Soft electrostatic repulsion in particle monolayers at liquid interfaces: surface pressure and effect of aggregation

Colloidal Stability of PFSA-Ionomer Dispersions. Part I. Single-Ion Electrostatic Interaction Potential Energies

Charged colloidal particles neutralized by a single counterion are increasingly important for many emerging technologies. Attention here is paid specifically to hydrogen fuel cells and water electrolyzers whose catalyst layers are manufactured from a perfluorinated sulfonic acid polymer (PFSA) suspended in aqueous/alcohol solutions. Partially dissolved PFSA aggregates, known collectively as ionomers, are stabilized by the electrostatic repulsion of overlapping diffuse double layers consisting of only protons dissociated from the suspended polymer. We denote such double layers containing no added electrolyte as "single ion". Size-distribution predictions build upon interparticle interaction potential energies from the Derjaguin-Landau-Verwey-Overbeek (DLVO) formalism. However, when only a single counterion is present in solution, classical DLVO electrostatic potential energies no longer apply. Accordingly, here a new formulation is proposed to describe how single-counterion diffuse double layers interact in colloidal suspensions. Part II (Srivastav, H.; Weber, A. Z.; Radke, C. J. Langmuir 2024 DOI: 10.1021/acs.langmuir.3c03904) of this contribution uses the new single-ion interaction energies to predict aggregated size distributions and the resulting solution pH of PFSA in mixtures of n-propanol and water. A single-counterion diffuse layer cannot reach an electrically neutral concentration far from a charged particle. Consequently, nowhere in the dispersion is the solvent neutral, and the diffuse layer emanating from one particle always experiences the presence of other particles (or walls). Thus, in addition to an intervening interparticle repulsive force, a backside osmotic force is always present. With this new construction, we establish that single-ion repulsive pair interaction energies are much larger than those of classical DLVO electrostatic potentials. The proposed single-ion electrostatic pair potential governs dramatic new dispersion behavior, including dispersions that are stable at a low volume fraction but unstable at a high volume fraction and finite volume-fraction dispersions that are unstable with fine particles but stable with coarse particles. The proposed single-counterion electrostatic pair potential provides a general expression for predicting colloidal behavior for any charged particle dispersion in ionizing solvents with no added electrolyte.

Tuning Electrostatic Interactions of Colloidal Particles at Oil-Water Interfaces with Organic Salts

Monolayers of colloidal particles at oil-water interfaces readily crystallize owing to electrostatic repulsion, which is often mediated through the oil. However, little attempts exist to control it using oil-soluble electrolytes. We probe the interactions among charged hydrophobic microspheres confined at a water-hexadecane interface and show that repulsion can be continuously tuned over orders of magnitude upon introducing nanomolar amounts of an organic salt into the oil. Our results are compatible with an associative discharging mechanism of surface groups at the particle-oil interface, similar to the charge regulation observed for charged colloids in nonpolar solvents.

Particle Size and Rheology of Silica Particle Networks at the Air-Water Interface

Silica nanoparticles find utility in different roles within the commercial domain. They are either employed in bulk within pharmaceutical formulations or at interfaces in anti-coalescing agents. Thus, studying the particle attributes contributing to the characteristics of silica particle-laden interfaces is of interest. The present work highlights the impact of particle size (i.e., 250 nm vs. 1000 nm) on the rheological properties of interfacial networks formed by hydrophobically modified silica nanoparticles at the air-water interface. The particle surface properties were examined using mobility measurements, Langmuir trough studies, and interfacial rheology techniques. Optical microscopy imaging along with Langmuir trough studies revealed the microstructure associated with various surface pressures and corresponding surface coverages (ϕ). The 1000 nm silica particle networks gave rise to a higher surface pressure at the same coverage compared to 250 nm particles on account of the stronger attractive capillary interactions. Interfacial rheological characterization revealed that networks with 1000 nm particles possess higher surface modulus and yield stress in comparison to the network obtained with 250 nm particles at the same surface pressure. These findings highlight the effect of particle size on the rheological characteristics of particle-laden interfaces, which is of importance in determining the stability and flow response of formulations comprising particle-stabilized emulsions and foams.

Use of Silica Nanoparticle Langmuir Films to Determine the Effect of Surface Roughness on the Change in the Forces between Two Silica Surfaces by a Liquid Flow

We aimed to determine how surface roughness changes the effect of a liquid flow on the forces between two charged surfaces. This is because many applications require liquid to flow through charged confined areas and because all surfaces show a degree of roughness. We prepared films of different roughness by making mixed Langmuir films of silica nanoparticles (NPs) of two different diameters at air-100 mM NaCl aqueous interfaces and then by transferring and sintering these films to silicon wafers. Atomic force microscope (AFM) imaging showed that the film roughness decreased (1) with an NP diameter decrease and (2) an increased ratio of small NPs in a mixed film of small and larger NPs. This decrease was explained by a decreased NP aggregation in the film, due to the increased Brownian velocity that accompanies an NP diameter decrease. Force-separation curves were next measured with an AFM between a microsized silica particle (probe) and a smooth substrate (silicon wafer) or the rough NP films in 1 mM NaCl. In the absence of a liquid flow, the repulsive forces decreased with an increased substrate roughness. This reduction was explained by an increased difference between the real zero separation distance and apparent zero separation distance (the distance between the first point of mechanical contact between the probe and substrate) with an increased surface roughness. In the presence of a liquid flow, the repulsive forces decreased in the case of a smooth substrate. However, the repulsive forces were reduced less by a liquid flow for rough substrates. This result was explained by the difference in the effect of liquid flow on the diffuse layer for the smooth and rough surfaces. Surface roughness is postulated to modify the liquid flow trajectory near the surfaces and to cause ion concentration gradients near the surface. These factors are proposed to lessen the change in the diffuse layer brought about by a liquid flow. This would then reduce the change in the forces.

Effects of Interfacial Shear on Particle Aggregation at an Oil/Water Interface

Using a Stokesian dynamics simulation, the microstructure of particle aggregates at an oil/water interface with an applied Couette flow is studied. The results of the aggregation are consistent with previously published experimental work demonstrating multiple regimes of behavior based on the relative strength of shear and capillary forces. In previous work, densification of aggregates at low shear rates was theorized to occur due to short time scale fragmentation/reaggregation of aggregates with rigid particle bonds. In simulations, densification is observed at low shear rates but occurs due to local reorganization of particles due to capillary torques over long time scales. Moderate shear rates create mobile bonds between particles at shorter time scales, allowing aggregates to fragment without reaggregation into smaller isolated clusters, consistent with prior experimental work. At the highest shear rates, aggregation is inhibited completely.

Interparticle Repulsion of Microparticles Delivered to a Pendent Drop by an Electric Field

We report an unusually large spacing observed between microparticles after delivery to the surface of a pendent water droplet using a DC nonuniform electrostatic field, primarily via dielectrophoresis. The influence of particle properties was investigated using core particles, which were either coated or surface-modified to alter their wettability and conductivity. Particles that exhibited this spacing were both hydrophobic and possessed some dielectric material exposed to the external field, such as a coating or exposed dielectric core. The origin of this behavior is proposed to be the induced dipole-dipole repulsion between particles, which increases with particle size and decreases when the magnitude of the electric field is reduced. When the particles were no longer subjected to an external field, this large interparticle repulsion ceased and the particles settled to the bottom of the droplet under the force of gravity. We derive a simple model to predict this spacing, with the dipole-dipole repulsion balanced against particle weight. The external electric field was calculated using the existing electric field models. The spacing was found to be dependent on particle density and the induced dipole moment as well as the number of particles present on the droplet interface. As the number of particles increased, a decrease in interparticle spacing was observed.

Inter-droplet force between magnetically polarizable Pickering oil-in-water nanoemulsions stabilized with γ-Al2O3 nanoparticles: Role of electrostatic and electric dipolar interactions

HYPOTHESIS

The presence of nanoparticles at oil-water interface influences the interaction forces between Pickering emulsions. When charged nanoparticles are at the oil-water interface of an electrostatically stabilized emulsion, in addition to the screened Coulombic interaction, electric dipolar force also influences the total inter-droplet force profiles. An in-depth understanding of the effects of such electric dipolar forces is essential for designing colloidally stable Pickering nanoemulsions for various applications.

EXPERIMENTS

Inter-droplet forces between γ-Al₂O₃ nanoparticle stabilized oil-in-water nanoemulsion, containing superparamagnetic nanoparticles (magnetically polarizable) in the oil phase, are measured using the magnetic-chaining technique at different pH and salt concentrations. The role of mono-, di- and tri-valent salts on the inter-droplet force profiles are assessed.

FINDINGS

Force measurement studies reveal a lowering of inter-droplet spacing, within the linear chains, for higher salt concentrations due to an increased screening. Strong interfacial attachment of the charged nanoparticles results in the formation of an asymmetric charge cloud leading to an electric dipolar interaction. Incorporating the contributions of electric dipolar and screened Coulombic interactions, the theoretically estimated total repulsive force magnitudes are in good agreement with the experimental data. The obtained results offer better insights into the nature of colloidal force between charged particle stabilized nanoemulsions.

Use of Mixed Langmuir Films of Nanoparticles to Form Metal Oxide Materials with the Optimal Surface Charge

We aimed to prepare metal oxide materials with the optimal surface charge by preparing mixed films of non-modified metal oxide nanoparticles (NPs) with dissimilar isoelectric points (iep). The purpose of preparing such surfaces was to expand the use of metal oxide materials in environments where the solution pH cannot be changed. Langmuir films of SiO₂ (iep: pH 2-3) and TiO₂ (iep: pH 5-6.6) NPs were first prepared at air-100 mM NaCl aqueous interfaces. This subphase allowed the formation of stable films of the NPs without the need to modify the NPs with surface-active chemicals, whose presence may detrimentally change the properties of the films. The Langmuir films were then transferred and sintered to silicon wafers and their physical properties were characterized using atomic force microscopy (AFM). The AFM images showed that the films were composed of NP aggregates. The average size of the aggregates decreased, and the uniformity of the aggregate sizes and their inter-aggregate spacing increased with the addition of SiO₂ NPs to the film of TiO₂ NPs. These changes were explained by an increased electrostatic and steric repulsion between the aggregates formed at the air-100 mM NaCl interface due to the adsorption of negatively charged SiO₂ NPs to the slightly positively charged TiO₂ aggregates. The force-distance curves measured between a SiO₂ probe and the sintered films of SiO₂ and/or TiO₂ NPs in a 1.0 mM NaCl solution adjusted to pH 4 showed that the magnitude of the repulsive force decreased with an increased number of TiO₂ NPs in the film. This force change indicated that the surface charge changed when different types of NPs were mixed. These results indicate that mixing different NP types in a Langmuir film at an air-aqueous interface can help change the physical properties of the transferred film.

Motion of Particles in a Monolayer Induced by Coalescing of a Bubble with a Planar Air-Water Interface

The motion of particles in a monolayer induced by the coalescing of a bare bubble with a planar air-water interface was investigated in a modified Langmuir trough. Experiments were performed to understand the effect of particle hydrophobicity, subphase pH, packing density, the presence of a weak surfactant, and particle size distribution on the behavior of particle movement in the monolayer during the coalescence process. Video tracking software was used to track the particles and extract data based on the video footage. Visual inspection indicated that the coalescence of the bubble with the monolayer was a chaotic process which led the interface to oscillate to an extent that the particles underwent complete rearrangement. A simple analysis was carried out on the main forces involved in particle motion and rearrangement at the oscillating air-water interface. The motion characteristic of particles was evaluated by speed and mean-square displacement (MSD). The results showed that the butanol-treated particles had higher speed and MSD than the particles with a stronger affinity to the air-water interface. Similar results were also found at high subphase pH and low packing factor.

Electrostatic pair-interaction of nearby metal or metal-coated colloids at fluid interfaces

In this paper, we theoretically study the electrostatic interaction between a pair of identical colloids with constant surface potentials sitting in close vicinity next to each other at the fluid interface. By employing a simplified yet reasonable model system, the problem is solved within the framework of classical density functional theory and linearized as well as nonlinear Poisson-Boltzmann (PB) theory. Apart from providing a sound theoretical framework generally applicable to any such problem, our novel findings, all of which contradict common beliefs, include the following: first, quantitative and qualitative differences between the interactions obtained within the linear and the nonlinear PB theories; second, the importance of the electrostatic interaction between the omnipresent three-phase contact lines in interfacial systems; and, third, the occurrence of an attractive electrostatic interaction between a pair of identical metal colloids. The unusual attraction we report largely stems from an attractive line interaction, which although scales linearly with the size of the particle can compete with the surface interactions and can be strong enough to alter the nature of the total electrostatic interaction. Our results should find applications in metal or metal-coated particle-stabilized emulsions where densely packed particle arrays are not only frequently observed but also sometimes required.

Coadsorption of Counterionic Colloids at Fluid Interfaces: A Coarse-Grained Simulation Study of Gibbs Monolayers

Monolayers of oppositely charged colloids form versatile self-organizing substrates, with a recognized potential to tailor functional interfaces. In this study, a coarse-grained Monte Carlo simulation approach is laid out to assess the structural properties of Gibbs monolayers, in which one of the counterionic species is partially soluble. It is shown that the composition of this type of monolayer varies in a nontrivial way with surface coverage, as a result of a subtle competition between steric and attractive forces. In the regime of weak electrostatic interactions, the monolayer is depleted of soluble colloids as the surface coverage is increased. At sufficiently strong interactions, the incorporation of soluble colloids is favored at high surface coverage, leading to a re-entrant-type behavior in the expansion/compression isotherms. Strong electrostatic interactions also favor the clustering of the colloids, leading to a range of aggregated configurations, qualitatively resembling those obtained in previous experimental studies. At sufficiently high surface coverage, the clusters collapse into a gel-like percolated mesoscopic structure and eventually into a square crystal lattice configuration. Such interfacial structures are in good agreement with the ones observed in the few experimental investigations available for these systems, showing that the simple methodology introduced in this study provides a valuable predictive framework to anticipate the landscape of interfacial structures that may be produced with oppositely charged colloids, through the modulation of pair interactions and thermodynamical conditions.

Simulation of dense non-Brownian suspensions with the lattice Boltzmann method: shear jammed and fragile states

Dense non-Brownian suspensions, including both hydrodynamic interactions and frictional contacts between particles, are numerically studied under simple and oscillatory shears in terms of the lattice Boltzmann method. We successfully reproduce the discontinuous shear thickening (DST) under a simple shear for bulk three-dimensional systems. For our simulation of an oscillatory shear in a quasi-two-dimensional system, we measure the mechanical response after the reduction of the strain amplitude from the initial oscillations. Here, we find the existence of a shear-jammed state under this protocol in which the storage modulus G' is only finite for high initial strain amplitude γI0. We also find the existence of a fragile state in which both fluid-like and solid-like responses can be detected for an identical area fraction and an initial strain amplitude γI0 depending on the initial phase Θ (or the asymmetricity of the applied strain) of the oscillatory shear. We also observe a DST-like behavior under the oscillatory shear in the fragile state. Moreover, we find that the stress anisotropy becomes large in the fragile state. Finally, we confirm that a stress formula based on the angular distribution of the contact force recovers the contact contributions to the stress tensors for both simple and oscillatory shears with large strains.

Experimental Technique to Study the Interaction Between a Bubble and the Particle-Laden Interface

An experimental apparatus was developed based on the Langmuir-Blodgett trough design to investigate the compression of monolayers of micron size spherical glass particles at the air-water interface and the interaction of an air bubble with the monolayers. The setup modifies the regular Langmuir-Blodgett trough by using a deep and clear glass cell. The cell allowed both the optical observation of the particle monolayer and the insertion of a capillary to produce a bubble under the layer of particles. Surface pressure-area (Π-A) isotherms were measured while the particles rearranged at the interface during compression and expansion for different pH values and particle wettability. We also analyzed the motion of particles in the monolayer by the surface pressure and packing factor to gain further insights into the behavior of particles during the coalescence process. The results suggested that the coalescence of a bubble was dependent on the formation of a defect in the particle layer and the defect size was both strongly influenced by particle hydrophobicity and the pH of the subphase.

Active Atoms and Interstitials in Two-Dimensional Colloidal Crystals

We study experimentally and numerically the motion of a self-phoretic active particle in two-dimensional loosely packed colloidal crystals at fluid interfaces. Two scenarios emerge depending on the interactions between the active particle and the lattice: the active particle either navigates throughout the crystal as an interstitial or is part of the lattice and behaves as an active atom. Active interstitials undergo a run-and-tumble-like motion, with the passive colloids of the crystal acting as tumbling sites. Instead, active atoms exhibit an intermittent motion, stemming from the interplay between the periodic potential landscape of the passive crystal and the particle's self-propulsion. Our results constitute the first step towards the realization of non-close-packed crystalline phases with internal activity.

Electrostatic interaction between dissimilar colloids at fluid interfaces

The electrostatic interaction between two nonidentical, moderately charged colloids situated in close proximity of each other at a fluid interface is studied. By resorting to a well-justified model system, this problem is analytically solved within the framework of linearized Poisson-Boltzmann density functional theory. The resulting interaction comprises a surface and a line part, both of which, as functions of the interparticle separation, show a rich behavior including monotonic as well as nonmonotonic variations. In almost all cases, these variations cannot be captured correctly by using the superposition approximation. Moreover, expressions for the surface tensions, the line tensions and the fluid-fluid interfacial tension, which are all independent of the interparticle separation, are obtained. Our results are expected to be particularly useful for emulsions stabilized by oppositely charged particles.

Rheology of particle/water/oil three-phase dispersions: Electrostatic vs. capillary bridge forces

HYPOTHESIS

Particle/water/oil three-phase capillary suspensions possess the remarkable property to solidify upon the addition of minimal amount of the second (dispersed) liquid. The hardening of these suspensions is due to capillary bridges, which interconnect the particles (pendular state). Electrostatic repulsion across the oily phase, where Debye screening by electrolyte is missing, could also influence the hardness of these suspensions.

EXPERIMENTS

We present data for oil-continuous suspensions with aqueous capillary bridges between hydrophilic SiO₂ particles at particle volume fractions 35-45%. The hardness is characterized by the yield stress Y for two different oils: mineral (hexadecane) and vegetable (soybean oil).

FINDINGS AND MODELLING

The comparison of data for the "mirror" systems of water- and oil-continuous capillary suspensions shows that Y is lower for the oil-continuous ones. The theoretical model of yield stress is upgraded by including a contribution from electrostatic repulsion, which partially counterbalances the capillary-bridge attraction and renders the suspensions softer. The particle charge density determined from data fits is close to that obtained in experiments with monolayers from charged colloid particles at oil/water interfaces. The results could contribute for better understanding, quantitative prediction and control of the mechanical properties of solid/liquid/liquid capillary suspensions.

2D Stokesian Approach to Modeling Flow Induced Deformation of Particle Laden Interfaces

A Stokesian dynamics simulation of the effect of surface Couette flow on the microstructure of particles irreversibly adsorbed to an interface is presented. Rather than modeling both bulk phases, the interface, and particles in a full 3D simulation, known interfacial interactions between adsorbed particles are used to create a 2D model from a top down perspective. This novel methodology is easy to implement and computationally inexpensive, which makes it favorable to simulate behavior of particles under applied flow at fluid-fluid interfaces. The methodology is used to examine microstructure deformation of monodisperse, rigid spherical colloids with repulsive interactions when a surface Couette flow is imposed. Simulation results compare favorably to experimental results taken from literature, showing that interparticle forces must be 1 order of magnitude greater than viscous drag for microstructure to transition from aligned particle strings to rotation of local hexagonal domains. Additionally, it is demonstrated that hydrodynamic interactions between particles play a significant role in the magnitude of these microstructure deformations.

Approaches to self-assembly of colloidal monolayers: A guide for nanotechnologists

Self-assembly of quasi-spherical colloidal particles in two-dimensional (2D) arrangements is essential for a wide range of applications from optoelectronics to surface engineering, from chemical and biological sensing to light harvesting and environmental remediation. Several self-assembly approaches have flourished throughout the years, with specific features in terms of complexity of the implementation, sensitivity to process parameters, characteristics of the final colloidal assembly. Selecting the proper method for a given application amidst the vast literature in this field can be a challenging task. In this review, we present an extensive classification and comparison of the different techniques adopted for 2D self-assembly in order to provide useful guidelines for scientists approaching this field. After an overview of the main applications of 2D colloidal assemblies, we describe the main mechanisms underlying their formation and introduce the mathematical tools commonly used to analyse their final morphology. Subsequently, we examine in detail each class of self-assembly techniques, with an explanation of the physical processes intervening in crystallization and a thorough investigation of the technical peculiarities of the different practical implementations. We point out the specific characteristics of the set-ups and apparatuses developed for self-assembly in terms of complexity, requirements, reproducibility, robustness, sensitivity to process parameters and morphology of the final colloidal pattern. Such an analysis will help the reader to individuate more easily the approach more suitable for a given application and will draw the attention towards the importance of the details of each implementation for the final results.

Concepts for soft interfaces

Concepts and opportunities of interfaces with soft properties are discussed. Such interfaces show a strong response to external fields. How can the interface tension which governs interfacial behavior become compatible with soft and fluctuating degrees of freedom at the interface?

Soft interfacial materials: from fundamentals to formulation

This article is part of the themed issue ‘Soft interfacial materials: from fundamentals to formulation’.