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Published on: December 4, 2017
Maximally random jamming of one-component and binary hard-disk fluids in two dimensions
1Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
Summary
We calculated the density of maximally random jamming for hard-disk fluids. Our findings align with experimental data for both single-component and binary systems.
Area of Science:
- Physics
- Materials Science
- Statistical Mechanics
Background:
- Understanding jamming transitions in hard-disk systems is crucial for materials science.
- Existing models often struggle to accurately predict the density of maximally random jammed states.
Purpose of the Study:
- To calculate the density of maximally random jamming for one-component and binary hard-disk fluids.
- To provide a theoretical framework for describing liquid-to-jammed state transitions.
Main Methods:
- Utilized integral equations for inhomogeneous single-particle density.
- Identified a specific bifurcation of solutions associated with the fluid's limit of stability.
- Applied approximations for binary systems, focusing on key order parameters.
Main Results:
- Predicted a packing fraction of 0.84 for the one-component hard-disk fluid, matching experimental values.
- Calculated a density of 0.84-0.87 for binary hard-disk fluids, showing weak dependence on composition and diameter ratio.
Conclusions:
- The theoretical framework accurately predicts maximally random jamming densities for hard-disk fluids.
- The study offers a unified approach for analyzing various hard-disk fluid transitions.
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