Scattering from fractals

Martin, James E.; Hurd, Alan J.

doi:10.1107/s0021889887087107

Cited by 568 publications

(393 citation statements)

References 66 publications

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“…This value of D is similar to the value of 1.75 which has been predicted by a computer simulation for cluster-cluster aggregation [8]. In this process an assembly of Brownian particles stick together upon contact to form clusters.…”

Section: I(h) =Ah -Dsupporting

confidence: 71%

“…The deviation from Porod's law (I(h) = b * h -4) have been observed by many authors for different types of silica (for example aerogels [5], colloidal aggregates [6], silica gels formed by controlled hydrolysis of tetra ethyl orthosilicates [7]). Especially the excellent review articles of Martin and Hurt [8] and Ramsay [9] give a good overall picture of the fractal properties of silica gels derived from SAXS or SANS spectra in the Porod region.…”

Section: I(h) =Ah -Dmentioning

confidence: 99%

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Saxs study of silica gel formation from aqueous silicate solutions

et al. 1989

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In situ SAXS measurements of silica gel formation in the" presence of different cations are presented as a function of reaction time. Conditions used are similar to those applied to prepare catalyst supports. The data can be interpreted in terms of aggregation of elementary silica particles with sizes of approximately 1 nm, thus finally forming a continuous silica gel network. The aggregates are fractal with respect to their masses, in the range 2-10 nm. The dimensionality of the fractals can be determined from the SAXS curves; it increases from 1.8 to 2.5 during gelformation, corresponding with a diffusion limited aggregation process (DLA) of gel formation followed by densification of the silica gel network. The finding that the rate of change in fractal dimensionality does not change as a function of cation, indicates strongly that gelformation is a diffusion limited aggregation process.

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Section: I(h) =Ah -Dsupporting

confidence: 71%

Section: I(h) =Ah -Dmentioning

confidence: 99%

Saxs study of silica gel formation from aqueous silicate solutions

et al. 1989

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“…The analysis of the limiting power law in the Porod region of the scattering curves can provide some information on the interface in the TEOS/PCL hybrid materials. Indeed, in case of fractal structures, the SAXS intensity l(s) agrees with the following power laws 17 where D m is the mass fractal dimension and D s is the surface fractal dimension. Figure 10 shows that each scattering profile approaches a limiting slope of 1.7 for curve A and 1.6 for curve B, respectively, indicating that the interface structure is mass fractal whatever the reactivity of the PCL end-groups.…”

Section: Resultsmentioning

confidence: 49%

Biodegradable and biocompatible inorganic-organic hybrid materials: 2. Dynamic mechanical properties, structure and morphology

Tian

Blacher

Dubois

et al. 1998

Polymer

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Dynamic mechanical properties, structure and morphology of tetraethoxysilane/poly(ε-caprolactone) (TEOS/ PCL) hybrid materials have been analysed by dynamic mechanical spectroscopy, small-angle X-ray scattering, transmission electron microscopy, and image analysis. The experimental observations agree with a microscopic phase separation of the two constitutive components: the organic polymer and the silica network. The effect of the PCL functional end-groups, the number of functional end-groups per PCL chain, the PCL molecular weight and content, and the curing conditions have been studied on the structure and properties of the hybrid materials. Finally, phase morphology has proved to be co-continuous, at least when the weight composition is close to 50% for each component (SiO 2 and PCL), with a characteristic length between the PCL and silica phases of ca. 5 nm, as estimated by image analysis of transmission electron micrographs.

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“…Over limited range of aggregate radii the mass of the fractal aggregate, m, is directly related to the radius of a circumscribing sphere within the aggregate, l , to the power of d f (Martin and Hurd 1987;Knöchel et al 1997):…”

Section: Aggregate Structurementioning

confidence: 99%

Contrasting Roles Of Natural Organic Matter On Colloidal Stabilization And Flocculation In Freshwaters

Reinhardt¹

2004

Flocculation in Natural and Engineered Environmental Systems

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Scattering from fractals

Cited by 568 publications

References 66 publications

Saxs study of silica gel formation from aqueous silicate solutions

Saxs study of silica gel formation from aqueous silicate solutions

Biodegradable and biocompatible inorganic-organic hybrid materials: 2. Dynamic mechanical properties, structure and morphology

Contrasting Roles Of Natural Organic Matter On Colloidal Stabilization And Flocculation In Freshwaters

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