Temporal Evolution of Interparticle Potentials of PMMA Colloids in CHB/Decalin

Colloidal dispersions composed of polymethylmetacrylate particles dispersed in a mixture of cyclohexyl bromide and decalin find widespread use as model systems in optical microscopy experiments. While the system allows simultaneous density and refractive index matching, preparing particles with hard potentials remains challenging, and strong variations in the physical parameters of samples prepared in the same manner are commonly observed. Here, we present data on the measurement of forces between individual pairs of particles in highly diluted dispersions over the course of tens of days using the blinking optical tweezers method. Our results show that the variations in the particle properties are indeed caused by a temporal evolution of the particles' charging. Additional measurements of the influence of the addition of tetrabutylammonium bromide (TBAB) to the dispersions show that already small concentrations of added TBAB salt drastically decrease the electrostatic forces between colloidal particles. However, small, non-negligible contact potentials remain even at the highest TBAB concentrations added.

Streaming Potential and Associated Electrokinetic Effects through a Channel Filled with Electrolyte Solution Surrounded by a Layer of Immiscible and Dielectric Liquid

The present article deals with the streaming potential-mediated pressure-driven flow across a channel in which the electrolyte solution is surrounded by a layer of cell membrane. Such a membrane of a biological cell may be modeled as an immiscible and dielectric liquid, which may bear free lipid molecules or charged surfactants. The presence of such additional charged molecules may lead to formation of liquid-liquid interfacial charge. In addition, the dielectric gradient-mediated ion partitioning effect further plays an important role in two-phase electrokinetic motion. We aim to study the generation of streaming potential and electrokinetic conversion efficiency as well as associated electroviscous effect for the undertaken problem. The mathematical model is based on the Poisson-Boltzmann equation for electrostatic potential and the Stokes equation for fluid flow, and the problem is studied considering suitable interfacial conditions for the flow variables along the liquid-liquid interface. The explicit analytical results for velocity and streaming field, electrokinetic energy conversion efficiency, and the parameter indicating the electroviscous effect are derived under the Donnan limit and within the Debye-Hückel electrostatic framework. We further numerically calculated the aforementioned intrinsic electrokinetic parameter associated with the problem undertaken for a wide range of pertinent parameters. The results are illustrated to indicate the impact of pertinent parameters on the generation of the streaming potential and associated electrokinetic effects.

Dynamic Electrophoresis of a Hydrophobic and Dielectric Fluid Droplet

Dynamic electrophoresis is the foundation for electroacoustical measurements, in which the electroacoustical signals may be used to analyze the size and electrostatic charge of colloidal entities by means of the results for dynamic electrophoretic mobility. Thus, the electrophoresis under an alternating electric field is the key foundation for electroacoustic theory. In this article, we develop a tractable analytical theory for the dynamic electrophoresis of hydrophobic and dielectric fluid droplets possessing uniform surface charge density. The tiny fluid droplets possess charged mobile surfaces and have found widespread applications in our day-to-day life. For dielectric fluid droplets (e.g., oil-water emulsions), the tangential electric stress at the interface is nonzero, which significantly affects its electrohydrodynamics under an oscillatory electric field, which has, however, a negligible impact on the electrophoretic motion of conducting droplets (e.g., mercury droplets). Besides, the micro/nanoscale fluid droplets often show hydrophobicity when they are immersed in an aqueous medium, and the impact of the electric field on hydrophobic surfaces remains a research frontier in the chemical discipline. Whereas a number of approximate expressions for electrophoretic mobility have been derived for the conducting droplet, none of them are applicable to such generic hydrophobic fluid droplets with dielectric permittivity that is significantly lower than or comparable to that of an aqueous medium. In this work, within the Debye-Hückel electrostatic framework, we elaborate an original analytical expression of dynamic electrophoretic mobility for this generic dielectric fluid droplet with a hydrophobic surface considering that the droplet retains its spherical shape during its oscillatory motion. We further derived a set of simplified expressions for dynamic electrophoretic mobility deduced under several limiting cases. The results are further illustrated, indicating the impact of pertinent parameters.

Diffusiophoresis of Weakly Charged Fluid Droplets in a General Electrolyte Solution: An Analytical Theory

Owing to the importance of analytical results for electrokinetics of colloidal entities, we performed a mathematical analysis to determine the closed form analytical results for the diffusiophoretic velocity of a hydrophobic and polarizable fluid droplet. A comprehensive mathematical model is developed for diffusiophoresis, considering the background aqueous medium as general electrolytes (e.g., binary valence-symmetric/asymmetric electrolytes and a mixed solution of binary electrolytes). We performed our analysis under a weak concentration gradient, and the analytical results for diffusiophoretic velocity are calculated within the Debye-Hückel electrostatic framework. The exact form of the diffusiophoretic velocity is further approximated with negligible error, and the approximate form is found to be free from any of the cumbersome exponential integrals and thus very convenient for practical use. The present theory also covers the diffusiophoresis of perfectly dielectric as well as perfectly conducting droplets as its limiting case. In addition, we have further derived a number of closed form expressions for diffusiophoretic velocity pertaining to several particular cases, and we observed that the derived limit correctly recovers the available existing analytical results for diffusiophoretic velocity. Thus, the present analytical theory for diffusiophoresis can be applied to a wide class of fluidic droplets, e.g., hydrophobic and dielectric oil/conducting mercury droplets, air bubbles, nanoemulsions, as well as any polarizable and hydrophobic fluidic droplet suspended in a solution of general electrolytes.

Understanding directed assembly of concentrated nanoparticles at energetically heterogeneous interfaces of cholesteric liquid crystal droplets

Colloidal self-assembly has gained significant interest in scientific and technological advances. We investigated the self-assembly of the colloids at fluidic interfaces that mediate elastic interactions. Whereas past studies have reported the assembly of micrometer- or molecular-sized species at aqueous interfaces of liquid crystals (LCs), herein we study the assembly of intermediate-sized nanoparticles. Specifically, surface-modified silica nanoparticles (50 to 500 nm) were adsorbed at the liquid crystal-water interfaces and their positioning was investigated using electron microscopy after polymerization. The study revealed that the electric double layer forces and the elastic forces caused by LC strain are dominant in the assembly of nanoparticles and their contributions can be tuned to direct the self-assembly guided by the sub-interface symmetry of confined cholesteric LCs. At high ionic strengths, we observed a strong localization of nanoparticles at the defects, whereas intermediate strengths resulted in their partial enrichment into cholesteric fingerprint patterns with an interaction energy of ≈3 k_BT. This result is comparable with the calculations based on the strength of the binary interactions of the nanoparticles. The findings also support the role of ion partitioning at the LC-aqueous interfaces on the formation of the assemblies. The results can be utilized for applications in sensors, microelectronics, and photonics.

Charge-Dipole Attraction as a Surface Interaction between Water Droplets Immersed in Organic Phases

The dynamic behavior of emulsion droplets during their interactions with one another or with solid surfaces plays a paramount role in their ultimate stability in various applications. While the interaction of oil droplets through a surrounding aqueous phase is well understood, recent studies on the interaction of water droplets through a surrounding pure organic phase showed the presence of an unexplained attraction between water droplets at relatively long ranges. In this research study, we propose fixed-surface-charge-bulk-dipole attraction as a new interaction force between water-in-oil droplets and then derive an equation for its disjoining pressure. The behavior of water droplets in the presence and absence of this charge-dipole interaction was numerically quantified using the Stokes-Reynolds-Young-Laplace model and compared to the experimental data. Numerically calculated net force curves are in excellent agreement with experimental data from the literature when charge-dipole attraction is included, while they deviate in its absence. In addition, the water droplet and thin oil film profiles in the presence and absence of charge-dipole attraction were calculated and compared. This research indicates that charge-dipole attraction can adequately explain the mysterious force observed in some studies, which demonstrates its unexplored potential to capture the physical properties and dynamic behavior of water droplets in organic phases with useful implications to unravel unidentified interactions between emulsion droplets in different industries.

Electrophoresis of Dielectric and Hydrophobic Spherical Fluid Droplets Possessing Uniform Surface Charge Density

The present article deals with the theoretical study on electrophoresis of hydrophobic and dielectric spherical fluid droplets possessing uniform surface charge density. Unlike the ideally polarizable liquid droplet bearing constant surface ζ-potential, the tangential component of the Maxwell stress is nonzero for dielectric fluid droplets with uniform surface charge density. We consider the continuity of the tangential component of total stress (sum of the hydrodynamic and Maxwell stresses) and jump in dielectric displacement along the droplet-to-electrolyte interface. The typical situation is considered here for which the interfacial tension of the fluid droplet is sufficiently high so that the droplet retains its spherical shape during its motion. The present theory can be applied to nanoemulsions, hydrophobic oil droplets, gas bubbles, droplets of immiscible liquid suspended in aqueous medium, etc. Based on weak field and low charge assumptions and neglecting the Marangoni effect, the resultant electrokinetic equations are solved using linear perturbation analysis to derive the closed form expression for electrophoretic mobility applicable for the entire range of Debye-Hückel parameter. We further deduced an alternate approximate expression for electrophoretic mobility without involving exponential integrals. Besides, we have derived analytical results for mobility pertaining to various limiting cases. The results are further illustrated to show the impact of pertinent parameters on the overall electrophoretic mobility.

Adsorption of Hydrophilic Silica Nanoparticles at Oil-Water Interfaces with Reversible Emulsion Stabilization by Ion Partitioning

Adsorption of particles at oil-water interfaces is the basis of Pickering emulsions, which are common in nature and industry. For hydrophilic anionic particles, electrostatic repulsion and the absence of wetting inhibit spontaneous adsorption and limit the scope of materials that can be used in emulsion-based applications. Here, we explore how adding ions that selectively partition in the two fluid phases changes the interfacial electric potential and drives particle adsorption. We add oil-soluble tetrabutyl ammonium perchlorate (TBAP) to the nonpolar phase and Ludox silica nanoparticles or silica microparticles to the aqueous phase. We find a well-defined threshold TBAP concentration, above which emulsions are stable for months. This threshold increases with the particle concentration and with the oil's dielectric constant. Adding NaClO₄ salt to water increases the threshold and causes spontaneous particle desorption and droplet coalescence even without agitation. The results are explained by a model based on the Poisson-Boltzmann theory, which predicts that the perchlorate anions (ClO₄^-) migrate into the water phase and leave behind a net positive charge in the oil. Our results show how a large class of inorganic hydrophilic, anionic nanoparticles can be used to stabilize emulsions in a reversible and stimulus-responsive way, without surface modifications.

Electrophoresis of Liquid-Layer Coated Particles: Impact of Ion Partitioning and Ion Steric Effects

The biomimetic core-shell nanoparticles coated with membranes of various biological cells have attracted significant research interest, because of their extensive applications in targeted drug delivery systems. The cell membrane consists of a lipid bilayer, which can be regarded as a two-dimensional oriented viscous liquid with low dielectric permittivity, compared to a bulk aqueous medium. Such a liquid layer comprised of cell membrane may bear additional mobile charges, because of the presence of free lipid molecules or charged surfactant molecules, which further results in nonzero charge along the surface of the peripheral layer. In this article, we present an analytical theory for electrophoresis of such cell membrane coated functionalized nanoparticles in the extent of electrolyte solution, considering the combined effects of finite ion size and of ion partitioning. Going beyond the Debye-Huckel approximations, we propose an analytical theory for Donnan potential and electrophoretic mobility. The derived expressions are applicable for moderate to highly charged undertaken core-shell particles when the thickness of the peripheral liquid layer greatly exceeds the electric double layer thickness. The impact of pertinent parameters on the electrophoretic response of such a particle is further discussed.

Effect of Bjerrum pairs on the electrostatic properties of an electrolyte solution near charged surfaces: a mean-field approach

In this paper, we investigate the consequences of ion association, coupled with the considerations of finite size effects and orientational ordering of Bjerrum pairs as well as ions and water molecules, on the electric double layer near charged surfaces. Based on the lattice statistical mechanics accounting for finite sizes and dipole moments of ions, Bjerrum pairs and solvent molecules, we consider the formation of Bjerrum pairs and derive the mathematical expressions for Bjerrum pair number density as well as cation/anion number density and water molecule number density. We reveal several significant phenomena. Firstly, it is shown that our approach naturally yields the equilibrium constant for dissociation-association equilibrium between Bjerrum pairs and ions. Secondly, at low surface charge densities, an increase in the bulk concentration of Bjerrum pairs enhances the permittivity and decreases the differential capacitance. Next, for the cases where Bjerrum pairs in an alcohol electrolyte solution have a high value of dipole moment, the Bjerrum pair number density increases with decreasing distance from the charged surface, and the differential capacitance and permittivity are high compared to those for the cases with lower values of Bjerrum-pair dipole moments. Finally, we show that the difference in the concentration and dipole moment of Bjerrum pairs can lead to some variation in osmotic pressure between two similarly charged surfaces.

Electrophoresis of dielectric and immiscible-liquid-layer-encapsulated colloids in aqueous media

In this paper we consider the electrophoresis of a functionalized nanoparticle in electrolyte solution. The undertaken particle is comprised of a rigid inner core encapsulated with a layer of dielectric liquid (e.g., oil or lipid layer), which is immiscible to the bulk aqueous medium. The peripheral liquid layer of the undertaken nanoparticle contains mobile charges due to presence of solubilized surfactants. The mobile electrolyte ions can penetrate across the peripheral layer depending on the difference in the Born energy of the both phases. Such types of nanoparticles have received substantial attention due to their widespread applications in biomedical research. The electric double layer (EDL) is governed by the linearized Poisson-Boltzmann equation under a low potential limit and the electroosmotic flow field is governed by modified Stokes equation. We adopt the flat-plate formalism to obtain the closed analytical expression for the electrophoretic mobility of the undertaken particle under a thin EDL approximation. The dependence of electrophoretic mobility on the pertinent parameters is also illustrated.

Dynamics of a driven confined polyelectrolyte solution

The transport of polyelectrolytes confined by oppositely charged surfaces and driven by a constant electric field is of interest in studies of DNA separation according to size. Using molecular dynamics simulations that include the surface polarization effect, we find that the mobilities of the polyelectrolytes and their counterions change non-monotonically with the confinement surface charge density. For an optimum value of the confinement charge density, efficient separation of polyelectrolytes can be achieved over a wide range of polyelectrolyte charge due to the differential friction imparted by oppositely charged confinement on the polyelectrolyte chains. Furthermore, by altering the placement of the charged confinement counterions, enhanced polyelectrolyte separation can be achieved by utilizing the surface polarization effect due to dielectric mismatch between the media inside and outside the confinement.

Effect of Aqueous Anions on Graphene Exfoliation

Ion partitioning behavior in electrolyte solutions plays an important role in drug delivery and therapeutics, protein folding, materials science, filtration, and energy applications such as supercapacitors. Here, we show that the segregation of ions in solutions also plays an important role in the exfoliation of natural flake graphite to pristine graphene. Polarizable anions such as iodide and acetate segregate to the interfacial region of the aqueous phase during solvent interfacial trapping exfoliation of graphene. Ordered water layers and accumulated charges near the graphene surface aid in separating graphene sheets from bulk graphite, and, more importantly, reduce the reversibility of the exfoliation event. The observed phenomenon results not only in the improved stability of graphene-stabilized emulsions but also in a low-cost and environmentally friendly way of enhancing the production of graphene.

Adsorption and interfacial structure of nanocelluloses at fluid interfaces

Nanocelluloses (NCs), more specifically cellulose nanocrystals and nanofibrils, are a green alternative for the stabilization of fluid interfaces. The adsorption of NCs at oil-water interfaces facilitates the formation of stable and biocompatible Pickering emulsions. In contrast, unmodified NCs are not able to stabilize foams. As a consequence, NCs are often hydrophobized by covalent modifications or adsorption of surfactants, allowing also the stabilization of foams or functional inverse, double, and stimuli-responsive emulsions. Although the interfacial stabilization by NCs is readily exploited, the driving force of adsorption and stabilization mechanisms remained long unclear. Here, we summarize the recent advances in the understanding of NC adsorption regarding kinetics, isotherms, and energetic aspects, as well as their interfacial structure, surface coverage, and contact angle. We thereby distinguish unmodified NCs, covalently modified NCs, and surfactant enhanced adsorption.

Aqueous Nanoclusters Govern Ion Partitioning in Dense Polymer Membranes

The uptake and sorption of charged molecules by responsive polymer membranes and hydrogels in aqueous solutions is of key importance for the development of soft functional materials. Here, we investigate the partitioning of simple monatomic (Na⁺, K⁺, Cs⁺, Cl^-, I^-) and one molecular ion (4-nitrophenolate; NP^-) within a dense, electroneutral poly(N-isopropylacrylamide) membrane using explicit-water molecular dynamics simulations. Inside the predominantly hydrophobic environment, water distributes in a network of polydisperse water nanoclusters. The average cluster size determines the mean electrostatic self-energy of the simple ions, which preferably reside deeply inside them; we therefore find substantially larger partition ratios K ≃10^-1 than expected from a simple Born picture using a uniform dielectric constant. Despite their irregular shapes, we observe that the water clusters possess a universal negative electrostatic potential with respect to their surroundings, as is known for aqueous liquid-vapor interfaces. This potential, which we find concealed in cases of symmetric monatomic salts, can dramatically impact the transfer free energies of larger charged molecules because of their weak hydration and increased affinity to interfaces. Consequently, and in stark contrast to the simple ions, the molecular ion NP^- can have a partition ratio much larger than unity, K ≃10-30 (depending on the cation type) or even 10³ in excess of monovalent salt, which explains recent observations of enhanced reaction kinetics of NP^- reduction catalyzed within dense polymer networks. These results also suggest that ionizing a molecule can even enhance the partitioning in a collapsed, rather hydrophobic gel, which strongly challenges the traditional simplistic reasoning.

Coalescence of a Water Drop with an Air-Liquid Interface: Electric Current Generation and Critical Micelle Concentration (CMC) Sensing Application

A phenomenon that electric current is generated when a pendant water droplet touches an air-electrolyte solution interface is investigated in this paper. A measurement system developed in this study consists of a hollow electrode for droplet generation, a counter electrode immersed in an electrolyte solution, and an electrometer with high precision. Once a droplet touches the air-electrolyte solution interface, it will be pulled into the electrolyte solution and an electric current is produced during this process. Experiments showed that the magnitude of the electric current depends only on the pendant droplet and has nothing to do with the types of the electrolyte solution (with a much larger volume than that of the droplet) below the drop. The electric current is generated by the electric potential difference between the droplet and air-electrolyte solution interface and the liquid bridge formed during droplet coalescence. As a result, the magnitude of the generated electrical current mainly depends on the size, pH, and the type of the solution forming the droplet. Determining the critical micelle concentration using this system was successfully achieved to show the powerfulness of this system.

Measured electrical charge of SiO2 in polar and nonpolar media

We present measurements of the net electrical surface charge of silicon dioxide (SiO₂) in contact with solvents of dielectric constants between 5 and 80. Our experimental approach relies on observing the thermal motion of single silica particles confined in an electrostatic fluidic trap created by SiO₂ surfaces. We compare the experimentally measured functional form of the trapping potential with that from free energy calculations and thereby determine the net surface charge in the system. Our findings clearly demonstrate that contrary to popular perception, even in the absence of surfactants, the net electrical charge of ionizable surfaces in contact with apolar solvents can be large enough to lead to significant repulsive forces. A charge regulation model for SiO₂ surfaces with a single tunable parameter explains our measurements. This model may find general applicability in estimating the net charge of ionizable surfaces, given system parameters such as the dissociation or association constants of the ionizable groups and the pH, ionic strength, and dielectric constant of the solvent phase.

Recent advances in liquid mixtures in electric fields

When immiscible liquids are subject to electric fields interfacial forces arise due to a difference in the permittivity or the conductance of the liquids, and these forces lead to shape change in droplets or to interfacial instabilities. In this topical review we discuss recent advances in the theory and experiments of liquids in electric fields with an emphasis on liquids which are initially miscible and demix under the influence of an external field. In purely dielectric liquids demixing occurs if the electrode geometry leads to sufficiently large field gradients. In polar liquids field gradients are prevalent due to screening by dissociated ions irrespective of the electrode geometry. We examine the conditions for these 'electro prewetting' transitions and highlight few possible systems where they might be important, such as in stabilization of colloids and in gating of pores in membranes.

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.

Ionic hydration-induced evolution of decane–water interfacial tension

We show that ionic hydration is responsible for the non-monotonic variation of the interfacial tension with increasing ionic concentration.

Repulsive van der Waals forces enable Pickering emulsions with non-touching colloids

Emulsions stabilized by solid particles, called Pickering emulsions, offer promising applications in drug delivery, cosmetics, food science and the manufacturing of porous materials. This potential stems from their high stability against coalescence and 'surfactant-free' nature. Generally, Pickering emulsions require that the solid particles are wetted by both phases and as a result, the adsorption free energy is often large with respect to the thermal energy (kBT). Here we provide the first experimental proof for an alternative scenario: non-touching (effectively non-wetting), charged, particles that are completely immersed in the oil phase through a balance of charge induced attractions and repulsions caused by van der Waals forces. These particles nonetheless stabilize the emulsion. The main advantage of this novel adsorption mechanism is that these particles can easily be detached from the interface simply by adding salt. This not only makes the finding fundamentally of interest, but also enables a triggered de-emulsification and particle recovery, which is useful in fields like enhanced oil recovery, heterogeneous catalysis, and emulsion polymerization.

Tuning Colloid-Interface Interactions by Salt Partitioning

We show that the interaction of an oil-dispersed colloidal particle with an oil-water interface is highly tunable from attractive to repulsive, either by varying the sign of the colloidal charge via charge regulation or by varying the difference in hydrophilicity between the dissolved cations and anions. In addition, we investigate the yet unexplored interplay between the self-regulated colloidal surface charge distribution with the planar double layer across the oil-water interface and the spherical one around the colloid. Our findings explain recent experiments and have direct relevance for tunable Pickering emulsions.

Alternating strings and clusters in suspensions of charged colloids

We report the formation of alternating strings and clusters in a binary suspension of repulsive charged colloids with double layers larger than the particle size. Within a binary cell model we include many-body and charge-regulation effects under the assumption of a constant surface potential, and consider their repercussions on the two-particle interaction potential. We find that the formation of induced dipoles close to a charge-reversed state may explain the formation of these structures. Finally, we will touch upon the formation of dumbbells and small clusters in a one-component system, where the effective electrostatic interaction is always repulsive.

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.

Anomalous system-size dependence of electrolytic cells with an electrified oil-water interface

Manipulation of the charge of the dielectric interface between two bulk liquids not only enables the adjustment of the interfacial tension but also controls the storage capacity of ions in the ionic double layers adjacent to each side of the interface. However, adjusting this interfacial charge by static external electric fields is difficult since the external electric fields are readily screened by ionic double layers that form in the vicinity of the external electrodes. This leaves the liquid-liquid interface, which is at a macroscopic distance from the electrodes, unaffected. In this study we show theoretically, in agreement with recent experiments, that control over this surface charge at the liquid-liquid interface is nonetheless possible for macroscopically large but finite closed systems in equilibrium, even when the distance between the electrode and interface is orders of magnitude larger than the Debye screening lengths of the two liquids. We identify a crossover system-size below which the interface and the electrodes are effectively coupled. Our calculations of the interfacial tension for various electrode potentials are in good agreement with recent experimental data.

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.

Non-Close-Packed Breath Figures via Ion-Partitioning-Mediated Self-Assembly

We report a one-step method of forming non-close-packed (NCP) pore arrays of micro- and sub-micropores using chloroform-based solutions of polystyrene acidified with hydrogen bromide for breath figure (BF) patterning. As BF patterning takes place, water vapor condenses onto the polystyrene solution, forming water droplets on the solution surface. Concurrently, preferential ion partitioning of hydrogen bromide leads to positively charged water droplets, which experience interdroplet electrostatic repulsion. Self-organization of charged water droplets because of surface flow and subsequent evaporation of the droplet templates result in ordered BF arrays with pore separation/diameter (L/D) ratios of up to 16.5. Evidence from surface potential scans show proof for preferential ion partitioning of HBr. Radial distribution functions and Voronoi polygon analysis of pore arrays show that they possess a high degree of conformational order. Past fabrication methods of NCP structures typically require multi-step processes. In contrast, we have established a new route for facile self-assembly of previously inaccessible patterns, which comprises of only a single operational step.

Thomson rings in a disk

We discuss the basic principles of self-organization of a finite number of charged particles interacting via the 1/r Coulomb potential in disk geometry. The analysis is based on the cyclic symmetry and periodicity of the Coulomb interaction between particles located on several rings. As a result, a system of equations is derived, which allows us readily to determine with high accuracy the equilibrium configurations of a few hundred charged particles. For n≳200, we predict the formation of a hexagonal core and valence circular rings for the centered configurations.

Interfacial localization and voltage-tunable arrays of charged nanoparticles

Experiments and computer simulations provide a new perspective that strong correlations of counterions with charged nanoparticles can influence the localization of nanoparticles at liquid-liquid interfaces and support the formation of voltage-tunable nanoparticle arrays. We show that ion condensation onto charged nanoparticles facilitates their transport from the aqueous-side of an interface between two immiscible electrolyte solutions to the organic-side, but contiguous to the interface. Counterion condensation onto the highly charged nanoparticles overcomes the electrostatic barrier presented by the low permittivity organic material, thus providing a mechanism to transport charged nanoparticles into organic phases with implications for the distribution of nanoparticles throughout the environment and within living organisms. After transport, the nanoparticles assemble into a two-dimensional (2D) nearly close-packed array on the organic side of the interface. Voltage-tunable counterion-mediated interactions between the nanoparticles are used to control the lattice spacing of the 2D array. Tunable nanoparticle arrays self-assembled at liquid interfaces are applicable to the development of electro-variable optical devices and active elements that control the physical and chemical properties of liquid interfaces on the nanoscale.

Hierarchical organization in liquid crystal-in-liquid crystal emulsions

We report the formation and characterization of hierarchical ordering in systems comprised of micrometer-sized droplets of thermotropic nematic liquid crystals (LCs) dispersed in continuous nematic phases of a lyotropic chromonic LC (disodium cromoglycate (DSCG)). Significantly, we find the orientations of the two LC phases to be coupled, with nematic droplets of 4'-pentyl-4-cyanobiphenyl (5CB) exhibiting a bipolar configuration with an axis of symmetry aligned orthogonal to the far-field director of the DSCG phase. We determine that this coupling of orientations does not result from either anisometric LC droplet shape or interfacial ionic phenomena but rather is consistent with the influence of van der Waals interactions that arise from the anisotropic polarizabilities of nematic 5CB (Δn = +0.18) and DSCG (Δn = -0.02) phases. We also find that it is possible to rotate and uniformly align the nematic droplets by using a weak magnetic field (B ∼ 0.3 T). An analysis of the dynamics of relaxation of the orientations of the 5CB droplets following removal of the magnetic field reveals the DSCG and 5CB droplets to be coupled by energies of ∼10(4) kT, consistent with a simple theoretical estimate of the influence of anisotropic van der Waals interactions. We also observed the nematic 5CB droplets to form dimers and larger assemblies mediated by the elasticity of the nematic DSCG. Overall, these results reveal that LC-in-LC emulsions define a new class of hierarchically ordered soft matter in which both thermotropic and lyotropic LCs are coupled in their ordering.

Water-mediated ion-ion interactions are enhanced at the water vapor-liquid interface

There is overwhelming evidence that ions are present near the vapor-liquid interface of aqueous salt solutions. Charged groups can also be driven to interfaces by attaching them to hydrophobic moieties. Despite their importance in many self-assembly phenomena, how ion-ion interactions are affected by interfaces is not understood. We use molecular simulations to show that the effective forces between small ions change character dramatically near the water vapor-liquid interface. Specifically, the water-mediated attraction between oppositely charged ions is enhanced relative to that in bulk water. Further, the repulsion between like-charged ions is weaker than that expected from a continuum dielectric description and can even become attractive as the ions are drawn to the vapor side. We show that thermodynamics of ion association are governed by a delicate balance of ion hydration, interfacial tension, and restriction of capillary fluctuations at the interface, leading to nonintuitive phenomena, such as water-mediated like charge attraction. "Sticky" electrostatic interactions may have important consequences on biomolecular structure, assembly, and aggregation at soft liquid interfaces. We demonstrate this by studying an interfacially active model peptide that changes its structure from α-helical to a hairpin-turn-like one in response to charging of its ends.

Crystalline particle packings on constant mean curvature (Delaunay) surfaces

We investigate the structure of crystalline particle arrays on constant mean curvature (CMC) surfaces of revolution. Such curved crystals have been realized physically by creating charge-stabilized colloidal arrays on liquid capillary bridges. CMC surfaces of revolution, classified by Delaunay in 1841, include the 2-sphere, the cylinder, the vanishing mean curvature catenoid (a minimal surface), and the richer and less investigated unduloid and nodoid. We determine numerically candidate ground-state configurations for 1000 pointlike particles interacting with a pairwise-repulsive 1/r(3) potential, with distance r measured in three-dimensional Euclidean space R(3). We mimic stretching of capillary bridges by determining the equilibrium configurations of particles arrayed on a sequence of Delaunay surfaces obtained by increasing or decreasing the height at constant volume starting from a given initial surface, either a fat cylinder or a square cylinder. In this case, the stretching process takes one through a complicated sequence of Delaunay surfaces, each with different geometrical parameters, including the aspect ratio, mean curvature, and maximal Gaussian curvature. Unduloids, catenoids, and nodoids all appear in this process. Defect motifs in the ground state evolve from dislocations at the boundary to dislocations in the interior to pleats and scars in the interior and then isolated sevenfold disclinations in the interior as the capillary bridge narrows at the waist (equator) and the maximal (negative) Gaussian curvature grows. We also check theoretical predictions that the isolated disclinations are present in the ground state when the surface contains a geodesic disk with integrated Gaussian curvature exceeding -π/3. Finally, we explore minimal energy configurations on sets of slices of a given Delaunay surface, and we obtain configurations and defect motifs consistent with those seen in stretching.

Influence of simple electrolytes on the orientational ordering of thermotropic liquid crystals at aqueous interfaces

We report orientational anchoring transitions at aqueous interfaces of a water-immiscible, thermotropic liquid crystal (LC; nematic phase of 4'-pentyl-4-cyanobiphenyl (5CB)) that are induced by changes in pH and the addition of simple electrolytes (NaCl) to the aqueous phase. Whereas measurements of the zeta potential on the aqueous side of the interface of LC-in-water emulsions prepared with 5CB confirm pH-dependent formation of an electrical double layer extending into the aqueous phase, quantification of the orientational ordering of the LC leads to the proposition that an electrical double layer is also formed on the LC-side of the interface with an internal electric field that drives the LC anchoring transition. Further support for this conclusion is obtained from measurements of the dependence of LC ordering on pH and ionic strength, as well as a simple model based on the Poisson-Boltzmann equation from which we calculate the contribution of an electrical double layer to the orientational anchoring energy of the LC. Overall, the results presented herein provide new fundamental insights into ionic phenomena at LC-aqueous interfaces, and expand the range of solutes known to cause orientational anchoring transitions at LC-aqueous interfaces beyond previously examined amphiphilic adsorbates.

Effects of Hofmeister anions on the aggregation behavior of PEO-PPO-PEO triblock copolymers

The effects of a series of Hofmeister anions on the phase behaviors of a poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) (PEO-PPO-PEO) triblock copolymer were investigated with an automated melting point system. Well hydrated anions and poorly hydrated anions interacted with the polymer differently and further affected the phase transition of the polymer. Poorly hydrated anions worked through changing the interfacial tension at the polymer/aqueous interface and in enhancing the polymer hydration by ion binding. The phase transition of the polymer in the presence of well hydrated anions correlated directly to the hydration entropy of the anions. As a consequence, the polymer showed a two-step phase transition in solutions containing poorly hydrated anions while displayed a single-step phase transition in the presence of well hydrated anions. The mechanisms of how ions interact with the polymer and further modulate its phase behaviors were discussed.

Particle self-assembly in ionic liquid-in-water Pickering emulsions

We report the self-assembly of a single species or a binary mixture of microparticles in ionic liquid-in-water Pickering emulsions, with emphases on the interfacial self-assembled particle structure and the partitioning preference of free particles in the dispersed and continuous phases. The particles form monolayers at ionic liquid-water interfaces and are close-packed on fully covered emulsion droplets or aggregated on partially covered droplets. In contrast to those at oil-water interfaces, no long-range-ordered colloidal lattices are observed. Interestingly, other than equilibrating at the ionic liquid-water interfaces, the microparticles also exhibit a partitioning preference in the dispersed and continuous phases: the sulfate-treated polystyrene (S-PS) and aldehyde-sulfate-treated polystyrene (AS-PS) microparticles are extracted to the ionic liquid phase with a high extraction efficiency, whereas the amine-treated polystyrene (A-PS) microparticles remain in the water phase.

Precipitation in aqueous mixtures with addition of a strongly hydrophilic or hydrophobic solute

We examine phase separation in aqueous mixtures due to preferential solvation with a low-density solute (hydrophilic ions or hydrophobic particles). For hydrophilic ions, preferential solvation can stabilize water domains enriched with ions. This precipitation occurs above a critical solute density n(p) in wide ranges of the temperature and the average composition, where the mixture solvent would be in a one-phase state without solute. The volume fraction of precipitated domains tends to zero as the average solute density n is decreased to np or as the interaction parameter χ is decreased to a critical value χ(p). If we start with one-phase states with n>n(p) or χ>χ(p), precipitation proceeds via homogeneous nucleation or via heterogeneous nucleation, for example, around suspended colloids. In the latter case, colloid particles are wrapped by thick wetting layers. We also predict a first-order prewetting transition for n or χ slightly below np or χ(p) for neutral colloids.

Computer simulations of the restricted primitive model at very low temperature and density

The problem of successfully simulating ionic fluids at low temperature and low density states is well known in the simulation literature: using conventional methods, the system is not able to equilibrate rapidly due to the presence of strongly associated cation-anion pairs. In this paper we present a numerical method for speeding up computer simulations of the restricted primitive model (RPM) at low temperatures (around the critical temperature) and at very low densities (down to 10(-10)σ(-3), where σ is the ion diameter). Experimentally, this regime corresponds to typical concentrations of electrolytes in nonaqueous solvents. As far as we are aware, this is the first time that the RPM has been equilibrated at such extremely low concentrations. More generally, this method could be used to equilibrate other systems that form aggregates at low concentrations.

Capillary forces between particles at a liquid interface: general theoretical approach and interactions between capillary multipoles

The liquid interface around an adsorbed colloidal particle can be undulated because of roughness or heterogeneity of the particle surface, or due to the fact that the particle has non-spherical (e.g. ellipsoidal or polyhedral) shape. In such case, the meniscus around the particle can be expanded in Fourier series, which is equivalent to a superposition of capillary multipoles, viz. capillary charges, dipoles, quadrupoles, etc. The capillary multipoles attract a growing interest because their interactions have been found to influence the self-assembly of particles at liquid interfaces, as well as the interfacial rheology and the properties of particle-stabilized emulsions and foams. As a rule, the interfacial deformation in the middle between two adsorbed colloidal particles is small. This fact is utilized for derivation of accurate asymptotic expressions for calculating the capillary forces by integration in the midplane, where the Young-Laplace equation can be linearized and the superposition approximation can be applied. Thus, we derived a general integral expression for the capillary force, which was further applied to obtain convenient asymptotic formulas for the force and energy of interaction between capillary multipoles of arbitrary orders. The new analytical expressions have a wider range of validity in comparison with the previously published ones. They are applicable not only for interparticle distances that are much smaller than the capillary length, but also for distances that are comparable or greater than the capillary length.