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

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.

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• Tessellated granular metamaterials with tunable elastic moduli
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• Enhanced Long Wavelength Mermin-Wagner Fluctuations in Active Crystals and Glasses
• Cavity averages for hard spheres in the presence of polydispersity and incomplete data
• Unearthing the anticrystal: criticality in the linear response of disordered solids
• Decoupling between thermodynamics and dynamics during rejuvenation in colloidal glasses