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.     

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.     

Diffusion of cationic polyelectrolytes into cellulosic fibers

The penetration of cationic polyelectrolytes into anionic cellulosic fibers was evaluated with fluorescent imaging techniques in order to clarify the mechanism and time scales for the diffusion process. The bulk charge of the cellulosic fibers indirectly creates a driving force for diffusion into the porous fiber wall, which is entropic in nature due to a release of counterions as the polyelectrolyte adsorbs. The individual bulk charges in the fiber cell wall also interact with the diffusing polyelectrolyte, such that the polyelectrolyte diffuses to the first available charge and consequently adsorbs and remains fixed. Thus, subsequent polyelectrolyte chains must first diffuse through the adsorbed polyelectrolyte layer before adsorbing to the next available bulk charges. This behavior differs from earlier suggested diffusion mechanisms, by which polyelectrolytes were assumed to first adsorb to the outermost surface and then reptate into the pore structure. The time scales for polyelectrolyte diffusion were highly dependent on the flexibility of the chain, which was estimated from calculations of the persistence length. The persistence length ultimately depended on the charge density and electrolyte concentration. The charge density of the polyelectrolyte had a greater influence on the time scales for diffusion. High charge density polyelectrolytes were observed to diffuse on a time scale of months, whereas the diffusion of low charge density polyelectrolytes was measured on the order of hours. An influence of the chain length, that is, steric interactions due the persistence length of the polyelectrolyte and to the tortuosity of the porous structure of the fiber wall, could only be noted for low charge density polyelectrolytes. Increasing the electrolyte concentration increased the chain flexibility by screening the electrostatic contribution to the persistence length, in turn inducing a faster diffusion process. However, a significant change in the diffusion behavior was observed at high electrolyte concentrations, at which the interaction between the polyelectrolyte charges and the fiber charges was almost completely screened.     

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.     

Brownian dynamics simulations of polyelectrolyte adsorption in shear flow

Brownian dynamics simulations are used to study the adsorption of an isolated polyelectrolyte molecule onto an oppositely charged flat surface in the absence and the presence of an imposed shear flow. The polyelectrolyte is modeled as a freely jointed bead-rod chain where excluded volume interactions are incorporated by using a hard-sphere potential. The total charge along the backbone is distributed uniformly among all the beads, and the beads are allowed to interact with one another and the charged surface through screened Coulombic interactions. The simulations are performed by placing the molecule a fixed distance above the surface, and the adsorption behavior is then studied as a function of screening length. In the absence of an imposed flow, the chain is found to lie flat and extended on the adsorbing surface in the limit of weak screening, whereas in the limit of strong screening it desorbs from the surface and attains free-solution behavior. For intermediate screening, only a small portion of the chain adsorbs and it becomes highly extended in the direction normal to the surface. An imposed shear flow tends to orient the chain in the direction of flow and also leads to increased contact of the chain with the surface.     

Conformation of poly(styrene sulfonate) layers physisorbed from high salt solution studied by force measurements on two different length scales

The conformation of poly(styrene sulfonate) (PSS) layers physisorbed from 1 M NaCl is determined by force measurements and imaging on two length scales. With colloidal probe technique steric forces as predicted for neutral grafted brushes are observed. On decrease and increase of the NaCl concentration, the grafting density remains constant, yet the brush thickness swells and shrinks reversibly with the salt concentration with an exponent of -0.3. At low salt conditions, the brush length amounts to 30% of the contour length, a behavior known for polyelectrolyte brushes and attributed to the entropy of the counterions trapped in the brush. Between a PSS layer and a pure colloidal silica sphere, the same steric forces are observed, and additionally at large separations (beyond the range of the steric repulsion) an electrostatic force is found. A negatively charged AFM tip penetrates the brush--a repulsive electrostatic force between the tip and surface is found, and single chains can be imaged. Thus, with the nanometer-sized AFM tip, the flatly adsorbed fraction of the PSS chains is seen, whereas the micrometer-sized colloidal probe interacts with the fraction of the chains penetrating into solution.     

Simulation of nonlinear shear rheology of dilute salt-free polyelectrolyte solutions

Brownian dynamics simulations are used to conduct a systematic analysis of the nonlinear shear rheology of dilute polyelectrolyte solutions, exploring its relationship to shear rate, Bjerrum length, and concentration. A simple coarse-grained bead-spring chain model that incorporates explicit counterions is used. It is found that the polyelectrolyte chains exhibit a shear thinning behavior at high shear rate (as characterized by bead Peclet number Pe) that is independent of the electrostatic strength due to the stripping of ions from close proximity to the chain caused by the flow. In contrast, at low values of Pe, the viscosity increases monotonically with increasing Bjerrum length over the range studied here, in contrast to the nonmonotonic trend displayed by the chain size. Furthermore, at fixed Bjerrum length, the reduced viscosity increases monotonically with concentration. The mechanism underlying these observations is essentially the primary electroviscous effect; the ion cloud surrounding a polyelectrolyte chain deforms in flow, causing a significant increase in viscosity as concentration increases. Finally, the authors have also considered the role of hydrodynamic interactions in these simulations, finding that for low concentration studies in shear flow, these do not qualitatively affect the results.     

Polyelectrolyte stars in planar confinement

We employ monomer-resolved molecular dynamics simulations and theoretical considerations to analyze the conformations of multiarm polyelectrolyte stars close to planar, uncharged walls. We identify three mechanisms that contribute to the emergence of a repulsive star-wall force, namely, the confinement of the counterions that are trapped in the star interior, the increase in electrostatic energy due to confinement as well as a novel mechanism arising from the compression of the stiff polyelectrolyte rods approaching the wall. The latter is not present in the case of interaction between two polyelectrolyte stars and is a direct consequence of the impenetrable character of the planar wall.     

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.     

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.     

Stress-Structure Relationship of the Reversible Associating Polymer Network under Start-up Shear Flow

We adopt Langevin dynamics to explore the stress-structure relationship of telechelic reversible associating polymer gel during startup shear flow, with shear strengths varying from Wi=12.6 to Wi=12640. At weak shear flow Wi=12.6, the shear stress proportionally increases with shear strain at short times, followed by a strain hardening behavior and then passes through a maximum(σmax, γmax) and finally decreases until it reaches the steady state. During the evolution of stress, the gel network is only slightly broken and essentially maintains its framework, and the strain hardening behavior originates from the excessive stretching of chains. On the other hand, the stress-strain curve at intermediate shear flow Wi=505.6 shows two differences from that at Wi=12.6, namely, the absence of strain hardening and a dramatic increase of stress at large strains,which is caused by the rupture of gel network at small strains and the network recovery at large strains, respectively. Finally, at very strong shear flow Wi=6319.7, the gel network is immediately broken by shear flow and the stress-strain curve exhibits similar behaviors to those of classical polymeric liquids.     

High elongation of polyelectrolyte chains in the osmotic limit of spherical polyelectrolyte brushes: a study by cryogenic transmission electron microscopy

We investigate the conformation of long polyelectrolyte chains attached to colloidal latex particles by cryogenic transmission electron microscopy (cryo-TEM). The dense grafting of the polyelectrolyte chains ("polyelectrolyte brush") leads to a confinement of the counterions and a concomitantly high osmotic pressure within the polyelectrolyte layer attached to the core particles. Cryo-TEM has provided first model-independent direct proof for the strong stretching of the polyelectrolyte chains by direct visualization. If salt is added, cryo-TEM clearly shows how chains collapse because of the strong screening of the electrostatic interaction. Moreover, the analysis of interacting particles by cryo-TEM shows that the polyelectrolyte chains retract at close contact. Hence, we demonstrate how cryo-TEM can be used to analyze directly the spatial structure of polyelectrolyte brushes in situ.     

Use of polyelectrolyte multilayer systems for membrane modification

Membranes with designed surface and filtration properties were prepared by the adsorption of polyelectrolyte multilayer systems on membrane surfaces using the layer-by-layer electrostatic self assembly (ESA) technique. Microfiltration membranes with a first polyelectrolyte layer grafted onto the surface showed excellent stability during filtration process. Although a twofold higher permeate flux was observed for a three-layer polyelectrolyte complex membrane compared to a just grafted one the protein retention did not change remarkably. Additionally, a reduced protein adsorption was detected for repulsive electrostatic forces between the substrate and the protein under applied conditions. Pervaporation membranes with an anionically functionalized polyamide-6 support or Nafion^®-117 support and a dense separating layer consisting of poly(acrylic acid) and poly(ethylenimine) were prepared. Those membranes were used to separate aqueous organic mixtures. Six double layers were sufficient to obtain membranes with high water permselectivity. Membranes with similar properties but a lower number of deposited layers were obtained, when the adsorption process was carried out at 80°C.     

Rheology of dilute polyelectrolyte solutions in narrow channels

The shear flow of dilute polyelectrolyte solutions bounded by either neutral or repulsive walls is modeled using a nonlinear dumbbell with conformation-dependent friction. Assuming that the configurational probability density function depends on the internal coordinates (r) and the distance of the center of mass of the molecule to the walls, coupled differential equations for the tensor moments <rr> are obtained. Coulombic repulsion between beads is considered to simulate the charge repulsion between ionized sites distributed along the backbone of a real polyelectrolyte. The repulsive interaction between the polyelectrolyte molecule and the charged walls is that of the DLVO model and the molecule is considered to be a charged sphere. Numerical solutions for the components of the tensor <rr> are worked out with the preaverage approach, and only when neutral walls considered are exact solutions obtained. Viscosity results show that in the limit of very wide channels, the corresponding viscosity in the bulk is obtained. The wall repulsion on the charged molecules produces migration of molecules towards the center of the channel resulting in a depleted layer with lower viscosity next to the walls. The calculated slip phenomenon using the method employed by Grisafi and Brunn is dependent on the beads repulsion and the shear rate. The slip velocity obtained with the Mooney method shows similarities with available experimental results for polyelectrolyte solutions. Birefringence calculations are performed in narrow and wide channels for different bead repulsions, with interesting results for both flexible and rigid molecules. Received: 26 September 1998 Accepted in revised form: 11 March 1999     

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.     

Wetting Films of the Aqueous Cationic Polyelectrolyte Solutions on Quartz

It was shown that the stability of the wetting films of aqueous cationic polyelectrolyte solutions on the flat quartz surface depends on solution concentration. At a low concentration, the films are stable owing to the electrostatic repulsive forces. At a high polyelectrolyte concentration, the films are unstable due to the hydrophobization of quartz and the appearance of the hydrophobic attractive forces in the films. In the intermediate concentration range, the films are metastable and their lifetime depends upon the competition between the electrostatic repulsive and hydrophobic attractive forces. Thus, the concentration of cationic polyelectrolyte substantially affects the wetting conditions of the quartz surface. This conclusion can also be extended to other solid surfaces negatively charged in aqueous solutions, which is inherent to the majority of natural materials.     

Brownian dynamics simulations of polyelectrolyte adsorption onto topographically patterned surfaces

The effect of patterned surface topography on the adsorption of single polyelectrolyte molecules is explored using Brownian dynamics simulations. The polyelectrolyte is modeled as a free-draining, freely jointed bead-rod chain, and electrostatic interactions are incorporated using a screened Coulombic potential with excluded volume interactions accounted for by the repulsive part of a Lennard-Jones potential. Topography consisting of periodically spaced valleys of square cross section separated by flat hills is considered. Chain conformations are characterized for a wide range of valley widths, depths, and spacings as well as for several different types of surface charge distributions. Depending on the parameter values describing the topography, the chains are found to adopt conformations ranging from flat and extended to those associated with bridge-, brush-, or semi-bridge-like structures. The formation of these structures is rationalized on the basis of a free-energy model that takes into account the increase in free energy due to entropic confinement, excluded volume interactions, and chain stretching as well as the decrease in free energy due to bead-surface electrostatic attraction. The results of this work are expected to be useful in designing patterned surface topography to control the conformations of adsorbed polyelectrolyte molecules.     

Structure of flexible and semiflexible polyelectrolyte chains in confined spaces of slit micro/nanochannels

Understanding the behavior of a polyelectrolyte in confined spaces has direct relevance in design and manipulation of microfluidic devices, as well as transport in living organisms. In this paper, a coarse-grained model of anionic semiflexible polyelectrolyte is applied, and its structure and dynamics are fully examined with Brownian dynamics (BD) simulations both in bulk solution and under confinement between two negatively charged parallel plates. The modeling is based on the nonlinear bead-spring discretization of a continuous chain with additional long-range electrostatic, Lennard-Jones, and hydrodynamic interactions between pairs of beads. The authors also consider the steric and electrostatic interactions between the bead and the confining wall. Relevant model parameters are determined from experimental rheology data on the anionic polysaccharide xanthan reported previously. For comparison, both flexible and semiflexible models are developed accompanying zero and finite intrinsic persistence lengths, respectively. The conformational changes of the polyelectrolyte chain induced by confinements and their dependence on the screening effect of the electrolyte solution are faithfully characterized with BD simulations. Depending on the intrinsic rigidity and the medium ionic strength, the polyelectrolyte can be classified as flexible, semiflexible, or rigid. Confined flexible and semiflexible chains exhibit a nonmonotonic variation in size, as measured by the radius of gyration and end-to-end distance, with changing slit width. For the semiflexible chain, this is coupled to the variations in long-range bond vector correlation. The rigid chain, realized at low ionic strength, does not have minima in size but exhibits a sigmoidal transition. The size of confined semiflexible and rigid polyelectrolytes can be well described by the wormlike chain model once the electrostatic effects are taken into account by the persistence length measured at long length scale.     

Interaction of dissolved proteins with spherical polyelectrolyte brushes

We consider the adsorption of bovine serum albumin (BSA) on spherical polyelectrolyte brushes (SPB). The SPB consist of a solid polystyrene core of 100nm diameter onto which linear polyelectrolyte chains (poly(acrylic acid), (PAA)) are grafted. The adsorption of BSA is studied at a pH of 6.1 at different concentrations of added salt and buffer (MES). We observe strong adsorption of BSA onto the SPB despite the effect that the particles as well as the dissolved BSA are charged negatively. The adsorption of BSA is strongest at low salt concentration and decreases drastically with increasing amounts of added salt. The adsorbed protein can be washed out again by raising the ionic strength. The various driving forces for the adsorption are discussed. It is demonstrated that the main driving force is located in the electrostatic interaction of the protein with the brush layer of the particles. All data show that the SPB present a new class of carrier particles whose interaction with proteins can be tuned in a well-defined manner.