Teleparallel equivalent of non-Abelian Kaluza-Klein theory

Based on the equivalence between a gauge theory for the translation group and general relativity, a teleparallel version of the non-Abelian Kaluza-Klein theory is constructed. In this theory, only the fiber-space turns out to be higher dimensional, spacetime being kept always four dimensional. The resulting model is a gauge theory that unifies, in the Kaluza-Klein sense, gravitational and gauge fields. In contrast with the ordinary Kaluza-Klein models, this theory defines a natural length scale for the compact submanifold of the fiber space, which is shown to be of the order of the Planck length.

Structural modifications in silica sonogels prepared with additions of poly(vinyl alcohol)

Silica wet gels were prepared from acid sonohydrolysis of tetraethoxysilane (TEOS) and additions of poly(vinyl alcohol) (PVA)-water solution. Aerogels were obtained from supercritical CO(2) extraction. The samples were studied by thermal gravimetric (TG) analysis, small-angle X-ray scattering (SAXS), and nitrogen adsorption. The structure of wet gels can be described as a mass fractal with dimension D equal to 2.0 on the whole length scale experimentally probed by SAXS, from similar to 0.3 to similar to 15 nm. Pure and low-PVA-addition wet gels exhibit an upper cutoff accounting for a finite characteristic length xi of the mass fractal structure. Additions , of PVA increase without modifying D, which was attributed to a steric effect of the polymer in the structure. The pore volume fraction of the aerogels diminishes typically about 11% with respect to that of the wet gels, although nitrogen adsorption could be underestimating some porosity. The pore size distribution of the aerogels is shifted toward the mesopore region with the additions of PVA, in a straight relationship with the increase of xi in the wet gels. The thermal stability of the pore size distribution of the aerogels was studied up to 1000 degrees C.

Structural features of silicas prepared in n-heptane/water/ethanol/sodium dodecylsulfate microemulsions

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

From sol to aerogel: a study of the nanostructural characteristics of TEOS derived sonogels

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.

Mass fractal characteristics of wet sonogels as determined by small-angle x-ray scattering and differential scanning calorimetry

Low density silica sonogels were prepared from acid sonohydrolysis of tetraethoxysilane. Wet gels were studied by small-angle x-ray scattering (SAXS) and differential scanning calorimetry (DSC). The DSC tests were carried out under a heating rate of 2 degrees C/min from -120 degrees C up to 30 degrees C. Aerogels were obtained by CO(2) supercritical extraction and characterized by nitrogen adsorption and SAXS. The DSC thermogram displays two distinct endothermic peaks. The first, a broad peak extending from about -80 degrees C up to practically 0 degrees C, was associated to the melting of ice nanocrystals with a crystal size distribution with pore diameter ranging from 1 or 2 nm up to about 60 nm, as estimated from Thomson's equation. The second, a sharp peak with onset temperature close to 0 degrees C, was attributed to the melting of macroscopic crystals. The DSC incremental nanopore volume distribution is in reasonable agreement with the incremental pore volume distribution of the aerogel as determined from nitrogen adsorption. No macroporosity was detected by nitrogen adsorption, probably because the adsorption method applies stress on the sample during measurement, leading to a underestimation of pore volume, or because often positive curvature of the solid surface is in aerogels, making the nitrogen condensation more difficult. According to the SAXS results, the solid network of the wet gels behaves as a mass fractal structure with mass fractal dimension D=2.20 +/- 0.01 in a characteristic length scale below xi=7.9 +/- 0.1 nm. The mass fractal characteristics of the wet gels have also been probed from DSC data by means of an earlier applied modeling for generation of a mass fractal from the incremental pore volume distribution curves. The results are shown to be in interesting agreement with the results from SAXS.

Structural characteristics of gels prepared from sonohydrolysis and conventional hydrolysis of TEOS: an emphasis on the mass fractal as determined from the pore size distribution

Silica gels were preparated from fixed proportion mixtures of tetraethoxysilane, water and hydrocloric acid, using either ultrasound stimulation (US) or conventional method (CO) in the hydrolysis step of the process. Wet gets were obtained with the same silica volume concentration and density. According to small-angle X-ray scattering, the structure of the wet gels can be described as mass fractal structures with mass fractal dimension D = 2.20 in a length scale xi = 7.9 nm, in the case of wet gels US, and D = 2.26 in a length scale 6.9 nm, in the case of wet gels CO. The mass fractal characteristics of the wet gels US and CO account for the different structures evolved in the drying of the gels US and CO in the obtaining of xerogels and aerogels. The pore structure of the dried gels was studied by nitrogen adsorption as a function of the temperature. Aerogels (US and CO) present high porosity with pore size distribution (PSD) curves in the mesopore region while xerogels (US and CO) present minor porosity with PSD curves mainly in the micropore region. The dried gels US (aerogels and xerogels) generally present pore volume and specific surface area greater than the dried gels CO. The mass fractal structure of the aerogels has been studied from an approach based on the PSD curves exclusively. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Structural evolution of aerogels prepared from TEOS sono-hydrolysis upon heat treatment up to 1100 degrees C

The structural evolution of aerogels prepared from TEOS sono-hydrolysis was studied as a function of the temperature of heat treatment up to 1100 degreesC by means of small angle X-ray scattering (SAXS) and density measurements. The mass fractal structure of the original wet sonogel (with scattering exponent alpha similar to 2.2) apparently transforms to a surface fractal structure in a length scale lesser than similar to1.5 nm, upon the process resulting in aerogel. Such a structural transformation is interpreted by the formation of new particles with characteristic dimension of similar to1.5 nm, with rough boundaries or electronic density fluctuations (or ultra-micropores) in their interior. The structural arrangement of these particles seem to preserve part of mass fractal characteristics of the original wet sonogel, now in a length scale greater than similar to1.5 nm. The electronic density heterogeneities in the particles start to be eliminated at around 800 degreesC and, at 900 degreesC, the particles become perfectly homogeneous, so the structure can be described as a porous structure with a porosity of similar to68% with similar to9.0 nm mean size pores and similar to4.3 nm mean size solid particles. Above 900 degreesC, a vigorous viscous flux sintering process sets in, eliminating most of the porosity and increasing rapidly the bulk density in an aerogel-glass transformation. (C) 2003 Elsevier B.V. All rights reserved.

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.

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.

Small-angle x-ray scattering study of the structural evolution of the drying of sonogels with the liquid phase exchanged by acetone

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.

Optimal Boussinesq model for shallow-water waves interacting with a microstructure

In this paper, we consider the propagation of water waves in a long-wave asymptotic regime, when the bottom topography is periodic on a short length scale. We perform a multiscale asymptotic analysis of the full potential theory model and of a family of reduced Boussinesq systems parametrized by a free parameter that is the depth at which the velocity is evaluated. We obtain explicit expressions for the coefficients of the resulting effective Korteweg-de Vries (KdV) equations. We show that it is possible to choose the free parameter of the reduced model so as to match the KdV limits of the full and reduced models. Hence the reduced model is optimal regarding the embedded linear weakly dispersive and weakly nonlinear characteristics of the underlying physical problem, which has a microstructure. We also discuss the impact of the rough bottom on the effective wave propagation. In particular, nonlinearity is enhanced and we can distinguish two regimes depending on the period of the bottom where the dispersion is either enhanced or reduced compared to the flat bottom case. © 2007 The American Physical Society.

Effective range from tetramer-dissociation data for cesium atoms

The shifts in the four-body recombination peaks, due to an effective range correction to the zero-range model close to the unitary limit, are obtained and used to extract the corresponding effective range of a given atomic system. The approach is applied to an ultracold gas of cesium atoms close to broad Feshbach resonances, where deviations of experimental values from universal model predictions are associated with effective range corrections. The effective range correction is extracted with a weighted average given by 3.9±0.8R vdW, where RvdW is the van der Waals length scale, which is consistent with the van der Waals potential tail for the Cs2 system. The method can be generally applied to other cold atom experimental setups to determine the contribution of the effective range to the tetramer dissociation position. © 2013 American Physical Society.

Propriedades estruturais de géis de sílica preparados a partir da sonohidrólise do tetraetilortosilicato com adições de dimetilformamida

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Propriedades nanoestruturais de géis de sílica preparados com adiçoes de surfactante anionico

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Propriedades estruturais de géis obtidos a partir de sono-hidrólise de TEOS e troca de fase líquida por acetona

Pós-graduação em Física - IGCE