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.     

A molecular simulation study of the structure and tribology of polymer brushes: Comparison of behavior in theta and good solvents

Implicit solvent Brownian dynamics simulations of the structure and tribology of opposing polymer-brush covered surfaces have been carried out as a function of surface separation and solvent quality. Consistent with experiment, shear forces were found to be greater under theta solvent conditions than in a good solvent at equal relative separations (normalized by the respective height of the brushes in theta and good solvents). Much higher relative compression is required before the onset of significant shear forces in good solvent compared to theta solvent. The dependence of shear force for a given relative separation on solvent quality can be accounted for by differences in interpenetration of the brushes. When compared as a function of absolute surface separation, greater interpenetration and greater shear force are observed at large separations for the brushes in good solvent than in theta solvent, consistent with the greater brush height in good solvent. At shorter separations, corresponding to moderate to high compression, brush-brush interactions result in significant deformation of the brushes. In this regime, greater interpenetration and greater shear forces are observed in theta solvent at a given separation, in qualitative agreement with experiment.     

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.     

Brownian dynamics simulation of grafted polymer brushes

We present results of computer simulations by the method of Brownian dynamics of polymeric brushes attached to impenetrable planes. For testing both model and method we have used one polymer brush attached to a repulsive plane and compare some results with Monte Carlo results of Lai and Binder on the bond fluctuation model. We have also studied two polymeric brushes attached to two parallel planes at different distances between planes, and investigate the interplay between the interpenetration of the brushes and the configurational properties of the grafted chains.     

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.     

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.     

Nanowear studies in reversibly switchable polystyrene-poly(acrylic acid) mixed brushes

Wear studies were performed on polystyrene (PS)-poly(acrylic acid) (PAA) mixed polymer brushes and corresponding monobrushes in a dried state. The aim was to study the wear mechanism in polymer brush surfaces as well as to investigate the effect of switching of PS + PAA binary brush surfaces (on treatment with the selective solvents for the PS and PAA) on the wear process. Wear experiments were carried out using atomic force microscopy (AFM) under a controlled environment. The wear experiments were performed as a function of scan number using a sharp silicon nitride tip to induce the wear on the sample surfaces. The wear mechanism on different brush surfaces was influenced by molecular entanglement as well as adhesion and friction on the sample surface. The wear process on the PS monobrush surface treated with toluene took place via formation of the ripples. On the other hand, a typical wear mode observed on the PAA monobrushes was removal of the polymeric material from the surface. For the mixed brush surface treated with toluene (selective solvent for PS) where PS chains dominated the top of the sample surface, the typical wear mode observed was ripple formation similar to that observed for the PS monobrushes. However, when a mixed brush was treated with ethanol and pH 10 water so that PAA chains dominated the top layer, wear occurred via removal of material. The amount of wear on the surfaces increased with the number of scans. Furthermore, the load and scan velocity dependence of the wear process was also investigated. Wear on polymer brush surfaces increased on increasing the load and/or decreasing the scan speed. The present study shows that wear can be controlled/tuned using mixed responsive brushes.     

Free energy of alternating two-component polymer brushes on cylindrical templates

We use computer simulations to investigate the stability of a two-component polymer brush de-mixing on a curved template into phases of different morphological properties. It has been previously shown via molecular dynamics simulations that immiscible chains having different length and anchored to a cylindrical template will phase separate into stripes of different widths oriented perpendicularly to the cylindrical axis. We calculate free energy differences for a variety of stripe widths, and extract simple relationships between the sizes of the two polymers, N(1) and N(2), and the free energy dependence on the stripe width. We explain these relationships using simple physical arguments based upon previous theoretical work on the free energy of polymer brushes.     

Binary hairy nanoparticles: Recent progress in theory and simulations

Binary polymer brushes, including mixed homopolymer brushes and diblock copolymer brushes, are an attractive class of environmentally responsive nanostructured materials. Owing to microphase separation of the two chemically distinct components in the brush, multifaceted nanomaterials with functionalized and patterned surfaces can be obtained. This review summarizes recent progress on the theory and simulations related to binary polymer brushes grafted to flat, spherical, and cylindrical substrates, with a focus on patterned morphologies of multifaceted hairy nanoparticles, an intriguing class of hybrid nanostructured particles (e.g., nanospheres and nanorods). In particular, powerful field theory and particle-based simulations suitable for revealing novel structures on these patterned surfaces, including self-consistent field theory and dissipative particle dynamics simulations, are emphasized. The unsolved yet critical issues in this research field, such as dynamic response of binary polymer brushes to environmental stimuli and the hierarchical self-assembly of binary hairy nanoparticles, are briefly discussed. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1583–1599     

Determining the density profile of confined polymer brushes with neutron reflectivity

Polymer molecules at solid or fluid interfaces have an enormous spectrum of applications in a wide variety of technologies as lubricants, adhesion modifiers, and protective surface coatings. Because polymer brushes have great potential to be used in such applications, there is a need to determine their structure and efficiency in reduced spaces. Using neutron reflectivity, we have directly quantified the density distribution of opposing polymer brushes under confinement in good solvent conditions under confinement. Our measurements show that the density profile in the overlap region between opposing polymer brushes flattens, consistent with predictions from molecular-dynamics simulations. In addition, a significant increase in the density at the anchoring surfaces due to the collapse of the brush layers was observed. This collapse of the brushes in restricted geometries suggests that high-density brushes do not interpenetrate significantly under good solvent conditions. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3290–3301, 2004     

Nanowear studies in chemically heterogeneous responsive polymeric brushes by surface force microscopy

In this study, we present nanowear studies using surface force microscopy (SFM), on nanoscopic thin films of reversibly switchable binary polymer brushes [polystyrene (PS) + poly(2-vinylpyridine) (P2VP)] and respective monobrushes [polystyrene and poly(2-vinylpyridine)] synthesized via “grafting to” method. The aim was to tune the wear in nanothin polymer brush surfaces. Therefore, the effect of conformational switching of PS + P2VP brush on treatment with selective solvents for PS and P2VP chains on the wear process was investigated. Wear process on thick spin-coated films of PS and P2VP was also investigated for comparison. Nanowear experiments were performed using SFM tip by repeating scans over the surface to follow the wear process closely. The wear process on different surfaces was explained on the basis of molecular entanglement as well as adhesion and friction on the sample surface. For spin-coated PS film as well as PS and PS + P2VP brush surfaces (treated with toluene) with molecular entanglements at surface, wear mechanism involved formation of ripples. However, in case of spin-coated P2VP films as well as P2VP and PS + P2VP brush surfaces (treated with ethanol) with no molecular entanglements at surface, wear occurred via removal of polymer chains and their accumulation at the rim. For PS + P2VP surface treated with acidic water, wear mechanism was complex and inhomogeneous ripple formation was followed by formation of heaps of polymeric material in the center of scanned area. The extent of wear as measured either by root mean square roughness of the surface or spacing between the ripples, increased with the number of scans for all the surfaces. Our study shows that wear mode of polymer brush surfaces is different for different polymers and can be controlled/tuned by the use of binary polymer brushes.     

Topological Polymer Chemistry Enters Surface Science: Linear versus Cyclic Polymer Brushes

The cyclic polymer topology strongly alters the interfacial, physico‐chemical properties of polymer brushes, when compared to the linear counterparts. In this study, we especially concentrated on poly‐2‐ethyl‐2‐oxazoline (PEOXA) cyclic and linear grafts assembled on titanium oxide surfaces by the “grafting‐to” technique. The smaller hydrodynamic radius of ring PEOXAs favors the formation of denser brushes with respect to linear analogs. Denser and more compact cyclic brushes generate a steric barrier that surpasses the typical entropic shield by a linear brush. This phenomenon, translates into an improved resistance towards biological contamination from different protein mixtures. Moreover, the enhancement of steric stabilization coupled to the intrinsic absence of chain ends by cyclic brushes, produce surfaces displaying a super‐lubricating character when they are sheared against each other. All these topological effects pave the way for the application of cyclic brushes for surface functionalization, enabling the modulation of physico‐chemical properties that could be just marginally tuned by applying linear grafts.     

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.     

A simple theory of the interaction between polymer brushes immersed in a supercritical fluid

We use a simple two-order parameter model to describe the interaction between the brushes of polymers terminally attached to flat surfaces immersed in a supercritical solvent. Our approach makes it possible to take into account the high compressibility of the supercritical solvent, which proves to give a significant contribution to the disjoining force acting between polymer brushes. Our theory explains why the interaction between brushes can change from repulsive to attractive with decreasing solvent density. This theoretical finding is verified by making a comparison with recent computer simulations. A reasonably good agreement between the results of the present theory and the simulations is found.     

Stochastic dynamics simulation of grafted polymer brushes under shear deformation

We present results of computer simulations of polymer brushes (layers of polymer chains attached at one end onto an impermeable planar surface) under shear deformation at constant shear rate. As the first stage of calculations the behavior of a single brush was studied. The monomer density profile, the distribution of the chain ends, the positions and orientations of different monomers along the chain were calculated. Dimensions of the polymer chains as functions of the shear rate were obtained for different grafting densities. An increase in the brush thickness over the grafting plane with an increase in the shear rate as predicted by the theory of Barrat was observed. However, the magnitude of the effect appears to be small. We explain this by finite extensibility of the grafted chains.     

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.     

Control of surface properties using fluorinated polymer brushes produced by surface-initiated controlled radical polymerization

Surface-grafted styrene-based homopolymer and diblock copolymer brushes bearing semifluorinated alkyl side groups were synthesized by nitroxide-mediated controlled radical polymerization on planar silicon oxide surfaces. The polymer brushes were characterized by X-ray photoelectron spectroscopy (XPS), near-edge X-ray absorption fine structure (NEXAFS), and time-dependent water contact angle measurements. Angle-resolved XPS studies and water contact angle measurements showed that, in the case of the diblock copolymer brushes, the second block to be added was always exposed at the polymer-air interface regardless of its surface energy. Values of z*/Rg were estimated based on the radius of gyration, Rg, of the grafted homopolymer or block copolymer chains for the grafted brushes and thickness of the brush, z*. The fact that z*/Rg > 1 suggests that all these brushes are stretched. These results support the idea that after grafting the first block onto the surface the nitroxide-end capped polymer chains were able to polymerize the second block in a "living" fashion and the stretched brush so formed was dense enough that the outermost block in all cases completely covers the surface. NEXAFS analysis showed a relationship between the surface orientation of the fluorinated side chains and brush thickness with thicker brushes having more oriented side chains. Time-dependent water contact angle measurements revealed that the orientation of the side chains of the brush improved the surface stability toward reconstruction upon prolonged exposure to water.     

Attractive bridging interactions in dense polymer brushes in good solvent measured by atomic force microscopy

Using an atomic force microscope (AFM), we have investigated the interaction forces exerted by latex particles bearing densely grafted polymer brushes consisting of poly(N,N-dimethylacrylamide) (PDMA), poly(methoxyethylacrylamide) (PMEA), poly(N-isopropylacrylamide) (PNIPAM), and PMEA-b-PNIPAM in aqueous media (good solvent). The brushes were prepared by controlled surface-initiated atom transfer radical polymerization, and the hydrodynamic thicknesses were measured by dynamic light scattering. The molecular weight (Mn), grafting density (sigma), and polydispersity (PDI) of the brushes were determined by gel permeation chromatography and multiangle laser light scattering after cleaving the polymer from the latex surface by hydrolysis. Force profiles of PDMA (0.017 nm(-2) < or = sigma < or = 0.17 nm-2) and PMEA (sigma = 0.054 nm-2) brushes were purely repulsive upon compression, with forces increasing with Mn and a, as expected, due to excluded volume interactions. At a sufficiently low grafting density (sigma = 0.012 nm-2), PDMA exhibited a long-range exponentially increasing attractive force followed by repulsion upon further compression. The long-range attractive force is believed to be due to bridging between the free chain ends and the AFM tip. The PNIPAM brush exhibited a bridging force at a grafting density of 0.037 nm(-2), a value lower than the sigma needed to induce bridging in the PDMA brush. Bridging was therefore found to depend on grafting density as well as on the nature of the monomer. The grafting densities of these polymers were larger than those typically associated with bridging. Bridging interactions were used to confirm the presence of PNIPAM in a block copolymer PMEA-b-PNIPAMA brush given that the original PMEA homopolymer brush produced a purely repulsive force. The attractive force was first detected in the block copolymer brush at a separation that increased with the length of the PNIPAM block.     

Mixed brushes consisting of oppositely charged Y-shaped polymers in salt free,monovalent, and divalent salt solutions

The conformation and the internal stratification of mixed brushes formed from oppositely charged Y(−) and Y(+)-shaped chains in salt free, monovalent, and divalent salt solutions were studied by means of molecular dynamics simulations using the primitive model. Scaling relations of mixed brush height with respect to the grafting surface per chain, the ratio of the total positive to the total negative charge of polyelectrolyte chains, and salt concentrations were obtained. The simulations predicted that mixed brushes show a unique response to divalent salt (1:2) solutions. For symmetric brushes having the same spacer lengths, number of chains and charged units fractions the increase of the salt concentration leads to the enrichment of the outer brush surface with Y(+) units and the lamella microphase separation. For asymmetric brushes in high salt concentration cylindrical domain microphases are formed.