Debye-Hückel theory for mixtures of rigid rodlike ions and salt

Like-charged surfaces are able to attract each other if they are embedded in an electrolyte solution of multivalent rodlike ions, even if the rods are long. To reproduce this ability the Poisson-Boltzmann model has recently been extended so as to account for the rodlike structure of the mobile ions. Our model properly accounts for intraionic correlations but still neglects correlations between different rodlike ions. For sufficiently long rods, the model shows excellent agreement with Monte Carlo simulations and exhibits two minima - a depletion and a bridging minimum - in the interaction free energy. In the present work, we generalize the Poisson-Boltzmann model to systems with polydisperse rod lengths and arbitrary charge distributions along the rods, including the presence of salt. On the level of the linearized Debye-Hu?ckel model we derive a general criterion for whether an electrolyte with given distribution of rodlike ions is able to mediate attraction between like-charged surfaces. We numerically analyze two special cases, namely the influence of salt on symmetric and asymmetric mixtures of monodisperse rodlike ions. The symmetric mixture is characterized by the presence of both negatively and positively charged (but otherwise identical) rodlike ions. For the asymmetric mixture, the system contains rodlike ions of only one type. We demonstrate that the addition of salt retains the depletion minimum but tends to eliminate the bridging minimum.     

Coagulation of tobacco mosaic virus in alcohol-water-LiCl solutions

The coagulation and colloidal stability of tobacco mosaic virus (TMV) in alcohol-water-LiCl solutions were studied. Without the addition of LiCl salt, the coagulation was promoted by the increase of hydrophobicity of the alcohols that is proportional to their alkyl chain length and concentration. Addition of the LiCl salt reduced the electrostatic repulsion between TMV particles resulting in coagulation in methanol-water and ethanol-water solutions. In water-alcohol-LiCl mixture, the coagulation of TMV was driven by both the hydrophobic interaction of the solution and the screening effect of the salt simultaneously. To understand the particle-particle interaction during the coagulation, the interaction energy was calculated using DLVO theory. Considering the electrostatic repulsive energy, van der Waals attractive energy, and hydrophobic interaction energy, the total energy profiles were obtained. The experiment and model calculation results indicated that the increase of alcohol concentration would increase hydrophobic attraction energy so that the coagulation is promoted. These results provide the fundamental understanding on the coagulation of biomolecular macromolecules.     

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.     

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).     

The role of hydrophobic surfaces in altering water-mediated peptide-peptide interactions in an aqueous environment

Using Born-Oppenheimer molecular dynamics within the density functional framework, we calculated the effective force acting on water-mediated peptide-peptide interaction between antiparallel β-sheets in an aqueous environment and also in the vicinity of a hydrophobic surface. From the magnitude of the effective force (corresponding to the slope of the free energy as a function of the interpeptide distance) and its sign (a negative value indicates an effective attraction, whereas a positive value indicates an effective repulsion) we can elucidate the fundamental differences of the water-mediated peptide-peptide interactions in those two environments. The computed effective forces indicate that the water-mediated interaction between peptides in an aqueous environment is attractive in the range of interpeptide distance d = 7-8 ? when hydrophobic surfaces are not nearby. Due to the stabilization of the water molecules bridging between the two β-sheets, a free energy barrier exists between the direct and indirect (water-mediated) interpeptide interactions. However, when the peptides are in the proximity of hydrophobic surfaces, this free energy barrier decreases because the hydrophobic surfaces enhance the interpeptide attraction by the destabilization and ease-to-libration of the bridging water molecules between them.     

Recent advances in the electric double layer in colloid science

The interaction between charged colloidal particles is mediated by their electric double layers. Given that pairs of like-charged particles experience a repulsion, why do some dilute colloidal dispersions become unstable and condense at low ionic strengths? This puzzling paradox appears to have been largely resolved over the past year by a careful analysis of all the contributions to the thermodynamic potential of the dispersion. Condensation can be predicted using the traditional pair repulsion of the Poisson–Boltzmann theory without invoking any long-range attractions in the pair potential. However, it has emerged that one has to go beyond the Poisson–Boltzmann theory to account for the instability that occurs in confined colloidal dispersions. Other recent advances in the ubiquitous Poisson–Boltzmann theory have included effective surface charge approaches in calculating the electrokinetic zeta potential, and the modelling of charge regulation in colloidal systems.     

Potentials of mean force between ionizable amino acid side chains in water

Potentials of mean force (PMF) between all possible ionizable amino acid side chain pairs in various protonation states were calculated using explicit solvent molecular dynamics simulations with umbrella sampling and the weighted histogram analysis method. The side chains were constrained in various orientations inside a spherical cluster of 200 water molecules. Beglov and Roux's Spherical Solvent Boundary Potential was used to account for the solvent outside this sphere. This approach was first validated by calculating PMFs between monatomic ions (K(+), Na(+), Cl(-)) and comparing them to results from the literature and results obtained using Ewald summation. The strongest interaction (-4.5 kcal/mol) was found for the coaxial Arg(+).Glu(-) pair. Many like-charged side chains display a remarkable lack of repulsion, and occasionally a weak attraction. The PMFs are compared to effective energy curves obtained with common implicit solvation models, namely Generalized Born (GB), EEF1, and uniform dielectric of 80. Overall, the EEF1 curves are too attractive, whereas the GB curves in most cases match the minima of the PMF curves quite well. The uniform dielectric model, despite some fortuitous successes, is grossly inadequate.     

Effective interaction between charged nanoparticles and DNA

We investigate the effective interaction mediated by salt ions between charged nanoparticles (NPs) and DNA. DNA is modeled as an infinite cylinder with a constant surface charge in an implicit solvent. Monte Carlo simulations are used to compute the free energy of the system described in the framework of the primitive model of electrolytes, which accounts for excluded volumes of salt ions. A mean-field Poisson-Boltzmann theory also allows us to compute the free energy and provides us with explicit formulae for its main characteristics (position and depth of the minimum). We intend here to identify the physical parameters that have a major impact on the NP-DNA interaction, in an attempt to evaluate physico-chemical properties which could play a role in genotoxicity or, which could be exploited for therapeutic use. Thus, we investigate the influence on the effective interaction of: the shape of the nanoparticle, the magnitude of the nanoparticle charge and its distribution, the value of the pH of the solution, the magnitude of Van der Waals interactions depending on the nature of the constitutive material of the NP (metal vs. dielectric). We show that for positively charged concave NPs the effective interaction is repulsive at short distance, so that it presents a minimum at distance from the DNA. This short-range repulsion is specific to indented particles and is a robust property that holds for a large range of materials and charge densities.     

Unusual halogen-bonded complex FBrdelta+...delta+BrF and hydrogen-bonded complex FBrdelta+...delta+HF formed by interactions between two positively charged atoms of different polar molecules

Using ab initio calculations, the authors' predicted for the first time that the halogen-bonded complex FBrdelta+...delta+BrF and hydrogen-bonded complex FBrdelta+...delta+HF formed by the interactions between two positively charged atoms of different polar molecules can be stable in gas phase. It shows that halogen bond or hydrogen bond not only exists between oppositely charged atoms but also between like-charged atoms. That the attraction arising from the special halogen bond or hydrogen bond can exceed the electrostatic repulsion between two contact positively charged atoms stabilizes the complex. Of course, from the point of view of physics they can consider the interactions in FBrdelta+...delta+BrF and FBrdelta+...delta+HF as mainly the sum of the long range molecular interactions, namely, electrostatic, induction, and dispersion with some short-range repulsion. They found that the intermolecular electron correlation contribution representing dispersion interaction plays a crucial role in the stabilities of seemingly repulsive complexes FBrdelta+...delta+BrF and FBrdelta+...delta+HF.     

Generalizations for the potential of mean force between two isolated colloidal particles from Monte Carlo simulations

A substantial amount of experimental and numerical evidence has shown that the Derjaguin-Landau-Verwey-Overbeek theory is not suitable for describing those colloidal solutions that contain multivalent counterions. Toward improved understanding of such solutions, the authors report Monte Carlo calculations wherein, following Rouzina and Bloomfield, they postulate that, in the absence of van der Waals forces, the overall force between two isolated charged colloidal particles in electrolyte solutions is determined by a dimensionless parameter Gamma=z(2)l(B)/a, which measures the electrostatic repulsion between counterions adsorbed on the macroion surface, where z = counterion valence, l(B)=Bjerrum length, and a = average separation between counterions on the macroion surface calculated as if the macroion were fully neutralized. The authors find, first, that the maximum repulsion between like-charged macroions occurs at Gamma approximately 0.5 and, second, that onset of attraction occurs at Gamma approximately 1.8, essentially independent of the valence and concentration of the surrounding electrolyte. These observations might provide new understanding of interactions between electrostatic double layers and perhaps offer explanations for some electrostatic phenomena related to interactions between DNA molecules or proteins.     

Selective coalescence of bubbles in simple electrolytes

Simple ions in electrolytes exhibit different degrees of affinity for the approach to the free surface of water. This results in strong ion-specific effects that are particularly dramatic in the selective inhibition of bubble coalescence. I present here the calculation of electrostatic interaction between free surfaces of electrolytes caused by the ion accumulation or depletion near a surface. When both anion and cation are attracted to the surface (like H+ and Cl- in HCl solutions), van der Waals attraction facilitates approach of the surfaces and the coalescence of air bubbles. When only an anion or cation is attracted to the surface (like Cl- in NaCl solutions), an electric double layer forms, resulting in repulsive interaction between free surfaces. I applied the method of effective potentials (evaluated from published ion density profiles obtained in simulations) to calculate the ionic contribution to the surface-surface interaction in NaCl and HCl solutions. In NaCl, but not in HCl, the double-layer interaction creates a repulsive barrier to the approach of bubbles, in agreement with the experiments. Moreover, the concentration where ionic repulsion in NaCl becomes comparable in magnitude to the short-range hydrophobic attraction corresponds to the experimentally found transition region toward the inhibition of coalescence.     

Interaction of nanometric clay platelets

The free energy of interaction between two nanometric clay platelets immersed in an electrolyte solution has been calculated using Monte Carlo simulations as well as direct integration of the configurational integral. Each platelet has been modeled as a collection of charged spheres carrying a unit charge the face of a platelet contains negative charges, and the edge, positive charges. The calculations predict that a configuration of "overlapping coins" is the global free energy minimum at intermediate salt concentrations (10-100 mM). A second weaker minimum, corresponding to the well-known "house of cards" configuration, also appears in this salt interval. At low salt concentrations the electrostatic repulsion dominates, while at intermediate concentrations electrostatic interactions alone can create a net attraction between the platelets. At sufficiently high salt content (>200 mM), the van der Waals interaction takes over and the net interaction becomes attractive at essentially all separations. From the calculated free energy and its derivative, we can derive a yield stress and elasticity modulus in fair agreement with experiment. The roughness of the platelets affects the quantitative behavior of the free energy of interaction but does not alter the results in a qualitative way. From the variation of the free energy of interaction, we would tentatively describe the phase behavior as follows: At low salt, the interaction is strongly repulsive and the dispersion should appear as a solid ("repulsive gel"). With increasing salt concentration, the repulsion is weakened and a liquid phase appears ("sol"). A further increase of the salt content leads a second solid phase ("attractive gel") governed by attractive interactions between the platelets. Finally, at sufficiently high salinity, the clay precipitates due to van der Waals forces.     

Entropic attraction condenses like-charged interfaces composed of self-assembled molecules

Like-charged solid interfaces repel and separate from one another as much as possible. Charged interfaces composed of self-assembled charged-molecules such as lipids or proteins are ubiquitous. The present study shows that although charged lipid-membranes are sufficiently rigid, in order to swell as much as possible, they deviate markedly from the behavior of typical like-charged solids when diluted below a critical concentration (ca. 15 wt %). Unexpectedly, they swell into lamellar structures with spacing that is up to four times shorter than the layers should assume (if filling the entire available space). This process is reversible with respect to changing the lipid concentration. Additionally, the research shows that, although the repulsion between charged interfaces increases with temperature, like-charged membranes, remarkably, condense with increasing temperature. This effect is also shown to be reversible. Our findings hold for a wide range of conditions including varying membrane charge density, bending rigidity, salt concentration, and conditions of typical living systems. We attribute the limited swelling and condensation of the net repulsive interfaces to their self-assembled character. Unlike solids, membranes can rearrange to gain an effective entropic attraction, which increases with temperature and compensates for the work required for condensing the bilayers. Our findings provide new insight into the thermodynamics and self-organization of like-charged interfaces composed of self-assembled molecules such as charged biomaterials and supramolecular assemblies that are widely found in synthetic and natural constructs.     

Effect of ions on the hydrophobic interaction between two plates

We use molecular dynamics simulations to investigate the solvent mediated attraction and drying between two nanoscale hydrophobic surfaces in aqueous salt solutions. We study these effects as a function of the ionic charge density, that is, the ionic charge per unit ionic volume, while keeping the ionic diameter fixed. The attraction is expressed by a negative change in the free energy as the plates are brought together, with enthalpy and entropy changes that both promote aggregation. We find a strong correlation between the strength of the hydrophobic interaction and the degree of preferential binding/exclusion of the ions relative to the surfaces. The results show that amplification of the hydrophobic interaction, a phenomenon analogous to salting-out, is a purely entropic effect and is induced by high-charge-density ions that exhibit preferential exclusion. In contrast, a reduction of the hydrophobic interaction, analogous to salting-in, is induced by low-charge-density ions that exhibit preferential binding, the effect being either entropic or enthalpic. Our findings are relevant to phenomena long studied in solution chemistry, as we demonstrate the significant, yet subtle, effects of electrolytes on hydrophobic aggregation and collapse.     

Long-range interaction between heterogeneously charged membranes

Despite their neutrality, surfaces or membranes with equal amounts of positive and negative charge can exhibit long-range electrostatic interactions if the surface charge is heterogeneous; this can happen when the surface charges form finite-size domain structures. These domains can be formed in lipid membranes where the balance of the different ranges of strong but short-ranged hydrophobic interactions and longer-ranged electrostatic repulsion result in a finite, stable domain size. If the domain size is large enough, oppositely charged domains in two opposing surfaces or membranes can be strongly correlated by the electrostatic interactions; these correlations give rise to an attractive interaction of the two membranes or surfaces over separations on the order of the domain size. We use numerical simulations to demonstrate the existence of strong attractions at separations of tens of nanometers. Large line tensions result in larger domains but also increase the charge density within the domain. This promotes correlations and, as a result, increases the intermembrane attraction. On the other hand, increasing the salt concentration increases both the domain size and degree of domain anticorrelation, but the interactions are ultimately reduced due to increased screening. The result is a decrease in the net attraction as salt concentration is increased.     

Entropy and enthalpy of polyelectrolyte complexation: Langevin dynamics simulations

We report a systematic study by Langevin dynamics simulation on the energetics of complexation between two oppositely charged polyelectrolytes of same charge density in dilute solutions of a good solvent with counterions and salt ions explicitly included. The enthalpy of polyelectrolyte complexation is quantified by comparisons of the Coulomb energy before and after complexation. The entropy of polyelectrolyte complexation is determined directly from simulations and compared with that from a mean-field lattice model explicitly accounting for counterion adsorption. At weak Coulomb interaction strengths, e.g., in solvents of high dielectric constant or with weakly charged polyelectrolytes, complexation is driven by a negative enthalpy due to electrostatic attraction between two oppositely charged chains, with counterion release entropy playing only a subsidiary role. In the strong interaction regime, complexation is driven by a large counterion release entropy and opposed by a positive enthalpy change. The addition of salt reduces the enthalpy of polyelectrolyte complexation by screening electrostatic interaction at all Coulomb interaction strengths. The counterion release entropy also decreases in the presence of salt, but the reduction only becomes significant at higher Coulomb interaction strengths. More significantly, in the range of Coulomb interaction strengths appropriate for highly charged polymers in aqueous solutions, complexation enthalpy depends weakly on salt concentration and counterion release entropy exhibits a large variation as a function of salt concentration. Our study quantitatively establishes that polyelectrolyte complexation in highly charged Coulomb systems is of entropic origin.     

Monte Carlo simulations of the hydrophobic effect in aqueous electrolyte solutions

The hydrophobic interaction between two methane molecules in salt-free and high salt-containing aqueous solutions and the structure in such solutions have been investigated using an atomistic model solved by Monte Carlo simulations. Monovalent salt representing NaCl and divalent salt with the same nonelectrostatic properties as the monovalent salt have been used to examine the influence of the valence of the salt species. In salt-free solution the effective interaction between the two methane molecules displayed a global minimum at close contact of the two methane molecules and a solvent-separated secondary minimum. In 3 and 5 M monovalent salt solution the potential of mean force became slightly more attractive, and in a 3 M divalent salt solution the attraction became considerably stronger. The structure of the aqueous solutions was determined by radial distribution functions and angular probability functions. The distortion of the native water structure increased with ion valence. The increase of the hydrophobic attraction was associated with (i) a breakdown of the tetrahedral structure formed by neighboring water molecules and of the hydrogen bonds between them and (i) the concomitant increase of the solution density.     

Effect of temperature on the reentrant condensation in polyelectrolyte-liposome complexation

Interactions of oppositely charged macroions in aqueous solution give rise to intriguing aggregation phenomena, resulting in finite-size, long-lived clusters, characterized by a quite narrow size distribution. Particularly, the adsorption of highly charged linear polyelectrolytes on oppositely charged colloidal particles is strongly correlated and some short-range order arises from competing electrostatic interactions between like-charged polymer chains (repulsion) and between polymer chains and particle surface (attraction). In these systems, in an interval of concentrations around the isoelectric point, relatively large clusters of polyelectrolyte-decorated particles form. However, the mechanisms that drive the aggregation and stabilize, at the different polymer/particle ratios, a well-defined size of the aggregates are not completely understood. Nor is clear the role that the correlated polyion adsorption plays in the aggregation, although the importance of "patchy interactions" has been stressed as the possible source of attractive interaction term between colloidal particles. Different models have been proposed to explain the formation of the observed cluster phase. However, a central question still remains unanswered, i.e., whether the clusters are true equilibrium or metastable aggregates. To elucidate this point, in this work, we have investigated the effect of the temperature on the cluster formation. We employed liposomes built up by DOTAP lipids interacting with a simple anionic polyion, polyacrylate sodium salt, over an extended concentration range below and above the isoelectric condition. Our results show that the aggregation process can be described by a thermally activated mechanism.     

Simple model for DNA adsorption onto a mica surface in 1:1 and 2:1 electrolyte solutions

We propose a simple theory of interactions between like-charged polyelectrolyte and a surface based on a mean-field Derjaguin-Landau-Verwey-Overbeek approach. It predicts that the van der Waals attractive interactions are responsible for irreversible physisorption of polyelectrolytes onto charged surfaces. We show that monovalent salts contribute significantly to repulsive interactions, while enhancing the attraction very slightly. The effect of the divalent counterions is reverse. Therefore, to achieve the adsorption, the overall repulsion due to 1:1 electrolyte should be counterbalanced by the stronger van der Waals attraction due to the presence of doubly charged counterions in solution. The theory has been validated experimentally against its ability to predict the minimum polymer/surface interaction energy required for the adsorption using DNA/mica in NaCl, MgCl2, and NiCl2 solutions as a test system. The theory explains the mechanism of linear DNA adsorption to a mica surface for different solvent compositions and can be used as a tool for predicting the optimum conditions for AFM experiments on linear polymer systems. The model can also be used to make general conclusions on the conformation of polymer molecules on a surface. We have shown for the DNA/mica surface system that when the adsorption of DNA is mostly governed by long-range van der Waals forces the molecule adopts an ideal 2D conformation. When the adsorption is mostly due to short-range ion-correlation forces, DNA will appear 3D --> 2D projected in agreement with experimental data.     

Effect of electric-field-induced capillary attraction on the motion of particles at an oil-water interface

Here, we investigate experimentally and theoretically the motion of spherical glass particles of radii 240-310 microm attached to a tetradecane-water interface. Pairs of particles, which are moving toward each other under the action of lateral capillary force, are observed by optical microscopy. The purpose is to check whether the particle electric charges influence the particle motion, and whether an electric-field-induced capillary attraction could be detected. The particles have been hydrophobized by using two different procedures, which allow one to prepare charged and uncharged particles. To quantify the hydrodynamic viscous effects, we developed a semiempirical quantitative approach, whose validity was verified by control experiments with uncharged particles. An appropriate trajectory function was defined, which should increase linearly with time if the particle motion is driven solely by the gravity-induced capillary force. The analysis of the experimental results evidences for the existence of an additional attraction between two like-charged particles at the oil-water interface. This attraction exceeds the direct electrostatic repulsion between the two particles and leads to a noticeable acceleration of their motion.