Small-Angle Scattering from Mass and Surface Fractals

Anitas, Eugen Mircea

doi:10.5772/intechopen.70870

Cited by 13 publications

(12 citation statements)

References 42 publications

(59 reference statements)

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“…Therefore, the amylopectin network is suspected of having a correlation length of 180 nm (the green triangle toward the right of Figure 10c ). This length is similar to that observed in a 2D SG (Anitas, 2018 ). These correlation lengths can potentially be assigned to the 2D diffusion‐limited clusters.…”

Section: Resultssupporting

confidence: 87%

“…The k ‐value obtained by us agrees well with the analytical value obtained by Muthukumar ( 1983 ) using the mean‐field theory for diffusion‐limited cluster formation. Furthermore, Anita studied the scattering curves from mass and surface fractals in a 2D Sierpinski Gasket (SG), a diffusion‐limited cluster (Anitas, 2018 ). The k ‐value calculated in this case is 1.59, which is comparable to the value obtained by us for a transparent gel.…”

Section: Resultsmentioning

confidence: 99%

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Analysis of the sol and gel structures of potato starch over a wide spatial scale

Nagasaki

Matsuba

Ikemoto

et al. 2021

Food Science & Nutrition

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The fine structure of amylopectin differs significantly from the structure of glycogen. Amylopectin has a unit structure designated as a cluster, whereas glycogen exhibits no such structure because the α-1,6 branch points in glycogen are randomly distributed. Amylopectin clusters are interconnected by long chains that span across two or three clusters. The short and intermediate chains within a single cluster are called nonbranched chains or branched chains (Jane et al., 1997;Peat et al., 1956).Starch is a vital source of energy that helps sustain human life.Starch that stores nutritive energy in plant roots, tubers, or endosperms such as potato, tapioca, corn, and rice primarily comprises of carbohydrates in the form of polysaccharides. On the micrometer scale, starch granules ∼1-100 µm in size have a growth-ring structure composed of alternately arranged semicrystalline and amorphous shells. The semicrystalline shells are composed primarily of branched-chain amylopectin clusters, in contrast to the amorphous shells, which contain long linear-chain amylose and low-molecularmass amylopectin. On the nanometer scale, each semicrystalline shell consists of lamellae of alternating crystalline and amorphous layers, with a typical lamellar spacing of ~9 nm (also known as the 9-nm repeat structure), with crystallinity ranging from 15% to 45%.At the atomic level, the packing of the crystal structure of starch can be classified as either monoclinic (A-type) or hexagonal (B-type)

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Section: Resultssupporting

confidence: 87%

Section: Resultsmentioning

confidence: 99%

Analysis of the sol and gel structures of potato starch over a wide spatial scale

Nagasaki

Matsuba

Ikemoto

et al. 2021

Food Science & Nutrition

View full text Add to dashboard Cite

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“…This widely used material-morphology investigation method has the advantage of sampling a statistically significant macroscopic volume. For ESS structures, the main advantage of SAS relies on its ability to distinguish between mass and surface fractals through the value of the scattering exponent τ in the fractal region [28][29][30][31]. More recently, it has been shown that SAS can also differentiate between ESS and statistically self-similar (SSS) structures [32] as well as between regular and fat fractals, that is, those with positive Lebesgue measure [33].…”

Section: Introductionmentioning

confidence: 99%

Structural Properties of Vicsek-like Deterministic Multifractals

et al. 2019

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Deterministic nano-fractal structures have recently emerged, displaying huge potential for the fabrication of complex materials with predefined physical properties and functionalities. Exploiting the structural properties of fractals, such as symmetry and self-similarity, could greatly extend the applicability of such materials. Analyses of small-angle scattering (SAS) curves from deterministic fractal models with a single scaling factor have allowed the obtaining of valuable fractal properties but they are insufficient to describe non-uniform structures with rich scaling properties such as fractals with multiple scaling factors. To extract additional information about this class of fractal structures we performed an analysis of multifractal spectra and SAS intensity of a representative fractal model with two scaling factors-termed Vicsek-like fractal. We observed that the box-counting fractal dimension in multifractal spectra coincide with the scattering exponent of SAS curves in mass-fractal regions. Our analyses further revealed transitions from heterogeneous to homogeneous structures accompanied by changes from short to long-range mass-fractal regions. These transitions are explained in terms of the relative values of the scaling factors.

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“…Note that since all the triangles composing the ST have the same size, the structure is a mass fractal. Therefore, the scattering exponent in the scattering curve shall coincide with the the analytical value of fractal dimension given by Equation (17) (see also [23,26,27]).…”

Section: St Modelmentioning

confidence: 82%

Structural Properties of Molecular Sierpiński Triangle Fractals

Anitas

2020

Nanomaterials

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The structure of fractals at nano and micro scales is decisive for their physical properties. Generally, statistically self-similar (random) fractals occur in natural systems, and exactly self-similar (deterministic) fractals are artificially created. However, the existing fabrication methods of deterministic fractals are seldom defect-free. Here, are investigated the effects of deviations from an ideal deterministic structure, including small random displacements and different shapes and sizes of the basic units composing the fractal, on the structural properties of a common molecular fractal—the Sierpiński triangle (ST). To this aim, analytic expressions of small-angle scattering (SAS) intensities are derived, and it is shown that each type of deviation has its own unique imprint on the scattering curve. This allows the extraction of specific structural parameters, and thus the design and fabrication of artificial structures with pre-defined properties and functions. Moreover, the influence on the SAS intensity of various configurations induced in ST, can readily be extended to other 2D or 3D structures, allowing for exploration of structure-property relationships in various well-defined fractal geometries.

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Small-Angle Scattering from Mass and Surface Fractals

Cited by 13 publications

References 42 publications

Analysis of the sol and gel structures of potato starch over a wide spatial scale

Analysis of the sol and gel structures of potato starch over a wide spatial scale

Structural Properties of Vicsek-like Deterministic Multifractals

Structural Properties of Molecular Sierpiński Triangle Fractals

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