Elasticity of colloidal gels: structural heterogeneity, floppy modes, and rigidity

Rheological measurements of model colloidal gels reveal that large variations in the shear moduli as colloidal volume-fraction changes are not reflected by simple structural parameters such as the coordination number, which remains almost a constant. We resolve this apparent contradiction by conducting a normal-mode analysis of experimentally measured bond networks of gels of colloidal particles with short-ranged attraction. We find that structural heterogeneity of the gels, which leads to floppy modes and a nonaffine-affine crossover as frequency increases, evolves as a function of the volume fraction and is key to understanding the frequency-dependent elasticity. Without any free parameters, we achieve good qualitative agreement with the measured mechanical response. Furthermore, we achieve universal collapse of the shear moduli through a phenomenological spring-dashpot model that accounts for the interplay between fluid viscosity, particle dissipation, and contributions from the affine and non-affine network deformation.

Automated summary

By analyzing the experimentally measured bond networks of colloidal particle gels, the contradiction between variations in shear moduli and colloidal volume fraction changes is resolved. It is found that structural heterogeneity of the gels is crucial in understanding frequency-dependent elasticity. A phenomenological spring-dashpot model that accounts for the interplay between fluid viscosity, particle dissipation, and contributions from the affine and non-affine network deformation leads to a universal collapse of shear moduli.