Density functional theory for rod-coil polymers with different size segments

A polymer density functional theory (PDFT) for rod-coil copolymers with different size segments is proposed, in which the PDFT approach combines a modified fundamental measure theory for the excluded-volume effects, Wertheim's first-order thermodynamics perturbation theory for the chain connectivity and the mean field approximation for van der Waals attraction. First, for testing the PDFT derived, we compare the density profiles from present theory to simulation data, and find that the present theory successfully reproduces the simulation data. Therefore, we use the PDFT to further investigate the local density and solvation forces of rod-coils with different size (A(5)D(3)) and the same size (A(5)B(3)) segments. Results indicate that the excluded volume effect from the coil part determines the solvation force profiles of two rod-coil brushes at strong surface energy. In addition, owing to the vacuum effect, the weak attraction around the classical contact of the rod-coil brushes is also observed. In short, the present theory can be easily applied to the other architecture polymers containing different size segments. It is expected that the calculation results in this work could provide useful reference to select the rod-coils as stabilizer for the protection of surfaces or the colloidal stabilization.     

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.     

Structures and Surface States of Polymer Brushes in Good Solvents: Effects of Surface Interactions

The influence of the surface interaction on the mesoscopic structure of grafted polymers in good solvents has been examined. At high surface coverage, tethered polymers are in the brush state and the parabolic segment density profile is confirmed by self-consistent field theory (SCFT) calculations. It is found that this is a universal behavior for a whole range of surface interactions from complete repulsion to strong attraction. More interestingly, finite surface repulsion may lead to the maximum in the proximal layer of its segment density profile, which is significantly different from both the depletion layer of pure repulsion and the adsorbing layer of attraction. In addition to the brush state on both repulsive and attractive surfaces, three additional surface states were identified by analyzing the scaling behavior of the layer thickness of polymer brushes: the mushroom state on repulsive substrates, the dilute and the semidilute surface states on attractive substrates.     

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.     

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.     

Gradient and patterned polymer brushes by photoinitiated “grafting through” approach

More than 2 decades of active investigations in the field of polymer brushes have revealed continuous and growing interest in different aspects of synthesis, properties, and applications of tethered polymers. In this article, we report on our recent advances in brush synthesis. The method we explore is based on the combination of “grafting through” approach with the functional anchoring polymer layer technique. We introduce the photoinitiated “version” of synthesis of polyacrylamide brushes. Both homogeneous depositions and laterally resolved gradient and patterned samples have been prepared by this technique. The results for flat polymer brushes, that is, thickness, stability, and contact angles, are complimented by kinetic parameters as deducted from analysis of gradient samples obtained by the method of a sliding mask. A microscopic shadow mask is used to fabricate patterned brushes. The microscopically patterned brushes demonstrate high lateral resolution limited by optical phenomena. Finally, we have performed a viability assaying of neuronal cell on both flat and patterned brushes. Sufficient restraint of cell adhesion on polyacrylamide photobrushes and very low cytotoxicity of the brush components (polymer brush itself, anchoring layer) make photografting a promising platform to control cell deposition and surface localization. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1616–1622, 2010     

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.     

Primary versus ternary adsorption of proteins onto PEG brushes

Polyethylene glycol (PEG) brushes are used to reduce protein adsorption at surfaces. Their design needs to allow for two leading adsorption modes at the brush-coated surface. One is primary adsorption at the surface itself. The second is ternary adsorption within the brush as a result of weak PEG-protein attraction. We present a scaling theory of the equilibrium adsorption isotherms allowing for concurrent primary and ternary adsorption. The analysis concerns the weak adsorption limit when individual PEG chains do not bind proteins. It also addresses two issues of special relevance to brushes of short PEGs: the consequences of large proteins at the surface protruding out of a shallow brush and the possibility of marginal solvent conditions leading to mean-field behavior. The simple expressions for the adsorption isotherms are in semiquantitative agreement with experiments.     

Friction and normal interaction forces between irreversibly attached weakly charged polymer brushes

Polyelectrolyte brushes were built on mica by anchoring polystyrene-poly(acrylic acid) (PS-b-PAA) diblock copolymers at a controlled surface density in a polystyrene monolayer covalently attached to OH-activated mica surfaces. Compared to physisorbed polymer brushes, these irreversibly attached charged brushes allow the polymer grafting density to remain constant upon changes in environmental conditions (e.g., pH, salt concentration, compression, and shear). The normal interaction and friction forces as a function of surface separation distance and at different concentrations of added salt (NaCl) were investigated using a surface forces apparatus. The interaction force profiles were completely reversible both on loading and receding and were purely repulsive. For a constant polymer grafting density, the influence of the polyelectrolyte charges and the Debye screening effect on the overall interaction forces was investigated. The experimental interaction force profiles agree very well with scaling models developed for neutral and charged polymer brushes. The variation of the friction force between two PAA brushes in motion with respect to each other as a function of surface separation distance appeared to be similar to that observed with neutral brushes. This similarity suggests that the increase in friction is associated with an increase in mutual interpenetration upon compression as observed with neutral polymers. The effect of the PAA charges and added ions was more significant on the repulsive normal forces than on the friction forces. The reversible characteristics of the normal force profiles and friction measurements confirmed the strong attachment of the PAA brushes to the mica substrate. High friction coefficients (ca 0.3) were measured at relatively high pressures (40 atm) with no surface damage or polymer removal.     

Synthesis and swelling behavior of pH-responsive polybase brushes

We synthesize polybase brushes and investigate their swelling behavior. Poly(2-(dimethylamino)ethyl methacrylate)) (PDMAEMA) brushes are prepared by the "grafting from" method using surface-initiated Atom Transfer Radical Polymerization to obtain dense brushes with relatively monodisperse chains (PDI = 1.35). In situ quaternization reaction can be performed to obtain poly(2-(trimethylamino)ethyl methacrylate)) (PTMAEMA) brushes. We determine the swollen thickness of the brushes using ellipsometry and neutron reflectivity techniques. Brushes are submitted to different solvent conditions to be investigated as neutral brushes and weak and strong polyelectrolyte brushes. The swelling of the brushes is systematically compared to scaling models. It should be pointed out that the scaling analysis of different types of brushes (neutral polymer and weak and strong polyelectrolyte brushes) is performed with identical samples. The scaling behavior of the PDMAEMA brush in methanol and the PTMAEMA brush in water is in good agreement with the predicted scaling laws for a neutral polymer brush in a good solvent and a polyelectrolyte brush in the osmotic regime. The salt-induced contraction of the quaternized brush is observed for high salt concentration, in agreement with the predicted transition between the regimes of the osmotic brush and the salted brush. From the crossover concentration, we calculate the effective charge ratio of the brush following the Manning counterion condensation. We also use PDMAEMA brushes as pH-responsive polybase brushes. The swelling behavior of the polybase brush is intermediate with respect to the behavior of the neutral polymer brush in a good solvent and the behavior of the quenched polyelectrolyte brush, as expected. The effective charge ratio of the PDMAEMA brush is determined as a function of pH using the scaling law of the polyelectrolyte brush in the osmotic regime.     

Wettability and antifouling behavior on the surfaces of superhydrophilic polymer brushes

The surface wettabilities of polymer brushes with hydrophobic and hydrophilic functional groups were discussed on the basis of conventional static and dynamic contact angle measurements of water and hexadecane in air and captive bubble measurements in water. Various types of high-density polymer brushes with nonionic and ionic functional groups were prepared on a silicon wafer by surface-initiated atom-transfer radical polymerization. The surface free energies of the brushes were estimated by Owens-Wendt equation using the contact angles of various probe liquids with different polarities. The decrease in the water contact angle corresponded to the polarity of fluoroalkyl, hydroxy, ethylene oxide, amino, carboxylic acid, ammonium salt, sulfonate, carboxybetaine, sulfobetaine, and phosphobetaine functional groups. The poly(2-perfluorooctylethyl acrylate) brush had a low surface free energy of approximately 8.7 mN/m, but the polyelectrolyte brushes revealed much higher surface free energies of 70-74 mN/m, close to the value for water. Polyelectrolyte brushes repelled both air bubbles and hexadecane in water. Even when the silicone oil was spread on the polyelectrolyte brush surfaces in air, once they were immersed in water, the oil quickly rolled up and detached from the brush surface. The oil detachment behavior observed on the superhydrophilic polyelectrolyte brush in water was explained by the low adhesion force between the brush and the oil, which could contribute to its excellent antifouling and self-cleaning properties.     

Interfacial friction and adhesion of polymer brushes

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

Theoretical study of cooperativity in multivalent polymers for colloidal stabilization

Multivalent polymers, i.e., copolymers with multiple binding sites, have been proposed recently for stabilization of fusogentic liposomes and other liposomal colloids useful for drug delivery. The performance of such polymers critically depends on their molecular architecture, in particular the strength and frequency of surface anchoring sites along the backbone of a highly soluble polymer. In this work, we investigate the adsorption and surface forces due to multivalent polymers based on coarse-grained polymer models. We find that for W-type polymers that form dangling tails when all anchoring segments are attached to a surface, increasing the chain length at fixed polymer composition leads to a stronger repulsive barrier in the polymer-mediated surface forces thereby increasing the ability of the polymer to stabilize colloidal particles. This prediction conforms to an earlier experiment indicating that increasing the number of hydrophobic anchors along poly(ethylene glycol) polymers results in the cooperative behavior for both surface adsorption and steric stabilization. For M-type multivalent polymers that have weakly anchoring sites placed at the ends, however, addition of binding sites at fixed polymer composition could lead to negative cooperativity, i.e., the more binding sites, the less the amount of adsorption or the weaker the ability of surface protection. The theory also predicts that polymers with two anchoring sites (e.g., telechelic copolymers) are most efficient for colloidal stabilization.     

An experimental-theoretical analysis of protein adsorption on peptidomimetic polymer brushes

Surface-grafted water-soluble polymer brushes are being intensely investigated for preventing protein adsorption to improve biomedical device function, prevent marine fouling, and enable applications in biosensing and tissue engineering. In this contribution, we present an experimental-theoretical analysis of a peptidomimetic polymer brush system with regard to the critical brush density required for preventing protein adsorption at varying chain lengths. A mussel adhesive-inspired DOPA-Lys (DOPA = 3,4-dihydroxy-phenylalanine; Lys = lysine) pentapeptide surface grafting motif enabled aqueous deposition of our peptidomimetic polypeptoid brushes over a wide range of chain densities. Critical densities of 0.88 nm(-2) for a relatively short polypeptoid 10-mer to 0.42 nm(-2) for a 50-mer were identified from measurements of protein adsorption. The experiments were also compared with the protein adsorption isotherms predicted by a molecular theory. Excellent agreements in terms of both the polymer brush structure and the critical chain density were obtained. Furthermore, atomic force microscopy (AFM) imaging is shown to be useful in verifying the critical brush density for preventing protein adsorption. The present coanalysis of experimental and theoretical results demonstrates the significance of characterizing the critical brush density in evaluating the performance of an antifouling polymer brush system. The high fidelity of the agreement between the experiments and molecular theory also indicate that the theoretical approach presented can aid in the practical design of antifouling polymer brush systems.     

Photochemical fixation of structures in binary polymer brushes-influence of layer thickness and grafting method

Polymer brushes consisting of hydrophilic and hydrophobic polymer components (poly-4-vinylpyridine, polymethacrylic acid and polystyrene, respectively) change their surface properties (as revealed by contact angles) when they are exposed to various solvents. In brushes prepared via grafting-from methods (using a specific surface initiator) layer thicknesses up to 300 nm were obtained. Copolymerization of the brush component monomers with 2-(4'-styryl)-indene yielded photo-cross-linkable brushes, which were used to fix the brushes in either the hydrophilic or hydrophobic state. Structural patterns differing in surface properties were produced and fixed by photo-cross-linking the hydrophobic component in that samples were irradiated through a mask. The patterns turned out most stable in moderately thick layers. AFM pictures confirm the contact angle results but reveal micro-domains of the two immiscible polymers in the grafted layers.     

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.     

Using Polymers to Impart Lubricity and Biopassivity to Surfaces: Are These Properties Linked?

Polymer brushes have been widely applied for the reduction of both friction and non‐specific protein adsorption. In many (but not all) applications, such as contact lenses or medical devices, this combination of properties is highly desirable. Indeed, for many polymer‐brush systems, lubricity and resistance to biofouling appear to go hand in hand, with modifications of brush architecture, for example, leading to a similar degree of enhancement (or degradation) in both properties. In the case of poly(ethylene glycol) (PEG) brushes, this has been widely demonstrated. There are, however, examples where this behavior breaks down. In systems where linear brushes are covalently crosslinked during surface‐initiated polymerization (SIP), for example, the presence and the chemical nature of links between grafted chains might or might not influence biopassivity of the films, while it always causes an increment in friction. Furthermore, when the grafted‐chain topology is shifted from linear to cyclic, chemically identical brushes show a substantial improvement in lubrication, whereas their protein resistance remains unaltered. Architectural control of polymer brush films can provide another degree of freedom in the design of lubricious and biopassive coatings, leading to new combinations of surface properties and their independent modulation.     

Theory of Liquid-crystalline Ordering in Polymer Brushes

Summary: We present a review of the works devoted to investigation of LC ordering in polymer brushes. This series has been carried out by the group of T. M. Birshtein and covers the following aspects of the problem: thermotropic LC phase transition in LCP brushes, microphase segregation, homeotropic and planar LC phases, LC polymer in LC solvent, lyotropic LCP brushes, LC transitions under normal or lateral force (shear flow). Analytical theory is developed for simplified model of polymer brush with accounting for thermotropic attraction in Mayer-Saupe approximation and lyotropic repulsion in DiMarzio formalism; numerical calculations are fulfilled in self-consistent field approximation (method of Scheutjens and Fleer). Brownian dynamics simulations are applied for modeling polymer brush in a shear flow.     

Polymer brushes on periodically nanopatterned surfaces

Structural properties of polymer brushes tethered on a periodically nanopatterned substrate are investigated by computer simulations. The substrate consists of an alternating succession of two different types of equal-width parallel stripes, and the polymers are end-tethered selectively on every second stripe. Three distinct morphologies of the nanopatterned brush have been identified, and their range of stability has been determined in terms of a single universal parameter that combines the grafting density, the polymer length, and the stripe width. We propose scaling relations for the average brush height and for the architectural properties of the outer surface of the nanopatterned brush under good solvent conditions. Our analysis provides guidelines for fabricating well-defined and tunable nanopatterned polymeric films.     

两亲性杂侧链聚合物刷的合成及其乳化功能

报道了一种随机高密度接枝亲水、疏水聚合物侧链的刷形两亲性聚合物.首先,结合可逆加成-断裂链转移(RAFT)聚合和后修饰方法,得到含叠氮侧基的聚甲基丙烯酸缩水甘油酯(PGMA-N3)作为主链;再分别合成端炔基聚苯乙烯(PS)和端炔基聚环氧乙烷(PEO),然后通过铜催化的叠氮-炔环加成反应,将疏水性PS和亲水性PEO同时高效的接到PGMA主链上,制得两亲性杂侧链的聚合物刷.由凝胶渗透色谱(SEC)分析得知,在主链叠氮基团与两侧链总炔基的摩尔投料比为1∶1的条件下,PS和PEO的接枝效率很高,都大于90%.通过调节主链长度和2种侧链的投料比,获得不同组成的聚合物刷.通过等质量的甲苯/水混合体系,考察两亲性聚合物刷的乳化能力,发现主链聚合度为100,PS∶PEO比例为70∶30的聚合物刷表现出最佳的乳化性能.