Polyelectrolyte adsorption on solid surfaces: theoretical predictions and experimental measurements.

This work utilizes a combination of theory and experiments to explore the adsorption of two different cationic polyelectrolytes onto oppositely charged silica surfaces at pH 9. Both polymers, poly(diallyldimethylammonium chloride), PDADMAC, and poly(4-vinyl N-methylpyridinium iodide), PVNP, are highly charged and highly soluble in water. Another important aspect is that a silica surface carries a relatively high surface charge density at this pH level. This means that we have specifically chosen to investigate adsorption under conditions where electrostatics can be expected to dominate the interactions. Of specific focus in this work is the response of the adsorption to the addition of simple salt (i.e., a process where electrostatics is gradually screened out). Theoretical predictions from a recently developed correlation-corrected classical density functional theory for polyelectrolytes are evaluated by direct quantitative comparisons with corresponding experimental data, as obtained by ellipsometry measurements. We find that, at low concentrations of simple salt, the adsorption increases with ionic strength, reaching a maximum at intermediate levels (about 200 mM). The adsorption then drops but retains a finite level even at very high salt concentrations, indicating the presence of nonelectrostatic contributions to the adsorption. In the theoretical treatment, the strength of this relatively modest but otherwise largely unknown nonelectrostatic surface affinity was estimated by matching predicted and experimental slopes of adsorption curves at high ionic strength. Given these estimates for the nonelectrostatic part, experimental adsorption data are essentially captured with quantitative accuracy by the classical density functional theory.

Monte Carlo simulations of parallel charged platelets as an approach to tactoid formation in clay.

The free energy of interaction between parallel charged platelets with divalent counterions has been calculated using Monte Carlo simulations to investigate the electrostatic effects on aggregation. The platelets are primarily intended to represent clay particles. With divalent counterions, the free energy for two platelets or two tactoids (clusters of parallel platelets) shows a minimum at a short separation due to the attraction caused by ion-ion correlations. In a salt-free system, the free energy of interaction has a long-range repulsive tail beyond the minimum. The repulsion increases for tactoids with larger aggregation numbers, whereas the depth of the free-energy minimum is gradually reduced. For large enough aggregation numbers, the repulsion is dominating and the minimum is no longer a global free-energy minimum. This is an effect of the depletion of counterions free in solution (outside tactoids) as counterions and platelets aggregate into tactoids and the resulting redistribution of counterions in the system changes the effective interactions between platelets and tactoids. The difference in tactoid-tactoid interactions as a function of aggregation number can be removed by adding enough salt to mask the depletion. Adding salt also reduces the repulsive tail of the free energy of interaction and enhances the minimum. No dependence on the aggregation number suggests that an isodesmic model with a monotonically decaying distribution of aggregation numbers can be used to describe a clay system. This may help to explain the experimental observations of low average numbers of platelets in tactoids, although factors not included in the simulation model may also play an important role.

Monte Carlo simulations of Donnan equilibrium in cartilage.

23Na magnetic resonance imaging and the delayed gadolinium-enhanced magnetic resonance imaging methods to investigate cartilage can be used to determine the fixed charge density of cartilage. The methods give results that differ by a factor of 2. In this study, we use Monte Carlo simulations on a model system of cartilage and find that the difference originates from the Coulombic intermolecular interactions between the ions in the cartilage, and in the synovial fluid. Those interactions are neglected in the standard Donnan analysis that generally is adopted to evaluate magnetic resonance imaging data.

Anisotropic Interactions in Protein Mixtures: Self Assembly and Phase Behavior in Aqueous Solution.

Recent experimental studies show that oppositely charged proteins can self-assemble to form seemingly stable microspheres in aqueous salt solutions. We here use parallel tempering Monte Carlo simulations to study protein phase separation of lysozyme/α-lactalbumin mixtures and show that anisotropic electrostatic interactions are important for driving protein self-assembly. In both dilute and concentrated protein phases, the proteins strongly align according to their charge distribution. While this alignment can be greatly diminished by a single point mutation, phase separation is completely suppressed when neglecting electrostatic anisotropy. The results highlight the importance of subtle electrostatic interactions even in crowded biomolecular environments where other short-ranged forces are often thought to dominate.

Molecular evidence of stereo-specific lactoferrin dimers in solution.

Gathering experimental evidence suggests that bovine as well as human lactoferrin self-associate in aqueous solution. Still, a molecular level explanation is unavailable. Using force field based molecular modeling of the protein-protein interaction free energy we demonstrate (1) that lactoferrin forms highly stereo-specific dimers at neutral pH and (2) that the self-association is driven by a high charge complementarity across the contact surface of the proteins. Our theoretical predictions of dimer formation are verified by electrophoretic mobility and N-terminal sequence analysis on bovine lactoferrin.

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.

Phase behavior in suspensions of highly charged colloids.

Attractive interactions between like-charged aggregates (macromolecules, colloidal particles, or micelles) in solution due to electrostatic correlation effects are revisited. The associated phenomenon of phase separation in a colloidal solution of highly charged particles is directly observed in Monte Carlo simulations. We start with a simple, yet instructive, description of polarization effects in a "cloud" of counterions around a single charged aggregate and show how the ion-ion correlations can be mapped onto a classical analogue of the quantum-mechanical dispersion force. We then extend our treatment to the effective pair interaction between two such aggregates and provide an analysis of different interaction regimes, based on a simple coupling parameter. By computing the potential of mean force, we illustrate the physics behind the crossover between the regimes of pure repulsion and attraction with increasing counterion valency. Finally, we turn to semi grand NpT simulations of the corresponding bulk systems where mono- and multivalent ions can exchange with an external reservoir. Thus, the coagulation and phase separation phenomena, widely observed and used in real-life applications, are directly studied in these computer simulations.

Block polyelectrolytes and colloidal stability.

We simulate interactions between charged flat surfaces in the presence of block polymers, where the end blocks carry a charge opposite to the surfaces. Using a recently developed simulation technique, we allow full equilibrium, i.e. the chemical potential of the polyelectrolyte is retained as the separation is changed. In general, the block polyions will adsorb strongly enough to overcharge the surfaces. This results in a double layer repulsion at large separation, with a concomitant free energy barrier. At short separations, the surfaces are pulled together by bridging forces. We make some efforts to theoretically design the polymers to be efficient flocculants, i.e. minimize the free energy barrier and still allow for a long-ranged bridging attraction. Here, we also take into account the possibility of nonequilibrium circumstances, which may be relevant in practice. Our results suggest that short chains, with small charged end blocks and a (relatively speaking) long neutral mid block, are likely to promote rapid flocculation.

Simulating equilibrium surface forces in polymer solutions using a canonical grid method.

A new simulation method for nonuniform polymer solutions between planar surfaces at full chemical equilibrium is described. The technique uses a grid of points in a two-dimensional thermodynamic space, labeled by surface area and surface separations. Free energy differences between these points are determined via Bennett's optimized rates method in the canonical ensemble. Subsequently, loci of constant chemical potential are determined within the grid via simple numerical interpolation. In this way, a series of free energy versus separation curves are determined for a number of different chemical potentials. The method is applied to the case of hard sphere polymers between attractive surfaces, and its veracity is confirmed via comparisons with established alternative simulation techniques, namely, the grand canonical ensemble and isotension ensemble methods. The former method is shown to fail when the degree of polymerization is too large. An interesting interplay between repulsive steric interactions and attractive bridging forces occurs as the surface attraction and bulk monomer density are varied. This behavior is further explored using polymer density functional theory, which is shown to be in good agreement with the simulations. Our results are also discussed in light of recent self-consistent field calculations which correct the original deGennes results for infinitely long polymers. In particular, we look at the role of chain ends by investigating the behavior of ring polymers.

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.

Simulations and density functional calculations of surface forces in the presence of semiflexible polymers.

We simulate interactions between adsorbing and nonadsorbing surfaces immersed in solutions containing monodisperse semiflexible chains. Apart from the nature of the surfaces, we investigate responses to changes of the intrinsic chain stiffness, the degree of polymerization, and the bulk concentration. Our simulations display a sufficient accuracy and precision to reveal free-energy barriers that are small on a typical scale of surface force simulations, but still of the same order as the expected van der Waals interactions. Two different approaches have been tested: grand canonical simulations, improved by configurational-biased techniques, and a perturbation method utilizing the isotension ensemble. We find the former to be preferable when the surfaces are nonadsorbing, whereas the isotension approach is superior for calculations of interactions between adsorbing surfaces, especially if the polymers are stiff. We also compare our simulation results with predictions from several versions of polymer density functional theory. We find that a crucial aspect of these theories, in quantitative terms, is that they recognize that end monomers exclude more volume to the surrounding than inner ones do. Those theories provide satisfactorily accurate predictions, particularly when the surfaces are nonadsorbing.

Interactions between charged surfaces immersed in a polyelectrolyte solution.

With grand canonical simulations invoking a configurationally weighted scheme, we have calculated interactions between charged surfaces immersed in a polyelectrolyte solution. In contrast to previous simulations of such systems, we have imposed full equilibrium conditions (i.e., we have included diffusive equilibrium with a bulk solution). This has a profound impact on the resulting interactions: even at modest surface charge densities, oppositely charged chains will, at sufficiently large separations, adsorb strongly enough to overcompensate for the nominal surface charge. This phenomenon, known as charge inversion, generates a double-layer repulsion and a free-energy barrier. Simpler canonical approaches, where the chains are assumed to neutralize the surfaces perfectly, will not capture this stabilizing barrier. The barrier height increases with the length of the polyions. Interestingly enough, the separation at which the repulsion becomes attractive is independent of chain length. The short chains here are unable to reach across from one surface to the other. We therefore conclude that the transition to an attractive regime is not provided by the formation of such "intersurface" bridges. With long chains and at large separations, charge inversion displays decaying oscillatory behavior (i.e., the apparent surface charge switches sign once again). This is due to polyion packing effects. We have also investigated responses to salt addition and changes in polyelectrolyte concentration. Our results are in qualitative and semiquantitative agreement with experimental findings, although it should be noted that our chains are comparatively short, and the experimental surface charge density is poorly established.

Repulsion between oppositely charged surfaces in multivalent electrolytes.

In answer to recent experimental force measurements between oppositely charged surfaces we here reproduce the repulsion in the presence of multivalent salt using Monte Carlo simulations within the primitive model. Our osmotic pressure curves are in good agreement with experimental results. In contrast with Poisson-Boltzmann calculations, both repulsion and charge inversion are seen in the simulations. Repulsion is observed only for conditions under which there is charge inversion at large separations. However, in these cases, the repulsion is present also at intermediate separations, where there is no charge inversion. The charge inversion is thereby not the cause of the repulsion. Instead the repulsion appears to be an effect of the large amount of excess salt in the slit. Both phenomena, however, are closely linked and a consequence of ion-ion correlations, promoted by a strong electrostatic coupling.

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.

On the complexation of proteins and polyelectrolytes.

Both natural and synthetic polyelectrolytes form strong complexes with a variety of proteins. One peculiar phenomenon is that association can take place even when the protein and the polyelectrolyte carry the same charge. This has been interpreted as if the ion-dipole interaction can overcome the repulsive ion-ion interaction. On the basis of Monte Carlo simulations and perturbation theory, we propose a different explanation for the association, namely, charge regulation. We have investigated three different protein-polymer complexes and found that the induced ionization of amino acid residues due to the polyelectrolyte leads to a surprisingly strong attractive interaction between the protein and the polymer. The extra attraction from this charge-induced charge interaction can be several kT and is for the three cases studied here, lysozyme, alpha-lactalbumin, and beta-lactoglobulin, of the same magnitude or stronger than the ion-dipole interaction. The magnitude of the induced charge is governed by a response function, the protein charge capacitance Z2-Z2. This fluctuation term can easily be calculated in a simulation or measured in a titration experiment.

Enhanced protein adsorption due to charge regulation.

When a protein molecule approaches a charged surface, its protonation state can undergo dramatic changes due to the imposed electric potential. This has a large impact on adsorption strengths that may be enhanced by several kT. Using mesoscopic simulation techniques as well as analytical theories, we have investigated this regulation mechanism and demonstrate how it is influenced by salt concentration and solution pH. Using hisactophilin as a test case, we show how the binding to a lipid membrane is governed by small changes in pH and that this is intimately coupled to the charge regulation mechanism.

Surface forces in polymer fluids: a comparison between simulations and density functional theory.

A polymer density functional theory is evaluated in terms of its ability to predict interactions between large surfaces in a polymer fluid. Comparisons are made with results from simulations in an expanded isotension ensemble. The variation of the net surface-surface interaction with adsorption strength is examined. Cases where the monomers interact via a pure hard sphere potential are investigated, but we have also studied the effect of attractions between the monomers. In all cases, we obtain an almost quantitative agreement between the simulated results and the predictions from the polymer density functional theory.

Simulation of phase equilibria in lamellar surfactant systems.

The coexistence of two lamellar liquid crystalline phases has been investigated by means of Monte Carlo simulations. The surfaces of the negatively charged bilayers formed by the surfactant molecules are modeled as planar infinite walls with a uniform surface charge density. Water is treated as a dielectric continuum, and only electrostatic interactions are considered. The counterions are mono- and divalent point ions, and their ratio is allowed to vary. Monovalent counterions lead to a repulsive osmotic pressure at all separations, while an attractive region exists when the counterions are divalent. In the latter case, one would expect a phase separation to take place, although it is not observed experimentally due to the limited stability of the lamellar phase at high water content. In a system with mixed counterions, however, the osmotic pressure exhibits a van der Waals loop under such conditions that two phases can coexist. A phase diagram is constructed, and the agreement with experimental data is excellent.