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

Characterizing dynamic heterogeneities during nanogel degradation

Understanding photodegradation of nanogels is critical for dynamic control of their properties and functionalities. We focus on nanogels formed by end-linking of four-arm polyethylene glycol precursors with photolabile groups and characterize dynamic heterogeneities in these systems during degradation. We use our recently developed dissipative particle dynamics framework that captures the controlled scission of bonds between the precursors and diffusion of degraded fragments at the mesoscale. To quantify spatiotemporal fluctuations in the local dynamic behavior, we calculate the self-part of the van-Hove correlation function for the reactive beads for nanogels degrading in various environments. We demonstrate strong deviations from the Gaussian behavior during the degradation and quantify variations in the non-Gaussian parameter as a function of the relative extent of degradation. We show that for the nanogels degrading in a good solvent, the peak values in the non-Gaussian parameter are observed significantly earlier than the reverse gel point, and earlier than the peak values in the dispersity of the broken off fragments. Further, our study shows that a systematic decrease in solvent quality significantly affects the behavior of the non-Gaussian parameter as a function of the relative extent of degradation. The findings of this study allow one to quantify the dynamic heterogeneities during degradation in various environments and can potentially provide guidelines for designing controllably degrading nanocarriers.

Kinetic Pathways to Gelation and Effects of Flow-Induced Structuring in Depletion Gels

The kinetic pathways to gelation and the effects of flow-induced restructuring are studied here in depletion flocculated gels with short-ranged attractions, both experimentally and using computer simulations. In the experiments, we first carefully diffuse a screening organic salt to destabilize colloid-polymer mixtures and form a gel. We hence avoid flow history effects, typical of traditional mixing protocols. The initial gelation phases are then accessible and observed by time-resolved confocal microscopy. These insights show that quiescent gelation reduces heterogeneity and strand size with increasing attraction strength, with deeper quenches leading to earlier arrest. These findings are consistent with the simulations which include long-range hydrodynamic interactions. We then compare these results with gels formed by high-rate preshear followed by cessation of colloid-polymer-salt mixtures. The obtained microstructures do not seem in this case to depend on depletant concentration. Indeed, confocal images reveal that shear flow significantly impacts gel structure, from fluidization at high shear rates to dense heterogeneous aggregates formation at lower rates. We especially show how the heterogeneity is controlled by the strength of the flow relative to the attraction forces between the colloids. This study highlights the subtleties behind the preparation protocols of colloidal gels. In particular, it shows that differences in kinetic aggregation pathways can overshadow attraction effects, such as those caused by varying flow conditions during mixing at different attraction strengths. These insights provide a framework for understanding gelation kinetics and optimizing structural reproducibility in colloidal gel experiments.

Viscoelasticity of diverse biological samples quantified by Acoustic Force Microrheology (AFMR)

In the context of soft matter and cellular mechanics, microrheology - the use of micron-sized particles to probe the frequency-dependent viscoelastic response of materials - is widely used to shed light onto the mechanics and dynamics of molecular structures. Here we present the implementation of active microrheology in an Acoustic Force Spectroscopy setup (AFMR), which combines multiplexing with the possibility of probing a wide range of forces ( ~ pN to ~nN) and frequencies (0.01-100 Hz). To demonstrate the potential of this approach, we perform active microrheology on biological samples of increasing complexity and stiffness: collagen gels, red blood cells (RBCs), and human fibroblasts, spanning a viscoelastic modulus range of five orders of magnitude. We show that AFMR can successfully quantify viscoelastic properties by probing many beads with high single-particle precision and reproducibility. Finally, we demonstrate that AFMR to map local sample heterogeneities as well as detect cellular responses to drugs.

Spatial confinement affects the heterogeneity and interactions between shoaling fish

Living objects are able to consume chemical energy and process information independently from others. However, living objects can coordinate to form ordered groups such as schools of fish. This work considers these complex groups as living materials and presents imaging-based experiments of laboratory schools of fish to understand how activity, which is a non-equilibrium feature, affects the structure and dynamics of a group. We use spatial confinement to control the motion and structure of fish within quasi-2D shoals of fish and use image analysis techniques to make quantitative observations of the structures, their spatial heterogeneity, and their temporal fluctuations. Furthermore, we utilize Monte Carlo simulations to replicate the experimentally observed data which provides insight into the effective interactions between fish and confirms the presence of a confinement-based behavioral preference transition. In addition, unlike in short-range interacting systems, here structural heterogeneity and dynamic activities are positively correlated as a result of complex interplay between spatial arrangement and behavioral dynamics in fish collectives.

Frequency-Dependent Microelectrophoresis Study of Colloids with Tunable Surface Charge

Nonaqueous poly(methyl methacrylate) (PMMA) colloidal suspensions in a solvent that is simultaneously matched in both density and refractive index have been important for real-space studies of colloidal self-assembly, but their complex electrostatic character remains largely unexplored. Electrophoresis is a powerful tool for determining the surface potential and charge of the colloidal suspension; however, because of refractive index matching, standard electrophoresis measurements are not feasible. We carry out microscope-based microelectrophoresis measurements on PMMA colloids in cyclohexyl bromide and cis-trans decalin to measure particle charge as a function of salt concentration in both DC and frequency-variable AC fields. The colloid charge depends on salt concentration and reverses sign near 0.35 μM, providing evidence that solution ions are actively modifying the colloid surface. The frequency dependence of the electrophoretic mobility yields the characteristic time scale for electric double-layer polarization and provides intriguing evidence for Manning condensation and polyion formation.

Network physics of attractive colloidal gels: Resilience, rigidity, and phase diagram

Colloidal gels exhibit solid-like behavior at vanishingly small fractions of solids, owing to ramified space-spanning networks that form due to particle-particle interactions. These networks give the gel its rigidity, and with stronger attractions the elasticity grows as well. The emergence of rigidity can be described through a mean field approach; nonetheless, fundamental understanding of how rigidity varies in gels of different attractions is lacking. Moreover, recovering an accurate gelation phase diagram based on the system's variables has been an extremely challenging task. Understanding the nature of colloidal clusters, and how rigidity emerges from their connections is key to controlling and designing gels with desirable properties. Here, we employ network analysis tools to interrogate and characterize the colloidal structures. We construct a particle-level network, having all the spatial coordinates of colloids with different attraction levels, and also identify polydisperse rigid fractal clusters using a Gaussian mixture model, to form a coarse-grained cluster network that distinctly shows main physical features of the colloidal gels. A simple mass-spring model then is used to recover quantitatively the elasticity of colloidal gels from these cluster networks. Interrogating the resilience of these gel networks shows that the elasticity of a gel (a dynamic property) is directly correlated to its cluster network's resilience (a static measure). Finally, we use the resilience investigations to devise [and experimentally validate] a fully resolved phase diagram for colloidal gelation, with a clear solid-liquid phase boundary using a single volume fraction of particles well beyond this phase boundary.

Effect of Shear History on Solid-Liquid Transition of Particulate Gel Fuels

Investigating the structural evolution of particulate gels is a very challenging task due to their vulnerability and true flow characteristics. In this work, deeper insight into the rheological properties of gel fuels filled with fumed silica (FS) and aluminum microparticles (Al MPs) was gained by changing shear procedures. Firstly, the flow curves were found to no longer follow the monotonic power law and exhibited subtle thixotropic responses. As the shear rate increased, the gel structure underwent a transition from local shear to bulk shear in the nonlinear region after yielding. This finding reveals the prevalence of nonideal local shear in industry. Secondly, the time-dependent rheological responses demonstrated that the strength spectrum of gel fuels depends on the applied shear rate, with stress relaxation more easily observed at lower shear rates. Those results involved the structural disruption, recovery, and equilibrium of particulate gels from two scales of shear rate and shear time.

Effects of Polymer Molecular Weight on Structure and Dynamics of Colloid-Polymer Bridging Systems

We investigate the effects of polymer molecular weight on the structure and dynamics of a model colloid-polymer bridging system using confocal microscopy. Polymer-induced bridging interactions between trifluoroethyl methacrylate-co-tert-butyl methacrylate (TtMA) copolymer particles and poly(acrylic acid) (PAA) polymers of molecular weight M_w of 130, 450, 3000, or 4000 kDa and normalized concentrations c/c* ranging from 0.05 to 2 are driven by hydrogen bonding of PAA to one of the particle stabilizers. At a constant particle volume fraction ϕ = 0.05, the particles form clusters or networks of maximal size at an intermediate polymer concentration and become more dispersed upon further addition of polymer. Increasing the polymer M_w at a fixed normalized concentration c/c* increases the cluster size: suspensions with 130 kDa polymer contain small clusters that remain diffusive, and those with 4000 kDa polymer form larger, dynamically arrested clusters. Biphasic suspensions with distinct populations of disperse and arrested particles form at low c/c*, where there is insufficient polymer to bridge all particles, or high c/c*, where some particles are sterically stabilized by the added polymer. Thus, the microstructure and dynamics in these mixtures can be tuned through the size and concentration of the bridging polymer.

Fibrillar biocompatible colloidal gels based on cellulose nanocrystals and poly(N-isopropylacrylamide) for direct ink writing

HYPOTHESIS

Hydrogels based on cellulose nanocrystals (CNC) have attracted great interest because of their sustainability, biocompatibility, mechanical strength and fibrillar structure. Gelation of colloidal particles can be induced by the introduction of polymers. Existing examples include gels based on CNC and derivatives of cellulose or poly(vinyl alcohol), however, gel structure and their application for extrusion printing were not shown. Hence, we rationalize formation of colloidal gels based on mixture of poly(N-isopropylacrylamide) (PNIPAM) and CNC and control their structure and mechanical properties by variation of components ratio.

EXPERIMENTS

State diagram for colloidal system based on mixture of PNIPAM and CNC were established at 25 and 37 °C. Biocompatibility, fiber diameter and rheological properties of the gels were studied for different PNIPAM/CNC ratio.

FINDINGS

We show that depending on the ratio between PNIPAM and CNC, colloidal system could be in sol or gel state at 25 °C and at gel state or phase separated at 37 °C. Physically crosslinked hydrogels were thermosensitive and could reversibly change it transparency from translucent to opaque in biologically relevant temperature range. These colloidal hydrogels were biocompatible, had fibrillar structure and demonstrate shear-thinning behavior, which makes them a promising material for bioapplications related to extrusion printing.

Non-equilibrium view of the amorphous solidification of liquids with competing interactions

The interplay between short-range attractions and long-range repulsions (SALR) characterizes the so-called liquids with competing interactions, which are known to exhibit a variety of equilibrium and non-equilibrium phases. The theoretical description of the phenomenology associated with glassy or gel states in these systems has to take into account both the presence of thermodynamic instabilities (such as those defining the spinodal line and the so called λ line) and the limited capability to describe genuine non-equilibrium processes from first principles. Here, we report the first application of the non-equilibrium self-consistent generalized Langevin equation theory to the description of the dynamical arrest processes that occur in SALR systems after being instantaneously quenched into a state point in the regions of thermodynamic instability. The physical scenario predicted by this theory reveals an amazing interplay between the thermodynamically driven instabilities, favoring equilibrium macro- and micro-phase separation, and the kinetic arrest mechanisms, favoring non-equilibrium amorphous solidification of the liquid into an unexpected variety of glass and gel states.

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.

Effect of scatterer interactions on photon transport in diffusing wave spectroscopy

We calculate the effect of particle size, concentration, and interactions on the photon transport mean-free path l^{*} that characterizes the multiple light scattering in diffusing wave spectroscopy (DWS). For scatterers of sufficient size, such that the first peak of the suspension structure factor S(q_{max}) remains in the range of accessible scattering vectors, neither repulsive nor attractive interactions between scatterers contribute strongly to l^{*}; its values are bounded by those for hard spheres and scatterers without interactions. However, for scatterers smaller than the wavelength of light, crowding induced by attraction or repulsion can lead to nonmonotonic behavior in l^{*} with increasing scatterer concentration. The effect is strongest for repulsive particles.

Aggregation and Gelation in a Tunable Aqueous Colloid-Polymer Bridging System

We report a colloid-polymer model system with tunable bridging interactions for microscopic studies of structure and dynamics using confocal imaging. The interactions between trifluoroethyl methacrylate-co-\emph{tert}-butyl methacrylate (TtMA) copolymer particles and poly(acrylic acid) (PAA) polymers were controllable via polymer concentration and pH. The strength of adsorption of PAA on the particle surface, driven by pH-dependent interactions with polymer brush stabilizers on the particle surfaces, was tuned via solution pH. Particle-polymer suspensions formulated at low pH, where polymers strongly adsorbed to the particles, contained clusters or weak gels at particle volume fractions of $\phi = 0.15$ and $\phi = 0.40$. At high pH, where the PAA only weakly adsorbed to the particle surface, particles largely remained dispersed and the suspensions behaved as a dense fluid. The ability to visualize suspension structure is likely to provide insight into the role of polymer-driven bridging interactions on the behavior of colloidal suspensions.

Direct Imaging of Contacts and Forces in Colloidal Gels

Colloidal dispersions are prized as model systems to understand basic properties of materials, and are central to a wide range of industries from cosmetics to foods to agrichemicals. Among the key developments in using colloids to address challenges in condensed matter is to resolve the particle coordinates in 3D, allowing a level of analysis usually only possible in computer simulation. However in amorphous materials, relating mechanical properties, and failure in particular to microscopic structure remains problematic. Here we address this challenge by studying the contacts and the forces between particles, as well as their positions. To do so, we use a colloidal model system (an emulsion) in which the interparticle forces and local stress can be linked to the microscopic structure. We demonstrate the potential of our method to reveal insights into the failure mechanisms of soft amorphous solids by determining local stress in a colloidal gel. In particular, we identify "force chains" of load--bearing droplets, and local stress anisotropy, and investigate their connection with locally rigid packings of the droplets.

Microscopic structural origin behind slowing down of colloidal phase separation approaching gelation

The gelation of colloidal particles interacting through a short-range attraction is widely recognized as a consequence of the dynamic arrest of phase separation into colloid-rich and solvent-rich phases. However, the microscopic origin behind the slowing down and dynamic arrest of phase separation remains elusive. In order to access microscopic structural changes through the entire process of gelation in a continuous fashion, we used core–shell fluorescent colloidal particles, laser scanning confocal microscopy, and a unique experimental protocol that allows us to initiate phase separation instantaneously and gently. Combining these enables us to track the trajectories of individual particles seamlessly during the whole phase-separation process from the early stage to the late arresting stage. We reveal that the enhancement of local packing and the resulting formation of locally stable rigid structures slow down the phase-separation process and arrest it to form a gel with an average coordination number of z = 6–7. This result supports a mechanical perspective on the dynamic arrest of sticky-sphere systems based on the microstructure, replacing conventional explanations based on the macroscopic vitrification of the colloid-rich phase. Our findings illuminate the microscopic mechanisms behind the dynamic arrest of colloidal phase separation, the emergence of mechanical rigidity, and the stability of colloidal gels.

Microstructure and elasticity of dilute gels of colloidal discoids

The linear elasticity of dilute colloidal gels formed from discoidal latex particles is quantified as a function of aspect ratio and modeled by confocal microscopy characterization of their fractal cluster microstructure. Colloidal gels are of fundamental interest because of their widespread use to stabilize complex fluids in industry. Technological interest in producing gels of desired moduli using the least number of particles drives formulators to produce gels at dilute concentrations. However, dilute gels self-assembled from isotropic spheres offer limited scope for rheological tunability due to the universal characteristics of their fractal microstructure. Our results show that changing the building block shape from sphere to discoid yields very large shifts in gel elasticity relative to the universal behavior reported for spheres. This shift - tunable through aspect ratio - yields up to a 100-fold increase in elastic modulus at a fixed volume fraction. From modeling the results using the theory for fractal cluster gel rheology, which is applicable at the dilute conditions of this study, we reveal that the efficient generation of elasticity by the colloidal discoids is the consequence of the combined effects of shape anisotropy on the fractal microstructure of the gel network, the anisotropy of the attractive interparticle pair potentials, and the volumetric compactness of the fractal cluster. These results extend prior characterizations of the rheology of non-spherical particulate gels by providing quantitative estimates of how the specific mechanisms of fractality, pair potential, and clustering mediate the profound effects of particle shape anisotropy on the elastic rheology of colloidal gels.

Yield Stress Aging in Attractive Colloidal Suspensions

We investigate the origin of yield stress aging in semidense, saline, and turbid suspensions in which structural evolution is rapidly arrested by the formation of thermally irreversible roll-resisting interparticle contacts. By performing optical tweezer three-point bending tests on particle rods, we show that these contacts yield by overcoming a rolling threshold, the critical bending moment of which grows logarithmically with time. We demonstrate that this time-dependent contact-scale rolling threshold controls the suspension yield stress and its aging kinetics. We identify a simple constitutive relation between the contact-scale flexural rigidity and rolling threshold, which transfers to macroscopic scales. This leads us to establishing a constitutive relation between macroscopic shear modulus and yield stress that is generic for an array of colloidal systems.

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.

Yielding and resolidification of colloidal gels under constant stress

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

Self-assembly in mixtures with competing interactions

A binary mixture of particles interacting with spherically-symmetrical potentials leading to microsegregation is studied by theory and molecular dynamics (MD) simulations. We consider spherical particles with equal diameters and volume fractions. Motivated by the mixture of oppositely charged particles with different adsorption preferences immersed in a near-critical binary solvent, we assume short-range attraction long-range repulsion for the interaction between like particles, and short-range repulsion long-range attraction for the interaction between different ones. In order to predict structural and thermodynamic properties of such complex mixtures, we develop a theory combining the density functional and field-theoretical methods. We show that concentration fluctuations in mesoscopic regions lead to a qualitative change of the phase diagram compared to mean-field predictions. Both theory and MD simulations show coexistence of a low-density disordered phase with a high-density phase with alternating layers rich in the first and second components. In these layers, crystalline structure is present in the solid, and absent in the liquid crystals. The density and the degree of order of the ordered phase decrease with increasing temperature, up to a temperature where the theory predicts a narrow two-phase region with increasing density of both phases for increasing temperature. MD simulations show that monocrystals of the solid and liquid crystals have a prolate shape with the axis parallel to the direction of concentration oscillations, and the deviation from the spherical shape increases with increasing periodic order.

Investigation of the swollen state of Carbopol molecules in non-aqueous solvents through rheological characterization

We explore how different types of solvent influence the rheological properties of non-aqueous Carbopol dispersions from the dilute to the jammed state. In novel non-aqueous formulations, polar solvents are used more and more frequently, because they can form Carbopol microgels without the need of any neutralizing agents. However, the swelling behaviour of Carbopol molecules in the absence of water, when ionic forces are weak, is still poorly understood. To this end, we study the swelling behaviour of Carbopol 974P NF in different polar solvents, i.e. glycerol, PEG400 and mixtures of the two solvents, by mapping the rheological behaviour of Carbopol suspensions from very dilute to highly concentrated conditions. The rheological study reveals that the onset of the jamming transition occurs at different critical polymer concentrations depending on the solvents used. Nevertheless, once the jammed state is reached, both elastic and yielding behaviours are scalable with the particle volume fraction. These results suggest that the type of solvent influences the final volume of the single Carbopol particles but does not alter the interactions between the particles. The final radius of the swollen particles is estimated from shear rheology measurements in dilute conditions, showing a decrease of the final swelling ratio of Carbopol molecules of almost 50% for PEG400 solutions, a result that confirms the shift to higher values of the critical jamming concentration obtained from linear viscoelasticity for the same solutions.

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

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

Connecting particle clustering and rheology in attractive particle networks

The structural properties of suspensions and other multiphase systems are vital to overall processability, functionality and acceptance among consumers. Therefore, it is crucial to understand the intrinsic connection between the microstructure of a material and the resulting rheological properties. Here, we demonstrate how the transitions in the microstructural conformations can be quantified and correlated to rheological measurements. We find semi-local parameters from graph theory, the mathematical study of networks, to be useful in linking structure and rheology. Our results, using capillary suspensions as a model system, show that the use of the clustering coefficient, in combination with the coordination number, is able to capture not only the agglomeration of particles, but also measures the formation of groups. These phenomena are tightly connected to the rheological properties. The present sparse networks cannot be described by established techniques such as betweenness centrality.

Microrheology imaging of fiber suspensions - a case study for lyophilized collagen I in HCl solutions

In fiber suspensions with low optical contrast, the in situ characterization of structural properties with conventional microscopy methods fails. However, overlaying subsequent images of multiple particle tracking (MPT) videos including short trajectories usually discarded in MPT analysis allowed for direct visualization of individual fibers and the network structure of lyophilized collagen I (Coll) distributed in hydrochloric acid solutions. MPT yielded a broad distribution of mean square displacements (MSDs). Freely diffusing tracer particles yielded viscosities indicating that, irrespective of concentration, a constant amount of Coll is dissolved in the aqueous phase. Particles found elastically trapped within fibrous Coll structures exhibited a broad range of time-independent MSDs and we propose a structure comprising multiple fiber bundles with dense regions inaccessible to tracers and elastic regions of different stiffness in between. Bulky aggregates inaccessible to the 0.2 μm tracers exist even at low Coll concentrations, a network of slender fibers evolves above the sol-gel transition and these fibers densify with increasing Coll concentration. This novel MPT-based imaging technique possesses great potential to characterize the fiber distribution in and structural properties of a broad range of biological and technical suspensions showing low contrast when imaged with conventional techniques. Thus, MPT imaging and microrheology will help to better understand the effect of fiber distribution and network structure on the viscoelastic properties of complex suspensions.

Contact and macroscopic ageing in colloidal suspensions

The ageing behaviour of dense suspensions or pastes at rest is almost exclusively attributed to structural dynamics. Here, we identify another ageing process, contact-controlled ageing, consisting of the progressive stiffening of solid-solid contacts of an arrested colloidal suspension. By combining rheometry, confocal microscopy and particle-scale mechanical tests using laser tweezers, we demonstrate that this process governs the shear-modulus ageing of dense aqueous silica and polymer latex suspensions at moderate ionic strengths. We further show that contact-controlled ageing becomes relevant as soon as Coulombic interactions are sufficiently screened out that the formation of solid-solid contacts is not limited by activation barriers. Given that this condition only requires moderate ion concentrations, contact-controlled ageing should be generic in a wide class of materials, such as cements, soils or three-dimensional inks, thus questioning our understanding of ageing dynamics in these systems.

Contact criterion for suspensions of smooth and rough colloids

We report a procedure to obtain the search distance used to determine particle contact in dense suspensions of smooth and rough colloids. This method works by summing physically relevant length scales in an uncertainty analysis and does not require detailed quantification of the surface roughness. We suspend sterically stabilized, fluorescent poly(methyl methacrylate) colloids in a refractive index-matched solvent, squalene, in order to ensure hard sphere-like behavior. High speed centrifugation is used to pack smooth and rough colloids to their respective jamming points, φ_J. The jammed suspensions are subsequently diluted with known volumes of solvent to φ < φ_J. Structural parameters obtained from confocal laser scanning micrographs of the diluted colloidal suspensions are extrapolated to φ_J to determine the mean contact number at jamming, 〈z〉_J. Contact below jamming refers to nearest neighbors at a length scale below which the effects of hydrodynamic or geometric friction come into play. Sensitivity analyses show that a deviation of the search distance by 1% of the particle diameter results in 〈z〉 changing by up to 10%, with the error in contact number distribution being magnified in dense suspensions (φ > 0.50) due to an increased number of nearest neighbors in the first coordination shell.

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.

Yield of reversible colloidal gels during flow start-up: release from kinetic arrest

Yield of colloidal gels during start-up of shear flow is characterized by an overshoot in shear stress that accompanies changes in network structure. Prior studies of yield of reversible colloidal gels undergoing strong flow model the overshoot as the point at which network rupture permits fluidization. However, yield under weak flow, which is of interest in many biological and industrial fluids shows no such disintegration. The mechanics of reversible gels are influenced by bond strength and durability, where ongoing rupture and re-formation impart aging that deepens kinetic arrest [Zia et al., J. Rheol., 2014, 58, 1121], suggesting that yield be viewed as release from kinetic arrest. To explore this idea, we study reversible colloidal gels during start-up of shear flow via dynamic simulation, connecting rheological yield to detailed measurements of structure, bond dynamics, and potential energy. We find that pre-yield stress grows temporally with the changing roles of microscopic transport processes: early time behavior is set by Brownian diffusion; later, advective displacements permit relative particle motion that stretches bonds and stores energy. Stress accumulates in stretched, oriented bonds until yield, which is a tipping point to energy release, and is passed with a fully intact network, where the loss of very few bonds enables relaxation of many, easing glassy arrest. This is immediately followed by a reversal to growth in potential energy during bulk plastic deformation and condensation into larger particle domains, supporting the view that yield is an activated release from kinetic arrest. The continued condensation of dense domains and shrinkage of network surfaces, along with a decrease in the potential energy, permit the gel to evolve toward more complete phase separation, supporting our view that yield of weakly sheared gels is a 'non-equilibrium phase transition'. Our findings may be particularly useful for industrial or other coatings, where weak, slow application via shear may lead to phase separation, inhibiting smooth distribution.

Reversible Aggregation and Colloidal Cluster Morphology: The Importance of the Extended Law of Corresponding States

Cluster morphology of spherical particles interacting with a short-range attraction has been extensively studied due to its relevance to many applications, such as the large-scale structure in amorphous materials, phase separation, protein aggregation, and organelle formation in cells. Although it was widely accepted that the range of the attraction solely controls the fractal dimension of clusters, recent experimental results challenged this concept by also showing the importance of the strength of attraction. Using Monte Carlo simulations, we conclusively demonstrate that it is possible to reduce the dependence of the cluster morphology to a single variable, namely, the reduced second virial coefficient, B_{2}^{*}, linking the local properties of colloidal systems to the extended law of corresponding states. Furthermore, the cluster size distribution exhibits two well-defined regimes: one identified for small clusters, whose fractal dimension, d_{f}, does not depend on the details of the attraction, i.e., small clusters have the same d_{f}, and another related to large clusters, whose morphology depends exclusively on B_{2}^{*}, i.e., d_{f} of large aggregates follows a master curve, which is only a function of B_{2}^{*}. This physical scenario is confirmed with the reanalysis of experimental results on colloidal-polymer mixtures.

Vitrification and gelation in sticky spheres

Glasses and gels are the two dynamically arrested, disordered states of matter. Despite their importance, their similarities and differences remain elusive, especially at high density, where until now it has been impossible to distinguish them. We identify dynamical and structural signatures which distinguish the gel and glass transitions in a colloidal model system of hard and "sticky" spheres. It has been suggested that "spinodal" gelation is initiated by gas-liquid viscoelastic phase separation to a bicontinuous network and the resulting densification leads to vitrification of the colloid-rich phase, but whether this phase has sufficient density for arrest is unclear [M. A. Miller and D. Frenkel, Phys. Rev. Lett. 90, 135702 (2003) and P. J. Lu et al., Nature 435, 499-504 (2008)]. Moreover alternative mechanisms for arrest involving percolation have been proposed [A. P. R. Eberle et al., Phys. Rev. Lett. 106, 105704 (2011)]. Here we resolve these outstanding questions, beginning by determining the phase diagram. This, along with demonstrating that percolation plays no role in controlling the dynamics of our system, enables us to confirm spinodal decomposition as the mechanism for gelation. We are then able to show that gels can be formed even at much higher densities than previously supposed, at least to a volume fraction of ϕ = 0.59. Far from being networks, these gels apparently resemble glasses but are still clearly distinguished by the "discontinuous" nature of the transition and the resulting rapid solidification, which leads to the formation of inhomogeneous (with small voids) and far-from-equilibrium local structures. This is markedly different from the glass transition, whose continuous nature leads to the formation of homogeneous and locally equilibrated structures. We further reveal that the onset of the attractive glass transition in the form of a supercooled liquid is in fact interrupted by gelation. Our findings provide a general thermodynamic, dynamic, and structural basis upon which we can distinguish gelation from vitrification.

Hunting mermaids in real space: known knowns, known unknowns and unknown unknowns

We review efforts to realise so-called mermaid (or short-ranged attraction/long ranged repulsion) interactions in 3d real space. The repulsive and attractive contributions to these interactions in charged colloids and colloid-polymer mixtures, may be accurately realised, by comparing particle-resolved studies with colloids to computer simulation. However, when we review work where these interactions have been combined, despite early indications of behaviour consistent with predictions, closer analysis reveals that in the non-aqueous systems used for particle-resolved studies, the idea of summing the attractive and repulsive components leads to wild deviations with experiment. We suggest that the origin lies in the weak ion dissociation in these systems with low dielectric constant solvents. Ultimately this leads even to non-centro-symmetric interactions and a new level of complexity in these systems.

Capillary-driven binding of thin triangular prisms at fluid interfaces

We observe capillary-driven binding between thin, equilateral triangular prisms at a flat air-water interface. The edge length of the equilateral triangle face is 120 μm, and the thickness of the prism is varied between 2 and 20 μm. For thickness to length (T/L) ratios of 1/10 or less, pairs of triangles preferentially bind in either tip-to-tip or tip-to-midpoint edge configurations; for pairs of prisms of thickness T/L = 1/5, the tip of one triangle binds to any position along the other triangle's edge. The distinct binding configurations for small T/L ratios result from physical bowing of the prisms, a property that arises during their fabrication. When bowed prisms are placed at the air-water interface, two distinct polarity states arise: prisms either sit with their center of mass above or below the interface. The interface pins to the edge of the prism's concave face, resulting in an interface profile that is similar to that of a capillary hexapole, but with important deviations close to the prism that enable directed binding. We present corresponding theoretical and numerical analysis of the capillary interactions between these prisms and show how prism bowing and contact-line pinning yield a capillary hexapole-like interaction that results in the two sets of distinct, highly-directional binding events. Prisms of all T/L ratios self-assemble into space-spanning open networks; the results suggest design parameters for the fabrication of building blocks of ordered open structures such as the Kagome lattice.

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.

Multiple particle tracking study of thermally-gelling nanoemulsions

We perform multiple particle tracking (MPT) on a thermally-gelling oil-in-water nanoemulsion system. Carboxylated and plain polystyrene probes are used to investigate the role of colloidal probe size and surface chemistry on MPT in the nanoemulsion system. As temperature increases, hydrophobic groups of PEG-based gelators (PEGDA) partition into the oil/water interface and bridge droplets. This intercolloidal attraction generates a wide variety of microstructures consisting of droplet-rich and droplet-poor phases. By tailoring the MPT colloidal probe surface chemistry, we can control the residence of probes in each domain, thus allowing us to independently probe each phase. Our results show stark differences in probe dynamics in each domain. For certain conditions, the mean squared displacement (MSD) can differ by over four orders of magnitude for the same probe size but different surface chemistry. Carboxylated probe surface chemistries result in "slippery" probes while plain polystyrene probes appear to tether to the nanoemulsion gel network. We also observe probe hopping between pores in the gel for carboxylated probes. Our approach demonstrates that probes with different surface chemistries are useful in probing the local regions of a colloidal gel and allows the measurement of local properties within structurally heterogeneous hydrogels.

Dynamics of Fractal Cluster Gels with Embedded Active Colloids

We find that embedded active colloids increase the ensemble-averaged mean squared displacement of particles in otherwise passively fluctuating fractal cluster gels. The enhancement in dynamics occurs by a mechanism in which the active colloids contribute to the average dynamics both directly through their own active motion and indirectly through their excitation of neighboring passive colloids in the fractal network. Fractal cluster gels are synthesized by addition of magnesium chloride to an initially stable suspension of 1.0  μm polystyrene colloids in which a dilute concentration of platinum coated Janus colloids has been dispersed. The Janus colloids are thereby incorporated into the fractal network. We measure the ensemble-averaged mean squared displacement of all colloids in the gel before and after the addition of hydrogen peroxide, a fuel that drives diffusiophoretic motion of the Janus particles. The gel mean squared displacement increases by up to a factor of 3 for an active to passive particle ratio of 1∶20 and inputted active energy-defined based on the hydrogen peroxide's effect on colloid swim speed and run length-that is up to 9.5 times thermal energy, on a per particle basis. We model the enhancement in gel particle dynamics as the sum of a direct contribution from the displacement of the Janus particles themselves and an indirect contribution from the strain field that the active colloids induce in the surrounding passive particles.

Shear-induced slab-like domains in a directed percolated colloidal gel

We explore the structural changes of a gel-forming colloid polymer mixture under shear by employing Brownian dynamics simulations of a colloidal system with short-ranged attractive depletion interaction in a linear flow profile. While the structure of unpercolated systems changes only slightly under shearing, we discover the formation of slab-like clusters in sheared directed percolated gel networks that are confined between two walls. These gel-slabs are stable over a long time and seem to be related to the syneresis phenomena that can be observed in directed percolated colloidal gels. Only at large shear strength the slabs are destroyed and a homogeneous state with many unbounded particles can be observed. We also quantitatively analyze our results by determining void volumes.

Phase behavior of colloid-polymer depletion mixtures with unary or binary depletants

Adding depletants to a colloidal suspension induces an attractive interparticle interaction that can be tuned to obtain desired structures or to probe phase behavior. When the depletant is not uniform in size, however, both the range and strength of the attraction become difficult to predict and hence control. We investigated the effects of depletant bidispersity on the non-equilibrium phase behavior of colloid-polymer mixtures. We added unary or binary mixtures of polystyrene as the depletant to suspensions of charged poly(methyl methacrylate) particles. The structure and dynamics of the particles were compared over three sets of samples with various mixtures of two different polystyrenes whose size varied by an order of magnitude. The structure and dynamics were nearly independent of depletant dispersity if the polymer concentration was represented as a sum of normalized concentrations of each species. Near the transition region between a fluid of clusters and an interconnected gel at intermediate volume fractions, partitioning of polymers in a binary mixture into colloid-rich and polymer-rich phase leads to a slightly different gelation pathway.

Colloidal gels tuned by oscillatory shear

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

Structural fingerprints of yielding mechanisms in attractive colloidal gels

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

Aggregation of cyclic polypeptoids bearing zwitterionic end-groups with attractive dipole–dipole and solvophobic interactions: a study by small-angle neutron scattering and molecular dynamics simulation

The aggregation behavior of cyclic polypeptoids has been studied using experiments and simulations.

Synthesis of aerogels: from molecular routes to 3-dimensional nanoparticle assembly

Colloidal nanocrystals are extensively used as building blocks in nanoscience, and amazing results have been achieved in assembling them into ordered, close-packed structures. But in spite of great efforts, the size of these structures is typically restricted to a few micrometers, and it is very hard to extend them into the macroscopic world. In comparison, aerogels are macroscopic materials, highly porous, disordered, ultralight and with immense surface areas. With these distinctive characteristics, they are entirely contrary to common nanoparticle assemblies such as superlattices or nanocrystal solids, and therefore cover a different range of applications. While aerogels are traditionally synthesized by molecular routes based on aqueous sol-gel chemistry, in the last few years the gelation of nanoparticle dispersions became a viable alternative to improve the crystallinity and to widen the structural, morphological and compositional complexity of aerogels. In this Review, the different approaches to inorganic non-siliceous and non-carbon aerogels are addressed. We start our discussion with wet chemical routes involving molecular precursors, followed by processing methods using nanoparticles as building blocks. A unique feature of many of these routes is the fact that a macroscopic, often monolithic body is produced by pure self-assembly of nanosized colloids without the need for any templates.

Simple microfluidic stagnation point flow geometries

A geometrically simple flow cell is proposed to generate different types of stagnation flows, using a separation flow and small variations of the geometric parameters. Flows with high local deformation rates can be changed from purely rotational, over simple shear flow, to extensional flow in a region surrounding a stagnation point. Computational fluid dynamic calculations are used to analyse how variations of the geometrical parameters affect the flow field. These numerical calculations are compared to the experimentally obtained streamlines of different designs, which have been determined by high speed confocal microscopy. As the flow type is dictated predominantly by the geometrical parameters, such simple separating flow devices may alleviate the requirements for flow control, while offering good stability for a wide variety of flow types.

Directed percolation identified as equilibrium pre-transition towards non-equilibrium arrested gel states

The macroscopic properties of gels arise from their slow dynamics and load-bearing network structure, which are exploited by nature and in numerous industrial products. However, a link between these structural and dynamical properties has remained elusive. Here we present confocal microscopy experiments and simulations of gel-forming colloid–polymer mixtures. They reveal that gel formation is preceded by continuous and directed percolation. Both transitions lead to system-spanning networks, but only directed percolation results in extremely slow dynamics, ageing and a shrinking of the gel that resembles synaeresis. Therefore, dynamical arrest in gels is found to be linked to a structural transition, namely directed percolation, which is quantitatively associated with the mean number of bonded neighbours. Directed percolation denotes a universality class of transitions. Our study hence connects gel formation to a well-developed theoretical framework, which now can be exploited to achieve a detailed understanding of arrested gels.

Gels exhibit very slow dynamics, for which a structural reason remains elusive. Here, Kohl et al. show the gel formation is accompanied by a succession of continuous and directed percolation, with only the latter found to lead to the arrested dynamics.