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.     

Atomic force microscopy study of the interaction between adsorbed poly(ethylene oxide) layers: effects of surface modification and approach velocity

The interaction forces between layers of the triblock copolymer Pluronic F108 adsorbed onto hydrophobic radio frequency glow discharge (RFGD) thin film surfaces and hydrophilic silica, in polymer-free 0.15 M NaCl solution, have been measured using the atomic force microscope (AFM) colloid probe technique. Compression of Pluronic F108 layers adsorbed on the hydrophobic RFGD surfaces results in a purely repulsive force due to the steric overlap of the layers, the form of which suggests that the PEO chains adopt a brush conformation. Subsequent fitting of these data to the polymer brush models of Alexander-de Gennes and Milner, Witten, and Cates confirms that the adsorbed Pluronic F108 adsorbs onto hydrophobic surfaces as a polymer brush with a parabolic segment density profile. In comparison, the interaction between Pluronic F108 layers adsorbed on silica exhibits a long ranged shallow attractive force and a weaker steric repulsion. The attractive component is reasonably well described by van der Waals forces, but polymer bridging cannot be ruled out. The weaker steric component of the force suggests that the polymer is less densely packed on the surface and is less extended into solution, existing as polymeric isolated mushrooms. When the surfaces are driven together at high piezo ramp velocities, an additional repulsive force is measured, attributable to hydrodynamic drainage forces between the surfaces. In comparing theoretical predictions of the hydrodynamic force to the experimentally obtained data, agreement could only be obtained if the flow profile of the aqueous solution penetrated significantly into the polymer brush. This finding is in line with the theoretical predictions of Milner and provides further evidence that the segment density profile of the adsorbed polymer brush is parabolic. A velocity dependent additional stepped repulsive force, reminiscent of a solvation oscillatory force, is also observed when the adsorbed layers are compressed under high loads. This additional force is presumably a result of hindered drainage of water due to the presence of a high volume fraction of polymer chains between the surfaces.     

Adsorption of polymers on a brush: Tuning the order of the wetting phase transition

We develop a computational methodology for the direct measurement of a wetting transition and its order via the effective interface potential. The method also allows to estimate contact angles in the nonwet state and to study adsorption isotherms. The proposed methodology is employed in order to study the wetting behavior of polymers on top of a brush consisting of identical polymers. In the absence of long-range forces, the system shows a sequence of nonwet, wet, and nonwet states as the brush density is increased. Including attractive long-range interactions we can make the polymer liquid wet the bush at all grafting densities, and both first- and second-order wetting transitions are observed. The latter case is limited to a small interval of grafting densities where the melt wets the brush in the absence of long-range interactions. Second-order wetting transitions are preceded by a first-order surface transition from a thin to a thick adsorbed layer. The interval of second-order wetting transitions is limited at low grafting densities by a surface critical end point and at high grafting densities by a tricritical wetting point. Our study highlights the rich wetting behavior that results when competing adsorbent-substrate interactions of different scales are tuned over a broad range.     

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.     

计算平均力势的理论方法

A universal theoretical framework is proposed for calculating potential of mean force (PMF) between two solute particles immersed in a solvent bath, the present method overcomes all of drawbacks of previous methods. The only input required to implement the recipe is solvent density distribution profile around a single solute particle. The universal framework is applied to calculate the PMF between two large spherical particles immersed in small hard sphere solvent bath. Comparison between the present predictions and existing simulation data shows reliability of the present recipe. Effects of solvent-solute interaction detail, solvent bulk density, and solute size on the excess PMF are investigated. The resultant conclusion is that depletion of solvent component by the solute particle induces attractive excess PMF, while gathering of solvent component by the solute particle induces repulsive excess PMF, high solvent bulk density and large solute size can strengthen the tendency of attraction or repulsion. Relevance of transition from depletion attraction to gathering repulsion with the biomolecular interaction, i.e. hydrophobic attraction and hydration repulsion, is discussed.     

Forces between nanorods with end-adsorbed chains in a homopolymer melt

Adsorbed or grafted polymers are often used to provide steric stabilization of colloidal particles. When the particle size approaches the nanoscale, the curvature of the particles becomes relevant. To investigate this effect for the case of cylindrical symmetry, I use a classical fluids density functional theory applied to a coarse-grained model to study the polymer-mediated interactions between two nanorods. The rods are coated with end-adsorbing chains and immersed in a polymer melt of chemically identical, nonadsorbing chains. The force between the nanorods is found to be nonmonotonic, with an attractive well when the two brushes come into contact with each other, followed by a steep repulsion at shorter distances. The attraction is due to the entropic phenomenon of autophobic dewetting, in which there is a surface tension between the brush and the matrix chains. These results are similar to previous results for planar and spherical polymer brushes in melts of the same polymer. The depth of the attractive well increases with matrix chain molecular weight and with the surface coverage. The attraction is very weak when the matrix chain molecular weight is similar to or smaller than the brush molecular weight, but for longer matrix chains the magnitude of the attraction can become large enough to cause aggregation of the nanorods.     

Surface forces,supramolecular polymers,and inversion symmetry

The effects of supramolecular equilibrium polymers on surface forces are studied by both a phenomenological Landau type analysis and a molecular model based on a Bethe-Guggenheim approximation. We point out that surface forces brought about by equilibrium polymers may be completely different from what can be found with "ordinary" polymers. The new feature is the role of inversion (a)symmetry or "directionality" of the associating unit molecules ("monomers"). Symmetric B-B monomers (where B denotes a self-complementary binding group) give rise to nondirectional chains and lead to attractive forces between similar surfaces. Asymmetric A-D monomers (where A and D denote complementary acceptor and donor groups, respectively) produce directional chains and can cause strong repulsion. The range of the attractive force has a maximum at intermediate concentration, while the range of the repulsive force increases over the whole concentration range.     

Attraction-driven disorder in a hard-core colloidal monolayer

Monte Carlo simulation techniques were employed to explore the effect of short-range attraction on the orientational ordering in a two-dimensional assembly of monodisperse spherical particles. We find that if the range of square-well attraction is approximately 15% of the particle diameter, the dense attractive fluid shows the same ordering behavior as the same density fluid composed of purely repulsive hard spheres. Fluids with an attraction range larger than 15% show an enhanced tendency to crystallization, while disorder occurs for fluids with an attractive range shorter than 15% of the particle diameter. A possible link with the existence of "repulsive" and "attractive" states in dense colloidal systems is discussed.     

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.     

Surface properties of bottle-brush polyelectrolytes on mica: effects of side chain and charge densities

Surface properties of a series of cationic bottle-brush polyelectrolytes with 45-unit-long poly(ethylene oxide) side chains were investigated by phase modulated ellipsometry and surface force measurements. The evaluation of the adsorbed mass of polymer on mica by means of ellipsometry is complex due to the transparency of mica and its birefringence and low dielectric constant. We therefore employed a new method to overcome these difficulties. The charge and the poly(ethylene oxide) side chain density of the bottle-brush polymers were varied from zero charge density and one side chain per segment to one charge per segment and no side chains, thus spanning the realm from a neutral bottle-brush polymer, via a partly charged brush polyelectrolyte, to a linear fully charged polyelectrolyte. The adsorption properties depend crucially on the polymer architecture. A minimum charge density of the polymer is required to facilitate adsorption to the oppositely charged surface. The maximum adsorbed amount and the maximum side chain density at the surface are obtained for the polymer with 50% charged segments and the remaining 50% of the segments carrying poly(ethylene oxide) side chains. It is found that brushlike layers are formed when 25-50% of the segments carry poly(ethylene oxide) side chains. In this paper, we argue that the repulsion between the side chains results in an adsorbed layer that is non-homogeneous on the molecular level. As a result, not all side chains will contribute equally to the steric repulsion but some will be stretched along the surface rather than perpendicular to it. By comparison with linear polyelectrolytes, it will be shown that the presence of the side chains counteracts adsorption. This is due to the entropic penalty of confining the side chains to the surface region.     

Interparticle interactions in concentrated suspensions and their bulk (rheological) properties

The interparticle interactions in concentrated suspensions are described. Four main types of interactions can be distinguished: (i) "Hard-sphere" interactions whereby repulsive and attractive forces are screened. (ii) "Soft" or electrostatic interactions determined by double layer repulsion. (iii) Steric repulsion produced by interaction between adsorbed or grafted surfactant and polymer layers. (iv)and van der Waals attraction mainly due to London dispersion forces. Combination of these interaction energies results in three main energy-distance curves: (i) A DLVO type energy-distance curves produced by combination of double layer repulsion and van der Waals attraction. For a stable suspension the energy-distance curve shows a "barrier" (energy maximum) whose height must exceed 25kT (where k is the Boltzmann constant and T is the absolute temperature). (ii) An energy-distance curve characterized by a shallow attractive minimum at twice the adsorbed layer thickness 2δ and when the interparticle-distance h becomes smaller than 2δ the energy shows a sharp increase with further decrease of h and this is the origin of steric stabilization. (iii) an energy-distance curve characterized by a shallow attractive minimum, an energy maximum of the DLVO type and a sharp increase in energy with further decrease of h due to steric repulsion. This is referred to as electrosteric repulsion. The flocculation of electrostatically and sterically stabilized suspensions is briefly described. A section is devoted to charge neutralization by polyelectrolytes and bridging flocculation by polymers. A distinction could be made between "dilute", "concentrated" and "solid suspensions" in terms of the balance between the Brownian motion and interparticle interaction. The states of suspension on standing are described in terms of interaction forces and the effect of gravity. The bulk properties (rheology) of concentrated suspensions are described starting with the case of very dilute suspensions (the Einstein limit with volume fraction Φ≤0.01), moderately concentrated suspensions (0.2>Φ≥0.1) taking into account the hydrodynamic interaction and concentrated suspensions (Φ>0.2) where semi-empirical theories are available. The rheological behavior of the above four main types of interactions is described starting with "hard-sphere" systems where the relative viscosity-volume fraction relationship could be described. The rheology of electrostatically stabilized suspensions was described with particular reference to the effect of electrolyte that controls the double layer extension. The rheology of sterically stabilized systems is described using model polystyrene suspensions with grafter poly(ethylene oxide) layers. Finally the rheology of flocculated suspensions was described and a distinction could be made between weakly and strongly flocculated systems.     

Normal and shear forces between a polyelectrolyte brush and a solid surface

The diblock copolymer poly(methyl methacrylate)‐b‐poly(sodium sulfonated glycidyl methacrylate) (PMMA‐b‐PSGMA) was end‐attached by its hydrophobic block (PMMA) onto mica hydrophobized by a stearic trimethylammonium iodide (STAI) layer, to form a polyelectrolyte brush immersed in water. With a surface force balance (SFB), we extended earlier measurements between two such brush layers for the case of normal and shear forces at different shear rates, surface separation, and compressions between one mica surface coated with STAI or a STAI‐diblock layer against a bare mica surface. After coating one of the surfaces with STAI, a long range attraction that results in a jump into an adhesive flat contact between the hydrophobic and hydrophilic surfaces was observed. A very different behavior was seen after forming the polyelectrolyte brush on the STAI‐coated surface. The long range attraction was replaced by repulsion, accompanied by very low friction during shear (ca. three orders of magnitude lower than with adsorbed polyelectrolytes). On further compression, a weak attraction to the adhesive contact was observed. From the final surface–surface contact separation, we deduce that most of the polyelectrolyte diblock brush layer was squeezed out from the gap, leaving the STAI layer and a small amount of the polymer attached to the surface. Stick‐sliding behavior was seen while applying shear, suggesting a dissipation mechanism caused by the trapped polyelectrolyte. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 193–204, 2005     

Adsorption of molecular brushes with polyelectrolyte backbones onto oppositely charged surfaces: a self-consistent field theory

The two-gradient version of the Scheutjens-Fleer self-consistent field (SF-SCF) theory is employed to model the interaction between a molecular bottle brush with a polyelectrolyte backbone and neutral hydrophilic side chains and an oppositely charged surface. Our system mimics graft-copolymers with a cationic main chain (among which poly( L-lysine)- graft-poly(ethylene glycol) (PLL- g-PEG) or poly( L-lysine)- graft-polyoxazoline are well-known examples) interacting with negatively charged (metal oxide) solid surfaces. We aim to analyze the copolymer-surface interaction patterns as a function of the molecular architecture parameters. Two regimes are investigated: First, we compute the effective interaction potential versus the distance from the surface for individual bottle brush macromolecules. Here, depending on the grafting ratio and the degree of polymerization of the side chains, the interplay of electrostatic attractions of the main chain to the surface and the steric repulsion of the grafts results in different patterns in the interaction potential and, therefore, in qualitatively different adsorption behavior. In particular, we demonstrate that, at high side chain grafting density and short grafts, the molecular brushes are strongly adsorbed electrostatically onto negatively charged substrates, whereas, in the opposite case of low grafting ratio and high molecular weight of grafts, the steric repulsion of the side chains from the surface dominates the polymer-surface interaction. At intermediate grafting ratios, the adsorption/depletion scenario depends essentially on the ratio between the electrostatic screening length and the thickness of the molecular bottle brush. We further have analyzed the equilibrium adsorbed amount as a function of the macromolecular architecture. Our results are based on a detailed account of attractive and repulsive (including intermolecular in-plane) interactions, and suggest a nonmonotonic dependence of the adsorbed amount on the grafting ratio, in good agreement with the experimental studies for PLL- g-PEG adsorption onto Nb2O5 surfaces. The results of the theoretical modeling are discussed in the context of the optimization of the PLL-g-PEG molecular design parameters in order to create protein-resistant surfaces.     

Compressible or incompressible blend of interacting monodisperse star and linear polymers near a surface

We consider a lattice model of a mixture of repulsive, attractive, or neutral monodisperse star (species A) and linear (species B) polymers with a third monomeric species C, which may represent free volume. The mixture is next to a hard, infinite plate whose interactions with A and C can be attractive, repulsive, or neutral. These two interactions are the only parameters necessary to specify the effect of the surface on all three components. We numerically study monomer density profiles using the method of Gujrati and Chhajer that has already been previously applied to study polydisperse and monodisperse linear-linear blends next to surfaces. The resulting density profiles always show an enrichment of linear polymers in the immediate vicinity of the surface due to entropic repulsion of the star core. However, the integrated surface excess of star monomers is sometimes positive, indicating an overall enrichment of stars. This excess increases with the number of star arms only up to a certain critical number and decreases thereafter. The critical arm number increases with compressibility (bulk concentration of C). The method of Gujrati and Chhajer is computationally ultrafast and can be carried out on a personal computer (PC), even in the incompressible case, when simulations are unfeasible. Calculations of density profiles usually take less than 20 min on PCs.     

Direct surface force measurements of polyelectrolyte multilayer films containing nanocrystalline cellulose

Polyelectrolyte multilayer films containing nanocrystalline cellulose (NCC) and poly(allylamine hydrochloride) (PAH) make up a new class of nanostructured composite with applications ranging from coatings to biomedical devices. Moreover, these materials are amenable to surface force studies using colloid-probe atomic force microscopy (CP-AFM). For electrostatically assembled films with either NCC or PAH as the outermost layer, surface morphology was investigated by AFM and wettability was examined by contact angle measurements. By varying the surrounding ionic strength and pH, the relative contributions from electrostatic, van der Waals, steric, and polymer bridging interactions were evaluated. The ionic cross-linking in these films rendered them stable under all solution conditions studied although swelling at low pH and high ionic strength was inferred. The underlying polymer layer in the multilayered film was found to dictate the dominant surface forces when polymer migration and chain extension were facilitated. The precontact normal forces between a silica probe and an NCC-capped multilayer film were monotonically repulsive at pH values where the material surfaces were similarly and fully charged. In contrast, at pH 3.5, the anionic surfaces were weakly charged but the underlying layer of cationic PAH was fully charged and attractive forces dominated due to polymer bridging from extended PAH chains. The interaction with an anionic carboxylic acid probe showed similar behavior to the silica probe; however, for a cationic amine probe with an anionic NCC-capped film, electrostatic double-layer attraction at low pH, and electrostatic double-layer repulsion at high pH, were observed. Finally, the effect of the capping layer was studied with an anionic probe, which indicated that NCC-capped films exhibited purely repulsive forces which were larger in magnitude than the combination of electrostatic double-layer attraction and steric repulsion, measured for PAH-capped films. Wherever possible, DLVO theory was used to fit the measured surface forces and apparent surface potentials and surface charge densities were calculated.     

On the mechanism of uptake of globular proteins by polyelectrolyte brushes: a two-gradient self-consistent field analysis

We present model calculations for the interaction of a protein-like inhomogeneously charged nanoscale object with a layer of densely grafted polyelectrolytes ("polyelectrolyte brush"). The motivation of this work is the recent experimental observation that proteins that carry an overall negative charge are absorbed into negatively charged polyelectrolyte brushes. Two-gradient self-consistent field (2G-SCF) calculations have been performed to unravel the physical mechanism of the uptake of protein thus effected. Our results prove that an overall neutral, protein-like object can electrostatically be attracted and therefore spontaneously driven into a polyelectrolyte brush when the object has two faces (patches, domains), one with a permanent positive charge and the other with a permanent negative charge. Using a 2G-SCF analysis, we evaluate the free energy of insertion, such that the electric dipole of the inclusion is oriented parallel to the brush surface. An electroneutral protein-like object is attracted into the brush because the polyelectrolyte brush interacts asymmetrically with the charged patches of opposite sign. At high ionic strength and low charge density on the patches, the attraction cannot compete with the repulsive excluded-volume interaction. However, for low ionic strengths and sufficiently high charge density on the patches, a gain on the order of k(B)T per charge becomes possible. Hence, the asymmetry of interaction for patches of different charges may result in a total attractive force between the protein and the brush. All results obtained herein are in excellent agreement with recent experimental data.     

Adsorption characteristics of bottle-brush polymers on silica: effect of side chain and charge density

The adsorption behavior of bottle-brush polymers with different charge/PEO ratio on silica was studied using optical reflectometry and QCM-D. The results obtained under different solution conditions clearly demonstrate the existence of two distinct adsorption mechanisms depending on the ratio of charge/PEO. In the case of low-charge density brush polymers (0-10 mol %), the adsorption occurs predominantly through the PEO side chains. However, the presence of a small amount of charge along the backbone (as low as 2 mol %) increases the adsorption significantly above that of the uncharged bottle-brush polymer in pure water. As the charge density of the brush polymers is increased to 25 mol % or larger the adsorption occurs predominantly through electrostatic interactions. The adsorbed layer structure was studied by measuring the layer dissipation using QCM-D. The adsorbed layer formed by the uncharged brush polymer dissipates only a small amount of energy that indicates that the brush lie along the surface, the scenario in which the maximum number of PEO side chains interact with the surface. The adsorbed layers formed by the low-charge density brush polymers (2-10 mol %) in water are more extended, which results in large energy dissipation, whereas those formed by the high-charge density brush polymers (50-100 mol %) have their backbone relatively flat on the surface and the energy dissipation is again low.     

Viscoelasticity and Stokes-Einstein relation in repulsive and attractive colloidal glasses

We report a numerical investigation of the viscoelastic behavior in models for steric repulsive and short-ranged attractive colloidal suspensions, along different paths in the attraction strength vs packing fraction plane. More specifically, we study the behavior of the viscosity (and its frequency dependence) on approaching the repulsive glass, the attractive glass, and in the reentrant region where viscosity shows a nonmonotonic behavior on increasing attraction strength. On approaching the glass lines, the increase of the viscosity is consistent with a power-law divergence with the same exponent and critical packing fraction previously obtained for the divergence of the density fluctuations. Based on mode-coupling calculations, we associate the increase of the viscosity with specific contributions from different length scales. We also show that the results are independent of the microscopic dynamics by comparing Newtonian and Brownian simulations for the same model. Finally, we evaluate the Stokes-Einstein relation approaching both glass transitions, finding a clear breakdown which is particularly strong for the case of the attractive glass.     

Molecular dynamics simulations of polyelectrolyte adsorption

We have performed molecular dynamics simulations of polyelectrolyte adsorption at oppositely charged surfaces from dilute polyelectrolyte solutions. In our simulations, polyelectrolytes were modeled by chains of charged Lennard-Jones particles with explicit counterions. We have studied the effects of the surface charge density, surface charge distribution, solvent quality for the polymer backbone, strength of the short-range interactions between polymers and substrates on the polymer surface coverage, and the thickness of the adsorbed layer. The polymer surface coverage monotonically increases with increasing surface charge density for almost all studied systems except for the system of hydrophilic polyelectrolytes adsorbing at hydrophilic surfaces. In this case the polymer surface coverage saturates at high surface charge densities. This is due to additional monomer-monomer repulsion between adsorbed polymer chains, which becomes important in dense polymeric layers. These interactions also preclude surface overcharging by hydrophilic polyelectrolytes at high surface charge densities. The thickness of the adsorbed layer shows monotonic dependence on the surface charge density for the systems of hydrophobic polyelectrolytes for both hydrophobic and hydrophilic surfaces. Thickness is a decreasing function of the surface charge density in the case of hydrophilic surfaces while it increases with the surface charge density for hydrophobic substrates. Qualitatively different behavior is observed for the thickness of the adsorbed layer of hydrophilic polyelectrolytes at hydrophilic surfaces. In this case, thickness first decreases with increasing surface charge density, then it begins to increase.     

Density and chain conformation profiles of square-well chains confined in a slit by density-functional theory

Density and chain conformation profiles of square-well chains between two parallel walls were studied by using density-functional theory. The free energy of square-well chains is separated into two contributions: the hard-sphere repulsion and the attraction. The Heaviside function is used as the weighting function for both of the two parts. The equation of state of Hu et al. is used to calculate the excess free energy of the repulsive part. The equation of state of statistical associating fluid theory for chain molecules with attractive potentials of variable range [A. Gil-Villegas et al. J. Chem. Phys. 106, 4168 (1997)] is used to calculate the excess free energy of the attractive part. Because the wall is inaccessible to a mass center of a longer chain, there exists a sharp fall in the distribution of end-to-end distance near the wall as the chain length increases. When the average density of the system is not too low, the prediction of this work is in good agreement with computer simulation results for the density profiles and the chain conformation over a wide range of chain length, temperature, and attraction strength of the walls. However, when the average density and the temperature are very low, the prediction deviates to a certain degree from the computer simulation results for molecules with long chain length. A more accurate functional approximation is needed.