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.     

Single ion diffusive transport within a Poly(styrene sulfonate) polymer brush matrix probed by fluorescence correlation spectroscopy

Diffusive transport within complex environments is a critical piece of the chemistry occurring in such diverse membrane systems as proton exchange and bilayer lipid membranes. In the present study, fluorescence correlation spectroscopy was used to evaluate diffusive charge transport within a strong polyelectrolyte polymer brush. The fluorescent cation rhodamine-6G was used as a counterion probe molecule, and the strong polyelectrolyte poly(styrene sulfonate) was the polymer brush. Such strong polyelectrolyte brushes show promise for charge storage applications, and thus it is important to understand and tune their transport efficiencies. The polymer brush demonstrated preferential solvation of the probe counterion as compared to solvation by the aqueous solvent phase. Additionally, diffusion within the polymer brush was strongly inhibited, as evidenced by a decrease in diffusion constant of 4 orders of magnitude. It also proved possible to tune the transport characteristics by controlling the solvent pH, and thus the ionic strength of the solvent. The diffusion characteristics within the charged brush system depend on the brush density as well as the effective interaction potential between the probe ions and the brush. In response to changes in ionic strength of the solution, it was found that these two properties act in opposition to each other within this strong polyelectrolyte polymer brush environment. A stochastic random walk model was developed to simulate interaction of a diffusing charged particle with a periodic potential, to show the response of characteristic diffusion times to electrostatic field strengths. The combined results of the experiments and simulations demonstrate that responsive diffusion characteristics in this brush system are dominated by changes in Coulombic interactions rather than changes in brush density. More generally, these results support the use of FCS to evaluate local charge transport properties within polyelectrolyte brush systems, and demonstrate that the technique shows promise in the development of novel polyelectrolyte films for charge storage/transport materials.     

Modified interfacial statistical associating fluid theory: application to tethered polymer chains

Modified interfacial statistical associating fluid theory density functional theory is extended to tethered polymer chains in the absence or presence of free polymer chains. The structures of the "dry" and "wet" polymer brushes have been calculated and compared with simulation results available in the literature. The comparisons show that the theory accurately predicts the structure of the tethered polymer brush. The average brush heights calculated from the theory agree with well-established scaling theories for tethered polymers. However, these scaling theories cannot predict the detailed structure, accurately. The effects of the segment-segment interactions of the tethered polymer and the free polymer have been effectively captured by the theory.     

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

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

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.     

Adsorption of the protein bovine serum albumin in a planar poly(acrylic acid) brush layer as measured by optical reflectometry

The adsorption of bovine serum albumin (BSA) in a planar poly(acrylic acid) (PAA) brush layer has been studied by fixed-angle optical reflectometry. The influence of polymer length, grafting density, and salt concentration is studied as a function of pH. The results are compared with predictions of an analytical polyelectrolyte brush model, which incorporates charge regulation and excluded volume interactions. A maximum in adsorption is found near the point of zero charge (pzc) of the protein. At the maximum, BSA accumulates in a PAA brush to at least 30 vol %. Substantial adsorption continues above the pzc, that is, in the pH range where a net negatively charged protein adsorbs into a negatively charged brush layer, up to a critical pH value. This critical pH value decreases with increasing ionic strength. The adsorbed amount increases strongly with both increasing PAA chain length and increasing grafting density. Experimental data compare well with the analytical model without having to include a nonhomogeneous charge distribution on the protein surface. Instead, charge regulation, which implies that the protein adjusts its charge due to the negative electrostatic potential in the brush, plays an important role in the interpretation of the adsorbed amounts. Together with nonelectrostatic interactions, it explains the significant protein adsorption above the pzc.     

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.     

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.     

High capacity, charge-selective protein uptake by polyelectrolyte brushes

Surface plasmon resonance was used to measure binding of proteins from solution to poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA) brushes end-grafted from gold surfaces by atom transfer radical polymerization (ATRP). PDMAEMA brushes were prepared with a variety of grafting densities and degrees of polymerization. These brushes displayed charge selective protein uptake. The extent of uptake for net negatively charged bovine serum albumin (BSA) scaled linearly with the surface mass concentration of grafted PDMAEMA, regardless of grafting density. BSA was bound at a constant ratio of 120 DMAEMA monomer units per protein molecule for all brushes examined. The equivalent three-dimensional concentration of BSA bound in the brush (i.e., the bound BSA surface excess concentration divided by the brush thickness) decreased monotonically with decreasing grafting density. The concentration of BSA bound within brushes prepared at higher grafting densities was comparable with the aqueous protein solubility limit. BSA desorption from the brush required changes in solution pH and/or ionic strength to eliminate its net electrostatic attraction to PDMAEMA. Net positively charged lysozyme was completely rejected by the PDMAEMA brushes.     

Magnetic particle‐loaded polymer brushes induced by external magnetic field: A Monte Carlo simulation

The effects of applied magnetic field on the system composed of polymer brushes and magnetic particles are studied by means of Monte Carlo simulation. The direction of the applied magnetic field is chosen to be perpendicular to the substrate plane. Polymer brushes and magnetic particles are attracted to each other. The average heights of polymer brushes depend not only on the strength of applied magnetic field (H) but also on the brush grafting density (σ) and the chain length (N). The applied magnetic field influences the arrangement of magnetic particles, and in turn, the arrangement of magnetic particles affects the spatial distribution of polymer brush monomers. When the strength of the magnetic field is increased, the average height of polymer brushes will be increased accordingly. The reason is that the orientations of the magnetic moments of particles must be along the magnetic field direction, and this leads polymer brushes to rearrange along the magnetic field direction. At the same time, the chain length and the grafting density of polymer brushes have also effects on the properties of the magnetic particles, such as the magnetic particles distribution, magnetic susceptibility, and pair correlation functions. Comparisons with the experimental ones are also made, and this investigation can provide some insights into statistical properties of magnetic particle‐loaded brushes induced by external magnetic field. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1873–1881, 2010     

Solvent response of mixed polymer brushes

We have performed classical density functional theory calculations to study the behavior of mixed polymer brushes tethered to a planar surface. We assume no lateral segregation of the polymer at the grafting density studied and consider an implicit solvent. For a binary mixture of short and long athermal polymer chains, the short chain is compressed while the long chain is stretched compared with corresponding pure polymer chains at the same grafting density, which is consistent with simulation. This results from configurational entropy effects. Furthermore, we add a mean-field interaction for each polymer brush to simulate their different response towards a solvent. The long chain is forced to dislike the solvent more than the short chain. Through the interplay between the solvent effects and configurational entropy effects, a switch of the polymer brush surface (or outer) layer is found with increasing chain length of the long chain. The transition chain length (long chain) increases with increasing the solvent selectivity, and decreases with increasing the grafting density of the long chain. These results can provide guidance for the design of smart materials based on mixed polymer brushes.     

Effect of the Ionic Strength on Collapse Transition in Star-like Polyelectrolytes

We present an analytical theory describing intramolecular conformational transition in a star-shaped polyelectrolyte (PE) molecule induced by a decrease in the solvent strength or/and increase in the ionic strength in the solution. We apply a mean-field Flory-type analysis in a box-like approximation, that is we assume fairly uniform distribution of densities of charged monomer units and all mobile ions (co- and counterions) in the intra-molecular volume of the star. We demonstrate that depending on the number of branches, fraction of charged monomers in the star and the ionic strength of the solution different scenario of the collapse transition may take place. At high ionic strength or low degree of ionization collapse transition occurs continuously resembling the collapse of a neutral polymer star. 1 On the contrary, at low ionic strength and high degree of ionization collapse transition features first order phase transition, that is, occurs discontinuously and involves coexistence of collapsed and stretched states.     

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.     

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.     

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.     

Surface forces between telechelic brushes revisited: the origin of a weak attraction

Telechelic polymers are useful for surface protection and stabilization of colloidal dispersions by the formation of polymer brushes. A number of theoretical investigations have been reported on a weak attraction between two telechelic brushes when they are at the classical contact, i.e., when the surface separation is approximately equal to the summation of the brush thicknesses. While recent experiments have confirmed the weak attraction between telechelic brushes, its origin remains elusive because of conflicting approximations used in the previous theoretical calculations. In this paper, we have investigated the telechelic polymer-mediated surface forces by using a polymer density functional theory (PDFT) that accounts for both the surface-adhesive energy and segment-level interactions specifically. Within a single theoretical framework, the PDFT is able to capture both the depletion-induced attraction in the presence of weakly adhesive polymers and the steric repulsion between compressed polymer brushes. In comparison of the solvation forces between telechelic brushes with those between brushes formed by surfactant-like polymers and with those between two asymmetric surfaces mediated by telechelic polymers, we conclude that the weak attraction between telechelic brushes is primarily caused by the bridging effect. Although both the surfactant-like and telechelic polymers exhibit a similar scaling behavior for the brush thickness, a significant difference has been observed in terms of the brush microstructures, in particular, the segment densities near the edges of the polymer brushes.     

Poisson-Boltzmann theory of the charge-induced adsorption of semi-flexible polyelectrolytes

A model is suggested for the structure of an adsorbed layer of a highly charged semi-flexible polyelectrolyte on a weakly charged surface of opposite charge sign. The adsorbed phase is thin, owing to the effective reversal of the charge sign of the surface upon adsorption, and ordered, owing to the high surface density of polyelectrolyte strands caused by the generally strong binding between polyelectrolyte and surface. The Poisson-Boltzmann equation for the electrostatic interaction between the array of adsorbed polyelectrolytes and the charged surface is solved for a cylindrical geometry, both numerically, using a finite element method, and analytically within the weak curvature limit under the assumption of excess monovalent salt. For small separations, repulsive surface polarization and counterion osmotic pressure effects dominate over the electrostatic attraction and the resulting electrostatic interaction curve shows a minimum at nonzero separations on the Angstrom scale. The equilibrium density of the adsorbed phase is obtained by minimizing the total free energy under the condition of equality of chemical potential and osmotic pressure of the polyelectrolyte in solution and in the adsorbed phase. For a wide range of ionic conditions and charge densities of the charged surface, the interstrand separation as predicted by the Poisson-Boltzmann model and the analytical theory closely agree. For low to moderate charge densities of the adsorbing surface, the interstrand spacing decreases as a function of the charge density of the charged surface. Above about 0.1 M excess monovalent salt, it is only weakly dependent on the ionic strength. At high charge densities of the adsorbing surface, the interstrand spacing increases with increasing ionic strength, in line with the experiments by Fang and Yang [J. Phys. Chem. B 101, 441 (1997)].     

In-situ investigation of the adsorption of globular model proteins on stimuli-responsive binary polyelectrolyte brushes

Binary brushes constituted from two incompatible polymers can be used in the form of ultrathin polymeric layers as a versatile tool for surface engineering to tune physicochemical surface characteristics such as wettability, surface charge, chemical composition, and morphology and furthermore to create responsive surface properties. Mixed brushes of oppositely charged weak polyelectrolytes represent a special case of responding surfaces that are sensitive to changes in the pH value of the aqueous environment and therefore represent interesting tools for biosurface engineering. The polyelectrolyte brushes used for this study were composed of two oppositely charged polyelelctrolytes poly(2-vinylpyridine) (P2VP) and poly(acrylic acid) (PAA). The in-situ properties and surface characteristics such as as surface charge, surface tension, and extent of swelling of these brush layers are functions of the pH value of the surrounding aqueous solution. To test the behavior of the mixed polylelctrolyte brushes in contact with biosystems, protein adsorption experiments with globular model proteins were performed at different pH values and salt concentrations (confinement of counterions) of the buffer solutions. The influence of the pH value, buffer salt concentration, and isoelectric points (IEP) of the brush and protein on the adsorbed amount and the interfacial tension during protein adsorption as well as the protein adsorption mechanism postulated in reference to recently developed theories of protein adsorption on polyelectrolyte brushes is discussed. In the salted regime, protein adsorption was found to be similar to the often-described adsorption at hydrophobic surfaces. However, in the osmotic regime the balance of electrostatic repulsion and a strong entropic driving force, "counterion release", was found to be the main influence on protein adsorption.     

受限于平行板中高分子刷/磁性纳米粒子体系的构象性质研究

采用蒙特卡洛模拟方法研究了在外磁场作用下磁性纳米粒子/高分子刷组成的共混体系的统计构象性质.共混体系受限于两平行板之间,高分子刷—端随机嫁接在乎行板上,另一端自由生长,高分子刷与高分子刷之间以及磁性纳米粒子与磁性纳米粒子之间存在相互排斥作用,而高分子刷和磁性纳米粒子之间存在相互吸引作用,所施加的磁场方向与两平行板垂直....