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The method of planes pressure tensor for a spherical subvolume
D M Heyes1, E R Smith1, D Dini1
1Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom.
The Journal of Chemical Physics
|February 12, 2014
Summary
This study extends the Method of Planes (MOP) formula for spherical geometries, revealing mathematical equivalence between MOP and Radial Irving-Kirkwood formulas for pressure tensor components. Novel off-diagonal elements crucial for momentum conservation are also identified.
Area of Science:
- Computational physics
- Statistical mechanics
- Materials science
Background:
- Local pressure tensor calculations are crucial for understanding material properties.
- Existing methods like the Method of Planes (MOP) are primarily suited for planar geometries.
- Extending these methods to spherical geometries is essential for analyzing nanoscale systems and complex fluid interfaces.
Purpose of the Study:
- To derive an extension of the Method of Planes (MOP) formula for spherical geometries.
- To investigate the relationship between spherical and planar pressure tensor formulas.
- To analyze the radial dependence of the pressure tensor in bulk liquids using Molecular Dynamics simulations.
Main Methods:
- Extension of the Method of Planes (MOP) formula using the Control Volume formulation.
- Mathematical comparison of the derived spherical MOP formula with the Radial Irving-Kirkwood formula.
- Molecular Dynamics simulations of a model bulk liquid with virtual spheres of varying radii.
Main Results:
- The MOP formula for the radial pressure tensor component is mathematically identical to the Radial Irving-Kirkwood formula.
- Novel off-diagonal elements essential for momentum conservation naturally arise in the spherical treatment.
- Planar pressure tensor formulas are confirmed as the large-radius limit of spherical formulas.
- Radial dependence of the pressure tensor was computed, and angular probability distributions were analyzed.
- Variance in shear stress converges slowly with increasing radius and depends significantly on the number of molecules in the simulation cell.
Conclusions:
- The Control Volume formulation provides a robust framework for extending planar methods to spherical geometries.
- The study establishes a clear link between spherical and planar pressure tensor calculations.
- Results highlight the importance of considering system size and radial effects in pressure tensor calculations for nanoscale systems.
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