Effects of counterion fluctuations in a polyelectrolyte brush

We investigate the effect of counterion fluctuations in a single polyelectrolyte brush in the absence of added salt by systematically expanding the counterion free energy about Poisson-Boltzmann mean-field theory. We find that for strongly charged brushes, there is a collapse regime in which the brush height decreases with increasing charge on the polyelectrolyte chains. The transition to this collapsed regime is similar to the liquid-gas transition, which has a first-order line terminating at a critical point. We find that, for monovalent counterions, the transition is discontinuous in theta solvent, while for multivalent counterions, the transition is generally continuous. For collapsed brushes, the brush height is not independent of grafting density as it is for osmotic brushes, but scales linear with it.Received: 26 November 2003, Published online: 11 May 2004PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc.     

Collapse of polyelectrolyte brushes: Scaling theory and simulations

We investigate polyelectrolyte brushes using both scaling arguments and molecular dynamics simulations. As a main result, we find a novel collapsed brush phase. In this phase, the height of the brush results from a competition between steric repulsion between ions and monomers and an attractive force due to electrostatic correlations. As a result, the monomer density inside the brush is independent of the grafting density and the polymerization index. For small ionic and monomer radii (or for large Bjerrum length) the brush undergoes a first-order phase transition from the osmotic into the collapsed state. Received 26 September 2000     

Morphologies of a spherical bimodal polyelectrolyte brush induced by polydispersity and solvent selectivity

It is commonly realized that polydispersity may significantly affect the surface modification properties of polymer brush systems. In light of this, we systematically study morphologies of bidisperse polyelectrolyte brush grafted onto a spherical nanocolloid in the presence of trivalent counterions using molecular dynamics simulations. Via varying polydispersity, grafting density, and solvent selectivity, the effects of electrostatic correlation and excluded volume are focused, and rich phase behaviors of binary mixed polyelectrolyte brush are predicted, including a variety of pinned-patch morphologies at low grafting density and micelle-like structures at high grafting density. To pinpoint the mechanism of surface structure formation, the shape factor of two species of polyelectrolyte chains and the pair correlation function between monomers from different polyelectrolyte ligands are analyzed carefully. Also, electrostatic correlations, manifested as the bridging through trivalent counterions, are examined by identifying four states of trivalent counterions. Our simulation results may be useful for designing smart stimuli-responsive materials based on mixed polyelectrolyte coated surfaces.     

Molecular dynamics simulations of end-grafted centipede-like polymers with stiff charged side chains

We use molecular dynamics simulations to investigate centipede-like polymers with stiff charged side chains, end-grafted to a planar wall. The effect of the grafting density and the Bjerrum length on the conformational behaviour of the brush is examined in detail. In addition, we make a comparison of centipede-like polyelectrolyte (CPE) brushes with neutral centipede-like polymer (NCP) and linear polyelectrolyte (LPE) brushes. At weak electrostatic interaction, the main chains of the CPE chains adopt a strongly stretched conformation, and the monomer density profiles of side chains exhibit a clear oscillatory behaviour. With increasing Bjerrum length, the CPE brush undergoes a collapse transition. Compared to the CPE brushes, the counterion condensation effect is stronger for the LPE brushes, regardless of whether the electrostatic interaction is weak or strong and of whether the grafting density is low or high. Additionally, it is shown that the architecture of the grafted chains makes a weak contribution to the counterion condensation at strong electrostatic interaction. We also find that the electrostatic repulsion between charged side chains can enhance the stiffness of the main chains and thus limit the range of movement of the free-end monomers.     

Grafted polymers with annealed excluded volume: A model for surfactant association in brushes

We present an analytical self-consistent-field (SCF) theory for a neutral polymer brush (a layer of long polymer chains end-grafted to a surface) with annealed excluded volume interactions between the monomer units. This model mimics the reversible adsorption of solute molecules or aggregates, such as small globular proteins or surfactant micelles, on the grafted chains. The equilibrium structural properties of the brush (the brush thickness, the monomer density profile, the distribution of the end segments of the grafted chains) as well as the overall adsorbed amount and the adsorbate density profile are analyzed as a function of the grafting density, the excluded volume parameters and the chemical potential (the concentration) of the adsorbate in the solution. We demonstrate that, when the grafting density is varied, the overall adsorbed amount always exhibits a maximum, whereas the root-mean-square brush thickness either increases monotonically or passes through a (local) minimum. At high grafting densities the chains are loaded by adsorbed aggregates preferentially in the distal region of the brush, whereas in the region proximal to the grafting surface depletion of aggregates occurs and the polymer brush retains an unperturbed structure. Depending on the relative strength of the excluded volume interactions between unloaded and loaded monomers both the degree of loading of the chains and the polymer density profile are either continuous or they exhibit a discontinuity as a function of the distance from the grafting surface. In the latter case intrinsic phase separation occurs in the brush: the dense phase consists of unloaded and weakly extended chains and occupies the region proximal to the surface, whereas a more dilute phase consisting of highly loaded and strongly extended chains forms the periphery of the brush. Received 26 November 1998 and Received in final form 2 April 1999     

Thickness and density profiles of polyelectrolyte brushes: dependence on grafting density and salt concentration

We have performed neutron reflectivity measurements on a monolayer of charged diblock copolymers in a Langmuir trough, and determined precise density profiles of the polyelectrolyte brush at different densities. We obtain profiles in good agreement with existing self-consistent field computations, both for the osmotic and the salted brush regime. We show that the osmotic brush's thickness increases with density.     

Polymer brushes near the crystallization density

In this paper, polymer brushes are studied via molecular-dynamics simulations at very high grafting densities, where the crossover between the brush regime and the polymer-crystal regime is taking place. This crossover is directly observed with the structure factor and pair-correlation function. With increasing grafting density, this crystallization is progressing from the core layer of the brush towards the surface layer. The same process is analyzed using the lateral fluctuations of the monomers as a signature of their diminishing mobility. Additionally, bond forces and the chain excess free energy indicate a transition from the brush regime to the overstretched regime, which is in agreement with predictions of a modified self-consistent field theory.     

Scaling Theory of Strongly Charged Cylindrical Polyelectrolyte Brushes

Scaling theory of charged cylindrical polyelectrolyte brushes is developed. The dependence of brush thickness on the grafting density, charge fraction, and chain length is analyzed. A full phase diagram is established. Characteristics and boundaries between different regimes of cylindrical polyelectrolyte brushes are summarized. Special attentions are paid to electrostatic interaction induced stiffening and counterion condensation effects. If the Bjerrum length of the solution is larger than the Kuhn length of the polyelectrolyte chains, counterion condensation occurs in the strongly charged polyelectrolyte brushes. On the contrary, the electrostatic interaction stretches the strongly charged grafted polyelectrolyte chains to their contour length.     

Spontaneous bending of 2D molecular bottle-brush

Using a scaling approach we consider a 2D comb copolymer brush under bending deformations. We show that the rectilinear brush is locally stable and can be characterized by a persistence length λ increasing with the molecular weight of grafting side chains as λ ∼ M³. A bending instability due to redistribution of the side chains appears in the non-linear regime where bending is strong. Arguments are presented that the brush conformations consist of alternating rectilinear and bent sections corresponding to the different free-energy minima.     

Volume exclusion effects in the ground-state dominance approximation for polyelectrolyte adsorption on charged interfaces

We consider the problem of polyelectrolyte molecules adsorbing on oppositely charged interfaces. For sufficiently long chains, the ground-state dominance approximation can be used which results in a (semi-)analytical solution of the self-consistent field equations (aSCF). Whereas existing aSCF theory assumes a low polyelectrolyte density, here the required electrostatic corrections for a high polymer density are implemented. Adsorbed polymer excludes volume for the solvent and small ions, a volume effect that also leads to a reduced dielectric permittivity and a resulting polarization term in the exchange potential. Calculations show the influence of volume exclusion on the polymer density profile.     

Forces of interaction between DNA-grafted colloids: an optical tweezer measurement

Optical tweezers are employed to measure the forces of interaction between single DNA-grafted colloids. Parameters to be varied are the length of the DNA, the grafting density, and the ion concentration of the surrounding medium. From the measured force-separation dependence an interaction length at a given force is deduced. It shows in the mushroom regime a scaling with the grafting density which levels off for brushes. For the latter the transition from an osmotic to a salted brush can be traced in detail by varying the ion concentration in accordance with mean field theories.     

Variational theory for a single polyelectrolyte chain

Variational methods are applied to a single polyelectrolyte chain. The polymer is modeled as a Gaussian chain with screened electrostatic repulsion between all monomers. As a variational Hamiltonian, the most general Gaussian kernel, including the possibility of a classical or mean polymer path, is employed. The resulting self-consistent equations are systematically solved both for large and small monomer-monomer separations along the chain. In the absence of screening, the polymer is stretched on average. It is described by a straight classical path with Gaussian fluctuations around it. If the electrostatic repulsion is screened, the polymer is isotropically swollen for large separations, and for small separations the polymer correlation function is calculated as an analytic expansion in terms of the monomer-monomer separation along the chain. The electrostatic persistence length and the electrostatic blobsize are inferred from the crossover between distinct scaling ranges. We perform a global analysis of the scaling behavior as a function of the screening length and electrostatic interaction strength , where is the Bjerrum length and A is the distance of charges along the polymer chain. We find three different scaling regimes. i) A Gaussian-persistent regime with Gaussian behavior at small, persistent behavior at intermediate, and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and only for intermediate values of the screening length. The electrostatic persistence length is defined as the crossover length between the persistent and the asymptotically swollen behavior and is given by and thus disagrees with previous (restricted) variational treatments which predict a linear dependence on the screening length .ii) A Gaussian regime with Gaussian behavior at small and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and/or strong screening, and the electrostatic repulsion between monomers only leads to subfluent corrections to Gaussian scaling at small separations. The concept of a persistence length is without meaning in this regime. iii) A persistent regime , where the chain resembles a stretched rod on intermediate and small scales. Here the persistence length is given by the original Odijk prediction, , if the overstretching of the chain is avoided. We also investigate the effects of a finite polymer length and of an additional excluded-volume interaction, which modify the resultant scaling behavior. Applications to experiments and computer simulations are discussed. Received 24 December 1997     

Curved polymer and polyelectrolyte brushes beyond the Daoud-Cotton model

We revise the classical Daoud-Cotton (DC) model to describe conformations of polymer and polyelectrolyte chains end-grafted to convex spherical and cylindrical surfaces. In the framework of the DC model, local stretching of chains in the brush does not depend on the degree of polymerization of grafted chains, and the polymer density profile follows a single-exponent power law. This model, however, does not correspond to a minimum in free energy of the curved brush. The nonlocal (NL) approximation exploited in the present paper implies the minimization of the overall free energy of the brush and predicts that the polymer density profile does not follow a single-exponent power law. In the limit of large surface curvature the NL approximation provides the same scaling laws for brush thickness and free energy as the local DC model. Numerical prefactors are however different. Extra extension of chains in the brush interior region leads to larger equilibrium brush thickness and lower free energy per chain. A significant difference between outcomes of the two models is found for brushes formed by ionic polymers, particularly for weakly dissociating (p H-sensitive) polyelectrolytes at low solution salinity.     

中性/聚电解质高分子混合刷对蛋白质的吸附/解吸附

本文应用分子理论,研究中性(A)/聚电解质(B)高分子混合刷对蛋白质的吸附/解吸附特性.理论模型考虑蛋白质与中性高分子A的排斥、以及与聚电解质高分子B的静电吸引.研究发现,在pH=4～6、中性高分子A处于弱水合状态时,混合刷中A高分子链塌缩,B聚电解质链溶胀.由于蛋白质和B聚电解质链间的静电吸引,导致高分子混合刷对蛋白质的吸附.当A高分子水合性增强时,A高分子链溶胀,B聚电解质链塌缩.由于蛋白质与A高分子链间的排斥作用增强,与B聚电解质链间的静电吸引减弱,混合刷对蛋白质解吸附.     

Molecular dynamics simulation of semiflexible polyampholyte brushes--The effect of charged monomers sequence

Planar brushes formed by end-grafted semiflexible polyampholyte chains, each chain containing an equal number of positively and negatively charged monomers, are studied using molecular dynamics simulations. Keeping the length of the chains fixed, the dependences of the average brush thickness and equilibrium statistics of the brush conformations on the grafting density and the salt concentration are obtained with various sequences of charged monomers. When similarly charged monomers of the chains are arranged in longer blocks, the average brush thickness is smaller and the dependence of brush properties on the grafting density and the salt concentration is stronger. With such long blocks of similarly charged monomers, the anchored chains bond to each other in the vicinity of the grafting surface at low grafting densities and buckle toward the grafting surface at high grafting densities.     

水合作用与pH调控聚电解质刷的构象转变

我们基于Flory-Huggins理论,建立理论模型研究水合作用与pH调控聚电解质刷的构象转变.理论模型考虑聚电解质链与水分子间的作用(聚电解质链的水合作用)、体系中的静电作用.研究发现,随着水合作用的改变,聚电解质刷出现由溶胀到塌缩的构象转变.由此表明了水合作用可在很大程度调节聚电解质刷的相变.通过分析pH的调控效应我们还发现,在碱性环境中(pH=8),聚电解质链单体的解离度增大,静电排斥会使得聚电解质刷溶胀.由此表明,聚电解质刷内水合作用与静电效应的耦合,将会共同决定聚电解质刷的构象转变特性.理论结果深刻揭示了水合作用的改变,会使得聚电解质刷体系发生相变,pH可在很大程度上改变其相变特性.     

Static and dynamic properties of polymer brush with topological ring structures: Molecular dynamic simulation

By defining a topological constraint value(rn),the static and dynamic properties of a polymer brush composed of moderate or short chains with different topological ring structures are studied using molecular dynamics simulation,and a comparison with those of linear polymer brush is also made.For the center-of-mass height of the ring polymer brush scaled by chain length h~N~v,there is no significant difference of exponent from that of a linear brush in the small topological constraint regime.However,as the topological constraint becomes stronger,one obtains a smaller exponent.It is found that there exists a master scaling power law of the total stretching energy scaled by chain length N for moderate chain length regime,F_(ene)~Np~v,for ring polymer brushes,but with a larger exponent v than 5/6,indicating an influence of topological constraint to the dynamic properties of the system.A topological invariant of free energy scaled by(c)~(5/4) is found.     

Static and dynamic properties of grafted ring polymer: Molecular dynamics simulation

The static and dynamic properties of a system of end-grafted flexible ring polymer chains grafted to a flat substrate and exposed to a good solvent are studied by using a molecular dynamics method. The monomers are described by a coarse-grained bead-spring model. Varying the grafting density ρ and the degree of polymerization or chain length N, we obtain the density profiles of monomers, study the structural properties of the chain (radius of gyration, bond orientational parameters, etc.), and also present the dynamic characteristics such as chain energy and bond force. Compared with a linear polymer brush, the ring polymer brush exhibits different static and dynamic properties for moderate or short chain length, while it behaves like linear polymer brush in the regime of long chain length.     

Adsorption of polyelectrolytes at an oppositely charged surface

We develop a scaling theory of polyelectrolyte adsorption at an oppositely charged surface. At low surface charge densities, the thickness of the adsorbed layer is determined by the balance between electrostatic attraction to the charged surface and chain entropy. At high surface charge densities, it is determined by the balance between electrostatic attraction and short-range monomer-monomer repulsion. These different stabilizing mechanisms result in the nonmonotonic dependence of the layer thickness on the surface charge density.     

Scaling Theory of Polyelectrolyte Nanogels

The present paper develops the scaling theory of polyelectrolyte nanogels in dilute and semidilute solutions.The dependencies of the nanogel dimension on branching topology, charge fraction, subchain length, segment number,solution concentration are obtained. For a single polyelectrolyte nanogel in salt free solution, the nanogel may be swelled by the Coulombic repulsion(the so-called polyelectrolyte regime) or the osmotic counterion pressure(the so-called osmotic regime). Characteristics and boundaries between different regimes of a single polyelectrolyte nanogel are summarized.In dilute solution, the nanogels in polyelectrolyte regime will distribute orderly with the increase of concentration. While the nanogels in osmotic regime will always distribute randomly. Different concentration dependencies of the size of a nanogel in polyelectrolyte regime and in osmotic regime are also explored.