Explaining the low-frequency shear elasticity of confined liquids

TL;DR

This paper presents a theoretical framework combining nonaffine lattice dynamics and Frenkel theory to explain the observed increase in shear rigidity of confined liquids at low frequencies, matching experimental scaling laws.

Contribution

It introduces a novel model that explains how confinement suppresses low-frequency modes, leading to increased shear rigidity in liquids, aligning with experimental observations.

Findings

Predicts G' ~ L^{-3} scaling law for confined liquids

Successfully matches experimental data on shear modulus

Provides a unified description of liquid elasticity across scales

Abstract

Experimental observations of unexpected shear rigidity in confined liquids, on very low frequency scales on the order of 0.01-0.1 Hz, call into question our basic understanding of the elasticity of liquids and have posed a challenge to theoretical models of the liquid state ever since. Here we combine the nonaffine theory of lattice dynamics valid for disordered condensed matter systems with the Frenkel theory of the liquid state. The emerging framework shows that applying confinement to a liquid can effectively suppress the low frequency modes that are responsible for nonaffine soft mechanical response, thus leading to an effective increase of the liquid shear rigidity. The new theory successfully predicts the scaling law $G'\sim L^{-3}$ for the low-frequency shear modulus of liquids as a function of the confinement length $L$, in agreement with experimental results, and provides the basis for a more general description of the elasticity of liquids across different time and length scales.