Dense random packing of disks with a power-law size distribution in thermodynamic limit

Alexander Yu Cherny; Eugen M Anitas; Artem A Vladimirov; Vladimir A Osipov

doi:10.1063/5.0177530

Dense random packing of disks with a power-law size distribution in thermodynamic limit

J Chem Phys. 2024 Jan 14;160(2):024107. doi: 10.1063/5.0177530.

Authors

Alexander Yu Cherny¹, Eugen M Anitas^{1

2}, Artem A Vladimirov¹, Vladimir A Osipov¹

Affiliations

¹ Joint Institute for Nuclear Research, Dubna 141980, Russian Federation.
² Horia Hulubei, National Institute of Physics and Nuclear Engineering, RO-077125 Bucharest-Magurele, Romania.

PMID: 38189610
DOI: 10.1063/5.0177530

Abstract

The correlation properties of a random system of densely packed disks, obeying a power-law size distribution, are analyzed in reciprocal space in the thermodynamic limit. This limit assumes that the total number of disks increases infinitely, while the mean density of the disk centers and the range of the size distribution are kept constant. We investigate the structure factor dependence on momentum transfer across various number of disks and extrapolate these findings to the thermodynamic limit. The fractal power-law decay of the structure factor is recovered in reciprocal space within the fractal range, which corresponds to the range of the size distribution in real space. The fractal exponent coincides with the exponent of the power-law size distribution as was shown previously by the authors of the work of Cherny et al. [J. Chem. Phys. 158(4), 044114 (2023)]. The dependence of the structure factor on density is examined. As is found, the power-law exponent remains unchanged but the fractal range shrinks when the packing fraction decreases. Additionally, the finite-size effects are studied at extremely low momenta of the order of the inverse system size. We show that the structure factor is parabolic in this region and calculate the prefactor analytically. The obtained results reveal fractal-like properties of the packing and can be used to analyze small-angle scattering from such systems.