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Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

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Thermodynamically consistent closure approximation for hard spheres systems.

Mauricio D Carbajal-Tinoco¹

¹Departamento de Física, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14-740, 07000 México DF, Mexico. mdct@fis.cinvestav.mx

The Journal of Chemical Physics

|March 10, 2012

Summary

We developed a new closure relation extending the Percus-Yevick approximation for hard sphere systems. This model shows good agreement with simulations for thermodynamic and structural properties at intermediate concentrations.

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Area of Science:

Statistical Mechanics
Thermodynamics
Soft Matter Physics

Background:

The Percus-Yevick (PY) approximation is a fundamental tool in statistical mechanics for describing fluid systems.
Accurate closure relations are crucial for predicting thermodynamic and structural properties of dense fluids.
Extending existing approximations can improve their applicability to more complex systems.

Purpose of the Study:

To introduce a novel closure relation that improves upon the standard Percus-Yevick approximation.
To incorporate thermodynamic self-consistency into the closure relation.
To validate the new closure relation for hard sphere systems and depletion potentials.

Main Methods:

Development of a new closure relation with an additional term and a mixing coefficient.
Determination of the mixing coefficient via thermodynamic self-consistency condition.
Analytical calculation of the mixing coefficient within a linear approximation.
Comparison of model results with established thermodynamic expressions and numerical simulations for hard spheres.
Extension of the closure relation to calculate depletion potentials between large spheres in a fluid of small spheres.

Main Results:

The proposed closure relation accurately reproduces thermodynamic and structural properties of monodisperse hard spheres.
Results align well with numerical simulations, particularly at intermediate concentrations.
The model successfully extends to describe the depletion potential between large spheres in a binary mixture.
The analytical calculation of the mixing coefficient provides a practical approach.

Conclusions:

The new closure relation offers a thermodynamically self-consistent and accurate extension of the Percus-Yevick approximation.
This approach provides a reliable method for studying both bulk properties and effective interactions in hard sphere systems.
The model's good agreement with simulations suggests its potential for broader applications in statistical physics and materials science.