Elasticity and clustering in concentrated depletion gels

Capturing the impact of protein unfolding on the dynamic assembly of protein networks

The rapid assembly of molecular or nanoscale building blocks into extended arrays is crucial to the construction of functional networks in vivo and in vitro and depends on various factors. One factor seldom considered is the dynamic changes of the building block shape. Folded protein building blocks offer a unique system to investigate dynamic shape changes due to their intrinsic ability to change from a compact and specific folded structure to an extended unfolded structure in response to a perturbation such as force. Here, we use photochemically crosslinked folded protein hydrogels constructed from force labile protein building blocks as a model dynamic shape-changing network system and characterise them by combining time-resolved rheology and small-angle X-ray scattering (SAXS). This approach probes both the load-bearing network structures, using rheology, and network architectures, using SAXS, thereby providing a crosslength scale understanding of the network formation. We propose a triple assembly model for the structural evolution of networks constructed from force labile protein building block consisting of: primary formation where monomeric folded proteins create the preliminary protein network scaffold; a subsequent secondary formation phase, where larger oligomers of protein diffuse to join the preliminary network scaffold; and finally in situ unfolding and relaxation which leads to the mature network structure of connected larger and denser fractal-like clusters. The time-resolved SAXS data provides evidence that protein unfolding occurs on the edges of the fractal-like clusters, resulting in a population of unfolded proteins in the space between clusters. Identifying the key stages of assembly in protein networks constructed from force labile proteins provides a greater understanding of the importance of protein unfolding in hierarchical biomechanics in vivo and creates future opportunities to develop bespoke biomaterials for novel biomedical applications.

Theoretical study of the impact of dilute nanoparticle additives on the shear elasticity of dense colloidal suspensions

Motivated by basic issues in soft matter physics and new experimental work on granule-nanoparticle mixtures, we systematically apply naive mode coupling theory with accurate microstructural input to investigate the elastic shear modulus of highly size asymmetric, dense, chemically complex, colloid-nanoparticle mixtures. Our analysis spans four equilibrium microstructural regimes: (i) entropic depletion induced colloid clustering, (ii) discrete adsorbed nanoparticle layers that induce colloid spatial dispersion, (iii) nanoparticle-mediated tight bridging network formation, and (iv) colloidal contact aggregation via direct attractions. Each regime typically displays a distinctive mechanical response to changing colloid-nanoparticle size ratio, packing fractions, and the strength and spatial range of interparticle attractive and repulsive interactions. Small concentrations of nanoparticles can induce orders of magnitude elastic reinforcements typically involving single or double exponential growth with increasing colloid and/or nanoparticle packing fraction. Depending on the system, the elementary stress scale can be controlled by the colloid volume, the nanoparticle volume, or a combination of both. Connections between local microstructural organization and the mixture elastic shear modulus are established. The collective structure factor of the relatively dilute nanoparticle subsystem exhibits strong spatial ordering and large osmotic concentration fluctuations imprinted by the highly correlated dense colloidal subsystem. The relevance of the theoretical results for experimental mixtures with large size asymmetry, particularly in the context of 3D ink printing and additive manufacturing, are discussed.

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

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

Pairing-specific microstructure in depletion gels of bidisperse colloids

We report the ensemble-averaged and pairing-specific network microstructure formed by short-range depletion attractions in hard sphere-like colloidal systems. Gelation is induced by adding polystyrene molecules at a fixed concentration to colloids with different colloid bidispersity ratios (α = 1, 0.72, and 0.60) across a range of volume fractions (0.10 ≤ ϕ ≤ 0.40). 3D confocal microscopy imaging combined with a scale-invariant feature transform algorithm show that monodisperse colloids pack more efficiently, whereas increasing the size disparity leads to looser, more disordered, and sub-isostatic packings. Categorizing the structures formed by small and large particles reveal that certain cluster configurations may be favored due to the complex interplay between the differences in particle surface areas and attractive potentials. These pairwise bonds assemble to affect the density of tetrahedral and poly-tetrahedral clusters in bidisperse systems. With the exception of non-percolating samples at ϕ = 0.10, increasing the gel volume fraction leads to an increase in the number of nearest neighbors. However, the internal density within each cluster decreases, possibly due to kinetic arrest from the deeper potential wells of tetrahedral clusters at low volume fractions in which vertices are primarily made out of larger particles.

Theoretical analysis of the structure, thermodynamics, and shear elasticity of deeply metastable hard sphere fluids

The structure, thermodynamics, and slow activated dynamics of the equilibrated metastable regime of glass-forming fluids remain a poorly understood problem of high theoretical and experimental interest. We apply a highly accurate microscopic equilibrium liquid state integral equation theory, in conjunction with naïve mode coupling theory of particle localization, to study in a unified manner the structural correlations, thermodynamic properties, and dynamic elastic shear modulus in deeply metastable hard sphere fluids. Distinctive behaviors are predicted including divergent inverse critical power laws for the contact value of the pair correlation function, pressure, and inverse dimensionless compressibility, and a splitting of the second peak and large suppression of interstitial configurations of the pair correlation function. The dynamic elastic modulus is predicted to exhibit two distinct exponential growth regimes with packing fraction that have strongly different slopes. These thermodynamic, structural, and elastic modulus results are consistent with simulations and experiments. Perhaps most unexpectedly, connections between the amplitude of long wavelength density fluctuations, dimensionless compressibility, local structure, and the dynamic elastic shear modulus have been theoretically elucidated. These connections are more broadly relevant to understanding the slow activated relaxation and mechanical response of colloidal suspensions in the ultradense metastable region and deeply supercooled thermal liquids in equilibrium.

Stiffening colloidal gels by solid inclusions

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

Microscopic interactions and emerging elasticity in model soft particulate gels

We discuss a class of models for particulate gels in which the particle contacts are described by an effective interaction combining a two-body attraction and a three-body angular repulsion. Using molecular dynamics, we show how varying the model parameters allows us to sample, for a given gelation protocol, a variety of gel morphologies. For a specific set of the model parameters, we identify the local elastic structures that get interlocked in the gel network. Using the analytical expression of their elastic energy from the microscopic interactions, we can estimate their contribution to the emergent elasticity of the gel and gain new insight into its origin.

Elasticity of colloidal gels: structural heterogeneity, floppy modes, and rigidity

Rheological measurements of model colloidal gels reveal that large variations in the shear moduli as colloidal volume-fraction changes are not reflected by simple structural parameters such as the coordination number, which remains almost a constant. We resolve this apparent contradiction by conducting a normal-mode analysis of experimentally measured bond networks of gels of colloidal particles with short-ranged attraction. We find that structural heterogeneity of the gels, which leads to floppy modes and a nonaffine-affine crossover as frequency increases, evolves as a function of the volume fraction and is key to understanding the frequency-dependent elasticity. Without any free parameters, we achieve good qualitative agreement with the measured mechanical response. Furthermore, we achieve universal collapse of the shear moduli through a phenomenological spring-dashpot model that accounts for the interplay between fluid viscosity, particle dissipation, and contributions from the affine and non-affine network deformation.

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.

Colloidal gel elasticity arises from the packing of locally glassy clusters

Colloidal gels formed by arrested phase separation are found widely in agriculture, biotechnology, and advanced manufacturing; yet, the emergence of elasticity and the nature of the arrested state in these abundant materials remains unresolved. Here, the quantitative agreement between integrated experimental, computational, and graph theoretic approaches are used to understand the arrested state and the origins of the gel elastic response. The micro-structural source of elasticity is identified by the l-balanced graph partition of the gels into minimally interconnected clusters that act as rigid, load bearing units. The number density of cluster-cluster connections grows with increasing attraction, and explains the emergence of elasticity in the network through the classic Cauchy-Born theory. Clusters are amorphous and iso-static. The internal cluster concentration maps onto the known attractive glass line of sticky colloids at low attraction strengths and extends it to higher strengths and lower particle volume fractions.

Linear and nonlinear rheology and structural relaxation in dense glassy and jammed soft repulsive pNIPAM microgel suspensions

We present an integrated experimental and quantitative theoretical study of the mechanics of self-crosslinked, slightly charged, repulsive pNIPAM microgel suspensions over a very wide range of concentrations (c) that span the fluid, glassy and putative "soft jammed" regimes. In the glassy regime we measure a linear elastic dynamic shear modulus over 3 decades which follows an apparent power law concentration dependence G' ∼ c5.64, a variation that appears distinct from prior studies of crosslinked ionic microgel suspensions. At very high concentrations there is a sharp crossover to a nearly linear growth of the modulus. To theoretically understand these observations, we formulate an approach to address all three regimes within a single conceptual Brownian dynamics framework. A minimalist single particle description is constructed that allows microgel size to vary with concentration due to steric de-swelling effects. Using a Hertzian repulsion interparticle potential and a suite of statistical mechanical theories, quantitative predictions under quiescent conditions of microgel collective structure, dynamic localization length, elastic modulus, and the structural relaxation time are made. Based on a constant inter-particle repulsion strength parameter which is determined by requiring the theory to reproduce the linear elastic shear modulus over the entire concentration regime, we demonstrate good agreement between theory and experiment. Testable predictions are then made. We also measured nonlinear rheological properties with a focus on the yield stress and strain. A theoretical analysis with no adjustable parameters predicts how the quiescent structural relaxation time changes under deformation, and how the yield stress and strain change as a function of concentration. Reasonable agreement with our observations is obtained. To the best of our knowledge, this is the first attempt to quantitatively understand structure, quiescent relaxation and shear elasticity, and nonlinear yielding of dense microgel suspensions using microscopic force based theoretical methods that include activated hopping processes. We expect our approach will be useful for other soft polymeric particle suspensions in the core-shell family.

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.

Multiscale Molecular Simulations of Polymer-Matrix Nanocomposites: or What Molecular Simulations Have Taught us About the Fascinating Nanoworld

Following the substantial progress in molecular simulations of polymer-matrix nanocomposites, now is the time to reconsider this topic from a critical point of view. A comprehensive survey is reported herein providing an overview of classical molecular simulations, reviewing their major achievements in modeling polymer matrix nanocomposites, and identifying several open challenges. Molecular simulations at multiple length and time scales, working hand-in-hand with sensitive experiments, have enhanced our understanding of how nanofillers alter the structure, dynamics, thermodynamics, rheology and mechanical properties of the surrounding polymer matrices.

Rheological reversibility and long-term stability of repulsive and attractive nanoemulsion gels

The storage modulus (G′) of a canola oil nanoemulsion gel depends on the storage time and SDS emulsifier concentration.

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.

Unexpected decoupling of stretching and bending modes in protein gels

We show that gels formed by arrested spinodal decomposition of protein solutions exhibit elastic properties in two distinct frequency domains, both elastic moduli exhibiting a remarkably strong dependence on volume fraction. Considering the large difference between the protein size and the characteristic length of the network we model the gels as porous media and show that the high and low frequency elastic moduli can be respectively attributed to stretching and bending modes. The unexpected decoupling of the two modes in the frequency domain is attributed to the length scale involved: while stretching mainly relates to the relative displacement of two particles, bending involves the deformation of a strand with a thickness of the order of a thousand particle diameters.

Rheological investigations on the creaming of depletion-flocculated emulsions

Preventing creaming or sedimentation by the addition of thickeners is an important industrial challenge. We study the effect of the addition of a "free" nonadsorbing polymer (xanthan gum) on the stability against creaming of sterically stabilized O/W emulsions. Therefore, we analyze our samples using microscopy and rheological measurements. At low xanthan concentrations, the emulsions cream. However, above a certain concentration a three-dimensional network of droplets is formed, which can prevent creaming. We attribute the formation of this structure to depletion attraction. The rheological behavior of an emulsion that is macroscopically stable should be elastic, while it should be viscous for a creaming emulsion. In order to distinguish between stable and unstable samples, we measure their relaxation time by mechanical rheology and find a good correlation to the visual observation. However, the measured relaxation times are much shorter than the time-scales, on which we observe creaming. We hypothesize that the measured relaxation time is related to the droplet-droplet interaction. This determines the frequency at which microscopic rearrangements occur, which weaken the network structure prior to creaming. Based on this interpretation, the relaxation time gives direct access to the microstructural processes involved in creaming. We therefore suggest using it as a predictive parameter of creaming stability.

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.

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.

Small-angle X-ray scattering studies of the intact eye lens: effect of crystallin composition and concentration on microstructure

BACKGROUND

The cortex and nucleus of eye lenses are differentiated by both crystallin protein concentration and relative distribution of three major crystallins (alpha, beta, and gamma). Here, we explore the effects of composition and concentration of crystallins on the microstructure of the intact bovine lens (37 degrees C) along with several lenses from Antarctic fish (-2 degrees C) and subtropical bigeye tuna (18 degrees C).

METHODS

Our studies are based on small-angle X-ray scattering (SAXS) investigations of the intact lens slices where we study the effect of crystallin composition and concentration on microstructure.

RESULTS

We are able to distinguish the nuclear and cortical regions by the development of a characteristic peak in the intensity of scattered X-rays. For both the bovine and fish lenses, the peak corresponds to that expected for dense suspensions of alpha-crystallins.

CONCLUSIONS

The absence of the scattering peak in the nucleus indicates that there is no characteristic wavelength for density fluctuations in the nucleus although there is liquid-like order in the packing of the different crystallins. The loss in peak is due to increased polydispersity in the sizes of the crystallins and due to the packing of the smaller gamma-crystallins in the void space of alpha-crystallins.

GENERAL SIGNIFICANCE

Our results provide an understanding for the low turbidity of the eye lens that is a mixture of different proteins. This will inform design of optically transparent suspensions that can be used in a number of applications (e.g., artificial liquid lenses) or to better understand human diseases pathologies such as cataract.

Electric-field-induced yielding of colloidal gels in microfluidic capillaries

We introduce a method to generate a purely internal rupture of colloidal particle gels by application of an electric field as they are confined in a microfluidic device. Characterization of the local, microstructural effect of yielding made possible by the device avoids the complication of shear banding that often occurs in attempts to generate yielding of colloidal gels. The gels are comprised of spherical sterically stabilized poly(methyl methacrylate) particles suspended in a density and refractive index matched organic solvent mixture. Because the particles are charged, application of an electric field imposes a force on the gel body that results in homogeneous internal rupture and yielding. After cessation of the electric field, the gel network rapidly reforms. The structure of the reformed gel differs significantly from the one present prior to the application of the electric field. The microstructural changes that accompany the yielding transition are quantified by comparing confocal microscopy image volumes acquired before and after rupture. We find that the local structure of the colloidal gel after recovery, as quantified by the contact number distribution, is negligibly affected by the yielding transition; however, the long-range structure of the gel, as quantified by spatial fluctuations in number density, is significantly impacted. The result highlights the effect of the small number of short-range bond-breaking events that induce the observed changes in collective, long-range structure.

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.

Collective diffusion in colloid-polymer suspensions: relative role of thermodynamics and hydrodynamics

Theories such as the mode coupling theory (MCT) have seen recent success in predicting the kinetic arrest boundaries and resultant flow properties of colloidal suspensions. A key assumption of such theories is that interparticle forces and equilibrium structure control slow dynamics and gelation, not long-time many-body hydrodynamics. Here we report measurements of short-time collective diffusivities of colloid-polymer suspensions aimed at elucidating the relative contributions of hydrodynamics and thermodynamics as a phase transition or gelation boundary is approached. The experimental system is a hard sphere octadecyl silica suspension to which nonadsorbing polystyrene is added. Two different polymer molecular weights are chosen such that they give rise to a liquid-liquid or a gel transition as the colloid volume fraction or polymer concentration is increased. The short-time diffusivities are measured for each polymer molecular weight as a function of polymer concentration and colloid volume fraction. At a fixed polymer molecular weight and concentration, the colloid volume fraction is varied from dilute to concentrated and near the phase separation boundary. It is found for all measured colloid volume fractions that the diffusivities decrease linearly with increasing strength of the polymer-mediated depletion attraction at a fixed polymer molecular weight. Comparisons are made with theoretical predictions in the dilute limit. When the effects of thermodynamics are normalized out by multiplying the measured diffusivities with the suspension structure factor, it is found that the hydrodynamic effects are essentially those of hard spheres independent of the range and strength of depletion attraction.

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."

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.

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.

Kinetic arrest and glass-glass transition in short-ranged attractive colloids

A thermally reversible repulsive hard-sphere to sticky-sphere transition was studied in a model colloidal system over a wide volume fraction range. The static microstructure was obtained from high resolution small angle x-ray scattering, the colloid dynamics was probed by dynamic x-ray and light scattering, and supplementary mechanical properties were derived from bulk rheology. At low concentration, the system shows features of gas-liquid type phase separation. The bulk phase separation is presumably interrupted by a gelation transition at the intermediate volume fraction range. At high volume fractions, fluid-attractive glass and repulsive glass-attractive glass transitions are observed. It is shown that the volume fraction of the particles can be reliably deduced from the absolute scattered intensity. The static structure factor is modeled in terms of an attractive square-well potential, using the leading order series expansion of Percus-Yevick approximation. The ensemble-averaged intermediate scattering function shows different levels of frozen components in the attractive and repulsive glassy states. The observed static and dynamic behavior are consistent with the predictions of a mode-coupling theory and numerical simulations for a square-well attractive system.

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.

Polymer-bridged gels of nanoparticles in solutions of adsorbing polymers

We use a combination of polymer mean field theory and Monte Carlo simulations to study the polymer-bridged gelation, clustering behavior, and elastic moduli of polymer-nanoparticle mixtures. Polymer self-consistent field theory is first numerically implemented to quantify both the polymer induced interparticle interaction potentials and the conformational statistics of polymer chains between two spherical particles. Subsequently, the formation and structure of polymer-bridged nanoparticle gels are examined using Monte Carlo simulations. Our results indicate a universality in the fractal structure for the polymer-bridged networks over a wide range of parametric conditions. Explicitly, near the gelation transition, the fractal dimension d(f) ranges between 2.2 and 2.5, and above the gelation thresholds, the elastic moduli are found to follow a universal power law G(') proportional, variant(eta-eta(c))(nu(eta) ) with a critical exponent nu(eta) approximately 1.82. The latter suggests strong similarities between polymer-bridging induced percolation and classical elastic resistor network percolation. Our results show a very good agreement with the experimental results for polymer-particle mixtures and suggest a possible framework for experimentally distinguishing the origins of gelation phenomena observed in polymer-particle mixtures.

Microscopic dynamics of recovery in sheared depletion gels

We report x-ray photon correlation spectroscopy and diffusing wave spectroscopy studies of depletion gels formed from nanoscale silica colloids in solutions of nonabsorbing polymer following the cessation of shear. The two techniques provide a quantitatively coherent picture of the dynamics as ballistic or convective motion of colloidal clusters whose internal motion is arrested. While the dynamics possesses features characteristic of nonergodic soft solids, including a relaxation time that grows linearly with the time since shear, comparison with behavior of quenched supercooled liquids indicates that this evolution is not directly related to traditional aging phenomena in glasses.

Plastic-to-elastic transition in aggregated emulsion networks, studied with atomic force microscopy-confocal scanning laser microscopy microrheology

In this paper, we demonstrate how the simultaneous application of atomic force microscopy (AFM) and confocal scanning laser microscopy (CSLM) can be used to characterize the (local) rheological properties of soft condensed matter at micrometer length scales. Measurement of AFM force curves as a function of the indentation amplitude and speed (magnitude and direction) can produce a "mechanical fingerprint" that contains information about material stiffness, hysteretic losses, and time scales for stress relaxation and/or network recovery. The simultaneous CSLM visualization of changes in the material's structure provides complementary information about how the material accommodates the indentation load. Since these experiments are done on areas of O(100 microm2) on materials having a surface of O(1 cm2), the measurements can be repeated on "fresh" material many times, contrary to traditional rheometers where the whole sample is loaded at once. As a particular example, we consider the case of a network of aggregated water-in-oil (W/O) emulsion droplets, in which the mechanical behavior changes drastically over time. Whereas the freshly prepared material shows a soft plastic behavior, after a time lapse of several weeks, the very same sample shows a much stiffer and elastic response. This drastic change in behavior is clearly reflected both in the signature of the AFM force curves and in (the reversibility of) the structural deformations observed with CSLM. The fact that these drastic mechanical changes take place without significant changes in the structure of the material (before loading) indicates that the stiffening of the droplet network is caused by an increase in the strength of the bonds between droplets. A remarkable finding for the elastic droplet network is that, while the structure recovers completely after the indenter is taken out, there is still an appreciable hysteresis in the force curves, indicating that dissipation also occurs. This hysteresis was not found to depend on the indentation speed.

Universality in structure and elasticity of polymer-nanoparticle gels

We propose a combination of polymer field theory and off-lattice computer simulations to study polymer-bridged gelation in polymer-nanoparticle mixtures. We use this method to study the structure of gels formed in attractive polymer-colloid systems. Our results indicate that such gels exhibit a universal structure with a fractal dimension d(f) approximately 2.5 characteristic of random percolation. By mapping to an affine-network model, the enhancement in elastic moduli is predicted to follow a critical exponent nu(eta) approximately 1.8 characteristic of the resistor network percolation. We analyze selected experimental results to suggest the existence of a universality class corresponding to our results.

Derivation of a microscopic theory of barriers and activated hopping transport in glassy liquids and suspensions

A recently proposed microscopic activated barrier hopping theory [K. S. Schweizer and E. J. Saltzman, J. Chem. Phys. 119, 1181 (2003)] of slow single-particle dynamics in glassy liquids, suspensions, and gels is derived using nonequilibrium statistical mechanics. Fundamental elements underlying the stochastic nonlinear Langevin equation description include an inhomogeneous liquid or locally solid-state perspective, dynamic density-functional theory (DDFT), a local equilibrium closure, and a coarse-grained free-energy functional. A dynamic Gaussian approximation is not adopted which is the key for avoiding a kinetic ideal glass transition. The relevant excess free energy is of a nonequilibrium origin and is related to dynamic force correlations in the fluid. The simplicity of the approach allows external perturbations to be rather easily incorporated. Dynamic heterogeneity enters naturally via mobility fluctuations associated with the stochastic barrier-hopping process. The derivation both identifies the limitations of the theory and suggests new avenues for its systematic improvement. Comparisons with ideal mode-coupling theory, alternative DDFT approaches and a field theoretic path-integral formulation are presented.

Clustering and mechanics in dense depletion and thermal gels

We report on the microstructure and mechanical properties (elastic modulus) of concentrated depletion and thermal gels of octadecyl-coated silica particles for different values of the strength of interaction--polymer concentration for depletion gels and temperature for thermal gels. The depletion gels are composed of dense clusters and voids, while the thermal gels are devoid of clusters. Shear breaks up clusters in depletion gels while it induces clustering in the thermal gels. In both of these gels, the microstructure recovers to the presheared state upon cessation of shear. The recovery of the elastic modulus mimics the microstructure in the sense that the elastic modulus recovers to the presheared sheared state after shearing is stopped. Calculations of the gel boundary by modeling the interactions with an effective one-component square-well model reveals that suspensions with similar ranges of attraction gel at the same volume fraction at a fixed strength of attraction. Calculations of the elastic modulus using the naïve mode coupling theory for depletion gels are in good agreement with experimental measurements provided clustering is taken into account and have the same magnitude as the elastic moduli of thermal gels with similar strengths of attraction. These calculations, in addition to the experimental observations reinforce the point that the microscopic parameter determining the elastic modulus of dense gels and its recovery is the localization length which is only a fraction of the particle diameter and not the structure on the length scale of the particle diameter and larger.

Large-scale structure in gels of attractive block copolymer micelles

We have used ultra-small-angle scattering (USANS) and fluorescence microscopy to demonstrate the existence of a nonfractal large-scale structure in attractive micellar gels of poly(styrene)-poly(acrylic acid) block copolymers, which have some characteristics of attractive colloidal glasses. The nature of the large-scale structure appears to depend systematically on the strength of attraction. Our systems display scattering that follows I approximately q(x) in the low q regime, with x varying from approximately -3 to -4 as the strength of attraction is decreased. This scattering behavior appears to be the result of surface scattering from large, highly polydisperse aggregates with rough interfaces.

Nonlinear elasticity and yielding of depletion gels

A microscopic activated barrier hopping theory of the viscoelasticity of colloidal glasses and gels has been generalized to treat the nonlinear rheological behavior of particle-polymer suspensions. The quiescent cage constraints and depletion bond strength are quantified using the polymer reference interaction site model theory of structure. External deformation (strain or stress) distorts the confining nonequilibrium free energy and reduces the barrier. The theory is specialized to study a limiting mechanical description of yielding and modulus softening in the absence of thermally induced barrier hopping. The yield stress and strain show a rich functional dependence on colloid volume fraction, polymer concentration, and polymer-colloid size asymmetry ratio. The yield stress collapses onto a master curve as a function of the polymer concentration scaled by its ideal mode-coupling gel boundary value, and sufficiently deep in the gel is of an effective power-law form with a universal exponent. A similar functional and scaling dependence of the yield stress on the volume fraction is found, but the apparent power-law exponent is nonuniversal and linearly correlated with the critical gel volume fraction. Stronger gels are generally, but not always, predicted to be more brittle in the strain mode of deformation. The theoretical calculations appear to be in accord with a broad range of observations.

Dynamic yielding, shear thinning, and stress rheology of polymer-particle suspensions and gels

The nonlinear rheological version of our barrier hopping theory for particle-polymer suspensions and gels has been employed to study the effect of steady shear and constant stress on the alpha relaxation time, yielding process, viscosity, and non-Newtonian flow curves. The role of particle volume fraction, polymer-particle size asymmetry ratio, and polymer concentration have been systematically explored. The dynamic yield stress decreases in a polymer-concentration- and volume-fraction-dependent manner that can be described as apparent power laws with effective exponents that monotonically increase with observation time. Stress- or shear-induced thinning of the viscosity becomes more abrupt with increasing magnitude of the quiescent viscosity. Flow curves show an intermediate shear rate dependence of an effective power-law form, becoming more solidlike with increasing depletion attraction. The influence of polymer concentration, particle volume fraction, and polymer-particle size asymmetry ratio on all properties is controlled to a first approximation by how far the system is from the gelation boundary of ideal mode-coupling theory (MCT). This emphasizes the importance of the MCT nonergodicity transition despite its ultimate destruction by activated barrier hopping processes. Comparison of the theoretical results with limited experimental studies is encouraging.

Barrier hopping, viscous flow, and kinetic gelation in particle-polymer suspensions

The naive mode coupling-polymer reference interaction site model (MCT-PRISM) theory of gelation and elasticity of suspensions of hard sphere colloids or nanoparticles mixed with nonadsorbing polymers has been extended to treat the emergence of barriers, activated transport, and viscous flow. The barrier makes the dominant contribution to the single particle relaxation time and shear viscosity, and is a rich function of the depletion attraction strength via the polymer concentration, polymer-particle size asymmetry ratio, and particle volume fraction. The dependences of the barrier on these three system parameters can be accurately collapsed onto a single scaling variable, and the resultant master curve is well described by a power law. Nearly universal master curves are also constructed for the hopping or alpha relaxation time for system conditions not too close to the ideal MCT transition. Based on the calculated barrier hopping time, a theory for kinetic gel boundaries is proposed. The form and dependence on system parameters of the kinetic gel lines are qualitatively the same as obtained from prior ideal MCT-PRISM studies. The possible relevance of our results to the phenomenon of gravity-driven gel collapse is studied. The general approach can be extended to treat nonlinear viscoelasticity and rheology of polymer-colloid suspensions and gels.