Scaled particle theory for hard sphere pairs. II. Numerical analysis

Area of Science:

• Physical Chemistry
• Statistical Mechanics
• Fluid Dynamics

Background:

• Understanding the structure of hard sphere fluids is fundamental in statistical mechanics.
• Existing theories often struggle to accurately describe fluid behavior across broad density ranges.

Purpose of the Study:

• To numerically calculate the pair correlation function of hard sphere fluids using an extended scaled particle theory.
• To validate the theory's accuracy by comparing predictions with computer simulation data.
• To investigate thermodynamic properties like pressure, surface tension, and Tolman length.

Main Methods:

• Numerical calculation of the pair correlation function.
• Extension of scaled particle theory (SPT) as presented by Stillinger et al.
• Comparison of theoretical predictions with established computer simulation results.

Main Results:

• The extended SPT accurately captures the hard sphere fluid's structure over the density range 0 <= rho*sigma^3 <= 0.96.
• Virial route pressure predictions are consistently lower than simulation results.
• Compressibility route pressure predictions show deviations at higher densities (rho*sigma^3 > 0.67).

Conclusions:

• The extended scaled particle theory provides a robust framework for describing hard sphere fluid structure.
• The study highlights the strengths and limitations of different routes for predicting thermodynamic properties.
• Numerical predictions for surface tension and Tolman length are provided for further research.