952 resultados para Fractal dimension


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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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The nanostructural characteristics of acid-catalyzed sonogels are studied along the aging process at 60 degreesC in saturated conditions and after the CO, supercritical extraction (aerogel). The structural evolution was studied by means of small-angle X-ray scattering (SAXS) and UV-Visible absorption techniques. The sonogel exhibits a mass fractal structure in a length scale between zeta - 1/q(0) similar to 5.3 and a(1) similar to 1/q(m) similar to 0.22 nm, as the length scale probed by SAXS. The apparent mass fractal dimension lightly increases from 2.0 for fresh gel until 2.2 for 14 days aging in wet conditions. The UV absorption also increases with the aging time in wet conditions. Both observations are consistent with the syneresis process accompanying the polycondensation progress during aging in saturated conditions. For long aging times, the wet sonogels show a light transition from a mass to a surface fractal. in a very small interval of the length scale, developing an extremely rough surface with fractal dimension D-S similar to 2.9, the fractal characteristics of the sonogels practically do not change with the alcohol exchange. With the CO2 supercritical extraction (aerogel). The interval in the length scale in which the surface fractal is defined increases, while the surface fractal dimension diminishes to D-S similar to 2.5. The mass fractal characteristics are less apparent in the aerogels. (C) 2001 Elsevier B.V. B.V. All rights reserved.

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The dynamic scale theory and fractal concepts are employed in the characterization of surface morphological properties of layer-by-layer (LBL) films from poly(o-methoxyaniline) (POMA) alternated with poly(vinyl sulfonic acid) (PVS). The fractal dimensions are found to depend on the procedures to fabricate the POMA/PVS multilayers, particularly with regard to the drying procedures. LBL films obtained via drying in ambient air show a more homogeneous surface, compared to films dried under vacuum or a flow of nitrogen, due to a uniform rearrangement of polymer molecules during solvent evaporation.

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The effect of temperature on the oxalic acid catalyzed sono-hydrolysis of tetramethoxysilane (TMOS) was studied by means of a heat flux calorimetric method. The activation energy of the process was measured as (24.5 +/- 0.8) kJ/mol in the temperature range between 10 and 50 degreesC. The structural characteristics of the resulting sonogels, after long period of aging in saturated conditions, were studied by means of small angle X-ray scattering. The structure can be described as formed by similar to2.7 nm mean size mass fractal-like aggregates (clusters) of primary silica particles of similar to0.3 nm mean size, all imbibed in a liquid phase. The average mass fractal dimension of the clusters was found to be 2.58. The primary particle density was estimated as 2.23 g/cm(3), in good agreement with the value frequently quoted for fused silica. The volume fraction of the clusters, in the saturated sonogels was estimated as about 28%. The moment in which the meniscus of the liquid phase penetrates into the clusters under rapid evaporation process has been detected by an inflection in the first derivative of the curve of weight loss in a simple thermogravimetric test. (C) 2003 Elsevier B.V. All rights reserved.

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We report on the use of dynamic scale theory and fractal analyses in a study of the growth stages of Langmuir-Blodgett (LB) films of polyaniline and a neutral biphosphinic ruthenium complex, namely mer-[ RuCl3 (dppb)(py)] (dppb = 1,4-bis(diphenylphosphine) buthane, py = pyridine), Rupy. The LB films were deposited onto indium-tin-oxide substrates and characterized with atomic force microscopy. From the granular morphology exhibited by the films one could infer growth processes inside and outside the grains. Growth outside was found to follow the Kardar-Parisi-Zhang model, with fractal dimensions of about 2.7. As one would expect, inside the grains the morphology is close to a Euclidian surface with fractal dimension of about 2.

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The purpose of this work was to study fragmentation of forest formations (mesophytic forest, riparian woodland and savannah vegetation (cerrado)) in a 15,774-ha study area located in the Municipal District of Botucatu in Southeastern Brazil (São Paulo State). A land use and land cover map was made from a color composition of a Landsat-5 thematic mapper (TM) image. The edge effect caused by habitat fragmentation was assessed by overlaying, on a geographic information system (GIS), the land use and land cover data with the spectral ratio. The degree of habitat fragmentation was analyzed by deriving: 1. mean patch area and perimeter; 2. patch number and density; 3. perimeter-area ratio, fractal dimension (D), and shape diversity index (SI); and 4. distance between patches and dispersion index (R). In addition, the following relationships were modeled: 1. distribution of natural vegetation patch sizes; 2. perimeter-area relationship and the number and area of natural vegetation patches; 3. edge effect caused by habitat fragmentation, the values of R indicated that savannah patches (R = 0.86) were aggregated while patches of natural vegetation as a whole (R = 1.02) were randomly dispersed in the landscape. There was a high frequency of small patches in the landscape whereas large patches were rare. In the perimeter-area relationship, there was no sign of scale distinction in the patch shapes, In the patch number-landscape area relationship, D, though apparently scale-dependent, tends to be constant as area increases. This phenomenon was correlated with the tendency to reach a constant density as the working scale was increased, on the edge effect analysis, the edge-center distance was properly estimated by a model in which the edge-center distance was considered a function of the to;al patch area and the SI. (C) 1997 Elsevier B.V. B.V.

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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.

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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.

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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.

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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.

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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.

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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.

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Wet silica gels with similar to 1.4 x 10(-3) mol SiO2/cm(3) and similar to 92 vol% liquid phase were obtained from sonohydrolysis of tetraethoxysilane (TEOS) with different additions of isopropyl alcohol ( IPA). The IPA/TEOS molar ratio R was changed from 0 to 4. Aerogels were obtained by supercritical CO2 extraction. The samples were analyzed by small-angle X-ray scattering (SAXS) and nitrogen adsorption. The wet gels exhibit mass fractal structure with fractal dimension increasing from D similar to 2.10 to D similar to 2.22, characteristic length xi decreasing from similar to 9.5 to similar to 6.9 nm, as R increases from 0 to 4, and an estimated characteristic length for the primary silica particles lower than similar to 0.3 nm. The supercritical process apparently eliminates a fraction of the porosity, increasing the mass fractal dimension and shortening the fractality domain in the mesopore region. The fundamental role of isopropyl alcohol on the structure of the resulting aerogels is to decrease the porosity and the pore mean size as R changes from pure TEOS to R = 4. A secondary structure appearing in the micropore region of the aerogels can be described as a mass/surface fractal structure, with correlated mass fractal dimension D-m similar to 2.7 and surface fractal dimension D-s similar to 2.3, as inferred from SAXS and nitrogen adsorption data.

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Silica-poly(oxypropylene) (PPO) nanocomposites containing PPO with weak physical bonds between the organic (PPO) and inorganic (silica) phases were obtained by the sol-gel procedure. Three precursor sols containing silica and PPO with molecular weights of 1000, 2000 and 4000g/mol were prepared. The structure changes during the whole sol-gel process, i.e. sol formation, sol-gel transition and gel aging and drying were investigated in situ by small angle X-ray scattering (SAXS). The experimental SAXS curves corresponding to sols and wet gels containing PPO of molecular weight 1000g/mol indicate that the aggregates formed during the studied process are fractal objects. Close to the sol-gel transition and during gel aging the fractal dimension is D=2.5. A clearly different structure evolution occurs in samples prepared with PPO with molecular weights 2000 and 4000 g/mol. Our SAXS results indicate the presence of two coexisting and well-defined structure levels, one of them corresponding to small silica clusters and the other to large silica aggregates. These two levels remain along the whole transformation. The SAXS curves of all dry samples are similar to those of the corresponding wet gels suggesting that no significant changes at nanoscopic scale occur during the drying process.