Precise simulation of near-critical fluid coexistence

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Computational Physics

Background:

• Determining liquid-gas coexisting densities is crucial for understanding phase transitions.
• Traditional methods often require prior knowledge of critical parameters like critical temperature (Tc) or criticality class.
• Accurate density predictions are essential for validating theoretical models and simulations.

Purpose of the Study:

• To develop a novel, unbiased method for deriving liquid-gas coexisting densities from grand canonical simulations.
• To achieve high accuracy in density predictions, especially near the critical point, without needing Tc or criticality class.
• To investigate pressure mixing effects and determine Yang-Yang ratios for different fluid models.

Main Methods:

• Utilizing the minima of Q(L) = (2)(L)/(L) within an LxLxL simulation box, where m represents density fluctuations.
• Employing recursive generation of an unbiased universal finite-size scaling function.
• Applying Monte Carlo simulations to a hard-core square-well fluid and a restricted primitive model electrolyte.

Main Results:

• The novel method successfully derived liquid-gas coexisting densities (ρ(+/-)) with high accuracy (+/-1%-2% of ρ(c)).
• Predictions were accurate down to 10⁻⁴-10⁻³ of the critical temperature (Tc).
• The method confirmed the Ising character of the models and revealed pressure mixing, yielding Yang-Yang ratios R(μ) of -0.04(4) and 0.2(6).

Conclusions:

• The presented simulation method offers a robust and accurate way to determine coexisting densities near critical points.
• This approach eliminates the need for prior knowledge of critical exponents or temperatures, simplifying phase transition studies.
• The findings provide valuable insights into fluid behavior and validate the universality of finite-size scaling.