Clustering and mechanics in dense depletion and thermal gels

Memory in aging colloidal gels with time-varying attraction

We report a combined rheology, x-ray photon correlation spectroscopy, and modeling study of gel formation and aging in suspensions of nanocolloidal spheres with volume fractions of 0.20 and 0.43 and with a short-range attraction whose strength is tuned by changing temperature. Following a quench from high temperature, where the colloids are essentially hard spheres, to a temperature below the gel point, the suspensions form gels that undergo aging characterized by a steadily increasing elastic shear modulus and slowing, increasingly constrained microscopic dynamics. The aging proceeds at a faster rate for stronger attraction strength. When the attraction strength is suddenly lowered during aging, the gel properties evolve non-monotonically in a manner resembling the Kovacs effect in glasses, in which the modulus decreases and the microscopic dynamics become less constrained for a period before more conventional aging resumes. Eventually, the properties of the gel following the decrease in attraction strength converge to those of a gel that has undergone aging at the lower attraction strength throughout. The time scale of this convergence increases as a power law with the age at which the attraction strength is decreased and decreases exponentially with the magnitude of the change in attraction. A model for gel aging in which particles attach and detach from the gel at rates that depend on their contact number reproduces these trends and reveals that the non-monotonic behavior results from the dispersion in the rates that the populations of particles with different contact number adjust to the new attraction strength.

Colloidal Gelation through Thermally Triggered Surfactant Displacement

Colloidal systems that undergo gelation attract much attention in both fundamental studies and practical applications. Rational tuning of interparticle interactions allows researchers to precisely engineer colloidal material properties and microstructures. Here, contrary to the traditional approaches where modulating attractive interactions is the major focus, we present a platform wherein colloidal gelation is controlled by tuning repulsive interactions. By including amphiphilic oligomers in colloidal suspensions, the ionic surfactants on the colloids are replaced by the nonionic oligomer surfactants at elevated temperatures, leading to a decrease in electrostatic repulsion. The mechanism is examined by carefully characterizing the colloids, and subsequently allowing the construction of interparticle potentials to capture the material behaviors. With the thermally triggered surfactant displacement, the dispersion assembles into a macroporous viscoelastic network and the gelling mechanism is robust over a wide range of compositions, colloid sizes, and component chemistries. This stimulus-responsive gelation platform is general and offers new strategies to engineer complex viscoelastic soft materials.

Dynamic Scaling of Colloidal Gel Formation at Intermediate Concentrations

We have examined the formation and dissolution of gels composed of intermediate volume-fraction nanoparticles with temperature-dependent short-range attractions using small-angle x-ray scattering, x-ray photon correlation spectroscopy, and rheology to obtain nanoscale and macroscale sensitivity to structure and dynamics. Gel formation after temperature quenches to the vicinity of the rheologically determined gel temperature, T_{gel}, was characterized via the slowdown of dynamics and changes in microstructure observed in the intensity autocorrelation functions and structure factor, respectively, as a function of quench depth (ΔT=T_{quench}-T_{gel}), wave vector, and formation time t_{f}. We find the wave-vector-dependent dynamics, microstructure, and rheology at a particular ΔT and t_{f} map to those at other ΔTs and t_{f}s via an effective scaling temperature, T_{s}. A single T_{s} applies to a broad range of ΔT and t_{f} but does depend on the particle size. The rate of formation implied by the scaling is a far stronger function of ΔT than expected from the attraction strength between colloids. We interpret this strong temperature dependence in terms of cooperative bonding required to form stable gels via energetically favored, local structures.

Structural arrest and dynamic localization in biocolloidal gels

Casein micelles interacting via an entropic intermediate-ranged depletion attraction exhibit a fluid-to-gel transition due to arrested spinodal decomposition. The bicontinuous networked structure of the gel freezes shortly after formation. We determine the timescales of structural arrest from the build-up of network rigidity after pre-shear rejuvenation, and find that the arrest time as well as the plateau elastic modulus of the gel diverge as a function of the volume fraction and interaction potential. Moreover, we show using scaling from naïve mode coupling theory that their mechanical properties are dictated by their microscopic dynamics rather than their heterogeneous large scale structure.

Concentration-dependent effective attractions between PEGylated nanoparticles

Effective attractions between colloidal particles bearing a grafted PEG layer in water have been studied and, from a quantitative SANS analysis, are found to be concentration dependent.

Role of shear-induced dynamical heterogeneity in the nonlinear rheology of colloidal gels

We report the effect of flow-induced dynamical heterogeneity on the nonlinear elastic modulus of weakly aggregated colloidal gels that have undergone yielding by an imposed step strain deformation. The gels are comprised of sterically stabilized poly(methyl methacrylate) colloids interacting through short-ranged depletion attractions. When a step strain of magnitude varying from γ = 0.1 to 80.0 is applied to the quiescent gels, we observe the development of a bimodal distribution in the single-particle van Hove self-correlation function. This distribution is consistent with the existence of a fast and slow subpopulation of colloids within sheared gels. We evaluate the effect of incorporating the properties of the slow, rigid subpopulation of the colloids into a recent mode coupling theory for the nonlinear elasticity of colloidal gels.

Echoes in x-ray speckles track nanometer-scale plastic events in colloidal gels under shear

We report x-ray photon correlation spectroscopy experiments on a concentrated nanocolloidal gel subject to in situ oscillatory shear strain. The strain causes periodic echoes in the speckle pattern that lead to peaks in the intensity autocorrelation function. Above a threshold strain that is near the first yield point of the gel, the peak amplitude decays exponentially with the number of shear cycles, signaling irreversible particle rearrangements. The wave-vector dependence of the decay rate reveals a power-law distribution in the size of regions undergoing shear-induced rearrangement. The gel also displays strain softening well below the threshold, indicating a range of strains at which the rheology is nonlinear but the microscopic deformations are reversible.

Mechanical properties of self-assembled Fmoc-diphenylalanine molecular gels

We explore the phase diagram and mechanical properties of molecular gels produced from mixing water with a dimethyl sulfoxide (DMSO) solution of the aromatic dipeptide derivative fluorenylmethoxycarbonyl-diphenylalanine (Fmoc-FF). Highly soluble in DMSO, Fmoc-FF assembles into fibrous networks that form gels upon addition of water. At high water concentrations, rigid gels can be formed at Fmoc-FF concentrations as low as 0.01 wt %. The conditions are established defining the Fmoc-FF and water concentrations at which gels are formed. Below the gel boundary, the solutions are clear and colorless and have long-term stability. Above the gel boundary, gels are formed with increasing rapidity with increasing water or Fmoc-FF concentrations. A systematic characterization of the effect of Fmoc-FF and water concentrations on the mechanical properties of the gels is presented, demonstrating that the elastic behavior of the gels follows a specific, robust scaling with Fmoc-FF volume fraction. Furthermore, we characterize the kinetics of gelation and demonstrate that these gels are reversible in the sense that they can be disrupted mechanically and rebuild strength over time.

Autonomic composite hydrogels by reactive printing: materials and oscillatory response

Autonomic materials are those that automatically respond to a change in environmental conditions, such as temperature or chemical composition. While such materials hold incredible potential for a wide range of uses, their implementation is limited by the small number of fully-developed material systems. To broaden the number of available systems, we have developed a post-functionalization technique where a reactive Ru catalyst ink is printed onto a non-responsive polymer substrate. Using a succinimide-amine coupling reaction, patterns are printed onto co-polymer or biomacromolecular films containing primary amine functionality, such as polyacrylamide (PAAm) or poly-N-isopropyl acrylamide (PNIPAAm) copolymerized with poly-N-(3-Aminopropyl)methacrylamide (PAPMAAm). When the films are placed in the Belousov-Zhabotinsky (BZ) solution medium, the reaction takes place only inside the printed nodes. In comparison to alternative BZ systems, where Ru-containing monomers are copolymerized with base monomers, reactive printing provides facile tuning of a range of hydrogel compositions, as well as enabling the formation of mechanically robust composite monoliths. The autonomic response of the printed nodes is similar for all matrices in the BZ solution concentrations examined, where the period of oscillation decreases in response to increasing sodium bromate or nitric acid concentration. A temperature increase reduces the period of oscillations and temperature gradients are shown to function as pace-makers, dictating the direction of the autonomic response (chemical waves).

Polymer-mediated clustering of charged anisotropic colloids

Formation of stable, dense nanoparticle clusters is interesting due to both the underlying physics and use of nanoclusters in applications such as digital printing, imaging and biosensing, and energy storage. Here, we explore formation of nanoparticle clusters in dispersions of the model disk-shaped colloid Laponite. Under basic conditions, the model disk-shaped colloid Laponite forms a repulsive glass in water due to strong electrostatic interactions. Addition of a nonadsorbing polymer, the sodium salt of poly(acrylic acid) (PAA), induces a depletion attraction between particles. Through dynamic light scattering (DLS) and rheology, we see that the polymer initially causes a transition from the glassy phase to an ergodic fluid. Samples at higher particle concentration age to a weak nonergodic state, while samples at lower Laponite remain as fluids. As the strength of attraction between particles is increased, we find an increase in the fast relaxation time measured via dynamic light scattering (e.g., slowing of the short-time diffusion of a single particle). While this may in part be attributed to an increase in the ionic strength, the aging behavior and glass-fluid transition we observe appear to be unique to the presence of polymer, suggesting that depletion plays an important role. DLS data on the fluid samples were consistent with two widely spaced diffusive relaxation modes, corresponding to motion of single particles and motion of large clusters, although other slow dynamic processes may be present. On the basis of the estimated volume fraction and depletion attraction, we believe the Laponite-PAA suspensions to be either fluids of stable clusters or glasses of clusters, although it is possible that the nonergodic state we observe is instead a gel of clusters. Additionally, the cluster size was found to be stable for at least 120 days and was directly related to the polymer concentration. This may serve as an important means of tuning cluster size in products and processes based on dense nanoparticle assemblies.

Theory of kinetic arrest, elasticity, and yielding in dense binary mixtures of rods and spheres

We extend the quiescent and stressed versions of naïve mode coupling theory to treat the dynamical arrest, shear modulus, and absolute yielding of particle mixtures where one or more species is a nonrotating nonspherical object. The theory is applied in detail to dense isotropic "chemically matched" mixtures of variable aspect ratio rods and spheres that interact via repulsive and short range attractive site-site pair potentials. A remarkably rich ideal kinetic arrest behavior is predicted with up to eight "dynamical phases" emerging: an ergodic fluid, partially localized states where the spheres remain fluid but the rods can be a gel, repulsive glass or attractive glass, doubly localized glasses and gels, a porous rod gel plus sphere glass, and a narrow window where a type of rod glass and gel localization coexist. Dynamical complexity increases with rod length and the introduction of attractive forces between all species which both enhance gel network formation. Multiple dynamic reentrant features and triple points are predicted, and each dynamic phase has unique particle localization characteristics and mechanical properties. Orders of magnitude variation of the linear shear modulus and absolute yield stress are found as rod length, mixture composition and the detailed nature of interparticle attractions are varied. The interplay of total (high) mixture packing fraction and composition at fixed temperature is also briefly studied. The present work provides a foundation to study more complex rod-sphere mixtures of both biological and synthetic interest that include physical features such as interaction site size asymmetry, rod-sphere specific attractions, and/or Coulomb repulsion.

Percolation, phase separation, and gelation in fluids and mixtures of spheres and rods

The relationship between kinetic arrest, connectivity percolation, structure and phase separation in protein, nanoparticle, and colloidal suspensions is a rich and complex problem. Using a combination of integral equation theory, connectivity percolation methods, naïve mode coupling theory, and the activated dynamics nonlinear Langevin equation approach, we study this problem for isotropic one-component fluids of spheres and variable aspect ratio rigid rods, and also percolation in rod-sphere mixtures. The key control parameters are interparticle attraction strength and its (short) spatial range, total packing fraction, and mixture composition. For spherical particles, formation of a homogeneous one-phase kinetically stable and percolated physical gel is predicted to be possible, but depends on non-universal factors. On the other hand, the dynamic crossover to activated dynamics and physical bond formation, which signals discrete cluster formation below the percolation threshold, almost always occurs in the one phase region. Rods more easily gel in the homogeneous isotropic regime, but whether a percolation or kinetic arrest boundary is reached first upon increasing interparticle attraction depends sensitively on packing fraction, rod aspect ratio and attraction range. Overall, the connectivity percolation threshold is much more sensitive to attraction range than either the kinetic arrest or phase separation boundaries. Our results appear to be qualitatively consistent with recent experiments on polymer-colloid depletion systems and brush mediated attractive nanoparticle suspensions.

Impact of solvent quality on nanoparticle dispersion in semidilute and concentrated polymer solutions

We investigated how solvent quality affects the stability of polymer-grafted nanoparticles in semidilute and concentrated polymer solutions, which extends our previous studies on these types of dispersions in good solvents [Langmuir 2008, 24, 5260-5269]. As discussed in the current article, dynamic light scattering (DLS) was used to quantify the diffusion of polydimethylsiloxane-grafted silica nanoparticles, or PDMS-g-silica, in bromocyclohexane as well as in PDMS/bromocyclohexane solutions. We established that bromocyclohexane is a theta solvent for PDMS by varying the temperature of the solutions with PDMS-g-silica nanoparticles and detecting their aggregation at a theta temperature of T(Θ) = 19.6 °C. Using this temperature as a benchmark for the transition between good and bad solvent conditions, further stability tests were carried out in semidilute and concentrated polymer solutions of PDMS in bromocyclohexane at T = 10-60 °C. Irrespective of temperature, i.e., solvent quality, we found that the nanoparticles dispersed uniformly when molecular weight of the graft polymer was greater than that of the free polymer. However, when the free polymer molecular weight was greater than that of the graft polymer, the nanoparticles aggregated. Visual studies were also used to confirm the correspondence between nanoparticle stability and graft and free polymer molecular weights in a wide range of marginally poor solvents with PDMS. Further, the correspondence between nanoparticle stability and instability with graft and free polymer molecular weight and solvent quality was also supported with self-consistent mean-field calculations. Thus, by relating experiment and theory, our results indicate that nanoparticle stability in semidilute and concentrated polymer solutions is governed by interactions between the graft and free polymers under conditions of variable solvency.

Self-organization in the flow of complex fluids (colloid and polymer systems): part 1: experimental evidence

Different types of regular and irregular self-organized structures observed in deformation of colloid and polymer substances ("complex fluids") are discussed and classified. This review is focused on experimental evidence of structure formation and self-organization in shear flows, which have many similar features in systems of different types. For single-phase (uniform) polymer systems regular periodic surface structures are observed. Two main types of these structures are possible: small-scale regular screw-like periodic structures along the whole stream (usually called "shark-skin") and long-period smooth and distorted parts of a stream attributed as a "stick-slip" effect. The origin of surface irregularities of both types is elasticity of a liquid. In the limiting case of high enough Weissenberg numbers, medium loses fluidity and should be treated as a rubbery matter. The liquid-to-rubbery transition at high Weissenberg numbers is considered as the dominating mechanism of instability, leading in particular to the wall slip and rupture of a stream. Secondary flows ("vorticity") in deformation polymeric substances and complex fluids are also obliged to their elasticity and the observed Couette-Taylor-like cells, though being similar to well-known inertial secondary flows, are completely determined by elasticity of colloid and polymeric systems. In deformation of colloidal systems, suspensions and other dense concentrated heterophase materials, structure formation takes place at rest and the destroying of the structure happens as the yield stress. In opposite to this case, strong deformations can lead to the shear-induced structure formation and jamming. These effects are of general meaning for any complex fluids as well as for dense suspensions and granular media. Strong deformations also lead to separation of a stream into different parts (several "bands") with various properties of liquids in these parts. So, two principal effects common for any polymers and complex fluids can be pointed at as the physical origin of self-organization in shearing. This is elasticity of a liquid and a possibility of its existence in different phases or relaxation states, while in many cases elasticity of a fluid is considered as the most important provoking factor for transitions between different types of rheological behavior, e.g. the fluid-to-rubbery-like behavior at high deformation rates and the transition from the real laminar flow to wall slip.

Rheology and microstructure of polymer nanocomposite melts: variation of polymer segment-surface interaction

We have studied the effects of particle packing fraction, polymer molecular weight (MW), and polymer-segment-particle-surface affinity on the phase behavior of 44 nm silica dispersions in unentangled, low MW polyethylene oxide (PEO), polyethylene oxide dimethyl ether (PEODME), and polytetrahydrofuran (PTHF) through rheological measurement and small-angle X-ray scattering. Particles are shown to be stable in PEO nanocomposites up to high volume fractions due to an adsorbed layer of polymer segments that stabilizes particles in the melt. Comparison of the PEO nanocomposite to PEODME and PTHF nanocomposites reveals little evidence of an adsorbed layer in the spirit of the PEO nanocomposite. Measurement of the PTHF nanocomposite viscosity reveals evidence of segment slip at the particle surface by the particle intrinsic viscosity being less than Einstein's value. At higher particle volume fractions, the viscosity diverges, yielding an elastic response. The elastic response of the PEO nanocomposite has the signatures of a colloidal glass, while the PEODME and PTHF nanocomposites resemble a gel. Measurement of the particle structure factor reveals a change from overall repulsive particles in PEO to attractive particles in PTHF as the segment-surface interaction is changed.

Connecting nanoscale motion and rheology of gel-forming colloidal suspensions

We report a combined x-ray photon correlation spectroscopy and rheometry study of moderately concentrated suspensions of silica colloids that form a gel on cooling. During gel formation, the suspensions acquire a shear modulus that increases with time, while the thermal motion of the colloids becomes localized over an increasingly restricted range. The nanometer-scale localization length characterizing this motion obeys an exact relationship with the shear modulus predicted theoretically from mode coupling calculations [K. S. Schweizer and G. Yatsenko, J. Chem. Phys. 127, 164505 (2007)]. This scaling thus demonstrates a direct quantitative connection between the microscopic dynamics and macroscopic rheology. It further indicates the importance of local structure over longer-range correlations in dictating the dynamical and mechanical properties of such gels.

Relationship between microstructure, dynamics, and rheology in polymer-bridging colloidal gels

We investigate the link between the microstructure, dynamics, and rheological properties in dense (phi = 0.3) mixtures of charge-stabilized colloidal silica and oppositely charged poly(ethylene imine) polymer in a mixed DMSO/H(2)O solvent. Over a finite range of polymer concentrations, the addition of polymer results in the formation of sample-spanning, self-supporting gel networks. As the polymer concentration is increased, a reentrant rheological transition is observed where the gel's elastic modulus and yield stress initially increase and subsequently drop. The dynamic and microstructural changes associated with this transition are resolved using quantitative confocal microscopy. Within the initial regime, a biphasic system consisting of a mixture of arrested and diffusive particles is observed. We segregate the particles with high accuracy into mobile and arrested populations based on their dynamics. The addition of polymer in this regime systematically decreases the proportion of free particles, until all the particles are arrested. Concurrent with this transition, the elastic modulus and yield stress go through their corresponding maxima. However, over the range of polymer concentrations studied, the reentrant transition to weak gels is not captured by the particle dynamics but is instead accompanied by subtle changes in the microstructure of the arrested phase. We discuss two possible scenarios for this behavior in view of the strength of interparticle bonds.

A metastable van der waals gel: transitioning from weak to strong attractions

Here we describe a method to create gels where the gel point is decoupled from gel elastic properties. Working with charge stabilized polystyrene latex particles with diameters, D, of 508-625 nm at ionic strengths of 0.1-1 M, the gel volume fraction is varied from 0.10-0.35 through the addition of less than monolayer coverage of hexaethylene glycol monododecyl ether (C6E12). At each surfactant concentration, the gel volume fraction depends on the background ionic strength. The changes in gel point with surfactant concentration suggest the strength of interparticle attraction decreases with increasing surfactant concentration. These changes are not reflected in the gel moduli, which are independent of surfactant concentration and ionic strength. We propose a model to describe this behavior based on gelation due to localization in a shallow truncated van der Waals minimum produced by the surfactant acting as a steric stabilizing layer. The surfactant remains mobile on the surface. Below the gel volume fraction, the time particles spend in the truncated well are not sufficient for the surfactant to be displaced such that the particles can only sample the shallow well. Above the gel volume fraction, particles are localized in the truncated van der Waals minima for sufficient periods of time to displace the surfactant layers with the result being that the particles fall into a primary van der Waals minimum. The result is gel points sensitive to surfactant concentration but moduli that are independent of the gel volume fraction.

Structure and dynamics of biphasic colloidal mixtures

We investigate the structure and dynamics of biphasic colloidal mixtures composed of coexisting attractive and repulsive microspheres by confocal microscopy. Attractive gels formed in the presence of repulsive microspheres are more spatially homogeneous and, on average, are both more locally tenuous and have fewer large voids than their unary counterparts. The repulsive microspheres within these mixtures display heterogeneous dynamics, with some species exhibiting freely diffusive Brownian motion while others are trapped within the gel network during aggregation.

Response of a colloidal gel to a microscopic oscillatory strain

We study the microscopic mechanical response of colloidal gels by manipulating single probe particles within the network. For this work, we use a refractive index and density-matched suspension of polymethylmethacrylate (PMMA) particles with nonadsorbing polymer: polystyrene. As the polymer concentration increases, a dynamically arrested, space-filling network is formed, exhibiting structural transitions from a clusterlike to a more homogeneous stringlike gel phase, consistent with observations by Dibble and co-workers [C. J. Dibble, M. Kogan, and M. J. Solomon, Phys. Rev. E 74, 041403 (2006)]. In a gel, probe particles are oscillated with an optical trap, creating the local strain field in the network. We find that the micromechanics correlate strongly with the gel structure. At high polymer concentration, the average deformation field decays as 1/r to a distance quite close to the probe particle, as expected for a purely elastic material. In contrast, at lower polymer concentrations, gels exhibit anomalous strain fields in the near field; the strain plateaus, indicating that many particles move together with the probe. By rescaling the probe size in the theoretical model, we obtain a micromechanical gel correlation length, which is consistent with the structural difference in terms of "clusterlike" and "stringlike."

Yielding behavior of thermo-reversible colloidal gels

The breakdown of structure in gelled suspensions due to the application of an external stress results in flow. Here we explore the onset of flow by investigating the onset of nonlinear behavior in the elastic moduli of a widely studied class of thermo-reversible gels over a range of volume fractions. We employ the system composed of octadecyl-coated silica particles (radius = 24 nm) suspended in decalin that displays a transition from a liquid to a gel below a volume-fraction-dependent gel temperature, Tgel. The perturbative yield stress at which the gel modulus drops to 90% of its value in the linear viscoelastic limit is found to increase monotonically with volume fraction and decreasing temperature. The recently proposed activated barrier-hopping theory of Schweizer and co-workers1,2 presents a framework to capture the impact of external forces on the mechanical properties of structurally arrested systems. By characterizing particle interactions with a Yukawa potential and employing the resultant static structure factor as input into the activated barrier-hopping theory, we make predictions for how the elastic modulus evolves with the applied stress. Comparisons of these calculations with experiments reveal that the theory does an excellent job of quantitatively capturing the perturbative yield stresses over the entire range of volume fractions and temperatures explored in the study. The match of predictions with experimental results suggests that the theory not only captures particle localization but also how this localization is modulated in the presence of an external stress.

Formation of Fibrous Materials from Dense Calcium Caseinate Dispersions

Application of shear and cross-linking enzyme transglutaminase (Tgase) induced fibrous hierarchical structures in dense (30% w/w) calcium caseinate (Ca-caseinate) dispersions. Using Tgase was essential for the anisotropic structure formation. The fibrous materials showed anisotropy on both micro- and macroscale as determined with scanning electron microscopy (SEM) and mechanical analyses, respectively. SEM revealed protein fibers with a diameter of approximately 100-200 nm; visually, we observed fibers of about 1 mm. Both shear and Tgase affected the reinforcement of the fibers to a large extent, whereas the mechanical properties in the direction perpendicular to the shear flow remained constant. Shearing Ca-caseinate without Tgase yielded a slightly anisotropic layered structure. Both cross-linking in the absence of shear and cross-linking during mixing resulted in gels without alignment. The formation of shear- and enzyme-induced anisotropic structures was explained by aligning of protein aggregates due to shear and concurrent solidification of the aligned protein aggregates.

Microstructure of equilibrium fluid clusters in colloid-polymer suspensions

Several studies on colloidal depletion systems have reported the existence of a fluid phase consisting of clusters of particles above a critical polymer concentration that acts as a precursor regime to the gel phase at low colloid volume fractions (phi<or=0.20) . The clusters are found to be stable against further aggregation suggesting that individual particles are localized within a cluster. However the clusters themselves behave as distinct entities in an equilibrium fluid phase. In this study, we probe the internal microstructure of the cluster entities by ultrasmall angle x-ray scattering (USAXS) techniques. These studies reveal that over the accessible length scales, the microstructure of the particle clusters are similar to that observed in dense space-spanning depletion gels. The origin of these clusters is unclear but the scattering patterns as they settle with time reveal that the percolation of the clusters to form space-spanning gels does not influence their internal microstructure. These observations lend support to the hypothesis that the formation of space-spanning depletion gels at a given volume fraction is driven by the percolation of the particle clusters. Settling experiments at phi=0.08 also provide rough estimates of the cluster sizes that appear consistent with the observations from the USAXS experiments.

Steric interactions between physically adsorbed polymer-coated colloidal particles: soft or hard?

The steric interaction potential between colloidal particles imparted by adsorbed polymer layers is directly related to their structure. Due to the complexity of these interfacial structures, the steric potential may behave differently at different interparticle separations. In this study, we proposed a combined model of the equivalent hard-sphere model (EHS) and the Hayter-Penfold/Yukawa model (HPY) to describe the steric potential due to adsorbed homopolymers on colloidal particles. The EHS potential describes the dense train/small-loop region and the HPY potential the more diffuse tail/long-loop region. The steric potential was extracted from the structure factors measured by small-angle neutron scattering (SANS). It was found that this combined model gave better agreement with experimental data than either of its component models alone. This study also shows that the adsorbed polymer layer in a good solvent partially collapses when the layers approach one another, which is also supported by an NMR solvent relaxation study.

Role of solvation forces in the gelation of fumed silica–alcohol suspensions

Aggregation and gelation kinetics of fumed silica were investigated by altering the solvent-surface interactions. Native and surface-modified (hydrophobic) fumed silica particles were dispersed in short-chain linear alcohols. Based on the kinetics of aggregation and gelation, we show that the solvent-surface interactions have a tremendous impact on the bulk suspension properties. The gelation kinetics were qualitatively similar in all of the fumed silica-alcohol samples, and the gel times for all the alcohols were captured on a master curve requiring two parameters. The two parameters, the stability ratio and critical volume fraction, describe the two regimes of gelation. At low concentrations, gelation occurs due to aggregation of the particles diffusing over a potential barrier (15-25 kT). The rate of aggregation and time to gelation then scales with the stability ratio. At high particle loadings, gelation occurs at a critical volume fraction due to localization in a secondary minimum with a depth of 3-4 kT. These observations are supported by evidence of hydrogen bonding between the solvent and the particle, creating oscillatory solvation forces that govern the magnitude of these two parameters.

Structure and dynamics of colloidal depletion gels: coincidence of transitions and heterogeneity

Transitions in structural heterogeneity of colloidal depletion gels formed through short-range attractive interactions are correlated with their dynamical arrest. The system is a density and refractive index matched suspension of 0.20 volume fraction poly(methyl methacyrlate) colloids with the nonadsorbing depletant polystyrene added at a size ratio of depletant to colloid of 0.043. As the strength of the short-range attractive interaction is increased, clusters become increasingly structurally heterogeneous, as characterized by number-density fluctuations, and dynamically immobilized, as characterized by the single-particle mean-squared displacement. The number of free colloids in the suspension also progressively declines. As an immobile cluster to gel transition is traversed, structural heterogeneity abruptly decreases. Simultaneously, the mean single-particle dynamics saturates at a localization length on the order of the short-range attractive potential range. Both immobile cluster and gel regimes show dynamical heterogeneity. Non-Gaussian distributions of single particle displacements reveal enhanced populations of dynamical trajectories localized on two different length scales. Similar dependencies of number density fluctuations, free particle number, and dynamical length scales on the order of the range of short-range attraction suggests a collective structural origin of dynamic heterogeneity in colloidal gels.

Aggregation and gelation kinetics of fumed silica-ethanol suspensions

The kinetics of aggregation and gelation of fumed silica suspended in ethanol were investigated as a function of volume fraction. At low particle concentrations, gelation is well described by aggregation into a primary minimum arising from hydrogen bonding and dispersion forces. The gelation is extremely slow due to an energetic barrier (approximately 25 kT) in the interparticle potential associated with solvation forces. The solvation forces also contribute to the formation of a secondary minimum in the interparticle potential. The depth of this minimum (approximately 3 kT) is sufficient that, at a critical particle concentration, long-range diffusion is arrested due to the short-range attractions and the cooperative nature of particle interactions, as described by mode coupling theory. The presence of the secondary minimum is also observed in the microstructure of the gels studied using X-ray scattering. These observations reinforce the importance of understanding the role of solvent-particle interactions in manipulating suspension properties.

Microstructure and rheology of thermoreversible nanoparticle gels

Naïve mode coupling theory is applied to particles interacting with short-range Yukawa attractions. Model results for the location of the gel line and the modulus of the resulting gels are reduced to algebraic equations capturing the effects of the range and strength of attraction. This model is then applied to thermo reversible gels composed of octadecyl silica particles suspended in decalin. The application of the model to the experimental system requires linking the experimental variable controlling strength of attraction, temperature, to the model strength of attraction. With this link, the model predicts temperature and volume fraction dependencies of gelation and modulus with five parameters: particle size, particle volume fraction, overlap volume of surface hairs, and theta temperature. In comparing model predictions with experimental results, we first observe that in these thermal gels there is no evidence of clustering as has been reported in depletion gels. One consequence of this observation is that there are no additional adjustable parameters required to make quantitative comparisons between experimental results and model predictions. Our results indicate that the naïve mode coupling approach taken here in conjunction with a model linking temperature to strength of attraction provides a robust approach for making quantitative predictions of gel mechanical properties. Extension of model predictions to additional experimental systems requires linking experimental variables to the Yukawa strength and range of attraction.

Surface molecular view of colloidal gelation

We investigate the phase behavior of surface-functionalized silica colloids at both the molecular and macroscopic levels. This investigation allows us to relate collective properties such as aggregation, gelation, and aging directly to molecular interfacial behavior. By using surface-specific vibrational spectroscopy, we reveal dramatic changes in the conformation of alkyl chains terminating submicrometer silica particles. In fluid suspension at high temperatures, the interfacial molecules are in a liquid-like state of conformational disorder. As the temperature is lowered, the onset of gelation is identified by macroscopic phenomena, including changes in turbidity, heat release, and diverging viscosity. At the molecular level, the onset of this transition coincides with straightening of the carbon-carbon backbones of the interfacial molecules. In later stages, their intermolecular crystalline packing improves. It is the increased density of this ordered boundary layer that increases the van der Waals attraction between particles, causing the colloidal gas to aggregate. The approach presented here can provide insights into phase transitions that occur through surface modifications in a variety of colloidal systems.