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.     

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.     

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.     

Influence of monovalent ion size on colloidal forces probed by Monte Carlo simulations

The present work studies the role of ionic size in the interactions between the electrical double layers of colloids immersed into electrolyte solutions of monovalent ions. Such interactions are studied by means of Monte Carlo (MC) simulations and the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Despite the omission of the steric effects and some other features of real electrolyte solutions, DLVO theory is known to work qualitatively well for 1:1 electrolyte solutions. However, this affirmation is based on previous tests where an ionic diameter around 0.4 nm was taken for all ionic species. In contrast, some experimental studies suggest that larger hydrated ions should be considered and even specified for each type of ion. In this work, the importance of ionic size is analyzed by applying the primitive model of electrolyte to the intermediate region between a pair of equally charged infinite planar surfaces. The double layer interactions were calculated from the ionic densities at the distance of closest approach to the charged surfaces, this method constitutes an alternative to the traditional calculations at the midplane. Our MC simulations predict the existence of negative net pressures for monovalent electrolytes in the case of zero charge density. In addition, MC simulations reveal some disagreements with theoretical predictions for ionic diameters larger than 0.4 nm. These discrepancies can become significant if surface charge density is large enough due to the restructuration of the double layer. The physical mechanisms for these deviations are also discussed.     

Characteristics of the series resonant-frequency shift of a quartz crystal microbalance in electrolyte solutions

We report the novel characteristics of the series resonant-frequency shift, DeltaF, of a one-face sealed quartz crystal microbalance (QCM) in solutions of monovalent electrolytes and divalent electrolytes. In the present study, we used NaCl, KCl, LiCl, NaNO3 and CH3COONa as monovalent electrolytes, and MgCl2, CaCl2, MgSO4 and Na2SO4 as divalent electrolytes. These experiments reveal that, in all the solutions, the DeltaF values vary linearly with an increase in the square root of the density-viscosity product of the solutions, and the immersion angle dependence of DeltaF appears. Moreover, we have found that the intercept values of DeltaF are dependent only on the cation species, and that the slope values of DeltaF with the viscosity and density of the solutions are related only to the valence of ions. We also suggest that the DeltaF values are independent of anion species, conductivity and permittivity of the solutions.     

Repulsion between oppositely charged macromolecules or particles

The interaction of two oppositely charged surfaces has been investigated using Monte Carlo simulations and approximate analytical methods. When immersed in an aqueous electrolyte containing only monovalent ions, two such surfaces will generally show an attraction at large and intermediate separations. However, if the electrolyte solution contains divalent or multivalent ions, then a repulsion can appear at intermediate separations. The repulsion increases with increasing concentration of the multivalent salt as well as with the valency of the multivalent ion. The addition of a second salt with only monovalent ions magnifies the effect. The repulsion between oppositely charged surfaces is an effect of ion-ion correlations, and it increases with increasing electrostatic coupling and, for example, a lowering of the dielectric permittivity enhances the effect. An apparent charge reversal of the surface neutralized by the multivalent ion is always observed together with a repulsion at large separation, whereas at intermediate separations a repulsion can appear without charge reversal. The effect is hardly observable for a symmetric multivalent salt (e.g., 2:2 or 3:3).     

Bipolar reverse osmosis membrane for separating mono-and divalent ions

Bipolar reverse osmosis membranes that have both negatively and positively charged layers have been prepared to enhance the selectivity towards mono- and divalent ions in respect of both cations and anions. Positively charged layers are formed on low pressure reverse osmosis membranes having negative charge (NTR-7410 and 7450) by an adsorption method using polyethyleneimine (PEI) or a quaternary ammonium polyelectrolyte (QAP). These layers attach to the membrane's dense layer, which is made of sulfonated polyether sulfone. The selectivity of mono- and divalent ions is proven by experimental results for single electrolytes (NaCl, Na₂SO₄ and MgCl₂). Although negatively charged membranes repulse divalent anions more strongly than cations and monovalent anions, bipolar reverse osmosis membranes reject both divalent cations and divalent anions better than monovalent ions. An optimal preparation method for bipolar membranes showing selectivity towards mono- and divalent ions were developed. The bipolar membranes showed good ion selectivity for artificial sea water.     

Forces between Carboxylic Acid Surfaces in Divalent Electrolyte Solutions

The behavior of self-assembled monolayers of thiohexadecanoic acid adsorbed onto gold interacting in asymmetric 2:1 electrolytes has been studied with direct force measurements. The effects of two divalent cations (Mg(2+) and Ca(2+)) were studied at concentrations ranging from 1 μM to 10 mM. As compared to interactions in the presence of Na(+), the divalent ions adsorb strongly to the surfaces, with the effect of lowering the surface potential and decreasing the double-layer repulsion. At concentrations above 10 μM, the Ca(2+) ions were found to adsorb stronger than Mg(2+). Ca(2+) ions cause charge reversal at high concentrations, and the net interactions at 10 mM were attractive over the measurable range. Copyright 2000 Academic Press.     

DNA attraction in monovalent and divalent electrolytes

The dependence of the effective force on the distance between two DNA molecules was directly computed from a set of extensive all-atom molecular dynamics simulations. The simulations revealed that in a monovalent electrolyte the effective force is repulsive at short and long distances but can be attractive in the intermediate range. This attractive force is, however, too weak (approximately 5 pN per turn of a DNA helix) to induce DNA condensation in the presence of thermal fluctuations. In divalent electrolytes, DNA molecules were observed to form a bound state, where Mg(2+) ions bridged minor groves of DNA. The effective force in divalent electrolytes was predominantly attractive, reaching a maximum of 42 pN per one turn of a DNA helix.     

Simulation of electric double layers undergoing charge inversion: mixtures of mono- and multivalent ions

In this paper, the electric double layer (EDL) of a charged plane in the presence of mixtures of 1:1 and 3:1 electrolytes has been investigated through Monte Carlo (MC) simulations using a nonrestrictive primitive model of EDL. In particular, the charge inversion in colloids (attributable to an accumulation of counterions on the surface) can be better understood by means of the simulations performed here. Moreover, two mechanisms proposed for charge inversion are probed: The formation of a strongly correlated layer (SCL) of multivalent counterions and excluded volume effects (to which we will also refer as ion size correlations). Our results are in agreement with the behavior found experimentally for some model colloids with increasing the concentration of monovalent salt in the presence of trivalent ions, which clearly supports the relevance of ion size correlations. In contrast, certain disagreement with predictions of SCL theories is reported.     

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.     

A multi-scale method for the calculation of charge transfer rates through the Pi-stack of DNA: application to DNA dynamics

We describe an ultra-fast, multi-scale method for calculating charge transfer rates through the pi-stack of DNA using a simple charge hopping model in conjunction with the Marcus equation. The calculation of the parameters required as input to the Marcus equation, such as the electronic coupling and the driving force, are calculated with a combination of quantum mechanical methods and conformations sampled from classical molecular dynamics (MD) simulations. The resulting set of time dependent rate equations are then solved stochastically using Monte Carlo (MC) methods. We have applied this model to investigate the importance of thermal fluctuations in DNA conformation over picosecond and nanosecond timescales, and have identified the timescales of most relevance to hole transfer through DNA.     

Mechanisms behind concentration profiles illustrated by charge and concentration distributions around ions in double layers

The mechanisms behind the behaviour of concentration and charge density profiles in diffuse electric double layers are investigated quantitatively for 1:1 and 2:2 electrolytes. This is done by analysing various contributions to the mean force that acts on each ion. The forces are obtained from the calculated ionic charge and concentration distributions around individual ions at various positions in the double layer. These distributions are presented graphically which allows an immediate visual illustration of the mechanisms in action. Some features studied are charge inversion in double layers for divalent aqueous electrolytes, overcompensation of surface charge due to large amounts of physisorbed counterions, ion size effects in the double layer structure and various mechanisms that cause deviations from the predictions of the Poisson–Boltzmann approximation. A major objective of the paper is to present the results in a visual form and explain aspects of modern double layer theory in a simple manner.     

Controlling the cohesion of cement paste

The main source of cohesion in cement paste is the nanoparticles of calcium silicate hydrate (C-S-H), which are formed upon the dissolution of the original tricalcium silicate (C(3)S). The interaction between highly charged C-S-H particles in the presence of divalent calcium counterions is strongly attractive because of ion-ion correlations and a negligible entropic repulsion. Traditional double-layer theory based on the Poisson-Boltzmann equation becomes qualitatively incorrect in these systems. Monte Carlo (MC) simulations in the framework of the primitive model of electrolyte solution is then an alternative, where ion-ion correlations are properly included. In addition to divalent calcium counterions, commercial Portland cement contains a variety of other ions (sodium, potassium, sulfate, etc.). The influence of high concentrations of these ionic additives as well as pH on the stability of the final concrete construction is investigated through MC simulations in a grand canonical ensemble. The results show that calcium ions have a strong physical affinity (in opposition to specific chemical adsorption) to the negatively charged silicate particles of interest (C-S-H, C(3)S). This gives concrete surprisingly robust properties, and the cement cohesion is unaffected by the addition of a large variety of additives provided that the calcium concentration and the C-S-H surface charge are high enough. This general phenomenon is also semiquantitatively reproduced from a simple analytical model. The simulations also predict that the affinity of divalent counterions for a highly and oppositely charged surface sometimes is high enough to cause a "charge reversal" of the apparent surface charge in agreement with electrophoretic measurements on both C(3)S and C-S-H particles.     

Probing multivalent interactions in a synthetic host-guest complex by dynamic force spectroscopy

Multivalency is present in many biological and synthetic systems. Successful application of multivalency depends on a correct understanding of the thermodynamics and kinetics of this phenomenon. In this Article, we address the stability and strength of multivalent bonds with force spectroscopy techniques employing a synthetic adamantane/β-cyclodextrin model system. Comparing the experimental findings to theoretical predictions for the rupture force and the kinetic off-rate, we find that when the valency of the complex is increased from mono- to di- to trivalent, there is a transition from quasi-equilibrium, with a constant rupture force of 99 pN, to a kinetically dependent state, with loading-rate-dependent rupture forces from 140 to 184 pN (divalent) and 175 to 210 pN (trivalent). Additional binding geometries, parallel monovalent ruptures, single-bound divalent ruptures, and single- and double-bound trivalent ruptures are identified. The experimental kinetic off-rates of the multivalent complexes show that the stability of the complexes is significantly enhanced with the number of bonds, in agreement with the predictions of a noncooperative multivalent model.     

Effects of image charges, interfacial charge discreteness, and surface roughness on the zeta potential of spherical electric double layers

We investigate the effects of image charges, interfacial charge discreteness, and surface roughness on spherical electric double layer structures in electrolyte solutions with divalent counterions in the setting of the primitive model. By using Monte Carlo simulations and the image charge method, the zeta potential profile and the integrated charge distribution function are computed for varying surface charge strengths and salt concentrations. Systematic comparisons were carried out between three distinct models for interfacial charges: (1) SURF1 with uniform surface charges, (2) SURF2 with discrete point charges on the interface, and (3) SURF3 with discrete interfacial charges and finite excluded volume. By comparing the integrated charge distribution function and the zeta potential profile, we argue that the potential at the distance of one ion diameter from the macroion surface is a suitable location to define the zeta potential. In SURF2 model, we find that image charge effects strongly enhance charge inversion for monovalent interfacial charges, and strongly suppress charge inversion for multivalent interfacial charges. For SURF3, the image charge effect becomes much smaller. Finally, with image charges in action, we find that excluded volumes (in SURF3) suppress charge inversion for monovalent interfacial charges and enhance charge inversion for multivalent interfacial charges. Overall, our results demonstrate that all these aspects, i.e., image charges, interfacial charge discreteness, their excluding volumes, have significant impacts on zeta potentials of electric double layers.     

Effect of cation size and charge on the interaction between silica surfaces in 1:1, 2:1, and 3:1 aqueous electrolytes

Application of two complementary AFM measurements, force vs separation and adhesion force, reveals the combined effects of cation size and charge (valency) on the interaction between silica surfaces in three 1:1, three 2:1, and three 3:1 metal chloride aqueous solutions of different concentrations. The interaction between the silica surfaces in 1:1 and 2:1 salt solutions is fully accounted for by ion-independent van der Waals (vdW) attraction and electric double-layer repulsion modified by cation specific adsorption to the silica surfaces. The deduced ranking of mono- and divalent cation adsorption capacity (adsorbability) to silica, Mg(2+) < Ca(2+) < Na(+) < Sr(2+) < K(+) < Cs(+), follows cation bare size as well as cation solvation energy but does not correlate with hydrated ionic radius or with volume or surface ionic charge density. In the presence of 3:1 salts, the coarse phenomenology of the force between the silica surfaces as a function of salt concentration resembles that in 1:1 and 2:1 electrolytes. Nevertheless, two fundamental differences should be noticed. First, the attraction between the silica surfaces is too large to be attributed solely to vdW force, hence implying an additional attraction mechanism or gross modification of the conventional vdW attraction. Second, neutralization of the silica surfaces occurs at trivalent cation concentrations that are 3 orders of magnitude smaller than those characterizing surface neutralization by mono- and divalent cations. Consequently, when trivalent cations are added to our cation adsorbability series the correlation with bare ion size breaks down abruptly. The strong adsorbability of trivalent cations to silica contrasts straightforward expectations based on ranking of the cationic solvation energies, thus suggesting a different adsorption mechanism which is inoperative or weak for mono- and divalent cations.     

Comparison of Electrolytic Conductivity Theories: Performance of Classical and New Theories

Conductivity equations, based on the mean spherical approximation (MSA), haverecently been derived. We compare their performance with that of classicalequations at the level of experimental uncertainty using conductivity data forsome typical electrolyte solutions. For symmetrical electrolytes, the pictureisconsistent showing a better performance for the classical equations. The Leeand Wheaton equation also shows advantages at moderate concentrations. Forunsymmetrical electrolytes, the differences between MSA and classical equationsis larger. There is, however, an inherent inconsistency with the equilibriuminformation, which cannot be resolved at present.     

The wall and multivalent counterion effects on the electrostatic force between like-charged spherical particles confined in a charged pore

The effect of wall confinement (wall charge and wall-sphere separation distance) on the electrostatic force between two charged spheres confined in a long charged pore in symmetric and asymmetric electrolytes have been quantified by solving the nonlinear Poisson-Boltzmann equation (PBE), using adaptive finite elements combined with error minimization techniques. The computed force indicated the strong effect of the wall potential on the reduction of the repulsive force for all type of electrolytes. The influence of the wall effect was reduced when the valence of the electrolyte was increased. A significant reduction in the repulsive force between the two spheres was also observed when the distance between the pore wall and the sphere surface was reduced. A smaller long-range repulsive interaction was observed between spheres when the solutions contained multivalent counterions as compared with a monovalent solution. However, at short ranges of separation distances multivalent counterions increase the electrostatic repulsive force between the spheres. The effect of the dimensionless radius of the spheres on the electrostatic force between them has been determined and a significant reduction observed as the dimensionless radius was reduced.