Phonon Dispersion and Elastic Moduli of Two-Dimensional Disordered Colloidal Packings of Soft Particles with Frictional Interactions

TL;DR

This study uses particle tracking and covariance matrix techniques to analyze phonon dispersion and elastic moduli in 2D colloidal glasses of soft particles, revealing quantitative agreement with jammed frictional particle models.

Contribution

It provides the first experimental validation of theoretical predictions for phonon dispersion and elastic moduli in frictional colloidal glasses, including estimates of inter-particle energy and friction.

Findings

Elastic moduli match numerical predictions for frictional particles.

The ratio G/B varies with packing fraction as predicted for jammed systems.

An inter-particle friction coefficient is estimated from elastic data.

Abstract

Particle tracking and displacement covariance matrix techniques are employed to investigate the phonon dispersion relations of two-dimensional colloidal glasses composed of soft, thermoresponsive microgel particles whose temperature-sensitive size permits \textit{in situ} variation of particle packing fraction. Bulk, $B$, and shear, $G$, moduli of the colloidal glasses are extracted from the dispersion relations as a function of packing fraction, and variation of the ratio $G/B$ with packing fraction is found to agree quantitatively with predictions for jammed packings of frictional soft particles. In addition, $G$ and $B$ individually agree with numerical predictions for frictional particles. This remarkable level of agreement enabled us to extract an energy scale for the inter-particle interaction from the individual elastic constants and to derive an approximate estimate for the inter-particle friction coefficient.