Effective interactions in the colloidal suspensions from hypernetted-chain theory

The hypernetted-chain (HNC) Ornstein-Zernike integral equations are used to determine the properties of simple models of colloidal solutions where the colloids and ions are immersed in a solvent considered as a dielectric continuum and have a size ratio equal to 80 and a charge ratio varying between 1 and 4000. At an infinite dilution of colloids, the effective interactions between colloids and ions are determined for ionic concentrations ranging from 0.001 to 0.1 mol/l and compared to those derived from the Poisson-Boltzmann theory. At finite concentrations, we discuss on the basis of the HNC results the possibility of an unambiguous definition of the effective interactions between the colloidal molecules.     

Charge reversal in real colloids: Experiments, theory and simulations

In the last years, the inclusion of ionic short-range correlations in the study of colloidal stability has led to significant disagreements with the predictions obtained from classical treatments. An example of these discrepancies is the occurrence of charge reversal of charged particles. In order to shed light on this issue, the charge reversal of latex particles in the presence of asymmetric electrolytes has been investigated through Monte Carlo (MC) simulations. In particular, experimental results concerning electrophoretic mobility reversals and the Hyper-Netted-Chain/Mean-Spherical-Approximation (HNC/MSA) predictions have been compared with simulations in which two alternative methods for evaluating energies have been applied. A realistic hydrated ion size is used in the HNC/MSA calculations and simulations. In this way, the existence of a reversal in the electrophoretic mobility due to ion size correlations and without requiring specific counterion adsorption is probed. Moreover, the simulations appears as a useful tool for explaining those results in which the HNC/MSA does not reproduce the experimental trends.     

Spatial‐Decomposition Analysis of Electrical Conductivity

Spatial decomposition is conducted for the electrical conductivity. The contribution per ion pair at a certain distance is identified in terms of a two‐body velocity time correlation function and is integrated over the whole distance of the ion pair to provide the cross‐correlation term of the conductivity. The spatial‐decomposition formula is an exact expression at any concentrations of ions and incorporates physically appealing pictures in the space domain into the theory of time correlation functions. Illustrative analyses are presented for 1m NaCl aqueous solution and the [C₄mim][NTf₂] ionic liquid. The contrast between the two systems is discussed for the time and spatial ranges of correlations, and it is shown that the ion‐pair contribution to the conductivity for the [C₄mim][NTf₂] system is not localized and extends beyond the first coordination shell of the cation‐anion pair.     

Distribution of colloidal particles in a spherical cavity

The spatial distribution of colloidal particles in a confined space is frequently a key issue to many phenomena of practical significance. This problem is investigated by considering the distribution of colloidal particles in a spherical cavity under the conditions of relatively large cavities, low cavity and colloidal particles potentials, and low monovalent electrolyte and colloidal concentrations. The analytical expression for the particle-cavity pair interaction energy is derived under various surface conditions. The results obtained are used to evaluate the direct correlation functions in the hypernetted chain approximation employed for the resolution of an Ornstein-Zernike equation. For a fixed particle number concentration at the center of a cavity, we make the following conclusions: (i) the spatial distribution of particles increases in an oscillatory manner with the distance away from the cavity surface, (ii) increasing the particle-cavity pair interaction energy has the effect of reducing the free space of particles inside a cavity, and (iii) the greater the pair interaction energy between two particles, the higher the average concentration of particles.     

Entropic effects in the electric double layer of model colloids with size-asymmetric monovalent ions

The structure of the electric double layer of charged nanoparticles and colloids in monovalent salts is crucial to determine their thermodynamics, solubility, and polyion adsorption. In this work, we explore the double layer structure and the possibility of charge reversal in relation to the size of both counterions and coions. We examine systems with various size-ratios between counterions and coions (ion size asymmetries) as well as different total ion volume fractions. Using Monte Carlo simulations and integral equations of a primitive-model electric double layer, we determine the highest charge neutralization and electrostatic screening near the electrified surface. Specifically, for two binary monovalent electrolytes with the same counterion properties but differing only in the coion's size surrounding a charged nanoparticle, the one with largest coion size is found to have the largest charge neutralization and screening. That is, in size-asymmetric double layers with a given counterion's size the excluded volume of the coions dictates the adsorption of the ionic charge close to the colloidal surface for monovalent salts. Furthermore, we demonstrate that charge reversal can occur at low surface charge densities, given a large enough total ion concentration, for systems of monovalent salts in a wide range of ion size asymmetries. In addition, we find a non-monotonic behavior for the corresponding maximum charge reversal, as a function of the colloidal bare charge. We also find that the reversal effect disappears for binary salts with large-size counterions and small-size coions at high surface charge densities. Lastly, we observe a good agreement between results from both Monte Carlo simulations and the integral equation theory across different colloidal charge densities and 1:1-electrolytes with different ion sizes.     

Theory of peak coalescence in Fourier transform ion cyclotron resonance mass spectrometry

Peak coalescence, i.e. the merging of two close peaks in a Fourier transform ion cyclotron resonance (FTICR) mass spectrum at a high number of ions, plays an important role in various FTICR experiments. In order to describe the coalescence phenomenon we would like to propose a new theory of motion for ion clouds with close mass‐to‐charge ratios, driven by a uniform magnetic field and Coulomb interactions between the clouds. We describe the motion of the ion clouds in terms of their averaged drift motion in crossed magnetic and electric fields. The ion clouds are considered to be of constant size and their motion is studied in two dimensions. The theory deals with the first‐order approximation of the equations of motion in relation to dm/m, where dm is the mass difference and m is the mass of a single ion. The analysis was done for an arbitrary inter‐cloud interaction potential, which makes it possible to analyze finite‐size ion clouds of any shape. The final analytical expression for the condition of the onset of coalescence is found for the case of uniformly charged spheres. An algorithm for finding this condition for an arbitrary interaction potential is proposed. The critical number of ions for the peak coalescence to take place is shown to depend quadratically on the magnetic field strength and to be proportional to the cyclotron radius and inversely proportional to the ion masses. Copyright © 2009 John Wiley & Sons, Ltd.     

Decay of correlation functions in hard-sphere mixtures: structural crossover

We investigate the decay of pair correlation functions in a homogeneous (bulk) binary mixture of hard spheres. At a given state point the asymptotic decay r-->infinity of all three correlation functions is governed by a common exponential decay length and a common wavelength of oscillations. Provided the mixture is sufficiently asymmetric, size ratios q less than or approximately 0.7, we find that the common wavelength reflects either the size of the small or that of the big spheres. By analyzing the (complex) poles of the partial structure factors we find a sharp structural crossover line in the phase diagram. On one side of this line the common wavelength is approximately the diameter of the smaller sized spheres whereas on the other side it is approximately the diameter of the bigger ones; the wavelength of the longest ranged oscillations changes discontinuously at the structural crossover line. Using density functional theory and Monte Carlo simulations we show that structural crossover also manifests itself in the intermediate range behavior of the pair correlation functions and we comment on the relevance of this observation for real (colloidal) mixtures. In highly asymmetric mixtures, q< or =0.1, where there is metastable fluid-fluid transition, we find a Fisher-Widom line with two branches. This line separates a region of the phase diagram where the decay of pair correlations is oscillatory from one in which it is monotonic.     

Colloidal Supercapattery: Redox Ions in Electrode and Electrolyte

Redox chemistry is the cornerstone of various electrochemical energy conversion and storage systems, associated with ion diffusion process. To actualize both high energy and power density in energy storage devices, both multiple electron transfer reaction and fast ion diffusion occurred in one electrode material are prerequisite. The existence forms of redox ions can lead to different electrochemical thermodynamic and kinetic properties. Here, we introduce novel colloid system, which includes multiple varying ion forms, multi‐interaction and abundant redox active sites. Unlike redox cations in solution and crystal materials, colloid system has specific reactivity‐structure relationship. In the colloidal ionic electrode, the occurrence of multiple‐electron redox reactions and fast ion diffusion leaded to ultrahigh specific capacitance and fast charge rate. The colloidal ionic supercapattery coupled with redox electrolyte provides a new potential technique for the comprehensive use of redox ions including cations and anions in electrode and electrolyte and a guiding design for the development of next‐generation high performance energy storage devices.     

Dressed ion theory of size-asymmetric electrolytes: effective ionic charges and the decay length of screened Coulomb potential and pair correlations

The effects of ionic size asymmetry on long-range electrostatic interactions in electrolyte solutions are investigated within the primitive model. Using the formalism of dressed ion theory we analyze correlation functions from Monte Carlo simulations and the hypernetted chain approximation for size asymmetric 1:1 electrolytes. We obtain decay lengths of the screened Coulomb potential, effective charges of ions, and effective permittivity of the solution. It is found that the variation of these quantities with the degree of size asymmetry depends in a quite intricate manner on the interplay between the electrostatic coupling and excluded volume effects. In most cases the magnitude of the effective charge of the small ion species is larger than that of the large species; the difference increases with increasing size asymmetry. The effective charges of both species are larger (in absolute value) than the bare ionic charge, except for high asymmetry where the effective charge of the large ions can become smaller than the bare charge.     

Ionic size dependent electroosmosis in ion‐selective microchannels and nanochannels

Electrokinetics in salt‐free media (in which counterions are only present) is central to the performance of many systems of modern technological relevance, ranging from ion‐selective nanopores to electronic papers. Here, we introduce an analytical theory to describe the size dependence of electroosmosis in such typical scenarios, exhibiting an interesting confluence of the implications of interdependence of the electroosmotic transport mechanisms, ionic sizes, and confinement dimensions along with the counterion concentration. Our results do reveal that the concerned mobility parameter, describing the strength of electroosmotic transport, increases simultaneously with increments in the surface charge density as well as an ionic size factor (also known as the steric factor), bearing far‐ranging consequences in microfluidic and nanofluidic technology.     

On attractive interaction of a colloid pair of like charge at infinite dilution

Numerical data on the potential of mean force W(r) at infinite dilution of a highly charged colloid pair embedded in a 1:1 electrolyte are reported. The authors obtain attractive minima (W<0) at short interparticle distance in these potential functions in hypernetted chain (HNC) approximation, as salt concentration is increased. These minima, however, disappear in all system sets studied when a self-consistent Zerah-Hansen (ZH) closure is used. The authors infer that the attractive minima obtained in a HNC closure are spurious and result from the neglect of bridge diagrams in HNC approximation. An expression of bridge function, which the ZH closure in effect incorporates in W(r) to remove attractive minima, is derived in terms of modification of correlation functions. Features of repulsive pair potentials obtained using the ZH closure, their dependence on particle charge and salt concentration, and their agreement with those of the Derajguin-Landau-Verwey-Overbeek theory are investigated.     

Preparation of amorphous aluminum oxide-hydroxide nanoparticles in amphiphilic silicone-based copolymer microemulsions

Organo-inorgano nanocomposites with colloidal dimensions have interesting optical, catalytic, and mechanical properties, particularly when such hybrids are reinforced with transition metal oxide nanoparticles. Nanoparticles with a mean size of 1.0-2.4 nm are obtained through hydrolysis of aluminum isopropoxide in the L(2) phase of amphiphilic (PDMS-POE) polydimethylsiloxane-polyoxyethylene Silwet L-7607-octanol/acetylacetone-water mixtures. The particle sizes are related weakly to the microemulsion composition: 0.8-1.2 nm for 20 wt% Silwet L-7607 and 2.0-2.4 nm for 50 wt% Silwet L-7607. Protection of the particles against aggregation is ensured through their confinement in the intraaggregate colloidal domains. Factors affecting the hydrolysis-condensation process of acetylacetone-complexed aluminum isopropoxide in copolymer-poor and copolymer-rich regions of PDMS-POE W/O microemulsions are studied by Fourier transform infrared spectroscopy, small angle X-ray scattering, and transmission electron microscopy. Prepared nanoparticulate dispersions possess long-term stability and form clear mixtures in different organic polar and nonpolar solvents.     

The Double‐Faced Nature of Hydrogen Bonding in Hydroxy‐Functionalized Ionic Liquids Shown by Neutron Diffraction and Molecular Dynamics Simulations

We characterize the double‐faced nature of hydrogen bonding in hydroxy‐functionalized ionic liquids by means of neutron diffraction with isotopic substitution (NDIS), molecular dynamics (MD) simulations, and quantum chemical calculations. NDIS data are fit using the empirical potential structure refinement technique (EPSR) to elucidate the nearest neighbor H???O and O???O pair distribution functions for hydrogen bonds between ions of opposite charge and the same charge. Despite the presence of repulsive Coulomb forces, the cation–cation interaction is stronger than the cation–anion interaction. We compare the hydrogen‐bond geometries of both “doubly charged hydrogen bonds” with those reported for molecular liquids, such as water and alcohols. In combination, the NDIS measurements and MD simulations reveal the subtle balance between the two types of hydrogen bonds: The small transition enthalpy suggests that the elusive like‐charge attraction is almost competitive with conventional ion‐pair formation.     

Electric double layers with electrolyte mixtures: integral equations theories and simulations

A study of a planar electric double layer (EDL) in the presence of mixtures of electrolyte is presented. In particular, results from the Hyper-Netted-Chain/Mean-Spherical-Approximation (HNC/MSA) theory are compared with Monte Carlo (MC) simulations. In this way, the charge inversion induced by mixtures of multivalent and monovalent counterions is probed. Since overcharging phenomena in nature emerge under such conditions, the role of ion-ion correlations in the EDL appears as a crucial point in this kind of study. Unlike previous related works, a realistic hydrated ion size is used in the HNC/MSA calculations and simulations. In this way, a qualitative agreement between the results obtained from the theory and MC simulations is found. However, some discrepancies arise when the charge inversion is expected to be more noticeable, namely at high surface charges and/or elevated concentrations of multivalent electrolytes. Such differences are explained in terms of an overestimation of the charge inversion by the integral equation (IE) formalism.     

Molecular dynamics simulations of LiCl association and NaCl association in water by means of ABEEM/MM

Constrained molecular dynamics simulations have been used to investigate the LiCl and NaCl ionic association in water in terms of atom-bond electronegativity equalization method fused into molecular mechanics (ABEEM/MM). The simulations make use of the seven-site fluctuating charge and flexible ABEEM-7P water model, based on which an ion-water interaction potential has been constructed. The mean force and the potential of mean force for LiCl and NaCl in water, the charge distributions, as well as the structural and dynamical properties of contact ion pair dissociation have been investigated. The results are reasonable and informative. For LiCl ion pair in water, the solvent-separated ion pair configurations are more stable than contact ion pair configurations. The calculated PMF for NaCl in water indicates that contact ion pair and solvent-separated ion pair configurations are of comparable stability.     

Monte Carlo simulation of electrical double-layer formation from mixtures of electrolytes inside nanopores

The formation of the electrical double layer (EDL) in the presence of trivalent and monovalent ions inside a slit-type nanopore was simulated via the canonical Monte Carlo method using a primitive model. In large pores, the distribution of ionic species is similar to that observed in an isolated planar double layer. Screening of surface charge is determined by the competitive effects between ion size and charge asymmetry of the counterions. On the other hand, as the pore size approaches the dimension of the ionic species, phenomena such as EDL overlapping become enhanced by ion-size effects. Simulation results demonstrate that EDL overlapping is not only a function of such parameters as ionic strength and surface charge density, but also a function of the properties of the ionic species involved in the EDL. Furthermore, charge inversion can be observed under certain conditions when dealing with mixtures of asymmetric electrolytes. This phenomenon results from strong ion-ion correlation effects and the asymmetries in size and charge of ionic species, and is most significant in the case of trivalent counterions with larger diameters. The simulation results provide insights into the fundamental mechanisms behind the formation of EDL within nanopores as determined by pore size and by the properties of ionic species present in solution. The findings of this work are relevant to ion sorption and transport within nanostructured materials.     

Ion Pairing in Protic Ionic Liquids Probed by Far‐Infrared Spectroscopy: Effects of Solvent Polarity and Temperature

The cation–anion and cation–solvent interactions in solutions of the protic ionic liquid (PIL) [Et₃NH][I] dissolved in solvents of different polarities are studied by means of far infrared vibrational (FIR) spectroscopy and density functional theory (DFT) calculations. The dissociation of contact ion pairs (CIPs) and the resulting formation of solvent‐separated ion pairs (SIPs) can be observed and analyzed as a function of solvent concentration, solvent polarity, and temperature. In apolar environments, the CIPs dominate for all solvent concentrations and temperatures. At high concentrations of polar solvents, SIPs are favored over CIPs. For these PIL/solvent mixtures, CIPs are reformed by increasing the temperature due to the reduced polarity of the solvent. Overall, this approach provides equilibrium constants, free energies, enthalpies, and entropies for ion‐pair formation in trialkylammonium‐containing PILs. These results have important implications for the understanding of solvation chemistry and the reactivity of ionic liquids.     

A local density functional approximation for the ion distribution near a charged electrode in the restricted primitive model electrolyte

A local HNC/MSA approximation is developed and applied to the 1:1 restricted primitive model electrolyte. Improvement of ion density profiles in front of a charged electrode is achieved by employing ion—ion direct correlation functions from homogeneous systems of non-neutral composition as found locally in the inhomogeneous double layer. This approximation is related to the density functional approach for inhomogeneous fluids. The local HNC/MSA method predicts, at higher surface charges, layering of counterions and charge inversion as seen in Monte Carlo data, a strong increase of the surface potential with charging and a maximum in the double layer capacitance.     

Dissociation pathways of protic ionic liquid clusters: Alkylammonium nitrates

Protic ionic liquids are promising candidates for many applications, including as spacecraft propellants. For both fundamental interest and understanding clustering and dissociation during electrospray‐based propulsion, it is useful to explore the dissociation pathways of protic ionic liquid clusters, as well as the factors affecting the relative contributions of each pathway to the observed MS/MS spectra. With that said, most of the published reports on ionic liquid cluster dissociation have focused on aprotic ionic liquids. The purpose of the current work is to explore the dissociation pathways (eg, loss of amine, nitric acid, or ion pair) of alkylammonium nitrates using energy‐resolved collision‐induced dissociation. Here, it was found that, in general, protic ionic liquids have multiple dissociation pathways—namely, protic ionic liquids can lose their neutralized cation (here, an alkylamine) or neutralized anion (here, nitric acid)—in addition to the ion pair dissociation familiar to aprotic salt and aprotic ionic liquid clusters. In general, increasing the basicity of the cation (here, through increasing the degree of alkylation) decreases the propensity to follow these alternative pathways. Interestingly, increasing the cluster size has a similar effect: as cluster size increases, nitric acid loss decreases. These results will help better model and design protic ionic liquids for electrospray‐based spacecraft propulsion and help provide a better understanding for the general behavior of protic ionic liquids versus aprotic ionic liquids within mass spectrometers.     

Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

The equilibrium electric double layer (EDL) that surrounds colloidal particles is essential for the response of a suspension under a variety of static or alternating external fields. An ideal salt-free suspension is composed of charged colloidal particles and ionic countercharges released by the charging mechanism. Existing macroscopic theoretical models can be improved by incorporating different ionic effects usually neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann equation (PB). The influence of the finite size of the ions seems to be quite promising because it has been shown to predict phenomena like charge reversal, which has been out of the scope of classical PB approximations. In this work we numerically obtain the surface electric potential and the counterion concentration profiles around a charged particle in a concentrated salt-free suspension corrected by the finite size of the counterions. The results show the high importance of such corrections for moderate to high particle charges at every particle volume fraction, especially when a region of closest approach of the counterions to the particle surface is considered. We conclude that finite ion size considerations are obeyed for the development of new theoretical models to study non-equilibrium properties in concentrated colloidal suspensions, particularly salt-free ones with small and highly charged particles.