Combined temperature and density series for fluid-phase properties. II. Lennard-Jones spheres

Area of Science:

• Statistical Mechanics
• Thermodynamics
• Computational Chemistry

Background:

• Thermodynamic perturbation theory (TPT) traditionally relies on molecular simulations of reference fluids.
• Previous work established a cluster integral-based methodology for calculating Helmholtz energy power series coefficients in reciprocal temperature (β) for square well spheres.
• Accurate calculation of these coefficients is crucial for developing reliable equations of state.

Purpose of the Study:

• To extend the cluster integral methodology to Lennard-Jones (LJ) spheres.
• To compare TPT coefficients calculated via cluster integrals with those from molecular simulations.
• To develop a foundation for accurate equation-of-state calculations for LJ systems.

Main Methods:

• Utilized cluster integrals to compute density series coefficients for the Helmholtz energy at each temperature order.
• Employed the Weeks-Chandler-Andersen potential as the reference fluid for LJ spheres.
• Developed a correlation for the second virial coefficient (B2(β)) of LJ spheres based on hard sphere fluid virial coefficients.

Main Results:

• Demonstrated good agreement between cluster integral-derived and simulation-derived TPT coefficients for LJ spheres through third order in β.
• Observed significantly better agreement for LJ spheres compared to previously studied square well spheres.
• Established a relationship between reference fluid coefficients and hard sphere virial coefficients, enabling extrapolation to infinite temperature.

Conclusions:

• The cluster integral methodology is effective for calculating TPT coefficients for LJ spheres.
• The established correlation for B2(β) facilitates accurate estimation of low-density TPT coefficients.
• The developed approach provides a robust method for estimating equations of state for LJ systems across various densities.