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Leaky cell model of hard spheres.
Thomas G Fai1, Jamie M Taylor2, Epifanio G Virga3
1Department of Mathematics and Volen Center for Complex Systems, Brandeis University, Waltham, Massachusetts 02453, USA.
The Journal of Chemical Physics
|March 16, 2021
Summary
We calculated free volumes for hard sphere packings on lattices using a leaky cell model. This reveals phase transitions and coexistence in crystalline materials.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Materials Science
Background:
- Understanding the behavior of hard sphere packings is crucial in statistical mechanics and materials science.
- Lattice models provide a simplified yet insightful framework for studying phase transitions and material properties.
Purpose of the Study:
- To develop a method for calculating the partition function and pressure of hard sphere lattice packings.
- To investigate the role of accessible free volume in determining the thermodynamic properties of these systems.
- To explore phase transitions and potential coexistence in crystalline materials.
Main Methods:
- Utilizing a leaky cell model to compute accessible free volumes, accounting for sphere mobility beyond local cages.
- Applying elementary geometry for exact free volume calculations in 2D and 3D lattice packings.
- Comparing results with established liquid models like Carnahan-Starling and Percus-Yevick.
- Employing the common tangent construction to identify phase transitions.
Main Results:
- Formulas for free volumes in various lattice packings were derived.
- The leaky cell model provides a distinct approach to free volume calculation compared to liquid models.
- Phase transitions were identified within the leaky cell regime for lattice packings.
Conclusions:
- The accessible free volume is a key determinant of thermodynamic properties in hard sphere lattice packings.
- The leaky cell model offers a valuable framework for understanding crystalline material behavior and phase transitions.
- The study indicates the potential for phase coexistence in crystalline systems, a significant finding for materials science.
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