Diblock polyampholytes grafted onto spherical particles: Monte Carlo simulation and lattice mean-field theory

Spherical brushes composed of diblock polyampholytes (diblock copolymers with oppositely charged blocks) grafted onto solid spherical particles in aqueous solution are investigated by using the primitive model solved with Monte Carlo simulations and by lattice mean-field theory. Polyampholyte chains of two compositions are considered: a copolymer with a long and a short block, A100B10, and a copolymer with two blocks of equal length, A50B50. The B block is end-grafted onto the surface, and its charge is varied, whereas the charge of the A block is fixed. Single-chain properties, radial and lateral spatial distributions of different types, and structure factors are analyzed. The brush structure strongly depends on the charge of the B block. In the limit of an uncharged B block, the chains are stretched and form an extended polyelectrolyte brush. In the other limit with the charges of the blocks compensating each other, the chains are collapsed and form a polyelectrolyte complex surrounding the particles. At intermediate charge conditions, a polyelectrolyte brush and a polyelectrolyte complex coexist and constitute two substructures of the spherical brush. The differences of the brush structures formed by the A100B10 and A50B50 polyampholytes are also analyzed. Finally, a comparison of the predictions of the two theoretical approaches is made.     

Polyelectrolyte brushes

The simple scaling theory of weakly-charged polyelectrolyte brush (the layer of polyelectrolyte chains grafted at one end onto an impermeable surface) immersed into a good solvent has been developed.The asymptotic scaling dependences of the free layer thickness on charge density and solvent strength are obtained. The behavior of polyelectrolyte brush subjected to normal and tangential external forces is considered. New “polyelectrolyte effect” is predicted: shear of a free polyelectrolyte brush leads to a decrease in brush thickness in contrast to the case of a free neutral brush. Such behavior is equivalent to that of a neutral brush subjected to external normal stretching force. This force in the case of polyelectrolyte brush is created by the osmotic pressure of mobile counterions neutralizing grafted chain charges.     

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.     

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.     

Fuzzy ternary particle systems by surface-initiated atom transfer radical polymerization from layer-by-layer colloidal core-shell macroinitiator particles

We report the synthesis of ternary polymer particle material systems composed of (a) a spherical colloidal particle core, coated with (b) a polyelectrolyte intermediate shell, and followed by (c) a grafted polymer brush prepared by surface-initiated polymerization as the outer shell. The layer-by-layer (LbL) deposition process was utilized to create a functional intermediate shell of poly(diallyl-dimethylammonium chloride)/poly(acrylic acid) multilayers on the colloid template with the final layer containing an atom transfer radical polymerization (ATRP) macroinitiator polyelectrolyte. The intermediate core-shell architecture was analyzed with FT-IR, electrophoretic mobililty (zeta-potential) measurements, atomic force microscopy, and transmission electron microscopy (TEM) techniques. The particles were then utilized as macroinitiators for the surface-initiated ATRP grafting process for poly(methyl methacrylate) polymer brush. The polymer grafting was confirmed with thermo gravimetric analysis, FT-IR, and TEM. The polymer brush formed the outermost shell for a ternary colloidal particle system. By combining the LbL and surface-initiated ATRP methods to produce controllable multidomain core-shell architectures, interesting functional properties should be obtainable based on independent polyelectrolyte and polymer brush behavior.     

Double layer interaction between two plates with polyelectrolyte brushes

When polyelectrolyte chains are grafted to colloidal particles, the electric field between particles is affected by the charges of the chains. In some previous theoretical attempts, the charge density of the polyelectrolyte chains per unit length was considered constant, and its effect was accounted for by introducing an additional constant charge density into the unidimensional Poisson-Boltzmann equation, which was evaluated assuming that it is uniformly distributed in the polyelectrolyte volume of the brush. In this paper, a more detailed model is employed for the calculation of the electrical potential between two plates on which polyelectrolyte brushes are present. In this model, the polyelectrolyte chain is viewed as a rigid cylinder, on the surface of which charges are generated through the dissociation of ionizable sites and adsorption of the cations of the electrolyte. To each of the chains an atmosphere is attached which for simplicity is assumed cylindrical. In the brush region, the electrical potential is described by a two-dimensional Poisson-Boltzmann equation, while in the region free of polyelectrolyte chains by a unidimensional Poisson-Boltzmann equation. Such a model is physically suitable when the charges of the chains are sufficiently large for the repulsion they generate to ensure that the chains are fully extended. Such cases are quite frequent, because relatively low charges lead to an almost complete extension of the chains. In this paper, both the plate surface and the surface of the cylinders are considered charged. The effects of electrolyte concentration, pH, brush thickness and chain coverage density on the repulsion between plates are examined.     

Influence of poly(ethylene oxide) brushes on the rheological properties of MgO colloidal suspensions in water

A combined experimental and multiscale simulation study of the influence of polymer brush modification on interactions of colloidal particles and rheological properties of dense colloidal suspensions has been conducted. Our colloidal suspension is comprised of polydisperse MgO colloidal particles modified with poly(ethylene oxide) (PEO) brushes in water. The shear stress as a function of shear rate was determined experimentally and from multiscale simulations for a suspension of 0.48 volume fraction colloids at room temperature for both bare and PEO-modified MgO colloids. Bare MgO particles exhibited strong shear thinning behavior and a yield stress on the order of several Pascals in both experiments and simulations. In contrast, simulations of PEO-modified colloids revealed no significant yielding or shear thinning and viscosity only a few times larger than solvent viscosity. This behavior is inconsistent with results obtained from experiments where modification of colloids with PEO brushes formed by adsorption of PEO-based comb-branched chains resulted in relatively little change in suspension rheology compared to bare colloids over the range of concentration of comb-branch additives investigated. We attribute this discrepancy in rheological properties between simulation and experiment for PEO-modified colloidal suspensions to heterogeneous adsorption of the comb-branch polymers.     

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.     

Adsorption of novel thermosensitive graft-copolymers: Core-shell particles prepared by polyelectrolyte multilayer self-assembly

The adsorption properties of thermosensitive graft-copolymers are investigated with the aim of developing self-assembled multilayers from these copolymers. The copolymers consist of a thermoreversible main chain of poly(N-isopropylacrylamid) and a weak polyelectrolyte, poly(2-vinylpyridine), as grafted side chains. Zeta-potential, single particle light scattering and adsorption isotherms monitor the adsorption of the thermoreversible copolymers to precoated colloidal particles. The results show a smaller surface coverage for a larger density of grafted chains. The surface coverage is discussed in terms of surface charge density in the adsorbed monolayer. Taking into account the monolayer adsorption properties, conditions are developed for the multilayer formation from these copolymers. A low pH provides a sufficient charge density of the grafted chains to achieve a surface charge reversal of the colloids upon adsorption. The charge reversal after each adsorbed layer is monitored by zeta-potential and the increase of the thickness is determined by light scattering. Stable and reproducible multilayers are obtained. The results imply that the conformation of the thermosensitive component in multilayers depends strongly on the grafting density, where the polymer with a higher grafting density adsorbs in a flat conformation while that with a lower grafting density adsorbs with more loops.     

Directed motion of a polyelectrolyte micelle along tethered chains of oppositely charged polyelectrolyte brush

The complexation of different single polyelectrolyte (PE) micelles formed by linear diblock copolymers with oppositely charged brushes with varying grafting densities and charge content was studied by means of molecular dynamics simulations using the primitive model. We found that all micelles perform a directed motion along the vertical z axis on the grafted surface where they trapped while on the other axes the motion is restricted in a circle in which the diameter decreases with the increase of the hydrophilic length of the linear diblock copolymer. The motion of micelles is characterized as super diffusion inside brushes with low densities and low charge content. At high grafting densities and charge content the diffusion becomes Fickian or slightly subdiffusive. The number of the absorbed brush chains on the micelle corona increases almost monotonically with the increase of brush grafting density or with the decrease of charge content. The distance from the surface in which the micelle is trapped can be controlled by the charge density along the grafted PE chain. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 621–631     

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.     

Ionic condensation and charge renormalization in colloidal suspensions

The very popular notion of effective or renormalized polyion charge is a concept of fundamental importance in the field of highly charged colloidal or polyelectrolyte solutions. In such suspensions, the electrostatic coupling between oppositely charged species induces a strong accumulation (or electrostatic “condensation”) of counterions in the vicinity of the macroion surface. The basic idea is thus to consider the structural colloid and the condensed counterionic shell as a whole which carries an effective charge, Z^eff, much weaker than the structural one, Z^str. Consequently, as long as what happens far from the colloid is concerned, all Debye–Hückel-like linearized approaches which fail to correctly treat the nonlinear condensation phenomenon can still be used if Z^str is more or less replaced by Z^eff. Beyond this basic idea, it remains to estimate a priori the value of Z^eff. It will be discussed how to deduce simple laws for the effective charge of spherical colloids from the Poisson–Boltzmann approach, analogous to Manning's law for linear polyelectrolytes. The validity of these laws will be tested, against more complete treatments. Lastly, it will be shown that while the notion of colloidal charge renormalization remains clear for dilute suspensions, it becomes incorrect at higher densities where the condensed counterionic shells overlap.     

Electrostatic self-assembly of neutral and polyelectrolyte block copolymers and oppositely charged surfactant

We investigated the phase behavior and the microscopic structure of the colloidal complexes constituted from neutral/polyelectrolyte diblock copolymers and oppositely charged surfactant by dynamic light scattering (DLS) and small-angle neutron scattering (SANS). The neutral block is poly(N-isopropylacrylamide) (PNIPAM), and the polyelectrolyte block is negatively charged poly(acrylic acid) (PAA). In aqueous solution with neutral pH, PAA behaves as a weak polyelectrolyte, whereas PNIPAM is neutral and in good-solvent condition at ambient temperature, but in poor-solvent condition above approximately 32 degrees C. This block copolymer, PNIPAM-b-PAA with a narrow polydispersity, is studied in aqueous solution with an anionic surfactant, dodecyltrimethylammonium bromide (DTAB). For a low surfactant-to-polymer charge ratio Z lower than the critical value ZC, the colloidal complexes are single DTAB micelles dressed by a few PNIPAM-b-PAA. Above ZC, the colloidal complexes form a core-shell microstructure. The core of the complex consists of densely packed DTA+ micelles, most likely connected between them by PAA blocks. The intermicellar distance of the DTA+ micelles is approximately 39 A, which is independent of the charge ratio Z as well as the temperature. The corona of the complex is constituted from the thermosensitive PNIPAM. At lower temperature the macroscopic phase separation is hindered by the swollen PNIPAM chains. Above the critical temperature TC, the PNIPAM corona collapses leading to hydrophobic aggregates of the colloidal complexes.     

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.     

Microsurface potential measurements: repulsive forces between polyelectrolyte brushes in the presence of multivalent counterions

We propose a new way to determine weak repulsive forces operative between colloidal particles by measuring the rate of slow coagulation. The rate of slow coagulation is directly related to the competition of the repulsion with thermal motion. Since the thermal forces are weak, measurements of the coagulation rate can lead to precise information on repulsive potentials having a magnitude of just a few kT. We demonstrate this novel way by studying colloidal spherical polyelectrolyte brush (SPB) particles in aqueous solution containing trivalent La3+ counterions. The particles consist of a monodisperse polystyrene core of 121 nm radius from which linear sodium poly(styrenesulfonate) (PSS) chains are densely grafted (contour length 48 nm). We determine the rate of coagulation by time-resolved simultaneous static and dynamic light scattering in the presence of LaCl3 (0.2 to 150 mM). Direct measurements of the repulsive force between macroscopic brush layers demonstrate that the potential is decaying exponentially with distance. This is in good agreement with a simple theoretical treatment that furthermore leads to the effective surface potential Psi0. The good agreement of data obtained by the novel microscopic method with direct macroscopic measurements underscores the general validity of our approach.     

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.     

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.     

High catalytic activity of platinum nanoparticles immobilized on spherical polyelectrolyte brushes

We present a study on the catalytic activity of platinum nanoparticles immobilized on spherical polyelectrolyte brushes that act as carriers. The spherical polyelectrolyte brushes consist of a solid core of poly(styrene) onto which long chains of poly(2-methylpropenoyloxyethyl) trimethylammonium chloride are grafted. These positively charged chains form a dense layer of polyelectrolytes on the surface of the core particles ("spherical polyelectrolyte brush") that tightly binds divalent PtCl6-(2) ions. The reduction of these ions within the brush layer leads to nearly monodisperse nanoparticles of metallic platinum. The average size of the particles is approximately 2 nm. The composite particles exhibit excellent colloidal stability. The catalytic activity is investigated by photometrically monitoring the reduction of p-nitrophenol by an excess of NaBH4 in the presence of the nanoparticles. The kinetic data could be explained by the assumption of a pseudo-first-order reaction with regard to p-nitrophenol. In all cases, a delay time t0 has been observed, after which the reactions start. This time is shorter when the catalyst has already been used. All data demonstrate that spherical polyelectrolyte brushes present an ideal carrier system for metallic nanoparticles.     

Steric and bridging interactions between two plates induced by grafted polyelectrolytes

If colloidal particles are grafted with a polymer, then the grafted chains can provide steric repulsion between them. If some of the grafted polymer chains are also adsorbed to a second particle, then a bridging force is generated as well. For uncharged plates and polymer, the following contributions to the free energy of the system have been taken into account in the calculation of the interaction force: (i) the Flory-Huggins expression for the mixing free energy of the grafted chains with the liquid; (ii) the entropy loss due to the connectivity of the polymeric segments; (iii) the van der Waals interactions between the segments and the plates; and (iv) the free energy of adsorption of the polymer segments of the grafted chains on the other plate. For charged plates, the electrostatic free energy as well as the free energy of the electrolyte are included in the total free energy of the system. By minimizing the free energy with respect to the segment concentration and, when it is the case, with respect to the electrical potential, equations for the segment number density distribution and for the electrical potential are obtained, on the basis of which the interactions between two plates grafted with polymer chains that can be also adsorbed on the other plate were calculated. The interaction thus obtained includes steric and bridging forces.