Correlation-function structure in square-gradient models of the liquid-gas interface: Exact results and reliable...

Area of Science:

• Physical Chemistry
• Statistical Mechanics
• Soft Matter Physics

Background:

• Microscopic structure of density-density correlations in fluid interfaces is crucial for understanding interfacial phenomena.
• Previous work identified resonances in the local structure factor at specific parallel wave vectors (q) for short-ranged forces.

Purpose of the Study:

• To further investigate and validate approximations for the local structure factor and pair correlation function.
• To compare these approximations against analytically solvable models within square-gradient theory.
• To assess the accuracy of these approximations for interfacial systems, including those near tricritical points.

Main Methods:

• Comparison of approximations for local structure factor and pair correlation function.
• Analysis using three new analytically solvable models within square-gradient theory.
• Evaluation against numerical solutions of the Ornstein-Zernike equation for a model near a tricritical point.

Main Results:

• Approximations accurately describe the pair correlation function and structure factor across the entire wave vector spectrum.
• The approximations capture the crossover from Goldstone mode divergence (small q) to bulk-like behavior (large q).
• Approximations are exact for some potentials and highly accurate (within a few percent) for others, including near tricritical points.

Conclusions:

• The validated approximations provide a robust framework for understanding density-density correlations in fluid interfaces.
• These approximations are versatile, accurately describing interfacial behavior across various conditions, including near critical points.
• The findings offer a simplified yet accurate method for analyzing complex interfacial structures.