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Random sequential adsorption of Platonic and Archimedean solids
1M. Smoluchowski Institute of Physics, Department of Statistical Physics, Jagiellonian University, 30-348 Kraków, Poland.
Computer simulations reveal that truncated tetrahedra achieve the highest packing fraction in random sequential adsorption. Regular tetrahedra yield the smallest packing fraction, with microstructural properties consistent across different polyhedral solids.
Area of Science:
- Materials Science
- Computational Physics
- Crystallography
Background:
- Random sequential adsorption (RSA) is a fundamental process for creating disordered materials.
- Understanding the packing efficiency of different geometric shapes is crucial for designing novel materials.
- Platonic and Archimedean solids offer a unique set of symmetries for studying packing phenomena.
Purpose of the Study:
- To analyze the packing fractions achieved by Platonic and Archimedean solids using RSA.
- To investigate the microstructural properties and growth kinetics of these packings.
- To develop and implement an efficient overlap detection method for polyhedral solids.
Main Methods:
- Utilized computer simulations to model random sequential adsorption of Platonic and Archimedean solids.
- Developed a fast overlap criterion for polyhedral solids based on the separating axis theorem.
- Generated large-scale packings to minimize statistical error.
Main Results:
- Determined the highest saturated packing fraction (θ=0.40210(68)) using truncated tetrahedra.
- Identified the smallest saturated packing fraction (θ=0.35635(67)) with regular tetrahedra.
- Observed typical RSA microstructural properties and confirmed kinetics are not solely dimension-dependent.
Conclusions:
- Truncated tetrahedra are optimal for RSA packing efficiency among the studied solids.
- The developed overlap criterion enables larger, more accurate simulations.
- Polyhedral order parameters offer a versatile tool for future research on symmetric particles.
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