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Updated: Aug 12, 2025

Assembly and Characterization of Polyelectrolyte Complex Micelles
Published on: March 2, 2020
Dense random packing with a power-law size distribution: The structure factor, mass-radius relation, and pair
Alexander Yu Cherny1, Eugen M Anitas1, Vladimir A Osipov1
1Joint Institute for Nuclear Research, Dubna 141980, Russian Federation.
Abstract:
We consider a dense random packing of disks with a power-law distribution of radii and investigate their correlation properties. We study the corresponding structure factor, mass-radius relation, and pair distribution function of the disk centers. A toy model of dense segments in one dimension (1D) is solved exactly. It is shown theoretically in 1D and numerically in 1D and 2D that such a packing exhibits fractal properties. It is found that the exponent of the power-law distribution and the fractal dimension coincide. An approximate relation for the structure factor in arbitrary dimensions is derived, which can be used as a fitting formula in small-angle scattering. These findings can be useful for understanding the microstructural properties of various systems such as ultra-high performance concrete, high-internal-phase-ratio emulsions, or biological systems.
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