Electrostatic binding of oppositely charged surfactants to spherical polyelectrolyte brushes

We use Brownian dynamics (BD) simulations to investigate the formation and structural characteristics of the complex between a spherical polyelectrolyte brush (SPB) and oppositely charged surfactants. Increasing the amount of added surfactants leads to a collapsed conformation of the SPB and the number of adsorbed surfactants exhibits a linear dependence. Nevertheless, the surfactant uptake into the SPB does not increase with further addition of surfactants. It is found that the surfactant length has a strong influence on the SPB conformation and the adsorption properties of surfactant. Upon changing the surfactant length from 3 to 11, the SPB undergoes a swelling-deswelling-reswelling conformational transition. The brush deswelling is due to the increase in the surfactant uptake. The increasing size of adsorbed aggregates is a main reason for reswelling of the SPB. A non-linear relationship between the brush thickness and the grafting density is observed. Especially at intermediate grafting densities, increasing the number of grafted chains has a weak effect on the brush thickness. We also find that a completely collapsed brush conformation occurs at high surfactant/SPB charge ratios or large surfactant lengths, while the brush layer is in a partly collapsed or extended state at an intermediate charge ratio and surfactant length.     

Diblock polyampholytes grafted onto spherical particles: effect of stiffness, charge density, and grafting density

The structure of spherical brushes formed by symmetric diblock polyampholytes end-grafted onto small spherical particles in aqueous solution is examined within the framework of the so-called primitive model using Monte Carlo simulations. The properties of the two blocks are identical except for the sign of their charges. Three different chain flexibilities corresponding to flexible, semiflexible, and stiff blocks are considered at various polyampholyte linear charge densities and grafting densities. The link between the two blocks is flexible at all conditions, and the grafted segments are laterally mobile. Radial and lateral spatial distribution functions of different types and single-chain properties are analyzed. The brush structure strongly depends on the chain flexibility. With flexible chains, a disordered polyelectrolyte complex is formed at the surface of the particle, the complex becoming more compact at increasing linear charge density. With stiff blocks, the inner blocks are radially oriented. At low linear charged density, the outer blocks are orientationally disordered, whereas at increasing electrostatic interaction the two blocks of a polyampholyte are parallel and close to each other, leading to an ordered structure referred to as a polyampholyte star. As the grafting density is increased, the brush thickness responds differently for flexible and nonflexible chains, depending on a different balance between electrostatic interactions and excluded volume effects.     

Molecular dynamics simulations of end‐grafted polymers with charged side chains

We report molecular dynamics simulations on bottle‐brush polyelectrolytes end‐grafted to a planar surface. For each bottle‐brush polyelectrolyte, flexible charged side chains are anchored to one neutral main chain. The effects of the counterion valence and the grafting density on the density profiles and the structural characteristics of the brush were studied in this work. It is found that the electrostatic repulsion between charged monomers in the side chains leads an extended conformation of the brush in a solution containing monovalent counterions, while strong electrostatic binding of multivalent counterions to the side chains has a significant contribution to the collapse of the brush. For the trivalent case, the distribution of end monomers in the main chains becomes broader upon decreasing the grafting density, as compared with the monovalent case. However, the position of the distribution for the monovalent case is relatively insensitive to the change of the grafting density. Additionally, with increased counterion valence, enhanced electrostatic correlation between counterions and charged side chains also weakens the diffusive ability of counterions. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Monte carlo simulations of polydisperse polymers grafted on spherical surfaces

This article presents effects of polydispersity in polymers grafted on spherical surfaces on grafted polymer chain conformations, grafted layer thickness, and free‐end monomer distribution within the grafted layer. At brush‐like grafting densities, as polydispersity index (PDI) increases, the scaling exponent of radius of gyration of grafted chains approaches that of a single chain grafted on the same nanoparticle, because polydispersity alleviates monomer crowding within the brush. At high PDI, the chains shorter than the number average chain length, N_n, have more compressed conformations, and the chains longer than N_n overall stretch less than in the monodisperse case. As seen in polydisperse flat brushes at high grafting densities, the grafted layer thickness on spherical nanoparticle increases with PDI. Polydispersity eliminates the region near the surface devoid of free‐end monomers seen in monodisperse cases, and it reduces the width of free‐end monomer distribution and shifts the free‐end monomer distribution close to the surface. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

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.     

Correlation between conformation change of polyelectrolyte brushes and lubrication

We directly monitor the absolute separation profiles that function as film thickness between a single glass disk and the charged polyelectrolyte brushes decorated steel slider in water using a home-made slider-on-disk apparatus, which reflects the structural conformation variations and interactions of polymer brushes under externally applied pressure, in addition to probing the relative variation of friction forces under different applied loads and sliding velocities. We find that the polyelectrolyte brushes modified surfaces can sustain high pressure and have extremely low friction coefficients(around 0.006 at pressures of 0.13 MPa; 0.5-0.6 without brushes). The water-lubrication characteristics are correlated to the structural conformation changes of the polyelectrolyte brushes that are mainly governed by electrostatic interactions and the osmotic pressure of counterions inside the polymer chains, which can be used to support and distribute the normal pressure. The apparent thickness of the brush decreases with the increase of loading forces, an increase in the ionic strength causes the polymer chains collapse, and the friction forces increase. This fundamental research is of great importance to understand the mechanical and structural properties of polyelectrolyte brushes and their influences on the tribological behaviors, and helps to design friction/lubrication-controlled surface/interface by taking advantage of polyelectrolyte brushes.     

Polymer Chain Conformation on Deuterated Polystyrene Nanoparticles Investigated by SANS

We previously reported that grafted polystyrene (PS) chains on silica nanoparticles at a low grafting density show similar conformations to free PS chains in the same solvent, THF (diameter ?50 nm, Colloid.poly.Sci. (2013), 291, 9, 2087–2099). As an extension of our previous study we choose an organic nanoparticle (deuterated polystyrene, dPS) instead of inorganic nanoparticle to see the impact of the substrate material on chain conformation. Additionally, a wider range of molecular weights were prepared to investigate the conformation feature of grafted PS chains more in detail. Small angle neutron scattering (SANS) experiments were performed to characterize PS grafted dPS particles in good solvent condition, with deuterated toluene and deuterated THF as solvent. To get insight into the conformation of the grafted PS layer we apply a scaling law describing the dimension of free PS polymer in good solvent condition to the obtained thickness of the grafted PS layer. We find an overall agreement with the scaling law where the thickness of the grafted PS layer is slightly larger than 2R_g of the free polymer chains in the respective solvent giving hint for semi dilute polymer brush (SDPB) situation.     

Interactions of polyelectrolyte brushes with oppositely charged surfactants

Using Brownian dynamics simulations, we study the effect of the charge ratio, the surfactant length, and the grafting density on the conformational behavior of the complex formed by the polyelectrolyte brush with oppositely charged surfactants. In our simulations, the polyelectrolyte chains and surfactants are represented by a coarse-grained bead-spring model, and the solvent is treated implicitly. It is found that varying the charge ratio induces different morphologies of surfactant aggregates adsorbed onto the brush. At high charge ratios, the density profiles of surfactant monomers indicate that surfactant aggregates exhibit a layer-by-layer arrangement. The surfactant length has a strong effect on the adsorption behavior of surfactants. The lengthening of surfactant leads to a collapsed brush configuration, but a reswelling of the brush with further increasing the surfactant length is observed. The collapse of the brush is attributed to the enhancement of surfactants binding to polyelectrolyte chains. The reswelling is due to an increase in the volume of adsorbed surfactant aggregates. At the largest grafting density investigated, enhanced excluded volume interactions limit the adsorption of surfactant within the polyelectrolyte brush. We also find that end monomers in polyelectrolyte chains exhibit a bimodal distribution in cases of large surfactant lengths and high charge ratios.     

Monte Carlo simulation and molecular theory of tethered polyelectrolytes

We investigate the structure of end-tethered polyelectrolytes using Monte Carlo simulations and molecular theory. In the Monte Carlo calculations we explicitly take into account counterions and polymer configurations and calculate electrostatic interaction using Ewald summation. Rosenbluth biasing, distance biasing, and the use of a lattice are all used to speed up Monte Carlo calculation, enabling the efficient simulation of the polyelectrolyte layer. The molecular theory explicitly incorporates the chain conformations and the possibility of counterion condensation. Using both Monte Carlo simulation and theory, we examine the effect of grafting density, surface charge density, charge strength, and polymer chain length on the distribution of the polyelectrolyte monomers and counterions. For all grafting densities examined, a sharp decrease in brush height is observed in the strongly charged regime using both Monte Carlo simulation and theory. The decrease in layer thickness is due to counterion condensation within the layer. The height of the polymer layer increases slightly upon charging the grafting surface. The molecular theory describes the structure of the polyelectrolyte layer well in all the different regimes that we have studied.     

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.     

A Monte Carlo simulation of grafted poly(ethylene oxide) chains

Conformational changes of a simplified model of grafted poly(ethylene oxide) (PEO) chains were simulated using an off-lattice Monte Carlo model. A random-walk scheme was used in our simulations. The initial polymer structure was modeled with molecular mechanics and models of grafted polymer chains were built using programs developed in our laboratory. During the simulation, all bond angles and bond lengths were kept fixed while the dihedral angles of backbones were changed to search for energy-favorite conformations. Torsional energy, van der Waals interaction, and Coulombic interaction were considered. Periodic boundary conditions were implemented. In addition, the solvent quality was simulated implicitly by modifying the Lennard-Jones 12–6 van der Waals expression. Each PEO chain, 50-monomer long, was represented with a united-atom model. Eight series of simulations with varying solvent quality, simulation temperature, and Coulombic interaction were carried out. For each series, nine different initial grafting densities of grafted PEO chains were considered. Five different conformations were simulated at each grafting density. The calculated system energies, scaling properties, and atom density profiles were studied. Changes in solvent quality produced different structural behaviors. As the grafting density increased, there was a mushroom-to-brush transition, and the scaling property of average layer thickness was dependent on the grafting density.     

Surface Patterns of a Tetrahedral Polyelectrolyte Brush Induced by Grafting Density and Charge Fraction

A tetrahedral polyelectrolyte brush in the presence of trivalent counterions is researched under the condition of good solution by mea ns of molecular dynamics simulati ons.Grafting density and charge fraction are varied to gen erate a series of surface patter ns.Lateral microphase separation happens and various interesting pinned patches appear at appropriate charge fraction and grafting density.Through a careful analysis on the brush thickness,the pair correlation functions,the distributions of net charge,and the four states of trivalent counterions in the brush,we find that the ordered surface patterns and special properties are induced by the pure electrostatic correlation effect of trivalent ions even in the good solvent.Furthermore,the dependences of electrostatic correlation on the charge fraction of tethered chains are evaluated for fixed grafting den sity.Also,our results can serve as a guide for precise control over the stimuli-responsive materials rational and self-assembly of nanoparticles.     

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.     

Solvent quality effects on scaling behavior of poly(methyl methacrylate) brushes in the moderate- and high-density regimes

Herein, we give a detailed experimental analysis for scaling law behavior in the "moderately dense" and "high-density" brush regimes for poly(methyl methacrylate) brushes swollen in a range of solvent conditions. This expansive experimental analysis aims to validate decades of mean field theory predictions on power law scaling behavior of grafted polymer chains. Brushes with grafting densities (σ) ranging from 0.1 to 0.8 nm(-2) are prepared by atom-transfer radical polymerization. The swollen thickness (h) is characterized using liquid cell ellipsometry, and the solvent quality is varied using mixtures of acetone and methanol. In a good solvent, the exponential scaling behavior (h ∝ σ(n)) has the typical n = 1/3 dependency for grafting densities of σ ≤ 0.4 nm(-2). For grafting densities of >0.4 nm(-2), n increases, indicating the transition from the moderately dense to the high-density brush regime. However, in a poor solvent, the scaling behavior is independent of σ and scales as h ∝ σ(0.80), approaching the theoretical expectations of h ∝ σ(1). An abrupt transition between these scaling law behaviors occurs at the Θ-solvent condition of ～45% (v/v) methanol in acetone. While our experimental results parallel trends predicted by mean field theory, differences are observed and appear to be attributed to self-solvation of the polymer, polydispersity in the molecular weight, and chain termination.     

Properties of star-branched polymer brushes

A simple model of a polymer brush was constructed. The star polymers with three arms were terminally attached with one arm (the stem) to an impenetrable surface with the other two arms (branches) free. The excluded volume effect was included into the model as the only interaction. Therefore, the system was studied in good solvent conditions. The simulations were carried out by means of the dynamic Monte Carlo method using the local changes of chain conformations to sample efficiently the conformational space. The influence of both the number of chains (the grafting density) and the length of chains on the static properties of the polymer brush was studied. The internal and local structure of a formed polymer layer was determined. It was shown that the size of the stems increased rapidly with the increase of the grafting density, while the size of the branches diminished. The changes of the spatial orientations of the stems and the branches for different grafting densities were shown and discussed.     

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.     

Mean‐field theoretical analysis of brush‐coated nanoparticle dispersion in polymer matrices

The equilibrium dispersion of nanoparticles with grafted polymer chains into polymer matrices, of the same chemical structure as the brush, is studied through the device of mean‐field theory. Our results show that the disperion of brush‐coated nanoparticles into a matrix polymer is improved with (i) decreasing particle radius and (ii) increasing brush chain length. Both of these aspects can be understood based on the fact that, unlike the case of planar surfaces, homopolymer chains end‐grafted to spherical nanoparticle surfaces tangentially spread away from the surface thus alleviating the packing frustration that is created by the relatively high grafting densities. This permits significant brush/matrix overlap, even at high grafting densities, a regime that has only recently become experimentally available due to advances in polymer synthesis (i.e., the “grafting‐to” methods). © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 351–358, 2008     

Molecular dynamics simulations of grafted layers of bottle-brush polyelectrolytes

Using molecular dynamics simulations, we study the effect of the brush grafting density and degree of polymerization of the side chains on conformations of brush layers made of charged bottle-brush macromolecules. The thickness of the brush layer first decreases with increasing brush grafting density; then, it saturates and remains constant in the wide interval of the brush grafting densities. The brush layers consisting of the bottle-brush macromolecules with longer side chains have a larger layer thickness. The elongation of the side chains of the bottle-brush macromolecules decreases with increasing brush grafting density. This contraction of the side chains is due to counterion condensation inside the volume occupied by bottle-brushes. Our simulations showed that counterion condensation is a multiscale process reflecting different symmetries of the bottle-brush layer.     

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.     

Structure and collapse of a surface-grown strong polyelectrolyte brush on sapphire

We have used neutron reflectometry to investigate the behavior of a strong polyelectrolyte brush on a sapphire substrate, grown by atom-transfer radical polymerization (ATRP) from a silane-anchored initiator layer. The initiator layer was deposited from vapor, following treatment of the substrate with an Ar/H(2)O plasma to improve surface reactivity. The deposition process was characterized using X-ray reflectometry, indicating the formation of a complete, cross-linked layer. The brush was grown from the monomer [2-(methacryloyloxy)ethyl]trimethylammonium chloride (METAC), which carries a strong positive charge. The neutron reflectivity profile of the swollen brush in pure water (D(2)O) showed that it adopted a two-region structure, consisting of a dense surface region ～100 ? thick, in combination with a diffuse brush region extending to around 1000 ? from the surface. The existence of the diffuse brush region may be attributed to electrostatic repulsion from the positively charged surface region, while the surface region itself most probably forms due to polyelectrolyte adsorption to the hydrophobic initiator layer. The importance of electrostatic interactions in maintaining the brush region is confirmed by measurements at high (1 M) added 1:1 electrolyte, which show a substantial transfer of polymer from the brush to the surface region, together with a strong reduction in brush height. On addition of 10(-4) M oppositely charged surfactant (sodium dodecyl sulfate), the brush undergoes a dramatic collapse, forming a single dense layer about 200 ? in thickness, which may be attributed to the neutralization of the monomers by adsorbed dodecyl sulfate ions in combination with hydrophobic interactions between these dodecyl chains. Subsequent increases in surfactant concentration result in slow increases in brush height, which may be caused by stiffening of the polyelectrolyte chains due to further dodecyl sulfate adsorption.