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.     

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.     

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.     

Interaction of micrometer-scale particles with nanotextured surfaces in shear flow

Dynamic particle adhesion from flow over collecting surfaces with nanoscale heterogeneity occurs in important natural systems and current technologies. Accurate modeling and prediction of the dynamics of particles interacting with such surfaces will facilitate their use in applications for sensing, separating, and sorting colloidal-scale objects. In this paper, the interaction of micrometer-scale particles with electrostatically heterogeneous surfaces is analyzed. The deposited polymeric patches that provide the charge heterogeneity in experiments are modeled as 11-nm disks randomly distributed on a planar surface. A novel technique based on surface discretization is introduced to facilitate computation of the colloidal interactions between a particle and the heterogeneous surface based on expressions for parallel plates. Combining these interactions with hydrodynamic forces and torques on a particle in a low Reynolds number shear flow allows particle dynamics to be computed for varying net surface coverage. Spatial fluctuations in the local surface density of the deposited patches are shown responsible for the dynamic adhesion phenomena observed experimentally, including particle capture on a net-repulsive surface.     

Effect of the surface charge discretization on electric double layers: a Monte Carlo simulation study

The structure of the electric double layer in contact with discrete and continuously charged planar surfaces is studied within the framework of the primitive model through Monte Carlo simulations. Three different discretization models are considered together with the case of uniform distribution. The effect of discreteness is analyzed in terms of charge density profiles. For point surface groups, a complete equivalence with the situation of uniformly distributed charge is found if profiles are exclusively analyzed as a function of the distance to the charged surface. However, some differences are observed moving parallel to the surface. Significant discrepancies with approaches that do not account for discreteness are reported if charge sites of finite size placed on the surface are considered.     

Parametric representation of molecular surfaces

This article is dedicated to the computation of a parametric representation of solvent excluded surfaces and isosurfaces by smooth four-sided patches. Such surface representations allow for the isoparametric discretization of the boundary integral equations which arise from solvation continuum models. Thus, higher-order ansatz functions can be applied in the boundary element method that is commonly used to solve the underlying equations, yielding a more accurate approximation of the sought apparent surface charge. Numerical results are reported to illustrate the approach.     

Particle capture via discrete binding elements: systematic variations in binding energy for randomly distributed nanoscale surface features

This work examines how the binding strength of surface-immobilized "stickers" (representative of receptors or, in nonbiological systems, chemical heterogeneities) influences the adhesion between surfaces that are otherwise repulsive. The study focuses on a series of surfaces designed with fixed average adhesive energy per unit area and demonstrates quantitatively how a redistribution of the adhesive functionality into progressively larger clusters (stronger stickers) increases the probability of adhesive events. The work employs an electrostatic model system: relatively uniform, negative 1 μm silica spheres flow gently over negative silica flats. The flats contain small amounts of randomly positioned nanoscale cationic patches. The silica-silica interaction is repulsive; however, the cationic patches (present at sufficiently low levels that the overall surface charge remains substantially negative) produce local attractions. In this study, the attractions are relatively weak so that multiple patches engage to capture flowing particles. Experiments reveal an adhesion signature characteristic of a renormalized random distribution when the sticker strength is increased at an overall fixed binding strength per unit area of surface. The form of the particle capture curves are in good quantitative agreement with a simple model that assumes only a fixed adhesion energy needed for particle capture. Aside from the quantitative details that provide a simple formalism for anticipating particle adhesion, this work demonstrates how increasing the heterogeneities in the surface functionality can cause a system to go from being nonadhesive to becoming strongly adhesive. Indeed, systems containing small amounts of discretized adhesive functionality are always more adhesive than systems in which the same functionality is distributed uniformly over the surface (the mean field scenario).     

Protein-coated beta-ferric hydrous oxide particles. An electrokinetic and electrooptic study

Using microelectrophoresis and electric light scattering techniques, we investigated the adsorption characteristics, surface coverage and surface electric parameters of superstructures from two isoforms of plastocyanin, PCa and PCb, in an oxidized state adsorbed on beta-ferric hydrous oxide particles. The surface electric charge and electric dipole moments of the composite particles and the thickness of the protein adsorption layer are determined in a wide pH range, at different ionic strengths and concentration ratios of PC to beta-FeOOH. The adsorption of the two proteins was found to shift the particles' isoelectric point and to alter the total electric charge and the electric dipole moments of the oxide particles to different extent. A "reversal" in the direction of the permanent dipole moment is observed at lower pH for PCb- than for PCa-coated oxide particles. Strict correlation is found between the changes in the electrokinetic charge of the composite particles and the variation in their "permanent" dipole moments. Data suggest that the adsorption of the proteins is driven by electrostatic and/or hydrophobic interactions with the oxide surfaces dependent on pH. The adsorption behaviour is consistent with the involvement of the "eastern" and "northern" patches of the plastocyanin molecules in their adsorption on the oxide surfaces that are differently charged depending on pH.     

On the mechanism of uptake of globular proteins by polyelectrolyte brushes: a two-gradient self-consistent field analysis

We present model calculations for the interaction of a protein-like inhomogeneously charged nanoscale object with a layer of densely grafted polyelectrolytes ("polyelectrolyte brush"). The motivation of this work is the recent experimental observation that proteins that carry an overall negative charge are absorbed into negatively charged polyelectrolyte brushes. Two-gradient self-consistent field (2G-SCF) calculations have been performed to unravel the physical mechanism of the uptake of protein thus effected. Our results prove that an overall neutral, protein-like object can electrostatically be attracted and therefore spontaneously driven into a polyelectrolyte brush when the object has two faces (patches, domains), one with a permanent positive charge and the other with a permanent negative charge. Using a 2G-SCF analysis, we evaluate the free energy of insertion, such that the electric dipole of the inclusion is oriented parallel to the brush surface. An electroneutral protein-like object is attracted into the brush because the polyelectrolyte brush interacts asymmetrically with the charged patches of opposite sign. At high ionic strength and low charge density on the patches, the attraction cannot compete with the repulsive excluded-volume interaction. However, for low ionic strengths and sufficiently high charge density on the patches, a gain on the order of k(B)T per charge becomes possible. Hence, the asymmetry of interaction for patches of different charges may result in a total attractive force between the protein and the brush. All results obtained herein are in excellent agreement with recent experimental data.     

Equilibrium domains on heterogeneously charged surfaces

Recent experiments have shown that salt solutions containing surfaces with two oppositely charged species show stable, possibly equilibrium, structures with finite domain sizes. The short-range interactions between the two species would normally result in phase separation that is driven by the line tension with macroscopically large domains of each species. In this paper, we show that, when at least one of the charged species is mobile, finite domains can occur in equilibrium. The domain size is determined by a competition of the electrostatic free energy that promotes charge mixing and small domains, with the line tension that promotes macroscopic phase separation. We calculate the equilibrium patch size as a function of the surface charge and the concentration of dissolved monovalent salts in the bulk phase. An important finding is the prediction of a first-order transition from finite patches to macroscopic phase separation of the two charge species as the salt concentration is increased.     

Protein-coated β-ferric hydrous oxide particles: An electrokinetic and electrooptic study

Using microelectrophoresis and electric light scattering techniques, we investigated the adsorption characteristics, surface coverage and surface electric parameters of superstructures from two isoforms of plastocyanin, PCa and PCb, in an oxidized state adsorbed on β-ferric hydrous oxide particles. The surface electric charge and electric dipole moments of the composite particles and the thickness of the protein adsorption layer are determined in a wide pH range, at different ionic strengths and concentration ratios of PC to β-FeOOH. The adsorption of the two proteins was found to shift the particles’ isoelectric point and to alter the total electric charge and the electric dipole moments of the oxide particles to different extent. A “reversal” in the direction of the permanent dipole moment is observed at lower pH for PCb- than for PCa-coated oxide particles. Strict correlation is found between the changes in the electrokinetic charge of the composite particles and the variation in their “permanent” dipole moments. Data suggest that the adsorption of the proteins is driven by electrostatic and/or hydrophobic interactions with the oxide surfaces dependent on pH. The adsorption behaviour is consistent with the involvement of the “eastern” and “northern” patches of the plastocyanin molecules in their adsorption on the oxide surfaces that are differently charged depending on pH.     

A novel method of aligning molecules by local surface shape similarity

A novel shape-based method has been developed for overlaying a series of molecule surfaces into a common reference frame. The surfaces are represented by a set of circular patches of approximately constant curvature. Two molecules are overlaid using a clique-detection algorithm to find a set of patches in the two surfaces that correspond, and overlaying the molecules so that the similar patches on the two surfaces are coincident. The method is thus able to detect areas of local, rather than global, similarity. A consensus overlay for a group of molecules is performed by examining the scores of all pairwise overlays and performing a set of overlays with the highest scores. The utility of the method has been examined by comparing the overlaid and experimental configurations of 4 sets of molecules for which there are X-ray crystal structures of the molecules bound to a protein active site. Results for the overlays are generally encouraging. Of particular note is the correct prediction of the `reverse orientation' for ligands binding to human rhinovirus coat protein HRV14.     

Image charges and dispersion forces in electric double layers: the dependence of wall-wall interactions on salt concentration and surface charge density

The interaction pressure between two planar charged walls is calculated for a range of conditions. The diffuse electric double layers between the two wall surfaces are treated with ion-wall dispersion forces and ionic image charge interactions taken into account. Both these interactions are due to dielectric discontinuities at the surfaces. Ion-ion and ion-image charge correlations are explicitly included. The ion-wall dispersion interactions can give rise to appreciable ion specific effects, which are particularly strong when the counterions to the surfaces are highly polarizable. The mechanisms of these effects are investigated, and their influence on the net interaction pressure between the walls is studied for a range of surface charge densities, strengths of the anion-wall dispersion interaction and bulk electrolyte concentrations. When the strength of the anion-wall dipersion interaction is increased, the pressure generally becomes less repulsive (or more attractive) for positive surfaces. The opposite happens in general for negative surfaces but to a much lesser extent. The effects are largest for large surface charge densities and high electrolyte concentrations. The image charge interactions give rise to a considerable depletion attraction between the walls for low surface charge densities.     

A complete shape characterization for molecular charge densities represented by Gaussian-type functions

An algorithm for a detailed 3-D characterization of the shapes of molecular charge distributions is implemented, tested and applied for a family of AB₂ molecules. The characterization is performed by computing a number of topological invariants (“shape groups”) associated with a continuum of molecular surfaces: the complete family of all electronic isodensity contours for the given molecules. These shape groups (the homology groups of truncated surfaces derived from isodensity contours) depend continuously on two parameters: a density value defining the density contour, and a reference curvature value, to which the local curvatures of the isodensity contours are compared. The electronic charge distribution is modeled by means of Gaussian-type functions. The method employs an explicit form of the charge density function in order to compute the curvature properties for the molecular surfaces analytically, from which the shape groups are derived by the algorithm. No visual inspection is required for the characterization and comparison of shapes of molecular charge densities, as these are done algorithmically by the computer. However, visual inspection of the results of the shape analysis is a possible option. For a given molecule, in a given nuclear configuration, the technique provides a two-dimensional shape map, displaying the distribution of shape groups as a function of the local curvature and the level set value (the value of the charge density at the contour). The computer program GSHAPE performs the analysis of shape maps automatically. This feature makes it potentially useful in the context of computer-aided drug design, where unbiased, automated shape characterization methods are valuable tools. As examples, several two-dimensional shape maps for simple systems are discussed. The changes induced in these maps by a change in the nuclear geometry, as well as by the changes of the nuclear charge, are also analyzed. The method is applicable to large biomolecules of interest if charge density information is available.     

Nonleaching antibacterial glass surfaces via "Grafting Onto": the effect of the number of quaternary ammonium groups on biocidal activity

Antimicrobial surfaces were prepared using the "grafting onto" technique. Well-defined block copolymers containing poly(2-(dimethylamino)ethyl methacrylate) and poly(3-(trimethoxysilyl)propyl methacrylate) segments (PDMAEMA/PTMSPMA) and corresponding random copolymers were prepared via atom transfer radical polymerization (ATRP), followed by covalent attachment to a glass surface through reaction of the trimethoxysilyl groups with surface silanol groups. The density of quaternary ammonium (QA) groups available to bind small molecules in solution increased with polymer solution concentration and immobilization time. For the PDMAEMA 97- b-PTMSPMA xdiblock copolymers with a fixed length of PDMAEMA segment (degree of polymerization (DP) = 97) and varied lengths of PTMSPMA segments, maximal available surface charge was observed when the ratio of DP PDMAEMA to DP PTMSPMA was 5:1. The tertiary amino groups in immobilized PDMAEMA segments were reacted with ethyl bromide to form QA groups. Alternatively, block copolymers with prequaternized PDMAEMA segments were attached to surfaces. Biocidal activity of the surfaces with grafted polymers versus Escherichia coli ( E. coli) increased with the density of available QA units on the surface. The number of bacteria killed by the surface increased from 0.06 x 10(5) units/cm2 to 0.6 x 10(5) units/cm2, when the density of surface QA increased from 1.0 x 10(14) unit/cm2 to 6.0 x 10(14) unit/cm2. The killing efficiency of QA on all surfaces was similar with approximately 1 x 10(10) units of QA needed to kill one bacterium. The AFM analysis indicated that grafting onto the surface resulted in small patches of highly concentrated polymer. These patches appear to increase the killing efficiency as compared to surfaces prepared by grafting onto with the same average polymer density but with a uniform distribution.     

Numerical Calculation of the Electrostatic Potential Around an Ionic Micelle with Counter Ion Binding

A numerical solution of the nonlinear Poisson-Boltzmann equation (PBE) is presented for a system of spherical micelles with counterfoil binding. The approach investigates the following effects on ion micelle interactions, (i) total surface charge, (ii) competitions of different counter ions on micellar surfaces and (iii) surface potential determination. The theory is applied to interpret the ion activities in micellar solution as measured by ion-selective electrodes.     

Ordered adsorption of coagulation factor XII on negatively charged polymer surfaces probed by sum frequency generation vibrational spectroscopy

Electrostatic interactions between negatively charged polymer surfaces and factor XII (FXII), a blood coagulation factor, were investigated by sum frequency generation (SFG) vibrational spectroscopy, supplemented by several analytical techniques including attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR), quartz crystal microbalance (QCM), ζ-potential measurement, and chromogenic assay. A series of sulfonated polystyrenes (sPS) with different sulfonation levels were synthesized as model surfaces with different surface charge densities. SFG spectra collected from FXII adsorbed onto PS and sPS surfaces with different surface charge densities showed remarkable differences in spectral features and especially in spectral intensity. Chromogenic assay experiments showed that highly charged sPS surfaces induced FXII autoactivation. ATR-FTIR and QCM results indicated that adsorption amounts on the PS and sPS surfaces were similar even though the surface charge densities were different. No significant conformational change was observed from FXII adsorbed onto surfaces studied. Using theoretical calculations, the possible contribution from the third-order nonlinear optical effect induced by the surface electric field was evaluated, and it was found to be unable to yield the SFG signal enhancement observed. Therefore it was concluded that the adsorbed FXII orientation and ordering were the main reasons for the remarkable SFG amide I signal increase on sPS surfaces. These investigations indicate that negatively charged surfaces facilitate or induce FXII autoactivation on the molecular level by imposing specific orientation and ordering on the adsorbed protein molecules. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

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.     

On the HSAB based estimate of charge transfer between adsorbates and metal surfaces

The applicability of the HSAB based electron charge transfer parameter, ΔN, is analyzed for molecular and atomic adsorbates on metal surfaces by means of explicit DFT calculations. For molecular adsorbates ΔN gives reasonable trends of charge transfer if work function is used for electronegativity of metal surface. For this reason, calculated work functions of low Miller index surfaces for 11 different metals are reported. As for reactive atomic adsorbates, e.g., N, O, and Cl, the charge transfer is proportional to the adatom valence times the electronegativity difference between the metal surface and the adatom, where the electronegativity of metal is represented by a linear combination of atomic Mulliken electronegativity and the work function of metal surface. It is further shown that the adatom-metal bond strength is linearly proportional to the metal-to-adatom charge transfer thus making the ΔN parameter a useful indicator to anticipate the corresponding adsorption energy trends.     

End effects for a rodlike polyelectrolyte molecule in salt solution

Electrostatic potentials around a single rodlike polyelectrolyte molecule are calculated by solving the nonlinear Poisson–Boltzmann equation numerically in the presence of externally added salt. The polyion is regarded as a cylinder with a finite length whose side surface is uniformly charged and end surfaces uncharged. The calculations show that the distance to which end effects extend is about half the Debye screening length and is almost independent of the surface charge density and concentration of added salt. For a long polyion whose length is much greater than the Debye length, the end effects can be neglected even for a polyelectrolyte with high surface charges, whereas they play an important role for a short polyion with a length of the same order as the Debye length. In addition, a strong charge condensation is found in the direction of the axis of the cylinder for a long polyion.