Computer simulations of colloidal gels: how hindered particle rotation affects structure and rheology

Enhanced contact flexibility from nanoparticles in capillary suspensions

HYPOTHESIS

Sample-spanning particle networks are used to induce structure and a yield stress, necessary for 3D printing of porous ceramics and paints. In capillary suspensions, a small quantity of immiscible secondary fluid is incorporated into a suspension. By further adding nanoparticles with a range of hydrophobicities, the structure of the bridges and microparticle-microparticle contacts is expected to be modified, resulting in a tunable yield stress and shear moduli. Moreover, the compressibility of these samples, important in many processing and application steps, is expected to be sensitive to these changes.

EXPERIMENT

The nanoparticle hydrophobicity was altered and their position relative to the microparticles and the bridges was examined using confocal microscopy where the correlation between bridge size and network structure was observed. A step-wise uniaxial compression test on the confocal was conducted to monitor the microparticle movement and structural changes between capillary suspension networks with and without nanoparticles.

FINDINGS

Our observation suggests that nanoparticles induce the formation of thin liquid films on the surface of the microparticles, mitigating contact line pinning and promoting internal liquid exchange. Additionally, nanoparticles at microparticle contact regions further diminish Hertzian contact, enhancing the capacity for rearrangement. These effects enhance microparticle movement, narrowing the bridge size distribution.

Formation dynamics of branching structure in the slippery DLCA model

We numerically investigated the aggregation dynamics and resulting network structures of colloidal gels using the slippery diffusion-limited cluster aggregation (DLCA) model. In this model, bonds are irreversibly formed upon the particle contacts, but the angles among them are not fixed, unlike the conventional DLCA. This allows clusters to be deformed in the process of aggregation. By characterizing the aggregation dynamics and using a reduced network scheme, our simulation revealed two distinct branching structure formation routes depending on the particle volume fraction ϕ. In lower volume fraction systems (ϕ ≤ 8%), the deformations of small-size clusters proceed prior to the percolation. When the Maxwell criterion is satisfied and the clusters become mechanically stable, the formation of the branching structure is nearly completed. After forming the branching structures, they aggregate and form a larger percolating network. Then, the aggregation proceeds through the elongation and straightening of the chain parts of the network. In higher volume fraction systems (ϕ > 8%), on the other hand, the clusters percolate, and a fine and homogeneous branching structure is formed at the early stage of the aggregation. In the aging stage, it collapses into a denser and more heterogeneous structure and becomes more stable. Our quantitative analyses of the branching structure will shed light on a new strategy for describing the network formation and elasticity of colloidal gels.

Unifying Atoms and Colloids near the Glass Transition through Bond-Order Topology

In this combined experimental and simulation study, we utilize bond-order topology to quantitatively match particle volume fraction in mechanically uniformly compressed colloidal suspensions with temperature in atomistic simulations. The obtained mapping temperature is above the dynamical glass transition temperature, indicating that the colloidal systems examined are structurally most like simulated undercooled liquids. Furthermore, the structural mapping procedure offers a unifying framework for quantifying relaxation in arrested colloidal systems.

Modeling Colloidal Particle Aggregation Using Cluster Aggregation with Multiple Particle Interactions

In this study, we investigate the aggregation dynamics of colloidal silica by generating simulated structures and comparing them to experimental data gathered through scanning transmission electron microscopy (STEM). More specifically, diffusion-limited cluster aggregation and reaction-limited cluster aggregation models with different functions for the probability of particles sticking upon contact were used. Aside from using a constant sticking probability, the sticking probability was allowed to depend on the masses of the colliding clusters and on the number of particles close to the collision between clusters. The different models of the sticking probability were evaluated based on the goodness-of-fit of spatial summary statistics. Furthermore, the models were compared to the experimental data by calculating the structures' fractal dimension and mass transport properties from simulations of flow and diffusion. The sticking probability, depending on the interaction with multiple particles close to the collision site, led to structures most similar to the STEM data.

Thermoresponsive oil-continuous gels based on double-interpenetrating colloidal-particle networks

Gels composed of multicomponent building blocks offer promising opportunities for the development of novel soft materials with unique and useful structures. While interpenetrating polymer networks have been extensively studied and applied in the creation of these gels, equivalent strategies utilizing colloidal particles have received limited scientific and technological attention. This study presents a novel class of thermo-responsive apolar double gels from interpenetrating networks of attractive colloidal silica and lipid particles. These double gels are easily assembled and suitable for the fabrication of 3D-printed edible soft constructs. Emphasis is focused on the rheological properties and structure emerging on the dilute regime (ϕ ≲ 0.1). Rheological investigations demonstrate that double gels exhibit greater stiffness and resilience to yielding compared to their single lipid gel counterparts. The scaling behavior of the oscillatory linear shear moduli and the critical strain for yielding with volume fraction remain comparable between single and double gels. Creep yielding in double gels exhibits two exponential decay regimes, suggesting the presence of thicker gel strands undergoing flow. Visualization and quantification of the quiescent microstructure confirms the existence of such denser aggregates devoid of larger clusters due to steric hindrance of interpenetrating networks in double gels. This is in stark contrast to lipid single gels where aggregates grow unrestrictedly into larger clusters. Our study constitutes the first demonstration on the assembly of apolar double gel networks as a promising avenue for the design of novel soft materials and foods with tailored structure and mechanics.

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.

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.

Microstructure and elasticity of dilute gels of colloidal discoids

The linear elasticity of dilute colloidal gels formed from discoidal latex particles is quantified as a function of aspect ratio and modeled by confocal microscopy characterization of their fractal cluster microstructure. Colloidal gels are of fundamental interest because of their widespread use to stabilize complex fluids in industry. Technological interest in producing gels of desired moduli using the least number of particles drives formulators to produce gels at dilute concentrations. However, dilute gels self-assembled from isotropic spheres offer limited scope for rheological tunability due to the universal characteristics of their fractal microstructure. Our results show that changing the building block shape from sphere to discoid yields very large shifts in gel elasticity relative to the universal behavior reported for spheres. This shift - tunable through aspect ratio - yields up to a 100-fold increase in elastic modulus at a fixed volume fraction. From modeling the results using the theory for fractal cluster gel rheology, which is applicable at the dilute conditions of this study, we reveal that the efficient generation of elasticity by the colloidal discoids is the consequence of the combined effects of shape anisotropy on the fractal microstructure of the gel network, the anisotropy of the attractive interparticle pair potentials, and the volumetric compactness of the fractal cluster. These results extend prior characterizations of the rheology of non-spherical particulate gels by providing quantitative estimates of how the specific mechanisms of fractality, pair potential, and clustering mediate the profound effects of particle shape anisotropy on the elastic rheology of colloidal gels.

DEM-Based Approach for the Modeling of Gelation and Its Application to Alginate

The gelation of biopolymers is of great interest in the material science community and has gained increasing relevance in the past few decades, especially in the context of aerogels─lightweight open nanoporous materials. Understanding the underlying gel structure and influence of process parameters is of great importance to predict material properties such as mechanical strength. In order to improve understanding of the gelation mechanism in aqueous solution, this work presents a novel approach based on the discrete element method for the mesoscale for modeling gelation of hydrogels, similarly to an extremely coarse-grained molecular dynamics (MD) approach. For this, polymer chains are abstracted as dimer units connected by flexible bonds and interactions between units and with the environment, that is, diffusion in implicit water, are described. The model is based on Langevin dynamics and includes an implicit probabilistic ion model to capture the effects of ion availability during ion-mediated gelation. The model components are fully derived and parameterized using literature data and theoretical considerations based on a simplified representation of atomistic processes. The presented model enables investigations of the higher-scale network formation during gelation on the micrometer and millisecond scale, which are beyond classical modeling approaches such as MD. As a model system, calcium-mediated alginate gelation is investigated including the influence of ion concentration, polymer composition, polymer concentration, and molecular weight. The model is verified against numerous literature data as well as own experimental results for the corresponding Ca-alginate hydrogels using nitrogen porosimetry, NMR cryoporometry, and small-angle neutron scattering. The model reproduces both bundle size and pore size distribution in a reasonable agreement with the experiments. Overall, the modeling approach paves the way to physically motivated design of alginate gels.

Microscopic interactions and emerging elasticity in model soft particulate gels

We discuss a class of models for particulate gels in which the particle contacts are described by an effective interaction combining a two-body attraction and a three-body angular repulsion. Using molecular dynamics, we show how varying the model parameters allows us to sample, for a given gelation protocol, a variety of gel morphologies. For a specific set of the model parameters, we identify the local elastic structures that get interlocked in the gel network. Using the analytical expression of their elastic energy from the microscopic interactions, we can estimate their contribution to the emergent elasticity of the gel and gain new insight into its origin.