Colloidal Gels Research Articles

Parallel accelerated Stokesian dynamics with Brownian motion

We present scalable algorithms to simulate large-scale stochastic particle systems amenable for modeling dense colloidal suspensions, glasses and gels. To handle the large number of particles and consequent many-body interactions present in such systems, we leverage an Accelerated Stokesian Dynamics (ASD) approach, for which we developed parallel algorithms in a distributed memory architecture. We present parallelization of the sparse near-field (including singular lubrication) interactions, and of the matrix-free many-body far-field interactions, along with a strategy for communicating and mapping the distributed data structures between the near- and far field. Scaling to up to tens of thousands of processors for a million particles is demonstrated. In addition, we propose a novel algorithm to efficiently simulate correlated Brownian motion with hydrodynamic interactions. The original Accelerated Stokesian Dynamics approach requires the separate computation of far-field and near-field Brownian forces. Recent advancements propose computation of a far-field velocity using positive spectral Ewald decomposition. We present an alternative approach for calculating the far-field Brownian velocity by implementing the fluctuating force coupling method and embedding it using a nested scheme into ASD. This straightforward and flexible approach reduces the computational time of the Brownian far-field force construction from O(NlogN)1+|α| to O(NlogN).

3D printed colloidal biomaterials based on photo-reactive gelatin nanoparticles

Biomaterials-based strategies have shown great promise for tissue regeneration. 3D printing technologies can deliver unprecedented control over architecture and properties of biomaterial constructs when combined with innovative material design strategies. Colloidal gels made of polymeric nanoparticles are attractive injectable and self-healing systems, but their use as bio-inks for extrusion-based printing is largely unexplored. Here, we report 3D printing of novel biomaterial constructs with shape memory behavior using photo-reactive gelatin nanoparticles as colloidal building blocks. These nanoparticles are stabilized with intraparticle covalent crosslinks, and also contain pendant methacryloyl groups as photo-reactive moieties. While non-covalent interactions between nanoparticles enable formation of colloidal gel inks that are printable at room temperature, UV-induced covalent interparticle crosslinks based on methacryloyl moieties significantly enhance mechanical properties of printed constructs. Additionally, the UV crosslinking modality enables remarkable control over swelling, degradation, and biomolecule release behavior of 3D constructs. Finally, by exploiting the mechanical properties of colloidal biomaterials after UV crosslinking, 3D constructs can be designed with shape memory properties, returning to their original programmed geometry upon re-hydration. Accordingly, these novel colloidal inks exhibit great potential to serve as bio-inks for 3D printing of biomaterials with shape-morphing features for a wide range of tissue engineering and regenerative medicine applications.

Lower critical concentration temperature as thermodynamic origin of syneresis: Case of kappa-carrageenan solution

Polysaccharide ubiquity is trimmed for applications of low syneresis impact. This syneresis may be crucial for specific applications that are very sensitive to gel dimension stability, namely, 3D scaffolds for cell culture for disease diagnosis and tissue engineering. We hypothesized that the syneresis origin results from the kappa-carrageenan (kC) polysaccharide thermodynamic instability, and we demonstrated this by measuring the critical (coil-to-coil contact) concentration as a function of temperature. The impact of 5 mM, 10 mM and 15 mM KCl salt on the critical concentration of the solution and the lower critical concentration temperature (LCCT) were particularly investigated. For the kC polysaccharide, the gelation temperature (Tg) falls at temperatures below the LCCT, which explains the shrinking or syneresis reaction of the polysaccharide gels. The gap between Tg and LCCT would be the thermomotive force of the syneresis of many colloidal gels.

Mechanics and structure of carbon black gels under high-power ultrasound

Colloidal gels made of carbon black particles dispersed in light mineral oil are “rheo-acoustic” materials, i.e., their mechanical and structural properties can be tuned using high-power ultrasound, sound waves with submicrometer amplitude and frequencies larger than 20 kHz. The effects of high-power ultrasound on the carbon black gel are demonstrated using two experiments: rheology coupled to ultrasound to test for the gel mechanical response and a time-resolved ultra-small-angle x-ray scattering experiment (TRUSAXS) coupled to ultrasound to test for structural changes within the gel. We show that high-power ultrasound above a critical amplitude leads to a complex viscoelastic transient response of the gels within a few seconds: a softening of its storage modulus accompanied by a strong overshoot in its loss modulus. Under high-power ultrasound, the gel displays a viscoelastic spectrum with glasslike features and a significant decrease in its yield strain. Those effects are attributed to the formation of intermittent microcracks in the bulk of the gel as evidenced by TRUSAXS. Provided that the shear rate is not large enough to fully fluidize the sample, high-power ultrasound also facilitates the flow of the gel, reducing its yield stress as well as increasing the shear-thinning index, thanks again to the formation of microcracks.

Dynamical properties of different models of elastic polymer rings: Confirming the link between deformation and fragility.

We report extensive numerical simulations of different models of 2D polymer rings with internal elasticity. We monitor the dynamical behavior of the rings as a function of the packing fraction to address the effects of particle deformation on the collective response of the system. In particular, we compare three different models: (i) a recently investigated model [N. Gnan and E. Zaccarelli, Nat. Phys. 15, 683 (2019)] where an inner Hertzian field providing the internal elasticity acts on the monomers of the ring, (ii) the same model where the effect of such a field on the center of mass is balanced by opposite forces, and (iii) a semi-flexible model where an angular potential between adjacent monomers induces strong particle deformations. By analyzing the dynamics of the three models, we find that in all cases, there exists a direct link between the system fragility and particle asphericity. Among the three, only the first model displays anomalous dynamics in the form of a super-diffusive behavior of the mean-squared displacement and of a compressed exponential relaxation of the density auto-correlation function. We show that this is due to the combination of internal elasticity and the out-of-equilibrium force self-generated by each ring, both of which are necessary ingredients to induce such a peculiar behavior often observed in experiments of colloidal gels. These findings reinforce the role of particle deformation, connected to internal elasticity, in driving the dynamical response of dense soft particles.

Time–connectivity superposition and the gel/glass duality of weak colloidal gels

Colloidal gels result from the aggregation of Brownian particles suspended in a solvent. Gelation is induced by attractive interactions between individual particles that drive the formation of clusters, which in turn aggregate to form a space-spanning structure. We study this process in aluminosilicate colloidal gels through time-resolved structural and mechanical spectroscopy. Using the time-connectivity superposition principle a series of rapidly acquired linear viscoelastic spectra, measured throughout the gelation process by applying an exponential chirp protocol, are rescaled onto a universal master curve that spans over eight orders of magnitude in reduced frequency. This analysis reveals that the underlying relaxation time spectrum of the colloidal gel is symmetric in time with power-law tails characterized by a single exponent that is set at the gel point. The microstructural mechanical network has a dual character; at short length scales and fast times it appears glassy, whereas at longer times and larger scales it is gel-like. These results can be captured by a simple three-parameter constitutive model and demonstrate that the microstructure of a mature colloidal gel bears the residual skeleton of the original sample-spanning network that is created at the gel point. Our conclusions are confirmed by applying the same technique to another well-known colloidal gel system composed of attractive silica nanoparticles. The results illustrate the power of the time-connectivity superposition principle for this class of soft glassy materials and provide a compact description for the dichotomous viscoelastic nature of weak colloidal gels.

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

HypothesisRelative 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 (ϕeff) during the volume phase transitions. The microrheological behaviors are expected to be governed by the near-wall microstructure and its spatial heterogeneity. ExperimentsThe 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 ϕeff-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 ϕeff; (2) Five regimes of ϕeff 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.

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.

Two modes of cluster dynamics govern the viscoelasticity of colloidal gels.

Colloidal gels formed by strongly attractive particles at low particle volume fractions are composed of space-spanning networks of uniformly sized clusters. We study the thermal fluctuations of the clusters using differential dynamic microscopy by decomposing them into two modes of dynamics, and link them to the macroscopic viscoelasticity via rheometry. The first mode, dominant at early times, represents the localized, elastic fluctuations of individual clusters. The second mode, pronounced at late times, reflects the collective, viscoelastic dynamics facilitated by the connectivity of the clusters. By mixing two types of particles of distinct attraction strengths in different proportions, we control the transition time at which the collective mode starts to dominate, and hence tune the frequency dependence of the linear viscoelastic moduli of the binary gels.

Predicting the early-stage creep dynamics of gels from their static structure by machine learning

Upon sustained loading, colloidal gels tend to feature delayed viscoplastic creep deformations. However, the relationship, if any, between the structure and creep dynamics of gels remains elusive. Here, based on accelerated molecular dynamics simulations and the recently developed softness approach (i.e., classification-based machine learning), we reveal that the propensity of a gel to exhibit long-time creep is encoded in its static, unloaded structure. By taking the example of a calcium–silicate–hydrate gel (the binding phase of concrete), we extract a local, non-intuitive structural descriptor (a revised version of the “softness” metric proposed by the pioneering work from Cubuk et al.) that is strongly correlated with the dynamics of the particles. Notably, the macroscopic creep rate exhibits an exponential dependence on the average softness. We find that creep results in a decrease in softness in the gel structure, which, in turn, explains the gradual decay of the creep rate over time. Finally, we demonstrate that the softness metric is strongly correlated with the average energy barrier that is accessible to the particles.

Brownian dynamics simulation on orthogonal superposition rheology: Time–shear rate superposition of colloidal gel

The dynamics of model colloidal gels under a steady shear flow is studied by means of a Brownian dynamics (BD) simulation while applying orthogonal superposition rheometry, which superimposes a small amplitude oscillatory flow orthogonal to the main flow direction. Orthogonal dynamic frequency sweep (ODFS) curves are obtained at various magnitudes of the main flow, which shows shear thinning behavior of the colloidal gel. The viscoelastic spectra of the ODFS can be superimposed onto a master curve by the horizontal shift factor, which is equivalent to particle viscosity. That is, the shear rate controls a single master clock for all viscoelastic spectra of the ODFS in the form of a time–shear rate superposition, which bears an analogy with the time–temperature superposition of polymeric systems. In the low-frequency region of the master curve, both orthogonal moduli are well superimposed onto a single master curve, whereas the loss modulus deviates slightly from the master curve in the high-frequency region, which coincides with the experimental findings. We observe spatial and time-varying structural properties in both low- and high-frequency regions on the ODFS curves by decomposing the pair distribution function. It is verified that each flow condition shifted onto the same stress level on the master curve shows identical spatial orthogonal moduli at all radial distances despite the differences in the aggregate size and average particle connectivity.

An experimental study comparing the stability of colloidal dispersion gels with normal polymeric solutions for enhanced‐oil‐recovery purposes

AbstractWaterflooding in oil reservoirs is associated with several drawbacks. Recently, colloidal dispersion gels (CDG) have been proposed as a new method for conformance control to address these drawbacks. CDGs are prepared by mixing crosslinkers and polymers in very low concentrations as a result of intramolecular crosslinking. In this research, a comprehensive study was conducted on the stability of sulfonated polyacrylamide (SPAM) solutions and CDGs prepared using the same SPAM in harsh conditions. The effects of high temperature, shear rate, salts, and high mechanical degrading on the viscosity of both polymeric solution types were studied using a rheometer. The results showed that, in similar conditions, CDGs are less susceptible to salts than are normal SPAM solutions. Moreover, both solutions have nearly the same sensitivity to temperature. The effect of extremely high shear rates was also studied, and the results suggested that, in similar conditions, CDG is less susceptible to high shear rates than normal SPAM solutions. Being treated at 2500 1/s for 2 hours, the CDG solution lost almost 0% of its original viscosity, while the SPAM solution lost 0.97% of its original viscosity. Given that CDG is more stable in harsh reservoir conditions, it may be a suitable substitute to the highly sensitive polymeric solutions for improving the volumetric sweep efficiency of waterfloods.

Kinetics of Network Formation and Heterogeneous Dynamics of an Egg White Gel Revealed by Coherent X-Ray Scattering

The kinetics of heat-induced gelation and the microscopic dynamics of a hen egg white gel are probed using x-ray photon correlation spectroscopy along with ultrasmall-angle x-ray scattering. The kinetics of structural growth reveals a reaction-limited aggregation process with a gel fractal dimension of ≈2 and an average network mesh size of ca. 400nm. The dynamics probed at these length scales reveals an exponential growth of the characteristic relaxation times followed by an intriguing steady state in combination with a compressed exponential correlation function and a temporal heterogeneity. The degree of heterogeneity increases with decreasing length scale. We discuss our results in the broader context of experiments and models describing attractive colloidal gels.

Local velocity of thermoresponsive colloidal gels in rate-driven flow

The interplay between flow and attractive interactions in colloidal gels results in complex particle trajectories and velocity profiles that are not evident from bulk rheological measurements. We use high-speed confocal microscopy to investigate the local velocity of a low volume fraction (ϕ = 0.20) thermogelling nanoemulsion system as it flows through a cylindrical capillary at temperatures below and above the gel point. The nanoemulsions are composed of poly(dimethyl siloxane) droplets in a continuous phase of sodium dodecyl sulfate, de-ionized water, and a gelator molecule, poly(ethylene glycol diacrylate). The trajectories of fluorescent polystyrene tracer beads in the oil-rich domains are tracked using two-dimensional image processing. While the velocity profiles agree with those computed from rheometry measurements for nanoemulsion suspensions below the gel point temperature, increasing attractive interactions above the gel point results in statistically significant deviations. Specifically, the velocity measurements indicate a higher yield stress and a larger degree of shear thinning than expected from bulk rheology measurements, resulting in a more plug-shaped velocity profile as temperature and associated interdroplet attraction increase. These deviations from theoretical predictions are likely due to structural heterogeneity. Confocal microscopy images show that small, fluidized clusters are found in high shear rate regions near the capillary walls, while large dense clusters form in low shear rate regions closer to the center of the capillary.

Spatiotemporal Control of Supramolecular Polymerization and Gelation of Metal-Organic Polyhedra.

In coordination-based supramolecular materials such as metallogels, simultaneous temporal and spatial control of their assembly remains challenging. Here, we demonstrate that the combination of light with acids as stimuli allows for the spatiotemporal control over the architectures, mechanical properties, and shape of porous soft materials based on metal-organic polyhedra (MOPs). First, we show that the formation of a colloidal gel network from a preformed kinetically trapped MOP solution can be triggered upon addition of trifluoroacetic acid (TFA) and that acid concentration determines the reaction kinetics. As determined by time-resolved dynamic light scattering, UV-vis absorption, and 1H NMR spectroscopies and rheology measurements, the consequences of the increase in acid concentration are (i) an increase in the cross-linking between MOPs; (ii) a growth in the size of the colloidal particles forming the gel network; (iii) an increase in the density of the colloidal network; and (iv) a decrease in the ductility and stiffness of the resulting gel. We then demonstrate that irradiation of a dispersed photoacid generator, pyranine, allows the spatiotemporal control of the gel formation by locally triggering the self-assembly process. Using this methodology, we show that the gel can be patterned into a desired shape. Such precise positioning of the assembled structures, combined with the stable and permanent porosity of MOPs, could allow their integration into devices for applications such as sensing, separation, catalysis, or drug release.

Yield stress behavior of colloidal gels with embedded active particles

The yield stress behavior of colloidal gels with embedded active particles is studied with three experiments: start-up of steady shear, oscillatory strain amplitude sweep, and creep testing. Activity is generated by Janus particles with a platinum hemisphere; these particles undergo self-diffusiophoretic and self-electrophoretic motion in hydrogen peroxide solutions. The free particle active motion of the Janus colloids is consistent with an active energy of 25 times thermal energy at the highest hydrogen peroxide concentration studied. Consistent with prior work, the gels with embedded active particles display enhanced microdynamics and a reduction in linear viscoelastic moduli. Furthermore, at the activity levels studied, the yield stress decreases by as much as threefold for gels with an active-to-passive particle ratio of only 1:1200. We additionally find the yield strain is independent of activity. The significant reduction in yield stress at a very low active-to-passive particle ratio is modeled by combining the theory of how activity changes the spring constant of interparticle bonds in the gel with an argument that the number of active fractal clusters in the gel—rather than the number of active particles—drives the activity-induced softening of rheological properties. We estimate that 1 in 40 fractal clusters in the gel is active due to the presence of an active particle. This approach explains how an extremely small fraction of active particles causes a substantial change in both linear and nonlinear rheological properties. The results and modeling are potentially useful for the creation of gels with multistate mechanical properties.

Injectable Nanostructured Colloidal Gels Resembling Native Nucleus Pulposus as Carriers of Mesenchymal Stem Cell for the Repair of Degenerated Intervertebral Discs

Intervertebral disc degeneration is strongly implicated as a cause of low-back pain. Stem cell-based tissue engineering in treating intervertebral disc (IVD) degeneration recently obtained increasing attention. An appropriately engineered scaffold is considered essential to maintain the viability and function of transplanted cells if it can provide a more physical-relevant condition to replicate the extracellular microenvironments and even to reverse the process of IVD degradation. Here we proposed to utilize nanostructured gelatin colloidal hydrogels loaded with mesenchymal stem cells for the treatment of IVD degeneration. The colloidal gel consisting of self-assembled gelatin nanoparticles formed a homogeneous porous network dispersed in a continuous phase of an aqueous solution. These special structural and compositional properties render the colloidal gels with shear-thinning and self-healing behavior, as well as injectability and moldability. More importantly, the mechanical properties of gelatin colloidal gels can be adjusted to resemble native nucleus pulposus (NP) which is also viscoelastic and thixotropic. Results demonstrated that gelatin colloidal gels were cytocompatible, biodegradable, and able to support the NP-like differentiation of MSCs. Also, gelatin colloidal gels had the potential to limit leakage and retained cell viability after injection. Upon transplantation into rabbit degenerated IVDs, mesenchymal stem cell-loaded nanostructured colloidal gels promoted IVD regeneration evidenced by the significant improvement in morphological and histological assessment, cellularity, glycosaminoglycan contents, disc height index, and MRI index. Taken together, these findings demonstrate the potential of stem cell-laden gelatin colloidal gels as a tissue-engineered construct for IVD repair and regeneration.

Strength and dilatancy of sand before and after stabilisation with colloidal-silica gel

To evaluate the effect of stabilisation by using a colloidal silica aqueous gel on the subsequent behaviour of sand, the dilatancy and peak and ultimate strength characteristics of M31 sand were investigated before and after stabilisation. Triaxial compression tests were performed in drained and undrained mode, at effective stresses ranging from 100 to 6000 kPa. Important changes in the sand's mechanical behaviour were observed after stabilisation, including a significant increase in stress ratio and dilatancy rate at peak and a relocation of the treated sand's critical state line in the e–p′ plane, substantially above that manifested by the untreated sand; however, the two lines converged at high stresses. The results confirm a state-dependent behaviour for the sand that is not applicable to the treated sand, which exhibits predominantly stress-dependent behaviour. A modified state parameter was used to normalise the treated sand's behaviour at peak failure.

Effects of linker flexibility on phase behavior and structure of linked colloidal gels.

Colloidal nanocrystal gels can be assembled using a difunctional "linker" molecule to mediate bonding between nanocrystals. The conditions for gelation and the structure of the gel are controlled macroscopically by the linker concentration and microscopically by the linker's molecular characteristics. Here, we demonstrate using a toy model for a colloid-linker mixture that linker flexibility plays a key role in determining both phase behavior and the structure of the mixture. We fix the linker length and systematically vary its bending stiffness to span the flexible, semiflexible, and rigid regimes. At fixed linker concentration, flexible-linker and rigid-linker mixtures phase separate at low colloid volume fractions, in agreement with predictions of first-order thermodynamic perturbation theory, but the semiflexible-linker mixtures do not. We correlate and attribute this qualitatively different behavior to undesirable "loop" linking motifs that are predicted to be more prevalent for linkers with end-to-end distances commensurate with the locations of chemical bonding sites on the colloids. Linker flexibility also influences the spacing between linked colloids, suggesting strategies to design gels with desired phase behavior, structure, and, by extension, structure-dependent properties.

Research on linking molecules in colloidal gels helps improve their tunability

Linking molecules offer novel self-assembling strategies for colloidal gels.