Attractive Colloidal Systems Research Articles

Role of interaction range on the microstructure and dynamics of attractive colloidal systems.

Colloidal gelation phase diagram has been traditionally characterized using three key factors: particle volume fraction, strength of attraction, and range of attraction. While there's a rich body of literature on the role of attraction strength and particle volume fraction, majority of studies have been limited to short range interactions. Using Brownian dynamics simulations, we explored the effect that the range of attractions has on the microstructure and dynamics of both weakly and strongly attractive colloidal systems. Although gelation occurs significantly faster at high attraction strength, by an order of magnitude compared to low strength, we did not observe any clear trend in gelation-rate with respect to a change in the range of interaction. However, as the attraction range increases in both systems, the final structure undergoes a transition from a single connected network to a fluid of dense clusters. This results in a new gelation phase boundary for long range attractive colloids.

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 (approx 5.6k_{textrm{B}}T), through micellar depletion leads to a striking notch in the measured inverse mean free path of optical transport, 1/ell ^*, as a function of droplet volume fraction, phi. This notch, which appears between the hard-sphere glass transition, phi _{textrm{g}}, and maximal random jamming, phi _{textrm{MRJ}}, 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 1/ell ^*(phi ), 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.

The Interplay between the Theories of Mode Coupling and of Percolation Transition in Attractive Colloidal Systems.

In the recent years a considerable effort has been devoted to foster the understanding of the basic mechanisms underlying the dynamical arrest that is involved in glass forming in supercooled liquids and in the sol-gel transition. The elucidation of the nature of such processes represents one of the most challenging unsolved problems in the field of material science. In this context, two important theories have contributed significantly to the interpretation of these phenomena: the Mode-Coupling theory (MCT) and the Percolation theory (PT). These theories are rooted on the two pillars of statistical physics, universality and scale laws, and their original formulations have been subsequently modified to account for the fundamental concepts of Energy Landscape (EL) and of the universality of the fragile to strong dynamical crossover (FSC). In this review, we discuss experimental and theoretical results, including Molecular Dynamics (MD) simulations, reported in the literature for colloidal and polymer systems displaying both glass and sol-gel transitions. Special focus is dedicated to the analysis of the interferences between these transitions and on the possible interplay between MCT and PT. By reviewing recent theoretical developments, we show that such interplay between sol-gel and glass transitions may be interpreted in terms of the extended F13 MCT model that describes these processes based on the presence of a glass-glass transition line terminating in an A3 cusp-like singularity (near which the logarithmic decay of the density correlator is observed). This transition line originates from the presence of two different amorphous structures, one generated by the inter-particle attraction and the other by the pure repulsion characteristic of hard spheres. We show here, combining literature results with some new results, that such a situation can be generated, and therefore experimentally studied, by considering colloidal-like particles interacting via a hard core plus an attractive square well potential. In the final part of this review, scaling laws associated both to MCT and PT are applied to describe, by means of these two theories, the specific viscoelastic properties of some systems.

Clusters in colloidal dispersions with a short-range depletion attraction: Thermodynamic identification and morphology

HypothesisParticle aggregation is ubiquitous for many colloidal systems, and drives the phase separation or the formation of materials with a highly heterogeneous large-scale structure, such as gels, porous media and attractive glasses. While the macroscopic properties of such materials strongly depend on the shape and size of these particle aggregates, the morphology and underlining aggregation physical mechanisms are far from being fully understood. Recently, it has been proposed that for reversible colloidal aggregation, the cluster morphology in the case of colloids interacting with short-range attractive forces is determined by a single variable, namely, the reduced second virial coefficient, B2∗. ExperimentsWe examined this proposal by performing confocal microscopy experiments and computer simulations on a large collection of short-ranged attractive colloidal systems with different values of the attraction strength and range. FindingsWe show that in all cases a connection between the colloidal cluster morphology and B2∗ can be established both in experiments and simulations. This physical scenario holds at all investigated thermodynamic conditions, namely, in the fluid state, in the metastable region and in non-equilibrium conditions. Our findings support the connection between reversible colloidal aggregation and the so-called extended law of corresponding states.

Nonequilibrium master kinetic equation modeling of colloidal gelation.

We present a detailed study of the kinetic cluster growth process during gelation of weakly attractive colloidal particles by means of experiments on critical Casimir attractive colloidal systems, simulations, and analytical theory. In the experiments and simulations, we follow the mean coordination number of the particles during the growth of clusters to identify an attractive-strength independent cluster evolution as a function of mean coordination number. We relate this cluster evolution to the kinetic attachment and detachment rates of particles and particle clusters. We find that single-particle detachment dominates in the relevant weak attractive-strength regime, while association rates are almost independent of the cluster size. Using the limit of single-particle dissociation and size-independent association rates, we solve the master kinetic equation of cluster growth analytically to predict power-law cluster mass distributions with exponents -3/2 and -5/2 before and after gelation, respectively, which are consistent with the experimental and simulation data. These results suggest that the observed critical Casimir-induced gelation is a second-order nonequilibrium phase transition (with broken detailed balance). Consistent with this scenario, the size of the largest cluster is observed to diverge with power-law exponent according to three-dimensional percolation on approaching the critical mean coordination number.

Tuning Material Properties of Nanoemulsion Gels by Sequentially Screening Electrostatic Repulsions and Then Thermally Inducing Droplet Bridging.

Nanoemulsions are widely used in applications such as food products, cosmetics, pharmaceuticals, and enhanced oil recovery for which the ability to engineer material properties is desirable. Moreover, nanoemulsions are emergent model colloidal systems because of the ease in synthesizing monodisperse samples, flexibility in formulations, and tunable material properties. In this work, we study a nanoemulsion system previously developed by our group in which gelation occurs through thermally induced polymer bridging of droplets. We show here that the same system can undergo a sol–gel transition at room temperature through the addition of salt, which screens the electrostatic interaction and allows the system to assemble via depletion attraction. We systematically study how the addition of salt followed by a temperature jump can influence the resulting microstructures and rheological properties of the nanoemulsion system. We show that the salt-induced gel at room temperature can dramatically restructure when the temperature is suddenly increased and achieves a different gelled state. Our results offer a route to control the material properties of an attractive colloidal system by carefully tuning the interparticle potentials and sequentially triggering the colloidal self-assembly. The control and understanding of the material properties can be used for designing hierarchically structured hydrogels and complex colloid-based materials for advanced applications.

Time-rate-transformation framework for targeted assembly of short-range attractive colloidal suspensions

The aggregation of attractive colloids has been extensively studied from both theoretical and experimental perspectives as the fraction of solid particles is changed, and the range, type, and strength of attractive or repulsive forces between particles varies. The resulting gels, consisting of disordered assemblies of attractive colloidal particles, have also been investigated with regards to percolation, phase separation, and the mechanical characteristics of the resulting fractal networks. Despite tremendous progress in our understanding of the gelation process, and the exploration of different routes for arresting the dynamics of attractive colloids, the complex interplay between convective transport processes and many-body effects in such systems has limited our ability to drive the system toward a specific configuration. Here, we study a model attractive colloidal system over a wide range of particle characteristics and flow conditions undergoing aggregation far from equilibrium. The complex multiscale dynamics of the system can be understood using a time-rate-transformation diagram adapted from understanding of materials processing in block copolymers, supercooled liquids, and much stiffer glassy metals to direct targeted assembly of attractive colloidal particles.

Real-Space Mapping of the Two-Dimensional Phase Diagrams in Attractive Colloidal Systems

Video microscopy reveals the full 2D phase diagram of a colloid with short- and long-range attractions, which could lead to a better understanding of the phase behavior of real-world 2D materials such as biological membranes and graphene.

Two-dimensional melting of colloids with long-range attractive interactions.

The solid-liquid melting transition in a two-dimensional (2-D) attractive colloidal system is visualized using superparamagnetic colloids that interact through a long-range isotropic attractive interaction potential, which is induced using a high-frequency rotating magnetic field. Various experiments, supported by Monte Carlo simulations, are carried out over a range of interaction potentials and densities to determine structure factors, Lindermann parameters, and translational and orientational order parameters. The system shows a first-order solid-liquid melting transition. Simulations and experiments suggest that dislocations and disclinations simultaneously unbind during melting. This is in direct contrast with reports of 2-D melting of paramagnetic particles that interact with a repulsive interaction potential.

Normal Stress Differences and Yield Stresses in Attractive Particle Networks

The nature of attractive particulate networks, yield stresses, and normal stress differences is systematically reviewed, each in terms of the relevant definitions, underlying mechanisms, and current measurement techniques. With this foundation, experimental observations of normal stress differences in some suspensions and colloidal systems are surveyed, along with constitutive models that allow for normal stress differences to arise prior to yielding. Yield stresses are a hallmark of attractive colloidal systems and vital in their processing. In contrast, little attention has been given to the role of normal stress differences in these systems. The presence or absence of normal stress differences necessarily affects the isotropy of the normal stress field through the solid particulate phase (treated as a continuum), in turn affecting estimation of yield stress. Given the importance of yield stresses in dealing with practical industrial problems, and in understanding fundamental behaviours, it is important to ensure that yield measurements can be relied upon.

Collective translational and rotational Monte Carlo cluster move for general pairwise interaction.

Virtual move Monte Carlo is a cluster algorithm which was originally developed for strongly attractive colloidal, molecular, or atomistic systems in order to both approximate the collective dynamics and avoid sampling of unphysical kinetic traps. In this paper, we present the algorithm in the form, which selects the moving cluster through a wider class of virtual states and which is applicable to general pairwise interactions, including hard-core repulsion. The newly proposed way of selecting the cluster increases the acceptance probability by up to several orders of magnitude, especially for rotational moves. The results have their applications in simulations of systems interacting via anisotropic potentials both to enhance the sampling of the phase space and to approximate the dynamics.

The dynamical fragile-to-strong crossover in attractive colloidal systems

The dynamics of a hierarchical colloid solution, dendrimer in methanol, has been studied using photon-correlation spectroscopy (PCS). The obtained relaxation curves are analyzed according to the mode-coupling theory (MCT). The main results are: i) the occurrence of a fragile to strong dynamical crossover as a function of the packing fraction at ϕc≃0.39, and ii) the observation of a secondary relaxation (β) that has its onset just at the dynamical crossover and is correlated with the primary α-relaxation. Finally we discuss the obtained findings in comparison with recent experiments in similar systems characterized by an attractive interaction obtaining a confirmation on the primary role of the dynamical crossover in the physics of the dynamical arrest.

The dynamical crossover in attractive colloidal systems

We study the dynamical arrest in an adhesive hard-sphere colloidal system. We examine a micellar suspension of the Pluronic-L64 surfactant in the temperature (T) and volume fraction (φ) phase diagram. According to mode-coupling theory (MCT), this system is characterized by a cusp-like singularity and two glassy phases: an attractive glass (AG) phase and a repulsive glass (RG) phase. The T - φ phase diagram of this system as confirmed by a previous series of scattering data also exhibits a Percolation Threshold (PT) line, a reentrant behavior (AG-liquid-RG), and a glass-to-glass transition. The AG phase can be generated out of the liquid phase by using T and φ as control parameters. We utilize viscosity and nuclear magnetic resonance (NMR) techniques. NMR data confirm all the characteristic properties of the colloidal system phase diagram and give evidence of the onset of a fractal-like percolating structure at a precise threshold. The MCT scaling laws used to study the shear viscosity as a function of φ and T show in both cases a fragile-to-strong liquid glass-forming dynamic crossover (FSC) located near the percolation threshold where the clustering process is fully developed. These results suggest a larger thermodynamic generality for this phenomenon, which is usually studied only as a function of the temperature. We also find that the critical values of the control parameters, coincident with the PT line, define the locus of the FSC. In the region between the FSC and the glass transition lines the system dynamics are dominated by clustering effects. We thus demonstrate that it is possible, using the conceptual framework provided by extended mode-coupling theory, to describe the way a system approaches dynamic arrest, taking into account both cage and hopping effects.

Shear-induced structuration of confined carbon black gels: steady-state features of vorticity-aligned flocs

Various dispersions of attractive particles are known to aggregate into patterns of vorticity-aligned stripes when sheared in confined geometries. We report a thorough experimental investigation of such shear-induced vorticity alignment through direct visualization of carbon black gels in both simple plane shear and rotational shear cells. Control parameters such as the gap width, the strain rate, and the gel concentration are systematically varied. It is shown that in steady states the wavelength of the striped pattern depends linearly on the gap width $h$ while being insensitive to both the gel concentration $C$ and the shear rate $\gp$. The width of the vorticity-aligned flocs coincides with the gap width and is also independent of $C$ and $\gp$, which hints to a simple picture in terms of compressible cylindrical flocs. Finally, we show that there exists a critical shear rate $\gp_c$ above which structuration does not occur and that $\gp_c$ scales as $h^{-\alpha}$ with $\alpha=1.4\pm 0.1$ independently of $C$. This extensive data set should open the way to quantitative modelling of the vorticity alignment phenomenon in attractive colloidal systems.

Optical experiments on a crystallizing hard-sphere–polymer mixture at coexistence

We report on the crystallization kinetics in an entropically attractive colloidal system using a combination of time resolved scattering methods and microscopy. Hard sphere particles are polystyrene microgels swollen in a good solvent (radius a=380 nm, starting volume fraction 0.534) with the short ranged attractions induced by the presence of short polymer chains (radius of gyration r g=3 nm, starting volume fraction 0.0224). After crystallization, stacking faulted face centered cubic crystals coexist with about 5% of melt remaining in the grain boundaries. From the Bragg scattering signal we infer the amount of crystalline material, the average crystallite size and the number density of crystals as a function of time. This allows to discriminate an early stage of conversion, followed by an extended coarsening stage. The small angle scattering (SALS) appears only long after completed conversion and exhibits Furukawa scaling for all times. Additional microscopic experiments reveal that the grain boundaries have a reduced Bragg scattering power but possess an increased refractive index. Fits of the Furukawa function indicate that the dimensionality of the scatterers decreases from 2.25 at short times to 1.65 at late times and the characteristic length scale is slightly larger than the average crystallite size. Together this suggests the SALS signal is due scattering from a foam like grain boundary network as a whole.

Highly anisotropic vorticity aligned structures in a shear thickening attractive colloidal system.

Vorticity aligned cylindrical flocs of carbon black particles are formed in steady flow at low shear rates and, strikingly, appear as transient structures in the flow response of gels produced by the quenching of high rate shear thickening flows.

Development of an ultra-small-angle X-ray scattering instrument for probing the microstructure and the dynamics of soft matter

A Bonse–Hart camera suitable for studying dilute and weakly scattering systems has been developed. The required level of reduction of the parasitic background scattering was realised by replacing channel-cut crystals by a pair of polished and deeply etched parallel crystals. The performance of this ultra-small-angle X-ray scattering instrument is illustrated by means of two examples: the microstructure of a short-range attractive colloidal system; and the growth dynamics of soot particles in a diffusion flame. In addition, the feasibility of performing dynamic X-ray scattering experiments is demonstrated.

Clusters in attractive colloids

We discuss how the anomalous increase of the viscosity in colloidal systems withshort-range attraction can be related to the formation of long-living clusters. Based onmolecular dynamics and Monte Carlo numerical simulations of different models, we proposea similar picture for colloidal gelation at low and intermediate volume fractions. On thisbasis, we analyze the distinct role played by the formation of long-living bonds and thecrowding of the particles in the slow dynamics of attractive colloidal systems.

Columnar and lamellar phases in attractive colloidal systems

In colloidal suspensions, at low volume fraction and temperature, dynamical arrest occurs via the growth of elongated structures that aggregate to form a connected network at gelation. Here we show that, in the region of parameter space where gelation occurs, the stable thermodynamical phase is a crystalline columnar one. Near and above the gelation threshold, the disordered spanning network slowly evolves and finally orders to form the crystalline structure. At higher volume fractions the stable phase is a lamellar one, which seems to have a still longer ordering time.

Microstructure and Rheology near an Attractive Colloidal Glass Transition

Microstructure and rheological properties of a thermally reversible short-ranged attractive colloidal system are studied in the vicinity of the attractive glass transition line. At high volume fractions, the static structure factor changes very little but the low frequency shear moduli varies over several orders of magnitude across the transition. From the frequency dependence of shear moduli, fluid-attractive glass and repulsive glass-attractive glass transitions are identified.