On the spectrum of fluctuations of a liquid surface: From the molecular scale to the macroscopic scale

TL;DR

This paper explores the full spectrum of liquid surface fluctuations, emphasizing the importance of bending rigidity at intermediate scales, and presents a molecular model aligning with simulation results.

Contribution

It introduces a molecular model that incorporates bending rigidity effects to extend classical capillary wave theory across all fluctuation scales.

Findings

Bending rigidity is negative when using the Gibbs surface.

Rigidity approaches zero near the critical point proportional to interfacial tension.

Model predictions agree with Monte Carlo simulations of colloid-polymer systems.

Abstract

We show that to account for the full spectrum of surface fluctuations from low scattering vector qd << 1 (classical capillary wave theory) to high qd > 1 (bulk-like fluctuations), one must take account of the interface's bending rigidity at intermediate scattering vector qd = 1, where d is the molecular diameter. A molecular model is presented to describe the bending correction to the capillary wave model for short-ranged and long-ranged interactions between molecules. We find that the bending rigidity is negative when the Gibbs equimolar surface is used to define the location of the fluctuating interface and that on approach to the critical point it vanishes proportionally to the interfacial tension. Both features are in agreement with Monte Carlo simulations of a phase-separated colloid-polymer system.