed by quasi-elastic light scattering and Si-29 solid state nuclear magnetic resonance measurements, shows that the mechanisms of gelation of siloxane-PPO hybrids depend on the molecular weight of the polymer and on the pH of the hybrid sol. For hybrids prepared in acid medium, a polymerization involving silicon reactive species located at the extremity of the polymer chains and presenting a functionality f = 2 occurs, forming a fractal structure during the first stage of sol-gel transition. For samples prepared under neutral pH, the fractal growth is only observed for hybrids containing short polymer chains (M-w similar to 130 gmol(-1)). The fractal dimensionality determined from the change in the rheological properties, indicates that the fractal growth mechanism changes from reaction-limited to diffusion-limited aggregation when the molecular weight of the PPO increases from 130 to 4000 gmol(-1) and as catalyst conditions change from acidic to neutral. Near the gel point, these hybrid gels have the typical scaling behavior expected from percolation theory. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Thermostimulated sol-gel transition in suspensions of sulfate zirconium oxychloride

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Role of the surface state and structural feature in the thermoreversible sol-gel transition of a zirconyl aqueous precursor modified by sulfuric acid

The sols produced by admixture of ZrOCl2 acidified solutions to hot H2SO4 aqueous solutions were studied to clarify the effects of Cl- and SO42- ions on the kinetic stability of nanoparticles and to obtain some new evidence concerning the mechanism of a thermoreversible sol-gel transition observed in this system. The study of suspensions prepared with different molar ratios R-S = [Zr]/[SO42-] and R-Cl = [Zr]/[Cl-] revealed domains of composition of formation of thermoreversible gels, thermostable sols, and powder precipitation. The effects of R-S and R-Cl on the structural features of nanoparticles and on the particle solution interface were systematically analyzed for samples of thermoreversible and thermostable sol domains. Small-angle X-ray scattering measurements revealed the presence of small fractal aggregates in all samples of thermoreversible domains, while compact packing aggregates of primary particles are present in the thermostable sol. Extended X-ray absorption fine structure and elemental chemical analysis revealed that irrespective of the nominal value of R-S and R-Cl all studied samples of the thermoreversible domain are constituted by a well-defined compound possessing an inner core made of hydroxyl and oxo groups bridging together zirconium atoms surrounded on the surface by complexing sulfate ligands. zeta potentials of powders extracted by freeze-drying from the thermoreversible gel revealed a point of surface charge inversion attributed to the specific adsorption of SO42- ion. Thermoreversible gel formation is rationalized by considering the effect of the specific adsorption on the electrical double-layer repulsion together with the temperature dependency of the physical chemical properties of ions in solution.

Rheological study of the thermoreversible sol-gel transition of sulfate modified zirconyl chloride aqueous sol

The sols prepared by mixing a ZrOCl2 acidified solution to a hot H2SO4 aqueous solutions were studied in order to clarify the mechanism of thermoreversible sol-gel transition observed in this system. The viscoelastic properties of these suspensions were analyzed during the sol-gel transition by dynamic rheological measurements and quasi-elastic light scattering. The rheological properties were correlated to mass fractal and nearly linear growth models, and percolation theory. The results evidence that the thermoreversible sol-gel transition in this system is due to the formation of a network of physically linked aggregates having fractal structure. The decrease of the SO42- contents in the initial solution leads to the decrease of the fractal dimensionality from 2.3 to 1.8, indicating a change of the kinetic mechanism of aggregate growth. Near the gel point these samples have the typical scaling expected from percolation theory. (C) 2004 Elsevier B.V. All rights reserved.

Morphology characterization of layer-by-layer films from PAH/MA-co-DR13: the role of film thickness

We report on the use of dynamic scale theory and fractal analyses in the Study of distinct growth stages of layer-by-layer (LBL) films of poly(allylamine hydrochloride) (PAH) and a side-chain-substituted azobenzene copolymer (Ma-co-DR13). The LBL films were adsorbed oil glass substrates and characterized with atomic force microscopy with the Ma-co-DR13 at the top layer. The ganular morphology exhibited by the films allowed the observation of the growth process inside and outside the grains. The growth outside the grains was found to follow the Kardar-Parisi-Zhang model, with fractal dimensions of ca. 2.6. One could expect that inside the grains the morphology would be close to a Euclidian surface with fractal dimension of ca. 2 for any growth stage. The latter, however, was observed only for thicker films containing more than 10 bilayers. For thinner films the morphology was well described by a self-affine fractal. Such dependence of the growth behavior with the film thickness is associated with a more complete coverage of adsorption sites in thicker films due to diffusion of polymer molecules. (c) 2004 Elsevier B.V. All rights reserved.

Sol-gel transition in SnO2 colloidal suspensions: viscoelastic properties

This paper describes particle aggregation process during gelation of SnO2 hydrosols. The effect of the concentration of SnO2 colloidal particles on the kinetics of gelation of hydrosols containing PVA (poly(vinyl alcohol)) was analysed by dynamic rheological measurements. The complex viscosity and the storage and loss moduli have been measured during the sol-gel transition and the results correlated to mass fractal growth, nearly linear growth models, and scalar percolation theory. The analysis of the experimental results shows that a linear aggregation occurs in the initial step of the gelation followed by a fractal growth to form a three-dimensional network. Near the gel point this physical gel exhibits the typical scaling expected from an electrical percolation analogy. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Structure of weakly bonded PPG-silica nanocomposites

The structure of silica-polypropyleneglycol (PPG) nanocomposites with weak physical bonds between the organic (PPG) and inorganic (silica) phase, prepared by the sol-gel process, was investigated by small angle X-ray scattering (SAXS). These nanocomposite materials are transparent, flexible, have good chemical stability and exhibit high ionic conductivity when doped with lithium salt. Their structure was studied as a function of silica weight fraction x (0.06 less than or equal to x less than or equal to 0.29) and [O]/[Li] ratio (oxygens being of ether-type). The shape of the experimental SAXS curves agrees with that expected for scattering intensity produced by fractal aggregates sized between 30 and 90 Angstrom. This result suggests that the structure of the studied hybrids consists of silica fractal aggregates embedded in a matrix of PPG. The correlation length of the fractal aggregates decreases and the fractal dimension increases for increasing silica content. The variations in structural parameters for increasing Li+ doping indicate that lithium ions favor the growth of fractal silica aggregates without modifying their internal structure and promote the densification of the oligomeric PPG matrix.

Structural properties of silica gels prepared from oxalic-acid-catalyzed tetraethoxysilane sonohydrolysis

About similar to 2.1 x 10(-3) Mol SiO2 cm(-3) and similar to 88%-volume liquid-phase silica wet gels were prepared from oxalic-acid-catalyzed tetraethoxysilane (TEOS) sonohydrolysis. Aerogels were obtained by supercritical CO2 extraction. The samples were analyzed by thermogravimetry, small-angle X-ray scattering and nitrogen adsorption. Wet gels can be described as mass fractal structures with fractal dimension D similar to 1.94 and structural characteristic length zeta changing between similar to 3.3 to similar to 3.0 nm in the studied range of the catalyst concentration. A fraction of the porosity is apparently eliminated in the supercritical process. The values of the BET specific surface S-BET, the total pore volume V-p and the mean pore size l(p) of the aerogels were found to change almost randomly around the mean values S-BET = 874 m(2) g(-1), V-p = 0.961 cm(3) g(-1) and l(p) = 4.4 nm with catalyst concentration variation. These values were not substantially different from those from an equivalent HCl-catalyzed aerogel. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Formation and maintenance of complex systems

A complex system is often identified by the absence of a characteristic length, e.g. as in a fractal. A very large system subject to a fragmentation and/or aggregation dynamics passes through such complex configurations. We study statistically creation and maintenance of such configurations in space dimensions d = 1 to 5 and find that they are easily created (maintained) for small (large) d. An intermediate d such as d = 3 seems to be ideal for the creation and maintenance of complex systems. This has consequences in a statistical description of the universe.

Multifractal characterization of saprolite particle-size distributions after topsoil removal

Multifractal analysis is now increasingly used to characterize soil properties as it may provide more information than a single fractal model. During the building of a large reservoir on the Parana River (Brazil), a highly weathered soil profile was excavated to a depth between 5 and 8 m. Excavation resulted in an abandoned area with saprolite materials and, in this area, an experimental field was established to assess the effectiveness of different soil rehabilitation treatments. The experimental design consisted of randomized blocks. The aim of this work was to characterize particle-size distributions of the saprolite material and use the information obtained to assess between-block variability. Particle-size distributions of the experimental plots were characterized by multifractal techniques. Ninety-six soil samples were analyzed routinely for particle-size distribution by laser diffractometry in a range of scales, varying from 0.390 to 2000 mu m. Six different textural classes (USDA) were identified with a clay content ranging from 16.9% to 58.4%. Multifractal models described reasonably well the scaling properties of particle-size distributions of the saprolite material. This material exhibits a high entropy dimension, D-1. Parameters derived from the left side (q > 0) of the f(alpha) spectra, D-1, the correlation dimension (D-2) and the range (alpha(0)-alpha(q+)), as well as the total width of the spectra (alpha(max) - alpha(min)) all showed dependence on the clay content. Sand, silt and clay contents were significantly different among treatments as a consequence of soil intrinsic variability. The D, and the Holder exponent of order zero, alpha(0), were not significantly different between treatments; in contrast, D-2 and several fractal attributes describing the width of the f(alpha) spectra were significantly different between treatments. The only parameter showing significant differences between sampling depths was (alpha(0) - alpha(q+)). Scale independent fractal attributes may be useful for characterizing intrinsic particle-size distribution variability. (c) 2006 Elsevier B.V. All rights reserved.