Electrostatic interactions of colloidal particles at vanishing ionic strength

Recent Developments in the Methods and Applications of Electrostatic Theory

ConspectusThe review improves our understanding of how electrostatic interactions in the electrolyte, gas phase, and on surfaces can drive the fragmentation and assembly of particles. This is achieved through the overview of our advanced theoretical and computational modeling toolbox suitable for interpretation of experimental observations and discovery of novel, tunable assemblies and architectures. In the past decade, we have produced a significant, fundamental body of work on the development of comprehensive theories based on a rigorous mathematical foundation. These solutions are capable of accurate predictions of electrostatic interactions between dielectric particles of arbitrary size, anisotropy, composition, and charge, interacting in solvents, ionized medium, and on surfaces. We have applied the developed electrostatic approaches to describe physical and chemical phenomena in dusty plasma and planetary environments, in Coulomb fission and electrospray ionization processes, and in soft matter, including a counterintuitive but widespread attraction between like-charged particles.Despite its long history, the search for accurate methods to provide a deeper understanding of electrostatic interactions remains a subject of significant interest, as manifested by a constant stream of theoretical and experimental publications. While major international effort in this area has focused predominantly on the computational modeling of biocatalytic and biochemical performance, we have expanded the boundaries of accuracy, generality, and applicability of underlying theories. Simple solvation models, often used in calculating the electrostatic component of molecular solvation energy and polarization effects of solvent, rarely go beyond the induced dipole approximation because of computational costs. These approximations are generally adequate at larger separation distances; however, as particles approach the touching point, more advanced charged-induced multipolar descriptions of the electrostatic interactions are required to describe accurately a collective behavior of polarizable neutral and charged particles. At short separations, the electrostatic forces involving polarizable dielectric and conducting particles become nonadditive which necessitates further developments of quantitatively accurate many-body approaches. In applications, the electrostatic response of materials is commonly controlled by externally applied electric fields, an additional complex many-body problem that we have addressed most recently, both theoretically and numerically.This review reports on the most significant results and conclusions underpinning these recent advances in electrostatic theory and its applications. We first discuss the limitations of classical approaches to interpreting electrostatic phenomena in electrolytes and complex plasmas, leading to an extended analytical theory suitable for accurate estimation of the electrostatic forces in a dilute solution of a strong electrolyte. We then introduce the concept and numerical realization of many-body electrostatic theory focusing on its performance in selected experimental cases. These experiments underpin, among other applications, electrostatic self-assembly of two-dimensional lattice structures, melting of ionic colloidal crystals in an external electric field, and coalescence of charged clusters.

Applicability of the linearized Poisson-Boltzmann theory to contact angle problems and application to the carbon dioxide-brine-solid systems

In colloidal science and bioelectrostatics, the linear Poisson Boltzmann equation (LPBE) has been used extensively for the calculation of potential and surface charge density. Its fundamental assumption rests on the premises of low surface potential. In the geological sequestration of carbon dioxide in saline aquifers, very low pH conditions coupled with adsorption induced reduction of surface charge density result in low pH conditions that fit into the LPB theory. In this work, the Gouy–Chapman model of the electrical double layer has been employed in addition to the LPBE theory to develop a contact angle model that is a second-degree polynomial in pH. Our model contains the point of zero charge pH of solid surface. To render the model applicable to heterogeneous surfaces, we have further developed a model for the effective value of the point of zero charge pH. The point of zero charge pH model when integrated into our model enabled us to determine the point of zero charge pH of sandstone, quartz and mica using literature based experimental data. In this regard, a literature based thermodynamic model was used to calculate carbon dioxide solubility and pH of aqueous solution. Values of point of zero charge pH determined in this paper agree with reported ones. The novelty of our work stems from the fact that we have used the LPB theory in the context of interfacial science completely different from the classical approach, where the focus is on interparticle electrostatics involving colloidal stabilization.

From Attraction to Repulsion to Attraction: Non-monotonic Temperature Dependence of Polymer-Mediated Interactions in Colloidal Dispersions

In this work, we have synthesized polystyrene particles that carry short end-grafted polyethylene glycol (PEG) chains. We then added dissolved 100 kDa PEG polymers and monitored potential flocculation by confocal microscopy. Qualitative predictions, based on previous theoretical developments in this field (Xie, F.; et al. Soft Matter 2016, 12, 658), suggest a non-monotonic temperature response. These theories propose that the "free" (dissolved) polymers will mediate attractive depletion interactions at room temperature, with a concomitant clustering/flocculation at a sufficiently high polymer concentration. At high temperatures, where the solvent is poorer, this is predicted to be replaced by attractive bridging interactions, again resulting in particle condensation. Interestingly enough, our theoretical framework, based on classical density functional theory, predicts an intermediate temperature regime where the polymer-mediated interactions are repulsive! This obviously implies a homogeneous dispersion in this regime. These qualitative predictions have been experimentally tested and confirmed in this work, where flocs of particles start to form at room temperature for a high enough polymer dosage. At temperatures near 45 °C, the flocs redisperse, and we obtain a homogeneous sample. However, samples at about 75 °C will again display clusters and eventually phase separation. Using results from these studies, we have been able to fine-tune parameters of our coarse-grained theoretical model, resulting in predictions of temperature-dependent stability that display semiquantitative accuracy. A crucial aspect is that under "intermediate" conditions, where the polymers neither adsorb nor desorb at the particle surfaces, the polymer-mediated equilibrium interaction is repulsive.

Charged dielectric spheres interacting in electrolytic solution: A linearized Poisson-Boltzmann equation model

We present an analytical theory of electrostatic interactions of two spherical dielectric particles of arbitrary radii and dielectric constants, immersed into a polarizable ionic solvent (assuming that the linearized Poisson-Boltzmann framework holds) and bearing arbitrary charge distributions expanded in multipolar terms. The presented development entails a novel two-center re-expansion analytical theory that expands upon and improves the existing ones, bypassing the conventional expansions in modified Bessel functions. On this basis, we develop a specific matrix formalism that facilitates the construction of asymptotic expansions in ascending order of Debye screening terms of potential coefficients, which are then employed to find exact closed-form expressions for the total electrostatic energy. In particular, this work allows us to explicitly and precisely quantify the k-screened terms of the potential coefficients and mutual interaction energy. Specific cases of monopolar and dipolar distributions are described in particular detail. Comprehensive numerical examples and tests of series convergence and the relative balance of leading and higher-order terms of the mutual interaction energy are presented depending on the inter-particle distance and particles' radii. The results of this work find application in soft matter modeling and, in particular, in computational biophysics and colloid science, where the availability of increasingly larger experimental structures at the atomic-level resolution makes numerical treatment challenging and calls for more efficient expressions and an increased range of validity.

Tunability of Interactions between the Core and Shell in Rattle-Type Particles Studied with Liquid-Cell Electron Microscopy

Yolk-shell or rattle-type particles consist of a core particle that is free to move inside a thin shell. A stable core with a fully accessible surface is of interest in fields such as catalysis and sensing. However, the stability of a charged nanoparticle core within the cavity of a charged thin shell remains largely unexplored. Liquid-cell (scanning) transmission electron microscopy is an ideal technique to probe the core-shell interactions at nanometer spatial resolution. Here, we show by means of calculations and experiments that these interactions are highly tunable. We found that in dilute solutions adding a monovalent salt led to stronger confinement of the core to the middle of the geometry. In deionized water, the Debye length κ-1 becomes comparable to the shell radius Rshell, leading to a less steep electric potential gradient and a reduced core-shell interaction, which can be detrimental to the stability of nanorattles. For a salt concentration range of 0.5-250 mM, the repulsion was relatively long-ranged due to the concave geometry of the shell. At salt concentrations of 100 and 250 mM, the core was found to move almost exclusively near the shell wall, which can be due to hydrodynamics, a secondary minimum in the interaction potential, or a combination of both. The possibility of imaging nanoparticles inside shells at high spatial resolution with liquid-cell electron microscopy makes rattle particles a powerful experimental model system to learn about nanoparticle interactions. Additionally, our results highlight the possibilities for manipulating the interactions between core and shell that could be used in future applications.

Quincke Oscillations of Colloids at Planar Electrodes

Dielectric particles in weakly conducting fluids rotate spontaneously when subject to strong electric fields. Such Quincke rotation near a plane electrode leads to particle translation that enables physical models of active matter. In this Letter, we show that Quincke rollers can also exhibit oscillatory dynamics, whereby particles move back and forth about a fixed location. We explain how oscillations arise for micron-scale particles commensurate with the thickness of a field-induced boundary layer in the nonpolar electrolyte. This work enables the design of colloidal oscillators.

The ENUF method-Ewald summation based on nonuniform fast Fourier transform: Implementation, parallelization, and application

Computer simulations of model systems are widely used to explore striking phenomena in promising applications spanning from physics, chemistry, biology, to materials science and engineering. The long range electrostatic interactions between charged particles constitute a prominent factor in determining structures and states of model systems. How to efficiently calculate electrostatic interactions in simulation systems subjected to partial or full periodic boundary conditions has been a grand challenging task. In the past decades, a large variety of computational schemes has been proposed, among which the Ewald summation method is the most reliable route to accurately deal with electrostatic interactions between charged particles in simulation systems. In addition, extensive efforts have been done to improve computational efficiencies of the Ewald summation based methods. Representative examples are approaches based on cutoffs, reaction fields, multi-poles, multi-grids, and particle-mesh schemes. We sketched an ENUF method, an abbreviation for the Ewald summation method based on the nonuniform fast Fourier transform technique, and have implemented this method in particle-based simulation packages to calculate electrostatic energies and forces at micro- and mesoscopic levels. Extensive computational studies of conformational properties of polyelectrolytes, dendrimer-membrane complexes, and ionic fluids demonstrated that the ENUF method and its derivatives conserve both energy and momentum to floating point accuracy, and exhibit a computational complexity of O N log N with optimal physical parameters. These ENUF based methods are attractive alternatives in molecular simulations where high accuracy and efficiency of simulation methods are needed to accelerate calculations of electrostatic interactions at extended spatiotemporal scales.

Experimental Evidence for Algebraic Double-Layer Forces

According to conventional wisdom, electric double-layer forces normally decay exponentially with separation distance. Here, we present experimental evidence of algebraically decaying double-layer interactions. We show that algebraic interactions arise in both strongly overlapping as well as counterion-only regimes, albeit the evidence is less clear for the former regime. In both of these cases, the disjoining pressure profile assumes an inverse square distance dependence. At small separation distances, another algebraic regime is recovered. In this regime, the pressure decays as the inverse of separation distance.

The formation of free ions and electrophoretic mobility of Ag and Au nanoparticles in n-hexadecane–chloroform mixtures at low concentrations of AOT

The electrophoretic mobility of Ag and Au nanoparticles in n-hexadecane–chloroform mixtures was studied as a function of the chloroform content (from 0 to 100 vol%).

Direct measurement of electrostatic interactions between poly(methyl methacrylate) microspheres with optical laser tweezers

In this study, we measured the force of electrostatic interactions between poly(methyl methacrylate) (PMMA) particles dispersed in organic solvent mixtures of cyclohexyl bromide (CHB) and n-decane. Optical laser tweezers were employed to directly measure interactive forces between paired PMMA particles in a CHB medium that contained n-decane in various volume ratios. CHB, having a moderate dielectric constant, provided an environment with a high charge storage capacity. The addition of n-decane lowered the effective refractive index of the medium, which increased the optical trapping efficiency. We also fabricated microscope flow cells with a commonly used UV-curable adhesive and quantified the effects of dissolved adhesive compounds through interactive force measurements and nuclear magnetic resonance analysis. In addition, we studied the impact of CHB dissociation into H⁺ and Br^- ions, which could screen electrostatic interactions.

Quincke rotor dynamics in confinement: rolling and hovering

The Quincke effect is an electrohydrodynamic instability which gives rise to a torque on a dielectric particle in a uniform DC electric field. Previous studies reported that a sphere initially resting on the electrode rolls with steady velocity. We experimentally find that in strong fields the rolling becomes unsteady, with time-periodic velocity. Furthermore, we find another regime, where the rotating sphere levitates in the space between the electrodes. Our experimental results show that the onset of Quincke rotation strongly depends on particle confinement and the threshold for rolling is higher compared to rotation in the hovering state.

Charge polarization near dielectric interfaces and the multiple-scattering formalism

Interfacial charge polarization is ubiquitous in systems with sharp dielectric contrast. Fully resolving the interfacial charges often relies on demanding numerical algorithms to solve the boundary value problem. The recent development of an analytical multiple-scattering formalism to solve the interfacial charge polarization problem for particles carrying monopolar, dipolar, and multipolar charges is reviewed. Every term produced in this formalism has a simple interpretation, and terms for spherical particles can be rapidly evaluated using an image-line construction. Several practical applications of this formalism are illustrated. A dielectric virial expansion for polarizable particles based on this formalism is also described. The origins of singular polarization charges for particles in close contact are explained and evaluated for both dielectric and conducting spheres.

Surfactant mediated particle aggregation in nonpolar solvents

The aggregation behavior of particles in nonpolar media is studied with time-resolved light scattering.

Proton transfer in nonpolar solvents: an approach to generate electrolytes in aprotic media

Stabilizing charged species in nonpolar solvents is challenging due to their low dielectric constant. As a contrast to formally ionic electrolytes, two series of acidic "potential" electrolytes have been developed in this study. These can be ionized by combining them stoichiometrically with a small molecule base in a typical nonpolar solvent, n-dodecane. The electrolytic conductivity of solutions of bis(2-ethylhexyl)phosphoric acid as mixtures with linear and branched dioctylamines and trioctylamines was measured, and the solutions were found to become increasingly conductive as the concentration increased, demonstrating that proton transfer occurred between the two species. Linear octylamines were found to be most effective at deprotonation. An acid-tipped poly(lauryl methacrylate) polymer (PLMA48-COOH) was also studied to give a polymer soluble in n-dodecane with a single ionizable group located precisely at the end of the polymer chain. Trioctylamine could successfully deprotonate this acid group. Even in an aprotic solvent, the transfer of protons between acidic and basic moieties is a useful method for controlling the properties of dissolved molecules.

Electrostatic interactions between charged dielectric particles in an electrolyte solution: constant potential boundary conditions

The problem of electrostatic interactions between colloidal particles in an electrolyte solution has been solved within the Debye-Hückel approximation using the boundary condition of constant potential. The model has been validated in two independent ways - by considering the limiting cases obtained from DLVO theory and comparison with the available experimental data. The presented methodology provides the final part of a complete theory of pairwise electrostatic interactions between spherical colloidal particles; one that embraces all possible chemical scenarios within the boundary conditions of constant potential and constant charge.

Linking slow dynamics and microscopic connectivity in dense suspensions of charged colloids

The quest to unravel the nature of the glass transition, where the viscosity of a liquid increases by many orders of magnitude, while its static structure remains largely unaffected, remains unresolved. While various structural and dynamical precursors to vitrification have been identified, a predictive and quantitative description of how subtle changes at the microscopic scale give rise to the steep growth in macroscopic viscosity is missing. It was recently proposed that the presence of long-lived bonded structures within the liquid may provide the long-sought connection between local structure and global dynamics. Here we directly observe and quantify the connectivity dynamics in liquids of charged colloids en route to vitrification using three-dimensional confocal microscopy. We determine the dynamic structure from the real-space van Hove correlation function and from the particle trajectories, providing upper and lower bounds on connectivity dynamics. Based on these data, we extend Dyre's model for the glass transition to account for particle-level structural dynamics; this results in a microscopic expression for the slowing down of relaxations in the liquid that is in quantitative agreement with our experiments. These results indicate how vitrification may be understood as a dynamical connectivity transition with features that are strongly reminiscent of rigidity percolation scenarios.

Charging Poly(methyl Methacrylate) Latexes in Nonpolar Solvents: Effect of Particle Concentration

The electrophoresis of a well-established model system of charged colloids in nonpolar solvents has been studied as a function of particle volume fraction at constant surfactant concentration. Dispersions of poly(12-hydroxystearic acid)-stabilized poly(methyl methacrylate) (PMMA) latexes in dodecane were prepared with added Aerosol OT surfactant as the charging agent. The electrophoretic mobility (μ) of the PMMA latexes is found to decrease with particle concentration. The particles are charged by a small molecule charging agent (AOT) at finite concentration, and this makes the origin of this decrease in μ unclear. There are two suggested explanations. The decrease could either be due to the reservoir of available surfactant being exhausted at high particle concentrations or the interactions between the charged particles at high particle number concentrations. Contrast-variation small-angle neutron scattering measurements of PMMA latexes and deuterated AOT-d₃₄ surfactant in latex core contrast-matched solvent were used to study the former, and electrokinetic modeling was used to study the latter. As the same amount of AOT-d₃₄ is found to be incorporated with the latexes at all volume fractions, the solvodynamic and electrical interactions between particles are determined to be the explanation for the decrease in mobility. These measurements show that, for small latexes, there are interactions between the charged particles at all accessible particle volume fractions and that it is necessary to account for this to accurately determine the electrokinetic ζ potential.

Charge transport by inverse micelles in non-polar media

Charged inverse micelles play an important role in the electrical charging and the electrodynamics of nonpolar colloidal dispersions relevant for applications such as electronic ink displays and liquid toner printing. This review examines the properties and the behavior of charged inverse micelles in microscale devices in the absence of colloidal particles. It is discussed how charge in nonpolar liquids is stabilized in inverse micelles and how conductivity depends on the inverse micelle size, water content and ionic impurities. Frequently used nonpolar surfactant systems are investigated with emphasis on aerosol-OT (AOT) and poly-isobutylene succinimide (PIBS) in dodecane. Charge generation in the bulk by disproportionation is studied from measurements of conductivity as a function of surfactant concentration and from generation currents in quasi steady-state. When a potential difference is applied, the steady-state situation can show electric field screening or complete charge separation. Different regimes of charge transport are identified when a voltage step is applied. It is shown how the transient and steady-state currents depend on the rate of bulk generation, on insulating layers and on the sticking or non-sticking behavior of charged inverse micelles at interfaces. For the cases of AOT and PIBS in dodecane, the magnitude of the generation rate and the type of interaction at the interface are very different.

Electrolyte-induced Instability of Colloidal Dispersions in Nonpolar Solvents

Dispersions of poly(methyl methacrylate) (PMMA) latexes were prepared in a low dielectric, nonpolar solvent (dodecane) both with and without the oil-soluble electrolyte, tetradodecylammonium-tetrakis(3,5-bis(trifluoromethyl)phenyl)borate. For dispersions with a high concentration of background electrolyte, the latexes become colloidally unstable and sediment in a short period of time (<1 h). This is completely reversible upon dilution. Instability of the dispersions is due to an apparent attraction between the colloids, directly observed using optical tweezers by bringing optically trapped particles into close proximity. Simple explanations generally used by colloid scientists to explain loss of stability (charge screening or stabilizer collapse) are insufficient to explain this observation. This unexpected interaction seems, therefore, to be a consequence of the materials that can be dispersed in low dielectric media and is expected to have ramifications for studying colloids in such solvents.

Formation of Charge Carriers in Liquids

After presenting a brief historical overview of the classic contributions of Faraday, Arrhenius, Kohlrausch, Bjerrum, Debye, Hückel and Onsager to understanding the conductivity of true electrolytes in aqueous solutions, we present an in-depth review of the 1933 work of Fuoss & Kraus who explored the effect of the solvent on electrolyte dissociation equilibria in either polar or nonpolar media. Their theory predicts that the equilibrium constant for dissociation decays exponentially with the ratio of the Bjerrum length λ_B to the ion-pair size a. Fuoss & Kraus experimentally confirmed the dependence on λ_B of the solvent, while more recent experiments explored the dependence on a. We also present an in-depth review of the charge-fluctuation theory used to explain the sharp increase in conductivity with added water for water-in-oil microemulsions stabilized by ionic surfactants. Water swells the droplets making a greater fraction of them charged. At least for low-water content, the same exponential dependence on λ_B/a is predicted, provided a is chosen as the size of the polar core of the droplet or inverted micelle. Potential electrolytes like alcohols acquire charge by exchanging a proton. The dissociation equilibrium of the resulting ion-pair in mixtures of toluene and alcohol appears to be well modelled by the Fuoss theory. Solutions of inverted micelles are also thought to acquire charge by exchanging a small ion between two net-neutral micelles. Except for the dissociation of true electrolytes, all of the charging scenarios described above can be represented by a two-reaction sequence: 1) the disproportionation of charge between two neutral molecules, inverted micelles or droplets; followed by 2) the dissociation of the "ion"-pair intermediates. (The dissociation of true electrolytes involves only the second.) For each of the above charging theories, the extent of the second reaction decays exponentially with λ_B/a.

Interaction and charge transfer between dielectric spheres: Exact and approximate analytical solutions

We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that describe polarization effects to infinite orders in the inverse of the distance between the sphere centers. In addition, we show that these exact solutions may be approximated by much simpler analytical expressions that are useful for many practical applications. This is exemplified through calculations of Langevin type cross sections for forming a compound system of two colliding spheres and through calculations of electron transfer cross sections. We find that it is important to account for dielectric properties and finite sphere sizes in such calculations, which for example may be useful for describing the evolution, growth, and dynamics of nanometer sized dielectric objects such as molecular clusters or dust grains in different environments including astrophysical ones.

Further Insight into the Definite Morphology and Formation Mechanism of Mesoporous Silica KCC-1

The unique three-dimensional pore structure of KCC-1 has attracted significant attention and has proven to be different compared to other conventional mesoporous silica such as the MCM-41 family, SBA-15, or even MSN nanoparticles. In this research, we carefully examine the morphology of KCC-1 to define more appropriate nomenclature. We also propose a formation mechanism of KCC-1 based on our experimental evidence. Herein, the KCC-1 morphology was interpreted mainly on the basis of compiling all observation and information taken from SEM and TEM images. Further analysis on TEM images was carried out. The gray value intensity profile was derived from TEM images in order to determine the specific pattern of this unique morphology that is found to be clearly different from that of other types of porous spherical-like morphologies. On the basis of these results, the KCC-1 morphology would be more appropriately reclassified as bicontinuous concentric lamellar morphology. Some physical characteristics such as the origin of emulsion, electrical conductivity, and the local structure of water molecules in the KCC-1 emulsion were disclosed to reveal the formation mechanism of KCC-1. The origin of the KCC-1 emulsion was characterized by the observation of the Tyndall effect, conductometry to determine the critical micelle concentration, and Raman spectroscopy. In addition, the morphological evolution study during KCC-1 synthesis completes the portrait of the formation of mesoporous silica KCC-1.

Different Types of Charged-Inverse Micelles in Nonpolar Media

Over the last few years, the electrodynamics of charged inverse micelles (CIMs) in nonpolar liquids and the generation mechanism and properties of newly generated CIMs have been studied extensively for the model system of polyisobutylene succinimide in dodecane. However, the newly generated CIMs, which accumulate at the electrodes when a continuous voltage is applied, behave differently compared to the regular CIMs present in equilibrium in the absence of a field. In this work, we use transient current measurements to investigate the behavior of the newly generated CIMs when the field is reduced to zero or reversed. We demonstrate that the newly generated CIMs do not participate in the diffuse double layer near the electrode formed by the regular CIMs but form an interface layer at the electrode surface. A fraction of the newly generated negative CIMs can be released from this interface layer when the field there becomes zero. The findings of this study provide a better understanding of fundamental processes in nonpolar liquids and are relevant for applications such as electronic ink displays and liquid toner printing.

Charge renormalization in nominally apolar colloidal dispersions

We present high-resolution measurements of the pair interactions between dielectric spheres dispersed in a fluid medium with a low dielectric constant. Despite the absence of charge control agents or added organic salts, these measurements reveal strong and long-ranged repulsions consistent with substantial charges on the particles whose interactions are screened by trace concentrations of mobile ions in solution. The dependence of the estimated charge on the particles' radii is consistent with charge renormalization theory and, thus, offers insights into the charging mechanism in this interesting class of model systems. The measurement technique, based on optical-tweezer manipulation and artifact-free particle tracking, makes use of optimal statistical methods to reduce measurement errors to the femtonewton frontier while covering an extremely wide range of interaction energies.

Triclinic nematic colloidal crystals from competing elastic and electrostatic interactions

The self-assembly of nanoparticles can enable the generation of composites with predesigned properties, but reproducing the structural diversity of atomic and molecular crystals remains a challenge. We combined anisotropic elastic and weakly screened electrostatic interactions to guide both orientational and triclinic positional self-ordering of inorganic nanocrystals in a nematic fluid host. The lattice periodicity of these low-symmetry colloidal crystals is more than an order of magnitude larger than the nanoparticle size. The orientations of the nanocrystals, as well as the crystallographic axes of the ensuing triclinic colloidal crystals, are coupled to the uniform alignment direction of the nematic host, which can be readily controlled on large scales. We examine colloidal pair and many-body interactions and show how triclinic crystals with orientational ordering of the semiconductor nanorods emerge from competing long-range elastic and electrostatic forces.

Singular electrostatic energy of nanoparticle clusters

The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on the particles. We show that the energy at small separation h has a singular logarithmic dependence on h. We derive a general form for this energy in terms of the singular capacitance of two spheres in near contact c(h), together with nonsingular geometric features of the cluster. Using this form, we determine the energies of various clusters, finding that more compact clusters are more stable. These energies are proposed to be significant for metal-semiconductor binary nanoparticle lattices found experimentally. We sketch how these effects should dictate the relative abundances of metal nanoparticle clusters in nonpolar solvents.

Space charge limited release of charged inverse micelles in non-polar liquids

Charged inverse micelles (CIMs) generated during a continuous polarizing voltage between electrodes in the model system of polyisobutylene succinimide in dodecane do not populate a diffuse double layer like CIMs present in equilibrium (regular CIMs), but instead end up in interface layers.

Progress in the theory of electrostatic interactions between charged particles

In this perspective we examine recent theoretical developments in methods for calculating the electrostatic properties of charged particles of dielectric materials.

Exploring the charging mechanisms in non-aqueous multiphase surfactant solutions, emulsions and colloidal systems via conductivity behaviors predicted with eyring's rate process theory

The schematic diagram shows charge separation induced and stabilized by an electric field and inverse micelles charged in the end.

Sulfosuccinate and Sulfocarballylate Surfactants As Charge Control Additives in Nonpolar Solvents

A series of eight sodium sulfonic acid surfactants with differently branched tails (four double-chain sulfosuccinates and four triple-chain sulfocarballylates) were studied as charging agents for sterically stabilized poly(methyl methacrylate) (PMMA) latexes in dodecane. Tail branching was found to have no significant effect on the electrophoretic mobility of the latexes, but the number of tails was found to influence the electrophoretic mobility. Triple-chain, sulfocarballylate surfactants were found to be more effective. Several possible origins of this observation were explored by comparing sodium dioctylsulfosuccinate (AOT1) and sodium trioctylsulfocarballylate (TC1) using identical approaches: the inverse micelle size, the propensity for ion dissociation, the electrical conductivity, the electrokinetic or ζ potential, and contrast-variation small-angle neutron scattering. The most likely origin of the increased ability of TC1 to charge PMMA latexes is a larger number of inverse micelles. These experiments demonstrate a small molecular variation that can be made to influence the ability of surfactants to charge particles in nonpolar solvents, and modifying molecular structure is a promising approach to developing more effective charging agents.

Celebrating Soft Matter's 10th Anniversary: Influencing the charge of poly(methyl methacrylate) latexes in nonpolar solvents

Sterically-stabilized poly(methyl methacrylate) (PMMA) latexes dispersed in nonpolar solvents are a classic, well-studied system in colloid science. This is because they can easily be synthesized with a narrow size distribution and because they interact essentially as hard spheres. These PMMA latexes can be charged using several methods (by adding surfactants, incorporating ionizable groups, or dispersing in autoionizable solvents), and due to the low relative permittivity of the solvents (εr ≈ 2 for alkanes to εr ≈ 8 for halogenated solvents), the charges have long-range interactions. The number of studies of these PMMA particles as charged species has increased over the past ten years, after few studies immediately following their discovery. A large number of variations in both the physical and chemical properties of the system (size, concentration, surfactant type, or solvent, as a few examples) have been studied by many groups. By considering the literature on these particles as a whole, it is possible to determine the variables that have an effect on the charge of particles. An understanding of the process of charge formation will add to understanding how to control charge in nonaqueous solvents as well as make it possible to develop improved technologically relevant applications for charged polymer nanoparticles.

Charging Dynamics of Aerosol OT Inverse Micelles

Aerosol OT (AOT) is a commonly used surfactant and charging agent in nonpolar liquids. Properties such as the conductivity of AOT suspensions in nonpolar liquids and the behavior of charged AOT inverse micelles at interfaces have been studied recently, but still little is known about the generation dynamics of charged AOT inverse micelles. In this article, the generation dynamics of charged AOT inverse micelles in dodecane are investigated with transient current measurements. At low applied voltages, the generation rate is sufficiently fast to maintain the equilibrium concentration of charged inverse micelles, such that the current scales proportionally with the applied voltage. However, above a threshold voltage the current becomes limited by the generation of charged inverse micelles. Al2O3-coated electrodes are used to achieve these high-voltage current measurements while reducing surface generation currents. The dependency of the resulting generation-limited currents with the micelle concentration and the liquid volume is compatible with a bulk disproportionation mechanism. The measured currents are analyzed using a model based on drift, generation, and recombination of charged inverse micelles and the corresponding generation and recombination rates of charged AOT inverse micelles have been determined.

Effective charges and virial pressure of concentrated macroion solutions

The stability of colloidal suspensions is crucial in a wide variety of processes, including the fabrication of photonic materials and scaffolds for biological assemblies. The ionic strength of the electrolyte that suspends charged colloids is widely used to control the physical properties of colloidal suspensions. The extensively used two-body Derjaguin-Landau-Verwey-Overbeek (DLVO) approach allows for a quantitative analysis of the effective electrostatic forces between colloidal particles. DLVO relates the ionic double layers, which enclose the particles, to their effective electrostatic repulsion. Nevertheless, the double layer is distorted at high macroion volume fractions. Therefore, DLVO cannot describe the many-body effects that arise in concentrated suspensions. We show that this problem can be largely resolved by identifying effective point charges for the macroions using cell theory. This extrapolated point charge (EPC) method assigns effective point charges in a consistent way, taking into account the excluded volume of highly charged macroions at any concentration, and thereby naturally accounting for high volume fractions in both salt-free and added-salt conditions. We provide an analytical expression for the effective pair potential and validate the EPC method by comparing molecular dynamics simulations of macroions and monovalent microions that interact via Coulombic potentials to simulations of macroions interacting via the derived EPC effective potential. The simulations reproduce the macroion-macroion spatial correlation and the virial pressure obtained with the EPC model. Our findings provide a route to relate the physical properties such as pressure in systems of screened Coulomb particles to experimental measurements.

Polar Solvents Trigger Formation of Reverse Micelles

We use molecular dynamics simulations and molecular thermodynamics to investigate the formation of reverse micelles in a system of surfactants and nonpolar solvents. Since the early observation of reverse micelles, the question has been whether the existence of polar solvent molecules such as water is the driving force for the formation of reverse micelles in nonpolar solvents. In this work, we use a simple coarse-grained model of surfactants and solvents to show that a small number of polar solvent molecules triggers the formation of large permanent aggregates. In the absence of polar molecules, both the thermodynamic model and molecular simulations show that small aggregates are more populated in the solution and larger ones are less frequent as the system evolves over time. The size and shape of reverse micelles depend on the size of the polar core: the shape is spherical for a large core and ellipsoidal for a smaller one. Using the coarse-grained model, we also investigate the effect of temperature and surfactant tail length. Our results reveal that the number of surfactant molecules in the micelle decreases as the temperature increases, but the average diameter does not change because the size of the polar core remains invariant. A reverse micelle with small polar core attracts fewer surfactants when the tail is long. The uptake of solvent particles by a micelle of longer surfactant tail is less than shorter ones when the polar solvent particles are initially distributed randomly.