Integrated Fractal Analysis of Silica: Adsorption, Electronic Energy Transfer, and Small-Angle X-ray Scattering

Rojanski, D.; Huppert, Dan; Bale, Harold D.; Xie, Dexin; Schmidt, Paul W.; Farin, Dina; Seri-Levy, Alon; Avnir, David

doi:10.1103/physrevlett.56.2505

Cited by 115 publications

(32 citation statements)

References 20 publications

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“…The feature Dϭ3 together with the behavior I(q)ϳq Ϫ4 for q ӷ1 could also be interpreted as the scattering from a system with an extremely rough boundary space filling fractal surface, in a length scale less than ϳ2.7 nm, as pointed by Rojanski et al 16 for mesoporous silica on basis of an integrated study combining adsorption, electronic energy transfer, and SAXS techniques. However, we think it would be a complex figure to be elucidated exclusively from our SAXS data.…”

Section: Discussionmentioning

confidence: 99%

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

et al. 2004

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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 ͑SAXS͒. 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 ͑microclusters͒, with characteristic length a ϳ0.67 nm and surface which is fractal, linking together to form mass fractal structures with mass fractal dimension Dϭ2.24 in a length scale ϳ6.7 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 , 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 , 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 and D.

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Section: Discussionmentioning

confidence: 99%

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

et al. 2004

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“…An increase in the resolving power used in the examination of the surface reveals smaller details morphologically similar to larger details previously observed. Regardless of the method used to measure the fractal dimension, fractality is detected by performing a resolution analysis, for examCopyright 9 1996, The Clay Minerals Society ple, analyzing the change in a measurable property as the resolving power is varied (Rojanski et al 1986). …”

Section: Introductionmentioning

confidence: 99%

Comparison of Techniques for Determining the Fractal Dimensions of Clay Minerals

Malekani

Rice

Lin

1996

Clays and clay miner.

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Abstract---Small-angle X-ray scattering (SAXS), adsorption and nuclear magnetic resonance (NMR) techniques were used to determine the fractal dimensions (D) of 3 natural reference clays: 1) a kaolinite (KGa-2); 2) a hectorite (SHCa-1), and 3) a Ca-montmorillonite (STx-1). The surfaces of these clays were found to be fractal with D values close to 2.0. This is consistent with the common description of clay mineral surfaces as smooth and planar. Some surface irregularities were observed for hectorite and Camontmorillonite as a result of impurities in the materials. The SAXS method generated comparable D values for KGa-2 and STx-1. These results are supported by scanning electron microscopy (SEM). The SAXS and adsorption methods were found to probe the surface irregularities of the clays while the nuclear magnetic resonance (NMR) technique seems to reflect the mass distribution of certain sites in the material. Since the surface nature of clays is responsible for their reactivity in natural systems, SAXS and adsorption techniques would be the methods of choice for their fractal characterization. Due to its wider applicable characterization size-range, the SAXS method appears to be better suited for the determination of the fractal dimensions of clay minerals.

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“…5 The analysis of the fractal characteristics when ␣ ϳ 3 may be a complex matter. 8 As we will see, this fine structure at a high resolution level is also apparent from the nitrogen adsorption study. Table I shows the SAXS structural parameters of the mass fractal D and obtained for the aerogels with r w = 66, 40, 25, and 19, together with the ratio / a, for this set of samples in which the crossover to the power-law decaying I͑q͒ϳq −␣ at high q is apparent.…”

Section: I͑q͒mentioning

confidence: 71%

“…͑1͒ to fit the data of systems with fractal dimension close to 3 ͑mass or surface͒ are discussable. 8 Figure 3 shows the nitrogen-adsorption isotherms as obtained at liquid-nitrogen temperature for the studied aerogels. Table II shows the bulk density and the BET-specific surface area S BET of the aerogels.…”

Section: I͑q͒mentioning

confidence: 99%

Mass fractal characteristics of silica sonogels as determined by small-angle x-ray scattering and nitrogen adsorption

Donatti

Vollet²,

Ruiz³

et al. 2005

Phys. Rev. B

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A sample series of silica sonogels was prepared using different water-tetraethoxysilane molar ratio ͑r w ͒ in the gelation step of the process in order to obtain aerogels with different bulk densities after the supercritical drying. The samples were analyzed by means of small-angle x-ray-scattering ͑SAXS͒ and nitrogen-adsorption techniques. Wet sonogels exhibit mass fractal structure with fractal dimension D increasing from ϳ2.1 to ϳ 2.4 and mass-fractal correlation length diminishing from ϳ13 nm to ϳ 2 nm, as r w is changed in the nominal range from 66 to 6. The process of obtaining aerogels from sonogels and heat treatment at 500°C, in general, increases the mass-fractal dimension D, diminishes the characteristic length of the fractal structure, and shortens the fractal range at the micropore side for the formation of a secondary structured particle, apparently evolved from the original wet structure at a high resolution level. The overall mass-fractal dimension D of aerogels was evaluated as ϳ2.4 and ϳ2.5, as determined from SAXS and from pore-size distribution by nitrogen adsorption, respectively. The fine structure of the "secondary particle" developed in the obtaining of aerogels could be described as a surface-mass fractal, with the correlated surface and mass-fractal dimensions decreasing from ϳ2.4 to ϳ 2.0 and from ϳ2.7 to ϳ 2.5, respectively, as the aerogel bulk density increases from 0.25 ͑r w =66͒ up to 0.91 g / cm 3 ͑r w =6͒.

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Integrated Fractal Analysis of Silica: Adsorption, Electronic Energy Transfer, and Small-Angle X-ray Scattering

Cited by 115 publications

References 20 publications

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

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

Comparison of Techniques for Determining the Fractal Dimensions of Clay Minerals

Mass fractal characteristics of silica sonogels as determined by small-angle x-ray scattering and nitrogen adsorption

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