Observation of Power-Law Correlations in Silica-Particle Aggregates by Small-Angle Neutron Scattering

Sinha, Sunil K.; Freltoft, T.; Kjems, Jørgen

doi:10.1016/b978-0-444-86912-8.50026-2

Cited by 72 publications

(67 citation statements)

References 8 publications

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“…A finite size of aggregates can be taken into account in the expression for g(r) by multiplying Eq. (7) by an exponential cut-off function [8][9][10][11][12] exp(−r/ξ), where ξ is the cut-off length. This length marks the perimeter of the aggregate, and it can be related to R g from Eq.…”

Section: Scattering From Mass Fractal Aggregates Of Primary Particlesmentioning

confidence: 99%

“…Important to note is that the mathematical formalism used for describing these structures is well established. [8][9][10][11][12] On the other hand, for surface fractal aggregates the current concepts do not explicitly consider primary particles as building blocks for the aggregates, since their surface fractal dimensions cannot be associated with the internal packing efficiency of primary particles. This is because, surface fractal scaling deals with an apparently dense object whose surface area, α, scales with the variable length scale r as follows: 3…”

Section: Introductionmentioning

confidence: 99%

“…The fractal nature of colloids can be experimentally quantified using scattering techniques, and based on a combination of theoretical and experimental evidence [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] two distinct scaling laws have been used to describe experimental observations: mass fractals and surface fractals. Mass fractal scaling can be associated with the packing efficiency of an aggregate, which in turn depends on the type of aggregation, e.g., diffusion or reaction limited mechanism.…”

Section: Introductionmentioning

confidence: 99%

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Not just fractal surfaces, but surface fractal aggregates: Derivation of the expression for the structure factor and its applications

Besselink

Stawski

Driessche

et al. 2016

The Journal of Chemical Physics

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Densely packed surface fractal aggregates form in systems with high local volume fractions of particles with very short diffusion lengths, which effectively means that particles have little space to move. However, there are no prior mathematical models, which would describe scattering from such surface fractal aggregates and which would allow the subdivision between inter-and intraparticle interferences of such aggregates. Here, we show that by including a form factor function of the primary particles building the aggregate, a finite size of the surface fractal interfacial sub-surfaces can be derived from a structure factor term. This formalism allows us to define both a finite specific surface area for fractal aggregates and the fraction of particle interfacial sub-surfaces at the perimeter of an aggregate. The derived surface fractal model is validated by comparing it with an ab initio approach that involves the generation of a "brick-in-a-wall" von Koch type contour fractals. Moreover, we show that this approach explains observed scattering intensities from in situ experiments that followed gypsum (CaSO 4 ·2H 2 O) precipitation from highly supersaturated solutions. Our model of densely packed "brick-in-a-wall" surface fractal aggregates may well be the key precursor step in the formation of several types of mosaic-and meso-crystals. C

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Section: Scattering From Mass Fractal Aggregates Of Primary Particlesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Not just fractal surfaces, but surface fractal aggregates: Derivation of the expression for the structure factor and its applications

Besselink

Stawski

Driessche

et al. 2016

The Journal of Chemical Physics

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“…When q~:-> 1, the intensity l(q) of the small-angle scattering from a mass fractal with fractal dimension D can be written (Sinha, Freltoft & Kjems, 1984;Teixeira, 1988) …”

Section: The Small-angle Scattering From Mass and Surface Fractalsmentioning

confidence: 99%

Small-angle scattering studies of disordered, porous and fractal systems

Schmidt¹

1991

J Appl Crystallogr

565

390

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Small-angle X-ray and neutron scattering are important techniques for studying the structure of fractals and other disordered systems on a scale of lengths from about 10 to 2000 A. This review begins with a brief outline of some properties of fractals. The small-angle scattering from fractal systems is then discussed and the effect of polydispersity is considered. The intensity of small-angle scattering from fractals and other disordered systems is often proportional to a negative power of the quantity q = 4~,t-Isin(0/2), where 0 is the scattering angle and ,~ is the X-ray or neutron wavelength. From the magnitude of the exponent that describes this type of scattering, which is often called power-law scattering, much important information can be obtained. Some situations in which power-law scattering can be expected are described. To illustrate the scattering from fractals and disordered systems, several experimental investigations of mass-fractal silicas and porous solids are reviewed and some calculations of the small-angle scattering from model fractal systems are outlined.

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“…One approach is to pick a simple function (Sinha, Freltoft & Kjems, 1984;Freltoft, Kjems & Sinha, 1986), exp(-r/R), and hope that this is sufficient.…”

Section: Limits Of Fractal Scattering Behaviormentioning

confidence: 99%

Scattering from fractals

Martin¹,

Hurd²

1987

J Appl Crystallogr

572

376

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The concepts of dilation symmetry and the fractal dimension are introduced, and from these basic concepts scattering functions are computed for surface and mass fractals. It is then shown how the fractal structure of various random media has been elucidated from scattering measurements, and how these observations relate to specific models of fractal geometry. Examples include colloidal aggregates, gels, soot and the fractal porosity of rocks of various sorts.

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Observation of Power-Law Correlations in Silica-Particle Aggregates by Small-Angle Neutron Scattering

Cited by 72 publications

References 8 publications

Not just fractal surfaces, but surface fractal aggregates: Derivation of the expression for the structure factor and its applications

Not just fractal surfaces, but surface fractal aggregates: Derivation of the expression for the structure factor and its applications

Small-angle scattering studies of disordered, porous and fractal systems

Scattering from fractals

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