Arrested phase separation in a short-ranged attractive colloidal system: A numerical study

Complex optical transport, dynamics, and rheology of intermediately attractive emulsions

Introducing short-range attractions in Brownian systems of monodisperse colloidal spheres can substantially impact their structures and consequently their optical transport and rheological properties. Here, for size-fractionated colloidal emulsions, we show that imposing an intermediate strength of attraction, well above but not much larger than thermal energy ([Formula: see text] [Formula: see text], through micellar depletion leads to a striking notch in the measured inverse mean free path of optical transport, [Formula: see text], as a function of droplet volume fraction, [Formula: see text]. This notch, which appears between the hard-sphere glass transition, [Formula: see text], and maximal random jamming, [Formula: see text], implies the existence of a greater population of compact dense clusters of droplets, as compared to tenuous networks of droplets in strongly attractive emulsion gels. We extend a prior decorated core-shell network model for strongly attractive colloidal systems to include dense non-percolating clusters that do not contribute to shear rigidity. By constraining this extended model using the measured [Formula: see text], we improve and expand the microrheological interpretation of diffusing wave spectroscopy (DWS) experiments made on attractive colloidal systems. Our measurements and modeling demonstrate richness and complexity in optical transport and shear rheological properties of dense, disordered colloidal systems having short-range intermediate attractions between moderately attractive glasses and strongly attractive gels.

SpiDec: Computing binodals and interfacial tension of biomolecular condensates from simulations of spinodal decomposition

Phase separation of intrinsically disordered proteins (IDPs) is a phenomenon associated with many essential cellular processes, but a robust method to compute the binodal from molecular dynamics simulations of IDPs modeled at the all-atom level in explicit solvent is still elusive, due to the difficulty in preparing a suitable initial dense configuration and in achieving phase equilibration. Here we present SpiDec as such a method, based on spontaneous phase separation via spinodal decomposition that produces a dense slab when the system is initiated at a homogeneous, low density. After illustrating the method on four model systems, we apply SpiDec to a tetrapeptide modeled at the all-atom level and solvated in TIP3P water. The concentrations in the dense and dilute phases agree qualitatively with experimental results and point to binodals as a sensitive property for force-field parameterization. SpiDec may prove useful for the accurate determination of the phase equilibrium of IDPs.

Modeling colloidal interactions that predict equilibrium and non-equilibrium states

Modulating the interaction potential between colloids suspended in a fluid can trigger equilibrium phase transitions as well as formation of non-equilibrium 'arrested states' such as gels and glasses. Faithful representation of such interactions are essential for using simulation to interrogate the microscopic details of non-equilibrium behavior, and for extrapolating observations to new regions of phase space that are difficult to explore in experiment. Although the extended law of corresponding states predicts equilibrium phases for systems with short-ranged interactions, it proves inadequate for equilibrium predictions of systems with longer-ranged interactions, and for predicting non-equilibrium phenomena in systems with either short-ranged or long-ranged interactions. These shortcomings highlight the need for new approaches to represent and disambiguate interaction potentials that replicate both equilibrium and non-equilibrium phase behavior. In this work, we use experiments and simulations to study a system with long-ranged thermoresponsive colloidal interactions and explore whether a resolution to this challenge can be found in regions of the phase diagram where temporal effects influence material state. We demonstrate that the conditions for non-equilibrium arrest by colloidal gelation are sensitive to both the shape of the interaction potential and the thermal quench rate. We exploit this sensitivity to propose a kinetics-based algorithm to extract distinct arrest conditions for candidate potentials that accurately selects between potentials that differ in shape but share the same predicted equilibrium structure. The method reveals that each potential has a quantitatively distinct arrest line, providing insight into how the shape of longer-ranged potentials influences the conditions for colloidal gelation.

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

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

The generalized continuous multiple step (GCMS) potential: model systems and benchmarks

The generalized continuous multiple step (GCMS) potential is presented in this work. Its flexible form allows forrepulsiveand/orattractivecontributions to be encoded through adjustable energy and length scales. The GCMS interaction provides a continuous representation of square-well, square-shoulder potentials and their variants for implementation in computer simulations. A continuous and differentiable energy representation is required to derive forces in conventional simulation algorithms. Molecular dynamics simulations are of particular interest when considering the dynamic properties of a system. The GCMS potential can mimic other interactions with a judicious choice of parameters due to the versatile sigmoid form. In this study, our benchmarks for the GCMS representation include triangular, Yukawa, Franzese, and Lennard-Jones potentials. Comparisons made with published data on volumetric phase diagrams, liquid structure, and diffusivity from model systems are in excellent agreement.

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.

Waiting-time dependent non-equilibrium phase diagram of simple glass- and gel-forming liquids

Under numerous circumstances, many soft and hard materials are present in a puzzling wealth of non-equilibrium amorphous states, whose properties are not stationary and depend on preparation. They are often summarized in unconventional "phase diagrams" that exhibit new "phases" and/or "transitions" in which time, however, is an essential variable. This work proposes a solution to the problem of theoretically defining and predicting these non-equilibrium phases and their time-evolving phase diagrams, given the underlying molecular interactions. We demonstrate that these non-equilibrium phases and the corresponding non-stationary (i.e., aging) phase diagrams can indeed be defined and predicted using the kinetic perspective of a novel non-equilibrium statistical mechanical theory of irreversible processes. This is illustrated with the theoretical description of the transient process of dynamic arrest into non-equilibrium amorphous solid phases of an instantaneously quenched simple model fluid involving repulsive hard-sphere plus attractive square well pair interactions.

Monodisperse patchy particle glass former

Glass formers are characterized by their ability to avoid crystallization. As monodisperse systems tend to rapidly crystallize, the most common glass formers in simulations are systems composed of mixtures of particles with different sizes. Here, we make use of the ability of patchy particles to change their local structure to propose them as monodisperse glass formers. We explore monodisperse systems with two patch geometries: a 12-patch geometry that enhances the formation of icosahedral clusters and an 8-patch geometry that does not appear to strongly favor any particular local structure. We show that both geometries avoid crystallization and present glassy features at low temperatures. However, the 8-patch geometry better preserves the structure of a simple liquid at a wide range of temperatures and packing fractions, making it a good candidate for a monodisperse glass former.

Cluster formation in symmetric binary SALR mixtures

The equilibrium cluster fluid state of a symmetric binary mixture of particles interacting through short-ranged attractive and long-ranged repulsive interactions is investigated through Monte Carlo simulations. We find that the clustering behavior of this system is controlled by the cross-interaction between the two types of particles. For a weak cross-attraction, the system displays a behavior that is a composite of the behavior of individual components, i.e., the two components can both form giant clusters independently and the clusters distribute evenly in the system. For a strong cross-attraction, we instead find that the resulting clusters are mixtures of both components. Between these limits, both components can form relatively pure clusters, but unlike clusters can join at their surfaces to form composite clusters. These insights should help to understand the mechanisms for clustering in experimental binary mixture systems and help tailor the properties of novel nanomaterials.

Glassy Behavior of Sticky Spheres: What Lies beyond Experimental Timescales?

We use the swap Monte Carlo algorithm to analyze the glassy behavior of sticky spheres in equilibrium conditions at densities where conventional simulations and experiments fail to reach equilibrium, beyond predicted phase transitions and dynamic singularities. We demonstrate the existence of a unique ergodic region comprising all the distinct phases previously reported, except for a phase-separated region at strong adhesion. All structural and dynamic observables evolve gradually within this ergodic region, the physics evolving smoothly from well-known hard sphere glassy behavior at small adhesions and large densities, to a more complex glassy regime characterized by unusually broad distributions of relaxation timescales and length scales at large adhesions.

Diffusing wave microrheology of strongly attractive dense emulsions

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

ALS/FTLD-Linked Mutations in FUS Glycine Residues Cause Accelerated Gelation and Reduced Interactions with Wild-Type FUS

The RNA-binding protein fused in sarcoma (FUS) can form pathogenic inclusions in neurodegenerative diseases like amyotrophic lateral sclerosis (ALS) and frontotemporal lobar dementia (FTLD). Over 70 mutations in Fus are linked to ALS/FTLD. In patients, all Fus mutations are heterozygous, indicating that the mutant drives disease progression despite the presence of wild-type (WT) FUS. Here, we demonstrate that ALS/FTLD-linked FUS mutations in glycine (G) strikingly drive formation of droplets that do not readily interact with WT FUS, whereas arginine (R) mutants form mixed condensates with WT FUS. Remarkably, interactions between WT and G mutants are disfavored at the earliest stages of FUS nucleation. In contrast, R mutants physically interact with the WT FUS such that WT FUS recovers the mutant defects by reducing droplet size and increasing dynamic interactions with RNA. This result suggests disparate molecular mechanisms underlying ALS/FTLD pathogenesis and differing recovery potential depending on the type of mutation.

Violation of Stokes-Einstein and Stokes-Einstein-Debye relations in polymers at the gas-supercooled liquid coexistence

Molecular dynamics simulations are performed on a system of model linear polymers to look at the violations of Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations near the mode coupling theory transition temperatureT_cat three (one higher and two lower) densities. At low temperatures, both lower density systems show stable gas-supercooled-liquid coexistence whereas the higher density system is homogeneous. We show that monomer density relaxation exhibits SE violation for all three densities, whereas molecular density relaxation shows a weak violation of the SE relation nearT_cin both lower density systems. This study identifies disparity in monomer mobility and observation of jumplike motion in the typical monomer trajectories resulting in the SE violations. In addition to the SE violation, a weak SED violation is observed in the gas-supercooled-liquid coexisting domains of the lower densities. Both lower density systems also show a decoupling of translational and rotational dynamics in this polymer system.

Multi-component colloidal gels: interplay between structure and mechanical properties

We present a detailed numerical study of multi-component colloidal gels interacting sterically and obtained by arrested phase separation. Under deformation, we found that the interplay between the different intertwined networks is key. Increasing the number of components leads to softer solids that can accommodate progressively larger strains before yielding. The simulations highlight how this is the direct consequence of the purely repulsive interactions between the different components, which end up enhancing the linear response of the material. Our work provides new insight into mechanisms at play for controlling the material properties and opens a road to new design principles for soft composite solids.

Glass transition and reversible gelation in asymmetric binary mixtures: A study by mode coupling theory and molecular dynamics

The glass transition and the binodals of asymmetric binary mixtures are investigated from the effective fluid approach in the mode coupling theory and by molecular dynamics. Motivated by previous theoretical predictions, the hard-sphere mixture and the Asakura-Oosawa models are used to analyze experimental results from the literature, relative to polystyrene spheres mixed either with linear polymers or with dense microgel particles. In agreement with the experimental observations, the specificity of the depletant particles is shown to favor lower density gels. It further favors equilibrium gelation by reducing also the tendency of the system to phase separate. These results are confirmed by a phenomenological modification of the mode coupling theory in which the vertex functions are computed at an effective density lower than the actual one. A model effective potential in asymmetric mixtures of hard particles is used to further check this phenomenological modification against molecular dynamics simulation.

α-relaxation, shear viscosity, and elastic moduli of hard-particle fluids from a mode-coupling theory with a retarded vertex

The recently proposed modification of the mode-coupling theory (MCT) in which the static structure used in the vertex is computed at a lower density than the actual one is tested on several dynamics-related properties. The predictions from this modified version of MCT calibrated on the one-component hard-sphere fluid are found in very good agreement with simulation data for one-component and binary hard-sphere fluids. They are also relevant for the stress moduli for models with attractive tails beyond the hard core. The clear improvement observed on several properties should give a new impetus to the use of MCT as a quantitative tool.

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.

Evolution of the pore size distribution in sheared binary glasses

Molecular dynamics simulations are carried out to investigate mechanical properties and porous structure of binary glasses subjected to steady shear. The model vitreous systems were prepared via thermal quench at constant volume to a temperature well below the glass transition. The quiescent samples are characterized by a relatively narrow pore size distribution whose mean size is larger at lower glass densities. We find that in the linear regime of deformation, the shear modulus is a strong function of porosity, and the individual pores become slightly stretched while their structural topology remains unaffected. By contrast, with further increasing strain, the shear stress saturates to a density-dependent plateau value, which is accompanied by pore coalescence and a gradual development of a broader pore size distribution with a discrete set of peaks at large length scales.

Optically transparent dense colloidal gels

Traditionally it has been difficult to study the porous structure of dense colloidal gels and (macro) molecular transport through them simply because of the difference in refractive index between the colloid material and the continuous fluid phase surrounding it, rendering the samples opaque even at low colloidal volume fractions. Here, we demonstrate a novel colloidal gel that can be refractive index-matched in aqueous solutions owing to the low refractive index of fluorinated latex (FL)-particles (n = 1.37). Synthesizing them from heptafluorobutyl methacrylate using emulsion polymerization, we demonstrate that they can be functionalized with short DNA sequences via a dense brush-layer of polystyrene-b-poly(ethylene oxide) block-copolymers (PS-PEO). The block-copolymer, holding an azide group at the free PEO end, was grafted to the latex particle utilizing a swelling-deswelling method. Subsequently, DNA was covalently attached to the azide-end of the block copolymer via a strain-promoted alkyne-azide click reaction. For comparison, we present a structural study of single gels made of FL-particles only and composite gels made of a percolating FL-colloid gel coated with polystyrene (PS) colloids. Further we demonstrate that the diffusivity of tracer colloids dispersed deep inside a refractive index matched FL-colloidal gel can be measured as function of the local confinement using Dynamic Differential Microscopy (DDM).

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.

Ultra-long-range dynamic correlations in a microscopic model for aging gels

We use large-scale computer simulations to explore the nonequilibrium aging dynamics in a microscopic model for colloidal gels. We find that gelation resulting from a kinetically arrested phase separation is accompanied by "anomalous" particle dynamics revealed by superdiffusive particle motion and compressed exponential relaxation of time correlation functions. Spatiotemporal analysis of the dynamics reveals intermittent heterogeneities producing spatial correlations over extremely large length scales. Our study is a microscopically resolved model reproducing all features of the spontaneous aging dynamics observed experimentally in soft materials.

Glass transition in hard-core fluids and beyond, using an effective static structure in the mode coupling theory

The dynamical arrest in classical fluids is studied using a simple modification of the mode coupling theory (MCT) aimed at correcting its overestimation of the tendency to glass formation while preserving its overall structure. As in previous attempts, the modification is based on the idea of tempering the static pair correlations used as input. It is implemented in this work by computing the static structure at a different state point than the one used to solve the MCT equation for the intermediate scattering function, using the pure hard-sphere glass for calibration. The location of the glass transition predicted from this modification is found to agree with simulations data for a variety of systems --pure fluids and mixtures with either purely repulsive interaction potentials or ones with attractive contributions. Besides improving the predictions in the long-time limit, and so reducing the non-ergodicity domain, the same modification works as well for the time-dependent correlators.

Structure of colloidal gels at intermediate concentrations: the role of competing interactions

Colloidal gels formed by colloid-polymer mixtures with an intermediate volume fraction (ϕ_c ≈ 0.4) are investigated by confocal microscopy. In addition, we have performed Monte Carlo simulations based on a simple effective pair potential that includes a short-range attractive contribution representing depletion interactions, and a longer-range repulsive contribution describing the electrostatic interactions due to the presence of residual charges. Despite neglecting non-equilibrium effects, experiments and simulations yield similar gel structures, characterised by, e.g., the pair, angular and bond distribution functions. We find that the structure hardly depends on the strength of the attraction if the electrostatic contribution is fixed, but changes significantly if the electrostatic screening is changed. This delicate balance between attractions and repulsions, which we quantify by the second virial coefficient, also determines the location of the gelation boundary.

Controlling Self-Assembly Kinetics of DNA-Functionalized Liposomes Using Toehold Exchange Mechanism

The selectivity of Watson-Crick base pairing has allowed the design of DNA-based functional materials bearing an unprecedented level of accuracy. Examples include DNA origami, made of tiles assembling into arbitrarily complex shapes, and DNA coated particles featuring rich phase behaviors. Frequently, the realization of conceptual DNA-nanotechnology designs has been hampered by the lack of strategies for effectively controlling relaxations. In this article, we address the problem of kinetic control on DNA-mediated interactions between Brownian objects. We design a kinetic pathway based on toehold-exchange mechanisms that enables rearrangement of DNA bonds without the need for thermal denaturation, and test it on suspensions of DNA-functionalized liposomes, demonstrating tunability of aggregation rates over more than 1 order of magnitude. While the possibility to design complex phase behaviors using DNA as a glue is already well recognized, our results demonstrate control also over the kinetics of such systems.

How do polydisperse repulsive colloids crystallize?

A modified version of the Gibbs-ensemble Monte-Carlo method reveals how polydisperse charged colloidal particles can build complex colloidal crystals. It provides general rules that are applicable to this fractionated crystallization that stems from size segregation. It explains the spontaneous formation of complex crystals with very large unit-cells in suspensions of nanoparticles with a broad size distribution.

Varying the counter ion changes the kinetics, but not the final structure of colloidal gels

We show that, while the gelation of colloidal silica proceeds much faster in the presence of added KCl than NaCl, the final gels are very similar in structure and properties. We have studied the gelation process by visual inspection and by small angle X-ray scattering for a range of salt and silica particle concentrations. The characteristic times of the early aggregation process and the formation of a stress-bearing structure with both salts are shown to collapse onto master curves with single multiplicative constants, linked to the stability ratio of the colloidal suspensions. The influence of the salt type and concentration is confirmed to be mainly kinetic, as the static structure factors and viscoelastic moduli of the gels are shown to be equivalent at normalized times. While there is strong variation in the kinetics, the structure and properties of the gel at long-times are shown to be mainly controlled by the concentration of particles, and hardly influenced by the type or the concentration of salt. This suggests that the differences between gels generated by different salts are only transient in time.

A minimal description of morphological hierarchy in two-dimensional aggregates

A dimensionless parameter Λ is proposed to describe a hierarchy of morphologies in two-dimensional (2D) aggregates formed due to varying competition between short-range attraction and long-range repulsion. Structural transitions from finite non-compact to compact to percolated structures are observed in the configurations simulated by molecular dynamics at a constant temperature and density. Configurational randomness across the transition, measured by the two-body excess entropy S2, exhibits data collapse with the average potential energy [small epsilon, Greek, macron] of the systems. Independent master curves are presented among S2, the reduced second virial coefficient B2* and Λ, justifying this minimal description. This work lays out a coherent basis for the study of 2D aggregate morphologies relevant to diverse nano- and bio-processes.

Microdynamics and arrest of coarsening during spinodal decomposition in thermoreversible colloidal gels

Coarsening and kinetic arrest of colloidal systems undergoing spinodal decomposition (SD) is a conserved motif for forming hierarchical, bicontinuous structures. Although the thermodynamic origins of SD in colloids are widely known, the microstructural processes responsible for its coarsening and associated dynamics en route to arrest remain elusive. To better elucidate the underlying large-scale microdynamical processes, we study a colloidal system with moderate-range attractions which displays characteristic features of arrested SD, and study its dynamics during coarsening through a combination of differential dynamic microscopy and real-space tracking. Using these recently developed imaging techniques, we reveal directly that the coarsening arises from collective dynamics of dense domains, which undergo slow, intermittent, and ballistic motion. These collective motions indicate interfacial effects to be the driving force of coarsening. The nature of the gelation enables control of the arrested length scale of coarsening by the depths of quenching into the spinodal regime, which we demonstrate to provide an effective means to control the elasticity of colloidal gels.

Monte Carlo simulation of kinetically slowed down phase separation

Supercooled colloidal or molecular systems at low densities are known to form liquid, crystalline or glassy drops, which may remain isolated for a long time before they aggregate. This paper analyses the properties of this large time window, and how it can be tackled by computer simulation. We use single-particle and virtual move Monte Carlo simulations of short-range attractive spheres which are undercooled to the temperature region, where the spinodal intersects the attractive glass line. We study two different systems and we report the following kinetic behavior. A low-density system is shown to exhibit universal linear growth regimes under single-particle Monte Carlo correlating the growth rate to the local structure. These regimes are suppressed under collective motion, where droplets aggregate into a single large disordered domain. It is shown that the aggregation can be avoided and linear regimes recovered, if long-range repulsion is added to the short-range attraction. The results provide an insight into the behavior of the virtual move algorithm generating cluster moves according to the local forcefields. We show that different choices of maximum Monte Carlo displacement affect the dynamical trajectories but lead to the same kinetically slowed down or arrested states.

Intermittent dynamics and logarithmic domain growth during the spinodal decomposition of a glass-forming liquid

We use large-scale molecular dynamics simulations of a simple glass-forming system to investigate how its liquid-gas phase separation kinetics depends on temperature. A shallow quench leads to a fully demixed liquid-gas system whereas a deep quench makes the dense phase undergo a glass transition and become an amorphous solid. This glass has a gel-like bicontinuous structure that evolves very slowly with time and becomes fully arrested in the limit where thermal fluctuations become negligible. We show that the phase separation kinetics changes qualitatively with temperature, the microscopic dynamics evolving from a surface tension-driven diffusive motion at high temperature to a strongly intermittent, heterogeneous, and thermally activated dynamics at low temperature, with a logarithmically slow growth of the typical domain size. These results elucidate the microscopic mechanisms underlying a specific class of viscoelastic phase separation.

Temperature dependence of aging kinetics of hectorite clay suspensions

The aging of salt-free hectorite suspensions with different concentrations (c(L)=2.9, 3.2 and 3.5 wt%) stored for 2 days or 4 days was studied by rheology at different temperatures. The evolution of storage and loss moduli G' and G″ during aging followed aging time-temperature superposition. The temperature dependence of the shift factor a(T), which reflected the aging kinetics, was interpreted by the reaction-limited colloidal aggregation (RLCA) mechanism with counterion condensation in calculating the double-layer interaction of the charged clay particles. Temperature dependence of the plateau modulus and yield stress of the suspension aged for 800 s was modeled with the soft glassy rheology (SGR) theory. The estimated noise temperature x indicated that the sample aged at higher temperature corresponded to a deeper quench in the nonergodic state. Under larger amplitude of oscillatory shear, the suspension exhibited a strain rate-frequency superposition (SRFS). The shearing eliminated the effects of aging and heating.

Gelation of large hard particles with short-range attraction induced by bridging of small soft microgels

In this study, mixed suspensions of large hard polystyrene microspheres and small soft poly(N-isopropylacrylamide) microgels are used as model systems to investigate the static and viscoelastic properties of suspensions which go through liquid to gel transitions. The microgels cause short-range attraction between microspheres through the bridging and depletion mechanism whose strength can be tuned by the microgel concentration. Rheological measurements are performed on suspensions with the volume fraction (Φ) of microspheres ranging from 0.02 to 0.15, and the transitions from liquid-like to solid-like behaviors triggered by the concentration of microgels are carefully identified. Two gel lines due to bridging attraction under unsaturated conditions are obtained. Ultra-small angle neutron scattering is used to probe the thermodynamic properties of suspensions approaching the liquid-solid transition boundaries. Baxter's sticky hard-sphere model is used to extract the effective inter-microsphere interaction introduced by the small soft microgels. It is found that the strength of attraction (characterized by a single stickiness parameter τ) on two gel lines formed by bridging is very close to the theoretical value for the spinodal line in the τ-Φ phase diagram predicted by Baxter's model. This indicates that the nature of the gel state may have the same thermodynamic origins, independent of the detailed mechanism of the short-range attraction. The relationship between the rheological criterion for the liquid-solid transition and the thermodynamic criterion for the equilibrium-nonequilibrium transition is also discussed.

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

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

Self-assembly and cooperative dynamics of a model colloidal gel network

We study the assembly into a gel network of colloidal particles, via effective interactions that yield local rigidity and make dilute network structures mechanically stable. The self-assembly process can be described by a Flory-Huggins theory, until a network of chains forms, whose mesh size is on the order of, or smaller than, the persistence length of the chains. The localization of the particles in the network, akin to some extent to caging in dense glasses, is determined by the network topology, and the network restructuring, which takes place via bond breaking and recombination, is characterized by highly cooperative dynamics. We use NVE and NVT molecular dynamics as well as Langevin dynamics and find a qualitatively similar time dependence of time correlations and of the dynamical susceptibility of the restructuring gel. This confirms that the cooperative dynamics emerge from the mesoscale organization of the network.

Aggregation dynamics, structure, and mechanical properties of bigels

Recently we have introduced bigels, inter-penetrating gels made of two different colloidal species. Even if particles with simple short-range isotropic potential are employed, the selective interactions enable the tunability of the self-assembly, leading to the formation of complex structures. In the present paper, we explore the non-equilibrium dynamics and the phenomenology underlying the kinetic arrest under quench and the formation of bigels. We demonstrate that the peculiar bigel kinetics can be described through an arrested spinodal decomposition driven by demixing of the colloidal species. The role played by the presence of a second colloidal species on the phase diagram, as expanded to account for the increased number of parameters, is clarified both via extensive numerical simulations and experiments. We provide details on the realisation of bigels, by means of DNA-coated colloids (DNACCs), and the consequent imaging techniques. Moreover we evidence, by comparison with the usual one-component gel formation, the emergence of controllable timescales in the aggregation of the bigels, whose final stages are also experimentally studied to provide morphological details. Finally, we use numerical models to simulate the bigel response to mechanical strain, highlighting how such a new material can bear significantly higher stress compared to the usual one-component gel. We conclude by discussing possible technological uses and by providing insights on the viable research steps to undertake for more complex and yet tuneable multi-component colloidal systems.

Collective translational and rotational Monte Carlo moves for attractive particles

Virtual move Monte Carlo is a Monte Carlo (MC) cluster algorithm forming clusters via local energy gradients and approximating the collective kinetic or dynamic motion of attractive colloidal particles. We carefully describe, analyze, and test the algorithm. To formally validate the algorithm through highlighting its symmetries, we present alternative and compact ways of selecting and accepting clusters which illustrate the formal use of abstract concepts in the design of biased MC techniques: the superdetailed balance and the early rejection scheme. A brief and comprehensive summary of the algorithms is presented, which makes them accessible without needing to understand the details of the derivation.

Active patterning and asymmetric transport in a model actomyosin network

Cytoskeletal networks, which are essentially motor-filament assemblies, play a major role in many developmental processes involving structural remodeling and shape changes. These are achieved by nonequilibrium self-organization processes that generate functional patterns and drive intracellular transport. We construct a minimal physical model that incorporates the coupling between nonlinear elastic responses of individual filaments and force-dependent motor action. By performing stochastic simulations we show that the interplay of motor processes, described as driving anti-correlated motion of the network vertices, and the network connectivity, which determines the percolation character of the structure, can indeed capture the dynamical and structural cooperativity which gives rise to diverse patterns observed experimentally. The buckling instability of individual filaments is found to play a key role in localizing collapse events due to local force imbalance. Motor-driven buckling-induced node aggregation provides a dynamic mechanism that stabilizes the two-dimensional patterns below the apparent static percolation limit. Coordinated motor action is also shown to suppress random thermal noise on large time scales, the two-dimensional configuration that the system starts with thus remaining planar during the structural development. By carrying out similar simulations on a three-dimensional anchored network, we find that the myosin-driven isotropic contraction of a well-connected actin network, when combined with mechanical anchoring that confers directionality to the collective motion, may represent a novel mechanism of intracellular transport, as revealed by chromosome translocation in the starfish oocyte.

Carbon nanotubes induced gelation of unmodified hyaluronic acid

This work reports an experimental study of the kinetics and mechanisms of gelation of carbon nanotubes (CNTs)-hyaluronic acid (HA) mixtures. These materials are of great interest as functional biogels for future medical applications and tissue engineering. We show that CNTs can induce the gelation of noncovalently modified HA in water. This gelation is associated with a dynamical arrest of a liquid crystal phase separation, as shown by small-angle light scattering and polarized optical microscopy. This phenomenon is reminiscent of arrested phase separations in other colloidal systems in the presence of attractive interactions. The gelation time is found to strongly vary with the concentrations of both HA and CNTs. Near-infrared photoluminescence reveals that the CNTs remain individualized both in fluid and in gel states. It is concluded that the attractive forces interplay are likely weak depletion interactions and not strong van der Waals interactions which could promote CNT rebundling, as observed in other biopolymer-CNT mixtures. The present results clarify the remarkable efficiency of CNT at inducing the gelation of HA, by considering that CNTs easily phase separate as liquid crystals because of their giant aspect ratio.

Enhanced tunneling conductivity induced by gelation of attractive colloids

We show that the formation of a gel by conducting colloidal particles leads to a dramatic enhancement in bulk conductivity, due to interparticle electron tunneling, combining predictions from molecular-dynamics simulations with structural measurements in an experimental colloid system. Our results show how colloidal gelation can be used as a general route to huge enhancements of conductivity, and suggest a feasible way for developing cheap materials with novel properties and low metal content.

Vascular networks due to dynamically arrested crystalline ordering of elongated cells

Recent experimental and theoretical studies suggest that crystallization and glass-like solidification are useful analogies for understanding cell ordering in confluent biological tissues. It remains unexplored how cellular ordering contributes to pattern formation during morphogenesis. With a computational model we show that a system of elongated, cohering biological cells can get dynamically arrested in a network pattern. Our model provides an explanation for the formation of cellular networks in culture systems that exclude intercellular interaction via chemotaxis or mechanical traction.