The concept of a local linear elastic strain field is commonly used in the metallurgical research community to approximate the collective effect of atomic displacements around crystalline defects. Here we show that the elastic strain field approximation is a useful tool in colloidal systems. For colloidal crystals with repulsive particle interaction potentials, given similar mechanical properties, sharper potentials lead to: 1) free energies of deformation dominated by entropy, 2) lower variance in strain field fluctuations, 3) increased tension-compression asymmetry near dislocation core regions, and 4) smaller windows of applicability of the linear elastic approximation. We show that the window of linear behavior for entropic colloidal crystals is broadened for pressures at which the inter-particle separation sufficiently exceeds the range of steep repulsive interactions.
Impurity-induced defects play a crucial role for the properties of crystals, but little is known about impurities with anisotropic shape. Here, we study how colloidal dumbbells distort and interact with a hexagonal crystal of charged colloidal spheres at a fluid interface. We find that subtle changes in the dumbbell length induce a transition from a local distortion to a particle-bound dislocation, and determine how the dumbbell moves inside the repulsive hexagonal lattice. Our results provide new routes towards controlling material properties through particle-bound dislocations.
We report a numerical study of the shear viscosity and the frequency dependent elastic moduli close to dynamical arrest for a model of short-range attractive colloids, both for the repulsive and the attractive glass transition. Calculating the stress autocorrelation functions, we find that density fluctuations of wavevectors close to the first peak in the structure factor control the viscosity rise on approaching the repulsive glass, while fluctuations of larger wavevectors control the viscosity close to the attractive glass. On approaching the glass transition, the viscosity diverges with a p…
Experiments with polymer latex solutions show the coexistence of order-disorder structures of macroions. Because of the large macroions' sizes, this order-disorder phase coexistence imply the existence of very long-range attractive and repulsive forces, which can not be explained in terms of conventional direct interaction potentials, which are short-range. Here we apply an integral equations theory to a simple model for colloidal dispersions, at finite concentrations, calculate the particles distribution functions and the involved effective forces. We find very long-range attractive and repul…
We report an extensive numerical study of a charged colloidal system with competing short-range depletion attraction and long-range electrostatic repulsion. By analizing the cluster properties, we identify two distinct regions in the phase diagram: a state composed of stable finite-size clusters, whose relative interactions are dominated by long-range repulsion, and a percolating network. Both states are found to dynamically arrest at low temperatures, providing evidence of the existence of two distinct non-ergodic states in these systems: a Wigner glass of clusters and a gel.
When amorphous solids are strained they display elastic deformation at small strain, however, beyond a critical strain they yield and begin to flow plastically. The origin of this plasticity lies in the irreversible rearrangement of particles. Such rearrangements have been shown to give rise to a long-ranged quadrupolar strain field, similar to Eshebly's spherical inclusions. However, their spatio-temporal organisation at finite temperatures and finite shear rate remains unclear. Here, we have investigated the strain field in sheared colloidal glasses. We show that the strain field in homogene…
We report a numerical investigation of the visco-elastic behavior in models for steric repulsive and short-range attractive colloidal suspensions, along different paths in the attraction-strength vs packing fraction plane. More specifically, we study the behavior of the viscosity (and its frequency dependence) on approaching the repulsive glass, the attractive glass and in the re-entrant region where viscosity shows a non monotonic behavior on increasing attraction strength. On approaching the glass lines, the increase of the viscosity is consistent with a power-law divergence with the same ex…
We use an analogue of nanoindentation on a colloidal glass to elucidate the incipient plastic deformation of glasses. By tracking the motion of the individual particles in three dimensions, we visualize the strain field and glass structure during the emerging deformation. At the onset of flow, we observe a power-law distribution of strain indicating strongly correlated deformation, and reflecting a critical state of the glass. At later stages, the strain acquires a Gaussian distribution, indicating that plastic events become uncorrelated. Investigation of the glass structure using both static …
Understanding the relaxation dynamics of colloidal suspensions is crucial to identify the elements that influence the mobility of their constituents, assess their macroscopic response across the relevant time and length scales, and thus disclose the fundamentals underpinning their exploitation in formulation engineering. In this work, we specifically assess the impact of long-ranged ordering on the relaxation dynamics of suspensions of soft-repulsive rod-like particles, which are able to self-organise into nematic and smectic liquid-crystalline phases. By performing Dynamic Monte Carlo simulat…
We monitor the relaxation of internal stresses in a fractal colloidal gel on cessation of flow and find a weak power law decay, $σ_i \sim t^{-α}$ over 5 decades of time where $α\approx 0.07$. The system exhibits physical aging of the elastic modulus, $G' \sim t^β$, with $β\approx α$. Imposition of zero stress after waiting time $t_w$ results in strain recovery as the system relaxes without constraint. Remarkably, recoveries at different $t_w$ can be shifted to construct a master curve where data are scaled vertically by $1/σ_i(t_w)$ and plotted horizontally as $(t-t_w)/t_w^μ$ where $μ\approx 1…
We present here a microscopic study of the effect of shear on a dense purely repulsive colloidal suspension. We use Multispeckle Diffusing Wave Spectroscopy to monitor the transient motions of colloidal particles after being submitted to an oscillatory strain. This technique proves efficient to record the time evolution of the relaxation times distribution. After a high oscillatory shear, we show that this distribution displays a full aging behavior. Oppositely, when a moderate shear is applied the distribution is modified in a non trivial way. Whereas high shear is able to erase all the sampl…
We show by computer simulation of a two-dimensional crystal confined by corrugated walls that confinement can be used to impose a controllable mesoscopic superstructure of predominantly mechanical elastic character. Due to an interplay of the particle density of the system and the width D of the confining channel, "soliton staircases" can be created along both parallel confining boundaries, that give rise to standing strain waves in the entire crystal. The periodicity of these waves is of the same order as D. This mechanism should be useful for structure formation in the self-assembly of vario…
We investigate the stress relaxation behavior on the application of step strains to aging aqueous suspensions of the synthetic clay Laponite. The stress exhibits a two-step decay, from which the slow relaxation modes are extracted as functions of the sample ages and applied step strain deformations. Interestingly, the slow time scales that we estimate show a dramatic enhancement with increasing strain amplitudes. We argue that the system ends up exploring the deeper sections of its energy landscape following the application of the step strain.
We examine 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 of a hard sphere colloidal suspension with the addition of non-adsorbing linear polymer chains. Results reveal three distinct regimes depending on the strain amplitude of oscillatory shear. Large shear strain amplitudes fully break the structure which results into a more homogenous and stronger gel afte…
Understanding the correlation between structure and rheology in colloidal suspensions is important as these suspensions are crucial in industrial applications. Moreover, colloids exhibit a wide range of structures under confinement that could considerably alter the viscosity. Here, we use a combination of experiments and simulations to elucidate how confinement induced structures alter the relative contributions of hydrodynamic and repulsive forces to produce up to a ten fold change in the viscosity. We use a custom built confocal rheoscope to image the particle configurations of a colloidal s…
We investigate the nonequilibrium behavior of dense, plastic-crystalline suspensions of mildly anisotropic colloidal hard dumbbells under the action of an oscillatory shear field by employing Brownian dynamics computer simulations. In particular, we extend previous investigations, where we uncovered novel nonequilibrium phase transitions, to other aspect ratios and to a larger nonequilibrium parameter space, that is, a wider range of strains and shear frequencies. We compare and discuss selected results in the context of novel scattering and rheological experiments. Both simulations and experi…
Recent computational and theoretical studies have shown that the deformation of colloidal suspensions under a steady shear is highly heterogeneous at the particle level and demonstrate a critical influence on the macroscopic deformation behavior. Despite its relevance to a wide variety of industrial applications of colloidal suspensions, scattering studies focusing on addressing the heterogeneity of the non-equilibrium colloidal structure are scarce thus far. Here, we report the first experimental result using small-angle neutron scattering. From the evolution of strain heterogeneity, we concl…
A comparison is made between the nonlinear rheological response of bulk metallic glass formers and of colloidal dispersions. Stress-strain curves measured after switch-on of constant deformation rates are analyzed quantitatively using a schematic model of mode coupling theory generalized to homogeneous and incompressible flows. A mapping between metallic and dispersion rheology is possible when stresses are rescaled by an entropic scale, accumulated strains by geometrical factors, and rates by the intrinsic relaxation time. Exploiting this similarity and the possibility to directly observe ind…
The depletion interaction mediated by non-adsorbing polymers promotes condensation and assembly of repulsive colloidal particles into diverse higher-order structures and materials. One example, with particularly rich emergent behaviors, is the formation of two-dimensional colloidal membranes from a suspension of filamentous $\it{fd}$ viruses, which act as rods with effective repulsive interactions, and dextran, which acts as a condensing, depletion-inducing agent. Colloidal membranes exhibit chiral twist even when the constituent virus mixture lacks macroscopic chirality, change from a circula…
The depletion potential between two hard spheres in a solvent of thin hard disclike platelets is investigated by using either the Derjaguin approximation or density functional theory. Particular attention is paid to the density dependence of the depletion potential. A second-order virial approximation is applied, which yields nearly exact results for the bulk properties of the hard-platelet fluid at densities two times smaller than the density of the isotropic fluid at isotropic-nematic phase coexistence. As the platelet density increases, the attractive primary minimum of the depletion potent…
Evolution of the energy landscape during physical aging of glassy materials can be understood from the frequency and strain dependence of the shear modulus but the non-stationary nature of these systems frustrates investigation of their instantaneous underlying properties. Using a series of time dependent measurements we systematically reconstruct the frequency and strain dependence as a function of age for a repulsive colloidal glass undergoing structural arrest. In this manner, we are able to unambiguously observe the structural relaxation time, which increases exponentially with sample age …
The translational dynamics in a repulsive colloidal glass-former is probed by time-resolved X-ray Photon Correlation Spectroscopy. In this dense dispersion of charge-stabilized and magnetic nanoparticles, the interaction potential can be tuned, from quasi-isotropic to anisotropic by applying an external magnetic field. Structural and dynamical anisotropies are reported on interparticle lengthscales associated with highly anisotropic cooperativity, almost two orders of magnitude larger in the field direction than in the perpendicular direction and in zero field.
The mechanical response of glasses remains challenging to understand. Recent results indicate that the oscillatory rheology of soft glasses is accompanied by a sharp non-equilibrium transition in the microscopic dynamics. Here, we use simultaneous x-ray scattering and rheology to investigate the reversibility and hysteresis of the sharp sharp symmetry change from anisotropic solid to isotropic liquid dynamics observed in the oscillatory shear of colloidal glasses [D. V. Denisov, M. T. Dang, B. Struth, A. Zaccone, and P. Schall, Sci. Rep. 5, 14359 (2015)]. We use strain sweeps with increasing a…
Dense supercooled colloidal melt in forward shear from a quiescent state shows overshoot in shear stress at 10% strain with an unchanged fluid structure at equal stress before and after overshoot. In addition, we find overshoot in normal stress with a monotonic increase in osmotic pressure at an identical strain. The first and second normal stress become comparable in magnitude and opposite in sign. Functional dependence of the steady state stress and osmotic pressure with Peclet number demonstrate signature of crossover between Newtonian and nearly- Newtonian regime. Moreover, instantaneous s…
We use a combination of original light scattering techniques and particles with unique optical properties to investigate the behavior of suspensions of attractive colloids under gravitational stress, following over time the concentration profile, the velocity profile, and the microscopic dynamics. During the compression regime, the sedimentation velocity grows nearly linearly with height, implying that the gel settling may be fully described by a (time-dependent) strain rate. We find that the microscopic dynamics exhibit remarkable scaling properties when time is normalized by strain rate, sho…
The rheology of dense amorphous materials under large shear strain is not fully understood, partly due to the difficulty of directly viewing the microscopic details of such materials. We use a colloidal suspension to simulate amorphous materials, and study the shear-induced structural relaxation with fast confocal microscopy. We quantify the plastic rearrangements of the particles in several ways. Each of these measures of plasticity reveals spatially heterogeneous dynamics, with localized regions where many particles are strongly rearranging by these measures. We examine the shapes of these r…
Glasses behave as solids on experimental time scales due to their slow relaxation. Growing dynamic length scales due to cooperative motion of particles are believed to be central to this slow response. For quiescent glasses, however, the size of the cooperatively rearranging regions has never been observed to exceed a few particle diameters, and the observation of long-range correlations that are signatures of an elastic solid has remained elusive. Here, we provide direct experimental evidence of long-range correlations during the deformation of a dense colloidal glass. By imposing an external…
We examine the response of a dense colloidal suspension to a local force applied by a small magnetic bead. For small forces, we find a linear relationship between the force and the displacement, suggesting the medium is elastic, even though our colloidal samples macroscopically behave as fluids. We interpret this as a measure of the strength of colloidal caging, reflecting the proximity of the samples' volume fractions to the colloidal glass transition. The strain field of the colloidal particles surrounding the magnetic probe appears similar to that of an isotropic homogeneous elastic medium.…
Mode coupling theory (MCT) has had notable successes in addressing the rheology of hard-sphere colloidal glasses, and also soft colloidal glasses such as star-polymers. Here, we explore the properties of a recently developed MCT-based schematic constitutive equation under idealized experimental protocols involving single and then double step strains. We find strong deviations from expectations based on factorable, BKZ-type constitutive models. Specifically, a nonvanishing stress remains long after the application of two equal and opposite step strains; this residual stress is a signature of pl…
We investigate the nonlinear viscoelastic behavior of a colloidal dispersion at the critical gel state using large amplitude oscillatory shear (LAOS) rheology. The colloidal gel at the critical point is subjected to oscillatory shear flow with increasing strain amplitude at different frequencies. We observe that the first harmonic of the elastic and viscous moduli exhibits a monotonic decrease as the material undergoes a linear to nonlinear transition. We analyze the stress waveform across this transition and obtain the nonlinear moduli and viscosity as a function of frequency and strain ampli…
Many metastable complex fluids such as colloidal glasses and gels show distinct nonlinear viscoelasticity with increasing oscillatory-strain amplitude; the storage modulus decreases monotonically as the strain amplitude increases whereas the loss modulus has a distinct peak before it decreases at larger strains. We present a qualitative argument to explain this ubiquitous behavior and use mode coupling theory (MCT) to confirm it. We compare theoretical predictions to the measured nonlinear viscoelasticity in a dense hard sphere colloidal suspensions; reasonable agreement is obtained. The argum…
Silica nanoparticles trapped at air-water interface form a 2D solid state with amorphous order. We propose a theoretical model to describe how this solid-like state deforms under a shear strain ramp up to and beyond a yielding point which leads to plastic flow. The model accounts for all the particle-level and many-body physics of the system: nonaffine displacements, local connectivity and its evolution in terms of cage-breaking, and interparticle interactions mediated by the particle chemistry and colloidal forces. The model is able to reproduce experimental data with only two non-trivial fit…
Tracking microscopic irreversibility during yielding of a colloidal fractal gel with Rheo-Echo-XPCS
ESRF, The European Synchrotron（欧洲同步辐射光源）；ENSL, CNRS, Laboratoire de Physique（里昂师范学院，法国国家科学研究中心，物理实验室）；C3M, ESPCI Paris, Université PSL, CNRS（C3M，巴黎高等物理化工学院，巴黎文理研究大学，法国国家科学研究中心）；Univ. Grenoble Alpes, CNRS, Grenoble INP, LRP（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，格勒诺布尔理工学院，L RP）；Department of Polymer Engineering, IPC, University of Minho（米尼奥大学，聚合物工程系，IPC）
We study numerically the influence of density and strain rate on the diffusion and mobility of a single tagged particle in a sheared colloidal suspension. We determine independently the time-dependent velocity autocorrelation functions and, through a novel method, the response functions with respect to a small force. While both the diffusion coefficient and the mobility depend on the strain rate the latter exhibits a rather weak dependency. Somewhat surprisingly, we find that the initial decay of response and correlation functions coincide, allowing for an interpretation in terms of an 'effect…
Confining a colloidal crystal within a long narrow channel produced by two parallel walls can be used to impose a meso-scale superstructure of a predominantly mechanical elastic character [Chui et al., EPL 2008, 83, 58004]. When the crystal is compressed in the direction perpendicular to the walls, we obtain a structural transition when the number of rows of particles parallel to the walls decreases by one. All the particles of this vanishing row are distributed throughout the crystal. If the confining walls are structured (say with a corrugation along the length of the walls), then these extr…
This mini-review is concerned with two-dimensional colloidal mixtures exposed to various kinds of external fields. By a magnetic field perpendicular to the plane, dipole moments are induced in paramagnetic particles which give rise to repulsive interactions leading to complex crystalline alloys in the composition-asymmetry diagram. A quench in the magnetic field induces complex crystal nucleation scenarios. If exposed to a gravitational field, these mixtures exhibit a brazil--nut effect and show a boundary layering which is explained in terms of a depletion bubble picture. The latter persists …
Computer simulations and theory are used to systematically investigate how the effective force between two big colloidal spheres in a sea of small spheres depends on the basic (big-small and small-small) interactions. The latter are modeled as hard-core pair potentials with a Yukawa tail which can be both repulsive or attractive. For a repulsive small-small interaction, the effective force follows the trends as predicted by a mapping onto an effective non-additive hard-core mixture: both a depletion attraction and an accumulation repulsion caused by small spheres adsorbing onto the big ones ca…
Using a phase field crystal model we study the structure and dynamics of a drop of colloidal suspension during evaporation of the solvent. We model an experimental system where contact line pinning of the drop on the substrate is non-existent. Under such carefully controlled conditions, evaporation of the drop produces an ordered or disordered arrangement of the colloidal residue depending on the initial average density of solute and the drying rate. We obtain a non-equilibrium phase boundary showing amorphous and crystalline phases of single component and binary mixtures of colloidal particle…
As an extension of the former study on 2-dimensional systems, we simulate phase behavior of polymer-grafted colloidal particles in 3 dimensions by molecular Monte Carlo technique in the canonical ensemble. We use a spherically symmetric square-step repulsive interaction potential, which has been obtained using self-consistent field calculation. In previous articles, we have studied these model colloids in 2 dimensions and found that these particles, although their interaction is purely repulsive, self-assemble into a string-like assembly, in a narrow region of physical parameter sets. In the p…
In this work we study onset of nonlinear rheological behavior of a colloidal dispersion of a synthetic hectorite clay, Laponite, at the critical gel state while undergoing sol-gel transition. When subjected to step strain in the nonlinear regime, the relaxation modulus shifts vertically to the lower values such that the deviation from linearity can be accommodated using a strain dependent damping function. We also perform creep-recovery and start-up shear experiments on the studied colloidal dispersion at the critical gel state and monitor deviation in response as the flow becomes nonlinear. A…
The elastic and capillary interactions between a pair of colloidal particles trapped on top of a nematic film are studied theoretically for large separations $d$. The elastic interaction is repulsive and of quadrupolar type, varying as $d^{-5}$. For macroscopically thick films, the capillary interaction is likewise repulsive and proportional to $d^{-5}$ as a consequence of mechanical isolation of the system comprised of the colloids and the interface. A finite film thickness introduces a nonvanishing force on the system (exerted by the substrate supporting the film) leading to logarithmically …
We study the inverse problem of tuning interaction parameters between charged colloidal particles interacting with a hard-core repulsive Yukawa potential, so that they assemble into specified crystal structures. Here, we target the body-centered-cubic (bcc) structure which is only stable in a small region in the phase diagram of charged colloids and is, therefore, challenging to find. In order to achieve this goal, we use the statistical fluctuations in the bond orientational order parameters to tune the interaction parameters for the bcc structure, while initializing the system in the fluid p…
We study the uniaxial compressive behavior of disordered colloidal free-standing micropillars composed of a bidisperse mixture of 3 and 6 um polystyrene particles. Mechanical annealing of confined pillars enables variation of the packing fraction across the phase space of colloidal glasses. The measured normalized strengths and elastic moduli of the annealed freestanding micropillars span almost three orders-of-magnitude despite similar plastic morphology governed by shear banding. We measure a robust correlation between ultimate strengths and elastic constants that is invariant to relative hu…
In mixtures of colloids and nonadsorbing polyelectrolytes, a Donnan potential arises across the region between surfaces that are depleted of polyelectrolyte and the rest of the system. This Donnan potential tends to shift the polyelectrolyte density profile towards the colloidal surface and leads to local accumulation of polyelectrolytes. We derive a zero-field theory for the disjoining pressure between two parallel flat plates. Polyelectrolyte is allowed to enter the confined interplate region at the cost of a conformational free energy penalty. The resulting disjoining pressure shows a cross…
Coarse-graining atomic displacements in a solid produces both local affine strains and "non-affine" fluctuations. Here we study the equilibrium dynamics of these coarse grained quantities to obtain space-time dependent correlation functions. We show how a subset of these thermally excited, non-affine fluctuations act as precursors for the nucleation of lattice defects and suggest how defect probabilities may be altered by an {\it experimentally realisable} "external" field conjugate to the global non-affinity parameter. Our results are amenable to verification in experiments on colloidal cryst…
In colloidal suspensions, the competition between attractive and repulsive interactions gives rise to a rich and complex phenomenology. Here, we study the equilibrium phase diagram of a model system using a DLVO interaction potential by means of molecular dynamics simulations and a thermodynamical approach. As a result, we find tubular and lamellar phases at low volume fraction. Such phases, extremely relevant for designing new materials, may be not easily observed in the experiments because of the long relaxation times and the presence of defects.
We study the phase behaviour of a fluid composed of particles which interact via a pair potential that is repulsive for large inter-particle distances, is attractive at intermediate distances and is strongly repulsive at short distances (the particles have a hard core). As well as exhibiting gas-liquid phase separation, this system also exhibits phase transitions from the uniform fluid phases to modulated inhomogeneous fluid phases. Starting from a microscopic density functional theory, we develop an order parameter theory for the phase transition in order to examine in detail the phase behavi…
Using simulation and theory we study the dynamics of a colloidal suspension in two dimensions subject to a time-delayed repulsive feedback that depends on the positions of the colloidal particles. The colloidal particles experience an additional potential that is a superposition of repulsive potential energies centered around the positions of all the particles a delay time ago. Here we show that such a feedback leads to self-organization of the particles into traveling bands. The width of the bands and their propagation speed can be tuned by the delay time and the range of the imposed repulsiv…
A two-dimensional crystal of repulsive dipolar particles is studied in the vicinity of its melting transition by using Brownian dynamics computer simulation, dynamical density functional theory and phase-field crystal modelling. A vacancy is created by taking out a particle from an equilibrated crystal and the relaxation dynamics of the vacancy is followed by monitoring the time-dependent one-particle density. We find that the vacancy is quickly filled up by diffusive hopping of neighbouring particles towards the vacancy center. We examine the temperature dependence of the diffusion constant a…
Electrostatic repulsions can drive crystallization in many-particle systems. For charged colloidal systems, the phase boundaries as well as crystal structure are highly tunable by experimental parameters such as salt concentration and pH. By using projections of the colloid-ion mixture to a system of (soft) repulsive spheres and the one-component plasma (OCP), we study the hitherto unexplained experimentally observed reentrant melting of electrostatically repelling colloids upon increasing the colloid density. Our study shows that the surface chemistry should involve a competition between adso…
The mechanical, structural and functional properties of crystals are determined by their defects and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect density rises to levels routinely found in real-world materials, transport is governed by local stresses that are predominantly nonlinear. Such stress fields however, cannot be measured using conventional bulk and local measurement techniques. Here, we report direct and spatially resolved experimental measurements of the nonlinear stresses surrounding collo…
We study experimentally and theoretically the interactions between paramagnetic particles dispersed in water and driven above the surface of a stripe patterned magnetic garnet film. An external rotating magnetic field modulates the stray field of the garnet film and generates a translating potential landscape which induces directed particle motion. By varying the ellipticity of the rotating field, we tune the inter-particle interactions from net attractive to net repulsive. For attractive interactions, we show that pairs of particles can approach each other and form stable doublets which after…
