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.     

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.     

Electrolyte-induced collapse of a polyelectrolyte brush

We have investigated the electrolyte-induced collapse of a polyelectrolyte brush covalently attached to a planar solid surface. Positively charged poly-4-vinyl [N-methyl-pyridinium] (MePVP) brushes were prepared in situ at the surface by free radical chain polymerization using a surface-immobilized initiator monolayer ("grafting from" technique) and 4-vinylpyridine as the monomer, followed by a polymer-analogous quaternization reaction. The height of the brushes was measured as a function of the external salt concentration via multiple-angle null ellipsometry. As predicted by mean-field theory, the height of the MePVP brushes remains unaffected by the addition of low amounts of external salt. At higher salt concentrations the brush height decreases. The extent to which the brush shrinks strongly depends on the nature of the salt present in the environment. MePVP brushes collapse to almost the dry layer thickness upon the addition of potassium iodide to a contacting aqueous medium. In contrast, the collapse of MePVP brushes having bromide or chloride counterions is much less pronounced. These brushes remain in a highly swollen state even after large amounts of salt have been added to the solution.     

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.     

Shear of a planar polyelectrolyte brush

The behavior of a planar polyelectrolyte brush subjected to normal and tangential external forces is considered. A new “polyelectrolyte effect” is predicted: shear of a free polyelectrolyte brush leads to a decrease in brush thickness contrary to the case of a free neutral brush. Such behavior is equivalent to that of a neutral brush subjected to an external normal stretching force. In the case of a polyelectrolyte brush this force is created by the osmotic pressure of mobile counterions neutralizing grafted chain charges. Addition of salt diminishes the polyelectrolyte effect and changes the sign of correlation between brush thickness and tangential deformation.     

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     

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.     

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.     

Exclusion zone of convex brushes in the strong-stretching limit

We investigate asymptotic properties of long polymers grafted to convex cylindrical and spherical surfaces, and, in particular, distribution of chain free ends. The parabolic potential profile, predicted for flat and concave brushes, fails in convex brushes, and chain free ends span only a finite fraction of the brush thickness. In this paper, we extend the self-consistent model developed by Ball, Marko, Milner, and Witten [Macromolecules 24, 693 (1991)] to determine the size of the exclusion zone, i.e., size of the region of the brush free from chain ends. We show that in the limit of strong stretching, the brush can be described by an alternative system of integral equations. This system can be solved exactly in the limit of weakly curved brushes, and numerically for the intermediate to strong curvatures. We find that going from melt state to theta solvent and then to marginal solvent decreases relative size of the exclusion zone. These relative differences grow exponentially as the curvature decreases to zero.     

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.     

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.     

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.     

Helix formation in the polymer brush

This work considers the physics of a brush formed by polymers capable of undergoing a helix-coil transition. A self-consistent field approximation for strongly stretched polymer chains is used in combination with a lattice model of the interaction energy in helix-coil mixtures. Crowding-induced chain stretching stabilizes helix formation at moderate tethering densities while high tethering density causes sufficiently strong stretching to unravel segments of the helix, resulting in distinct layers of monomer density and helical content. Compared to a random-coil brush at low-to-moderate tethering density, a helicogenic brush is less resistant to compression in the direction perpendicular to stretching due to easy alignment of helices and fewer unfavorable interactions between helical segments. At higher tethering density, the abovementioned stretch-induced decrease in helical content resists further compression. The proposed model is useful for understanding an emerging class of biomaterials that utilize helix-forming polymer brushes to induce shape changes or to stabilize biofunctional helical peptide sequences.     

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.     

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.     

Facile surface immobilization of ATRP initiators on colloidal polymers for grafting brushes and application to colloidal crystals

Bromo-initiators for atom transfer radical polymerization (ATRP) were successfully immobilized on the surfaces of cross-linked poly(methyl methacrylate) (PMMA) spheres by soap-free emulsion polymerization using CBr(4) as the chain transfer agent. Subsequent surface-initiated ATRP (SI-ATRP) afforded a layer of PMMA brushes covalently attached to the sphere surfaces. Colloidal crystal films of these monodisperse spheres were then studied to identify the relationship between variation in particle diameter and the optical properties. The particle diameters were controlled by varying the feed monomer proportions in soap-free emulsion polymerization and the thickness of the grafted brush layer. It was found that the particle diameter could successfully be controlled to obtain crystal films that produce a variety of brilliant colors in the visible region. The results of this study can provide useful information for facile preparation of surface-immobilized ATRP initiators on colloidal polymers and can be employed for grafting polymer brushes.     

Molecular dynamics simulations of grafted polyelectrolytes on two apposing walls

Molecular dynamics simulations of polyelectrolytes grafted to two apposing surfaces were performed. Bead-spring polymer models are used to treat flexible chains [e.g., sodium poly(styrene sulfonate)] and stiff chains (double-stranded DNA). The counterions are explicitly treated. The effect of the surface density of the grafted polymer, the chain length, and the gap width on the structure and the pressure were studied. Results are compared to experimental measurements and to simulations of polyelectrolyte brushes on a single surface. The density profiles exhibit a maximum not found in single surface data. The maximum is due to the brushes shrinking to avoid interpenetration.     

Poisson-Boltzmann theory of pH-sensitive (annealing) polyelectrolyte brush

We present a self-consistent field analytical theory of a polymer brush formed by weakly charged pH-sensitive (annealing) polyelectrolytes tethered to a solid-liquid interface and immersed in buffer solution of low molecular weight salt. We use the Poisson-Boltzmann framework, applied by us previously to polyelectrolyte (PE) brushes with quenched charge (Zhulina, E. B.; Borisov, O. V. J. Chem. Phys. 1997, 107, 5952). This approach allows for detailed analysis of the internal structure of annealing PE brush in terms of polymer density distribution, profiles of electrostatic potential and of local degree of chain ionization as a function of buffer ionic strength and pH without any assumptions on mobile ion distribution imposed in earlier scaling-type models. The presented analytical theory recovers all major asymptotic dependences for average brush properties predicted earlier. In particular, a nonmonotonic dependence of brush thickness on ionic strength and grafting density is confirmed and specified with accuracy of numerical coefficients including crossover regions. Moreover, the theory predicts qualitatively new effects, such as, e.g., disproportionation of tethered polyions into weakly charged concentrated proximal and strongly charged sparse distal brush domains at low salt and moderate grating densities. The presented results allow us to quantify responsive features of annealing PE brushes whose large-scale and local conformational properties can be manipulated by external stimuli.     

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.     

Ionizable polyelectrolyte brushes: brush height and electrosteric interaction

Semi-analytical scaling theory is used to describe quenched and annealed (weakly charged, ionizable, charge-regulating) polyelectrolyte brushes in electrolyte solutions of arbitrary salt concentration. An Alexander-De Gennes box model with homogeneous distribution of polymer segments and the free ends located at the edge of the brush is assumed, as is local electroneutrality in the brush. For annealed polyelectrolyte and in the low-salt regime, the theory predicts that for sufficiently dense brushes, the salt concentration has a small influence on brush height, while the brush expands with increasing grafting density, in agreement with experiment. Expressions are presented for the interaction free energy of compressed ionizable and quenched polyelectrolyte brushes (proportional to the force between particles or curved surfaces). In all cases, the required prefactors are explicitly stated. The theory is compared directly with published experiments on the influence of salt concentration, pH, and grafting density on the thickness and interaction force of polystyrene sulfonate (quenched) and poly(meth)acrylic acid (annealed) brushes. In general, trends are well reproduced but significant deviations remain.