双峰聚合物分子刷的层化机理

建立了用于模拟双峰聚合物分子刷相结构的自洽场理论. 模拟结果表明, 良溶剂条件能够促使双峰聚合物分子刷裂分为内外两个亚分子层, 其中短链居于内分子层, 而长链伸展到外分子层. 体系溶解性的加强不仅使聚合物的密度分布逐渐趋近强分凝理论的解析结果, 而且加大了分子链的伸展和链段的局部取向程度. 分子链接枝密度的增加能够促使分子刷的层化, 并且在良溶剂区域, 不同接枝密度的分子链密度分布可以回归到同一条主线. 在良溶剂条件下, 长链的聚合度对短链的密度分布影响不大, 但能够导致长链向外分子层扩展.     

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.     

Phase transitions in polymer brushes

Liquid crystalline ordering in planar polymer brushes is investigated theoretically by numerical calculations within a self-consistent field approximation. The brushes are formed by macromolecules with mesogenic groups in main chain and immersed in a solvent. Existence of a microphase segregated brush (MSB) regime with a collapsed orientationally ordered intrinsic sublayer and a swollen external sublayer is shown. At small grafting density, the transition from a conventional brush state to the microphase segregated state is a jump-wise first order phase transition for a finite chain length (N). The magnitudes of the jumps in the average characteristics of the brush tend to zero in the limit N → ∞ since this transition occurs only in a vanishingly small part (∝ N^−1/2) of the brush. High compressibility of MSB brush is demonstrated. The origin of phase transition in planar brushes is discussed.     

Memory of surface patterns in mixed polymer brushes: simulation and experiment

The correlation between the morphology of mixed polymer brushes and fluctuations of the grafting points is investigated by single-chain-in-mean-field simulations and experiments. The local topography of two types of mixed polystyrene-polymethylmethacrylate (PS-PMMA) brushes that differ in their modes of attachment has been studied during repeated microphase separation into laterally structured and homogeneous morphologies upon changing solvents. In the first type of brush (conventional), each of the surface-attached initiator groups starts the growth of either a PS or a PMMA chain in a random fashion. In the second case (Y-shaped mixed brushes), two chains of different types are attached to the same anchor group on the substrate. Whereas in the first case statistical fluctuations of the chemical composition occur on a local scale, such composition fluctuations are strongly suppressed in the latter case. The microphase-separated morphology is similar in both cases, but Y-shaped brushes exhibit a significantly weaker domain memory than do conventional PS-PMMA mixed brushes. The results of the experiment are compared with simulations, and a simple phenomenological argument and qualitative agreement are found. The observations demonstrate that small fluctuations in the grafting points are amplified by the microphase separation and nucleate the location of the domains in the mixed brush.     

Interfacial properties of statistical copolymer brushes in contact with homopolymer melts

We use polymer self-consistent field theory to quantify the interfacial properties of random copolymer brushes (AB) in contact with a homopolymer melt chemically identical to one of the blocks (A). We calculate the interfacial widths and interfacial energies between the melt and the brush as a function of the relative chain sizes, grafting densities, compositions of the random copolymer in the brush, and degree of chemical incompatibility between the A and B species. Our results indicate that the interfacial energies between the melt and the brush increase (signifying expulsion of the free chains from the brush) with increasing grafting density, chemical incompatibility between A and B components, and size of the free chains relative to the grafted chains. We also compare the interfacial energies of random copolymers of different sequence characteristics and find that, except for the case of very blocky or proteinlike chains, blockiness of the copolymer has only little effect on interfacial properties. Our results for interfacial energies are rationalized based on the concept of an "effective volume fraction" of the brush copolymers, f(eff), which quantifies the chemical composition of the brush segments in the interfacial zone between the brush and melt copolymers. Using this concept, we modify the strong-stretching theory of brush-melt interfaces to arrive at a simple model whose results qualitatively agree with our results from self-consistent field theory. We discuss the ramifications of our results for the design of neutral surfaces.     

Communication: lateral phase separation of mixed polymer brushes physisorbed on planar substrates

Here, we present a new method to model lateral phase separation in mixed polymer brushes physisorbed to a planar surface with mobile grafting points. The model is based on a local mean field theory that combines a Flory-Huggins approximation for interaction enthalpies with an Alexander-de Gennes brush entropy contribution. Using Monte Carlo sampling, the application of these two interactions to a lattice model yields a range of phase behavior consistent with previous theoretical and experimental work. This model will be useful for predicting mixed polymer brush morphologies on planar surfaces and in principle can be extended to other geometries (e.g., spheres) and polymer systems.     

Homeotropic and planar structures in liquid-crystalline polymer brushes

The ordering in polymer brushes formed by macromolecules with mesogenic groups in the main chain is investigated. The numerical method of self-consistent field approximation was used. The existence of two different liquid crystalline nematic states is shown: homeotropic (HLC) and planar (PLC) states. The free energy of the HLC state is always less than that of the PLC state. However, with the increase of energy of anisotropic interactions, (with decrease in temperature) our numerical procedure leads us to either one or another state depending on the grafting density. The results obtained show that both brush surfaces, play an essential role in establishing the concrete LC state structure. The grafting surface and the external surface force the planar order.     

Scaling behavior of a brush-homopolymer interface in the limit of high grafting density

The interface between a polymer brush and a chemically equivalent homopolymer is examined using self-consistent field theory (SCFT). Focusing on ultrahigh grafting densities, we extract how the properties scale with the brush thickness, L, and compare with predictions based on strong-stretching theory (SST). Although the scaling exponents are consistent, the overall agreement is poor. We attribute this to the inaccurate way the SST-based calculation treats chain fluctuations at the extremity of the brush. This accounts for a previous disagreement between SCFT and SST in regards to autophobic dewetting, and brings into question a number of other SST predictions. Our conclusion is that SST requires a more sophisticated treatment of finite-stretching corrections, along the lines of that proposed by Likhtman and Semenov [Europhys. Lett. 51, 307 (2000)].     

Poisson-Boltzmann theory of pH-sensitive (annealing) polyelectrolyte brush

We present a self-consistent field analytical theory of a polymer brush formed by weakly charged pH-sensitive (annealing) polyelectrolytes tethered to a solid-liquid interface and immersed in buffer solution of low molecular weight salt. We use the Poisson-Boltzmann framework, applied by us previously to polyelectrolyte (PE) brushes with quenched charge (Zhulina, E. B.; Borisov, O. V. J. Chem. Phys. 1997, 107, 5952). This approach allows for detailed analysis of the internal structure of annealing PE brush in terms of polymer density distribution, profiles of electrostatic potential and of local degree of chain ionization as a function of buffer ionic strength and pH without any assumptions on mobile ion distribution imposed in earlier scaling-type models. The presented analytical theory recovers all major asymptotic dependences for average brush properties predicted earlier. In particular, a nonmonotonic dependence of brush thickness on ionic strength and grafting density is confirmed and specified with accuracy of numerical coefficients including crossover regions. Moreover, the theory predicts qualitatively new effects, such as, e.g., disproportionation of tethered polyions into weakly charged concentrated proximal and strongly charged sparse distal brush domains at low salt and moderate grating densities. The presented results allow us to quantify responsive features of annealing PE brushes whose large-scale and local conformational properties can be manipulated by external stimuli.     

Surface instabilities of minority chains in dense polymer brushes: A comparison of density functional theory and quasi-off-lattice self-consistent field theory

This work studies surface instabilities in switchable homopolymer brushes where the minority chain differs in length from the brush chains. Both off-lattice numerical self-consistent field theory and classical density functional theory are employed. It is found that the two methods agree well with each other as long as the same equation of state for the polymer chains is used.     

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     

Interactions between polymer-grafted particles and bare particles for biocompatibility applications

We use self-consistent field theory (SCFT) to study the interactions between a polymer-grafted spherical particle and a bare spherical particle and explore how these interaction energies depend on the radii of the two particles and the grafting density. We find that the magnitude of the interaction energies increases with the radii of both the grafted and bare particles and with increasing grafting density. We also find a universal scaling law for the interaction potential which exhibits a power-law dependence on both particle sizes, a linear dependence on grafting density, and a logarithmic dependence on interparticle distance with a range of interaction that scales with brush height. We compare our numerical results to those obtained using the Derjaguin approximation. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2566–2577, 2009     

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.     

Mixed homopolymer brushes grafted onto a nanosphere

Microphase separation of mixed A∕B polymer brushes grafted onto a nanosphere with its radius comparable to the size of polymers is investigated by numerical implementation of the self-consistent field theory. The idea is to embed the sphere within a larger cubic computational cell and use a "masking" technique to treat the spherical boundary. The partial differential equations for the chain propagator on the sphere can thus be readily solved with an efficient and high-order accurate pseudospectral method involving fast Fourier transform on a cubic cell. This numerical technique can circumvent the "pole problem" due to the use of a spherical coordinate system in conventional finite difference or finite element grid. We systematically investigate the effect of the total grafting density, composition, chain length asymmetry between two grafted homopolymers as well as spherical radius, i.e., substrate curvature on the formation of island structure with specific arrangement in a regular lattice. A series of island structures with different island numbers representing specific structure symmetry ranging from 2 to 12 except for 11 are found, in contrast to conventional hexagonal arrangement for polymer brushes on a planar substrate. Among these parameters, the spherical radius plays a significant role in determining the type of island structures, i.e., the morphology formed on the sphere.     

Stochastic dynamics simulation of grafted polymer brushes under shear deformation

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

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.     

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.     

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

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

Mean field theory of charged dendrimer molecules

Using self-consistent field theory (SCFT), we study the conformational properties of polyelectrolyte dendrimers. We compare results for three different models of charge distributions on the polyelectrolytes: (1) a smeared, quenched charge distribution characteristic of strong polyelectrolytes; (2) a smeared, annealed charge distribution characteristic of weak polyelectrolytes; and (3) an implicit counterion model with Debye-Huckel interactions between the charged groups. Our results indicate that an explicit treatment of counterions is crucial for the accurate characterization of the conformations of polyelectrolyte dendrimers. In comparing the quenched and annealed models of charge distributions, annealed dendrimers were observed to modulate their charges in response to the density of polymer monomers, counterions, and salt ions. Such phenomena is not accommodated within the quenched model of dendrimers and is shown to lead to significant differences between the predictions of quenched and annealed model of dendrimers. In this regard, our results indicate that the average dissociated charge α inside the dendrimer serves as a useful parameter to map the effects of different parametric conditions and models onto each other. We also present comparisons to the scaling results proposed to explain the behavior of polyelectrolyte dendrimers. Inspired by the trends indicated by our results, we develop a strong segregation theory model whose predictions are shown to be in very good agreement with the numerical SCFT calculations.