171 resultados para multiscale fractal dimension


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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.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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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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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.

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The methodology for fracture analysis of polymeric composites with scanning electron microscopes (SEM) is still under discussion. Many authors prefer to use sputter coating with a conductive material instead of applying low-voltage (LV) or variable-pressure (VP) methods, which preserves the original surfaces. The present work examines the effects of sputter coating with 25 nm of gold on the topography of carbon-epoxy composites fracture surfaces, using an atomic force microscope. Also, the influence of SEM imaging parameters on fractal measurements is evaluated for the VP-SEM and LV-SEM methods. It was observed that topographic measurements were not significantly affected by the gold coating at tested scale. Moreover, changes on SEM setup leads to nonlinear outcome on texture parameters, such as fractal dimension and entropy values. For VP-SEM or LV-SEM, fractal dimension and entropy values did not present any evident relation with image quality parameters, but the resolution must be optimized with imaging setup, accompanied by charge neutralization. © Wiley Periodicals, Inc.

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Supercritical drying (SCD) and hydrophobic ambient pressure drying (APD) aerogels were prepared from hydrolysis of tetraethoxysilane in solutions of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (P123) in the range of composition below the threshold for the ordered mesoporous silica precipitation. APD was carried out after silylation of wet gels with trimethylchlorosilane (TMCS) or hexamethyldisilazane (HMDZ). The samples were analyzed by small-angle X-ray scattering and nitrogen adsorption. Wet gels are formed by mass-fractal domains, with fractal dimension close to 2, and larger pores superposing the pores belonging to the fractal structure in case of high P123 concentrations. Aerogels exhibit smaller-sized mass-fractal domains with larger mass-fractal dimension accounting for some porosity elimination on drying. The pore volume of the aerogels increases significantly with the P123 amount and it is even larger in the APD aerogels than in the SCD aerogels. © 2013 Elsevier B.V. All rights reserved.

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The structure and the kinetics of formation of APTS/GPTS-derived organic/inorganic hybrids were studied in situ by small-angle-X-ray scattering. The data were interpreted in terms of a process of primary particles formation and growth of mass-fractal clusters. At the very early stage, the population of the nonfractal primary particles (D = 3) increases with time. As the mass-fractal clusters appear (D < 3) as a result of the aggregation process, the radius of gyration, Rg, of the clusters increases on average. At advanced stages of aggregation, the clusters grow in a mechanism in which the number of particles per clusters increases while the number of clusters diminishes with time, in such a way that the correlation volume of the clusters, Vc, fulfills the relationship Vc â̂ R g D, in agreement with a mass-fractal character of the clusters. These results supporting a cluster-cluster aggregation process, together with the typically very low value found for the mass-fractal dimension D, are in favor of a diffusion-controlled cluster aggregation mechanism. © 2013 American Chemical Society.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)