806 resultados para fractal
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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.
Small-angle X-ray scattering study of the smart thermo-optical behavior of zirconyl aqueous colloids
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The smart thermo-optical systems studied here are based on the unusual thermoreversible sol-gel transition of zirconyl chloride aqueous solution modified by sulfuric acid in the molar ratio Zr/SO4:3/1. The transparency to the visible light changes during heating due to light scattering. This feature is related to the aggregates growth that occurs during gelation. These reversible changes can be controlled by the amount of chloride ions in solution. The thermoreversible sol-gel transition temperature increases from 323 to 343 K by decreasing the molar ratio Cl/Zr from 7.0 to 1.3. In this work the effect of the concentration of chloride ions on the structural characteristics of the system has been analyzed by in situ SAXS measurements during the sol-gel transition carried out at 323 and 333 K. The experimental SAXS curves of sols exhibit three regions at small, medium and high scattering vectors characteristics of Guinier, fractal and Porod regimes, respectively. The radius of primary particles, obtained from the crossover between the fractal and Porod regimes, remains almost invariable with the chloride concentration, and the value (4 Angstrom) is consistent with the size of the molecular precursor. During the sol-gel transition the aggregates grow with a fractal structure and the fractal dimensionality decreases from 2.4 to 1.8. This last value is characteristic of a cluster-cluster aggregation controlled by a diffusion process. Furthermore, the time exponent of aggregate growth presents values of 0.33 and 1, typical of diffusional and hydrodynamic motions. A crossover between these two regimes is observed.
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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.
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A thermostimulated sol-gel transition in a system prepared by mixing a ZrOCl(2) acidified solution to a hot H(2)SO(4) aqueous solution was studied by dynamic theological measurements and quasi-elastic light scattering. The effect of temperature and of molar ratio R(S) = [Zr]/[SO(4)] on the gelation kinetics was analyzed using the mass fractal aggregate growth model. This study shows that the linear growth of aggregates occurs at the early period of transformation, while bidimensional growth occurs at the advanced stage. The bidimensional growth can be shifted toward monodimensional growth by decreasing the aggregation rate by controlling the temperature and/or molar ratio R(S). EXAFS and Raman results gave evidence that the linear chain growth is supported by covalent sulfate bonding between primary building blocks. At the advanced stage of aggregation, the assembly of linear chains through hydrogen bonding gave rise to the growth of bidimensional particles.
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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
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The fractal and multifractal approaches in the geographical analysis. This paper results from a bibliographical research showing the applications of the fractal and multifractal approaches in the geographical studies. At first describes some text books about fractals and, after, focuses the works did concerned with Physical Geography, Meteorology, Climatology, Geomorphology, Pedology and Human Geography.
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This article presents a quantitative and objective approach to cat ganglion cell characterization and classification. The combination of several biologically relevant features such as diameter, eccentricity, fractal dimension, influence histogram, influence area, convex hull area, and convex hull diameter are derived from geometrical transforms and then processed by three different clustering methods (Ward's hierarchical scheme, K-means and genetic algorithm), whose results are then combined by a voting strategy. These experiments indicate the superiority of some features and also suggest some possible biological implications.
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The structural characteristics of saturated silica sonogels were studied by means of small-angle x-ray scattering (SAXS) and thermogravimetric analysis (TG), after a long time of aging in saturated conditions. The sonogels were obtained by a sol-gel routine from ultrasound stimulated tetramethoxysilane (TMOS) hydrolysis carried out with the initial water/TMOS molar ratio (r) ranging from 2 to 10. The saturated sonogel structure can be described as composed by mass fractal-like aggregates (clusters) of primary silica particles, all imbibed in a liquid phase. The values of the mass fractal dimension (D) of the clusters was found all around 2.5, while the characteristic size of the clusters (ξ) was found generally increasing with r, going from approximately 2.3 nm (r = 2) to 4.5 nm (r = 10). The volume fraction of the clusters was estimated from the SAXS data. The results were compared to the values of weight loss fraction at the inflection point that has been found in the derivative of the TG curve, which should accounts for the instant in which the meniscus of the liquid phase penetrates into the clusters under a rapid evaporation process as in a TG test.
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A comparative study using small-angle x-ray scattering (SAXS) and nitrogen adsorption has been carried out in the structural characterization of silica xerogels and aerogels, obtained from tetraethoxysilane sonohydrolysis. The specific surface and the mean pore size as measured by both the techniques were found to be in notable agreement in all cases for aerogels and xerogels. According to the SAXS data, aerogels at 500 °C exhibit a mass fractal structure with fractal dimension D∼2.4 in the range between the correlation length ξ∼5.3 nm and a∼0.75 nm. An experimental method to probe the mass fractal structure of aerogels from exclusively nitrogen adsorption isotherms has been presented. For aerogels at 500 °C, we have found D∼2.4 in the range between the pore width 2rξ∼33 nm and 2ra∼4.5 nm, which is in notable agreement with the SAXS results (D ∼2.4, ξ∼5.3 nm, a∼0.75 nm) if we assign the pore width 2r probed by the Kelvin equation in the adsorption method to the Bragg distance 2π/q associated to the correlation length 1/q probed by SAXS.
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The structural evolution on the drying of wet sonogels of silica with the liquid phase exchanged by acetone, obtained from tetraethoxisilane sonohydrolysis, was studied in situ by small-angle x-ray scattering (SAXS). The periods associated to the structural evolution as determined by SAXS are in agreement with those classical ones established on basis of the features of the evaporation rate of the liquid phase in the obtaining of xerogels. The wet gel can be described as formed by primary particles (microclusters), with characteristic length a ∼ 0.67 nm and surface which is fractal, linking together to form mass fractal structures with mass fractal dimension D=2.24 in a length scale ξ∼6.7 nm. As the network collapses while the liquid/vapor meniscus is kept out of the gel volume, the mass fractal structure becomes more compacted by increasing D and decreasing ξ, with smoothing of the fractal surface of the microclusters. The time evolution of the density of the wet gels was evaluated exclusively from the SAXS parameters ξ, D, and a. The final dried acetone-exchanged gel presents Porod's inhomogeneity length of about 2.8 nm and apparently exhibits an interesting singularity D →3, as determined by the mass fractal modeling used to fit the SAXS intensity data for the obtaining of the parameters ξ and D.
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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
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Due to the increased incidence of skin cancer, computational methods based on intelligent approaches have been developed to aid dermatologists in the diagnosis of skin lesions. This paper proposes a method to classify texture in images, since it is an important feature for the successfully identification of skin lesions. For this is defined a feature vector, with the fractal dimension of images through the box-counting method (BCM), which is used with a SVM to classify the texture of the lesions in to non-irregular or irregular. With the proposed solution, we could obtain an accuracy of 72.84%. © 2012 AISTI.