Physically based equation of state for Mie ν-6 fluids.

Area of Science:

• Thermodynamics
• Physical Chemistry
• Statistical Mechanics

Background:

• Accurate equations of state are crucial for predicting fluid behavior.
• Empirical models for Mie fluids often lack broad applicability and physical grounding.
• Existing theoretical models may not fully capture thermodynamic properties across all relevant densities and temperatures.

Purpose of the Study:

• To develop a physically based equation of state for Mie ν-6 fluids.
• To achieve accuracy comparable to state-of-the-art empirical models.
• To extend the applicability of equations of state to a wider range of Mie exponents and fluid states.

Main Methods:

• Developed a physically based equation of state within the uv-theory framework.
• Incorporated the third virial coefficient (B3) for improved low-density description.
• Interpolated between Weeks-Chandler-Andersen (WCA) perturbation theory at high densities and a modified WCA theory at low densities.
• Derived a new algebraic equation for the third virial coefficient of Mie fluids.

Main Results:

• The new equation of state accurately describes Mie ν-6 fluids (9 ≤ ν ≤ 48).
• Model performance for the Lennard-Jones fluid (ν = 12) matches leading empirical equations of state.
• The model is applicable to densities up to ρ*(T*)⪅1.1+0.12T* and temperatures T* > 0.3.
• Accurate prediction of thermodynamic properties and phase equilibria validated against molecular simulation data.

Conclusions:

• The physically based equation of state offers a robust alternative to empirical models for Mie fluids.
• The model provides superior description of metastable and unstable regions, beneficial for density functional theory applications.
• The theoretical foundation allows for potential extensions to complex systems like non-spherical fluids and mixtures.