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Hypothesis: The dynamics of colloidal suspension confined within porous materials strongly differs from that in the bulk. In particular, within porous materials, the presence of boundaries with complex shapes entangles the longitudinal and transverse degrees of freedom inducing a coupling between the transport of the suspension and the density inhomogeneities induced by the walls. Method: Colloidal suspension confined within model porous media are characterized by means of active microrheology where a net force is applied on a single colloid (tracer particle) whose transport properties are then studied. The trajectories provided by active microrheology are exploited to determine the local transport coefficients. In order to asses the role of the colloid-colloid interactions we compare the case of a tracer embedded in a colloidal suspension to the case of a tracer suspended in an ideal bath. Finding: Our results show that the friction coefficient increases and the passage time distribution widens upon increasing the corrugation of the channel. These features are obtained for a tracer suspended in a (thermalized) colloidal bath as well as for the case of an ideal thermal bath. These results highlight the relevance of the confinement on the transport and show a mild dependence on the colloidal/thermal bath. Finally, we rationalize our numerical results with a semi-analytical model. Interestingly, the predictions of the model are quantitatively reliable for mild external forces, hence providing a reliable tool for predicting the transport across porous materials. (c) 2021 Elsevier Inc. All rights reserved.

Complex fluids are characterized with both solid and fluid properties by their elasticity and viscosity, or rheological behaviour. The flow of complex fluids is a focus of interest in a very wide range of applications in biophysics and soft matter, such as problems involving live cells, processing of plastic, glass, paints, foods, oil recovery and so on. Recently, microrheology has been developed as an accurate technique to obtain rheological properties in soft matter from the microscopic motion of colloidal tracers used as probes, either freely diffusing in the host medium (passive), or subjected to external forces (active). A drawback for the models that simulate these techniques is their high computational cost. Therefore, the use of high performance computing is mandatory to develop the microrheology models. In this work, a microrheology model based on simulations of a tracer in a bath of Brownian quasi-hard spheres is proposed and parallelized. The analysis of the results of the evaluation using different sizes of the problem shows that GPU programming is very appropriate to accelerate these kinds of models.

We study by computer simulations the interaction between two similarly charged colloidal particles confined between parallel planes, in salt free conditions. Both the colloids and ions are simulated explicitly, in a fine-mesh lattice, and the electrostatic interaction is calculated using Ewald summation in two dimensions. The internal energy is measured by setting the colloidal particles at a given position and equilibrating the ions, whereas the free energy is obtained introducing a bias (attractive) potential between the colloids. Our results show that upon confining the system, the internal energy decreases, resulting in an attractive contribution to the interaction potential for large charges and strong confinement. However, the loss of entropy of the ions is the dominant mechanism in the interaction, irrespective of the confinement of the system. The interaction potential is therefore repulsive in all cases, and is well described by the DLVO functional form, but effective values have to be used for the interaction strength and Debye length.

We study the dynamics of a probe particle driven by a constant force through a colloidal glass of hard spheres. This nonequilibrium and anisotropic problem is investigated using a new implementation of the mode-coupling approximation with multiple relaxation channels and Langevin dynamics simulations. A force threshold is found, below which the probe remains localized, while above it the probe acquires a finite velocity. We focus on the localized regime, comparing theory and simulations concerning the dynamics in the length scale of the cage and the properties of the transition to the delocalized regime, such as the critical power-law decay of the probe correlation function. Probe van Hove functions predicted by the theory show exponential tails reminiscent of an intermittent dynamics of the probe. This scenario is microscopically supported by simulations.

The phase behavior of equimolar mixtures of oppositely charged colloidal systems with similar absolute charges is studied experimentally as a function of the salt concentration in the system and the colloid volume fraction. As the salt concentration increases, fluids of irreversible clusters, gels, liquid-gas coexistence, and finally, homogeneous fluids, are observed. Previous simulations of similar mixtures of Derjaguin-Landau-Verwey-Overbeek (DLVO) particles indeed showed the transition from homogeneous fluids to liquid-gas separation, but also predicted a reentrant fluid phase at low salt concentrations, which is not found in the experiments. Possibly, the fluid of clusters could be caused by a nonergodicity transition responsible for the gel phase in the reentrant fluid phase. Liquid-gas separation takes a delay time after the sample is prepared, whereas gels collapse from the beginning. The density of the liquid in coexistence with a vapor phase depends linearly on the overall colloid density of the system. The vapor, on the other hand, is comprised of equilibrium clusters, as expected from the simulations.

The structure of colloidal clusters formed by long-range attractive interactions under diluted conditions is studied by means of Monte Carlo simulations. For a not-too-long attraction range, clusters show self-similar internal structure with lower density than that typical for diffusive aggregation. For long-range interactions, low kappa, nonfractal clusters are formed (dense at short scales but open at long ones). The dependence on the volume fraction shows that more-compact clusters are grown the higher the colloidal density for diffusive aggregation and attraction-driven aggregation in the fractal regime. The whole trend is explained in terms of the interpenetration among aggregates. In attraction-driven aggregations, the interpenetration of clusters competes with aggregation in the tips of the clusters, causing low-density clusters.

The equilibrium phase diagram of a colloidal system composed of 1:1 mixture of positive and negative particles with equal charge is studied by means of Monte Carlo simulations. The system is the colloidal analog of the restricted primitive model (RPM) for ionic fluids. A liquid-gas transition is found in the low-temperature-low-density region, similar to the liquid-gas transition in the RPM. The fluid-crystal transition is also studied, and the liquid phase is shown to be stable in a narrow range of temperatures. In the liquid, the pair distribution function shows alternating layers of particles with opposite sign of charge surrounding every particle. In the vapor phase, clusters of particles are observed, again in agreement with the RPM. However, a decreasing distribution of clusters is obtained, instead of the discrimination between charged and neutral clusters found in the RPM.

Aggregation in a colloidal system composed of positive and negative particles is studied by simulations and theoretically. The system is comprised of a 50/50 mixture of particles with the same size and opposite charge. Brownian dynamics simulations are performed, varying the range of interaction to study the effect of interactions on the aggregation behavior. Homoaggregation results are recovered for very short range interactions, while important differences are observed when the interactions control the aggregation. It is found that cluster discrimination occurs at late stages of aggregation; neutral clusters are observed to disappear faster than charged ones. Also, the total number of clusters decay according to a power law, the exponent being a function of the interaction range. A theoretical model is developed to account for these effects. By introducing a two-fold homogeneous kernel, it is possible to reproduce most of the features of charge heteroaggregation.

Microrheology was proposed almost twenty years ago as a technique to obtain rheological properties in soft matter from the microscopic motion of colloidal tracers used as probes, either freely diffusing in the host medium, or subjected to external forces. The former case is known as passive microrheology, and is based on generalizations of the Stokes?Einstein relation between the friction experienced by the probe and the host-fluid viscosity. The latter is termed active microrheology, and extends the measurement of the friction coefficient to the nonlinear-response regime of strongly driven probes. In this review article, we discuss theoretical models available in the literature for both passive and active microrheology, focusing on the case of single-probe motion in model colloidal host media. A brief overview of the theory of passive microrheology is given, starting from the work of Mason and Weitz. Further developments include refined models of the host suspension beyond that of a Newtonian-fluid continuum, and the investigation of probe-size effects. Active microrheology is described starting from microscopic equations of motion for the whole system including both the host-fluid particles and the tracer; the many-body Smoluchowski equation for the case of colloidal suspensions. At low fluid densities, this can be simplified to a two-particle equation that allows the calculation of the friction coefficient with the input of the density distribution around the tracer, as shown by Brady and coworkers. The results need to be upscaled to agree with simulations at moderate density, in both the case of pulling the tracer with a constant force or dragging it at a constant velocity. The full many-particle equation has been tackled by Fuchs and coworkers, using a mode-coupling approximation and the scheme of integration through transients, valid at high densities. A localization transition is predicted for a probe embedded in a glass-forming host suspension. The nonlinear probe-friction coefficient is calculated from the tracer's position correlation function. Computer simulations show qualitative agreement with the theory, but also some unexpected features, such as superdiffusive motion of the probe related to the breaking of nearest-neighbor cages. We conclude with some perspectives and future directions of theoretical models of microrheology.

Colloidal aggregation induced by attractive interactions is tackled experimentally and by Brownian dynamics simulations using a mixture of positive and negative particles. The structure of the aggregates and the aggregation kinetics are used to characterize the aggregation behavior. The clusters show uniform internal structures, with a fractal dimension lower than that of clusters formed in diffusion, indicating a more branched architecture. The aggregation kinetics also differs from the diffusive one, slowing down as time proceeds. Both results are totally confirmed by simulation. The transition from the attractive driven to the diffusion controlled regimes is studied varying the range of interaction. Continuous transitions are observed both for the aggregation kinetics and cluster structure.

The internal structure of clusters formed by colloidal heteroaggregation of particles with opposite signs of charge is studied by means of computer simulations. Every particle is surrounded by a layer of particles of opposite sign, a second neighbors shell of particles mainly with the same sign, a third one of opposite sign, etc. As the distance from the particle increases, the system becomes more homogeneous and no difference between the numbers of particles with similar or opposite signs of charge can be noticed for distances larger than ten times the particle radius. For low ionic concentrations the local environment of particles is formed by quasi-straight branches, where the sign of charge alternates, and at high concentrations the structure of the cluster is typical of DLCA and the alternation is restricted to very short distances. However, this effect is not responsible for the low fractal dimensions observed in charge heteroaggregates.

The effective interaction between two colloidal particles in a bath of monovalent co- and counterions is studied by means of lattice Monte Carlo simulations with the primitive model. The internal electrostatic energy as a function of the colloid distance is studied fixing the position of the colloids. The free energy of the whole system is obtained introducing a bias parabolic potential, that allows us to sample efficiently small separations between the colloidal particles. For small charges, both the internal and free energy increase when the colloids approach each other, resulting in an effective repulsion driven by the electrostatic repulsion. When the colloidal charge is large enough, on the other hand, the colloid-ion coupling is strong enough to form double layers. The internal energy in this case decreases upon approaching the colloids because more ions enter the double layer. This attractive contribution to the interaction between the colloids is stronger for larger charges and larger ionic concentrations. However, the total free energy increases due to the loss of ionic entropy, and resulting finally in a repulsive interaction potential driven by the entropic contributions. The loss of ionic entropy can be almost quantitatively reproduced with the ideal contribution, the same level of approximation as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The overall behavior is captured by the DLVO theory qualitatively, and a comparison is made with the functional form predicted by the theory, showing moderate agreement.

We report simulation and experimental evidence of multiple cluster-formation mechanisms arising in coagulation in a binary mixture composed of oppositely charged colloids with large asymmetry in the relative particle concentration. These mechanisms can be clearly distinguished from one another as they cause the appearance of several maxima in the cluster-size distribution curves at well-separated time scales. We show that this behavior is caused by the fact that clusters of a given size can have different internal compositions. Moreover, the peaks collapse into a single maximum when electrostatic interactions are screened, which is a confirmation that this effect is very sensitive to the strength and range of the interparticle electrostatic interactions. The experimental confirmation of the simulation results represents the first evidence of non bell-shaped cluster-size distribution curves. 4.457 JCR (2010) Q1, 28/127 Chemistry, physical, 23/225 Materials science, multidisciplinary, 7/80 Physics, multidisciplinary, 6/79 Polymer science

A novel particulate membrane, comprised of a confined fluid of colloidal hard spheres, is presented and studied by means of simulations. Using a fluid of smaller hard spheres as feed, the transport properties of the membrane are studied as a function of the volume fractions of both the feed solution and membrane and the size ratio between both types of particles. Our simulations show that the fluid in the membrane is compressed to the permeate side due to the pressure of the feed. This effect controls the permeability behavior of the membrane: impermeable when the feed pressure is too low, or when the pressure is high enough to induce crystallization of the membrane fluid. Thus, the permeability first increases and then decreases, upon increasing the feed concentration. Finally we focus in systems with high concentrations of the feed and membrane fluids, where completely impermeable membranes are obtained only when the feed spheres are big enough (sigma(f)>0.38sigma(m)).

We present a first-principles theory for the active nonlinear microrheology of colloidal model systems: for constant external force on a spherical probe particle embedded in a dense host dispersion, neglecting hydrodynamic interactions, we derive an exact expression for the friction. Within mode-coupling theory (MCT), we discuss the threshold external force needed to delocalize the probe from a host glass, and its relation to strong nonlinear velocity-force curves in a host fluid. Experimental microrheology data and simulations, which we performed, are explained with a simplified model.

The aggregate structure and long-time kinetics of aggregation between oppositely charged particles is studied. Experimental and simulation results show that heteroaggregation produces more branched aggregates than diffusive aggregation. The kinetics is shown to slow down as time proceeds. Both results are connected by considering the friction of the aggregates with the suspension medium.

We have studied the link between the kinetics of clustering and the phase behavior of dilute colloids with short range attractions of moderate strength. This was done by means of computer simulations and a theoretical kinetic model originally developed to deal with reversible colloidal aggregation. Three different regions of the phase diagram were accessed. For weak attractions, a gas phase of small clusters in equilibrium forms in the system. For intermediate attractions, the system undergoes liquid-gas separation, which is signatured by the formation of a few large droplike aggregates, a gas phase of small clusters, and an overall kinetics where a few seeds succeed in explosively growing at long times, after a lag time. Finally, for very strong attractions, fractal unbreakable clusters form and grow following DLCA-like (diffusion limited cluster aggregation) kinetics; liquid-gas separation is prevented by the strength of the bonds, which do not allow restructuration. Good qualitative and quantitative agreement is found between the dynamic simulations and the kinetic model in all the three regions.

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 exponent and critical packing fraction previously obtained for the divergence of the density fluctuations. Based on mode-coupling calculations, we associate the increase of the viscosity with specific contributions from different length scales. We also show that the results are independent on the microscopic dynamics by comparing newtonian and brownian simulations for the same model. Finally we evaluate the Stokes-Einstein relation approaching both glass transitions, finding a clear breakdown which is particularly strong for the case of the attractive glass., Comment: 12 pages; sent to J. Chem. Phys

We report on the low temperature behavior of the colloidal electrolyte by means of molecular dynamics simulations, where the electrostatic interactions were modeled using effective screened interactions. As in previous works, we have found a region of gas-liquid coexistence located in the low $T$--low $\ensuremath{\rho}$ region. At temperatures much lower than the critical one, the system cannot reach equilibrium, that is, the gas-liquid transition is arrested. Two different mechanisms have been identified to cause arrest: crowding at intermediate $T$ values, associated with the crossing point between the binodal and the glass line, and a gelationlike arrest at very low $T$. To test the latter, the dynamics of the colloidal electrolyte near this crossing point has been computed and compared to the universal predictions of the ideal mode-coupling theory. As in other glass-forming liquids, we found good agreement between this mean field theory and the dynamics of this complex system, although it fails just at the transition. Interestingly, in this region we found that the dynamics of this system is driven mainly by the steric interactions, showing all the typical properties of a repulsive colloidal glass. Finally, the isodiffusivity lines show that in this system with short-range attractions, there is no reentrant glass phenomenon as opposed to monocomponent attractive systems.

Aging in an attraction-driven colloidal glass is studied by computer simulations. The system is equilibrated without attraction and instantaneously ``quenched'', at constant colloid volume fraction, to one of two states beyond the glass transition; one is close to the transition, and the other one deep in the glass. The evolution of structural properties shows that bonds form in the system, increasing the local density, creating density deficits (holes) elsewhere. This process slows down with the time elapsed since the quench. As a consequence of bond formation, there is a slowing down of the dynamics, as measured by the mean squared displacement and the density, bond, and environment correlation functions. The density correlations can be time-rescaled to collapse their long time (structural) decay. The time scale for structural relaxation shows for both quenches a super-linear dependence on waiting time; it grows faster than the bond lifetime, showing the collective origin of the transition. At long waiting times and high attraction strength, we observe {\rem completely} arrested dynamics for more than three decades in time, although individual bonds are not permanent on this time scale. The localization length decreases as the state moves deeper in the glass; the non-ergodicity parameter oscillates in phase with the structure factor. Our main results are obtained for systems with a barrier in the pair potential that inhibits phase separation. However, when this barrier is removed for the case of a deep quench, we find changes in the static structure but almost none in the dynamics. Hence our results for the aging behavior remain relevant to experiments in which the glass transition competes with phase separation., 12 pages, 15 figures

The liquid-gas transition of an electroneutral mixture of oppositely charged colloids, studied by Monte Carlo simulations, is found in the low temperature -- low density region. The critical temperature shows a non-monotonous behavior as a function of the interaction range, $\kappa^{-1}$, with a maximum at $\kappa \sigma \approx 10$, implying an island of coexistence in the $\kappa$-$\rho$ plane. The system is arranged in such a way that each particle is surrounded by shells of particles with alternating charge. In contrast with the electrolyte primitive model, both neutral and charged clusters are obtained in the vapor phase, Comment: 6 pages

We present simulation results addressing the dynamics of a colloidal system with attractive interactions close to gelation. Our interaction also has a soft, long range repulsive barrier which suppresses liquid-gas type phase separation at long wavelengths. The new results presented here lend further weight to an intriguing picture emerging from our previous simulation work on the same system. Whereas mode coupling theory (MCT) offers quantitatively good results for the decay of correlators, closer inspection of the dynamics reveals a bimodal population of fast and slow particles with a very long exchange timescale. This population split represents a particular form of dynamic heterogeneity (DH). Although DH is usually associated with activated hopping and/or facilitated dynamics in glasses, the form of DH observed here may be more collective in character and associated with static (i.e., structural) heterogeneity., Comment: 12 pages, 12 figures

The dynamical heterogeneities (DH) in non-ergodic states of an attractive colloidal glass are studied, as a function of the waiting time. Whereas the fluid states close to vitrify showed strong DH, the distribution of squared displacements of the glassy states studied here only present a tail of particles with increased mobility for the lower attraction strength at short waiting times. These particles are in the surface of the percolating cluster that comprises all of the particles, reminiscent of the fastest particles in the fluid. The quench deeper into the attractive glass is dynamically more homogeneous, in agreement with repulsive glasses (i.e. Lennard-Jones glass)., Comment: Proceedings of 5th IDMRCS - Lille 2005

The equilibrium phase diagram of a 1:1 symmetrical mixture composed of oppositely charged colloids is calculated using Monte Carlo simulations. We model the system by the DLVO effective interaction potential. The phase diagram is similar to that of its atomic analog (the ionic fluid), where a liquid-gas first order transition emerges in the low $T-\rho$ regions being stable with respect to crystallization. As in the ionic fluids, we have found two different crystals: at high $T$ the fluid crystallizes in a FCC lattice, whereas at low $T$, the liquid coexists with a BCC crystal. The region of gas-liquid stability is observed to be narrower as the interaction range is diminished., Comment: Proceedings of Quitel-2005 (Margarita, Venezuela)

We present some recent theory and simulation results addressing the phenomena of colloidal gelation at both high and low volume fractions, in the presence of short-range attractive interactions. We discuss the ability of mode-coupling theory and its adaptations to address situations with strong heterogeneity in density and/or dynamics. We include a discussion of the effect of attractions on the shear-thinning and yield behaviour under flow., Comment: 17 pages, 6 figures

Experiments, theory, and simulation were used to study glass formation in a simple model system composed of hard spheres with short-range attraction (“sticky hard spheres”). The experiments, using well-characterized colloids, revealed a reentrant glass transition line. Mode-coupling theory calculations and molecular dynamics simulations suggest that the reentrance is due to the existence of two qualitatively different glassy states: one dominated by repulsion (with structural arrest due to caging) and the other by attraction (with structural arrest due to bonding). This picture is consistent with a study of the particle dynamics in the colloid using dynamic light scattering.

Using computer simulations, we identify the mechanisms causing aggregation and structural arrest of colloidal suspensions interacting with a short-ranged attraction at moderate and high densities. Two different non-ergodicity transitions are observed. As the density is increased, a glass transition takes place, driven by excluded volume effects. In contrast, at moderate densities, gelation is approached as the strength of the attraction increases. At high density and interaction strength, both transitions merge, and a logarithmic decay in the correlation function is observed. All of these features are correctly predicted by mode coupling theory.

Colloidal stability of two latexes with variable charge surface groups has been studied at a range of pH. Experimental log W vs log[electrolyte] plots were fitted using the DLVO theory, and values for the diffuse potential, psi(d), and the Hamaker constant, A, were obtained. Reasonable tendency was found for the diffuse potential of both latexes, decreasing when the surface charge decreased. However, the Hamaker constant, which was expected to be constant over the range of pH covered, also showed a decreasing behavior with decreasing charge. Several theories for the electric repulsive potential have been used to try to explain this paradoxing trend, although none of them was successful. Finally, two explanations are proposed, one based on coion adsorption and the other on the hairy layer model, although the first one seems to be the most probable on the basis of thermodynamics considerations. Copyright 1999 Academic Press.

The phase behaviour of a colloid-polymer mixture is studied at very low colloid concentrations (below 0.5%). The size ratio between the polymer and the colloidal particles is around 0.09, so that the colloids experience short-range attractions. At these low volume fractions, fluid-crystal coexistence is found at moderate polymer concentrations and the kinetics of crystallization are analyzed by turbidimetry. At higher polymer concentrations, clustering of the particles occurs, but some of them remain in a diluted, gas, phase composed mainly of single particles. These states do not correspond to vapor-liquid coexistence, as shown by studying the density of the gas phase. Strong interactions induce flocculation of the system, producing fractal aggregates with dimension df ≈ 1.8, compatible with diffusion limited cluster aggregation (DLCA). These results are discussed in connection with the phase diagram of colloid-polymer mixtures, obtained at much higher colloid concentrations. For low colloid volume fractions, below ∼0.05%, no clustering of the particles is observed for any polymer concentration.

We present simulation results addressing the phenomena of colloidal gelation induced by attractive interactions. The liquid-gas transition is prevented by the glass arrest at high enough attraction strength, resulting in a colloidal gel. The dynamics of the system is controlled by the glass, with little effect of the liquid-gas transition. When the system separates in a liquid and vapor phases, even if the denser phase enters the non-ergodic region, the vapor phase enables the structural relaxation of the system as a whole., Comment: Proceedings of the glass conference in Pisa (September 06)

Dynamical heterogeneities in a colloidal fluid close to gelation are studied by means of computer simulations. A clear distinction between some fast particles and the rest, slow ones, is observed, yielding a picture of the gel composed by two populations with different mobilities. Analyzing the statics and dynamics of both sets of particles, it is shown that the slow particles form a network of stuck particles, whereas the fast ones are able to move over long distances. Correlation functions show that the environment of the fast particles relaxes much faster than that of the slow ones, but at short times the bonds between fast particles are longer lived due to the flexibility of their structure. No string-like motion is observed for the fast particles, but they occupy preferential sites in the surface of the structure formed by the slow ones.

A model for describing heteroaggregation kinetics has been developed and tested with experiments in a colloidal system composed of positively and negatively charged particles. At first order, the model reduces to the classical Hogg, Healy, and Fuerstenau approximation. Static light scattering was used to monitor the aggregations. The dependence of the initial aggregation rate on the relative particle fraction and on the surface charges was studied and compared with the theoretical predictions. The experimental results indicated that first-order approximation cannot be used to describe the kinetics. However, good agreement was found when second order was introduced in the theoretical model.

The influence of steric interactions in the initial stages of aggregation kinetics in colloidal systems has been studied by simulation and experiments. A simulation model has been proposed to study the initial stages of aggregation under short range repulsive potentials. A polystyrene latex was used as model colloid and the steric interaction was provided by adsorption of a nonionic surfactant. Depending on the range or strength of the interactions, sensitive or insensitive systems to electrolyte concentration can be observed. At low κa, the long-range electrostatic repulsion dominates the system behavior, stabilizing the colloidal system. In conditions of screened electrostatic potential, particle collision is the result of a competition between van der Waals attraction and steric repulsion, leading to a decrease in the dimer formation constant as the range or strength of the steric interaction increases. The steric interaction energy has been included in the theoretical calculation of the aggregation rate constant by means of Fuchs’ stability factor. Good agreement between simulation, experimental, and theoretical calculations was obtained.