A consistent calculation of the chemical potential for dense simple fluids

Area of Science:

• Physical Chemistry
• Statistical Mechanics
• Thermodynamics

Background:

• Calculating excess chemical potential (betamuex) is crucial for understanding fluid behavior.
• Existing methods often rely on complex approximations or simulations.
• The Kirkwood coupling parameter approach offers a theoretical framework for these calculations.

Purpose of the Study:

• To present a general method for calculating excess chemical potential (betamuex).
• To derive the one-particle bridge function (B(1)r) for simple fluids.
• To validate the method using a dense hard sphere fluid model.

Main Methods:

• Utilizing the Kirkwood coupling parameter's dependence on correlation functions.
• Deriving the expression for the one-particle bridge function (B(1)r).
• Employing the known bridge function (B(2)r) and pressure-consistency condition.

Main Results:

• A novel expression for B(1)r is derived for simple fluids.
• For dense hard sphere fluids, B(1)r simplifies to a normalized form of B(2)r at high densities.
• The method ensures implicit satisfaction of the Gibbs-Duhem constraint.

Conclusions:

• The presented method provides a consistent and accurate way to calculate excess chemical potential (betamuex).
• It simplifies calculations by requiring only knowledge of B(2)r.
• The approach is effective for determining structural and thermodynamic properties of fluids.