Two-step yielding and directional strain-induced strengthening in dilute colloidal gels

Yield stress analysis of cellulose nanocrystals (CNCs) in hyaluronic acid suspensions

Due to their biodegradability features, cellulose nanocrystals (CNCs) and hyaluronic acid (HA) have been simultaneously used in the matrix of hydrogels for biomedical applications, such as corneal transplantation, and skin regeneration. Although rheology of these hydrogels may provide useful information for their applications, little to no attention has been paid to rheological characterization. In this study, we analyzed the rheology of HA-CNC suspensions and more specifically their yielding behavior. Through different rheological experiments, known as stress ramp, shear rate ramp and amplitude sweep; it was observed that HA-CNC gels possessed two yield points. Reproducible magnitudes of yield stress were obtained by optimizing the experimental conditions. The rheo-optics characterizations confirmed that the first and second yield points could be attributed to the bond and cage breakage phenomena. Studying the effect of concentration, the second yield stress increased linearly by CNC concentration, whereas the first yield point manifested a power-law dependence on concentration (exponent of 0.5). This power-law relationship was further justified by the evolution of average distance between the CNC individual particles (d), calculated through SAXS analysis.

Size-dependent viscoelasticity in hybrid colloidal gels based on spherical soft nanoparticles and two-dimensional nanosilicates of varying size

HYPOTHESIS

Hetero-aggregation of oppositely charged colloidal particles with controlled architectural and interactional asymmetry allows modifying gel nanostructure and properties. We hypothesize the relative size ratio between cationic nanospheres and varied-size anionic two-dimensional nanoclays will influence the gel formation mechanisms and resulting rheological performance.

EXPERIMENTS

Hybrid colloidal gels formed via hetero-aggregation of cationic gelatin nanospheres (∼400 nm diameter) and five types of nanoclays with similar 1 nm thickness but different lateral sizes ranging from ∼ 30 nm to ∼ 3000 nm. Structure-property relationships were elucidated using a suite of techniques. Microscopy and scattering probed gel nanostructure and particle configuration. Rheology quantified linear and non-linear viscoelastic properties and yielding behavior. Birefringence and polarized imaging assessed size-dependent nanoclay alignment during shear flow.

FINDINGS

Nanoclay size ratio relative to nanospheres affected the gelation process, network structure, elasticity, yielding, and shear response. Gels with comparably sized components showed maximum elasticity, while yield stress depended on nanoclay rotational mobility. Shear-induced nanoclay alignment was quantified by birefringence, which is more pronounced for larger nanoclay. Varying nanoclay size and interactions with nanospheres controlled dispersion, aggregation, and nematic ordering. These findings indicate that architectural and interactional asymmetry enables more control over gel properties through controlled assembly of anisotropic building blocks.

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.

Shear induced tuning and memory effects in colloidal gels of rods and spheres

Shear history plays an important role in determining the linear and nonlinear rheological response of colloidal gels and can be used for tuning their structure and flow properties. Increasing the colloidal particle aspect ratio lowers the critical volume fraction for gelation due to an increase in the particle excluded volume. Using a combination of rheology and confocal microscopy, we investigate the effect of steady and oscillatory preshear history on the structure and rheology of colloidal gels formed by silica spheres and rods of length L and diameter D (L/D = 10) dispersed in 11 M CsCl solution. We use a non-dimensional Mason number, Mn (=F_visc./F_attr.), to compare the effect of steady and oscillatory preshear on gel viscoelasticity. We show that after preshearing at intermediate Mn, attractive sphere gel exhibits strengthening, whereas attractive rod gel exhibits weakening. Rheo-imaging of gels of attractive rods shows that at intermediate Mn, oscillatory preshear induces large compact rod clusters in the gel microstructure, compared to steady preshear. Our study highlights the impact of particle shape on gel structuring under flow and viscoelasticity after shear cessation.

Yield precursor in primary creep of colloidal gels

Colloidal gels under constant moderate stress flow only after a prolonged solid-like deformation. Predicting the time-dependent yielding of the gels would facilitate control of their mechanical stability and transport, but early detectable signs of such delayed solid-to-fluid transition remain unknown. We show that the shear rate of colloidal gels under constant stress can forecast an eventual yielding during the earliest stage of deformation known as primary creep. The shear rate before failure exhibits a characteristic power-law decrease as a function of time, distinct from the linear viscoelastic response. We model this early-stage behavior as a series of uncorrelated local plastic events that are thermally activated, which illuminates the exponential dependence of the yield time on the applied stress. By revealing underlying viscoplasticity, this precursor to yield in the macroscopic shear rate provides a convenient tool to predict the yielding of a gel well in advance of its actual occurrence.

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.

Yielding and resolidification of colloidal gels under constant stress

We examine the macroscopic deformation of a colloidal depletion gel subjected to a step shear stress. Three regimes are identified depending on the magnitude of the applied stress: (i) for stresses below yield stress, the gel undergoes a weak creep in which the bulk deformation grows sublinearly with time similar to crystalline and amorphous solids. For stresses above yield stress, when the bulk deformation exceeds approximately the attraction range, the sublinear increase of deformation turns into a superlinear growth which signals the onset of non-linear rearrangements and yielding of the gel. However, the long-time creep after such superlinear growth shows two distinct behaviors: (ii) under strong stresses, a viscous flow is reached in which the strain increases linearly with time. This indicates a complete yielding and flow of the gel. In stark contrast, (iii) for weak stresses, the gel after yielding starts to resolidify. More homogenous gels that are produced through enhancement of either interparticle attraction strength or strain amplitude of the oscillatory preshear, resolidify gradually. In contrast, in gels that are more heterogeneous resolidification occurs abruptly. We also find that heterogenous gels produced by oscillatory preshear at intermediate strain amplitude yield in a two-step process. Finally, the characteristic time for the onset of delayed yielding is found to follow a two-step decrease with increasing stress. This is comprised of an exponential decrease at low stresses, during which bond reformation is decisive and resolidification is detected, and a power law decrease at higher stresses where bond breaking and particle rearrangements dominate.

Rheological characterization of CNC-CTAB network below and above critical micelle concentration (CMC)

The network of Cellulose Nanocrystal (CNC) suspension is explored below and above the critical micelle concentration (CMC), in the presence of cetyltrimethylammonium bromide (CTAB) with a positively charged head using TEM imaging and rheological characterization. CNC-CTAB gels show shear thinning behavior, complex relationship between strain amplitudes and CTAB concentration, diminishing thixotropic behavior as a function of CTAB and single and two yielding stress maxima as a function of CTAB, resulting from different microstructure below and above the critical Micelle Concentration (CMC) of CTAB. Comparing the flow curves of CNC-CTAB suspension/gel revealed the role played by CTAB content, CNC concentration and sonication energy in strengthening of the network. We analyzed and obtained yield stress from steady shear, creep testing and oscillatory experiments and compared them.

Two-step yielding behavior of densely packed microgel mixtures with chemically dissimilar surfaces and largely different sizes

Steady-state flow and elastic behavior is investigated for the moderately concentrated binary suspensions of soft microgels (pastes) with chemically dissimilar surfaces, and various degrees of size- and stiffness disparities. The pastes of poly(N-isopropyl acrylamide) (N) and poly(N-isopropyl methacrylamide) (NM) microgels with different values of yield strain γc (γNc > γNMc) are employed as the components. For the single microgel pastes (φ ≈ 1 where φ is apparent volume fraction), the values of γc are governed by the chemical species of constituent polymer in microgel surface whereas γc is insensitive to cross-link density and particle size. We demonstrate that the binary N/NM pastes with large size disparity (RN/NM = DN/DNM < 0.26 where D is the microgel diameter) at low φN (φN: weight fraction of small N microgels) exhibit the peculiarities in several rheological aspects, i.e., the two-step yielding in steady-state flow, and their values of γc and equilibrium shear modulus (G0) being equivalent to those of the single large NM microgel paste. These peculiarities are attributed to the characteristic packing resulting from large size disparity in which all or almost of the small N microgels tend to be accommodated in the gap between the large NM microgels even in moderately concentrated state. This characteristic packing substantially masks the contribution of the small N microgels at low φN, explaining the φN-independent G0 and γc as well as the first yielding governed solely by the large NM microgels. The second yielding results from the emerged contribution of the small N microgels expelled out from the gap by the positional rearrangements after the first yielding. The binary homo-N/N pastes with the similarly large size disparity at low φsmall also exhibit the φsmall-independent values of G0, but they show one-step yielding, indicating that the two-step yielding requires not only sufficiently large size disparity but also chemical dissimilarity (different values of γc) between the two components.

Two step yielding in soft materials

A review is presented on the topic of two-step yielding observed in complex fluids that cover a broad variety of materials ranging from colloidal gels, attractive glasses, emulsions, suspensions, and several commercial paste-like materials. The common features in various systems displaying two-step yielding behavior are the presence of two characteristic forces between the interacting particles or two varying representative length or time scales. This focused review aims to provide physical insights, mechanistic understanding of the two-step yielding and other associated rheological consequences of this nonlinear behavior. A discussion is provided on the microstructural details with an overview of different experimental systems exhibiting double-yielding studied so far highlighting the similarities and differences among them. Particularly, the effects of continuous phase properties, dispersed particle phase factors (size, shape, softness and surface charge) and external force field (electric, magnetic, thermal and shear flows) on two-step yielding are considered.

Embedding orthogonal memories in a colloidal gel through oscillatory shear

It has recently been shown that in a broad class of disordered systems oscillatory shear training can embed memories of specific shear protocols in relevant physical parameters such as the yield strain. These shear protocols can be used to change the physical properties of the system and memories of the protocol can later be "read" out. Here we investigate shear training memories in colloidal gels, which include an attractive interaction and network structure, and discover that such systems can support memories both along and orthogonal to the training flow direction. We use oscillatory shear protocols to set and read out the yield strain memories and confocal microscopy to analyze the rearranging gel structure throughout the shear training. We find that the gel bonds remain largely isotropic in the shear-vorticity plane throughout the training process suggesting that structures formed to support shear along the training shear plane are also able to support shear along the orthogonal plane. Orthogonal memory extends the usefulness of shear memories to more applications and should apply to many other disordered systems as well.

Nonlinear rheological characteristics of single species bacterial biofilms

Bacterial biofilms in natural and artificial environments perform a wide array of beneficial or detrimental functions and exhibit resistance to physical as well as chemical perturbations. In dynamic environments, where periodic or aperiodic flows over surfaces are involved, biofilms can be subjected to large shear forces. The ability to withstand these forces, which is often attributed to the resilience of the extracellular matrix. This attribute of the extracellular matrix is referred to as viscoelasticity and is a result of self-assembly and cross-linking of multiple polymeric components that are secreted by the microbes. We aim to understand the viscoelastic characteristic of biofilms subjected to large shear forces by performing Large Amplitude Oscillatory Shear (LAOS) experiments on four species of bacterial biofilms: Bacillus subtilis, Comamonas denitrificans, Pseudomonas fluorescens and Pseudomonas aeruginosa. We find that nonlinear viscoelastic measures such as intracycle strain stiffening and intracycle shear thickening for each of the tested species, exhibit subtle or distinct differences in the plot of strain amplitude versus frequency (Pipkin diagram). The biofilms also exhibit variability in the onset of nonlinear behaviour and energy dissipation characteristics, which could be a result of heterogeneity of the extracellular matrix constituents of the different biofilms. The results provide insight into the nonlinear rheological behaviour of biofilms as they are subjected to large strains or strain rates; a situation that is commonly encountered in nature, but rarely investigated.

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

The effects of particle roughness and short-ranged non-central forces on colloidal gels are studied using computer simulations in which particles experience a sinusoidal variation in energy as they rotate. The number of minima n and energy scale K are the key parameters; for large K and n, particle rotation is strongly hindered, but for small K and n particle rotation is nearly free. A series of systems are simulated and characterized using fractal dimensions, structure factors, coordination number distributions, bond-angle distributions and linear rheology. When particles rotate easily, clusters restructure to favor dense packings. This leads to longer gelation times and gels with strand-like morphology. The elastic moduli of such gels scale as G'∝ω^0.5 at high shear frequencies ω. In contrast, hindered particle rotation inhibits restructuring and leads to rapid gelation and diffuse morphology. Such gels are stiffer, with G'∝ω^0.35. The viscous moduli G'' in the low-barrier and high-barrier regimes scale according to exponents 0.53 and 0.5, respectively. The crossover frequency between elastic and viscous behaviors generally increases with the barrier to rotation. These findings agree qualitatively with some recent experiments on heterogeneously-surface particles and with studies of DLCA-type gels and gels of smooth spheres.

Plasticity in colloidal gel strands

Colloidal gels are space-spanning networks of aggregated particles. The mechanical response of colloidal gels is governed, to a large extent, by the properties of the individual gel strands. To study how colloidal gels respond to repeated deformations, we perform Brownian dynamics simulations on single strands of aggregated colloidal particles. While current models assume that gel failure is due to the brittle rupture of gel strands, our simulations show that gel strands undergo large plastic deformations prior to breaking. Rearrangement of particles within the strands leads to plastic lengthening and softening of the strands, which may ultimately lead to strand necking and ductile failure. This failure mechanism occurs irrespective of the thickness and length of the strands and the range and strength of the interaction potential. Rupture of gel strands is more likely for long and thin strands and for a long-ranged interaction potential.

Rheological Behavior and in Situ Confocal Imaging of Bijels Made by Mixing

Bijels (bicontinuous interfacially jammed emulsion gels) have the potential to be useful in many different applications due to their internal connectivity and the possibility of efficient mass transport through the channels. Recently, new methods of making the bijel have been proposed, which simplify the fabrication process, making commercial application more realistic. Here, we study the flow properties of bijels prepared by mixing alone using oscillatory rheology combined with confocal microscopy and also squeezing flow experiments. We found that the bijel undergoes a two-step yielding process where the first step corresponds to the fluidizing of the interface, allowing the motion of the structure, and the second step corresponds to the breaking of the structure. In the squeeze flow experiments, the yield stress of the bijel is observed to show a power law dependence on squeezing speed. However, when stress in excess of yield stress is plotted against shear rate, all the different squeeze flow data show a superposition.

Microscopic Theory of Two-Step Yielding in Attractive Colloids

Attractive colloids display two distinct amorphous solid phases: the attractive glass due to particle bonding and the repulsive glass due to the hard-core repulsion. By means of a microscopic mean field approach, we analyze their response to a quasistatic shear strain. We find that the presence of two distinct interaction length scales may result in a sharp two-step yielding process, which can be associated with a hysteretic stress response or with a reversible but nonmonotonic stress-strain curve. We derive a generic phase diagram characterized by two distinct yielding lines, an inverse yielding and a critical point separating the hysteretic and reversible regimes. Our results should be applicable to a large class of glassy materials characterized by two distinct interaction length scales.

Decoupling Arrest Origins in Hydrogels of Cellulose Nanofibrils

Colloidal gels with various architectures and different types of interactions provide a unique opportunity to shed light on the interplay between microscopic structures and mechanical properties of soft glassy materials. Here, we prepare acetylated cellulose nanofibrils with 2 degrees of substitution and make a structural and rheological characterization of their hydrogels. Two-step yielding processes are observed in the shear experiments, which allow us to deduce more precise knowledge regarding localized structural changes of the fibrils. We separate the viscoelastic response into two contributions: the establishment of cross-linked clusters on a fibril level and the arrested phase separation on a cluster level. We hypothesize that with the addition of salt, the hydrogels exhibit different arrested states that are identified as unable to access the thermodynamic equilibrium. Our results highlight that the coexistence of gelation and glass transitions are experimentally recognized in the hydrogels, with a global gelation driven by a local glasslike arrest during spinodal decomposition.

Evaluating the Dispersant Stabilization of Colloidal Suspensions from the Scaling Behavior of Gel Rheology and Adsorption Measurements

Maintaining suspension stability by effective particle dispersion in systems with attractive interactions can be accomplished by the addition of dispersants that modify the interparticle potential to provide steric or electrostatic barriers against aggregation. The efficacy of such dispersants is typically considered simply by the modification of suspension rheological properties as a function of the overall added dispersant concentration. However, such considerations do little to reveal the molecular origin of differences in dispersant efficacy because they do not consider differences in surface activity. We combine measured adsorption isotherms with the rheological characterization of the elasticity of colloidal gels formed by particle aggregation to provide a more meaningful assessment of dispersant efficacy. The rheological data show that the dispersants are effective at reducing particle aggregation, whereas, from the adsorption isotherms, they differ considerably in their surface coverage at constant overall concentration. When compared at constant dispersant particle surface coverage, the gel rheology shows marked differences across the different dispersants, as opposed to comparisons at constant overall dispersant concentration in the suspensions. In particular, the power-law volume fraction scaling of gel elasticity at constant coverage reveals clear differences in the critical volume fraction for gel formation for the different dispersants. The most efficacious dispersant is that associated with the largest critical volume fraction for gel formation at a given surface coverage. This work demonstrates the utility of rheological investigations coupled with accurate determinations of surface coverage to better differentiate dispersant performance, which may improve efforts to engineer new dispersant molecules.

Colloidal gels tuned by oscillatory shear

We examine the microstructural and mechanical changes which occur during oscillatory shear flow and reformation after flow cessation of an intermediate volume fraction colloidal gel using rheometry and Brownian Dynamics (BD) simulations. A model depletion colloid-polymer mixture is used, comprising a hard sphere colloidal suspension with the addition of non-adsorbing linear polymer chains. The results reveal three distinct regimes depending on the strain amplitude of oscillatory shear. Large shear strain amplitudes fully break the structure which results in a more homogenous and stronger gel after flow cessation. Intermediate strain amplitudes densify the clusters and lead to highly heterogeneous and weak gels. Shearing the gel to even lower strain amplitudes creates a less heterogonous stronger solid. These three regimes of shearing are connected to the microscopic shear-induced structural heterogeneity. A comparison with steady shear flow reveals that the latter does not produce structural heterogeneities as large as oscillatory shear. Therefore oscillatory shear is a much more efficient way of tuning the mechanical properties of colloidal gels. Moreover, colloidal gels presheared at large strain amplitudes exhibit a distinct nonlinear response characterized largely by a single yielding process while in those presheared at lower rates a two-step yielding process is promoted due to the creation of highly heterogeneous structures.

Structural fingerprints of yielding mechanisms in attractive colloidal gels

Core-Modified Dissipative Particle Dynamics (CM-DPD) with a modified depletion potential and full hydrodynamics description is used to study non-equilibrium properties of colloidal gels with short range attraction potentials at an intermediate volume fraction (ϕ = 0.2) under start-up shear deformation. Full structural and rheological analysis using the stress fabric tensor complemented by bond number and bond distribution evolution under flow reveals that similarly to dilute colloidal gels, flow-induced anisotropy and strain-induced stretching of bonds are present during the first yielding transition. Unlike in low volume fraction depletion gels however, a small fraction of bond dissociation is required to facilitate bond rotation at intermediate volume fractions. The strain at which structural stretching and anisotropy in bond distribution emerge coincides with the first maximum in the shear stress (first yielding transition). At higher strains, depending on flow strength, a second peak in stress signal appears which is attributed to the compaction and melting of clusters. In this work, for the first time we provide evidence that multibody hydrodynamic interactions are essential to predict the correct dynamics of depletion gels under flow, namely two-step yielding process.

Structure and Yielding of Colloidal Silica Gels Varying the Range of Interparticle Interactions

The relationship between interaction range, structure, fluid-gel transition, and viscoelastic properties of silica dispersions at intermediate volume fraction, Φv ≈ 0.1 and in alkaline conditions, pH = 9 was investigated. For this purpose, rheological, physicochemical, and structural (synchrotron-SAXS) analyses were combined. The range of interaction and the aggregation state of the dispersions were tuned by adding either divalent counterions (Ca(2+)) or polycounterions (PDDA). With increasing calcium chloride concentration, a progressive aggregation was observed which precludes a fluid-gel transition at above 75 mM of calcium chloride. In this case, the aggregation mechanism is driven by short-range ion-ion correlations. Upon addition of PDDA, a fluid-gel transition, at a much lower concentration, followed by a reentrant gel-fluid transition was observed. The gel formation with PDDA was induced by charge neutralization and longer range polymer bridging interactions. The refluidification at high PDDA concentrations was explained by the overcompensation of the charge of the silica particles and by the steric repulsions induced by the polycation chains. Rheological measurements on the so-obtained gels reveal broad yielding transition with two steps when the size of the silica particle clusters exceeds ≈0.5 μm.

Structural change and dynamics of colloidal gels under oscillatory shear flow

The dynamics and rheological behavior of colloidal gels under oscillatory shear flow have been studied by using the Brownian dynamics simulations. The dynamics is studied under the oscillatory shear of small, medium, and large amplitudes. In the small amplitude oscillatory shear (SAOS) regime, the colloidal gel retains a rigid-chain network structure. The colloidal gel oscillates with small structural fluctuations and the elastic stress shows a linear viscoelastic response. In the medium amplitude oscillatory shear (MAOS) regime, the rigid network structure is ruptured, and a negative correlation between the absolute value of strain and the average bond number is observed. The elastic stress shows a transient behavior in between the SAOS and LAOS responses. In the large amplitude oscillatory shear (LAOS) regime, the colloidal gel shows a soft chain structure. Contrary to the negative correlation in the MAOS regime, the colloidal gel shows an oscillating dynamics with a positive correlation between the absolute value of strain and the average bond number. The soft chain structure exhibits no elasticity at small strain, while it shows strong elasticity at large strain. The oscillating dynamics and the rheological behavior are discussed in terms of the microstructural change from the rigid to soft chain structure.

Avalanche-like fluidization of a non-Brownian particle gel

We report on the fluidization dynamics of an attractive gel composed of non-Brownian particles made of fused silica colloids. Extensive rheology coupled to ultrasonic velocimetry allows us to characterize the global stress response together with the local dynamics of the gel during shear startup experiments. In practice, after being rejuvenated by a preshear, the gel is left to age for a time tw before being subjected to a constant shear rate [small gamma, Greek, dot above]. We investigate in detail the effects of both tw and [small gamma, Greek, dot above] on the fluidization dynamics and build a detailed state diagram of the gel response to shear startup flows. The gel may display either transient shear banding towards complete fluidization or steady-state shear banding. In the former case, we unravel that the progressive fluidization occurs by successive steps that appear as peaks on the global stress relaxation signal. Flow imaging reveals that the shear band grows until complete fluidization of the material by sudden avalanche-like events which are distributed heterogeneously along the vorticity direction and correlated to large peaks in the slip velocity at the moving wall. These features are robust over a wide range of tw and [small gamma, Greek, dot above] values, although the very details of the fluidization scenario vary with [small gamma, Greek, dot above]. Finally, the critical shear rate [small gamma, Greek, dot above]* that separates steady-state shear-banding from steady-state homogeneous flow depends on the width of the shear cell and exhibits a nonlinear dependence with tw. Our work brings about valuable experimental data on transient flows of attractive dispersions, highlighting the subtle interplay between shear, wall slip and aging whose modeling constitutes a major challenge that has not been met yet.

Coupling of gelation and glass transition in a biphasic colloidal mixture-from gel-to-defective gel-to-glass

The state transition from gel to glass is studied in a biphasic mixture of polystyrene core/poly(N-isopropylacrylamide) shell (CS) microgels and sulfonated polystyrene (PSS) particles. At 35 °C, the interaction between CS microgels is due to short-range van der Waals attraction, while that between PSS particles is from long-range electrostatic repulsion. During the variation of the relative ratio of the two species at a fixed apparent total volume fraction, the mixture exhibits a gel-to-defective gel-to-glass transition. When small amounts of PSS are introduced into the CS gel network, some of them are kinetically trapped, causing a change in its fractal structure, and act as defects to weaken the macroscopic gel strength. An increase of the PSS content in the mixture promotes the switch from the gel to the defective gel, e.g., the typical two-step yielding gel merges into one-step yielding. This phenomenon is an indication that inter-cluster bond breakage coincides with intra-cluster bond fracture. As the relative volume fraction of PSS exceeds a critical threshold, the gel network can no longer be formed; hence, the mixture exhibits characteristics of glass. A state diagram of the biphasic mixture is constructed, and the landscapes of the different transitions will be described in future studies.

On the rheology of pendular gels and morphological developments in paste-like ternary systems based on capillary attraction

We investigate capillary bridging-induced gelation phenomena in silica particle suspensions and pastes, where a particle-wetting fluid is added as the third component. Increasing the wetting fluid loading in the ternary system induces a morphological transition from a pendular network to compact capillary aggregates network, with an intermediate funicular state. To our knowledge, the formation of percolated structures from compact capillary aggregates when the volume fraction of a wetting fluid approaches that of the particles is unprecedented. Such structures appear to result from the arrested coalescence of compact capillary aggregates due to the balance between the Laplace pressure and solid-like properties (yield stress, elasticity) of the aggregates. Shear-induced yielding of the ternary systems, linked to their percolating nature, is strongly influenced by the amount of wetting fluid phase. A non-monotonic dependence of the yield stress on the amount of wetting fluid is found, with the maximum yield stress obtained for a wetting fluid-to-particle volume fraction ratio of 0.2-0.3. For pendular systems, linear viscoelastic properties display a soft glassy rheological behavior above the percolation threshold (around 4 vol% particles), and complex viscosity data can be scaled using the high frequency plateau value, as well as a single characteristic relaxation time, which decreases when the particle concentration is increased. In addition, the particle concentration dependence of the yielding transition in the pendular regime appears to be efficiently described by two parameters extracted from the steady state flow curves: the yield stress and the limiting viscosity at a high shear rate. Although these non-colloidal networks result from flow-driven assembly, the scaling laws for our pendular gels are reminiscent of colloidal gels with a fractal geometry. Our studies pinpoint new pathways to create physical gels where the interparticle attraction strength is determined by capillary interactions.

Yielding behavior in colloidal glasses: comparison between "hard cage" and "soft cage"

Rheological measurements are utilized to examine the yielding behavior of a polystyrene (PS) core and poly(N-isopropylacrylamide) (PNIPAM) shell microgel system with varying shell/core ratio. For a shell/core ratio of 0.15 at high concentrations, the suspensions show a typical hard sphere (HS) yielding response where the loss modulus (G″) exhibits a single peak due to cage breaking. As a result of tighter cages and less cage distortion prior to yielding, the peak location of G″ decreases with volume fraction. For a shell/core ratio of 1.10, which behaves like a soft jammed glass at high concentration, the suspensions exhibit a one-step yielding behavior similar to that of HS glass. However, the location of the peak in G″ increases with volume fraction, demonstrating the important role of particle deformation in the breakage of cages. For an intermediate shell/core ratio of 0.34, the system displays a two-step yielding behavior, as observed in previous reports for attractive glasses. By increasing the volume fraction, the strain of the first peak increases while the second one decreases. In addition, as the effective volume fraction increases to 112%, the two peaks merge into one broad peak. It is demonstrated that the first peak of G″ is due to deformation of the shell, and the second peak of G″ is attributed to cage breaking as a result of the cores colliding with each other. Combining these results, a yielding state diagram from typical HS to soft jammed glass is demonstrated.

Homogeneous percolation versus arrested phase separation in attractively-driven nanoemulsion colloidal gels

We elucidate mechanisms for colloidal gelation of attractive nanoemulsions depending on the volume fraction (ϕ) of the colloid. Combining detailed neutron scattering, cryo-transmission electron microscopy and rheological measurements, we demonstrate that gelation proceeds by either of two distinct pathways. For ϕ sufficiently lower than 0.23, gels exhibit homogeneous fractal microstructure, with a broad gel transition resulting from the formation and subsequent percolation of droplet-droplet clusters. In these cases, the gel point measured by rheology corresponds precisely to arrest of the fractal microstructure, and the nonlinear rheology of the gel is characterized by a single yielding process. By contrast, gelation for ϕ sufficiently higher than 0.23 is characterized by an abrupt transition from dispersed droplets to dense clusters with significant long-range correlations well-described by a model for phase separation. The latter phenomenon manifests itself as micron-scale "pores" within the droplet network, and the nonlinear rheology is characterized by a broad yielding transition. Our studies reinforce the similarity of nanoemulsions to solid particulates, and identify important qualitative differences between the microstructure and viscoelastic properties of colloidal gels formed by homogeneous percolation and those formed by phase separation.

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

We report a simple correlation between microstructure and strain-dependent elasticity in colloidal gels by visualizing the evolution of cluster structure in high strain-rate flows. We control the initial gel microstructure by inducing different levels of isotropic depletion attraction between particles suspended in refractive index matched solvents. Contrary to previous ideas from mode coupling and micromechanical treatments, our studies show that bond breakage occurs mainly due to the erosion of rigid clusters that persist far beyond the yield strain. This rigidity contributes to gel elasticity even when the sample is fully fluidized; the origin of the elasticity is the slow Brownian relaxation of rigid, hydrodynamically interacting clusters. We find a power-law scaling of the elastic modulus with the stress-bearing volume fraction that is valid over a range of volume fractions and gelation conditions. These results provide a conceptual framework to quantitatively connect the flow-induced microstructure of soft materials to their nonlinear rheology.