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.     

Revisiting the dispersion mechanism of grafted nanoparticles in polymer matrix: a detailed molecular dynamics simulation

By focusing on the grafted nanoparticles (NPs) embedded in polymer melts, a detailed coarse-grained molecular dynamics simulation is adopted to investigate the effects of the grafting density, the length of the matrix and grafted chains on the dispersion of the NPs. We have employed visualization snapshots, radial distribution functions (RDFs), the interaction energy between NPs, the number of neighbor NPs, and the conformation of the brush chains to clearly analyze the dispersion state of the grafted NPs. Our simulated results generally indicate that the dispersion of the NPs is controlled by both the excluded volume of the grafted NPs and the interface between the brushes and the matrix. It is found that increasing grafting density or grafted chain length leads to better dispersion, owing to larger excluded volume; however, increasing the length of the matrix chains leads to aggregation of NPs, attributed to both a progressive loss of the interface between the brushes and the matrix and the overlap between brushes of different NPs, intrinsically driven by entropy. Meanwhile, it is found that there exists an optimum grafting density (σ(c)) for the dispersion of the NPs, which roughly obeys the following mathematical relation: σ(c) is proportional to N(m)(K)/N(g)(L), where K, L > 0 and N(m) and N(g) represent the length of the matrix and grafted chain length, respectively. Considering the practical situation that the grafted brushes and the matrix polymer are mostly not chemically identical, we also studied the effect of the compatibility between the brushes and the matrix polymer by taking into account the attraction between the grafted chains and the matrix chains. In general, our comprehensive simulation results are believed to guide the design and preparation of high-performance polymer nanocomposites with good or even tailored dispersion of NPs.     

Brownian dynamics of a compressed polymer brush model. Off-equilibrium response as a function of surface coverage and compression rate

We study the compressive behaviour of a polymer-covered surface (i.e., a "polymer brush") using Brownian dynamics simulations. The model consists of grafted chains with variable flexibility, variable intra- and inter-chain interactions, as well as different surface coverage. We discuss the polymer brush response to confinement by considering variable rates of compression under a hard plane. Our results show a small degree of inter-chain entanglement, regardless of whether the interaction is attractive or merely excluded volume. We observe that the molecular shape depends strongly on the surface coverage. Dense brushes exhibit a limited degree of lateral deformation under compression; instead, chains undergo a transition that produces a local patch with near-solid packing. This effect due to surface density can be undone partially by increasing the attractive nature of the chain interaction, by modulating the rate of compression, or by allowing "soft anchoring", i.e., the possible Brownian drift of the grafting bead on the surface. We have also studied the polymer brush relaxation while maintaining the compressing plane, as well as after its sudden removal. We find evidence that also the relaxation depends on surface density; dense brushes appear to be configurationally frustrated at high compression and are unable to undergo swelling, regardless of the pressure applied.     

Domain memory of mixed polymer brushes

The nano-phase-separation in mixed polymer brushes consisting of polystyrene and poly(methyl methacrylate) (PS-PMMA) chains attached to a silicon surface is studied. The topographies of the mixed brushes are examined after they have been exposed to solvents which induce or erase nano-phase-separation. It is discussed whether the brush locally forms the same pattern every time the transition from the smooth and featureless to the nanopatterned state occurs ("domain memory") or if the local assembly of the domains emerges in a different arrangement after each cycle of topography switching. A memory measure parameter is introduced, which characterizes quantitatively the domain memory effect in the nanopattern. It is shown that at constant grafting density but with increasing molecular weight of the brush chains the memory measure parameter decreases. In contrast to this, brushes with constant molecular weight, but differing in grafting density, all have a similar domain memory. We discuss a possible origin of the domain memory effect in the mixed brush systems studied and point out its impact on the motion of nanoparticles adsorbed on top of such systems.     

Evaluation of an atomic force microscopy pull-off method for measuring molecular weight and polydispersity of polymer brushes: effect of grafting density

The accuracy of the molecular weights Mn and polydispersities of polymer brushes, determined by stretching the grafted chains using atomic force microscopy (AFM) and measuring the contour length distribution, was evaluated as a function of grafting density sigma. Poly(N,N-dimethylacrylamide) brushes were prepared by surface initiated atom transfer radical polymerization on latex particles with sigma ranging between 0.17 and 0.0059 chains/nm2 and constant Mn. The polymer, which could be cleaved from the grafting surface by hydrolysis and characterized by gel permeation chromatography (GPC), had a Mn of 30,600 and polydispersity (PDI) of 1.35. The Mn determined by the AFM technique for the higher density brushes agreed quite well with the GPC results but was significantly underestimated for the lower sigma. At high grafting density in good solvent, the extended structure of the brush increases the probability of forming segment-tip contacts located at the chain end. When the distance between chains approached twice the radius of gyration of the polymer, the transition from brush to mushroom structure presumably enabled the formation of a larger number of segment-tip contacts having separations smaller than the contour length, which explains the discrepancy between the two methods at low sigma. The PDI was typically higher than that obtained by GPC, suggesting that sampling of chains with above average contour length occurs at a frequency that is greater than their spatial distribution.     

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.     

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.     

Interactions between polymer brushes in solvents of variable quality: a density functional theory study

We present a density functional theory study of interactions between sterically stabilized colloidal particles in solvents of variable quality. Both flat and spherical polymer brushes are considered, as well as both monatomic and polymeric solvents. It is shown that the interaction between sterically stabilized particles can be tuned from repulsive to attractive by varying the solvent quality, the relative length of free and grafted chains, and by employing a mixed brush consisting of both well and poorly solvated chains.     

Functionalization and patterning of reactive polymer brushes based on surface reversible addition and fragmentation chain transfer polymerization

We present the synthesis of reactive polymer brushes prepared by surface reversible addition–fragmentation chain transfer polymerization of pentafluorophenyl acrylate. The reactive ester moieties can be used to functionalize the polymer brush film with virtually any functionality by simple post‐polymerization modification with amines. Dithiobenzoic acid benzyl‐(4‐ethyltrimethoxylsilyl) ester was used as the surface chain transfer agent (S‐CTA) and the anchoring group onto the silicon substrates. Reactive polymer brushes with adjustable molecular weight, high grafting density, and conformal coverage through the grafting‐from approach were obtained. Subsequently, the reactive polymer brushes were converted with amino‐spiropyrans resulting in reversible light‐responsive polymer brush films. The wetting behavior could be altered by irradiation with ultraviolet (UV) or visible light. Furthermore, a patterned surface of polymer brushes was obtained using a lithography technique. UV irradiation of the S‐CTA‐modified substrates leads to a selective degradation of S‐CTA in the exposed areas and gives patterned activated polymer brushes after a subsequent RAFT polymerization step. Conversion of the patterned polymer brushes with 5‐((2‐aminoethyl)amino)naphthalene‐1‐sulfonic acid resulted in patterned fluorescent polymer brush films. The utilization of reactive polymer brushes offers an easy approach in the fabrication of highly functional brushes, even for functionalities whose introduction is limited by other strategies. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Strongly stretched polymer brushes

Polymer “brushes” are formed when long-chain molecules are somehow attached by one end at an interface with a relatively small area per chain. Such adsorbed brushes in the presence of solvent may be used to modify surface properties, stabilize colloidal particles, etc. Strongly segregated block copolymer phases, or interfacial layers of such “polymeric surfactants” may also be modeled in terms of “melt brushes,” (i.e., brushes without solvent). In both cases, when chain attachments are crowded on the interface, the chains stretch out to avoid neighboring chains. The resulting physical state has properties markedly different from polymer solutions, gels, or weakly adsorbed polymer layers. When the chains are strongly stretched, their statistical mechanics become simpler, as fluctuations around the set of most probable conformations are suppressed. This makes possible many pencil-and-paper calculations of brush properties, including bending and compressional moduli, and detailed knowledge of the chain conformations. As a recent example, I will describe calculations of phase diagrams of strongly segregated block copolymers including bicontinuous double-diamond phases. © 1994 John Wiley & Sons, Inc.     

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.     

Molecular weight distribution effects on the structure of strongly adsorbed polymers by Monte Carlo simulation

Monte Carlo simulations are reported to study the structure of polymers adsorbed from solution onto strongly attractive, perfectly smooth substrates. Six systems spanning a range of molecular weight distributions are investigated with a coarse-grained united atom model for freely rotating chains. By employing a global replica exchange algorithm and topology altering Monte Carlo moves, a range of monomer-surface attraction from weak (0.27kT) to strong (4kT) is simultaneously explored. Thus for the first time ever, equilibrium polymer adsorption on highly attractive surfaces is studied, with all adsorbed molecules displaying similar properties and statistics. The architecture of the adsorbed layers, including density profiles, bond orientation order parameters, radii of gyration, and distribution of the adsorbed chain fractions, is shown to be highly dependent on the polydispersity of the polymer phase. The homology of polymer chains, and the ergodicity of states explored by the molecules is in contrast to the metastable, kinetically constrained paradigm of irreversible adsorption. The structure of more monodisperse systems is qualitatively similar to experimental results and theoretical predictions, but result from very different chain conformations and statistics. The polydispersity-dependent behavior is explained in the context of the competition between polymers to make contact with the surface.     

Effect of bidispersity in grafted chain length on grafted chain conformations and potential of mean force between polymer grafted nanoparticles in a homopolymer matrix

In efforts to produce polymeric materials with tailored physical properties, significant interest has grown around the ability to control the spatial organization of nanoparticles in polymer nanocomposites. One way to achieve controlled particle arrangement is by grafting the nanoparticle surface with polymers that are compatible with the matrix, thus manipulating the interfacial interactions between the nanoparticles and the polymer matrix. Previous work has shown that the molecular weight of the grafted polymer, both at high grafting density and low grafting density, plays a key role in dictating the effective inter-particle interactions in a polymer matrix. At high grafting density nanoparticles disperse (aggregate) if the graft molecular weight is higher (lower) than the matrix molecular weight. At low grafting density the longer grafts can better shield the nanoparticle surface from direct particle-particle contacts than the shorter grafts and lead to the dispersion of the grafted particles in the matrix. Despite the importance of graft molecular weight, and evidence of non-trivial effects of polydispersity of chains grafted on flat surfaces, most theoretical work on polymer grafted nanoparticles has only focused on monodisperse grafted chains. In this paper, we focus on how bidispersity in grafted chain lengths affects the grafted chain conformations and inter-particle interactions in an implicit solvent and in a dense homopolymer polymer matrix. We first present the effects of bidispersity on grafted chain conformations in a single polymer grafted particle using purely Monte Carlo (MC) simulations. This is followed by calculations of the potential of mean force (PMF) between two grafted particles in a polymer matrix using a self-consistent Polymer Reference Interaction Site Model theory-Monte Carlo simulation approach. Monte Carlo simulations of a single polymer grafted particle in an implicit solvent show that in the bidisperse polymer grafted particles with an equal number of short and long grafts at low to medium grafting density, the short grafts are in a more coiled up conformation (lower radius of gyration) than their monodisperse counterparts to provide a larger free volume to the longer grafts so they can gain conformational entropy. The longer grafts do not show much difference in conformation from their monodisperse counterparts at low grafting density, but at medium grafting density the longer grafts exhibit less stretched conformations (lower radius of gyration) as compared to their monodisperse counterparts. In the presence of an explicit homopolymer matrix, the longer grafts are more compressed by the matrix homopolymer chains than the short grafts. We observe that the potential of mean force between bidisperse grafted particles has features of the PMF of monodisperse grafted particles with short grafts and monodisperse grafted particles with long grafts. The value of the PMF at contact is governed by the short grafts and values at large inter-particle distances are governed by the longer grafts. Further comparison of the PMF for bidisperse and monodisperse polymer grafted particles in a homopolymer matrix at varying parameters shows that the effects of matrix chain length, matrix packing fraction, grafting density, and particle curvature on the PMF between bidisperse polymer grafted particles are similar to those seen between monodisperse polymer grafted particles.     

Molecular Transport within Polymer Brushes: A FRET View at Aqueous Interfaces

Molecular permeability through polymer brush chains is implicated in surface lubrication, wettability, and solute capture and release. Probing molecular transport through polymer brushes can reveal information on the polymer nanostructure, with a permeability that is dependent on chain conformation and grafting density. Herein, we introduce a brush system to study the molecular transport of fluorophores from an aqueous droplet into the external “dry” polymer brush with the vapour phase above. The brushes consist of a random copolymer of N-isopropylacrylamide and a Förster resonance energy transfer (FRET) donor-labelled monomer, forming ultrathin brush architectures of about 35 nm in solvated height. Aqueous droplets containing a separate FRET acceptor are placed onto the surfaces, with FRET monitored spatially around the 3-phase contact line. FRET is used to monitor the transport from the droplet to the outside brush, and the changing internal distributions with time as the droplets prepare to recede. This reveals information on the dynamics and distances involved in the molecular transport of the FRET acceptor towards and away from the droplet contact line, which are strongly dependent on the relative humidity of the system. We anticipate our system to be extremely useful for studying lubrication dynamics and surface droplet wettability processes.     

Thermodynamic Parameters of Temperature‐Induced Phase Transition for Brushes onto Nanoparticles: Hydrophilic versus Hydrophobic End‐Groups Functionalization

Quantification of the stimuli‐responsive phase transition in polymers is topical and important for the understanding and development of novel stimuli‐responsive materials. The temperature‐induced phase transition of poly(N‐isopropylacrylamide) (PNIPAm) with one thiol end group depends on the confinement—free polymer or polymer brush—on the molecular weight and on the nature of the second end. This paper describes the synthesis of heterotelechelic PNIPAm of different molecular weights with a thiol end group—that specifically binds to gold nanorods and a hydrophilic NIPAm end group by reversible addition‐fragmentation chain‐transfer polymerization. Proton high‐resolution magic angle sample spinning NMR spectra are used as an indicator of the polymer chain conformations. The characteristics of phase transition given by the transition temperature, entropy, and width of transition are obtained by a two‐state model. The dependence of thermodynamic parameters on molecular weight is compared for hydrophilic and hydrophobic end functional‐free polymers and brushes.     

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.     

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.     

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.     

Semiflexible polymers grafted to a solid planar substrate: changing the structure from polymer brush to "polymer bristle"

Monte Carlo simulations are presented for a coarse-grained model of polymer brushes with polymers having a varying degree of stiffness. Both linear chains and ring polymers grafted to a flat structureless non-adsorbing substrate surface are considered. Applying good solvent conditions, it is shown that with growing polymer stiffness the brush height increases significantly. The monomer density profiles for the case of ring polymers (chain length N(R) = 64) are very similar to the case of corresponding linear chains (N(L) = 32, grafting density larger by a factor of two) in the case of flexible polymers, while slight differences appear with increasing stiffness. Evidence is obtained that the chain dynamics in brushes is slowed down dramatically with increasing stiffness. Very short stiff rings (N(R) ≤ 16) behave like disks, grafted to the substrate such that the vector, perpendicular to the disk plane, is oriented parallel to the substrate surface. It is suggested that such systems can undergo phase transitions to states with liquid crystalline order.     

环境响应性聚合物刷的制备与应用

聚合物在材料表面通过物理吸附或化学接枝所形成的刷子状单分子层被称为聚合物刷,环境响应性聚合物刷能够根据环境微小变化可逆改变自身的物理化学性质,高分子链构象呈现伸展或塌缩状态等,显示了潜在的应用价值。本文综述了环境响应性聚合物刷的研究进展,讨论了温度响应性、pH值响应性、光响应性聚合物刷的结构特征和环境响应性机制,以及聚合物刷的各种制备方法,并着重介绍了其在智能膜、药物控释、催化、自组装、分子器件等领域的应用。