Improvement on macroscopic compressibility approximation and beyond

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Computational Physics

Background:

• Thermodynamic perturbation expansion (TPE) is a key method in statistical mechanics.
• Existing TPE methods have limitations in accuracy and applicability.
• Higher-order expansions are needed for more precise predictions of fluid behavior.

Purpose of the Study:

• To develop a numerical procedure for extending TPE to higher orders.
• To assess the accuracy of the proposed higher-order TPE against existing approximations and simulation data.
• To provide a computationally efficient alternative to complex theories.

Main Methods:

• Development of a numerical procedure for higher-order TPE.
• Comparison of the proposed method with macroscopic compressibility approximation (MCA), local compressibility approximation, superposition approximation, analytical mean spherical approximation, and generalized van der Waals theory.
• Validation against existing literature and simulation data for hard core attractive Yukawa fluids.

Main Results:

• The proposed second-order TPE outperforms previous approximations.
• The third-order TPE shows superior accuracy compared to prior second-order TPE and other perturbation theories.
• Calculated critical temperatures for Yukawa fluids show excellent agreement with hierarchical reference theory.
• The method is computationally less demanding than self-consistent integral equation theory.

Conclusions:

• The developed numerical procedure effectively extends TPE to higher orders.
• The higher-order TPE offers improved accuracy and is a viable alternative to more complex theories.
• This work advances the predictive capabilities of statistical mechanics for fluid systems.