Particle-laden fluid/fluid interfaces: physico-chemical foundations

Particle-laden fluid/fluid interfaces are ubiquitous in academia and industry, which has fostered extensive research efforts trying to disentangle the physico-chemical bases underlying the trapping of particles to fluid/fluid interfaces as well as the properties of the obtained layers. The understanding of such aspects is essential for exploiting the ability of particles on the stabilization of fluid/fluid interface for the fabrication of novel interface-dominated devices, ranging from traditional Pickering emulsions to more advanced reconfigurable devices. This review tries to provide a general perspective of the physico-chemical aspects associated with the stabilization of interfaces by colloidal particles, mainly chemical isotropic spherical colloids. Furthermore, some aspects related to the exploitation of particle-laden fluid/fluid interfaces on the stabilization of emulsions and foams will be also highlighted. It is expected that this review can be used for researchers and technologist as an initial approach to the study of particle-laden fluid layers.

Crystalline shielding mitigates structural rearrangement and localizes memory in jammed systems under oscillatory shear

The nature of yield in amorphous materials under stress has yet to be fully elucidated. In particular, understanding how microscopic rearrangement gives rise to macroscopic structural and rheological signatures in disordered systems is vital for the prediction and characterization of yield and the study of how memory is stored in disordered materials. Here, we investigate the evolution of local structural homogeneity on an individual particle level in amorphous jammed two-dimensional (athermal) systems under oscillatory shear and relate this evolution to rearrangement, memory, and macroscale rheological measurements. We define the structural metric crystalline shielding, and show that it is predictive of rearrangement propensity and structural volatility of individual particles under shear. We use this metric to identify localized regions of the system in which the material's memory of its preparation is preserved. Our results contribute to a growing understanding of how local structure relates to dynamic response and memory in disordered systems.

Self-assembly of charged colloidal cubes

In this work, we show how and why the interactions between charged cubic colloids range from radially isotropic to strongly directionally anisotropic, depending on tuneable factors. Using molecular dynamics simulations, we illustrate the effects of typical solvents to complement experimental investigations of cube assembly. We find that in low-salinity water solutions, where cube self-assembly is observed, the colloidal shape anisotropy leads to the strongest attraction along the corner-to-corner line, followed by edge-to-edge, with a face-to-face configuration of the cubes only becoming energetically favorable after the colloids have collapsed into the van der Waals attraction minimum. Analysing the potential of mean force between colloids with varied cubicity, we identify the origin of the asymmetric microstructures seen in experiment.

General theory of charge regulation within the Poisson-Boltzmann framework: Study of a sticky-charged wall model

This work introduces a sticky-charge wall model as a simple and intuitive representation of charge regulation. Implemented within the mean-field level of description, the model modifies the boundary conditions without affecting the underlying Poisson-Boltzmann (PB) equation of an electrolyte. Employing various modified PB equations, we are able to assess how various structural details of an electrolyte influence charge regulation.

Mean-field theory of active electrolytes: Dynamic adsorption and overscreening

We investigate active electrolytes within the mean-field level of description. The focus is on how the double-layer structure of passive, thermalized charges is affected by active dynamics of constituting ions. One feature of active dynamics is that particles adhere to hard surfaces, regardless of chemical properties of a surface and specifically in complete absence of any chemisorption or physisorption. To carry out the mean-field analysis of the system that is out of equilibrium, we develop the "mean-field simulation" technique, where the simulated system consists of charged parallel sheets moving on a line and obeying active dynamics, with the interaction strength rescaled by the number of sheets. The mean-field limit becomes exact in the limit of an infinite number of movable sheets.

Interfacial rheology of model particles at liquid interfaces and its relation to (bicontinuous) Pickering emulsions

Interface-dominated materials are commonly encountered in both science and technology, and typical examples include foams and emulsions. Conventionally stabilised by surfactants, emulsions can also be stabilised by micron-sized particles. These so-called Pickering-Ramsden (PR) emulsions have received substantial interest, as they are model arrested systems, rather ubiquitous in industry and promising templates for advanced materials. The mechanical properties of the particle-laden liquid-liquid interface, probed via interfacial rheology, have been shown to play an important role in the formation and stability of PR emulsions. However, the morphological processes which control the formation of emulsions and foams in mixing devices, such as deformation, break-up, and coalescence, are complex and diverse, making it difficult to identify the precise role of the interfacial rheological properties. Interestingly, the role of interfacial rheology in the stability of bicontinuous PR emulsions (bijels) has been virtually unexplored, even though the phase separation process which leads to the formation of these systems is relatively simple and the interfacial deformation processes can be better conceptualised. Hence, the aims of this topical review are twofold. First, we review the existing literature on the interfacial rheology of particle-laden liquid interfaces in rheometrical flows, focussing mainly on model latex suspensions consisting of polystyrene particles carrying sulfate groups, which have been most extensively studied to date. The goal of this part of the review is to identify the generic features of the rheology of such systems. Secondly, we will discuss the relevance of these results to the formation and stability of PR emulsions and bijels.

Colloid–oil–water-interface interactions in the presence of multiple salts: charge regulation and dynamics

The salt-induced dislodgement of charged colloidal particles from an oil–water interface is investigated theoretically and experimentally.

Positioning colloids at the surfaces of cholesteric liquid crystal droplets

We report on the internal configurations of aqueous dispersions of droplets of cholesteric liquid crystals (LCs; 5-50 μm-in-diameter; comprised of 4-cyano-4'-pentylbiphenyl and 4-(1-methylheptyloxycarbonyl)phenyl-4-hexyloxybenzoate) and their influence on the positioning of surface-adsorbed colloids (0.2 or 1 μm-in-diameter polystyrene (PS)). When N = 2D/P was less than 4, where D is the droplet diameter and P is the cholesteric pitch, the droplets adopted a twisted bipolar structure (TBS) and colloids were observed to assume positions at either the poles or equator of the droplets. A statistical analysis of the distribution of locations of the colloids revealed a potential well of depth 2.7 k_BT near the equator, a conclusion that was supported by computer simulations performed via the minimization of the Landau-de Gennes free energy (well depth of 7 k_BT from simulation). In contrast, for N > 4, a majority of the droplets exhibited a radial spherical structure (RSS) characterized by a pair of closely spaced surface defects (angle of separation with respect to the center of the droplet θ < 5°) connected by a disclination winding to/from the droplet center, which led to the positioning of pairs of colloids with well-defined spacing at these surface defects. The separation of the pairs of surface-adsorbed colloids was colloid size-dependent, ranging from 1.11 ± 0.04 μm for 1 μm-in-diameter colloids to 1.7 ± 0.2 μm for 200 nm-in-diameter colloids. We also observed long-lived metastable configurations in which the two surface point defects were separated by much larger distances (corresponding to populations with angles of θ = 20 ± 10° and 85 ± 10° with respect to the center), and observed these pairs of defects to also position pairs of colloids. A third configuration, the diametrical spherical structure (DSS) was also observed. Consistent with the predictions of computer simulations, we found experimentally that the DSS is indeed composed of disconnected defect rings positioned along the diameter of the droplet. Overall, these results reveal that the rich palette of defects exhibited by confined cholesteric LC systems (equilibrium and metastable) provide the basis of a versatile class of templates that enable the surface positioning of colloids in ways that are not possible with achiral LC droplets.

Tuning the Structure and Rheology of Polystyrene Particles at the Air-Water Interface by Varying the pH

We form films of carboxylated polystyrene particles (C-PS) at the air-water interface and investigate the effect of subphase pH on their structure and rheology by using a suite of complementary experimental techniques. Our results suggest that electrostatic interactions drive the stability and the structural order of the films. In particular, we show that by increasing the pH of the subphase from 9 up to 13, the films exhibit a gradual transition from solid to liquidlike, which is accompanied by a loss of the long-range order (that characterizes them at lower values of pH). Direct optical visualization of the layers, scanning electron microscopy, and surface pressure isotherms indicate that the particles deposited at the interface form three-dimensional structures involving clusters, with the latter being suppressed and a quasi-2D particle configuration eventually reached at the highest pH values. Evidently, the properties of colloidal films can be tailored significantly by altering the pH of the subphase.

The apparent charge of nanoparticles trapped at a water interface

Charged spherical nanoparticles trapped at the interface between water and air or water and oil exhibit repulsive electrostatic forces that contain a long-ranged dipolar and a short-ranged exponentially decaying component. The former are induced by the unscreened electrostatic field through the non-polar low-permittivity medium, and the latter result from the overlap of the diffuse ion clouds that form in the aqueous phase close to the nanoparticles. The magnitude of the long-ranged dipolar interaction is largely determined by the residual charges that remain attached to the air- (or oil-) exposed region of the nanoparticle. In the present work we address the question to what extent the charges on the water-immersed part of the nanoparticle provide an additional contribution to the dipolar interaction. To this end, we model the electrostatic properties of a spherical particle - a nanoparticle or a colloid - that partitions equatorially to the air-water interface, thereby employing nonlinear Poisson-Boltzmann theory in the aqueous solution and accounting for the propagation of the electric field through the interior of the particle. We demonstrate that the apparent charge density on the air-exposed region of the particle, which determines the dipole potential, is influenced by the electrostatic properties in the aqueous solution. We also show that this electrostatic coupling through the particle can be reproduced qualitatively by a simple analytic planar capacitor model. Our results help to rationalize the experimentally observed weak but non-vanishing salt dependence of the forces that stabilize ordered two-dimensional arrays of interface-trapped nanoparticles or colloids.

Hard and soft colloids at fluid interfaces: Adsorption, interactions, assembly & rheology

Soft microgel particles inherently possess qualities of both polymers as well as particles. We review the similarities and differences between soft microgel particles and stiff colloids at fluid-fluid interfaces. We compare two fundamental aspects of particle-laden interfaces namely the adsorption kinetics and the interactions between adsorbed particles. Although it is well established that the transport of both hard particles and microgels to the interface is driven by diffusion, the analysis of the adsorption kinetics needs reconsideration and a proper equation of state relating the surface pressure to the adsorbed mass should be used. We review the theoretical and experimental investigations into the interactions of particles at the interface. The rheology of the interfacial layers is intimately related to the interactions, and the differences between hard particles and microgels become pronounced. The assembly of particles into the layer is another distinguishing factor that separates hard particles from soft microgel particles. Microgels deform substantially upon adsorption and the stability of a microgel-stabilized emulsion depends on the conformational changes triggered by external stimuli.

Organized assemblies of colloids formed at the poles of micrometer-sized droplets of liquid crystal

We report on the formation of organized assemblies of 1 μm-in-diameter colloids (polystyrene (PS)) at the poles of water-dispersed droplets (diameters 7-20 μm) of nematic liquid crystal (LC). For 4-cyano-4'-pentylbiphenyl droplets decorated with two to five PS colloids, we found 32 distinct arrangements of the colloids to form at the boojums of bipolar droplet configurations. Significantly, all but one of these configurations (a ring comprised of five PS colloids) could be mapped onto a local (non-close packed) hexagonal lattice. To provide insight into the origin of the hexagonal lattice, we investigated planar aqueous-LC interfaces, and found that organized assemblies of PS colloids did not form at these interfaces. Experiments involving the addition of salts revealed that a repulsive interaction of electrostatic origin prevented formation of assemblies at planar interfaces, and that regions of high splay near the poles of the LC droplets generated cohesive interactions between colloids that could overcome the repulsion. Support for this interpretation was obtained from a model that included (i) a long-range attraction between adsorbed colloids and the boojum due to the increasing rate of strain (splay) of LC near the boojum (splay attraction), (ii) an attractive inter-colloid interaction that reflects the quadrupolar symmetry of the strain in the LC around the colloids, and (iii) electrostatic repulsion between colloids. The model predicts that electrostatic repulsion between colloids can lead to a ∼1000kBT energy barrier at planar interfaces of LC films, and that the repulsive interaction can be overcome by splay attraction of the colloids to the boojums of the LC droplets. Overall, the results reported in this paper advance our understanding of the directed assembly of colloids at interfaces of LC droplets.

The influence of particle size and residual charge on electrostatic interactions between charged colloidal particles at an oil-water interface

Electrostatic repulsive interaction forces between charged spherical colloidal particles at an oil-water interface are numerically studied by solving the standard three-dimensional Poisson-Nernst-Planck model. We directly compute the electrostatic force on a finite-size spherical particle and our results are applicable to all inter-particle distances without distinguishing short ranges and long ranges. The model successfully captures the scaling relationship of the force and the separation distance (d) between two charged particles at both short ranges (exponential dependence) and long ranges (∼d(-4)). The model also bridges these two ranges and provides quantitative information in the middle range. In addition, by assuming that there is a small residual electric charge at the particle-oil interface, the standard model is capable of quantitatively predicting the repulsive particle-particle interaction force over a large range of the separation distance between two particles. The favorable agreement between experiments and theoretical predictions also leads one to conclude that the standard model adequately describes the particle-particle interactions trapped at the oil-water interface.

Weak electrolyte dependence in the repulsion of colloids at an oil-water interface

The two-particle interaction between 3.1-μm-diameter polystyrene latex particles at a decane-water interface was measured with time-shared optical tweezers. The water subphase contained either 0.103 mM RbCl or 0.0342 mM MgCl2, which have hydrated cations of different size but identical anions. The choice of both the anion and the concentrations makes a comparison with published data on NaCl possible and also isolates the effect of the nature of the cation on the electrostatic interaction. The measured magnitude of the dipolar force and the relative changes as a function of electrolyte were in quantitative agreement with predictions from a recently published model that uses the Langevin-Poisson-Boltzmann equation including steric effects and the polarization saturation of the medium to predict the dipolar interaction (Frydel, D.; Oettel, M. Phys. Chem. Chem. Phys. 2011, 13, 4109-4118). These results support the hypothesis that a condensed layer of counterions contributes to the electrostatic interaction between colloidal particles at an oil-water interface. Although it has been suggested that the electrostatic interactions between particles at liquid interfaces could serve as a sensitive probe of the structural details of the electric double layer, both the model predictions and experimental measurements showed a maximum change of only ~25% in the magnitude of the interaction with a change in electrolyte under the conditions tested. The ability to resolve this small change was confounded by the heterogeneous nature of the interaction. Thus, despite the apparent importance of the choice of electrolyte, the subtlety of competing effects makes it unlikely that colloidal force measurements could be used to probe the fine structure of the electric double layer.

Self-assembly of two-dimensional colloidal clusters by tuning the hydrophobicity, composition, and packing geometry

We study the structure of binary monolayers of large (3  μm diameter) very hydrophobic (A) and large (3  μm diameter) hydrophilic (B) or small (1  μm diameter) hydrophilic (C) silica particles at an octane-water interface. By tuning the composition and packing geometry of the mixed monolayer, we find that a rich variety of two-dimensional hexagonal superlattices of mixed A/B or A/C clusters are formed, stabilized by short-ranged electrostatic induced dipole interactions. The cluster structures obtained are in excellent agreement with zero temperature calculations, indicating that the self-assembly process can be effectively controlled.

Influence of nonelectrostatic ion-ion interactions on double-layer capacitance

Recently a Poisson-Helmholtz-Boltzmann (PHB) model [Bohinc et al., Phys. Rev. E 85, 031130 (2012)] was developed by accounting for solvent-mediated nonelectrostatic ion-ion interactions. Nonelectrostatic interactions are described by a Yukawa-like pair potential. In the present work, we modify the PHB model by adding steric effects (finite ion size) into the free energy to derive governing equations. The modified PHB model is capable of capturing both ion specificity and ion crowding. This modified model is then employed to study the capacitance of the double layer. More specifically, we focus on the influence of nonelectrostatic ion-ion interactions on charging a double layer near a flat surface in the presence of steric effects. We numerically compute the differential capacitance as a function of the voltage under various conditions. At small voltages and low salt concentrations (dilute solution), we find out that the predictions from the modified PHB model are the same as those from the classical Poisson-Boltzmann theory, indicating that nonelectrostatic ion-ion interactions and steric effects are negligible. At moderate voltages, nonelectrostatic ion-ion interactions play an important role in determining the differential capacitance. Generally speaking, nonelectrostatic interactions decrease the capacitance because of additional nonelectrostatic repulsion among excess counterions inside the double layer. However, increasing the voltage gradually favors steric effects, which induce a condensed layer with crowding of counterions near the electrode. Accordingly, the predictions from the modified PHB model collapse onto those computed by the modified Poisson-Boltzmann theory considering steric effects alone. Finally, theoretical predictions are compared and favorably agree with experimental data, in particular, in concentrated solutions, leading one to conclude that the modified PHB model adequately predicts the diffuse-charge dynamics of the double layer with ion specificity and steric effects.

Immersion depth of positively versus negatively charged nanoparticles at the air-water interface: a Poisson-Boltzmann model

Electrostatic interactions affect the immersion depth of charged nanoparticles that are trapped at an air-water interface. Recent experiments indicate that upon adding salt negatively charged nanoparticles penetrate deeper into the aqueous phase, whereas positively charged nanoparticles exhibit opposite behavior. It has been proposed that this unexpected lack of invariance with respect to the nanoparticle's charge reversal is caused by a negative surface potential of the air-water interface. To support this hypothesis, we have performed detailed calculations based on nonlinear Poisson-Boltzmann theory of individual spherical particles that are either negatively or positively charged and reside at the interface between air and water. The nanoparticles possess dissociable surface groups that become charged when exposed to the aqueous environment. We calculate the optimal immersion depth from a numerical minimization of the total free energy, which we express as the sum of a surface tension term and an electrostatic contribution. In all calculations we fix the surface potential at the air-water surface at -50 mV. In qualitative agreement with recent experiments, our model predicts opposite behaviors of negatively versus positively charged nanoparticles: adding salt increases/decreases the water immersion depth of negatively/positively charged nanoparticles.

Polarizable Poisson-Boltzmann equation: the study of polarizability effects on the structure of a double layer

We incorporate ion polarizabilities into the Poisson-Boltzmann equation by modifying the effective dielectric constant and the Boltzmann distribution of ions. The extent of the polarizability effects is controlled by two parameters, γ(1) and γ(2); γ(1) determines the polarization effects in a dilute system and γ(2) regulates the dependence of the polarizability effects on the concentration of ions. For a polarizable ion in an aqueous solution γ(1) ≈ 0.01 and the polarizability effects are negligible. The conditions where γ(1) and/or γ(2) are large and the polarizability is relevant involve the low dielectric constant media, high surface charge, and/or large ionic concentrations.