Attraction of electrostatic origin between colloids

The long-range attraction between hydrophobic macroscopic surfaces

Direct measurements of the long-range strongly attractive force observed between macroscopic hydrophobic surfaces across aqueous solutions are reexamined in light of recent experiments and theoretical developments. The focus is on systems in the absence of submicroscopic bubbles (preexistent or induced) to avoid capillary bridging forces. Other possible interferences to the measurements are also eliminated. The force-distance profiles are obtained directly (no contributions from electrical double layer or hydrodynamics) between symmetric identical hydrophobic surfaces, overall charge-neutral, at the thermodynamic equilibrium and in a quenched state. Therefore in the well-defined geometry of crossed-cylinders, sphere-flat, or sphere-sphere, there is no additional interaction to be considered except the ever-present dispersion forces, negligible at large separations. For the three main categories of substrates rendered hydrophobic, namely surfaces obtained with surfactant monolayers physically adsorbed from solution to deposited ones, and substrates coated with a hydrophobizing agent bonded chemically onto the surface, the interaction energy scales as A exp (-2κD)/2κD at large separations, with measured decay lengths in accord with theoretical predictions, simply being half the Debye screening length, κ^-1/2, at least in non vanishing electrolyte. Taken together with the prefactor A scaling as the ionic strength, the interaction energy is demonstrated to have an electrostatic origin in all the systems. Thanks to our recent SFAX coupling force measurements with x-ray solution scattering under controlled nano-confinement, the microstructuration of the adsorbed film emerges as an essential feature in the molecular mechanism for explaining the observed attraction of larger magnitude than dispersion forces. The adsorption of pairs of positive and negative ions on small islands along the interface, the fluctuation of the surface charge density around a zero mean-value with desorption into or adsorption from the electrolyte solution, the correlations in the local surface ion concentrations along the surfaces, the redistribution of counterions upon intersurface variation, all contribute and are tuned finely by the inhomogeneities and defects present in the hydrophobic layers. It appears that the magnitude of the interacting energy can be described by a single master curve encompassing all the systems.

Electrostatic interaction between nonuniformly charged colloids: experimental and numerical study

The influence of the surface charge distribution on the interaction between nanosized particles in water is reported. The distribution of charges at the surface of initially neutral microemulsion droplets has been modulated by additions of various oligomeric cationic surfactants. The osmotic compressibility of the doped microemulsions was measured by light and small-angle neutrons scattering and reveals that the overall effective interaction induced by the ionic groups is repulsive. However, particular charge distributions decrease the osmotic compressibility much less than others. Independent measurements of the activity of the bromide counterions with specific electrodes evidence a significant decrease in the effective charge, which, however, cannot account for the osmotic compressibility in the framework of the primitive model. The q dependence of the structure factor reveals an attractive contribution over a short distance. Numerical studies assign this attractive contribution to the overlap of hydration shells that are extended as a result of the charge localization.

Simulations of latex particles immersed in dendrimer solutions

In this work, we present Monte Carlo simulations of mixtures containing negatively charged latex particles and positively charged dendrimers. We focus on the interaction between two latex particles as salt concentration, dendrimer dose, and generation number are varied. Interaction free energies and corresponding stability ratios are calculated. Minimal stability is found near the isoelectric point, i.e., where the amount of adsorbed dendrimer charge matches the charge of the latex particles. Away from the isoelectric point, the stability increases as the latex particles get more and more under- or overcompensated, an increase that is more steep on the overcompensated side. Increasing the dendrimer generation leads to a more "patchy" surface. This heterogeneity is particularly relevant close to the isoelectric point. Given the relative simplicity of the model, the simulation results are in surprisingly good agreement with the experimental data.

Symmetry breaking and electrostatic attraction between two identical surfaces

By allowing the surface charge of one surface to affect the adsorption equilibrium of the other, we establish the existence of a long-range attractive interaction between two identical surfaces in an electrolyte containing polyvalent counterions with a mean-field Poisson-Boltzmann approach. A Stern electrostatic condition from linearization of the mass-action adsorption isotherm is used to capture how polyvalent ion condensation affects and reverses the surface charge. We furthermore establish a direct mapping between this Stern-layer condition and previously derived modified mean-field formulations associated with correlated fluctuations theory. For a sufficiently potential-sensitive isotherm, antisymmetric charge inversion can occur to produce an attractive force that increases with decreasing ionic strengths. Analyses of a mass-action isotherm produce force-separation relations, including an exponential far-field force decay distinct but consistent with previously proposed correlated fluctuation theories and in quantitative agreement with experimental data.

Field theory for size- and charge-asymmetric primitive model of ionic systems: mean-field stability analysis and pretransitional effects

The primitive model of ionic systems is investigated within a field-theoretic description for the whole range of diameter-, lambda , and charge, Z ratios of the two ionic species. Two order parameters (OP) are identified. The relation of the OP's to physically relevant quantities is nontrivial. Each OP is a linear combination of the charge density and the number-density waves. Instabilities of the disordered phase associated with the two OP's are determined in the mean-field approximation (MF). In MF a gas-liquid separation occurs for any Z and lambda is not equal to 1 . In addition, an instability with respect to various types of periodic ordering of the two kinds of ions is found. Depending on lambda and Z , one or the other transition is metastable in different thermodynamic states. For sufficiently large size disparity we find a sequence of fluid-crystal-fluid transitions for the increasing volume fraction of ions, in agreement with experimental observations. The instabilities found in MF represent weak ordering of the most probable instantaneous states, and are identified with structural loci associated with pretransitional effects.

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.

Salt screening and specific ion adsorption determine neutral-lipid membrane interactions

The simplest, single-component biological membrane challenges accepted models of macromolecular interactions: lipid lamellar phases swell when immersed in monovalent salt solutions. Moreover, typical of a Hofmeister series, Br salts swell multilayers more than Cl salts, offering an excellent opportunity to investigate long-standing questions of ionic specificity. In accord with earlier measurements of liposome mobilities in electric fields, we find an added electrostatic repulsion of membranes due to anion binding, with a much stronger Br binding compared with Cl. However, contrary to the expectation that electrostatic repulsion should vanish in high salinity, swelling of lipid multilayers is monotonic with increasing salt concentration for both Br and Cl salts. The apparent contradiction is resolved by recognizing that although the electrostatic repulsion is progressively screened by increasing salt concentration, so is the van der Waals (vdW) attraction. Negligible in low salt, weakening of vdW forces becomes significant by the time electrostatic forces vanish. The result is a smooth monotonic swelling curve with no apparent distinction between low and high salt concentration regimes. Furthermore, when compared with theoretical predictions, measured vdW forces decay much too slowly with added salt. However, by accounting for the recently measured salt deficit near lipid bilayers, the expected scaling with Debye screening length is recovered. The combination of ion-specific binding and nonspecific ionic screening of low-frequency fluctuations explains salt effects on lipid membrane interactions and, by extension, explains specific (Hofmeister) effects at macromolecular interfaces between low and high dielectric.

Colloidal stabilization via nanoparticle halo formation

We present a detailed numerical study of effective interactions between micrometer-sized silica spheres, induced by highly charged zirconia nanoparticles. It is demonstrated that the effective interactions are consistent with a recently discovered mechanism for colloidal stabilization. In accordance with the experimental observations, small nanoparticle concentrations induce an effective repulsion that counteracts the intrinsic van der Waals attraction between the colloids and thus stabilizes the suspension. At higher nanoparticle concentrations an attractive potential is recovered, resulting in reentrant gelation. Monte Carlo simulations of this highly size-asymmetric mixture are made possible by means of a geometric cluster Monte Carlo algorithm. A comparison is made to results obtained from the Ornstein-Zernike equations with the hypernetted-chain closure.

Effects of urea and trimethylamine-N-oxide (TMAO) on the interactions of lysozyme in solution

The effect of two physiological cosolutes (urea and trimethylamine-N-oxide) and of KCl on the intermolecular interactions in concentrated lysozyme solutions were studied by synchrotron radiation small angle x-ray scattering. The evolution of the structure factors as a function of cosolute and/or salt concentration was modeled using pair potentials following an approach recently described in the literature. It was found that the structure factors for salt and/or cosolute concentration series at a fixed protein concentration can best be described using a variable depth attractive potential and a constant effective charge rather than a constant attractive potential and a variable effective charge as done in previous work.

Ageing and vision: structure, stability and function of lens crystallins

The alpha-, beta- and gamma-crystallins are the major protein components of the vertebrate eye lens, alpha-crystallin as a molecular chaperone as well as a structural protein, beta- and gamma-crystallins as structural proteins. For the lens to be able to retain life-long transparency in the absence of protein turnover, the crystallins must meet not only the requirement of solubility associated with high cellular concentration but that of longevity as well. For proteins, longevity is commonly assumed to be correlated with long-term retention of native structure, which in turn can be due to inherent thermodynamic stability, efficient capture and refolding of non-native protein by chaperones, or a combination of both. Understanding how the specific interactions that confer intrinsic stability of the protein fold are combined with the stabilizing effect of protein assembly, and how the non-specific interactions and associations of the assemblies enable the generation of highly concentrated solutions, is thus of importance to understand the loss of transparency of the lens with age. Post-translational modification can have a major effect on protein stability but an emerging theme of the few studies of the effect of post-translational modification of the crystallins is one of solubility and assembly. Here we review the structure, assembly, interactions, stability and post-translational modifications of the crystallins, not only in isolation but also as part of a multi-component system. The available data are discussed in the context of the establishment, the maintenance and finally, with age, the loss of transparency of the lens. Understanding the structural basis of protein stability and interactions in the healthy eye lens is the route to solve the enormous medical and economical problem of cataract.

Attraction between DNA molecules mediated by multivalent ions

The effective force between two parallel DNA molecules is calculated as a function of their mutual separation for different valencies of counterion and salt ions and different salt concentrations. Computer simulations of the primitive model are used and the shape of the DNA molecules is accurately modeled using different geometrical shapes. We find that multivalent ions induce a significant attraction between the DNA molecules whose strength can be tuned by the averaged valency of the ions. The physical origin of the attraction is traced back either to electrostatics or to entropic contributions. For multivalent counterions and monovalent salt ions, we find a salt-enhanced repulsion effect: the force is first attractive but gets repulsive with increasing salt concentration. Furthermore, we show that the multivalent-ion-induced attraction does not necessarily correlate with DNA overcharging.

Nonmonotonic variation with salt concentration of the second virial coefficient in protein solutions

The osmotic virial coefficient B2 of globular protein solutions is calculated as a function of added salt concentration at fixed pH by computer simulations of the "primitive model." The salt and counterions as well as a discrete charge pattern on the protein surface are explicitly incorporated. For parameters roughly corresponding to lysozyme, we find that B2 first decreases with added salt concentration up to a threshold concentration, then increases to a maximum, and then decreases again upon further raising the ionic strength. Our studies demonstrate that the existence of a discrete charge pattern on the protein surface profoundly influences the effective interactions and that linear and nonlinear Poisson Boltzmann theories fail for large ionic strength. The observed nonmonotonicity of B2 is compared with experiments. Implications for protein crystallization are discussed.

Effective interactions between electric double layers

This review summarizes and assesses recent theoretical and experimental advances, with special emphasis on the effective interaction between charge-stabilized colloids, in the bulk or in confined geometries, and on the ambiguities of defining an effective charge of the colloidal particles. Some consideration is given to the often neglected discrete solvent effects.

Electrolytic depletion interactions

We consider the interactions between two uncharged planar macroscopic surfaces, immersed in an electrolyte solution, which are induced by interfacial selectivity. These forces are taken into account by introducing a depletion free-energy density functional, in addition to the usual mean-field Poisson-Boltzmann functional. The minimization of the total free-energy functional yields the density profiles of the microions and the electrostatic potential. The disjoining pressure is obtained by differentiation of the total free energy with respect to the separation of the surfaces, holding the range and strength of the depletion forces constant. We find that the induced interaction between the two surfaces is always repulsive for sufficiently large separations, and becomes attractive at shorter separations. The nature of the induced interactions changes from attractive to repulsive at a distance corresponding to the range of the depletion forces.