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An asymptotically consistent approximant method with application to soft- and hard-sphere fluids.

N S Barlow¹, A J Schultz, S J Weinstein

¹Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA. barlow.nate@gmail.com

The Journal of Chemical Physics

|December 5, 2012

Summary

This summary is machine-generated.

A new equation of state using modified Padé approximants accurately describes soft sphere fluids across densities. This method improves upon virial series, especially for less hard spheres, and provides accurate hard sphere equations of state.

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Area of Science:

Thermodynamics
Statistical Mechanics
Computational Physics

Background:

Traditional equations of state struggle to accurately represent fluid behavior across all densities.
Virial series expansions are accurate at low densities but diverge at high densities.
Padé approximants offer a way to extend the validity of series expansions.

Purpose of the Study:

To develop a robust equation of state for soft sphere fluids using a modified Padé approximant approach.
To ensure the equation of state captures both low-density virial behavior and high-density asymptotic behavior.
To create a general, accurate equation of state for soft spheres as a function of particle hardness.

Main Methods:

Constructing an equation of state via modified Padé approximants.
Ensuring analytic behavior in the physical domain and correct asymptotic limits.
Applying the method to soft spheres with inverse-power potentials (φ ∝ r⁻ⁿ).
Comparing results against molecular simulation data for various 'hardness' values (n).

Main Results:

The modified Padé approximants significantly outperform the 8-term virial series for n < 9.
For n ≥ 9, both approximants and the 8-term virial series accurately describe fluid behavior.
The derived hard sphere equation of state (n → ∞) shows improved accuracy over the 10-term virial series.
A least-squares fit yields a general soft-sphere equation of state accurate over the full fluid density range.

Conclusions:

Modified Padé approximants provide a superior framework for developing equations of state for soft sphere fluids.
The method offers a unified approach, accurately describing fluid behavior from low to high densities.
The resulting general equation of state for soft spheres is a valuable tool for thermodynamic modeling.