Role of isostaticity and load-bearing microstructure in the elasticity of yielded colloidal gels

Abstract

We report a simple correlation between microstructure and straindependent elasticity in colloidal gels by visualizing the evolution of cluster structure in high strain-rate flows. We control the initial gel microstructure by inducing different levels of isotropic depletion attraction between particles suspended in refractive index matched solvents. Contrary to previous ideas from mode coupling and micromechanical treatments, our studies show that bond breakage occurs mainly due to the erosion of rigid clusters that persist far beyond the yield strain. This rigidity contributes to gel elasticity even when the sample is fully fluidized; the origin of the elasticity is the slow Brownian relaxation of rigid, hydrodynamically interacting clusters. We find a power-law scaling of the elastic modulus with the stress-bearing volume fraction that is valid over a range of volume fractions and gelation conditions. These results provide a conceptual framework to quantitatively connect the flow-induced microstructure of soft materials to their nonlinear rheology.colloids | confocal microscopy | suspensions | shear flow C olloidal gels form sample-spanning networks (1) and are used to generate solid-like properties in a broad range of materials such as direct-write inks (2), nanoemulsions (3), tissue scaffolds (4), and membranes (5). When gels undergo large deformations, their network ruptures into clusters via a complex process. The ability to connect structural changes to suspension rheology is critical in understanding the mechanism of yielding. The network of clusters that makes up colloidal gels arises due to percolation, dynamic arrest, and phase separation, where the volume fraction and pair potential play an important part in their structure and rheology (6-8). Interparticle bonds rupture under a sufficiently large stress; the result is a flow-induced fluidization transition accompanied by the formation of voids and aggregates that continuously break and reform along the principal axes of flow (9, 10). A complex two-step yielding process has been observed in gels at intermediate volume fractions (0.05 ≤ ϕ ≤ 0.30) (11,12). Within this regime, a small number of bonds are broken in gels undergoing steady shear yielding (9, 10). Methods that track the evolution of ensemble-averaged structure, such as mode coupling theory (6) and light scattering, lack sensitivity to these subpopulations. On the other hand, micromechanical treatments directly model the contributions of local microstructure to the macroscopic elasticity of the material (13-15). However, experiments to connect the yield stress to different interparticle potentials, volume fractions, and particle sizes show little agreement. Presently, these theories can only provide estimates of colloidal rheology under specific conditions.We demonstrate that a simple, general correlation between microstructure and strain-dependent rheology exists for colloidal depletion gels undergoing large deformations at high shear rates. Our experiments harness confocal laser scanning mi...

Aqueous Colloid + Polymer Depletion System for Confocal Microscopy and Rheology

“…Hardsphere colloidal glasses in shear flow exhibit strongly localized yielding [29], leading to shear-banding [30,31], or jamming and self-filtration [32]. Finally, colloidal gels deform non-linearly [33] and yield under shear flow [25,34]. Single-particle imaging also aids in elucidating the contribution of hydrodynamic forces vs. short-range repulsions [35] and of normal stress differences to particle migration [36] in sheared or flowing hard-sphere colloids.…”

“…Depletion interactions can also generate other kinds of nonequilibrium solids such as attractive glasses [21] and colloidal gels [22,23], whose mechanical properties depend upon the strength and nature of the interparticle attractions. Imaging experiments, in this context, allow the microscopic particle structure to be linked to the macroscopic mechanical properties [24,25].…”

Local structure of percolating gels at very low volume fractions

“…In order to predict the mechanical properties of gels, it is important to know both their local [13][14][15] and global [16][17][18] structure, but a deep understanding of both remains today a challenge. For example, in the very dilute limit, the study of gel formation via molecular dynamics is challenged by the very long times required to form aggregates, with equilibration times that easily exceed 10 8 integration steps 19 .…”

Depletion gels from dense soft colloids: Rheology and thermoreversible melting

“…It can also characterize shear-induced melting of colloidal gels made from the same colloidpolymer mixtures at lower colloid volume fractions, due to the different length scales involved [Koumakis and Petekidis (2011)]. In fact, shear yielding in a variety of systems from emulsions to foams and nanocomposites, which often consist of gel-like networks, is a macroscopic process that takes place via a gradual evolution involving microscopic structural rearrangements [Rouyer et al (2003); Osman et al (2004); Masschaele and Vermant (2009);Putz and Burghelea (2009);Hsiao et al (2012); Kamble et al (2013); Moll et al (2013)]. …”