Journal ArticleDOI
Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering.
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TLDR
Small-angle neutron scattering from normal, compressed, and water-suspended powders of aggregates of fine silica particles has been studied and the intensity of scattering was found to scale with the correlation length in the manner expected for a fractal system.Abstract:
Small-angle neutron scattering from normal, compressed, and water-suspended powders of aggregates of fine silica particles has been studied. The samples possessed average densities ranging from 0.008 to 0.45 g/${\mathrm{cm}}^{3}$. Assuming power-law correlations between particles and a finite correlation length \ensuremath{\xi}, we derive the scattering function S(q) from specific models for particle-particle correlation in these systems. S(q) was found to provide a satisfactory fit to the data for all samples studied. The fractal dimension ${d}_{f}$ corresponding to the power-law correlation was 2.61\ifmmode\pm\else\textpm\fi{}0.1 for all dry samples, and 2.34\ifmmode\pm\else\textpm\fi{}0.1 for the water-suspended samples. The intensity of scattering was found to scale with the correlation length in the manner expected for a fractal system.read more
Citations
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Light Scattering by Fractal Aggregates: A Review
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Composition and density of nanoscale calcium–silicate–hydrate in cement
TL;DR: This study measures the composition and solid density of the principal binding reaction product of cement hydration, calcium-silicate-hydrate (C-S-H) gel, one of the most complex of all gels, and quantifies a nanoscale calcium hydroxide phase that coexists with C- S-H gel.
Book ChapterDOI
Fractals in physics
TL;DR: In this article, the authors give a brief overview of the impact of fractal geometry on physical sciences and the recent developments in the direction of the formulation of an analytical theory that allows to understand why natural phenomena often give rise to fractal structures.
Journal ArticleDOI
Surface modifications for the effective dispersion of carbon nanotubes in solvents and polymers
Sangwon Kim,Taehoon Kim,Yern Seung Kim,Hongsoo Choi,Hyeong Jun Lim,Seung Jae Yang,Chong Rae Park +6 more
TL;DR: In this paper, a review of the state of the art in surface modifications and the resultant dispersibility of CNTs is provided, with particular emphasis on the quantitative characterization of surface modification and dispersions.
Journal ArticleDOI
Small-angle neutron scattering study of structural changes in temperature sensitive microgel colloids
TL;DR: The structure of temperature-sensitive poly(N-isopropylacrylamide) microgels in dilute suspension was investigated by means of small-angle neutron scattering and clearly showed that the segment density in the swollen state is not homogeneous, but gradually decays at the surface.
References
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Journal ArticleDOI
Diffusion-limited aggregation, a kinetic critical phenomenon
Abstract: A model for random aggregates is studied by computer simulation The model is applicable to a metal-particle aggregation process whose correlations have been measured previously Density correlations within the model aggregates fall off with distance with a fractional power law, like those of the metal aggregates The radius of gyration of the model aggregates has power-law behavior The model is a limit of a model of dendritic growth
Journal ArticleDOI
Diffusion-limited aggregation
TL;DR: In this article, the authors show that diffusion-limited aggregation has no upper critical dimension and apply scale invariance to study growth, gelation, and the structure factor of aggregates.
Journal ArticleDOI
Fractal structures formed by kinetic aggregation of aqueous gold colloids
David A. Weitz,M. Oliveria +1 more
TL;DR: In this article, the authors used transmission-electron micrographs to study the structure formed by the irreversible kinetic aggregation of uniformly sized aqueous gold colloids and found that the structures are highly ramified and exhibit a scale invariance that is well described as a fractal with a Hausdorff dimension of 1.75.
Journal ArticleDOI
Long-range correlations in smoke-particle aggregates
S R Forrest,T A Witten +1 more
TL;DR: In this article, the particle density has long-range correlations of the same form in iron, zinc or silicon dioxide aggregates, and the correlation data suggest a power-law spatial dependence giving a Hausdorff dimension between 1.7 and 1.9.
Journal ArticleDOI
Fractal geometry of colloidal aggregates
TL;DR: In this article, the fractal dimension of colloidal aggregates of small silica particles is measured by both light and x-ray scattering, showing that the aggregates are fractal.