Counterion condensation on spheres in the salt-free limit

Globular pattern formation of hierarchical ceria nanoarchitectures

Dissipative structures often appear as an unstable counterpart of ordered structures owing to fluctuations that do not form a homogeneous phase. Even a multiphase mixture may simultaneously undergo one chemical reaction near equilibrium and another one that is far from equilibrium. Here, we observed in real time crystal seed formation and simultaneous nanocrystal aggregation proceeding from CeIV complexes to CeO2 nanoparticles in an acidic aqueous solution, and investigated the resultant hierarchical nanoarchitecture. The formed particles exhibited two very different size ranges, resulting in further pattern formation with opalescence. The hierarchically assembled structures in solutions were CeO2 colloids, viz. primary core clusters (1-3 nm) of crystalline ceria and secondary clusters (20-30 nm) assembled through surface ions. Such self-assembly is widespread in multi-component complex fluids, paradoxically moderating hierarchical reactions. Stability and instability are not only critical but also complementary for co-optimisation around the nearby free energy landscape prior to bifurcation.

Arbitrary-Shape Dielectric Particles Interacting in the Linearized Poisson-Boltzmann Framework: An Analytical Treatment

This work considers the interaction of two dielectric particles of arbitrary shape immersed into a solvent containing a dissociated salt and assuming that the linearized Poisson-Boltzmann equation holds. We establish a new general spherical re-expansion result which relies neither on the conventional condition that particle radii are small with respect to the characteristic separating distance between particles nor on any symmetry assumption. This is instrumental in calculating suitable expansion coefficients for the electrostatic potential inside and outside the objects and in constructing small-parameter asymptotic expansions for the potential, the total electrostatic energy, and forces in ascending order of Debye screening. This generalizes a recent result for the case of dielectric spheres to particles of arbitrary shape and builds for the first time a rigorous (exact at the Debye-Hückel level) analytical theory of electrostatic interactions of such particles at arbitrary distances. Numerical tests confirm that the proposed theory may also become especially useful in developing a new class of grid-free, fast, highly scalable solvers.

Electrokinetic and dielectric response of a concentrated salt-free colloid: Different approaches to counterion finite-size effects

In the present work, a general model is developed for the electrokinetics and dielectric response of a concentrated salt-free colloid that takes into account the finite size of the counterions released by the particles to the solution. The effects associated with the counterion finite size have been addressed using a hard-sphere model approach elaborated by Carnahan and Starling [N. F. Carnahan and K. E. Starling, Equation of state for nonattracting rigid spheres, J. Chem. Phys. 51, 635 (1969)0021-960610.1063/1.1672048]. A more simple description of the finite size of the counterions based on that by Bikerman has also been considered for comparison. The studies carried out in this work include predictions on the effect of the finite counterion size on the equilibrium properties of the colloid and its electrokinetic and dielectric response when it is subjected to constant or alternating electric fields. The results show how important the counterion finite-size effects are for most of the electrokinetic and dielectric properties of highly charged and concentrated colloids, mainly for the static and dynamic electrophoretic mobilities. Furthermore, new insights are provided on the counterion condensation effect when counterions are allowed to have finite size. Focus is placed on the changes undergone by their concentration in the condensation layer for low-salt and highly charged colloids.

Morphology of Ionic Micelles as Studied by Numerical Solution of the Poisson Equation

The existing concepts of the ionic micelle structure were specified. It was noted that the composition of dispersed phase particles in a liquid dispersion medium should necessarily include adsorbed counterions rigidly bound to these particles. By numerical solution of the Poisson equation for the two most often used approximations, the Poisson-Boltzmann (PB) model and the Jellium-approximation (JA), the electric potential decay from the Stern potential of dispersed phase particles was defined. A new methodological approach to analyze the reaction of micelle potential decay based on small variability of the CMC value was proposed. It made possible to determine the dimension parameter, which in the presence of weak thermal effects approximately corresponds to the micelle hydrodynamic radius, and to calculate the electrokinetic potential of micelles. The results of theoretical calculations were compared with our previous experimental data on the thickness of the SDS micelle hydrophilic layer obtained by SAXS. A good agreement between the calculated and measured values was obtained, and it was noted that for low concentrations the experimental values are more correctly described by the PB model, but for concentrations greater than 100 mM the JA model is more preferable. It was found that the slipping plane is located near the outer Stern plane and is separated from it only by a few molecular layers of water. The influence stronger than the thermal one can shift the slipping plane closer to the micelle core. Accordingly, the smallest hydrodynamic micelle size is determined by the outer Stern plane. The results of our work allowed us to conclude that the micelle is not something soft and watery, but according to its specified structure, it is a more solid-like particle than was previously assumed. The proposed approach can be extended to investigate other effects of a physicochemical nature, in particular, those observed with the addition of an external electrolyte or nanoparticles.

Where in the world are condensed counterions?

A scaling model of the concentration profiles of both condensed and free counterions is presented for solutions of spherical and cylindrical charged nanoparticles of different charge valences, nanoparticle sizes, and salt concentrations. The distribution of counterions for both spherical and cylindrical charged particles in salt-free solutions is determined by the condensation parameter γ₀ defined as the ratio of nanoparticle valence Z₀ to the number of Bjerrum lengths l_B = e²/(εkT) per nanoparticle size (γ₀ = Z₀l_B/(2r₀) for spherical nanoparticles with radii r₀ or γ₀ = Z₀l_B/L for cylindrical particles with length L), where ε is solution dielectric permittivity, e is elementary charge and kT is thermal energy. Depending on the magnitudes of the condensation parameter γ₀ and nanoparticle volume fraction ϕ, we find three qualitatively different regimes for the counterion distribution near charged particles: (i) weakly charged particles with no condensed counterions, (ii) regime of weak counterion condensation with less than half of the counterions condensed, and (iii) regime of strong counterion condensation with the majority of counterions condensed. The magnitude of electrostatic energy of a condensed counterion with respect to solution locations with zero electric field is larger than thermal energy kT, and the fraction of condensed counterions increases from less than half in the weak condensation regime to the majority of all counterions in the strong condensation regime. The condensed counterions are not bound to the nanoparticle surface but instead are localized within the condensed counterion zone near the charged particle. The thickness of the condensed counterion zone varies with the condensation parameter γ₀, the nanoparticle shape and volume fraction ϕ, and the salt concentration and can be as narrow as Bjerrum length (∼nm) or as large as the particle size (∼L the length of charged cylinder).

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.

Electrophoresis and electric conduction in a salt-free suspension of charged particles

The electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.

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.

Influence of ion size effects on the electrokinetics of aqueous salt-free colloids in alternating electric fields

Electrokinetics is the science of the physical phenomena appearing at the solid-liquid interface of dispersed particles subjected to external fields. Techniques based on electrokinetic phenomena constitute an important set of tools for the electrical characterization of colloids because of their sensitivity to the properties of particle-solution interfaces. Their rigorous description may require inclusion of the effects of finite size of chemical species in the theoretical models, and, particularly in the case of salt-free (no external salt added) aqueous colloids, also consideration of water dissociation and possible carbon dioxide contamination in the aqueous solution. A new ac electrokinetic model is presented for concentrated salt-free spherical colloids for arbitrary characteristics of the particles and aqueous solution, including finite-size effects of chemical species by appropriate modifications of the chemical reaction equations to include such non-ideal aspects. The numerical solution of the electrokinetic equations in an alternating electric field has also been carried out by using a realistic non-equilibrium scenario accounting for association-dissociation processes in the chemical reactions. The results demonstrate the importance of including finite-size effects in the electrokinetic response of the colloid, mainly at high frequencies of the electric field, and for highly charged colloids. Findings of previous models for pointlike ions or for ideal salt-free colloids including finite ion size effects are recovered with the present model, for the appropriate limiting conditions.

The extent of counterion dissociation at the interface of cationic diblock copolymer nanoparticles in non-polar solvents

HYPOTHESIS

Diblock copolymer nanoparticles prepared in non-polar solvents that are sterically stabilized but possess ionic functionality from the inclusion of cationic comonomers in the stabilizer shell are known to exhibit complex electrokinetic behavior (Chem. Sci. 9 (2018) 922-934). For example, core-shell nanoparticles with cationic comonomers located solely within the shell layer have lower magnitude electrophoretic mobilities than nanoparticles containing the same cationic comonomers located within the core, whereas nanoparticles prepared using a minor fraction of steric stabilizer chains containing cationic comonomer repeat units have comparable electrophoretic mobilities to nanoparticles prepared with this cationic comonomer solely located within the core. We hypothesize that these observations can be explained in terms of the strength of the Coulombic interaction between counterions and the nanoparticle interface.

EXPERIMENTS

The highly-fluorinated anionic counterion associated with these cationic nanoparticles is studied by ¹⁹F nuclear magnetic resonance (NMR) spectroscopy in n-dodecane. This revealed only one type of ¹⁹F environment for a soluble macromolecular cation (the oil-soluble steric stabilizer chains used to prepare the nanoparticles), whereas two distinct environments were observed for the sterically-stabilized cationic nanoparticles. Both ¹⁹F diffusion NMR and ¹⁹F-¹³C heteronuclear single quantum correlation (HSQC) measurements support the existence of two environments for this counterion.

FINDINGS

The existence of two distinct ¹⁹F environments for the highly-fluorinated anion associated with the sterically-stabilized nanoparticles demonstrates the presence of spectroscopically distinguishable populations of ion pairs and of fully dissociated free anions. ¹⁹F NMR spectra recorded for sterically-stabilized nanoparticles with a fully ionic shell (all stabilizer chains containing the cationic comonomer) and those with a partly ionic shell (10% of stabilizer chains containing the cationic comonomer) reveal a higher proportion of dissociated anions in the partly ionic case. This suggests a stronger Coulombic interaction between counterions and the cationic interface when the shell is fully ionic, which accounts for the observed reduction in the magnitude of the electrophoretic mobility.

Electrolytic conductivity of ionic polymers in a nonpolar solvent

The electrolytic conductivity of two electrolytes as solutions in the nonpolar solvent, n -dodecane, as a function of concentration has been studied. One was a small molecule electrolyte (tetraalkyl cation and a highly fluorinated tetraphenylborate anion), and the other was a macromolecular electrolyte (cation-containing poly(alkyl methacrylate) chain with the same anion). Two series of the macromolecular cation were prepared: one with entirely cation-containing molecules and the other with a small proportion (10%) cation-containing and the rest nonionic. The conductivity data were qualitatively similar for all systems, which formed both single ions and triple ions. The data from the two series of macromolecular electrolytes were particularly informative to understand some recent and counterintuitive electrokinetic data for particles that were stabilized by these polymers. Reducing the proportion of cationic chains in the stabilizer of the particles was found to increase their electrophoretic mobility. In the conductivity data in this study, reducing the proportion of cationic chains in solution was found to increase the magnitude of the single-ion equilibrium constant and suppress the formation of triple ions. These data should support the development of models to understand these electrokinetic results.

A Neutron Scattering Study of the Structure of Poly(dimethylsiloxane)-Stabilized Poly(methyl methacrylate) (PDMS-PMMA) Latexes in Dodecane

Hard-sphere particles in nonpolar solvents are an essential tool for colloid scientists. Sterically stabilized poly(methyl methacrylate) (PMMA) particles have long been used as the exemplary hard-sphere system. However, neither the particles themselves nor the poly(12-hydroxystearic acid) (PHSA) stabilizer necessary to prevent aggregation in nonpolar solvents are commercially available. To counter this, several alternatives have been proposed. In recent years, there has been an increased interest in poly(dimethylsiloxane) (PDMS) stabilizers as a commercially available alternative to PHSA, yet the structure of particles made in this way is not as well understood as those produced using PHSA. In this work, we employ small-angle neutron scattering to determine the internal structure of PDMS-stabilized PMMA particles, synthesized with and without an additional crosslinking agent. We report data consistent with a homogeneous PMMA core with a linearly decaying PDMS shell. The thickness of the shell was in excess of 50 nm, thicker than the PHSA layer typically used to stabilize PMMA but consistent with reports of the layer thickness for similar molecular weight PDMS at planar surfaces. We also show that the amount of the hydrogenous material in the particle core of the crosslinked particles notably exceeds the amount of added ethylene glycol dimethacrylate crosslinker, suggesting some entrapment of the PDMS stabilizer in the PMMA matrix.

Electrokinetic Flow of Salt-Free Solutions in a Fibrous Porous Medium

The electrokinetic flow of a salt-free solution in the fibrous porous medium constituted by an array of parallel charged circular cylinders subject to a pressure gradient and an electric field imposed in the axial direction is analytically studied via the use of a unit cell model. The Poisson-Boltzmann equation and modified Navier-Stokes equation applicable to a unit cell accommodating the salt-free solution around an individual cylinder are solved to determine the electric potential profile and fluid velocity distribution. Results of the electroosmotic velocity and effective electric conductivity in the fiber matrix are obtained as functions of the surface charge density of the dielectric cylinders and the porosity of the fiber matrix. The effects of the porosity or interactions among the cylinders on the electric potential distribution, electroosmotic velocity, and effective electric conductivity are significant and interesting under practical conditions. The apparent zeta potential, electroosmotic velocity, and effective electric conductivity increase monotonically with an increase in the surface charge density of the cylinders. When the porosity of the fiber matrix and surface charge density of the cylinders are high, the increases of the apparent zeta potential and electroosmotic velocity with the surface charge density are substantially suppressed due to the counterion condensation effect. However, this effect becomes weak when the porosity is low.

Colloidal electro-phoresis in the presence of symmetric and asymmetric electro-osmotic flow

We characterize the electro-phoretic motion of charged sphere suspensions in the presence of substantial electro-osmotic flow using a recently introduced small angle super-heterodyne dynamic light scattering instrument (ISASH-LDV). Operation in integral mode gives access to the particle velocity distribution over the complete cell cross-section. Obtained Doppler spectra are evaluated for electro-phoretic mobility, wall electro-osmotic mobility and particle diffusion coefficient. Simultaneous measurements of differing electro-osmotic mobilities leading to asymmetric solvent flow are demonstrated in a custom made electro-kinetic cell fitting standard microscopy slides as exchangeable sidewalls. The scope and range of our approach are discussed demonstrating the possibility of an internal calibration standard and using the simultaneously measured electro-kinetic mobilities in the interpretation of a microfluidic pumping experiment involving an inhomogeneous electric field and a complex solvent flow pattern.

Characterization of the interface of binary mixed DOPC:DOPS liposomes in water: The impact of charge condensation

Solutions of liposomes composed of binary mixtures of anionic dioleoylphosphatidylserine (DOPS) and zwitterionic dioleoylphosphatidylcholine (DOPC) are investigated with label-free angle-resolved (AR) second harmonic scattering (SHS) and electrophoretic mobility measurements. The membrane surface potential is extracted from the AR-SHS response. The surface potential changes from -10 to -145 mV with varying DOPS content ( from 0% to 100%) and levels off already at ∼ 10 % DOPS content. The ζ-potential shows the same trend but with a drastically lower saturation value (-44 mV). This difference is explained by the formation of a condensed layer of Na⁺ counterions around the outer leaflet of the liposome as predicted by charge condensation theories for polyelectrolyte systems.

Charge and hydration structure of dendritic polyelectrolytes: molecular simulations of polyglycerol sulphate

Macromolecules based on dendritic or hyperbranched polyelectrolytes have been emerging as high potential candidates for biomedical applications. Here we study the charge and solvation structure of dendritic polyglycerol sulphate (dPGS) of generations 0 to 3 in aqueous sodium chloride solution by explicit-solvent molecular dynamics computer simulations. We characterize dPGS by calculating several important properties such as relevant dPGS radii, molecular distributions, the solvent accessible surface area, and the partial molecular volume. In particular, as the dPGS exhibits high charge renormalization effects, we address the challenges of how to obtain a well-defined effective charge and surface potential of dPGS for practical applications. We compare implicit- and explicit-solvent approaches in our all-atom simulations with the coarse-grained simulations from our previous work. We find consistent values for the effective electrostatic size (i.e., the location of the effective charge of a Debye-Hückel sphere) within all the approaches, deviating at most by the size of a water molecule. Finally, the excess chemical potential of water insertion into dPGS and its thermodynamic signature are presented and rationalized.

Charge regulation of nonpolar colloids

Individual colloids often carry a charge as a result of the dissociation (or adsorption) of weakly-ionized surface groups. The magnitude depends on the precise chemical environment surrounding a particle, which in a concentrated dispersion is a function of the colloid packing fraction η. Theoretical studies have suggested that the effective charge Z_eff in regulated systems could, in general, decrease with increasing η. We test this hypothesis for nonpolar dispersions by determining Z_eff(η) over a wide range of packing fractions (10^-5 ≤ η ≤ 0.3) using a combination of small-angle X-ray scattering and electrophoretic mobility measurements. All dispersions remain entirely in the fluid phase regime. We find a complex dependence of the particle charge as a function of the packing fraction, with Z_eff initially decreasing at low concentrations before finally increasing at high η. We attribute the non-monotonic density dependence to a crossover from concentration-independent screening at low η, to a high packing fraction regime in which counterions outnumber salt ions and electrostatic screening becomes η-dependent. The efficiency of charge stabilization at high concentrations may explain the unusually high stability of concentrated nanoparticle dispersions which has been reported.

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.

Synthesis and electrokinetics of cationic spherical nanoparticles in salt-free non-polar media

Cationic diblock copolymer nanoparticles have been prepared in n-dodecane via polymerization-induced self-assembly (PISA). A previously reported poly(stearyl methacrylate)-poly(benzyl methacrylate) (PSMA-PBzMA) PISA formulation (Chem. Sci. 2016, 7, 5078-5090) was modified by statistically copolymerizing an oil-soluble cationic methacrylic monomer, (2-(methacryloyloxy)ethyl)trimethylammonium tetrakis[3,5-bis(trifluoromethyl)phenyl]borate, with either SMA or BzMA, to produce either charged shell or charged core nanoparticles. The electrokinetics were studied as a function of many variables (function of volume function, particle size, solvent viscosity, and number of ions per chain). These data are consistent with electrophoresis controlled by counterion condensation, which is typically observed in salt-free media. However, there are several interesting and unexpected features of interest. In particular, charged shell nanoparticles have a lower electrophoretic mobility than the equivalent charged core nanoparticles, and the magnitude of the electrophoretic mobility increases as the fraction of cationic stabilizer chains in the shell layer is reduced. These results show that cationic PSMA-PBzMA spheres provide an interesting new example of electrophoretic nanoparticles in non-polar solvents. Moreover, they should provide an ideal model system to evaluate new electrokinetic theories.

Dipolar colloids in apolar media: direct microscopy of two-dimensional suspensions

Spherical colloids, in an absence of external fields, are commonly assumed to interact solely through rotationally-invariant potentials, u(r). While the presence of permanent dipoles in aqueous suspensions has been previously suggested by some experiments, the rotational degrees of freedom of spherical colloids are typically neglected. We prove, by direct experiments, the presence of permanent dipoles in commonly used spherical poly(methyl methacrylate) (PMMA) colloids, suspended in an apolar organic medium. We study, by a combination of direct confocal microscopy, computer simulations, and theory, the structure and other thermodynamical properties of organic suspensions of colloidal spheres, confined to a two-dimensional (2D) monolayer. Our studies reveal the effects of the dipolar interactions on the structure and the osmotic pressure of these fluids. These observations have far-reaching consequences for the fundamental colloidal science, opening new directions in self-assembly of complex colloidal clusters.

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.

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.

Particle Segregation at Contact Lines of Evaporating Colloidal Drops: Influence of the Substrate Wettability and Particle Charge-Mass Ratio

Segregation of particles during capillary/convective self-assembly is interesting for self-stratification in colloidal deposits. In evaporating drops containing colloidal particles, the wettability properties of substrate and the sedimentation of particles can affect their accumulation at contact lines. In this work we studied the size segregation and discrimination of charged particles with different densities. We performed in-plane particle counting at evaporating triple lines by using fluorescence confocal microscopy. We studied separately substrates with very different wettability properties and particles with different charge-mass ratios at low ionic strength. We used binary colloidal suspensions to compare simultaneously the deposition of two different particles. The particle deposition rate strongly depends on the receding contact angle of the substrate. We further observed a singular behavior of charged polystyrene particles in binary mixtures under "salt-free" conditions explained by the "colloidal Brazil nut" effect.

Coulomb energy of uniformly charged spheroidal shell systems

We provide exact expressions for the electrostatic energy of uniformly charged prolate and oblate spheroidal shells. We find that uniformly charged prolate spheroids of eccentricity greater than 0.9 have lower Coulomb energy than a sphere of the same area. For the volume-constrained case, we find that a sphere has the highest Coulomb energy among all spheroidal shells. Further, we derive the change in the Coulomb energy of a uniformly charged shell due to small, area-conserving perturbations on the spherical shape. Our perturbation calculations show that buckling-type deformations on a sphere can lower the Coulomb energy. Finally, we consider the possibility of counterion condensation on the spheroidal shell surface. We employ a Manning-Oosawa two-state model approximation to evaluate the renormalized charge and analyze the behavior of the equilibrium free energy as a function of the shell's aspect ratio for both area-constrained and volume-constrained cases. Counterion condensation is seen to favor the formation of spheroidal structures over a sphere of equal area for high values of shell volume fractions.

Interaction between surfactants and colloidal latexes in nonpolar solvents studied using contrast-variation small-angle neutron scattering

The interaction between deuterium-labeled Aerosol OT surfactant (AOT-d34) and sterically stabilized poly(methyl methacrylate) (PMMA) latex particles dispersed in nonpolar solvents has been studied using contrast-variation small-angle neutron scattering (CV-SANS). The electrophoretic mobilities (μ) of the latexes have been measured by phase-analysis light scattering, indicating that μ is negative. Two analogues of the stabilizers for the particles have been studied as free polymers in the absence of PMMA latexes: poly(12-hydroxystearic acid) (PHSA) polyester and poly(methyl methacrylate)-graft-poly(12-hydroxystearic acid) (PMMA-graft-PHSA) stabilizer copolymer. The scattering from both PHSA in dodecane and PMMA-graft-PHSA in toluene is consistent with extended polymer chains in good solvents. In dodecane, PMMA-graft-PHSA forms polymer micelles, and SANS is consistent with ellipsoidal aggregates formed of around 50 polymer chains. CV-SANS measurements were performed by measuring SANS from systems of PHSA, PMMA-graft-PHSA, and PMMA latexes with 10 and 100 mM surfactant solutions of AOT-d34 in both polymer/particle and AOT contrast-matched solvent. No excess scattering above the polymer or surfactant was found for PHSA in dodecane or PMMA-graft-PHSA in dodecane and toluene. This indicates that AOT does not significantly interact with the free polymers. Excess scattering was observed for systems with AOT-d34 and PMMA latexes dispersed in particle contrast-matched dodecane, consistent with the penetration of AOT into the PMMA latexes. This indicates that AOT does not interact preferentially with the stabilizing layers but, rather, is present throughout the colloids. Previous research ( Langmuir 2010, 26, 6967-6976 ) suggests that AOT surfactant is located in the latex PHSA-stabilizer layer, but all the results in this study are consistent with AOT poorly interacting with alkyl-stabilizer polymers.