Plasticity in colloidal gel strands

Necking and failure of a particulate gel strand: signatures of yielding on different length scales

"Sticky" spheres with a short-ranged attraction are a basic model of a wide range of materials from the atomic to the granular length scale. Among the complex phenomena exhibited by sticky spheres is the formation of far-from-equilibrium dynamically arrested networks which comprise "strands" of densely packed particles. The aging and failure of such gels under load is a remarkably challenging problem, given the simplicity of the model, as it involves multiple length- and time-scales, making a single approach ineffective. Here we tackle this challenge by addressing the failure of a single strand with a combination of methods. We study the mechanical response of a single strand of a model gel-former to deformation, both numerically and analytically. Under elongation, the strand breaks by a necking instability. We analyse this behaviour at three different length scales: a rheological continuum model of the whole strand; a microscopic analysis of the particle structure and dynamics; and the local stress tensor. Combining these different approaches gives a coherent picture of the necking and failure. The strand has an amorphous local structure and has large residual stresses from its initialisation. We find that neck formation is associated with increased plastic flow, a reduction in the stability of the local structure, and a reduction in the residual stresses; this indicates that the system loses its solid character and starts to behave more like a viscous fluid. These results will inform the development of more detailed models that incorporate the heterogeneous network structure of particulate gels.

Hydrodynamic lubrication in colloidal gels

Colloidal gels are elasto-plastic materials composed of an out-of-equilibrium, self-assembled network of micron-sized (solid) particles suspended in a fluid. Recent work has shown that far-field hydrodynamic interactions do not change gel structure, only the rate at which the network forms and ages. However, during gel formation, the interplay between short-ranged attractions leading to gelation and equally short-ranged hydrodynamic lubrication interactions remains poorly understood. Here, we therefore study gelation using a range of hydrodynamic descriptions: from single-body (Brownian Dynamics), to pairwise (Rotne-Prager-Yamakawa), to (non-)lubrication-corrected many-body (Stokesian Dynamics). We confirm the current understanding informed by simulations accurate in the far-field. Yet, we find that accounting for lubrication can strongly impact structure at low colloid volume fraction. Counterintuitively, strongly dissipative lubrication interactions also accelerate the aging of a gel, irrespective of colloid volume fraction. Both elements can be explained by lubrication forces facilitating collective dynamics and therefore phase-separation. Our findings indicate that despite the computational cost, lubricated hydrodynamic modeling with many-body far-field interactions is needed to accurately capture the evolution of the gel structure.

Toughening colloidal gels using rough building blocks

Colloidal gels, commonly used as mesoporous intermediates or functional materials, suffer from brittleness, often showing small yield strains on the order of 1% or less for gelled colloidal suspensions. The short-range adhesive forces in most such gels are central forces-combined with the smooth morphology of particles, the resistance to yielding and shear-induced restructuring is limited. In this study, we propose an innovative approach to improve colloidal gels by introducing surface roughness to the particles to change the yield strain, giving rise to non-central interactions. To elucidate the effects of particle roughness on gel properties, we prepared thermoreversible gels made from rough or smooth silica particles using a reliable click-like-chemistry-based surface grafting technique. Rheological and optical characterization revealed that rough particle gels exhibit enhanced toughness and self-healing properties. These remarkable properties can be utilized in various applications, such as xerogel fabrication and high-fidelity extrusion 3D-printing, as we demonstrate in this study.

Hydrodynamic stability criterion for colloidal gelation under gravity

Attractive colloids diffuse and aggregate to form gels, solidlike particle networks suspended in a fluid. Gravity is known to strongly impact the stability of gels once they are formed. However, its effect on the process of gel formation has seldom been studied. Here, we simulate the effect of gravity on gelation using both Brownian dynamics and a lattice-Boltzmann algorithm that accounts for hydrodynamic interactions. We work in a confined geometry to capture macroscopic, buoyancy-induced flows driven by the density mismatch between fluid and colloids. These flows give rise to a stability criterion for network formation, based on an effective accelerated sedimentation of nascent clusters at low volume fractions that disrupts gelation. Above a critical volume fraction, mechanical strength in the forming gel network dominates the dynamics: the interface between the colloid-rich and colloid-poor region moves downward at an ever-decreasing rate. Finally, we analyze the asymptotic state, the colloidal gel-like sediment, which we find not to be appreciably impacted by the vigorous flows that can occur during the settling of the colloids. Our findings represent the first steps toward understanding how flow during formation affects the life span of colloidal gels.

A new fractal structural-mechanical theory of particle-filled colloidal networks with heterogeneous stress translation

This work addresses the role of rigid inclusions in determining the elastic modulus of particle-filled colloidal networks by modifying an established fractal scaling model. The approach acknowledges the heterogeneous nature of stress distribution at length scales beyond the colloidal aggregates, while maintaining structural information at the level of individual clusters. This was achieved by introducing a scaling factor to account for system heterogeneity which contains intrinsic information about the network's capacity to form load-bearing links. Rigid fillers bound to the network induce stress concentration, but additionally serve as junction zones which introduce additional load-bearing pathways. This gives rise to the observed increase in the modulus with filler volume fraction. The proposed relationship between the load-bearing network connectivity and scaling behavior may have additional implications on the fractal dimension determined by rheological methods. Further, this model accommodates an experimentally observed correlation between the scaling behavior of the modulus associated with the addition of fillers and that arising from increasing structurant concentration. The modified fractal model thus provides an alternative view of how fillers contribute to the small- and large-deformation mechanical behavior of filled colloidal gels in a manner consistent with experimental observations.

Real space analysis of colloidal gels: triumphs, challenges and future directions

Colloidal gels constitute an important class of materials found in many contexts and with a wide range of applications. Yet as matter far from equilibrium, gels exhibit a variety of time-dependent behaviours, which can be perplexing, such as an increase in strength prior to catastrophic failure. Remarkably, such complex phenomena are faithfully captured by an extremely simple model-'sticky spheres'. Here we review progress in our understanding of colloidal gels made through the use of real space analysis and particle resolved studies. We consider the challenges of obtaining a suitable experimental system where the refractive index and density of the colloidal particles is matched to that of the solvent. We review work to obtain a particle-level mechanism for rigidity in gels and the evolution of our understanding of time-dependent behaviour, from early-time aggregation to ageing, before considering the response of colloidal gels to deformation and then move on to more complex systems of anisotropic particles and mixtures. Finally we note some more exotic materials with similar properties.

Potential-invariant network structures in Asakura-Oosawa mixtures with very short attraction range

We systematically investigated the structure and aggregate morphology of gel networks formed by colloid-polymer mixtures with a moderate colloid volume fraction and different values of the polymer-colloid size ratio, always in the limit of short-range attraction. Using the coordinates obtained from confocal microscopy experiments, we determined the radial, angular, and nearest-neighbor distribution functions together with the cluster radius of gyration as a function of size ratio and polymer concentration. The analysis of the structural correlations reveals that the network structure becomes increasingly less sensitive to the potential strength with the decreasing polymer-colloid size ratio. For the larger size ratios, compact clusters are formed at the onset of network formation and become progressively more branched and elongated with increasing polymer concentration/attraction strength. For the smallest size ratios, we observe that the aggregate structures forming the gel network are characterized by similar morphological parameters for different values of the size ratio and the polymer concentration, indicating a limited evolution of the gel structure with variations of the parameters that determine the interaction potential between colloids.

Particle Dynamics in Colloid-Polymer Mixtures with Different Polymer Architectures

Nonadsorbing polymers are widely used as thickening agents for colloids. A quantitative description of the structure and dynamics of such colloid-polymer mixtures is crucial to reveal the mechanisms accounting for the desired mechanical properties. We use confocal microscopy to study colloids with three types of commonly used polymers with different architectures: linear, subgranular cross-linked, and branched microgels. All three thickeners give rise to heterogeneous colloidal dynamics, characterized by non-Gaussian displacement distributions. However, while the ensemble-averaged particle dynamics in these materials are very similar, the underlying individual particle dynamics are not. Linear polymers give rise to depletion attraction and the formation of colloidal gels, in which the majority of particles are immobilized, while a few weakly bound particles have much higher mobility. By contrast, the branched and cross-linked polymers thicken the continuous phase of the colloid, squeezing the particles into dense pockets, where the mobility is reduced and requires more cooperative rearrangements.