Molecular dynamics simulations of polyelectrolyte brushes: from single chains to bundles of chains

Using molecular dynamics simulations in combination with scaling analysis, we have studied the effects of the solvent quality and the strength of the electrostatic interactions on the conformations of spherical polyelectrolyte brushes in salt-free solutions. The spherical polyelectrolyte brush could be in one of four conformations: (1) a star-like conformation, (2) a "star of bundles" conformation in which the polyelectrolyte chains self-assemble into pinned cylindrical micelles, (3) a micelle-like conformation with a dense core and charged corona, or (4) a conformation in which there is a thin polymeric layer uniformly covering the particle surface. These different brush conformations appear as a result of the fine interplay between electrostatic and monomer-monomer interactions. The brush thickness depends nonmonotonically on the value of the Bjerrum length. This dependence of the brush thickness is due to counterion condensation inside the brush volume. We have also established that bundle formation in poor solvent conditions for the polymer backbone can also occur in a planar polyelectrolyte brush. In this case, the grafted polyelectrolyte chains form hemispherical aggregates at low polymer grafting densities, cylindrical aggregates at an intermediate range of the grafting densities, and vertically oriented ribbon-like aggregates at high grafting densities.     

Surface friction of hydrogels with well-defined polyelectrolyte brushes

Hydrogels of poly(2-hydroxyethyl methacrylate) (PHEMA) with well-defined polyelectrolyte brushes of poly(sodium 4-styrenesulfonate) (PNaSS) of various molecular weights were synthesized, keeping the distance between the polymer brushes constant at ca. 20 nm. The effect of polyelectrolyte brush length on the sliding friction against a glass plate, an electrorepulsive solid substrate, was investigated in water in a velocity range of 7.5 x 10(-5) to 7.5 x 10(-2) m/s. It is found that the presence of polymer brush can dramatically reduce the friction when the polymer brushes are short. With an increase in the length of the polymer brush, this drag reduction effect only works at a low sliding velocity, and the gel with long polymer brushes even shows a higher friction than that of a normal network gel at a high sliding velocity. The strong polymer length and sliding velocity dependence indicate a dynamic mechanism of the polymer brush effect.     

Friction and normal interaction forces between irreversibly attached weakly charged polymer brushes

Polyelectrolyte brushes were built on mica by anchoring polystyrene-poly(acrylic acid) (PS-b-PAA) diblock copolymers at a controlled surface density in a polystyrene monolayer covalently attached to OH-activated mica surfaces. Compared to physisorbed polymer brushes, these irreversibly attached charged brushes allow the polymer grafting density to remain constant upon changes in environmental conditions (e.g., pH, salt concentration, compression, and shear). The normal interaction and friction forces as a function of surface separation distance and at different concentrations of added salt (NaCl) were investigated using a surface forces apparatus. The interaction force profiles were completely reversible both on loading and receding and were purely repulsive. For a constant polymer grafting density, the influence of the polyelectrolyte charges and the Debye screening effect on the overall interaction forces was investigated. The experimental interaction force profiles agree very well with scaling models developed for neutral and charged polymer brushes. The variation of the friction force between two PAA brushes in motion with respect to each other as a function of surface separation distance appeared to be similar to that observed with neutral brushes. This similarity suggests that the increase in friction is associated with an increase in mutual interpenetration upon compression as observed with neutral polymers. The effect of the PAA charges and added ions was more significant on the repulsive normal forces than on the friction forces. The reversible characteristics of the normal force profiles and friction measurements confirmed the strong attachment of the PAA brushes to the mica substrate. High friction coefficients (ca 0.3) were measured at relatively high pressures (40 atm) with no surface damage or polymer removal.     

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.     

Peptidic molecular brushes with enhanced chirality

Tethering oligopeptides through one end densely packed onto a linear polymer main chain will greatly reduce freedom of the peptide chains, which affords an easy access to investigate the secondary structure of peptides under constrained condition. Herein, molecular brushes with densely grafted monodispersed Cbz‐protected oligolysine were efficiently synthesized via free radical polymerization of the macromonomer‐bearing lysine octamer, and the secondary structures of the oligopeptide side chains in solutions were investigated. To examine the architecture effects on helical conformation, circular dichroism spectra from the polymer were compared with that from the corresponding macromonomer. To check the chemical structural effects on conformation of the oligopeptide, Cbz groups from the molecular brushes were deprotected, and the secondary structures of the polymers were compared before and after the deprotection. Conformation of the deprotected polymer was further explored by varying solution pH values. Complexation of the positively charged, deprotected polymer with anionic surfactant provides an alternative route to mediate the secondary structures of the short peptides in the constrained environment. It has been found that oligolysine side chains within the molecular brushes can adopt enhanced α‐helical conformation through the crowding structures or can form β‐sheet by hydrophobic interactions between the complexed surfactants. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Nanotribology of surface-grafted PEG layers in an aqueous environment

The lubrication properties of adsorbed poly(L-lysine)-graft-poly(ethylene glycol) in aqueous buffer solution were studied with the surface forces apparatus. In general, the polymer brushes revealed extremely low friction forces. Two distinct regimes could be identified. In response to lateral shear, the friction forces of intact polymer films at moderate loads were below the detection limit. At high loads, when the films were compressed to about 10% of the original equilibrium film thickness, the friction showed a reversible increase with load. Under certain conditions, film destruction was observed, immediately followed by a dramatic increase in the frictional force and an expansion of the adsorbed brush layer. By the addition of free polymer to the buffer solution, the resistance of the polymer brushes to abrasion was dramatically increased by readsorption of the polymer following friction-induced desorption. This self-healing capacity and the extremely low friction of the adsorbed copolymer films contribute to their excellent properties as lubricant additives for water-based lubrication under boundary conditions.     

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.     

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.     

Synthesis and swelling behavior of pH-responsive polybase brushes

We synthesize polybase brushes and investigate their swelling behavior. Poly(2-(dimethylamino)ethyl methacrylate)) (PDMAEMA) brushes are prepared by the "grafting from" method using surface-initiated Atom Transfer Radical Polymerization to obtain dense brushes with relatively monodisperse chains (PDI = 1.35). In situ quaternization reaction can be performed to obtain poly(2-(trimethylamino)ethyl methacrylate)) (PTMAEMA) brushes. We determine the swollen thickness of the brushes using ellipsometry and neutron reflectivity techniques. Brushes are submitted to different solvent conditions to be investigated as neutral brushes and weak and strong polyelectrolyte brushes. The swelling of the brushes is systematically compared to scaling models. It should be pointed out that the scaling analysis of different types of brushes (neutral polymer and weak and strong polyelectrolyte brushes) is performed with identical samples. The scaling behavior of the PDMAEMA brush in methanol and the PTMAEMA brush in water is in good agreement with the predicted scaling laws for a neutral polymer brush in a good solvent and a polyelectrolyte brush in the osmotic regime. The salt-induced contraction of the quaternized brush is observed for high salt concentration, in agreement with the predicted transition between the regimes of the osmotic brush and the salted brush. From the crossover concentration, we calculate the effective charge ratio of the brush following the Manning counterion condensation. We also use PDMAEMA brushes as pH-responsive polybase brushes. The swelling behavior of the polybase brush is intermediate with respect to the behavior of the neutral polymer brush in a good solvent and the behavior of the quenched polyelectrolyte brush, as expected. The effective charge ratio of the PDMAEMA brush is determined as a function of pH using the scaling law of the polyelectrolyte brush in the osmotic regime.     

Mesoscale simulations of the behavior of charged polymer brushes under normal compression and lateral shear forces

Dissipative particle dynamics (DPD) was used to investigate the behavior of two opposing end-grafted charged polymer brushes in aqueous media under normal compression and lateral shear. The effect of polymer molecular weight, degree of ionization, grafting density, ionic strength, and compression on the polymer conformation and the resulting shear force between the opposing polymer layers were investigated. The simulations were carried out for the poly(tert-butyl methacrylate)-block-poly(sodium sulfonate glycidyl methacrylate) copolymer, referred as PtBMA-b-PGMAS, end-attached to a hydrophobic surface for comparison with previous experimental data. Mutual interpenetration of the opposing end-grafted chains upon compression is negligible for highly charged polymer brushes for compression ratios ranging from 2.5 to 0.25. Under electrostatic screening effects or for weakly charged polymer brushes, a significant mutual interpenetration was measured. The variation of interpenetration thickness with separation distance, grafting density, and polymer size follows the same scaling law as the one observed for two opposing grafted neutral brushes in good solvent. However, compression between two opposing charged brushes results in less interpenetration relative to neutral brushes when considering equivalent grafting density and molecular weight. The friction coefficient between two opposing polymer-coated surfaces sliding past each other is shown to be directly correlated with the interpenetration thickness and more specifically to the number of polymer segments within the interpenetration layer.     

Structure and Surface Properties of High-density Polyelectrolyte Brushes at the Interface of Aqueous Solution

Zwitterionic and cationic polyelectrolyte brushes were prepared by surface-initiated atom transfer radical polymerization of 2-methacryloyloxy- ethyl phosphorylcholine (MPC) and 2-(N,N-dimethylamino)ethyl methacrylate (DMAEMA), respectively. The poly(DMAEMA) brush was treated with methyl iodide to form poly[2-(methacryloyloxy) ethyltrimethylammonium iodide] [poly(METAI)]. The effects of ionic strength on brush structure and surface properties of densely grafted polyelectrolyte brushes were analyzed by contact angle measurements, neutron reflectivity (NR) and macroscopic friction tests. Both polyelectrolyte brushes exhibited hydrophilic properties. The contact angle of the poly(MPC) brush surface against water was ca. 0° in air and the contact angle of the air bubble in water was ca. 170°. The air bubble in water hardly attached to the poly(MPC) brush surface, indicating super hydrophilic characteristics. NR measurements of poly(MPC) and poly(METAI) brushes showed that the grafted polymer chains were extended from the substrate surface in a good solvent such as water. Interestingly, NR study did not reveal the shrinkage of the brush chain in salt solution. The polyelectrolyte brushes immersed in both water and NaCl solution at various concentrations showed a low friction coefficient and low adhesion force.     

Stimuli-responsive polyelectrolyte polymer brushes prepared via atom-transfer radical polymerization

We present an account of our research into polyelectrolyte polymer brushes that are capable of acting as stimuli-responsive films. We first detail the synthesis of poly(acrylic acid) polymer brushes using ATRP in a "grafting from" strategy. Significantly, we employed a chemical-free deprotection step that should leave the anchoring ester groups intact. We have demonstrated how these polymer assemblies respond to stimuli such as pH and electrolyte concentration. We have used poly(acrylic acid) polymer brushes for the synthesis of metallic nanoparticles and review this work. We have used XPS, ATR-FTIR, and AFM spectroscopy to show the presence of silver and palladium nanoparticles within polymer brushes. Finally, we report the synthesis of AB diblock polyampholyte polymer brushes that represent an extension of polyelectrolyte polymer brushes.     

Brownian dynamics of a compressed polymer brush model. Off-equilibrium response as a function of surface coverage and compression rate

We study the compressive behaviour of a polymer-covered surface (i.e., a "polymer brush") using Brownian dynamics simulations. The model consists of grafted chains with variable flexibility, variable intra- and inter-chain interactions, as well as different surface coverage. We discuss the polymer brush response to confinement by considering variable rates of compression under a hard plane. Our results show a small degree of inter-chain entanglement, regardless of whether the interaction is attractive or merely excluded volume. We observe that the molecular shape depends strongly on the surface coverage. Dense brushes exhibit a limited degree of lateral deformation under compression; instead, chains undergo a transition that produces a local patch with near-solid packing. This effect due to surface density can be undone partially by increasing the attractive nature of the chain interaction, by modulating the rate of compression, or by allowing "soft anchoring", i.e., the possible Brownian drift of the grafting bead on the surface. We have also studied the polymer brush relaxation while maintaining the compressing plane, as well as after its sudden removal. We find evidence that also the relaxation depends on surface density; dense brushes appear to be configurationally frustrated at high compression and are unable to undergo swelling, regardless of the pressure applied.     

Adhesion of spherical polyelectrolyte brushes on mica: an in situ AFM investigation

We demonstrate that the adsorption of cationic spherical polyelectrolyte brushes (SPB) on negatively charged mica substrates can be controlled in situ by the ionic strength of the suspension. The SPB used in our experiments consist of colloidal core particles made of polystyrene. Long cationic polyelectrolyte chains are grafted onto these cores that have diameters in the range of 100 nm. These particles are suspended in aqueous solution with a fixed ionic strength. Atomic force microscopy (AFM) in suspension as well as in air was used for surface characterization. In pure water the polymer particles exhibit a strong adhesion to the mica surface. AFM investigations of the dry samples show that the particles occupy the identical positions as they did in liquid. They were not removed by the capillary forces within the receding water front during the drying process. The strong interaction between the particles and the mica surface is corroborated by testing the adhesion of individual particles on the dried surface by means of the AFM tip: after a stepwise increase of the force applied to the surface by the AFM tip, the polymer particles still were not removed from the surface, but they were cut through and remained on the substrate. Moreover, in situ AFM measurements showed that particles which adsorb under liquid in a stable manner are easily desorbed from the surface after electrolyte is added to the suspension. This finding is explained by a decreasing attractive particle-substrate interaction, and the removal of the particles from the surface is due to the significant reduction of the activation barrier of the particle desorption. All findings can be explained in terms of the counterion release force.     

On the monomer density of grafted polyelectrolyte brushes and their interactions

Most of the modern theories of grafted polyelectrolyte brushes are valid only for moderate stretching of the polyelectrolyte. However, particularly at low ionic strength and high grafting densities, even a moderate charge of the polyelectrolyte can generate a strong stretching. A simple mean field model for strongly stretched grafted polyelectrolyte brushes is suggested, based on an approximate calculation of the partition function of a polyelectrolyte chain. It is shown that the average Boltzmann factor of a possible chain configuration can be approximated by the Boltzmann factor of a configuration with a constant monomer distribution, for which the free energy can be readily obtained. The monomer density in the brush and the interaction between two surfaces with grafted polyelectrolyte brushes could be calculated as a statistical average over all possible configurations. Some simple analytical results are derived, and their accuracy is examined. The dependence of the brush thickness on the electrolyte concentration is investigated, and it is shown that the trapping of a fraction of counterions in the brush influences strongly the thickness of the brush. When two surfaces with grafted polyelectrolyte brushes approach each other more rapidly than the ion diffusion parallel to the surface, the trapping of the counterions between the brushes can affect the interactions by orders of magnitude.     

Polyelectrolyte brushes

We survey recent progress made in the field of polyelectrolyte brushes. These systems consist of long polyelectrolyte chains that are grafted densely to planar or curved surfaces. The main feature of all polyelectrolyte brushes is the strong confinement of the counterions within the brush layer. The high osmotic pressure which is thus built up explains the unusual features of these systems. Here we focus on the most recent experimental developments which are rationalized on the basis of existing theoretical predictions and opens new challenging problems. In particular, we shall discuss briefly the experimental systems used for comparing theory and experiment lately. Moreover, we review various aspects related to the experimental analysis of polyelectrolyte brushes. As a final point, we survey trends in recent applications which demonstrate that polyelectrolyte brushes have an excellent prospect for future nanotechnology.     

Mixed brushes consisting of oppositely charged Y-shaped polymers in salt free,monovalent, and divalent salt solutions

The conformation and the internal stratification of mixed brushes formed from oppositely charged Y(−) and Y(+)-shaped chains in salt free, monovalent, and divalent salt solutions were studied by means of molecular dynamics simulations using the primitive model. Scaling relations of mixed brush height with respect to the grafting surface per chain, the ratio of the total positive to the total negative charge of polyelectrolyte chains, and salt concentrations were obtained. The simulations predicted that mixed brushes show a unique response to divalent salt (1:2) solutions. For symmetric brushes having the same spacer lengths, number of chains and charged units fractions the increase of the salt concentration leads to the enrichment of the outer brush surface with Y(+) units and the lamella microphase separation. For asymmetric brushes in high salt concentration cylindrical domain microphases are formed.     

Simple model for grafted polymer brushes

The first theories of grafted polymer brushes assumed a step profile for the monomer density. Later, the real density profile was obtained from Monte Carlo or molecular dynamics simulations and calculated numerically using a self-consistent field theory. The analytical approximations of the solutions of the self-consistent field equations provided a parabolic dependence of the self-consistent field, which in turn led to a parabolic distribution for the monomer density in neutral brushes. As shown by numerical simulations, this model is not accurate for dense polymer brushes, with highly stretched polymers. In addition, the scaling laws obtained from the analytical approximations of the self-consistent field theory are identical to those derived from the earlier step-profile-approximation and predict a vanishing thickness of the brush at low graft densities, and a thickness exceeding the length of the polymer chains at high graft densities. Here a simple model is suggested to calculate the monomer density and the interaction between surfaces with grafted polymer brushes, based on an approximate calculation of the partition function of the polymer chains. The present model can be employed for both good and poor solvents, is compatible with a parabolic-like profile at moderate graft densities, and leads to an almost steplike density for highly stretched brushes. While the thickness of the brush depends strongly on solvent quality, it is a continuous function in the vicinity of the temperature. In good and moderately poor solvents, the interactions between surfaces with grafted polymer brushes are always repulsive, whereas in poor solvents the interactions are repulsive at small separations and become attractive at intermediate separation distances, in agreement with experiment. At large separations, a very weak repulsion is predicted.     

Molecular bottle brushes in a solution of semiflexible polyelectrolytes and block copolymers with an oppositely charged block: a molecular dynamics simulation

Using a coarse-grained model, we performed molecular dynamics simulations of the electrostatically driven self-assembly of strongly charged polyelectrolytes and diblock copolymers composed of oppositely charged and neutral blocks. Stoichiometric micelle-like complexes formed in a dilute solution represent cylindrical brushes whose conformation is determined by the linear charge density on the polyelectrolyte and by temperature. The core-shell morphology of the cylindrical brushes is proven. The core of these anisotropic micelles consists of an insoluble complex coacervate formed by the ionic chains and a shell made up of the neutral solvophilic blocks. As the concentration of macromolecules increases, the orientational ordering of ionic micelles takes place. The complexation can induce effective steric stiffening of the polyelectrolyte chains.     

Ion transport and molecular organization are coupled in polyelectrolyte-modified nanopores

Chemically modified nanopores show a strong and nontrivial coupling between ion current and the structure of the immobilized species. In this work we study theoretically the conductance and structure in polymer modified nanopores and explicitly address the problem of the coupling between ion transport and molecular organization. Our approach is based on a nonequilibrium molecular theory that couples ion conductivity with the conformational degrees of freedom of the polymer and the electrostatic and nonelectrostatic interactions among polyelectrolyte chains, ions, and solvent. We apply the theory to study a cylindrical nanopore between two reservoirs as a function of pore diameter and length, the length of the polyelectrolyte chains, their grafting density, and whether they are present or not on the outer reservoir walls. In the very low applied potential regime, where the distribution of polyelectrolyte and ions is similar to that in equilibrium, we present a simple analytical model based on the combination of the different resistances in the system that describes the conductance in excellent agreement with the calculations of the full nonequilibrium molecular theory. On the other hand, for a large applied potential bias, the theory predicts a dramatic reorganization of the polyelectrolyte chains and the ions. This reorganization results from the global optimization of the different interactions in the system under nonequilibrium conditions. For nanopores modified with long chains, this reorganization leads to two interesting physical phenomena: (i) control of polyelectrolyte morphology by the direction and magnitude of ion-fluxes and (ii) an unexpected decrease in system resistance with the applied potential bias for long chains due to the coupling between polyelectrolyte segment distribution and ion currents.