Image charges and dispersion forces in electric double layers: the dependence of wall-wall interactions on salt concentration and surface charge density

The interaction pressure between two planar charged walls is calculated for a range of conditions. The diffuse electric double layers between the two wall surfaces are treated with ion-wall dispersion forces and ionic image charge interactions taken into account. Both these interactions are due to dielectric discontinuities at the surfaces. Ion-ion and ion-image charge correlations are explicitly included. The ion-wall dispersion interactions can give rise to appreciable ion specific effects, which are particularly strong when the counterions to the surfaces are highly polarizable. The mechanisms of these effects are investigated, and their influence on the net interaction pressure between the walls is studied for a range of surface charge densities, strengths of the anion-wall dispersion interaction and bulk electrolyte concentrations. When the strength of the anion-wall dipersion interaction is increased, the pressure generally becomes less repulsive (or more attractive) for positive surfaces. The opposite happens in general for negative surfaces but to a much lesser extent. The effects are largest for large surface charge densities and high electrolyte concentrations. The image charge interactions give rise to a considerable depletion attraction between the walls for low surface charge densities.     

On the interactions of ions with the air/water interface

In the vicinity of a charged interface, the Poisson-Boltzmann approach considers that the ions obey Boltzmann distributions in a mean electrical field that satisfies the Poisson equation. However, the boundary between two dielectrics generates additional interactions between ions and the interface. The traditional models of ion hydration interactions, that assume that water is a homogeneous dielectric, predict that these interactions are repulsive for all kinds of ions, since all ions should prefer the medium with a larger dielectric constant, where they are better hydrated. In reality, the interactions between the ions and the neighboring water molecules can generate additional short-range ion-hydration interactions, which are either repulsive (for structure-making ions) or attractive (for structure-breaking ions). In the present paper, various models for the ion-hydration forces are examined and compared with the results of molecular dynamics simulations. At large ionic strengths, the latter results could be reproduced qualitatively only when short-ranged attractions between the structure-breaking ions and the interface were taken into account.     

Direct surface force measurements of polyelectrolyte multilayer films containing nanocrystalline cellulose

Polyelectrolyte multilayer films containing nanocrystalline cellulose (NCC) and poly(allylamine hydrochloride) (PAH) make up a new class of nanostructured composite with applications ranging from coatings to biomedical devices. Moreover, these materials are amenable to surface force studies using colloid-probe atomic force microscopy (CP-AFM). For electrostatically assembled films with either NCC or PAH as the outermost layer, surface morphology was investigated by AFM and wettability was examined by contact angle measurements. By varying the surrounding ionic strength and pH, the relative contributions from electrostatic, van der Waals, steric, and polymer bridging interactions were evaluated. The ionic cross-linking in these films rendered them stable under all solution conditions studied although swelling at low pH and high ionic strength was inferred. The underlying polymer layer in the multilayered film was found to dictate the dominant surface forces when polymer migration and chain extension were facilitated. The precontact normal forces between a silica probe and an NCC-capped multilayer film were monotonically repulsive at pH values where the material surfaces were similarly and fully charged. In contrast, at pH 3.5, the anionic surfaces were weakly charged but the underlying layer of cationic PAH was fully charged and attractive forces dominated due to polymer bridging from extended PAH chains. The interaction with an anionic carboxylic acid probe showed similar behavior to the silica probe; however, for a cationic amine probe with an anionic NCC-capped film, electrostatic double-layer attraction at low pH, and electrostatic double-layer repulsion at high pH, were observed. Finally, the effect of the capping layer was studied with an anionic probe, which indicated that NCC-capped films exhibited purely repulsive forces which were larger in magnitude than the combination of electrostatic double-layer attraction and steric repulsion, measured for PAH-capped films. Wherever possible, DLVO theory was used to fit the measured surface forces and apparent surface potentials and surface charge densities were calculated.     

Normal Forces between Cellulose Surfaces Measured with Colloidal Probe Microscopy

Colloidal probe microscopy was employed to study interactions between cellulose surfaces in aqueous solutions. Hydrodynamic forces must be accounted for in data analysis. Long-range interactions betweeen cellulose surfaces are governed by double-layer forces and, once surfaces contact, by osmotic repulsive forces and viscoelasticity. Increasing the ionic strength decreases surface potentials and increases adhesive forces. Polyelectrolytes cause strong steric repulsion at high surface coverage, where interactions are sensitive to probe velocity. Polymer bridging occurs at low coverage. The conformation of adsorbed polyelectrolytes depends on the polymer concentration. Copyright 2000 Academic Press.     

The bridging force between two plates by polyelectrolyte chains

The interaction between particles in a colloidal system can be significantly affected by their bridging by polyelectrolyte chains. In this paper, the bridging is investigated by using a self-consistent field approach which takes into account the van der Waals interactions between the segments of the polyelectrolyte molecules and the plates, as well as the electrostatic and volume exclusion interactions. A positive contribution to the force between two plates is generated by the van der Waals interactions between the segments and the plates. This positive (repulsive) contribution plays an important role in the force when the distances between the plates are small. With increasing van der Waals interaction strength between segments and plates, the force between the plates becomes more repulsive at small distances and more attractive at large distances. When the surfaces of the plates have a constant surface electrical potential and a charge sign opposite to that of the polyelectrolyte chains, the force between the two plates becomes less attractive as the bulk polyelectrolyte concentration increases. This behavior is due to a higher bulk counterion concentration dissociated from the polyelectrolyte molecules. At short distances, the force between plates is more repulsive for stiffer chains. A comparison between theoretical and experimental results regarding the contraction of the interlayer separation between the platelets of vermiculite clays against the concentration of poly(vinyl methyl ether) was made.     

Polyelectrolyte/Ionomer behavior in polymer gel collapse

The theory of collapse of weakly charged polyelectrolyte gels is generalized by taking into account the possibility of counter ion trapping with the formation of ion pairs, which becomes progressively important as the gel shrinks and the dielectric constant of the gel medium decreases. A phenomenon well known in the theory of ionomers, namely the aggregation of ion pairs due to dipole-dipole interactions with the formation of multiplets, is also taken into account. These multiplets act as additional physical cross-links. It is shown that accounting for the two effects mentioned above generally leads to an increase of the region of stability of the collapsed phase and to an increase of the jump in volume at the transition point. The most important, qualitatively new effect is the possibility of existence of a new supercollapsed state of a polymer gel which is very close to the densely packed dry gel. The reason for the thermodynamic stability of the supercollapsed state is a loop of positive feedback: the decrease of the volume of the gel leads to a decrease of the dielectric constant and hence to progressive formation of ion pairs, thus the concentration of mobile counter ions and the corresponding osmotic pressure decrease, the gel shrinks further etc. It is possible to realize the phase transitions between all three states of a polymer gel: swollen, ordinary collapsed and supercollapsed.     

Ion–Dipole Interactions in Concentrated Organic Electrolytes

An algorithm is proposed for calculating the energy of ion–dipole interactions in concentrated organic electrolytes. The ion–dipole interactions increase with increasing salt concentration and must be taken into account when the activation energy for the conductivity is calculated. In this case, the contribution of ion–dipole interactions to the activation energy for this transport process is of the same order of magnitude as the contribution of ion–ion interactions. The ion–dipole interaction energy was calculated for a cell of eight ions, alternatingly anions and cations, placed on the vertices of an expanded cubic lattice whose parameter is related to the mean interionic distance (pseudolattice theory). The solvent dipoles were introduced randomly into the cell by assuming a randomness compacity of 0.58. The energy of the dipole assembly in the cell was minimized by using a Newton–Raphson numerical method. The dielectric field gradient around ions was taken into account by a distance parameter and a dielectric constant of ε=3 at the surfaces of the ions. A fair agreement between experimental and calculated activation energy has been found for systems composed of γ‐butyrolactone (BL) as solvent and lithium perchlorate (LiClO₄), lithium tetrafluoroborate (LiBF₄), lithium hexafluorophosphate (LiPF₆), lithium hexafluoroarsenate (LiAsF₆), and lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) as salts.     

Hofmeister effects in the restabilization of IgG--latex particles: testing Ruckenstein's theory

The hydration interaction is responsible for the colloidal stability observed in protein-coated particles at high ionic strengths. The origin of this non-DLVO interaction is related not only to the local structure of the water molecules located at the surface but also to the structure of those molecules involved in the hydration of the ions that surround the colloidal particles. Ruckenstein and co-workers have recently developed a new theory based on the coupling of double-layer and hydration interactions. Its validity was contrasted by their fitting of experimental data obtained with IgG-latex particles restabilized at high salt concentration. The theory details the important role played by the counterions in the stability at high salt concentrations by proposing an ion pair reaction forming surface dipoles. These surface dipoles are responsible of repulsive interactions between two approaching surfaces. This paper checks the theory with recent data where some ions associated with the Hofmeister series (NO(3)(-), SCN(-) and Ca(2+)) restabilize the same kind of IgG-latex systems by means of hydration forces. Surprisingly, these ions induce stability acting even as co-ions, likely by modifying the water structure at the surface, but not forming surface ion pairs. Therefore, this experimental evidence would question Ruckenstein's theory based on the surface dipole formation for explaining the observed restabilization phenomena.     

Cation-induced collapse of low-molecular-weight polyacrylic acid in the dispersion of barium titanate

Observations on the steric layers formed by the adsorption of low-molecular-weight polyacrylic acid (PAA) were taken using the colloidal probe method in an atomic force microscope. The effects of divalent barium ions and of monovalent potassium ions at varying concentrations were observed on the repulsive interaction profiles. High ionic concentrations screened double-layer forces to small distances, whereby the acting forces were reduced to steric interactions. De Gennes scaling theory was used to model the effect of electrolyte on an aqueous barium titanate system, which was stabilized with PAA. The brush model was found to represent the force curves better than the mushroom model. The collapse of PAA layers with increasing salt approximated a grafted polymer brush in monovalent electrolyte, but the addition of barium ions caused markedly less steric collapse. It is suggested that the formation of a Ba(2+)-PAA complex in the adsorbed layer increases its compressibility parameter.     

An approach to the method for determination of surface potential on solid/liquid interface: theory

The electrochemical properties on solid particle surfaces in an aqueous system have found wide application in many fields. However, for some of them there are no reliable methods of determination. What is particularly worth mentioning is the surface potentials of solid particles. Though this is a most important property and a most basic parameter in colloid interface electrochemistry, no reliable method for its determination is available yet. In the present paper, based on the diffuse double-layer theory, mathematical relations are constructed between the average concentration of ions positively adsorbed in the diffuse double layer and the surface potential of solid particles, thus transforming the determination of surface potential of solid particles into that of the average concentration of ions in the diffuse double layer, and then by applying the standard relationships of Gouy-Chapman theory, the mathematical relations of the average concentration of ions in the diffuse double layer with surface charge density, electrical field strength at surface, and specific surface area of solid particles are constructed.     

The influence of discrete surface charges on the force between charged surfaces

The force between two parallel charged flat surfaces, with discrete surface charges, has been calculated with Monte Carlo simulations for different values of the electrostatic coupling. For low electrostatic coupling (small counterion valence, small surface charge, high dielectric constant, and high temperature) the total force is dominated by the entropic contribution and can be described by mean field theory, independent of the character of the surface charges. For moderate electrostatic coupling, counterion correlation effects lead to a smaller repulsion than predicted by mean field theory. This correlation effect is strengthened by discrete surface charges and the repulsive force is further reduced. For large electrostatic coupling the total force for smeared out surface charges is known to be attractive due to counterion correlations. If discrete surface charges are considered the attractive force is weakened and can even be turned into a repulsive force. This is due to the counterions being strongly correlated to the discrete surface charges forming effective, oppositely directed, dipoles on the two walls.     

Repulsive interface forces in overlapping electric double layers in electrolyte solutions

The historical development of the problem of the electric interaction of particles in electrolyte solutions is comprehensively discussed. The existing approaches are divided into force-based methods, where the mechanical (ponderomotive) forces of the electric field are directly calculated, and energy-based methods calculating the free energy of the colloid system (at least the part of the free energy which is determined by the repulsive forces of electrical nature). The fundamental works of Langmuir, Derjaguin, Levine, Verwey and Overbeek are discussed in detail. At the same time, new original methods are proposed: the method of effective displacements; the formula of free energy of overlapping double layers.Special attention is paid to the analysis of electrostriction forces in liquids, particularly in electric double layers. The non-contradictory application of the concepts of classic macroelectrostatics is shown to result in the need to take into account electrostriction forces in overlapping double layers. The main formulas are given for force and energy of repulsion in flat surfaces with a constant density of the electric charge on them. These formulas are derived with electrostriction forces taken into account. A number of the theoretical results are new.Some experiments are discussed in measuring repulsive forces in colloid systems. A qualitative agreement is established between the experimental results of Ottewill et al. and the theory of electrostriction forces in double layers.     

Interactions between polymer brush-coated spherical nanoparticles: the good solvent case

The interaction between two spherical polymer brushes is studied by molecular dynamics simulation varying both the radius of the spherical particles and their distance, as well as the grafting density and the chain length of the end-grafted flexible polymer chains. A coarse-grained bead-spring model is used to describe the macromolecules, and purely repulsive monomer-monomer interactions are taken throughout, restricting the study to the good solvent limit. Both the potential of mean force between the particles as a function of their distance is computed, for various choices of the parameters mentioned above, and the structural characteristics are discussed (density profiles, average end-to-end distance of the grafted chains, etc.). When the nanoparticles approach very closely, some chains need to be squeezed out into the tangent plane in between the particles, causing a very steep rise of the repulsive interaction energy between the particles. We consider as a complementary method the density functional theory approach. We find that the quantitative accuracy of the density functional theory is limited to large nanoparticle separation and short chain length. A brief comparison to Flory theory and related work on other models also is presented.     

Dielectric decrement as a source of ion-specific effects

Many theoretical studies were devoted in the past to ion-specific effects trying to interpret a large body of experimental evidence, such as surface tension at air/water interfaces and force measurements between charged objects. Although several mechanisms were suggested to explain the results, such as dispersion forces and specific surface-ion interactions, we would like to suggest another source of ion-specificity originating from the local variations of the dielectric constant due to the presence of ions in the solution. We present a mean-field model to account for the heterogeneity of the dielectric constant caused by the ions. In particular, for ions that decrease the dielectric constant we find a depletion of ions from the vicinity of charged surfaces. For a two-plate system, the same effect leads to an increase of the pressure in between two surfaces. Our results suggest that the effect of ions on the local dielectric constant should be taken into account when interpreting experiments that address ion-specific effects.     

Stabilization of magnetorheological suspensions by polyacrylic acid polymers

This work is devoted to the synthesis and stabilization of magnetorheological suspensions constituted by monodisperse micrometer-sized magnetite spheres in aqueous media. The electrical double-layer characteristics of the solid/liquid interface were studied in the absence and presence of adsorbed layers of high molecular weight polyacrylic acids (PAA; Carbopol). Since the Carbopol-covered particles can be thought of as "soft" colloids, Ohshima's theory was used to gain information of the surface potential and the charge density of the polymer layer. The effect of the pH of the solution on the double-layer characteristics is related to the different conformations of the adsorbed molecules provoked by the dissociation of the acrylic groups present in polymer molecules. The stability of the suspensions was experimentally studied for different pH and polymer concentrations, and in the absence or presence of a weak magnetic field applied. The stability of the suspensions was explained using the classical DLVO theory of colloidal stability extended to account for hydration, steric, and magnetic interactions between particles. Diagrams of potential energy vs interparticle distance show the predominant effect of steric, hydrophilic/hydrophobic, and magnetic interactions on the whole stability of the system. The best conditions to obtain stable suspensions were found when strong steric and hydrophilic repulsions hinder the coagulation between polymer-covered particles, simultaneously avoiding sedimentation by the thickening effect of the polymer solution. When a not too high molecular weight PAA was employed in a low concentration, the task of a long-time antisettling effect compatible with the desired magnetic response of the fluid was achieved.     

Combined depletion and electrostatic forces in polymer-induced membrane adhesion: a theoretical model

We develop a semi-quantitative analytical theory to describe adhesion between two identical planar charged surfaces embedded in a polymer-containing electrolyte solution. Polymer chains are uncharged and differ from the solvent by their lower dielectric permittivity. The solution mimics physiological fluids: It contains 0.1 M of monovalent ions and a small number of divalent cations that form tight bonds with the headgroups of charged lipids. The components have heterogeneous spatial distributions. The model was derived self-consistently by combining: (a) a Poisson-Boltzmann like equation for the charge densities, (b) a continuum mean-field theory for the polymer profile, (c) a solvation energy forcing the ions toward the polymer-poor regions, and (d) surface interactions of polymers and electrolytes. We validated the theory via extensive coarse-grained Molecular Dynamics (MD) simulations. The results confirm our analytical model and reveal interesting details not detected by the theory. At high surface charges, polymer chains are mainly excluded from the gap region, while the concentration of ions increases. The model shows a strong coupling between osmotic forces, surface potential and salting-out effects of the slightly polar polymer chains. It highlights some of the key differences in the behaviour of monomeric and polymeric mixed solvents and their responses to Coulomb interactions. Our main findings are: (a) the onset of long-ranged ion-induced polymer depletion force that increases with surface charge density and (b) a polymer-modified repulsive Coulomb force that increases with surface charge density. Overall, the system exhibits homeostatic behaviour, resulting in robustness against variations in the amount of charges. Applications and extensions of the model are briefly discussed.     

Bond energy calculation for the negative ions of heavy elements

Electron bond energies are calculated for the negative ions of complex heavy elements Ge, Sn, Pb using the polarization potential formalism and relativistic perturbation theory of Rayleigh-Schrödinger type with a model potential of zero-order approximation. Basic correlation effects: polarizing interactions of outermost particles via the polarized core and mutual screening of outermost particles are taken into account to provide an acceptable accuracy of calculations. The paper gives refined values for the negative ions involved.     

Steric and bridging interactions between two plates induced by grafted polyelectrolytes

If colloidal particles are grafted with a polymer, then the grafted chains can provide steric repulsion between them. If some of the grafted polymer chains are also adsorbed to a second particle, then a bridging force is generated as well. For uncharged plates and polymer, the following contributions to the free energy of the system have been taken into account in the calculation of the interaction force: (i) the Flory-Huggins expression for the mixing free energy of the grafted chains with the liquid; (ii) the entropy loss due to the connectivity of the polymeric segments; (iii) the van der Waals interactions between the segments and the plates; and (iv) the free energy of adsorption of the polymer segments of the grafted chains on the other plate. For charged plates, the electrostatic free energy as well as the free energy of the electrolyte are included in the total free energy of the system. By minimizing the free energy with respect to the segment concentration and, when it is the case, with respect to the electrical potential, equations for the segment number density distribution and for the electrical potential are obtained, on the basis of which the interactions between two plates grafted with polymer chains that can be also adsorbed on the other plate were calculated. The interaction thus obtained includes steric and bridging forces.     

Interaction between dissimilar double layers with like signs under charge regulation on the basis of the Gouy-Chapman-Stern-Grahame model

The force of interaction between two flat double layers with dissimilar surface potentials but of the same signs, in contact with 1-1 electrolyte solutions (0.001, 0.01, and 0.1 M), was calculated as a function of the surface separation. The calculation was carried out on the basis of the Gouy-Chapman-Stern-Grahame double-layer model, incorporating the site-dissociation and site-binding model used previously for many oxide studies. The results demonstrated that the interaction force under surface charge regulation was always repulsive, increasing progressively with decreasing surface separation. This result is in contrast to the predictions of previous theories that are based on the Gouy-Chapman (GC) double-layer model. Dependence of surface potentials and surface charge densities on the surface separation is also presented.     

Collapse transitions of a supersized neutral chain due to irreversibly adsorbed small colloidal particles

 We performed Monte Carlo simulations to study the destabilization processes of large neutral and flexible polymer chains due to irreversibly adsorbed colloidal particles attached to the chains like beads on a necklace. The particles are modeled as charged spherical units which interact with each other via repulsive electrostatic and attractive van der Waals (vdW) potentials. The usual Monte Carlo search procedure is extended and carefully checked to completely sample the chain conformational space and achieve dense conformations in the limit of both strong attractive and repulsive interaction potentials. Configurational properties, such as the radius of gyration, the end-to-end length, and the Kuhn length, are calculated as a function of the intensity of the vdW interactions and ionic strength values. It is observed that chains exhibit a new range of possible conformations compared to the classical random walk and self avoiding walk chains or polyelectrolytes. In the limit of low salt concentration, by gradually increasing vdW interactions, chains undergo a cascade of transitions from extended structures to dumbbells, from dumbbells to pearl necklaces, and from pearl necklaces to collapsed coils. Because of strong competition between the vdW and electrostatic forces, the distance along the chain between the interacting particles, and the sampling limitations, these transitions are found to sample metastable domains and to depend on the initial conformations. To gain insight into the spatial organization of the collapsed conformations, the pair correlation functions of both monomers and particles are calculated. It is shown that collapsed conformations which are the result of strong particle–particle interactions exhibit two distinct parts: a hard core mainly composed of particles and a surrounding polymeric shell composed of loops and tails. Possible effects of such a collapsed transition on the kinetics of flocculation of a mixture containing large flexible chains and small adsorbing colloidal particles are discussed. Received: 26 July 1999 Accepted in revised form: 9 November 1999