Self-consistent construction of bridge functional based on the weighted density approximation.

Area of Science:

• Statistical mechanics
• Physical chemistry
• Computational fluid dynamics

Background:

• Developing accurate theoretical models for inhomogeneous fluids is crucial for understanding liquid behavior at interfaces.
• Existing methods often require empirical parameters or struggle with diverse interaction potentials.

Purpose of the Study:

• To introduce a novel, parameter-free bridge functional for describing inhomogeneous fluids.
• To validate the functional's accuracy across different potential models and confinement geometries.

Main Methods:

• Utilized a weighted density approximation (WDA) combined with Baxter's relation.
• Employed Percus's test particle method for self-consistent determination of free energy density.
• Applied the functional to hard-sphere, Lennard-Jones, and hard-core Yukawa potentials.

Main Results:

• The parameter-free functional accurately predicts density distribution functions for inhomogeneous fluids.
• Demonstrated applicability to external fields from planar walls and slit pores.
• Showcased versatility across various interparticle potentials.

Conclusions:

• The proposed WDA-based bridge functional offers a robust and versatile tool for studying inhomogeneous fluids.
• Eliminates the need for empirical parameters, enhancing predictive power.
• Provides a reliable framework for diverse liquid-state theories and simulations.