Cluster mode-coupling approach to weak gelation in attractive colloids

Phase separation and dynamical arrest of protein solutions dominated by short-range attractions

The interplay of liquid-liquid phase separation (LLPS) and dynamical arrest can lead to the formation of gels and glasses, which is relevant for such diverse fields as condensed matter physics, materials science, food engineering, and the pharmaceutical industry. In this context, protein solutions exhibit remarkable equilibrium and non-equilibrium behaviors. In the regime where attractive and repulsive forces compete, it has been demonstrated, for example, that the location of the dynamical arrest line seems to be independent of ionic strength, so that the arrest lines at different ionic screening lengths overlap, in contrast to the LLPS coexistence curves, which strongly depend on the salt concentration. In this work, we show that the same phenomenology can also be observed when the electrostatic repulsions are largely screened, and the range and strength of the attractions are varied. In particular, using lysozyme in brine as a model system, the metastable gas-liquid binodal and the dynamical arrest line as well as the second virial coefficient have been determined for various solution conditions by cloud-point measurements, optical microscopy, centrifugation experiments, and light scattering. With the aim of understanding this new experimental phenomenology, we apply the non-equilibrium self-consistent generalized Langevin equation theory to a simple model system with only excluded volume plus short-range attractions, to study the dependence of the predicted arrest lines on the range of the attractive interaction. The theoretical predictions find a good qualitative agreement with experiments when the range of the attraction is not too small compared with the size of the protein.

On the dynamically arrested states of equilibrium and non-equilibrium gels: a comprehensive Brownian dynamics study

In this work a systematic study over a wide number of final thermodynamic states for two gel-forming liquids was performed. Such two kind of gel formers are distinguished by their specific interparticle interaction potential. We explored several thermodynamic states determining the thermodynamic, structural and dynamic properties of both liquids after a sudden temperature change. The thermodynamic analysis allows to identify that the liquid with short range attraction and long range repulsion lacks of a stable gas-liquid phase separation liquid, in contrast with the liquid with short range attractions. Thus, although for some thermodynamic states the structural behavior, measured by the static structure factor, is similar to and characteristic of the gel phase, for the short range attractive fluid the gel phase is a consequence of a spinodal decomposition process. In contrast, gelation in the short range attraction and long range repulsion liquid is not due to a phase separation. We also analyze the similarities and differences of the dynamic behavior of both systems through the analysis of the mean square displacement, the self part of the intermediate scattering function, the diffusion coefficient and theαrelaxation time. Finally, using one of the main results of the non-equilibrium self-consistent generalized Langevin equation theory (NE-SCGLE), we determine the dynamic arrest phase diagram in the volume fraction and temperature (φvsT) plane.

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.

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.

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.

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.

Diffusing wave microrheology of strongly attractive dense emulsions

We advance the microrheological interpretation of optical diffusing wave spectroscopy (DWS) measurements of strongly attractive emulsions at dense droplet volume fractions, ϕ. Beyond accounting for collective scattering, we show that measuring the mean free path of optical transport over a wide range of ϕ is necessary to quantify the effective size of the DWS probes, which we infer to be local dense clusters of droplets through a decorated core-shell network model. This approach yields microrheological elastic shear moduli that are in quantitative agreement with mechanical rheometry.

A unique route of colloidal phase separation yields stress-free gels

Phase separation often leads to gelation in soft and biomatter. For colloidal suspensions, we have a consensus that gels form by the dynamical arrest of phase separation. In this gelation, percolation of the phase-separated structure occurs before the dynamical arrest, leading to the generation of mechanical stress in the gel network. Here, we find a previously unrecognized type of gelation in dilute colloidal suspensions, in which percolation occurs after the local dynamical arrest, i.e., the formation of mechanically stable, rigid clusters. Thus, topological percolation generates little mechanical stress, and the resulting gel is almost stress-free when formed. We also show that the selection of these two types of gelation (stressed and stress-free) is determined solely by the volume fraction as long as the interaction is short-ranged. This universal classification of gelation of particulate systems may have a substantial impact on material and biological science.

Interplay between Glass Formation and Liquid-Liquid Phase Separation Revealed by the Scattering Invariant

The interplay of the glass transition with liquid-liquid phase separation (LLPS) is a subject of intense debate. We use the scattering invariant Q to probe how approaching the glass transition affects the shape of LLPS boundaries in the temperature/volume fraction plane. Two protein systems featuring kinetic arrest with a lower and an upper critical solution temperature phase behavior, respectively, are studied varying the quench depth. Using Q we noninvasively identify system-dependent differences for the effect of glass formation on the LLPS boundary. The glassy dense phase appears to enter the coexistence region for the albumin-YCl₃ system, whereas it follows the equilibrium binodal for the γ-globulin-PEG system.

Interference between the glass, gel, and gas-liquid transitions

Recent experiments and computer simulations have revealed intriguing phenomenological fingerprints of the interference between the ordinary equilibrium gas-liquid phase transition and the non-equilibrium glass and gel transitions. We thus now know, for example, that the liquid-gas spinodal line and the glass transition loci intersect at a finite temperature and density, that when the gel and the glass transitions meet, mechanisms for multistep relaxation emerge, and that the formation of gels exhibits puzzling latency effects. In this work we demonstrate that the kinetic perspective of the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory of irreversible processes in liquids provides a unifying first-principles microscopic theoretical framework to describe these and other phenomena associated with spinodal decomposition, gelation, glass transition, and their combinations. The resulting scenario is in reality the competition between two kinetically limiting behaviors, associated with the two distinct dynamic arrest transitions in which the liquid-glass line is predicted to bifurcate at low densities, below its intersection with the spinodal line.

Correlated Rigidity Percolation and Colloidal Gels

Rigidity percolation (RP) occurs when mechanical stability emerges in disordered networks as constraints or components are added. Here we discuss RP with structural correlations, an effect ignored in classical theories albeit relevant to many liquid-to-amorphous-solid transitions, such as colloidal gelation, which are due to attractive interactions and aggregation. Using a lattice model, we show that structural correlations shift RP to lower volume fractions. Through molecular dynamics simulations, we show that increasing attraction in colloidal gelation increases structural correlation and thus lowers the RP transition, agreeing with experiments. Hence, the emergence of rigidity at colloidal gelation can be understood as a RP transition, but occurs at volume fractions far below values predicted by the classical RP, due to attractive interactions which induce structural correlation.

Colloidal systems with a short-range attraction and long-range repulsion: Phase diagrams, structures, and dynamics

Colloidal systems with both a short-range attraction and long-range repulsion (SALR) have rich phases compared with the traditional hard sphere systems or sticky hard sphere systems. The competition between the short-range attraction and long-range repulsion results in the frustrated phase separation, which leads to the formation of intermediate range order (IRO) structures and introduces new phases to both equilibrium and nonequilibrium phase diagrams, such as clustered fluid, cluster percolated fluid, Wigner glass, and cluster glass. One hallmark feature of many SALR systems is the appearance of the IRO peak in the interparticle structure factor, which is associated with different types of IRO structures. The relationship between the IRO peak and the clustered fluid state has been careful investigated. Not surprisingly, the morphology of clusters in solutions can be affected and controlled by the SALR potential. And the effect of the SALR potential on the dynamic properties is also reviewed here. Even though much progress has been made in understanding SALR systems, many future works are still needed to have quantitative comparisons between experiments and simulations/theories and understand the differences from different experimental systems. Owing to the large parameter space available for SALR systems, many exciting features of SALR systems are not fully explored yet. Because proteins in low-salinity solutions have SALR interactions, the understanding of SALR systems can greatly help understand protein behavior in concentrated solutions or crowded conditions.

Coupling between criticality and gelation in "sticky" spheres: a structural analysis

We combine experiments and simulations to study the link between criticality and gelation in sticky spheres. We employ confocal microscopy to image colloid-polymer mixtures and Monte Carlo simulations of the square-well (SW) potential as a reference model. To this end, we map our experimental samples onto the SW model. We find an excellent structural agreement between experiments and simulations, both for locally favored structures at the single particle level and large-scale fluctuations at criticality. We follow in detail the rapid structural change in the critical fluid when approaching the gas-liquid binodal and highlight the role of critical density fluctuations for this structural crossover. Our results link the arrested spinodal decomposition to long-lived energetically favored structures, which grow even away from the binodal due to the critical scaling of the bulk correlation length and static susceptibility.

Dynamics of a network fluid within the liquid-gas coexistence region

Low-density networks of molecules or colloids are formed at low temperatures when the interparticle interactions are valence limited. Prototypical examples are networks of patchy particles, where the limited valence results from highly directional pairwise interactions. We combine extensive Langevin simulations and Wertheim's theory of association to study these networks. We find a scale-free (relaxation) dynamics within the liquid-gas coexistence region, which differs from that usually observed for isotropic particles. While for isotropic particles the relaxation dynamics is driven by surface tension (coarsening), when the valence is limited, the slow relaxation proceeds through the formation of an intermediate non-equilibrium gel via a geometrical percolation transition in the Random Percolation universality class. We show that the slow dynamics is universal, being also observed outside the coexistence region at low temperatures in the single phase region.

Arrested and temporarily arrested states in a protein-polymer mixture studied by USAXS and VSANS

We investigate the transition of the phase separation kinetics from a complete to an arrested liquid-liquid phase separation (LLPS) in mixtures of bovine γ-globulin with polyethylene glycol (PEG). The solutions feature LLPS with upper critical solution temperature phase behavior. At higher PEG concentrations or low temperatures, non-equilibrium, gel-like states are found. The kinetics is followed during off-critical quenches by ultra-small angle X-ray scattering (USAXS) and very-small angle neutron scattering (VSANS). For shallow quenches a kinetics consistent with classical spinodal decomposition is found, with the characteristic length (ξ) growing with time as ξ ∼ t^1/3. For deep quenches, ξ grows only very slowly with a growth exponent smaller than 0.05 during the observation time, indicating an arrested phase separation. For intermediate quench depths, a novel growth kinetics featuring a three-stage coarsening is observed, with an initial classical coarsening, a subsequent slowdown of the growth, and a later resumption of coarsening approaching again ξ ∼ t^1/3. Samples featuring the three-stage coarsening undergo a temporarily arrested state. We hypothesize that, while intermittent coarsening and collapse might contribute to the temporary nature of the arrested state, migration-coalescence of the minority liquid phase through the majority glassy phase may be the main mechanism underlying this kinetics, which is also consistent with earlier simulation results.

Clustering and Percolation in Suspensions of Carbon Black

High-structured carbon fillers are ubiquitous as the conductive additive comprising suspension-based electrochemical energy storage technologies. Carbon black networks provide the necessary electrical conductivity as well as mechanical percolation in the form of a yield stress. Despite their critical role in determining system performance, a full mechanistic understanding of the relationship between the electrical transport characteristics of the percolated, conductive networks of carbon black, and the rheological properties is lacking, which hinders the rational design and optimization of flowable electrodes and the processing of electrolytes for batteries. Here, we report on the microstructural origin of the rheological and electrical properties of two commonly used conductive additives in neat propylene carbonate. From quiescent mechanical and structural studies, we find that the gelation of these carbon black suspensions is best described by the dynamic arrest of a clustered fluid phase. In contrast, the temperature and frequency dependence of the ac conductivity near this transition shows that mesoscale charge transport is determined by hopping between localized states that does not require a stress-bearing network. This unique combination of microstructural characterization with rheological and electrical measurements enables testing prevailing theories of the connection between electrical and mechanical percolation as well as improving conductive additives to enhance electrochemical performance.

Kinetics of liquid-liquid phase separation in protein solutions exhibiting LCST phase behavior studied by time-resolved USAXS and VSANS

We study the kinetics of the liquid-liquid phase separation (LLPS) and its arrest in protein solutions exhibiting a lower critical solution temperature (LCST) phase behavior using the combination of ultra-small angle X-ray scattering (USAXS) and very-small angle neutron scattering (VSANS). We employ a previously established model system consisting of bovine serum albumin (BSA) solutions with YCl₃. We follow the phase transition from sub-second to 10⁴ s upon an off-critical temperature jump. After a temperature jump, the USAXS profiles exhibit a peak that grows in intensity and shifts to lower q values with time. Below 45 °C, the characteristic length scale (ξ) obtained from this scattering peak increases with time with a power of about 1/3 for different sample compositions. This is in good agreement with the theoretical prediction for the intermediate stage of spinodal decomposition where the growth is driven by interface tension. Above 45 °C, ξ follows initially the 1/3 power law growth, then undergoes a significant slowdown, and an arrested state is reached below the denaturation temperature of the protein. This growth kinetics may indicate that the final composition of the protein-rich phase is located close to the high density branch of the LLPS binodal when a kinetically arrested state is reached.

Probing Colloidal Gels at Multiple Length Scales: The Role of Hydrodynamics

Colloidal gels are out-of-equilibrium structures, made up of a rarefied network of colloidal particles. Comparing experiments to numerical simulations, with hydrodynamic interactions switched off, we demonstrate the crucial role of the solvent for gelation. Hydrodynamic interactions suppress the formation of larger local equilibrium structures of closed geometry, and instead lead to the formation of highly anisotropic threads, which promote an open gel network. We confirm these results with simulations which include hydrodynamics. Based on three-point correlations, we propose a scale-resolved quantitative measure for the anisotropy of the gel structure. We find a strong discrepancy for interparticle distances just under twice the particle diameter between systems with and without hydrodynamics, quantifying the role of hydrodynamics from a structural point of view.

Different mechanisms for dynamical arrest in largely asymmetric binary mixtures

Using confocal microscopy we investigate binary colloidal mixtures with large size asymmetry, in particular the formation of dynamically arrested states of the large spheres. The volume fraction of the system is kept constant, and as the concentration of small spheres is increased we observe a series of transitions of the large spheres to different arrested states: an attractive glass, a gel, and an asymmetric glass. These states are distinguished by the degree of dynamical arrest and the amount of structural and dynamical heterogeneity. The transitions between two different arrested states occur through melting and the formation of a fluid state. While a space-spanning network of bonded particles is found in both arrested and fluid states, only arrested states are characterized by the presence of a space-spanning network of dynamically arrested particles.

Snapshotted glass and gel transitions of stable colloidal dispersions after shear-driven aggregation in a microchannel

Intense shear can lead to aggregation of colloids that are highly stable at rest. The aggregation process typically has an induction time, and then becomes explosive, leading to rapid phase transitions. We study the phase evolution during shear-driven aggregation in a short microchannel (MC) under intense shear for a colloid with a high interaction energy barrier that ensures high stability of particles and clusters before and after intense shear. The short residence time allows us to snapshot the phase evolution by repeatedly cycling the colloid in the MC. It is found that, depending on the particle concentration, in addition to a fluid of clusters and a solid-like gel, there is another solid-like state between them: Wigner glass of clusters. Their transitions occur over a large range of particle concentrations. We have proposed a phase diagram that describes how the transitions of the three phases evolve in the aggregation steady state in the colloidal interaction vs. particle concentration plane.

Range effect on percolation threshold and structural properties for short-range attractive spheres

Percolation or aggregation in colloidal system is important in many fields of science and technology. Using molecular dynamics simulations, we study the percolation behavior for systems consisting of spheres interacting with short-range square-well (SRSW) which mimic colloidal particles, with different interaction ranges. We specifically focus on how the interaction range affects the percolation thresholds in the supercritical region. We find that the contact percolation boundaries are strongly dependent on the interaction ranges of SRSW, especially away from the liquid-liquid critical point. However, varying the interaction ranges of SRSW does not affect much the structure along percolation boundaries especially for low packing fractions. For instance, along the percolation boundary, distributions of coordination number show convergence, and distributions of cluster size are universal for different interaction ranges considered. In addition, either the bond percolation boundaries or isolines of average bond coordination number collapse to those for Baxter sticky model on phase diagram, which confirms the extended law of corresponding states.

Structure and dynamics of model colloidal clusters with short-range attractions

We examine the structure and dynamics of small isolated N-particle clusters interacting via short-ranged Morse potentials. "Ideally prepared ensembles" obtained via exact enumeration studies of sticky hard-sphere packings serve as reference states allowing us to identify key statistical-geometrical properties and to quantitatively characterize how nonequilibrium ensembles prepared by thermal quenches at different rates T[over ̇] differ from their equilibrium counterparts. Studies of equilibrium dynamics show nontrivial temperature dependence: nonexponential relaxation indicates both glassy dynamics and differing stabilities of degenerate clusters with different structures. Our results should be useful for extending recent experimental studies of small colloidal clusters to examine both equilibrium relaxation dynamics at fixed T and a variety of nonequilibrium phenomena.

Inter-particle correlations in a hard-sphere colloidal suspension with polymer additives investigated by Spin Echo Small Angle Neutron Scattering (SESANS)

Using a neutron scattering technique that measures a statistically-averaged density correlation function in real space rather than the conventional reciprocal-space structure factor, we have measured correlations between poly(methyl-methacrylate) (PMMA) colloidal particles of several sizes suspended in decalin. The new method, called Spin Echo Small Angle Neutron Scattering (SESANS) provides accurate information about particle composition, including the degree of solvent penetration into the polymer brush grafted on to the PMMA spheres to prevent aggregation. It confirms for particles, between 85 nm and 150 nm in radius that inter-particle correlations closely follow the Percus-Yevick hard-sphere model when the colloidal volume-fraction is between 30% and 50% provided the volume-fraction is used as a fitted parameter. No particle aggregation occurs in these systems. When small amounts of polystyrene are added as a depletant to a concentrated suspension of PMMA particles, short-range clustering of the particles occurs and there is an increase in the frequency of near-neighbor contacts. Within a small range of depletant concentration, near-neighbor correlations saturate and large aggregates with power law density correlations are formed. SESANS clearly separates the short- and long-range correlations and shows that, in this case, the power-law correlations are visible for inter-particle distances larger than roughly two particle diameters. In some cases, aggregate sizes are within our measurement window, which can extend out to 16 microns in favorable cases. We discuss the advantages of SESANS for measurements of the structure of concentrated colloidal systems and conclude that the method offers several important advantages.

Dynamics of colloidal glasses and gels

Many household and industrially important soft colloidal materials, such as pastes, concentrated suspensions and emulsions, foams, slurries, inks, and paints, are very viscous and do not flow over practical timescales until sufficient stress is applied. This behavior originates from restricted mobility of the constituents arrested in disordered structures of varying length scales, termed colloidal glasses and gels. Usually these materials are thermodynamically out of equilibrium, which induces a time-dependent evolution of the structure and the properties. This review presents an overview of the rheological behavior of this class of materials. We discuss the experimental observations and theoretical developments regarding the microstructure of these materials, emphasizing the complex coupling between the deformation field and nonequilibrium structures in colloidal glasses and gels, which leads to a rich array of rheological behaviors with profound implications for various industrial processes and products.

Colloidal gelation with variable attraction energy

We present an approximation scheme to the master kinetic equations for aggregation and gelation with thermal breakup in colloidal systems with variable attraction energy. With the cluster fractal dimension df as the only phenomenological parameter, rich physical behavior is predicted. The viscosity, the gelation time, and the cluster size are predicted in closed form analytically as a function of time, initial volume fraction, and attraction energy by combining the reversible clustering kinetics with an approximate hydrodynamic model. The fractal dimension df modulates the time evolution of cluster size, lag time and gelation time, and of the viscosity. The gelation transition is strongly nonequilibrium and time-dependent in the unstable region of the state diagram of colloids where the association rate is larger than the dissociation rate. Only upon approaching conditions where the initial association and the dissociation rates are comparable for all species (which is a condition for the detailed balance to be satisfied) aggregation can occur with df = 3. In this limit, homogeneous nucleation followed by Lifshitz-Slyozov coarsening is recovered. In this limited region of the state diagram the macroscopic gelation process is likely to be driven by large spontaneous fluctuations associated with spinodal decomposition.

Morphogenetic Transition in Weak Gelation of Crystallizable Linear Polymers

Fibrillar networks and spherulite assemblies are the two most frequently observed textures in weak gelation of crystallizable linear polymers. We find such two textures in response to the kinetic distinction between instability/spinodal and metastability/nucleation of the polymer crystallization and prove the morphogenetic transition in between. Moreover, it comes as a surprise when such a transition exhibits a spinodal singularity that reveals a mean-field-like "mesoscopic" phase transition behavior.

Mesoporous organohydrogels from thermogelling photocrosslinkable nanoemulsions

We report the formation of mesoporous organohydrogels from oil-in-water nanoemulsions containing an end-functionalized oligomeric gelator in the aqueous phase. The nanoemulsions exhibit an abrupt thermoreversible transition from a low-viscosity liquid to a fractal-like colloidal gel of droplets with mesoscale porosity and solid-like viscoelasticity with moduli approaching 100 kPa, possibly the highest reported for an emulsion-based system. We hypothesize that gelation is brought about by temperature-induced interdroplet bridging of the gelator, as shown by its dependence on the gelator chemistry. The use of photocrosslinkable gelators enables the freezing of the nanoemulsion's microstructure into a soft hydrogel nanocomposite containing a large fraction of dispersed liquid hydrophobic compartments, and we show its use in the encapsulation and release of lipophilic biomolecules. The tunable structural, mechanical and optical properties of these organohydrogels make them a robust material platform suitable for a wide range of applications.

Dynamical arrest, percolation, gelation, and glass formation in model nanoparticle dispersions with thermoreversible adhesive interactions

We report an experimental study of the dynamical arrest transition for a model system consisting of octadecyl coated silica suspended in n-tetradecane from dilute to concentrated conditions spanning the state diagram. The dispersion's interparticle potential is tuned by temperature affecting the brush conformation leading to a thermoreversible model system. The critical temperature for dynamical arrest, T*, is determined as a function of dispersion volume fraction by small-amplitude dynamic oscillatory shear rheology. We corroborate this transition temperature by measuring a power-law decay of the autocorrelation function and a loss of ergodicity via fiber-optic quasi-elastic light scattering. The structure at T* is measured using small-angle neutron scattering. The scattering intensity is fit to extract the interparticle pair-potential using the Ornstein-Zernike equation with the Percus-Yevick closure approximation, assuming a square-well interaction potential with a short-range interaction (1% of particle diameter). (1) The strength of attraction is characterized using the Baxter temperature (2) and mapped onto the adhesive hard sphere state diagram. The experiments show a continuous dynamical arrest transition line that follows the predicted dynamical percolation line until ϕ ≈ 0.41 where it subtends the predictions toward the mode coupling theory attractive-driven glass line. An alternative analysis of the phase transition through the reduced second virial coefficient B(2)* shows a change in the functional dependence of B(2)* on particle concentration around ϕ ≈ 0.36. We propose this signifies the location of a gel-to-glass transition. The results presented herein differ from those observed for depletion flocculated dispersion of micrometer-sized particles in polymer solutions, where dynamical arrest is a consequence of multicomponent phase separation, suggesting dynamical arrest is sensitive to the physical mechanism of attraction.

Mode-coupling theory for the glass transition: test of the convolution approximation for short-range interactions

We reexamine the convolution approximation commonly used in the mode-coupling theory (MCT) of nonergodic states of classical fluids. This approximation concerns the static correlation functions used as input in the MCT treatment of the dynamics. Besides the hard-sphere model, we consider interaction potentials that present a short-range tail, either attractive or repulsive, beyond the hard core. By using accurate static correlation functions obtained from the fundamental measures functional for hard spheres, we show that the role of three-body direct correlations can be more significant than what is inferred from previous simple ansatzs for pure hard spheres. This may in particular impact the location of the glass transition line and the nonergodicity parameter.

Effect of surfactants on shear-induced gelation and gel morphology of soft strawberry-like particles

The role of surfactant type in the aggregation and gelation of strawberry-like particles induced by intense shear without any electrolyte addition is investigated. The particles are composed of a rubbery core, partially covered by a plastic shell, and well stabilized by fixed (sulfate) charges in the end group of the polymer chains originating from the initiator. In the absence of any surfactant, after the system passes through a microchannel at a Peclet number equal to 220 and a particle volume fraction equal to 0.15, not only shear-induced gelation but also partial coalescence among the particles occurs. The same shear-induced aggregation/gelation process has been carried out in the presence of an ionic (sulfonate) surfactant or a nonionic (Tween 20) steric surfactant. It is found that for both surfactants shear-induced gelation does occur at low surfactant surface density but the conversion of the primary particles to the clusters constituting the gel decreases as the surfactant surface density increases. When the surfactant surface density increases above certain critical values, shear-induced gelation and eventually even aggregation do not occur any longer. For the sulfonate surfactant, this was explained in the literature by the non-DLVO, short-range repulsive hydration forces generated by the adsorbed surfactant layer. In this work, it is shown that the steric repulsion generated by the adsorbed Tween 20 layer can also protect particles from aggregation under intense shear. Moreover, the nonionic steric surfactant can also protect the strawberry-like particles from coalescence. This implies a decrease in the fractal dimension of the clusters constituting the gel from 2.76 to 2.45, which cannot be achieved using the ionic sulfonate surfactant.

Activated dynamics in dense fluids of attractive nonspherical particles. I. Kinetic crossover, dynamic free energies, and the physical nature of glasses and gels

We apply the center-of-mass versions of naïve mode coupling theory and nonlinear Langevin equation theory to study how short-range attractive interactions modify the onset of localization, activated single-particle dynamics, and the physical nature of the transiently arrested state of a variety of dense nonspherical particle fluids (and the spherical analog) as a function of volume fraction and attraction strength. The form of the dynamic crossover boundary depends on particle shape, but the reentrant glass-fluid-gel phenomenon and the repulsive glass-to-attractive glass crossover always occur. Diverse functional forms of the dynamic free energy are found for all shapes including glasslike, gel-like, a glass-gel form defined by the coexistence of two localization minima and two activation barriers, and a "mixed" attractive glass characterized by a single, very short localization length but an activation barrier located at a large displacement as in repulsive-force caged glasses. For the latter state, particle trajectories are expected to be of a two-step activated form and can be accessed at high attraction strength by increasing volume fraction, or by increasing attraction strength at fixed high enough volume fraction. A new classification scheme for slow dynamics of fluids of dense attractive particles is proposed based on specification of both the nature of the localized state and the particle displacements required to restore ergodicity via activated barrier hopping. The proposed physical picture appears to be in qualitative agreement with recent computer simulations and colloid experiments.

Stochastic qualifier of gel and glass transitions in laponite suspensions

The existence of the important similarities between gelation and glass transition makes it hard to distinguish between the two types of nonergodic states experimentally. Here, we report on a stochastic analysis of the scattered light intensity through a colloidal particles suspension during the gel and glass formation. In this analysis, we exploit the methods developed for complex hierarchical systems, such as turbulence. Using the multiplicative log-normal cascade models, we provide a criterion to distinguish gels from glasses.

Structural and dynamical features of multiple metastable glassy states in a colloidal system with competing interactions

Systems in which a short-ranged attraction and long-ranged repulsion compete are intrinsically frustrated, leading their structure and dynamics to be dominated either by mesoscopic order or by metastable disorder. Here, we report the latter case in a colloidal system with long-ranged electrostatic repulsions and short-ranged depletion attractions. We find a variety of states exhibiting slow nondiffusive dynamics: a gel, a glassy state of clusters, and a state reminiscent of a Wigner glass. Varying the interactions, we find a continuous crossover between the Wigner and cluster glassy states, and a sharp discontinuous transition between the Wigner glassy state and gel. Our results suggest that a balance between repulsions and attractions controls the nature of dynamic arrest of these glassy states.

Amorphous freezing in two dimensions: from soft coils to rigid particles

The topic of the gel transition in two dimensions is revisited by considering data on the shear elasticity of Langmuir monolayers of different spherical objects. Amorphous freezing can be associated to structural percolation in a lattice able to resist shear stresses. The shear modulus and its dependence on the packing fraction are found to strongly depend on the details of the interaction potential and largely differ from expectations for entropic networks. This behaviour can be interpreted in terms of more elaborated percolation theories including central forces and bond-bending forces.

Elasticity of arrested short-ranged attractive colloids: homogeneous and heterogeneous glasses

We evaluate the elasticity of arrested short-ranged attractive colloids by combining an analytically solvable elastic model with a hierarchical arrest scheme. This new approach allows us to discriminate the microscopic (primary particle-level) from the mesoscopic (cluster-level) contribution to the macroscopic shear modulus. The results quantitatively predict experimental data in a wide range of volume fractions and indicate in which cases the relevant contribution is due to mesoscopic structures. On this basis we propose that different arrested states of short-ranged attractive colloids can be meaningfully distinguished as homogeneous or heterogeneous colloidal glasses in terms of the length scale which controls their elastic behavior.

Geometric frustration in small colloidal clusters

We study the structure of clusters in a model colloidal system with competing interactions using Brownian dynamics simulations. A short-ranged attraction drives clustering, while a weak, long-ranged repulsion is used to model electrostatic charging in experimental systems. The former is treated with a short-ranged Morse attractive interaction, the latter with a repulsive Yukawa interaction. We consider the yield of clusters of specific structure as a function of the strength of the interactions, for clusters with m = 3,4,5,6,7,10 and 13 colloids. At sufficient strengths of the attractive interaction (around 10k(B)T), the average bond lifetime approaches the simulation timescale and the system becomes nonergodic. For small clusters, m≤5, where geometric frustration is not relevant, despite nonergodicity, for sufficient strengths of the attractive interaction the yield of clusters which maximize the number of bonds approaches 100%. However for m = 7 and higher, in the nonergodic regime we find a lower yield of these structures where we argue geometric frustration plays a significant role. m = 6 is a special case, where two structures, of octahedral and C(2v) symmetry, compete, with the latter being favoured by entropic contributions in the ergodic regime and by kinetic trapping in the nonergodic regime. We believe that our results should be valid as long as the one-component description of the interaction potential is valid. A system with competing electrostatic repulsions and van der Waals attractions may be such an example. However, in some cases, the one-component description of the interaction potential may not be appropriate.

A closer look at arrested spinodal decomposition in protein solutions

Concentrated aqueous solutions of the protein lysozyme undergo a liquid-solid transition upon a temperature quench into the unstable spinodal region below a characteristic arrest temperature of T(f) = 15 °C. We use video microscopy and ultra-small angle light scattering in order to investigate the arrested structures as a function of initial concentration, quench temperature and rate of the temperature quench. We find that the solid-like samples show all the features of a bicontinuous network that is formed through an arrested spinodal decomposition process. We determine the correlation length ξ and demonstrate that ξ exhibits a temperature dependence that closely follows the critical scaling expected for density fluctuations during the early stages of spinodal decomposition. These findings are in agreement with an arrest scenario based on a state diagram where the arrest or gel line extends far into the unstable region below the spinodal line. Arrest then occurs when during the early stage of spinodal decomposition the volume fraction φ(2) of the dense phase intersects the dynamical arrest threshold φ(2,Glass), upon which phase separation gets pinned into a space-spanning gel network with a characteristic length ξ.