We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of hard spheres in d = 3 dimensions and, thus, obtain an estimate of the random close packing volume fraction, ϕRCP, as a function of size polydispersity. We first consider mixtures of particle sizes with discrete distributions. For binary systems, we show agreement between our predictions and simulations using both our own results and results reported in previous studies, as well as agreement with recent experiments from the literature. We then apply our approach to systems with continuous polydispersity using three different particle size distributions, namely, the log-normal, Gamma, and truncated power-law distributions. In all cases, we observe agreement between our theoretical findings and numerical results up to rather large polydispersities for all particle size distributions when using as reference our own simulations and results from the literature. In particular, we find ϕRCP to increase monotonically with the relative standard deviation, sσ, of the distribution and to saturate at a value that always remains below 1. A perturbative expansion yields a closed-form expression for ϕRCP that quantitatively captures a distribution-independent regime for sσ < 0.5. Beyond that regime, we show that the gradual loss in agreement is tied to the growth of the skewness of size distributions.
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28 January 2023
Research Article|
January 23 2023
Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowding
Carmine Anzivino
;
Carmine Anzivino
a)
(Data curation, Formal analysis, Investigation, Methodology, Validation, Writing – original draft, Writing – review & editing)
1
Department of Physics “A. Pontremoli,” University of Milan
, Via Celoria 16, 20133 Milan, Italy
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Mathias Casiulis;
Mathias Casiulis
(Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Writing – original draft, Writing – review & editing)
2
Center for Soft Matter Research, Department of Physics, New York University
, New York, New York 10003, USA
3
Simons Center for Computational Physical Chemistry, Department of Chemistry, New York University
, New York, New York 10003, USA
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Tom Zhang;
Tom Zhang
(Formal analysis, Investigation, Visualization)
2
Center for Soft Matter Research, Department of Physics, New York University
, New York, New York 10003, USA
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Amgad Salah Moussa;
Amgad Salah Moussa
(Funding acquisition, Project administration, Resources, Supervision)
4
Syngenta AG
, 4058 Basel, Switzerland
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Stefano Martiniani
;
Stefano Martiniani
(Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Supervision, Validation, Writing – original draft, Writing – review & editing)
2
Center for Soft Matter Research, Department of Physics, New York University
, New York, New York 10003, USA
3
Simons Center for Computational Physical Chemistry, Department of Chemistry, New York University
, New York, New York 10003, USA
5
Courant Institute of Mathematical Sciences, New York University
, New York, New York 10003, USA
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Alessio Zaccone
Alessio Zaccone
b)
(Conceptualization, Funding acquisition, Investigation, Methodology, Project administration, Supervision, Validation, Writing – original draft, Writing – review & editing)
1
Department of Physics “A. Pontremoli,” University of Milan
, Via Celoria 16, 20133 Milan, Italy
b)Author to whom correspondence should be addressed: [email protected]
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a)
Electronic mail: [email protected]
b)Author to whom correspondence should be addressed: [email protected]
J. Chem. Phys. 158, 044901 (2023)
Article history
Received:
November 30 2022
Accepted:
December 28 2022
Citation
Carmine Anzivino, Mathias Casiulis, Tom Zhang, Amgad Salah Moussa, Stefano Martiniani, Alessio Zaccone; Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowding. J. Chem. Phys. 28 January 2023; 158 (4): 044901. https://doi.org/10.1063/5.0137111
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