Forces acting on dielectric colloidal spheres at a water/nonpolar fluid interface in an external electric field. 2. Charged particles

Deformation of confined liquid interfaces by inhomogeneous electric fields and localized particle forces

HYPOTHESIS

Oil-water interfaces that are created by confining a certain amount of oil in a square shaped pixel (∼200 x 200 μm2 with a height of ∼10 μm) topped by a layer of water, have a curvature that depends on the amount of oil that happens to be present in the confining area. Under the application of an electric field normal to the interface, the interface will deform due to inhomogeneities in the electric field. These inhomogeneities are expected to arise from the initial curvature of the meniscus, from fringe fields that emerge at the confining pixel walls and, if applicable, from interfacially adsorbed particles.

MODELING AND EXPERIMENTS

We model the shape of the confined oil-water interface invoking capillarity and electrostatics. Furthermore, we measure the initial curvature by tracking the position of interfacially adsorbed particles depending on sample tilt.

FINDINGS

We found that the pixels exhibited meniscus curvature radii ranging from 0.6-7 mm. The corresponding model based minimum oil film thicknesses range between 0.7 and 9 μm. Furthermore, the model shows that the initial meniscus curvature can increase up to 76 percent relative to the initial curvature by the electric field before the oil film becomes unstable. The pixel wall and particles are shown to have minimal impact on the interface deformation.

Stimuli-responsive viscosity modifiers

Stimuli responsive viscosity modifiers entail an important class of materials which allow for smart material formation utilizing various stimuli for switching such as pH, temperature, light and salinity. They have seen applications in the biomedical space including tissue engineering and drug delivery, wherein stimuli responsive hydrogels and polymeric vessels have been extensively applied. Applications have also been seen in other domains like the energy sector and automobile industry, in technologies such as enhanced oil recovery. The chemistry and microstructural arrangements of the aqueous morphologies of dissolved materials are usually sensitive to the aforementioned stimuli which subsequently results in rheological sensitivity as well. Herein, we overview different structures capable of viscosity modification as well as go over the rheological theory associated with classical systems studied in literature. A detailed analysis allows us to explore correlations between commonly discussed models such as molecular packing parameter, tube reptation and stress relaxation with structural and rheological changes. We then present five primary mechanisms corresponding to stimuli responsive viscosity modification: (i) packing parameter modification via functional group conditioning and (ii) via dynamic bond formation, (iii) mesh formation by interlinking of network nodes, (iv) viscosity modification by chain conformation changes and (v) viscosity modification by particle jamming. We also overview several recent examples from literature that employ the concepts discussed to create novel classes of intriguing stimuli responsive structures and their corresponding rheological properties. Furthermore, we also explore systems that are responsive to multiple stimuli which can provide enhanced functionality and versatility by providing multi-level and precise actuation. Such systems have been used for programmed site-specific drug delivery.

Probing Colloidal Assembly on Non-Axisymmetric Droplet Surfaces via Electrospray

Microparticles trapped on the surface of a sessile droplet interact via electrostatic and capillary forces. The assembly of colloids at a fluid-fluid interface is governed by particle size, surface chemistry, and contact line roughness. We created nonspherical droplets using surface energy patterning and delivered microparticles to the liquid-air interface with electrospray atomization. Using a water droplet as the target, the particle assembly was observed over time. We found that the underlying surface energy pattern significantly influenced the colloidal assembly and drove particles toward the center of the droplet. The particles were arranged into a single, non-close-packed cluster with local hexagonal ordering but left a clear region with very few particles near the contact line. This depletion region is attributed to long-range electrostatic repulsion from the photoresist used to create the surface energy pattern, which retained electric charge from the electrospray. To understand the effect of electrostatic interactions, we explored target droplets with dissimilar dielectric properties. Using patterned substrates and electrospray for particle deposition, we can harness the assembly of colloids at a fluid interface to build repeatable monolayer patterns.

A broad perspective to particle-laden fluid interfaces systems: from chemically homogeneous particles to active colloids

Particles adsorbed to fluid interfaces are ubiquitous in industry, nature or life. The wide range of properties arising from the assembly of particles at fluid interface has stimulated an intense research activity on shed light to the most fundamental physico-chemical aspects of these systems. These include the mechanisms driving the equilibration of the interfacial layers, trapping energy, specific inter-particle interactions and the response of the particle-laden interface to mechanical perturbations and flows. The understanding of the physico-chemistry of particle-laden interfaces becomes essential for taking advantage of the particle capacity to stabilize interfaces for the preparation of different dispersed systems (emulsions, foams or colloidosomes) and the fabrication of new reconfigurable interface-dominated devices. This review presents a detailed overview of the physico-chemical aspects that determine the behavior of particles trapped at fluid interfaces. This has been combined with some examples of real and potential applications of these systems in technological and industrial fields. It is expected that this information can provide a general perspective of the topic that can be exploited for researchers and technologist non-specialized in the study of particle-laden interfaces, or for experienced researcher seeking new questions to solve.

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.

Exploiting Additives for Directing the Adsorption and Organization of Colloid Particles at Fluid Interfaces

The self-assembly of colloids at fluid interfaces is a well-studied research field both for gaining fundamental insights and for material fabrication. The fluid interface allows the confinement of particles in two dimensions and may act as a template for guiding their organization into soft and reconfigurable structures. Additives (e.g., surfactants, salts, and polymers) in the colloidal suspension are routinely used as a practical and effective tool to drive particle adsorption and tune their interfacial organization. However, some phenomena lying at the heart of the accumulation and self-assembly of particles at fluid interfaces remain poorly understood. This Feature Article aims to critically analyze the mechanisms involved in the adsorption and self-organization of micro- and nanoparticles at various fluid interfaces. In particular, we address the role of additives in both promoting the adsorption of particles from the bulk suspension to the fluid interface and in mediating the interactions between interfacial particles. We emphasize how different types of additives play a crucial role in controlling the interactions between suspended particles and the fluid interface as well as the interactions between adsorbed particles, thus dictating the final self-assembled structure. We also critically summarize the main experimental protocols developed for the complete adsorption of particles initially suspended in the bulk. Furthermore, we highlight some special properties (e.g., reconfigurability upon external stimulation and dissipative self-assembly) and the application potential of structures formed by colloid self-organization at fluid interfaces mediated/promoted by additives. We believe our contribution serves both as a practical roadmap to scientists coming from other fields and as a valuable information resource for all researchers interested in this exciting research field.

Electrohydrodynamic assembly of colloidal particles on a drop interface

A mathematical model to simulate the dynamics of colloidal particles on a drop interface in an applied electric field is presented. The model accounts for the electric field driven flow within the drop and suspending fluid, particle-particle electrostatic interaction, and the particle motion and rotation due to the induced flow and the applied electric field. The model predicts the formation of chains in the case of conducting particles or an undulating band around the equator in the case of dielectric particles. The model results are in agreement with recent experimental work. A study is presented on the impact of particle concentration and electric field strength on the collective motions of the particles. In the case of non-conducting particles, we find that in the presence of Quincke rotation, the amplitude of the undulations of the observed equatorial particle belt increases with particle concentration but decreases with electric field strength. We also show that the wavelength of the undulations appears independent of the applied field strength.

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

Non-densely packed interfacial monolayers from charged micrometre-sized colloid particles find applications for producing micropatterned surfaces. The soft electrostatic repulsion between the particles in a monolayer on an air/water (or oil/water) interface is mediated by the non-polar fluid, where Debye screening is absent and the distances between the particles are considerably greater than their diameters. Surface pressure versus area isotherms were measured at the air/water interface. The experiments show that asymptotically the surface pressure is inversely proportional to the third power of the interparticle distance. A theoretical model is developed that predicts not only the aforementioned asymptotic law but also the whole surface pressure versus area dependence. An increase in the surface pressure upon aggregation of charged particles in the interfacial monolayers is experimentally established. This effect is explained by the developed theoretical model, which predicts that the surface pressure should linearly increase with the square root of the particle mean aggregation number. The effect of added electrolyte on the aggregation is also investigated. The data lead to the conclusion that 'limited aggregation' exists in the monolayers of charged particles. In brief, the stronger electrostatic repulsion between the bigger aggregates leads to a higher barrier to their coalescence that, in turn, prevents any further aggregation, i.e. negative feedback is present.This article is part of the themed issue 'Soft interfacial materials: from fundamentals to formulation'.

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.

Dipole Moment of a Charged Particle Trapped at the Air-Water Interface

The interaction between two charged particles (such as nanoparticles or colloids) trapped at the air-water interface becomes dipolar at large separations. The corresponding dipole moment can be modeled by considering a single point charge located exactly at the interface, but this model fails to correctly predict the dipole moment's dependence on the salt concentration in the aqueous medium. We extend the single point charge model to two point charges that are separated by a fixed distance and are located at the air-water interface, with one charge being immersed in air and the other in the solvent. The two point charges represent the surface charges at the air-exposed and water-exposed regions of an interface-trapped particle. The two point charges also account for the spatial extension of the particle. On the basis of the Debye-Hückel model, we derive mathematical expressions for the interaction between two pairs of charges and discuss the salt concentration dependence of the dipolar moment at large separations. Our results reveal a residual dipole moment in the limit of large salt content that originates from the charge attached to the air-exposed region of the particle. We discuss nonlinear screening effects and compare the predicted dipolar moments with recent experimental results.

Monolayers of charged particles in a Langmuir trough: Could particle aggregation increase the surface pressure?

The effect of aggregation on the surface pressure, Π, of monolayers from charged micrometer-sized colloidal particles on the air/water interface is investigated. Π is completely due to the long-range electrostatic repulsion between the particles mediated by their electrostatic field in the air. The most probable origin of particle aggregation is the attraction between capillary quadrupoles due to undulated contact lines on particle surfaces. Aggregates have higher charge and repel each other stronger than single particles. The data analysis by means of a theoretical model implies that Π linearly increases with n(1/2); n is the mean aggregation number, which can be determined from the experimental Π vs. area curves. The presence of electrolyte promotes aggregation, which tends to increase Π, but simultaneously reduces the surface charge that leads to lower Π. For our system, the first effect prevails and apparently paradoxical behavior is observed: the addition of salt in water enhances the electrostatic surface pressure. The data indicate limited aggregation: the rise of the electrostatic barrier prevents the further coalescence of aggregates if they have become sufficiently large. The results contribute for a better understanding of the factors that control the interactions in monolayers of charged particles at liquid interfaces.

Signature of time-dependent hydrodynamic interactions on collective diffusion in colloidal monolayers

It has been shown recently that the coefficient of collective diffusion in a colloidal monolayer is divergent due to the hydrodynamic interactions mediated by the ambient fluid in bulk. The analysis is extended to allow for time-dependent hydrodynamic interactions. Observational features specific to this time dependency are predicted. The possible experimental detection in the dynamics of the monolayer is discussed.