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.     

Ion induced lamellar-lamellar phase transition in charged surfactant systems

We propose a model for the liquid-liquid (L(alpha)-->L(alpha(') )) phase transition observed in osmotic pressure measurements of certain charged lamellae-forming amphiphiles. The model free energy combines mean-field electrostatic and phenomenological nonelectrostatic interactions, while the number of dissociated counterions is treated as a variable degree of freedom that is determined self-consistently. The model, therefore, joins two well-known theories: the Poisson-Boltzmann theory for ionic solutions between charged lamellae and the Langmuir-Frumkin-Davies adsorption isotherm modified to account for charged adsorbing species. Minimizing the appropriate free energy for each interlamellar spacing, we find the ionic density profiles and the resulting osmotic pressure. While in the simple Poisson-Boltzmann theory the osmotic pressure isotherms are always smooth, we observe a discontinuous liquid-liquid phase transition when the Poisson-Boltzmann theory is self-consistently augmented by the Langmuir-Frumkin-Davies adsorption. This phase transition depends on the area per amphiphilic head group, as well as on nonelectrostatic interactions of the counterions with the lamellae and interactions between counterion-bound and counterion-dissociated surfactants. Coupling the lateral phase transition in the bilayer plane with electrostatic interactions in the bulk, our results offer a qualitative explanation for the existence of the L(alpha)-->L(alpha(') ) phase transition of didodecyldimethylammonium bromide (DDABr), but the transition's apparent absence for the chloride and the iodide homologs. More quantitative comparisons with experiment require better understanding of the microscopic basis of the phenomenological model parameters.     

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.     

Cylindrical cell model for the electrostatic free energy of polyelectrolyte complexes

Associative phase separation (complex coacervation) in a mixture of oppositely charged polyelectrolytes can lead to different types of (inter-)polyelectrolyte complexes (soluble micelles, macroscopic precipitation). In a previous report [Langmuir 2004, 20, 2785-2791], we presented a model for the electrostatic free energy change when (weakly charged) polyelectrolyte forms a homogeneous complex phase. The influence of ionization of the polymer on the electrostatic free energy of the complex was incorporated but the influence of complex density neglected. In the present effort, cylindrical cells are assumed around each polyelectrolyte chain in the complex, and on the basis of the Poisson-Boltzmann equation, the electrostatic free energy is calculated as a function of the complex density. After combination with Flory-Huggins mixing free energy terms and minimization of the total free energy, the equilibrium complex density is obtained, for a given ratio of polycations to polyanions in the complex. The analysis is used in an example calculation ofpolyelectrolyte film formation by alternatingly applying a polycation and a polyanion solution. The calculation suggests that the often observed exponential growth of a polyelectrolyte film when the polymer is weakly charged has a thermodynamic origin: the polyelectrolyte complex shifts repeatedly between two equilibrium states of different densities and compositions. However, when the polyelectrolytes are strongly charged the difference in the compositions between the two equilibrium states is very small, and exponential growth by an absorption mechanism is no longer possible.     

Deposition and wetting characteristics of polyelectrolyte multilayers on plasma-modified porous polyethylene

Hydrophilic and chemically reactive porous media were prepared by adsorbing functional polymers at the surface of sintered polyethylene membranes. Modification of the membrane was accomplished by first exposing the membrane to an oxygen glow discharge gas plasma to introduce an electrostatic charge at the membrane surfaces. Cationic polyelectrolyte polyethylenimine (PEI) was adsorbed from solution to the anionic-charged surface to form an adsorbed monolayer. The adsorption of a second anionic polyelectrolyte onto the PEI layer allows further modification of the membrane surface to form a polyelectrolyte-bilayer complex. The conformation and stability of the adsorbed monolayers and bilayers comprising the modified surface are probed as a function of the polymer structure, charge density, and solubility. Using X-ray photoelectron spectroscopy analysis, we demonstrate that the presence of the polyelectrolyte multilayers drastically increases the density and specificity of the functional groups at the surface, more than what can be achieved through the plasma modification alone. Also, using the wicking rate of deionized, distilled water through the porous membrane to gauge the interfacial energy of the modified surface, we show that the membrane wicking rate can be controlled by varying the chemistry of the adsorbing polyelectrolytes and, to a lesser extent, by adjusting the polarity or ionic strength of the polyelectrolyte solution.     

Poisson-Boltzmann theory of pH-sensitive (annealing) polyelectrolyte brush

We present a self-consistent field analytical theory of a polymer brush formed by weakly charged pH-sensitive (annealing) polyelectrolytes tethered to a solid-liquid interface and immersed in buffer solution of low molecular weight salt. We use the Poisson-Boltzmann framework, applied by us previously to polyelectrolyte (PE) brushes with quenched charge (Zhulina, E. B.; Borisov, O. V. J. Chem. Phys. 1997, 107, 5952). This approach allows for detailed analysis of the internal structure of annealing PE brush in terms of polymer density distribution, profiles of electrostatic potential and of local degree of chain ionization as a function of buffer ionic strength and pH without any assumptions on mobile ion distribution imposed in earlier scaling-type models. The presented analytical theory recovers all major asymptotic dependences for average brush properties predicted earlier. In particular, a nonmonotonic dependence of brush thickness on ionic strength and grafting density is confirmed and specified with accuracy of numerical coefficients including crossover regions. Moreover, the theory predicts qualitatively new effects, such as, e.g., disproportionation of tethered polyions into weakly charged concentrated proximal and strongly charged sparse distal brush domains at low salt and moderate grating densities. The presented results allow us to quantify responsive features of annealing PE brushes whose large-scale and local conformational properties can be manipulated by external stimuli.     

THEORETICAL MODELING OF IONIC SURFACTANT ADSORPTION ON MINERAL OXIDE SURFACES

A model for the adsorption of ionic surfactants on oppositely charged solid surfaces of uniform charge density is developed. The model is based on the assumption that, on the solid surface, adsorbed surfactant monomers, monolayered and bilayered surfactant aggregates of different sizes and specifically adsorbing ions of added electrolyte constitute a mixture of hard discs. It means that only excluded area interactions between the surface discs are taken into account. To avoid a rapid two-dimensional condensation of the adsorbed surfactant the potential energy per molecule in the surface aggregates, which is a sum of chemical and electrostatic interactions, is assumed to decrease linearly with the increasing aggregate size. The electrostatic interactions of ionic species with the charged solid surface are described in terms of the Guy-Chapman theory of the double layer formation. The appropriate equations for adsorption isotherms of surfactant and electrolyte ions are derived and used to predict the experimental adsorption isotherms of DTAB on the precipitated silica at two different salt concentrations in the aqueous solution, On the basis of the obtained results the evolution of the adsorbed phase structure and the charge of silica particles with an increasing surface coverage is discussed.     

Theory of polyelectrolyte adsorption onto surfaces patterned with charge and topography

Mean-field theory is used to derive criteria for the adsorption of a weakly charged polyelectrolyte molecule from salt solution onto surfaces patterned with charge and topography. For flat surfaces patterned with periodic arrays of charged patches, the adsorbed layer thickness predicted using mean-field theory and that found by Brownian dynamics simulations are in quantitative agreement in the strong-adsorption regime, which corresponds to sufficiently small kappa or sufficiently large |sigma(eff)q|, where kappa is the inverse Debye screening length, sigma(eff) is an effective surface charge density, and q is the charge on each segment of the polyelectrolyte. Qualitative agreement is obtained in the weak-adsorption regime, and for the case where surfaces are patterned with both charge and topography. For uniformly charged, sinusoidally corrugated surfaces, the theory predicts that the critical temperature required for adsorption can be greater than or less than the corresponding value for a flat surface depending on the relative values of kappa and the corrugation wave number. If the surface charge is also allowed to vary sinusoidally, then adsorption is predicted to occur only when the topography crests have a surface charge opposite to that of the polyelectrolyte. Surfaces patterned with rectangular indentations having charged bottoms which are separated by flat charged plateaus are investigated as well. Adsorption is predicted to occur even when the net surface charge is zero, provided that the plateaus have a charge opposite to that of the polyelectrolyte. If the charge on the plateaus and polyelectrolyte is the same, adsorption may still occur if electrostatic attraction from the indentation bottoms is sufficiently strong.     

Ionic effects in collapse of polyelectrolyte brushes

We investigated the effect of counterion valence on the structure and swelling behavior of polyelectrolyte brushes using a nonlocal density functional theory that accounts for the excluded-volume effects of all ionic species and intrachain and electrostatic correlations. It was shown that charge correlation in the presence of multivalent counterions results in collapse of a polyelectrolyte brush at an intermediate polyion grafting density. At high grafting density, the brush reswells in a way similar to that in a monovalent ionic solution. In the presence of multivalent counterions, the nonmonotonic swelling of a polyelectrolyte brush in response to the increase of the grafting density can be attributed to a competition of the counterion-mediated electrostatic attraction between polyions with the excluded-volume effect of all ionic species. While a polyelectrolyte brush exhibits an "osmotic brush" regime at low salt concentration and a "salted brush" regime at high salt concentration regardless of the counterion valence, we found a smoother transition as the valence of the counterions increases. As observed in recent experiments, a quasi-power-law dependence of the brush thickness on the concentration ratio can be identified when the monovalent counterions are replaced with trivalent counterions at a fixed ionic strength.     

A modified Poisson-Boltzmann model including charge regulation for the adsorption of ionizable polyelectrolytes to charged interfaces, applied to lysozyme adsorption on silica

The equilibrium adsorption of polyelectrolytes with multiple types of ionizable groups is described using a modified Poisson-Boltzmann equation including charge regulation of both the polymer and the interface. A one-dimensional mean-field model is used in which the electrostatic potential is assumed constant in the lateral direction parallel to the surface. The electrostatic potential and ionization degrees of the different ionizable groups are calculated as function of the distance from the surface after which the electric and chemical contributions to the free energy are obtained. The various interactions between small ions, surface and polyelectrolyte are self-consistently considered in the model, such as the increase in charge of polyelectrolyte and surface upon adsorption as well as the displacement of small ions and the decrease of permittivity. These interactions may lead to complex dependencies of the adsorbed amount of polyelectrolyte on pH, ionic strength, and properties of the polymer (volume, permittivity, number, and type of ionizable groups) and of the surface (number of ionizable groups, pK, Stern capacity). For the adsorption of lysozyme on silica, the model qualitatively describes the gradual increase of adsorbed amount with pH up to a maximum value at pHc, which is below the iso-electric point, as well as the sharp decrease of adsorbed amount beyond pHc. With increasing ionic strength the adsorbed amount decreases (for pH > pHc), and pHc shifts to lower values.     

The relationship between polymer/substrate charge density and charge overcompensation by adsorbed polyelectrolyte layers

This work examines polyelectrolyte adsorption (exclusively driven by electrostatic attractions) for a model system (DMAEMA, polydimethylaminoethyl methacrylate, adsorbing onto silica) where the adsorbing polycation is more densely charged than the substrate. Variations in the relative charge densities of the polymer and substrate are accomplished by pH, and the polycation is of sufficiently low molecular weight that the adsorbed conformation is generally flat under all conditions examined. We demonstrate, quantitatively, that the charge overcompensation observed on the isotherm plateau can be attributed to the denser positive charge on the adsorbing polycation and that the ultimate coverage obtained corresponds to the adsorption of one oligomer onto each original negative silica charge, when the silica charge is most sparse, at pH 6. This limiting behavior breaks down at higher pHs where the greater silica charge density accommodates single chains adsorbing onto multiple negative sites. As a result of the greater substrate charge density and reduced polycation charge at higher pHs, the extent of charge overcompensation diminishes while the coverage increases on the plateau of the isotherm. Ultimately at the highest pHs, a regime is approached where the coil's excluded surface area, not surface charge, limits the ultimate coverage. In addition to quantifying the crossover from the charge-limiting to the area-limiting behaviors, this paper quantitatively reports adsorption-induced changes in bound counterion density and ionization at the interface, which were generally found to be independent of coverage for this model system.     

Adsorption of polyelectrolyte modified graphene to silica surfaces: monolayers and multilayers

Exfoliated graphene particles stabilised by the cationic polyelectrolyte polyethyleneimine (PEI) were used in conjunction with an anionic polyelectrolyte, poly(acrylic acid), to construct multilayers using the layer-by-layer technique on a silica substrate. In the first adsorption step, the surface excess of the cationic graphene was dependent on the overall charge on the nanoparticle which in turn can be tuned through modifying solution pH as PEI has weakly ionisable charged amine groups. The adsorbed amount onto the silica surface increased as the solution pH increased. Subsequently, a layer of PAA was adsorbed on top of the cationic graphene through electrostatic interaction. The multilayer could be assembled through this alternate deposition, with the influence of solution conditions investigated. The pH of the adsorbing solutions was the chief determinant of the overall adsorbed amounts, with more mass added at the elevated pH of 9 in comparison with pH 4. Atomic force microscopy confirmed that the graphene particles were adsorbed to the silica interface and that the surface coverage of the disc-like nanoparticles was complete after the deposition of five graphene-polyelectrolyte bi-layers. Furthermore, the graphene nanoparticles themselves could be modified through the consecutive addition of the oppositely charged polymers. A multilayered assembly of negatively charged graphene sheets modified with a bi-layer of PEI and PAA was also deposited on a silica surface with adsorbed PEI.     

Strong and weak adsorptions of polyelectrolyte chains onto oppositely charged spheres

We investigate the complexation of long thin polyelectrolyte (PE) chains with oppositely charged spheres. In the limit of strong adsorption, when strongly charged PE chains adapt a definite wrapped conformation on the sphere surface, we analytically solve the linear Poisson-Boltzmann equation and calculate the electrostatic potential and the energy of the complex. We discuss some biological applications of the obtained results. For weak adsorption, when a flexible weakly charged PE chain is localized next to the sphere in solution, we solve the Edwards equation for PE conformations in the Hulthen potential, which is used as an approximation for the screened Debye-Huckel potential of the sphere. We predict the critical conditions for PE adsorption. We find that the critical sphere charge density exhibits a distinctively different dependence on the Debye screening length than for PE adsorption onto a flat surface. We compare our findings with experimental measurements on complexation of various PEs with oppositely charged colloidal particles. We also present some numerical results of the coupled Poisson-Boltzmann and self-consistent field equation for PE adsorption in an assembly of oppositely charged spheres.     

Polyelectrolyte–particle complex formation. Polyelectrolyte linear charge density and ionic concentration effects. Monte Carlo simulations

The influence of the linear charge density (LCD) of a polyelectrolyte on its adsorption on an oppositely charged colloidal particle is investigated by Monte Carlo simulations. Adsorption characteristics are studied at different linear charge densities and ionic concentrations and for a given polyelectrolyte/particle size ratio so that particle curvature has full effect. The isolated polyelectrolyte goes through a smooth transition from a collapsed structure to an extended rod-like conformation with increasing the linear charge density in the low ionic concentration regime. In the high ionic concentration regime, the polyelectrolyte is less sensitive to the increase in the linear charge density and adopts a coil conformation. We found that complex formation is promoted by decreasing the ionic concentration and increasing the linear charge density and that large changes in the polymer dimensions are observed at the adsorption-desorption limit. By adjusting the linear charge density and ionic strength, we demonstrate that the adsorption-desorption limit corresponds to a sharp transition from non-adsorbed to adsorbed conformations and that the mean adsorption energy per monomer has to be less than -0.4 kT to achieve adsorption. We calculated that the linear charge density at the adsorption-desorption limit is related to the Debye-Hückel length according to LCD^crit ~3². At small values of the linear charge density and low ionic strength (no adsorption is observed at high ionic strength), a large amount of monomers are present in loops and tails. By increasing LCD, the amount of monomers in trains reaches a maximum value and the polyelectrolyte adopt flat conformation at the surface of the particle.     

Mixed systems of hydrophobically modified polyelectrolytes: controlling rheology by charge and hydrophobe stoichiometry and interaction strength

Rheology and phase separation were investigated for aqueous mixtures of two oppositely charged hydrophobically modified polyelectrolytes. The typical phase separation, normally seen for oppositely charged polymer mixtures, is dramatically reduced by the presence of hydrophobic modification, and phase separation is only detected close to the point of charge neutralization. While the two polyelectrolytes separately can give high viscosities and a gel-like behavior, a pronounced maximum in viscosity and storage modulus with the mixing ratio of the polyelectrolytes is observed; the maximum is located between the points of charge and hydrophobe stoichiometry and reflects a combination of hydrophobic and electrostatic association. Lowering the charge density of the anionic polymer leads to a strengthened association at first, but at lower charge densities there is a weakened association due to the onset of phase separation. The strength of the electrostatic interaction was modified by adding salt. Increased ionic strength can lead to phase separation and to increased or decreased viscosity depending on the polyelectrolyte mixing ratio.     

Influence of the degree of ionization and molecular mass of weak polyelectrolytes on charging and stability behavior of oppositely charged colloidal particles

Positively charged amidine latex particles are studied in the presence of poly(acrylic acid) (PAA) with different molecular masses under neutral and acidic conditions by electrophoresis and time-resolved dynamic light scattering. Under neutral conditions, where PAA is highly charged, the system is governed by the charge reversal induced by the quantitatively adsorbing polyelectrolyte and attractive patch-charge interactions. Under acidic conditions, where PAA is more weakly charged, the following two effects come into play. First, the lateral structure of the adsorbed layers becomes more homogeneous, which weakens the attractive patch-charge interactions. Second, polyelectrolyte adsorption is no longer quantitative and partitioning into the solution phase is observed, especially for PAA of low molecular mass.     

Aqueous suspensions of natural swelling clay minerals. 1. Structure and electrostatic interactions

In this article, we present a general overview of the organization of colloidal charged clay particles in aqueous suspension by studying different natural samples with different structural charges and charge locations. Small-angle X-ray scattering experiments (SAXS) are first used to derive swelling laws that demonstrate the almost perfect exfoliation of clay sheets in suspension. Using a simple approach based on geometrical constraints, we show that these swelling laws can be fully modeled on the basis of morphological parameters only. The validity of this approach was further extended to other clay data from the literature, in particular, synthetic Laponite. For all of the investigated samples, experimental osmotic pressures can be properly described by a Poisson-Boltzmann approach for ionic strength up to 10(-3) M, which reveals that these systems are dominated by repulsive electrostatic interactions. However, a detailed analysis of the Poisson-Boltzmann treatment shows differences in the repulsive potential strength that are not directly linked to the structural charge of the minerals but rather to the charge location in the structure for tetrahedrally charged clays (beidellite and nontronites) undergoing stronger electrostatic repulsions than octahedrally charged samples (montmorillonites, laponite). Only minerals subjected to the strongest electrostatic repulsions present a true isotropic to nematic phase transition in their phase diagrams. The influence of ionic repulsions on the local order of clay platelets was then analyzed through a detailed investigation of the structure factors of the various clay samples. It appears that stronger electrostatic repulsions improve the liquidlike positional local order.     

Adsorption of poly(amido amine) (PAMAM) dendrimers on silica: importance of electrostatic three-body attraction

Adsorption of poly(amido amine) (PAMAM) dendrimers to silicon oxide surfaces was studied as a function of pH, ionic strength, and dendrimer generation. By combining optical reflectometry and atomic force microscopy (AFM), the adsorbed layers can be fully characterized and an unequivocal determination of the adsorbed mass becomes possible. For early stages, the adsorption process is transport limited and of first order with respect to the dendrimer solution concentration. For later stages, the surface saturates and the adsorbed dendrimers form loose but correlated liquidlike surface structures. This correlation is evidenced by a peak in the pair correlation function determined by AFM. The maximum adsorbed amount increases with increasing ionic strength and pH. The increase with the ionic strength is explained by the random sequential adsorption (RSA) model and electrostatic repulsion between the dendrimers. The adsorbing dendrimers interact by the repulsive screened Coulomb potential, whose range decreases with increasing ionic strength and thus leads to increasing adsorbed densities. The pH increase is interpreted as an effect of the substrate and is quantitatively explained by the extended three-body RSA model. This model stipulates the importance of a three-body interaction acting between two adsorbing dendrimers and the charged substrate. The presence of the charged substrate weakens the repulsion between the adsorbing dendrimers and thus leads to higher surface densities. This effect can be interpreted as an additional attractive three-body interaction, which acts in addition to the usual two-body repulsion and originates from the additional screening of the Coulomb repulsion by the counterions accumulating in the diffuse layer.