Colloidal gel elasticity arises from the packing of locally glassy clusters

Competition between cross-linking and force-induced local conformational changes determines the structure and mechanics of labile protein networks

Folded protein hydrogels are emerging as promising new materials for medicine and healthcare applications. Folded globular proteins can be modelled as colloids which exhibit site specific cross-linking for controlled network formation. However, folded proteins have inherent mechanical stability and unfolded in response to an applied force. It is not yet understood how colloidal network theory maps onto folded protein hydrogels and whether it models the impact of protein unfolding on network properties. To address this, we study a hybrid system which contains folded proteins (patchy colloids) and unfolded proteins (biopolymers). We use a model protein, bovine serum albumin (BSA), to explore network architecture and mechanics in folded protein hydrogels. We alter both the photo-chemical cross-linking reaction rate and the mechanical properties of the protein building block, via illumination intensity and redox removal of robust intra-protein covalent bonds, respectively. This dual approach, in conjunction with rheological and structural techniques, allows us to show that while reaction rate can 'fine-tune' the mechanical and structural properties of protein hydrogels, it is the force-lability of the protein which has the greatest impact on network architecture and rigidity. To understand these results, we consider a colloidal model which successfully describes the behaviour of the folded protein hydrogels but cannot account for the behaviour observed in force-labile hydrogels containing unfolded protein. Alternative models are needed which combine the properties of colloids (folded proteins) and biopolymers (unfolded proteins) in cross-linked networks. This work provides important insights into the accessible design space of folded protein hydrogels without the need for complex and costly protein engineering, aiding the development of protein-based biomaterials.

Yielding behaviour of chemically treated Pseudomonas fluorescens biofilms

The mechanics of biofilms are intrinsically shaped by their physicochemical environment. By understanding the influence of the extracellular matrix composition, pH and elevated levels of cationic species on the biofilm rheology, novel living materials with tuned properties can be formulated. In this study, we examine the role of a chaotropic agent (urea), two divalent cations and distilled deionized water on the nonlinear viscoelasticity of a model biofilm Pseudomonas fluorescens. The structural breakdown of each biofilm is quantified using tools of non-linear rheology. Our findings reveal that urea induced a softening response, and displayed strain overshoots comparable to distilled deionized water, without altering the microstructural packing fraction and macroscale morphology. The absorption of divalent ferrous and calcium cations into the biofilm matrix resulted in stiffening and a reduction in normalized elastic energy dissipation, accompanied by macroscale morphological wrinkling and moderate increases in the packing fraction. Notably, ferrous ions induced a predominance of rate dependent yielding, whereas the calcium ions resulted in equal contribution from both rate and strain dependent yielding and structural breakdown of the biofilms. Together, these results indicate that strain rate increasingly becomes an important factor controlling biofilm fluidity with cation-induced biofilm stiffening. The finding can help inform effective biofilm removal protocols and in development of bio-inks for additive manufacturing of biofilm derived materials.

Topological Data Analysis for Particulate Gels

Soft gels, formed via the self-assembly of particulate materials, exhibit intricate multiscale structures that provide them with flexibility and resilience when subjected to external stresses. This work combines particle simulations and topological data analysis (TDA) to characterize the complex multiscale structure of soft gels. Our TDA analysis focuses on the use of the Euler characteristic, which is an interpretable and computationally scalable topological descriptor that is combined with filtration operations to obtain information on the geometric (local) and topological (global) structure of soft gels. We reduce the topological information obtained with TDA using principal component analysis (PCA) and show that this provides an informative low-dimensional representation of the gel structure. We use the proposed computational framework to investigate the influence of gel preparation (e.g., quench rate, volume fraction) on soft gel structure and to explore dynamic deformations that emerge under oscillatory shear in various response regimes (linear, nonlinear, and flow). Our analysis provides evidence of the existence of hierarchical structures in soft gels, which are not easily identifiable otherwise. Moreover, our analysis reveals direct correlations between topological changes of the gel structure under deformation and mechanical phenomena distinctive of gel materials, such as stiffening and yielding. In summary, we show that TDA facilitates the mathematical representation, quantification, and analysis of soft gel structures, extending traditional network analysis methods to capture both local and global organization.

Small variations in particle-level interactions lead to large structural heterogeneities in colloidal gels

Colloidal gels typically exhibit mechanical properties akin to a viscoelastic solid, influenced by their underlying particulate network. Hence, the structural and morphological characteristics of the colloidal network have a significant effect on the rigidity of the gel. In this study, we show how seemingly small variations in the particle-level interactions throughout the system result in larger scale structural heterogeneities. While the microscale particle level descriptors of the colloidal network remain largely unaffected by heterogeneous interactions, larger scale properties of a colloidal gel change appreciably. The overall cluster-level mesostructure of a colloidal gel is found to be sensitive to the small variations in the interaction potential at the particle level.

Rheological behavior of Pluronic/Pluronic diacrylate hydrogels used for bacteria encapsulation in engineered living materials

Pluronic (Plu) hydrogels mixed with variable fractions of Pluronic diacrylate (PluDA) have become popular matrices to encapsulate bacteria and control their growth in engineered living materials. Here we study the rheological response of 30 wt% Plu/PluDA hydrogels with PluDA fraction between 0 and 1. We quantify the range of viscoelastic properties that can be covered in this system by varying in the PluDA fraction. We present stress relaxation and creep-recovery experiments and describe the variation of the critical yield strain/stress, relaxation and recovery parameters of Plu/PluDA hydrogels as function of the covalent crosslinking degree using the Burgers and Weilbull models. The analyzed hydrogels present two stress relaxations with different timescales which can be tuned with the covalent crosslinking degree. We expect this study to help users of Plu/PluDA hydrogels to estimate the mechanical properties of their systems, and to correlate them with the behaviour of bacteria in future Plu/PluDA devices of similar composition.

Network physics of attractive colloidal gels: Resilience, rigidity, and phase diagram

Colloidal gels exhibit solid-like behavior at vanishingly small fractions of solids, owing to ramified space-spanning networks that form due to particle-particle interactions. These networks give the gel its rigidity, and with stronger attractions the elasticity grows as well. The emergence of rigidity can be described through a mean field approach; nonetheless, fundamental understanding of how rigidity varies in gels of different attractions is lacking. Moreover, recovering an accurate gelation phase diagram based on the system's variables has been an extremely challenging task. Understanding the nature of colloidal clusters, and how rigidity emerges from their connections is key to controlling and designing gels with desirable properties. Here, we employ network analysis tools to interrogate and characterize the colloidal structures. We construct a particle-level network, having all the spatial coordinates of colloids with different attraction levels, and also identify polydisperse rigid fractal clusters using a Gaussian mixture model, to form a coarse-grained cluster network that distinctly shows main physical features of the colloidal gels. A simple mass-spring model then is used to recover quantitatively the elasticity of colloidal gels from these cluster networks. Interrogating the resilience of these gel networks shows that the elasticity of a gel (a dynamic property) is directly correlated to its cluster network's resilience (a static measure). Finally, we use the resilience investigations to devise [and experimentally validate] a fully resolved phase diagram for colloidal gelation, with a clear solid-liquid phase boundary using a single volume fraction of particles well beyond this phase boundary.

Interfacial Fluid Rheology of Soft Particles

In situ interfacial rheology and numerical simulations are used to investigate microgel monolayers in a wide range of packing fractions, ζ_{2D}. The heterogeneous particle compressibility determines two flow regimes characterized by distinct master curves. To mimic the microgel architecture and reproduce experiments, an interaction potential combining a soft shoulder with the Hertzian model is introduced. In contrast to bulk conditions, the elastic moduli vary nonmonotonically with ζ_{2D} at the interface, confirming long-sought predictions of reentrant behavior for Hertzian-like systems.

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.

Microstructural and Rheological Transitions in Bacterial Biofilms

Biofilms are aggregated bacterial communities structured within an extracellular matrix (ECM). ECM controls biofilm architecture and confers mechanical resistance against shear forces. From a physical perspective, biofilms can be described as colloidal gels, where bacterial cells are analogous to colloidal particles distributed in the polymeric ECM. However, the influence of the ECM in altering the cellular packing fraction (ϕ) and the resulting viscoelastic behavior of biofilm remains unexplored. Using biofilms of Pantoea sp. (WT) and its mutant (ΔUDP), the correlation between biofilm structure and its viscoelastic response is investigated. Experiments show that the reduction of exopolysaccharide production in ΔUDP biofilms corresponds with a seven-fold increase in ϕ, resulting in a colloidal glass-like structure. Consequently, the rheological signatures become altered, with the WT behaving like a weak gel, whilst the ΔUDP displayed a glass-like rheological signature. By co-culturing the two strains, biofilm ϕ is modulated which allows us to explore the structural changes and capture a change in viscoelastic response from a weak to a strong gel, and to a colloidal glass-like state. The results reveal the role of exopolysaccharide in mediating a structural transition in biofilms and demonstrate a correlation between biofilm structure and viscoelastic response.

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.

Electrosteric Control of the Aggregation and Yielding Behavior of Concentrated Portlandite Suspensions

Portlandite (calcium hydroxide: CH: Ca(OH)2) suspensions aggregate spontaneously and form percolated fractal aggregate networks when dispersed in water. Consequently, the viscosity and yield stress of portlandite suspensions diverge at low particle loadings, adversely affecting their processability. Even though polycarboxylate ether (PCE)-based comb polyelectrolytes are routinely used to alter the particle dispersion state, water demand, and rheology of similar suspensions (e.g., ordinary portland cement suspensions) that feature a high pH and high ionic strength, their use to control portlandite suspension rheology has not been elucidated. This study combines adsorption isotherms and rheological measurements to elucidate the role of PCE composition (i.e., charge density, side chain length, and grafting density) in controlling the extent of PCE adsorption, particle flocculation, suspension yield stress, and thermal response of portlandite suspensions. We show that longer side-chain PCEs are more effective in affecting suspension viscosity and yield stress, in spite of their lower adsorption saturation limit and fractional adsorption. The superior steric hindrance induced by the longer side chain PCEs results in better efficacy in mitigating particle aggregation even at low dosages. However, when dosed at optimal dosages (i.e., a dosage that induces a dynamically equilibrated dispersion state of particle aggregates), different PCE-dosed portlandite suspensions exhibit identical fractal structuring and rheological behavior regardless of the side chain length. Furthermore, it is shown that the unusual evolution of the rheological response of portlandite suspensions with temperature can be tailored by adjusting the PCE dosage. The ability of PCEs to modulate the rheology of aggregating charged particle suspensions can be generally extended to any colloidal suspension with a strong screening of repulsive electrostatic interactions.

Design, characterization and applications of nanocolloidal hydrogels

Nanocolloidal gels (NCGs) are an emerging class of soft matter, in which nanoparticles act as building blocks of the colloidal network. Chemical or physical crosslinking enables NCG synthesis and assembly from a broad range of nanoparticles, polymers, and low-molecular weight molecules. The synergistic properties of NCGs are governed by nanoparticle composition, dimensions and shape, the mechanism of nanoparticle bonding, and the NCG architecture, as well as the nature of molecular crosslinkers. Nanocolloidal gels find applications in soft robotics, bioengineering, optically active coatings and sensors, optoelectronic devices, and absorbents. This review summarizes currently scattered aspects of NCG formation, properties, characterization, and applications. We describe the diversity of NCG building blocks, discuss the mechanisms of NCG formation, review characterization techniques, outline NCG fabrication and processing methods, and highlight most common NCG applications. The review is concluded with the discussion of perspectives in the design and development of NCGs.

Forecasting landslides using community detection on geophysical satellite data

As a result of extreme weather conditions, such as heavy precipitation, natural hillslopes can fail dramatically; these slope failures can occur on a dry day, due to time lags between rainfall and pore-water pressure change at depth, or even after days to years of slow motion. While the prefailure deformation is sometimes apparent in retrospect, it remains challenging to predict the sudden transition from gradual deformation (creep) to runaway failure. We use a network science method-multilayer modularity optimization-to investigate the spatiotemporal patterns of deformation in a region near the 2017 Mud Creek, California landslide. We transform satellite radar data from the study site into a spatially embedded network in which the nodes are patches of ground and the edges connect the nearest neighbors, with a series of layers representing consecutive transits of the satellite. Each edge is weighted by the product of the local slope (susceptibility to failure) measured from a digital elevation model and ground surface deformation (current rheological state) from interferometric synthetic aperture radar (InSAR). We use multilayer modularity optimization to identify strongly connected clusters of nodes (communities) and are able to identify both the location of Mud Creek and nearby creeping landslides which have not yet failed. We develop a metric, i.e., community persistence, to quantify patterns of ground deformation leading up to failure, and find that this metric increased from a baseline value in the weeks leading up to Mud Creek's failure. These methods hold promise as a technique for highlighting regions at risk of catastrophic failure.

Active Colloids as Models, Materials, and Machines

Active colloids use energy input at the particle level to propel persistent motion and direct dynamic assemblies. We consider three types of colloids animated by chemical reactions, time-varying magnetic fields, and electric currents. For each type, we review the basic propulsion mechanisms at the particle level and discuss their consequences for collective behaviors in particle ensembles. These microscopic systems provide useful experimental models of nonequilibrium many-body physics in which dissipative currents break time-reversal symmetry. Freed from the constraints of thermodynamic equilibrium, active colloids assemble to form materials that move, reconfigure, heal, and adapt. Colloidal machines based on engineered particles and their assemblies provide a basis for mobile robots with increasing levels of autonomy. This review provides a conceptual framework for understanding and applying active colloids to create material systems that mimic the functions of living matter. We highlight opportunities for chemical engineers to contribute to this growing field.

Diversity of viscoelastic properties of an engineered muscle-inspired protein hydrogel

Folded protein hydrogels are prime candidates as tuneable biomaterials but it is unclear to what extent their mechanical properties have mesoscopic, as opposed to molecular origins. To address this, we probe hydrogels inspired by the muscle protein titin and engineered to the polyprotein I27₅, using a multimodal rheology approach. Across multiple protocols, the hydrogels consistently exhibit power-law viscoelasticity in the linear viscoelastic regime with an exponent β = 0.03, suggesting a dense fractal meso-structure, with predicted fractal dimension d_f = 2.48. In the nonlinear viscoelastic regime, the hydrogel undergoes stiffening and energy dissipation, indicating simultaneous alignment and unfolding of the folded proteins on the nanoscale. Remarkably, this behaviour is highly reversible, as the value of β, d_f and the viscoelastic moduli return to their equilibrium value, even after multiple cycles of deformation. This highlights a previously unrevealed diversity of viscoelastic properties that originate on both at the nanoscale and the mesoscopic scale, providing powerful opportunities for engineering novel biomaterials.

Structuring colloidal gels via micro-bubble oscillations

Locally (re)structuring colloidal gels - micron-sized particles forming a connected network with arrested dynamics - can enable precise tuning of the micromechanical and -rheological properties of the system. A recent experimental study [B. Saint-Michel, G. Petekidis, and V. Garbin, Soft Matter, 2022, 18, 2092] showed that local ordering can be rapidly induced by acoustically modulating an embedded microbubble. Here, we perform Brownian dynamics simulations to understand the mechanical effect of an oscillating microbubble on the next-to-bubble structure of the embedding colloidal gel. Our simulations reveal hexagonal-close-packed structures over a range that is comparable to the amplitude of the oscillations. However, we were unable to reproduce the unexpectedly long-ranged modification of the gel structure - dozens of amplitudes - observed in experiment. This suggests including long-ranged effects, such as fluid flow, should be considered in future computational work.

Structural and mechanical properties of folded protein hydrogels with embedded microbubbles

Globular folded proteins are powerful building blocks to create biomaterials with mechanical robustness and inherent biological functionality. Here we explore their potential as advanced drug delivery scaffolds, by embedding microbubbles (MBs) within a photo-activated, chemically cross-linked bovine serum albumin (BSA) protein network. Using a combination of circular dichroism (CD), rheology, small angle neutron scattering (SANS) and microscopy we determine the nanoscale and mesoscale structure and mechanics of this novel multi-composite system. Optical and confocal microscopy confirms the presence of MBs within the protein hydrogel, their reduced diffusion and their effective rupture using ultrasound, a requirement for burst drug release. CD confirms that the inclusion of MBs does not impact the proportion of folded proteins within the cross-linked protein network. Rheological characterisation demonstrates that the mechanics of the BSA hydrogels is reduced in the presence of MBs. Furthermore, SANS reveals that embedding MBs in the protein hydrogel network results in a smaller number of clusters that are larger in size (∼16.6% reduction in number of clusters, 17.4% increase in cluster size). Taken together, we show that MBs can be successfully embedded within a folded protein network and ruptured upon application of ultrasound. The fundamental insight into the impact of embedded MBs in protein scaffolds at the nanoscale and mesoscale is important in the development of future platforms for targeted and controlled drug delivery applications.

Impact of granular inclusions on the phase behavior of colloidal gels

Colloidal gels formed from small attractive particles are commonly used in formulations to keep larger components in suspension. Despite extensive work characterising unfilled gels, little is known about how the larger inclusions alter the phase behavior and microstructure of the colloidal system. Here we use numerical simulations to examine how larger 'granular' particles can alter the gel transition phase boundaries. We find two distinct regimes depending on both the filler size and native gel structure: a 'passive' regime where the filler fits into already-present voids, giving little change in the transition, and an 'active' regime where the filler no longer fits in these voids and instead perturbs the native structure. In this second regime the phase boundary is controlled by an effective colloidal volume fraction given by the available free volume.

Topological origins of yielding in short-ranged weakly attractive colloidal gels

Yielding of the particulate network in colloidal gels under applied deformation is accompanied by various microstructural changes, including rearrangement, bond rupture, anisotropy, and reformation of secondary structures. While much work has been done to understand the physical underpinnings of yielding in colloidal gels, its topological origins remain poorly understood. Here, employing a series of tools from network science, we characterize the bonds using their orientation and network centrality. We find that bonds with higher centralities in the network are ruptured the most at all applied deformation rates. This suggests that a network analysis of the particulate structure can be used to predict the failure points in colloidal gels a priori.

Effect of scatterer interactions on photon transport in diffusing wave spectroscopy

We calculate the effect of particle size, concentration, and interactions on the photon transport mean-free path l^{*} that characterizes the multiple light scattering in diffusing wave spectroscopy (DWS). For scatterers of sufficient size, such that the first peak of the suspension structure factor S(q_{max}) remains in the range of accessible scattering vectors, neither repulsive nor attractive interactions between scatterers contribute strongly to l^{*}; its values are bounded by those for hard spheres and scatterers without interactions. However, for scatterers smaller than the wavelength of light, crowding induced by attraction or repulsion can lead to nonmonotonic behavior in l^{*} with increasing scatterer concentration. The effect is strongest for repulsive particles.

The elastic response of graphene oxide gels as a crumpling phenomenon

The broad spectrum of chemical and electronic properties of 2D nanomaterials makes them attractive in a wide range of applications, especially in the context of printed electronics. Therefore, understanding the rheological properties of nanosheet suspensions is crucial for many additive manufacturing techniques. Here, we study the viscoelastic properties of aqueous suspensions of graphene oxide nanosheets. We show that in the gel phase, the magnitude of the elastic response and its scaling with volume fraction is independent of the lateral size of the particles and the interaction strength between them. We explain this behavior by modelling the elasticity of these gels as a crumpling phenomenon where the magnitude of the response is determined by the bending stiffness and thickness of the sheets. Due to their low bending stiffness these nanosheets crumple upon deformation and may therefore be considered soft colloids. Furthermore, we provide an explanation why the yield strain decreases with packing fraction for these gels.

Brownian dynamics simulations of hard rods in external fields and with contact interactions

We propose a simulation method for Brownian dynamics of hard rods in one dimension for arbitrary continuous external force fields. It is an event-driven procedure based on the fragmentation and mergers of clusters formed by particles in contact. It allows one to treat particle interactions in addition to the hard-sphere exclusion as long as the corresponding interaction forces are continuous functions of the particle coordinates. We furthermore develop a treatment of sticky hard spheres as described by Baxter's contact interaction potential.

Interpenetration of fractal clusters drives elasticity in colloidal gels formed upon flow cessation

Colloidal gels are out-of-equilibrium soft solids composed of attractive Brownian particles that form a space-spanning network at low volume fractions. The elastic properties of these systems result from the network microstructure, which is very sensitive to shear history. Here, we take advantage of such sensitivity to tune the viscoelastic properties of a colloidal gel made of carbon black nanoparticles. Starting from a fluidized state at an applied shear rate ₀, we use an abrupt flow cessation to trigger a liquid-to-solid transition. We observe that the resulting gel is all the more elastic when the shear rate ₀ is low and that the viscoelastic spectra can be mapped on a master curve. Moreover, coupling rheometry to small angle X-ray scattering allows us to show that the gel microstructure is different from gels solely formed by thermal agitation where only two length scales are observed: the dimension of the colloidal and the dimension of the fractal aggregates. Competition between shear and thermal energy leads to gels with three characteristic length scales. Such gels structure in a percolated network of fractal clusters that interpenetrate each other. Experiments on gels prepared with various shear histories reveal that cluster interpenetration increases with decreasing values of the shear rate ₀ applied before flow cessation. These observations strongly suggest that cluster interpenetration drives the gel elasticity, which we confirm using a structural model. Our results, which are in stark contrast to previous literature, where gel elasticity was either linked to cluster connectivity or to bending modes, highlight a novel local parameter controlling the macroscopic viscoelastic properties of colloidal gels.

Structure and Dynamics of Force Clusters and Networks in Shear Thickening Suspensions

Dense suspensions can exhibit shear thickening in response to large deformation. A consensus has emerged over the past few years on the formation of force networks, that span the entire system size, that lead to increased resistance to motion. Nonetheless, the characteristics of these networks are to a large extent poorly understood. Here, force networks formed in continuous and discontinuous shear thickening dense suspensions (CST and DST, respectively) are studied. We first show the evolution of the network formation and its topological heterogeneities as the applied stress increases. Subsequently, we identify force communities and coarse grain the suspension into a cluster network, and show that cluster-level dynamics are responsible for stark differences between the CST and DST behavior. Our results suggest that the force clusters formed in the DST regime are considerably more constrained in their motion, while CST clusters are loosely connected to their surrounding clusters.

Tuning Protein Hydrogel Mechanics through Modulation of Nanoscale Unfolding and Entanglement in Postgelation Relaxation

Globular folded proteins are versatile nanoscale building blocks to create biomaterials with mechanical robustness and inherent biological functionality due to their specific and well-defined folded structures. Modulating the nanoscale unfolding of protein building blocks during network formation (in situ protein unfolding) provides potent opportunities to control the protein network structure and mechanics. Here, we control protein unfolding during the formation of hydrogels constructed from chemically cross-linked maltose binding protein using ligand binding and the addition of cosolutes to modulate protein kinetic and thermodynamic stability. Bulk shear rheology characterizes the storage moduli of the bound and unbound protein hydrogels and reveals a correlation between network rigidity, characterized as an increase in the storage modulus, and protein thermodynamic stability. Furthermore, analysis of the network relaxation behavior identifies a crossover from an unfolding dominated regime to an entanglement dominated regime. Control of in situ protein unfolding and entanglement provides an important route to finely tune the architecture, mechanics, and dynamic relaxation of protein hydrogels. Such predictive control will be advantageous for future smart biomaterials for applications which require responsive and dynamic modulation of mechanical properties and biological function.

Microscopic dynamics underlying the stress relaxation of arrested soft materials

Arrested soft materials such as gels and glasses exhibit a slow stress relaxation with a broad distribution of relaxation times in response to linear mechanical perturbations. Although this macroscopic stress relaxation is an essential feature in the application of arrested systems as structural materials, consumer products, foods, and biological materials, the microscopic origins of this relaxation remain poorly understood. Here, we elucidate the microscopic dynamics underlying the stress relaxation of such arrested soft materials under both quiescent and mechanically perturbed conditions through X-ray photon correlation spectroscopy. By studying the dynamics of a model associative gel system that undergoes dynamical arrest in the absence of aging effects, we show that the mean stress relaxation time measured from linear rheometry is directly correlated to the quiescent superdiffusive dynamics of the microscopic clusters, which are governed by a buildup of internal stresses during arrest. We also show that perturbing the system via small mechanical deformations can result in large intermittent fluctuations in the form of avalanches, which give rise to a broad non-Gaussian spectrum of relaxation modes at short times that is observed in stress relaxation measurements. These findings suggest that the linear viscoelastic stress relaxation in arrested soft materials may be governed by nonlinear phenomena involving an interplay of internal stress relaxations and perturbation-induced intermittent avalanches.

Flow-Switched Bistability in a Colloidal Gel with Non-Brownian Grains

We show that mixing a colloidal gel with larger, non-Brownian grains generates novel flow-switched bistability. Using a combination of confocal microscopy and rheology, we find that prolonged moderate shear results in liquefaction by collapsing the gel into disjoint globules, whereas fast shear gives rise to a yield-stress gel with granular inclusions upon flow cessation. We map out the state diagram of this new "mechanorheological material" with varying granular content and demonstrate that its behavior is also found in separate mixture using different particles and solvents.

Experimental characterization of colloidal silica gel for water conformance control in oil reservoirs

High water production in oil fields is an area of concern due to economic issues and borehole/wellhead damages. Colloidal gels can be a good alternative to polymers to address this as they can tolerate harsh oil reservoir conditions. A series of bottle tests with different silica and NaCl concentrations were first conducted. The gelation time, cation valence, rheology, and viscosity were investigated to characterize the gels. The applicability of solid gels in porous media was finally inspected in a dual-patterned glass micromodel. Bottle test results showed that increasing NaCl concentration at a constant silica concentration can convert solid gels into two-phase gels and then viscous suspensions. Na⁺ replacement with Mg²⁺ resulted a distinctive behaviour probably due to higher coagulating ability of Mg²⁺. Rheology and viscosity results agreed with gelation times: gel with shortest gelation time had the highest viscosity and storage/loss modulus but was not the most elastic one. Water injection into glass micromodel half-saturated with crude oil and solid gel proved that the gel is strong against pressure gradients applied by injected phase which is promising for water conformance controls. The diverted injected phase recorded an oil recovery of 53% which was not feasible without blocking the water zone.

A Thermodynamically Consistent, Microscopically-Based, Model of the Rheology of Aggregating Particles Suspensions

In this work, we outline the development of a thermodynamically consistent microscopic model for a suspension of aggregating particles under arbitrary, inertia-less deformation. As a proof-of-concept, we show how the combination of a simplified population-balance-based description of the aggregating particle microstructure along with the use of the single-generator bracket description of nonequilibrium thermodynamics, which leads naturally to the formulation of the model equations. Notable elements of the model are a lognormal distribution for the aggregate size population, a population balance-based model of the aggregation and breakup processes and a conformation tensor-based viscoelastic description of the elastic network of the particle aggregates. The resulting example model is evaluated in steady and transient shear forces and elongational flows and shown to offer predictions that are consistent with observed rheological behavior of typical systems of aggregating particles. Additionally, an expression for the total entropy production is also provided that allows one to judge the thermodynamic consistency and to evaluate the importance of the various dissipative phenomena involved in given flow processes.

Direct Imaging of Contacts and Forces in Colloidal Gels

Colloidal dispersions are prized as model systems to understand basic properties of materials, and are central to a wide range of industries from cosmetics to foods to agrichemicals. Among the key developments in using colloids to address challenges in condensed matter is to resolve the particle coordinates in 3D, allowing a level of analysis usually only possible in computer simulation. However in amorphous materials, relating mechanical properties, and failure in particular to microscopic structure remains problematic. Here we address this challenge by studying the contacts and the forces between particles, as well as their positions. To do so, we use a colloidal model system (an emulsion) in which the interparticle forces and local stress can be linked to the microscopic structure. We demonstrate the potential of our method to reveal insights into the failure mechanisms of soft amorphous solids by determining local stress in a colloidal gel. In particular, we identify "force chains" of load--bearing droplets, and local stress anisotropy, and investigate their connection with locally rigid packings of the droplets.

Stiffening colloidal gels by solid inclusions

The elastic properties of a soft matter material can be greatly altered by the presence of solid inclusions whose microscopic properties, such as their size and interactions, can have a dramatic effect. In order to shed light on these effects we use extensive rheology computer simulations to investigate colloidal gels with solid inclusions of different sizes. We show that the elastic properties vary in a highly non-trivial way as a consequence of the interactions between the gel backbone and the inclusions. In particular, we show that the key aspects are the presence of the gel backbone and its mechanical alteration originating from the inclusions. To confirm our observations and their generality, we performed experiments on an emulsion that presents strong analogies with colloidal gels and confirms the trends observed in the simulations.

Tuning local microstructure of colloidal gels by ultrasound-activated deformable inclusions

Colloidal gels possess a memory of previous shear events, both steady and oscillatory. This memory, embedded in the microstructure, affects the mechanical response of the gel, and therefore enables precise tuning of the material properties under careful preparation. Here we demonstrate how the dynamics of a deformable inclusion, namely a bubble, can be used to locally tune the microstructure of a colloidal gel. We examine two different phenomena of bubble dynamics that apply a local strain to the surrounding material: dissolution due to gas diffusion, with a characteristic strain rate of ∼10^-3 s^-1; and volumetric oscillations driven by ultrasound, with a characteristic frequency of ∼10⁴ s^-1. We characterise experimentally the microstructure of a model colloidal gel around bubbles in a Hele-Shaw geometry using confocal microscopy and particle tracking. In bubble dissolution experiments, we observe the formation of a pocket of solvent next to the bubble surface, but marginal changes to the microstructure. In experiments with ultrasound-induced bubble oscillations, we observe a striking rearrangement of the gel particles into a microstructure with increased local ordering. High-speed bright-field microscopy reveals the occurrence of both high-frequency bubble oscillations and steady microstreaming flow; both are expected to contribute to the emergence of the local order in the microstructure. These observations open the way to local tuning of colloidal gels based on deformable inclusions controlled by external pressure fields.

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.

Effects of the blade shape on the slicing of soft gels

Slicing soft gels with a knife is eased by rapidly sliding the blade along its edge. This common observation has been recently explained thanks to a model in which the split of the gel results from a failure occurring at a critical stress and consisting of the transformation of the solid gel into a liquid phase (Phys Rev Lett 125:038002, 2020). Here, the cutting process is shown to be independent of the yield criterion of the gel, and the model investigated further by considering the thickness and the shape of the blade. Features of the slicing process converge toward the zero-thickness limit as the sharpness of the blade increases. The model does predict that a thinner edge facilitates the cleavage. In addition, a symmetric cross section of the blade is found to be more efficient than a bevel.

ArGSLab: a tool for analyzing experimental or simulated particle networks

Microscopy and particle-based simulations are both powerful techniques to study aggregated particulate matter such as colloidal gels. The data provided by these techniques often contains information on a wide array of length scales, but structural analysis methods typically focus on the local particle arrangement, even though the data also contains information about the particle network on the mesoscopic length scale. In this paper, we present a MATLAB software package for quantifying mesoscopic network structures in colloidal samples. ArGSLab (Arrested and Gelated Structures Laboratory) extracts a network backbone from the input data, which is in turn transformed into a set of nodes and links for graph theory-based analysis. The routines can process both image stacks from microscopy as well as explicit coordinate data, and thus allows quantitative comparison between simulations and experiments. ArGSLab furthermore enables the accurate analysis of microscopy data where, e.g., an extended point spread function prohibits the resolution of individual particles. We demonstrate the resulting output for example datasets from both microscopy and simulation of colloidal gels, in order to showcase the capability of ArGSLab to quantitatively analyze data from various sources. The freely available software package can be used either with a provided graphical user interface or directly as a MATLAB script.

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.

Migration and Morphology of Colloidal Gel Clusters in Cylindrical Channel Flow

We report the cluster-level structural parameters of colloidal thermogelling nanoemulsions in channel flow as a function of attractive interactions and local shear stress. The spatiotemporal evolution of the gel microstructure is obtained by directly visualizing the dispersed phase near the edge of a cylindrical channel. We observe the flow of the nanoemulsion gels in a range of radial positions (r) and shear stresses between 70 and 220 Pa, finding that the r-dependent cluster sizes are due to a balance between shear forces that yield bonds and attractive interactions that rebuild the inter-colloid bonds. In addition, the largest clusters appear to be affected by confinement and accumulate toward the central axis of the channel, resulting in a volume fraction gradient. Cluster size and volume fraction variabilities are most prominent when the attractive interactions are the strongest. Specifically, a distinct transition from sparse, fluidized clusters near the walls to concentrated, large clusters toward the center is observed. These two structural states coincide with a velocity-based transition from higher shear rates near the walls to lower shear rates toward the center of the channel. We find a compounding effect where larger gel clusters, formed under strong attractions and low shear stresses, are susceptible to shear-induced migration that intensifies r-dependent heterogeneity and deviations in the flow behavior from predictive models.

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.

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.

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.

Control of Nanoscale In Situ Protein Unfolding Defines Network Architecture and Mechanics of Protein Hydrogels

Hierarchical assemblies of proteins exhibit a wide-range of material properties that are exploited both in nature and by artificially by humankind. However, little is understood about the importance of protein unfolding on the network assembly, severely limiting opportunities to utilize this nanoscale transition in the development of biomimetic and bioinspired materials. Here we control the force lability of a single protein building block, bovine serum albumin (BSA), and demonstrate that protein unfolding plays a critical role in defining the architecture and mechanics of a photochemically cross-linked native protein network. The internal nanoscale structure of BSA contains "molecular reinforcement" in the form of 17 covalent disulphide "nanostaples", preventing force-induced unfolding. Upon addition of reducing agents, these nanostaples are broken rendering the protein force labile. Employing a combination of circular dichroism (CD) spectroscopy, small-angle scattering (SAS), rheology, and modeling, we show that stapled protein forms reasonably homogeneous networks of cross-linked fractal-like clusters connected by an intercluster region of folded protein. Conversely, in situ protein unfolding results in more heterogeneous networks of denser fractal-like clusters connected by an intercluster region populated by unfolded protein. In addition, gelation-induced protein unfolding and cross-linking in the intercluster region changes the hydrogel mechanics, as measured by a 3-fold enhancement of the storage modulus, an increase in both the loss ratio and energy dissipation, and markedly different relaxation behavior. By controlling the protein's ability to unfold through nanoscale (un)stapling, we demonstrate the importance of in situ unfolding in defining both network architecture and mechanics, providing insight into fundamental hierarchical mechanics and a route to tune biomaterials for future applications.

Life and death of colloidal bonds control the rate-dependent rheology of gels

Colloidal gels exhibit rich rheological responses under flowing conditions. A clear understanding of the coupling between the kinetics of the formation/rupture of colloidal bonds and the rheological response of attractive gels is lacking. In particular, for gels under different flow regimes, the correlation between the complex rheological response, the bond kinetics, microscopic forces, and an overall micromechanistic view is missing in previous works. Here, we report the bond dynamics in short-range attractive particles, microscopically measured stresses on individual particles and the spatiotemporal evolution of the colloidal structures in different flow regimes. The interplay between interparticle attraction and hydrodynamic stresses is found to be the key to unraveling the physical underpinnings of colloidal gel rheology. Attractive stresses, mostly originating from older bonds dominate the response at low Mason number (the ratio of shearing to attractive forces) while hydrodynamic stresses tend to control the rheology at higher Mason numbers, mostly arising from short-lived bonds. Finally, we present visual mapping of particle bond numbers, their life times and their borne stresses under different flow regimes.

A facile evanescent-field imaging approach for monitoring colloidal gel evolution near a surface

A facile evanescent-field imaging approach is developed to probe the aggregation behavior of near-wall colloids/clusters during colloidal gel evolution. Total internal reflection microscope (TIRM) images are directly utilized to access the structural relaxation time via density-fluctuation theory. The behaviors of cluster-cluster aggregation and physical aging of the colloidal gel networks are resolved in both time and space under fractal scaling criteria.

Microrheology of thermoresponsive poly(N-isopropylacrylamide) microgel dispersions near a substrate surface

HYPOTHESIS

Relative to the bulk systems, the near-wall (<500 nm) rheological responses of soft poly(N-isopropylacrylamide) (PNIPAM) microgel dispersions may exhibit distinct dependence on the frequency (ω), temperature (T), and effective volume fraction (ϕ_eff) during the volume phase transitions. The microrheological behaviors are expected to be governed by the near-wall microstructure and its spatial heterogeneity.

EXPERIMENTS

The combination of active microrheometry (multipole magnetic tweezers) and total internal reflection microscopy (TIRM) was employed to probe the structure-rheology relationships of microgel dispersions near a substrate surface. The ω, T, and ϕ_eff-dependences of the storage modulus (G'), loss modulus (G"), and softness (J) were analyzed by power-law and Arrhenius-like scaling theories. The fluctuation of J was further analyzed to give a quantitative description of the inhomogeneity in the near-wall regions.

FINDINGS

(1) Remarkable differences in the rheological behaviors between the bulk and near-wall cases are revealed, where the latter shows a segmented overlap behavior in ϕ_eff; (2) Five regimes of ϕ_eff that correspond to distinct physical states of the microgel dispersions are determined; (3) The near-wall local structures exhibit more heterogeneity in the glass and colloidal gel regimes as compared to the liquid regime.

Glassy Behavior of Sticky Spheres: What Lies beyond Experimental Timescales?

We use the swap Monte Carlo algorithm to analyze the glassy behavior of sticky spheres in equilibrium conditions at densities where conventional simulations and experiments fail to reach equilibrium, beyond predicted phase transitions and dynamic singularities. We demonstrate the existence of a unique ergodic region comprising all the distinct phases previously reported, except for a phase-separated region at strong adhesion. All structural and dynamic observables evolve gradually within this ergodic region, the physics evolving smoothly from well-known hard sphere glassy behavior at small adhesions and large densities, to a more complex glassy regime characterized by unusually broad distributions of relaxation timescales and length scales at large adhesions.