Simulations of surface forces in polyelectrolyte solutions

We have simulated interactions between charged surfaces in the presence of oppositely charged polyelectrolytes by coupling perturbations in the isotension ensemble to a free energy variance minimization scheme. For polymeric systems, this method completely outperforms configurationally biased versions of grand canonical simulations. Proper diffusive equilibrium between bulk and slit has been established for polyelectrolytes with up to 60 monomers per chain. A consequence of imposing diffusive equilibrium conditions, in contrast to previous more restricted models, is the possibility of surface charge inversion; ion-ion correlation and the cooperativity of monomer adsorption drive the formation of a polyion layer close to the surface, that overcompensates the nominal surface charge. This is observed even at modest surface charge densities, and leads to a build up of a long ranged electrostatic barrier. In addition, the onset of charge inversion requires very low bulk polymer densities. Due to screening effects, this leads to a higher and more long-ranged free energy barrier at low, compared to high, bulk densities. Oscillatory forces, reminiscent of those found in simple hard sphere systems, are resolved in the high concentration regime. As a consequence of a second surface charge inversion, the system "stratifies" to form a stable polyelectrolyte layer in the central part of the slit, stabilized by the adsorbed surface layers.     

Molecular dynamics simulations of polyelectrolyte adsorption

We have performed molecular dynamics simulations of polyelectrolyte adsorption at oppositely charged surfaces from dilute polyelectrolyte solutions. In our simulations, polyelectrolytes were modeled by chains of charged Lennard-Jones particles with explicit counterions. We have studied the effects of the surface charge density, surface charge distribution, solvent quality for the polymer backbone, strength of the short-range interactions between polymers and substrates on the polymer surface coverage, and the thickness of the adsorbed layer. The polymer surface coverage monotonically increases with increasing surface charge density for almost all studied systems except for the system of hydrophilic polyelectrolytes adsorbing at hydrophilic surfaces. In this case the polymer surface coverage saturates at high surface charge densities. This is due to additional monomer-monomer repulsion between adsorbed polymer chains, which becomes important in dense polymeric layers. These interactions also preclude surface overcharging by hydrophilic polyelectrolytes at high surface charge densities. The thickness of the adsorbed layer shows monotonic dependence on the surface charge density for the systems of hydrophobic polyelectrolytes for both hydrophobic and hydrophilic surfaces. Thickness is a decreasing function of the surface charge density in the case of hydrophilic surfaces while it increases with the surface charge density for hydrophobic substrates. Qualitatively different behavior is observed for the thickness of the adsorbed layer of hydrophilic polyelectrolytes at hydrophilic surfaces. In this case, thickness first decreases with increasing surface charge density, then it begins to increase.     

Surface interactions during polyelectrolyte multilayer buildup. 1. Interactions and layer structure in dilute electrolyte solutions

We report the investigation of surface forces between polyelectrolyte multilayers of poly(allylamine hydrochloride) (PAH) and poly(styrenesulfonate sodium salt) (PSS) assembled on mica surfaces during film buildup using a surface force apparatus. Up to four polyelectrolyte layers were prepared on each surface ex situ, and the surface interactions were measured in 10(-4) M KBr solutions. The film thickness under high compressive loads (above 2000 microN/m) increased linearly with the number of deposited layers. In all cases, the interaction between identical surfaces at large separations (>100 A from contact) was dominated by electrostatic double-layer repulsion. By fitting DLVO theory to the experimental force curves, the apparent double-layer potential of the interacting surfaces was calculated. At shorter separations, an additional non-DLVO repulsion was present due to polyelectrolyte chains extending some distance from the surface into solution, thus generating an electrosteric type of repulsion. Forces between dissimilar multilayers (i.e., one of the multilayers terminated with PSS and the other with PAH) were attractive at large separations (30-400 A) owing to a combination of electrostatic attraction and polyelectrolyte bridging.     

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.     

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).     

Proteins and polyelectrolytes: A charged relationship

We review the interaction of charged polymeric systems with proteins. In solutions of low ionic strength there are many examples of proteins attracted to polyelectrolytes even if both systems carry the same overall charge. This attractive interaction is widespread, having been observed for single polyelectrolyte chains as well as for polyelectrolytes grafted to surfaces (polyelectrolyte brushes) and charged polymeric networks. In all cases, adding salt weakens the interaction considerably. We discuss the suggestion that the attractive force at low salinity originates from the asymmetry of interaction between charged polymer segments and charged patches on the surface of the protein globule. This can be explained if the attractive force is mainly due to a counterion release force, i.e., the polyelectrolyte chains become the multivalent counterions for the patches of opposite charge localized on the surface of the proteins. We review a selection of simple models that lead to semi-quantitative estimates of this force as the function of salt concentration.     

Interaction of similarly charged surfaces mediated by nanoparticles

We study the interaction between two like charged surfaces embedded in a solution of oppositely charged multivalent rod-like counterions.The counterions consist of two rigidly bonded point charges,each of valency Z.The strength of the electrostatic coupling increases with increasing surface charge density or valency of the charges.The system is analyzed by employing a self-consistent field theory,which treats the short and long range interactions of the counterions within different approximations.We find that in the weak coupling limit,the interactions are only repulsive.In the intermediate coupling regime,the multivalent rod-like counterions can mediate attractive interactions between the surfaces. For sufficiently long rods,bridging contributes to the attractive interaction.In the strong coupling limit,the charge correlations can contribute to the attractive interactions at short separations between the charged surfaces.Two minima can then appear in the force curve between surfaces.     

Water Structure and Phase Transition Near a Surface

This article concerns the density and orientational structure of water near uncharged (hydrophobic) and charged (hydrophilic) surfaces and the surface-induced phase transition accompanying a powerful, attractive surface force. Previously reported studies on the water structure using the integral equation theories and computer simulations are critically reviewed, and some controversial aspects are reexamined by additional calculations. Effects of the surface curvature and surface charge density on the structure are analyzed in detail. A new analysis is performed on the phase transition for water containing a trace amount of a hydrophobic component at surfaces. It is shown that the transition occurs even at charged surfaces and the attraction induced between surfaces predominates over the strong Coulombic repulsion at sufficiently small separations. At highly charged surfaces, however, the transition does not occur.     

Interactions between Adsorbed Layers of a Low Charge Density Cationic Polyelectrolyte on Mica in the Absence and Presence of Anionic Surfactant

Interactions between two negatively charged mica surfaces across aqueous solutions containing various amounts of a 10% charged cationic polyelectrolyte have been studied. It is found that the mica surface charge is neutralized when the polyelectrolyte is adsorbed from a 10–50 ppm aqueous solution. Consequently no electrostatic double-layer force is observed. Instead an attractive force acts between the surfaces in the distance regime 250–100 Å. We suggest that this attraction is caused by bridging. Additional adsorption takes place when the polyelectrolyte concentration is increased to 100 and 300 ppm, and a long-range repulsion develops. This repulsive force is both of electrostatic and steric origin. The polyelectrolyte layer adsorbed from a 50 ppm solution does not desorb when the polyelectrolyte solution is replaced with an aqueous polyelectrolyte-free solution. Injection of sodium dodecyl sulfate (SDS) into the measuring chamber to a concentration of about 0.01 CMC (8.3 × 10⁻⁵M) does not affect the adsorbed layers or the interaction forces. However, when the SDS concentration is increased to 0.02 CMC (0.166 mM) the adsorbed layer expands dramatically due to adsorption of SDS to the polyelectrolyte chains. The sudden swelling suggests a cooperative adsorption of SDS to the preadsorbed polyelectrolyte layer and that the critical aggregation concentration between the polyelectrolyte and SDS at the surface is about 0.02 CMC. The flocculation behavior of the polyelectrolyte in solution upon addition of SDS was also examined. It was found that 0.16–0.32 mol SDS/mol charged segments on the polyelectrolyte is enough to make the solution slightly turbid.     

Influence of charged intramolecular hydrogen bonds in weak polyelectrolytes: A Monte Carlo study of flexible and extendible polymeric chains in solution and near charged spheres

For weak polyelectrolytes, the interplay between pH, solvent properties, and polymer structure affects the amount of charges, their distribution, and hence their conformations via Coloumb repulsion. Attractive interactions can also develop between charged and neutral sites counteracting the expected Coulomb‐induced expansion. To gauge how such competition affects polyelectrolyte structure and ionization, the titration of a single polyelectrolyte chain, isolated or close to a charged sphere, mimicked with a novel many‐body potential model is simulated with Monte Carlo. Apart from showing a 10‐fold higher ionization than isolated monomers at low pH, interacting species contracted forming short‐range clusters of charged and neutral ionizable groups. The presence of a charged sphere synergically boosted both effects due to monomer interactions, forcing the chains to condense onto its surface at much lower pH. Structural properties, however, seem to be controlled only by the ionization degree despite the presence of the topological restraint represented by the spherical surface. Using Monte Carlo titration results, the equilibrium ionization of isolated chains is also estimated; the results evidence that even weak interactions can easily lead to a doubling of the total charge. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 650–663     

Adsorption of molecular brushes with polyelectrolyte backbones onto oppositely charged surfaces: a self-consistent field theory

The two-gradient version of the Scheutjens-Fleer self-consistent field (SF-SCF) theory is employed to model the interaction between a molecular bottle brush with a polyelectrolyte backbone and neutral hydrophilic side chains and an oppositely charged surface. Our system mimics graft-copolymers with a cationic main chain (among which poly( L-lysine)- graft-poly(ethylene glycol) (PLL- g-PEG) or poly( L-lysine)- graft-polyoxazoline are well-known examples) interacting with negatively charged (metal oxide) solid surfaces. We aim to analyze the copolymer-surface interaction patterns as a function of the molecular architecture parameters. Two regimes are investigated: First, we compute the effective interaction potential versus the distance from the surface for individual bottle brush macromolecules. Here, depending on the grafting ratio and the degree of polymerization of the side chains, the interplay of electrostatic attractions of the main chain to the surface and the steric repulsion of the grafts results in different patterns in the interaction potential and, therefore, in qualitatively different adsorption behavior. In particular, we demonstrate that, at high side chain grafting density and short grafts, the molecular brushes are strongly adsorbed electrostatically onto negatively charged substrates, whereas, in the opposite case of low grafting ratio and high molecular weight of grafts, the steric repulsion of the side chains from the surface dominates the polymer-surface interaction. At intermediate grafting ratios, the adsorption/depletion scenario depends essentially on the ratio between the electrostatic screening length and the thickness of the molecular bottle brush. We further have analyzed the equilibrium adsorbed amount as a function of the macromolecular architecture. Our results are based on a detailed account of attractive and repulsive (including intermolecular in-plane) interactions, and suggest a nonmonotonic dependence of the adsorbed amount on the grafting ratio, in good agreement with the experimental studies for PLL- g-PEG adsorption onto Nb2O5 surfaces. The results of the theoretical modeling are discussed in the context of the optimization of the PLL-g-PEG molecular design parameters in order to create protein-resistant surfaces.     

Molecular dynamics simulations of polyelectrolyte-polyampholyte complexes. Effect of solvent quality and salt concentration

Complexation between polyelectrolyte and polyampholyte chains in poor solvent conditions for the polyelectrolyte backbone has been studied by molecular dynamics simulations. In a poor solvent a polyelectrolyte forms a necklace-like structure consisting of polymeric globules (beads) connected by strings of monomers. The simulation results can be explained by assuming the existence of two different mechanisms leading to the necklace formation. In the case of weak electrostatic interactions, the necklace formation is driven by optimization of short-range monomer-monomer attraction and electrostatic repulsion between charged monomers on the polymer backbone. In the case of strong electrostatic interactions, the necklace structure appears as a result of counterion condensation. While the short-range attractions between monomers are still important, the correlation-induced attraction between condensed counterions and charged monomers and electrostatic repulsion between uncompensated charges provide significant contribution to optimization of the necklace structure. Upon forming a complex with both random and diblock polyampholytes, a polyelectrolyte chain changes its necklace conformation by forming one huge bead. The collapse of the polyelectrolyte chain occurs due to the neutralization of the polyelectrolyte charge by polyampholytes. In the case of the random polyampholyte, the more positively charged sections of the chain mix with negatively charged polyelectrolyte forming the globular bead while more negatively charged chain sections form loops surrounding the collapsed core of the aggregate. In the case of diblock polyampholyte, the positively charged block, a part of the negatively charged block, and a polyelectrolyte chain form a core of the aggregate with a substantial section of the negatively charged block sticking out from the collapsed core of the aggregate. In both cases the core of the aggregate has a layered structure that is characterized by the variations in the excess of concentration of monomers belonging to polyampholyte and polyelectrolyte chains throughout the core radius. These structures appear as a result of optimization of the net electrostatic energy of the complex and short-range attractive interactions between monomers of the polyelectrolyte chain.     

Adsorption of Polyelectrolyte-Nanoparticle Systems on Silica: Influence on Interaction Forces

In this work, we have studied the interfacial properties of cationic polyelectrolyte (PE) and silica nanoparticle (NP) systems at macroscopic silica surfaces by means of ellipsometry. The influence of adsorbed layers on the interactions between silica surfaces was also investigated using the bimorph surface force apparatus. Added nanoparticles were observed to strongly swell the interfacial polyelectrolyte layers, an effect partly related to neutralization of charged polyelectrolyte groups. The effect was more pronounced for low charged than for highly charged polyelectrolytes. Overall, the presence of nanoparticles seemed to increase the repulsive interaction measured between silica surfaces. The force measured on approach was long range and quite strongly repulsive. On separation, an attractive bridging interaction was measured for polyelectrolyte-covered surfaces. For the low charged polyelectrolyte used in the study, the force turned repulsive on addition of nanoparticles. For the highly charged polyelectrolyte used, a change from a very strong attraction (involving a jump of the surfaces out of contact) to a very long-range elastic attractive force was observed on adding nanoparticles. The long-range elastic force indicates that polymer chains and nanoparticles form a transient network in the gap between the surfaces. The observed difference in the outward force curves may explain why the addition of nanoparticles appears to improve, e.g., shear-resistance and reflocculation characteristics of polymeric flocculants. 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.     

Surface forces mediated by charged polymers: effects of intrinsic chain stiffness

The strength and range of surface forces in a system consisting of charged polymers with variable intramolecular stiffness confined between two charged planar surfaces have been investigated by Monte Carlo simulations. The negatively charged surfaces are neutralized by polymers carrying charges of opposite sign. Introducing the intermediate intrinsic stiffness of the chains gives rise to a weaker, but more long-ranged attraction between the surfaces. In the limit of infinitely stiff chains, this bridging attraction is lost, but it is replaced by a strong correlation attraction at short distances. Comparisons with predictions by a correlation-corrected polyelectrolyte Poisson-Boltzmann theory are made. The theory predicts surface attractions that are somewhat too weak, but all qualitative features are correctly reproduced. Given the crudeness of the model, the quantitative agreement is satisfactory.     

A theoretical investigation on the pH-induced switching of mixed polyelectrolyte brushes

A theoretical investigation on the pH-induced switching of mixed polyelectrolyte brushes was performed by using a molecular theory. The results indicate that the switching properties of mixed polyelectrolyte brushes are dependent on the pH values. At low pH, negatively charged chains adopt a compact conformation on the bottom of the brush while positively charged chains are highly stretched away from the surface. At high pH values, the inverse transformation takes place. The role of pH determining the polymer chains conformation and charge behavior of mixed polyelectrolyte brushes was analyzed. It is found that there exists a mechanism for reducing strong electrostatic repulsions： stretching of the chains. The H＋ and OH- units play a more important role as counterions of the charged polymers do. The collapse of the polyelectrolyte chains for different pH values could be attributed to the screening of the electrostatic interactions and the counterion-mediated attractive interaction along the chains.     

Experimental and theoretical evidence of overcharging of calcium silicate hydrate

Electrokinetic measurements such as electrophoresis may show an inversion of the effective surface charge of colloidal particle called overcharging. This phenomenon has been studied by various theoretical approaches but up to now very few attempts of confrontation between theory and experiment have been conducted. In this work we report electrophoretic measurements as well as Monte Carlo simulations of the electrokinetic potential for the surface of calcium silicate hydrate (CSH), which is the major constituent of hydrated cement. In the simulations, the surface charge of CSH nanoparticles in equilibrium with the ionic solution is determined by a single site characteristic and electrostatic interactions between all explicit charges at the surface and in the electric double layer. We will show that ordinary electrostatic interactions are enough to describe all experimental observations. Actually, an excellent agreement is found between experimental and simulated results without any fitting parameter, both with respect to surface titration and electrokinetic behaviour. The agreement extends over a wide range of electrostatic coupling, from a weakly charged surface with mainly monovalent counter-ions to a highly charged one with divalent counter-ions.     

Brownian dynamics simulations of polyelectrolyte adsorption in shear flow: effects of solvent quality and charge patterning

We probe the effects of solvent quality and charge patterning on polyelectrolyte adsorption in shear flow using Brownian dynamics simulations with hydrodynamic interaction (HI). The polyelectrolyte is modeled as a freely jointed bead-rod chain, and electrostatic and non-electrostatic interactions are accounted for by using screened Coulombic and Lennard-Jones potentials, respectively. In the absence of flow, the conformation of a polyelectrolyte molecule adsorbed onto a uniformly charged surface changes from flat to globular with an increase in bead-bead attraction (hydrophobicity), consistent with prior experimental observations. In the presence of flow, migration due to bead-wall HI and, as a consequence, desorption decrease with an increase in bead-bead attraction, implying that flow-induced desorption is more difficult under poor-solvent conditions. When bead-bead non-electrostatic attraction is strong, desorption can be enhanced by increasing bead-bead electrostatic repulsion. Analogous to the effect of bead-surface electrostatic attraction, an increase in the strength of bead-surface non-electrostatic attraction reduces desorption. We also study the effect of shear flow on the adsorption of a polyelectrolyte molecule onto surfaces decorated with periodic arrays of charged patches. An increase in patch periodicity increases desorption even when the effective surface charge density is kept the same. The results of this work suggest mechanisms for controlling the desorption of polyelectrolyte molecules in shear flows.     

Molecular dynamics simulations of multilayer polyelectrolyte films: effect of electrostatic and short-range interactions

The effect of the strength of electrostatic and short-range interactions on the multilayer assembly of oppositely charged polyelectrolytes at a charged substrate was studied by molecular dynamics simulations. The multilayer buildup was achieved through sequential adsorption of charged polymers in a layer-by-layer fashion from dilute polyelectrolyte solutions. The strong electrostatic attraction between oppositely charged polyelectrolytes at each deposition step is a driving force behind the multilayer growth. Our simulations have shown that a charge reversal after each deposition step is critical for steady multilayer growth and that there is a linear increase in polymer surface coverage after the first few deposition steps. Furthermore, there is substantial intermixing between chains adsorbed during different deposition steps. We show that the polymer surface coverage and multilayer structure are each strongly influenced by the strength of electrostatic and short-range interactions.     

Brownian dynamics simulations of polyelectrolyte adsorption onto charged patterned surfaces

The adsorption of single polyelectrolyte molecules onto surfaces decorated with periodic arrays of charged patches was studied using Brownian dynamics simulations. A free-draining, freely jointed bead-rod chain was used to model the polyelectrolyte, and electrostatic interactions were incorporated using a screened Coulombic potential with the excluded volume accounted for by a hard-sphere potential. The simulations predicted that the polyelectrolyte lies close to the adsorbing surface if the patch length, surface charge density, and screening length are sufficiently large. Chain conformations were found to be very sensitive to patch length, patch spacing, and the nature of the charge on adjacent patches. This is due both to the size of the polymer relative to patch length and spacing and to the structure of the electric field near the surface. In some cases, the component of the radius of gyration parallel to the surface can be made smaller than its free-solution value, which is contrary to what is observed for a uniformly charged surface. Isolated charged patches were also considered, and significant adsorption was observed above a critical surface charge density. The results demonstrate how polyelectrolyte conformations can be controlled by the design of the charged patches and may be useful for applications in which adsorbed polyelectrolyte films play a key role.