Theory of the observed ultralow friction between sliding polyelectrolyte brushes

It is shown using a method based on a modified version of the mean field theory of Miklavic and Marcelja [J. Phys. Chem. 92, 6718 (1988)] that it should be possible for osmotic pressure due to the counterions associated with the two polyelectrolyte polymer brush coated surfaces to support a reasonable load (i.e., about 10(6) Pa) with the brushes held sufficiently far apart to prevent entanglement of polymers belonging to the two brushes, thus avoiding what is believed to be the dominant mechanisms for static and dry friction.     

Surface sliding friction of negatively charged polyelectrolyte gels

The friction between two polyelectrolyte gels carrying the same or opposite sign of charges has been investigated using a rheometer. It is found that the friction was strongly dependent on the interfacial interaction between two gel surfaces. In the repulsive interaction case, especially, the friction was extremely low. The friction behavior is attempted to be described in terms of the hydrodynamic lubrication of the solvent layer between two like-charged gel surfaces, which is formed due to the electrostatic repulsion of the two gel surfaces. From the theoretical analysis (hydrodynamic mechanism), the friction behaviors were explained qualitatively, all of the experimental results, nevertheless, could not be understood well. The viscoelastic feature of the gel and the non-Newtonian behavior of water at the friction interface are considered to be important to elucidate the gel friction.     

Surface potential of spherical polyelectrolyte brushes in the presence of trivalent counterions

We consider the ζ-potential and the effective charge of spherical polyelectrolyte brushes (SPBs) in aqueous solution in the presence of trivalent europium ions. The SPB consists of a polystyrene core of ca. 250 nm diameter onto which long chains of the strong polyelectrolyte poly(styrene sulfonate) are grafted (contour length: 82 nm). At low concentration of EuCl₃ the chains are stretched to nearly full length. If the concentration of the trivalent ions is raised, the surface layer of the polyelectrolyte chains collapses. The ζ-potential of the SPB is calculated from the electrophoretic mobilities measured at different concentrations of EuCl₃. At the collapse, ζ decreases by the partial neutralization of the charges by the trivalent ions. The experimental ζ-potential thus obtained agrees with the theoretical surface potential Ψ_theo calculated for the effective shear plane by a variational free energy model of the SPB.     

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.     

Electrochemical characteristics of polyelectrolyte brushes with electroactive counterions

Cyclic voltammetry (CV) was employed to characterize the electrochemical behavior of polyelectrolyte brushes with immobilized electroactive counterions in response to external changes in concentration and composition of the supporting electrolyte and as a function of brush thickness. Poly(methacryloyloxy)ethyl-trimethyl-ammonium chloride (PMETAC) brushes were synthesized on Au substrates via atom transfer radical polymerization followed by ion-exchange with ferricyanide ions ([Fe(CN)6]3-) as redox probes. CV measurements of the modified PMETAC brushes showed the typical electrochemical response corresponding to a surface-confined electroactive species and the redox counterions, as [Fe(CN)6]3- species form stable ion pairs with the quaternary ammonium groups of the brush. The electron-transfer features of PMETAC brushes with different thicknesses, as characterized by CV and UV-vis spectroscopy, revealed that the charge density probed by CV was lower than the charge density measured by UV-vis spectroscopy. The electrode current decreased significantly with increasing concentration of supporting electrolyte due to the effect of the Donnan potential. Hydrophobic counterions, ClO4-, which induced brush collapse, lead to significantly reduced electrode currents.     

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.     

Formation of surface-attached microstructured polyelectrolyte brushes

Surface-attached micropattemed polyelectrolyte brushes on planar solid surfaces are generated using free radical polymerization photo-initiated by self-assembled initiator monolayers. It is shown that the formed patterns can be either negative or positive with different patterning processes.     

Controlled growth of triblock polyelectrolyte brushes

We have achieved a significant breakthrough in the synthesis of polyelectrolyte brushes of controlled thickness and density, which has been demonstrated by the synthesis of triblock copolymer brushes composed of cationic, neutral, and anionic segments.     

Salt-regulated attraction and repulsion of spherical polyelectrolyte brushes towards polyelectrolyte multilayers

Adsorption of colloidal particles presents an interesting alternative to the modification of surfaces using covalent coupling or physisorption of molecules. However, to tailor the properties of these materials full control over the effective particle-substrate interactions is required. We present a systematic investigation of the adsorption of spherical polyelectrolyte brushes (SPB) onto polyelectrolyte multilayers (PEM). A brush layer grafted from colloidal particles allows the incorporation of various functional moieties as well as the precise adjustment of their adsorption behaviour. In the presence of oppositely charged surfaces the amount of adsorbed SPB monotonically increases with the ionic strength, whereas equally charged substrates efficiently prevent colloidal attachment below a threshold salt concentration. We found that the transition from the osmotic to the salted brush regime at approximately 100 mM coincided with a complete loss of substrate selectivity. In this regime of high ionic strength, attractive secondary interactions become dominant over electrosteric repulsion. Due to the soft polyelectrolyte corona a surface coverage exceeding the theoretical jamming limit could be realized. Both the adsorption kinetics and the resulting thin film morphologies are discussed. Our study opens avenues for the production of two-dimensional arrays and three-dimensional multilayered structures of SPB particles.     

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.     

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.     

Entropic death of nonpatterned and nanopatterned polyelectrolyte brushes

The stability of nonpatterned and nanopatterned strong polyelectrolyte brushes (PEBs) is studied as a function of both brush character and the properties of a contacting liquid. High‐molecular‐weight PEBs of poly(4‐methyl vinylpyridinium iodide) (PMeVP) are synthesized using surface‐initiated radical‐chain polymerization. Nanopatterned brushes (NPBs) line with pattern sizes ranging from 50 to 200 nm are generated by patterning the initiator layer using deep‐ultraviolet photolithography followed by brush growth initiated from the patterned layer. Homogeneous PEBs with different degrees of charging and grafting densities are exposed to water and salt solutions with different temperatures for different periods. The degradation is monitored through dry‐state ellipsometry and atomic force microscopy measurements. Enhanced degrafting for more strongly swollen polymer brushes can be observed in agreement with an “entropic spring” model. Based on the results of the nonpatterned brushes, the NPBs are exposed to water at different temperatures and external salt content for varying periods of time. Counterintuitively, the NPBs show increased degrafting for smaller patterns, which is attributed to different polymer chain dynamics for nanobrushes and microbrushes. We investigate the influence of thermodynamic and kinetic parameters on the stability of (nanopatterned) PEBs and discuss the role of entanglements and formation of complexes in such films. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1283–1295     

New optical properties of polyelectrolyte hydrogels

A new optically active medium for lasers — a polyelectrolyte hydrogen swollen in a mixture of water + alcohol + dye — is presented. An anomalous dependence of the absorbance on the composition of the mixture is observed. It shows a maximum which corresponds to the composition when the hydrogel starts to swell as a hydrophilic network.     

Counterion distributions and effective interactions of spherical polyelectrolyte brushes

We consider the electrosteric repulsion of colloidal particles whose surface carries a dense layer of long polyelectrolyte chains (spherical polyelectrolyte brushes). The theory of electrosteric repulsion of star polyelectrolytes developed recently is augmented to include particles with a finite core radius. It is shown that most of the counterions are confined within the brush layer. The strong osmotic pressure thus created within the brush layer dominates the repulsive interaction between two such particles. Because of this the pair interaction potential between spherical polyelectrolyte brushes can be given in terms of an analytic expression. The theoretical predictions are compared with available experimental data and semi-quantitative agreement between the two is found.     

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.     

Interfacial friction and adhesion of polymer brushes

A bead-probe lateral force microscopy (LFM) technique is used to characterize the interfacial friction and adhesion properties of polymer brushes. Our measurements attempt to relate the physical structure and chemical characteristics of the brush to their properties as thin-film, tethered lubricants. Brushes are synthesized at several chain lengths and surface coverages from polymer chains of polydimethylsiloxane (PDMS), polystyrene (PS), and a poly(propylene glycol)-poly(ethylene glycol) block copolymer (PPG/PEG). At high surface coverage, PDMS brushes manifest friction coefficients (COFs) that are among the lowest recorded for a dry lubricant film (μ ≈ 0.0024) and close to 1 order of magnitude lower than the COF of a bare silicon surface. Brushes synthesized from higher molar mass chains exhibit higher friction forces than those created using lower molar mass polymers. Increased grafting density of chains in the brush significantly reduces the COF by creating a uniform surface of stretched chains with a decreased surface viscosity. Brushes with lower surface tension and interfacial shear stresses manifest the lowest COF. In particular, PDMS chains exhibit COFs lower than PS by a factor of 3.7 and lower than PPG/PEG by a factor of 4.7. A scaling analysis conducted on the surface coverage (σ) in relation to the fraction (ε) of the friction force developing from adhesion predicts a universal relation ε ~ σ(4/3), which is supported by our experimental data.     

Normal and frictional forces between surfaces bearing polyelectrolyte brushes

Normal and shear forces were measured as a function of surface separation, D, between hydrophobized mica surfaces bearing layers of a hydrophobic-polyelectrolytic diblock copolymer, poly(methyl methacrylate)- block-poly(sodium sulfonated glycidyl methacrylate) copolymer (PMMA- b-PSGMA). The copolymers were attached to each hydrophobized surface by their hydrophobic PMMA moieties with the nonadsorbing polyelectrolytic PSGMA tails extending into the aqueous medium to form a polyelectrolyte brush. Following overnight incubation in 10 (-4) w/v aqueous solution of the copolymer, the strong hydrophobic attraction between the hydrophobized mica surfaces across water was replaced by strongly repulsive normal forces between them. These were attributed to the osmotic repulsion arising from the confined counterions at long-range, together with steric repulsion between the compressed brush layers at shorter range. The corresponding shear forces on sliding the surfaces were extremely low and below our detection limit (+/-20-30 nN), even when compressed down to a volume fraction close to unity. On further compression, very weak shear forces (130 +/- 30 nN) were measured due to the increase in the effective viscous drag experienced by the compressed, sliding layers. At separations corresponding to pressures of a few atmospheres, the shearing motion led to abrupt removal of most of the chains out of the gap, and the surfaces jumped into adhesive contact. The extremely low frictional forces between the charged brushes (prior to their removal) is attributed to the exceptional resistance to mutual interpenetration displayed by the compressed, counterion-swollen brushes, together with the fluidity of the hydration layers surrounding the charged, rubbing polymer segments.     

Wetting transition on hydrophobic surfaces covered by polyelectrolyte brushes

We study the wetting by water of complex "hydrophobic-hydrophilic" surfaces made of a hydrophobic substrate covered by a hydrophilic polymer brush. Polystyrene (PS) substrates covered with polystyrene- block-poly(acrylic acid) PS- b-PAA diblock copolymer layers were fabricated by Langmuir-Schaefer depositions and analyzed by atomic force microscopy (AFM) and ellipsometry. On bare PS substrate, we measured advancing angles theta A = 93 +/- 1 degrees and receding angles theta R = 81 +/- 1 degrees . On PS covered with poorly anchored PS- b-PAA layers, we observed large contact angle hysteresis, theta A approximately 90 degrees and theta R approximately 0 degrees , that we attributed to nanometric scale dewetting of the PS- b-PAA layers. On well-anchored PS- b-PAA layers that form homogeneous PAA brushes, a wetting transition from partial to total wetting occurs versus the amount deposited: both theta A and theta R decrease close to zero. A model is proposed, based on the Young-Dupre equation, that takes into account the interfacial pressure of the brush Pi, which was determined experimentally, and the free energy of hydration of the polyelectrolyte monomers Delta G PAA (hyd), which is the only fitting parameter. With Delta G PAA (hyd) approximately -1300 J/mol, the model renders the wetting transition for all samples and explains why the wetting transition depends mainly on the average thickness of the brush and weakly on the length of PAA chains.