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     

Flory theorem for structurally asymmetric mixtures

The generalization of the Flory theorem for structurally asymmetric mixtures was derived and tested by direct visualization of conformational transformations of brushlike macromolecules embedded in a melt of linear chains. Swelling of a brush molecule was shown to be controlled not only by the degree of polymerization (DP) of the surrounding linear chains, N(B), but also by the DP of the brush's side chains, N, which determines the structural asymmetry of the mixed species. The boundaries of the swelling region were established by scaling analysis as N(2) < N (B) < N (A)/N, where N (A) is the degree of polymerization of the brush backbone. Experiment and theory demonstrated good agreement.     

Local entropic effects of polymers grafted to soft interfaces

In this paper, we study the equilibrium properties of polymer chains end-tethered to a fluid membrane. The loss of conformational entropy of the polymer results in an inhomogeneous pressure field that we calculate for Gaussian chains. We estimate the effects of excluded volume through a relation between pressure and concentration. Under the polymer pressure, a soft surface will deform. We calculate the deformation profile for a fluid membrane and show that close to the grafting point, this profile assumes a cone-like shape, independently of the boundary conditions. Interactions between different polymers are also mediated by the membrane deformation. This pair-additive potential is attractive for chains grafted on the same side of the membrane and repulsive otherwise. Received 20 April 2000     

Unusual conformation of molecular cylindrical brushes strongly adsorbed on a flat solid surface

Conformational properties of comb-like polymers strongly adsorbed on a flat solid surface were investigated using computer simulation and scanning force microscopy. The computer simulation showed that the macromolecules with asymmetric distribution of the side chains relatively to the backbone are effectively in a collapsed state even under conditions of a good solvent. They formed peculiar helical superstructures which could be observed by scanning force microscopy of cylindrical brushes of polymethylmethacrylate on mica. Received 13 September 1999     

熵驱动下柱状高分子刷螺旋结构的研究

自然界中广泛存在螺旋结构,在特定情形下熵能驱动高分子链形成螺旋结构.本文采用分子动力学方法研究柱状高分子刷吸附在无限长圆柱表面时的构象行为.发现其构象与嫁接支链条数、柱状高分子刷与圆柱表面之间的吸附能密切相关.在较弱的吸附能下,具有较多支链条数的柱状高分子刷能形成完整的螺旋结构,其本质就是熵驱动下形成的螺旋结构.该研究有助于加深对生物大分子螺旋结构的理解.     

Diblock copolymers adsorbed at a water-oil interface

We probe the conformation of a diblock copolymer layer adsorbed at the surface of water-in-oil emulsion droplets at various concentration of a molecular surfactant. The diblock copolymer is made of a hydrophobic polybutadiene part linked to a hydrophilic polyethylene oxide one. The measure provides the equilibrium thickness of the polymer layer that is obtained with two different techniques, i.e. dynamic light scattering and force measurements. The structure of the layer is shown to change from a “mushroom” conformation in which the adsorbed chains form independent Gaussian coils to a conformation where they interact and extend in the continuous phase. The transition from one regime to the other is progressive as the ratio surfactant/polymer bulk concentration varies. Received 5 May 2000 and Received in final form 6 July 2000     

Adsorption of a polyampholyte on a charged spherical particle

We develop a scaling theory for a single polyampholyte chain adsorbed on a charged spherical particle in a theta-solvent. Adsorption of a polyampholyte molecule is due to its polarization in the electrostatic field of the particle. For large particles with sizes exceeding the thickness of the adsorbed layer, the conformations of the chain are similar to the one found for polyampholyte adsorption on charged planar surface. However, an adsorbed polyampholyte chain forms a self-similar flower-like structure near the particles with sizes smaller than its Gaussian size. These self-similar structures result from the balance of the polarization energy of loops and the excluded volume interactions between monomers. The structure of an adsorbed polyampholyte in the flower-like conformation is similar to that of a neutral star polymer. Received 3 March 2000 and Received in final form 5 July 2000     

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     

Oppositely charged polyelectrolytes grafted onto planar surface: Mean-field lattice theory

Equilibrium structures of planar polyelectrolyte brushes formed by grafted chains carrying charges of opposite sign are examined by employing mean-field lattice theory. Two brushes of different architecture are considered: one formed by grafted diblock copolymers with oppositely charged blocks and the other being a mixed brush composed of oppositely charged homopolymers. The systems display nontrivial intrinsically inhomogeneous brush structures originating from the chain connectivity and the electrostatic interaction among the segments. In addition, a coexistence of stretched and coiled chains inside the brush is observed. The influence of the charges of the blocks, the relative length of the oppositely charged blocks, and the ionic strength of the solution on the brush inhomogeneity and structural differences between the two types of brushes are discussed. Received 14 March 2001 and Received in final form 18 June 2001     

Adsorption of hydrophobic polyelectrolytes at the air/water interface: Conformational effect and history dependence

We present an experimental study of the adsorption of hydrophobic highly charged polyelectrolytes on a neutral and hydrophobic surface, the air/water interface. The polymer was a randomly sulphonated polystyrene with charge fractions between 0.3 and 0.9 and the adsorbed layers were characterised by Langmuir through measurements, ellipsometry and X-ray reflectivity. The adsorption rate is always very slow and the resulting layers are very thin (< 3 nm). A maximum of adsorption with the charge fraction is observed which we relate to the conformation of the chains in solution. We show that adsorption is partially irreversible, strongly hysteretic and that the state of an adsorbed layer depends on its history. Received 16 June 2000     

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.     

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.     

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.     

Orientation of grafted polymer chains at the air-water interface studied by PM-IRRAS

Monolayers of polystyrene-polyethylene oxide (PS-PEO) copolymers at the air-water interface have been studied with the Modulation Polarization Infra Red Spectroscopy technique (PM-IRRAS) to measure the orientation of the PEO chains with respect to the normal to the interface. At surface densities intermediate between the dilute regime and the brush regime, the average tilt angle has been determined: it decreases continuously with the surface density in the monolayer, in good agreement with previous results (M.C. Fauréet al., Macromolecules 32, 8538 (1999)). The further stretching of the molecules in the brush regime has also been measured. No substantial volume fraction of PEO crystal domains has been detected in the very dense regime Received 16 April 1999 and Received in final form 26 August 1999     

Non-linear osmotic brush regime: Simulations and mean-field theory

We investigate polyelectrolyte brushes in the osmotic regime using both theoretical analysis and molecular dynamics simulation techniques. In the simulations at moderate Bjerrum length, we observe that the brush height varies weakly with grafting density, in contrast to the accepted scaling law, which predicts a brush thickness independent of the grafting density. We show that such behavior can be explained by considering lateral electrostatic effects (within the non-linear Poisson-Boltzmann theory) combined with the coupling between lateral and longitudinal degrees of freedom due to the conserved polymer volume (which are neglected in scaling arguments). We also take the non-linear elasticity of polyelectrolyte chains into consideration, which makes significant effects as chains are almost fully stretched in the osmotic regime. It is shown that all these factors lead to a non-monotonic behavior for the brush height as a function of the grafting density. At large grafting densities, the brush height increases with increasing the grafting density due to the volume constraint. At small grafting densities, we obtain a re-stretching of the chains for decreasing grafting density, which is caused by lateral electrostatic contributions and is controlled by the counterion-condensation process around polyelectrolyte chains. These results are obtained assuming all counterions to be trapped within the brush, which is valid for sufficiently long chains of large charge fraction.Received: 14 May 2003, Published online: 11 November 2003PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 36.20.-r Macromolecules and polymer molecules - 61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc.     

Reptation and interdiffusion in polystyrene networks

We have used helium-3 nuclear reaction analysis to measure the interdiffusion of linear polystyrene into a film of crosslinked polystyrene and the intradiffusion of polystyrene in polystyrene networks. The interdiffusion is compared with that predicted from the Kramer-Sillescu theory, and is found to be considerably faster. This is attributed to the relaxation of inhomogeneities in the network. The molecular weight and crosslinking dependence of the intradiffusion coefficients of free polystyrene chains trapped inside networks is discussed in terms of the simple tube model and provides reasonably good agreement with that predicted from reptation theory. Received 2 August 2000 and Received in final form 6 November 2000     

A new simulation method for the determination of forces in polymer/colloid systems

We introduce a new simulation method, which we call the contact-distribution method, for the determination of the Helmholtz potential for polymer/colloid systems from lattice Monte-Carlo simulations. This method allows one to obtain forces between finite or semi-infinite objects of any arbitrary shape and dimensions in the presence of polymer chains in solution or physisorbed or chemisorbed at interfaces. We illustrate the application of the method using two examples: (i) the interaction between the tip of an atomic force microscope (AFM) and a single, end-grafted polymer chain and (ii) the interaction between an AFM tip and a polymer brush. Numerical results for the first two cases illustrate how the method can be used to confirm and extend scaling laws for forces and Helmholtz potentials, to examine the effects of the shapes and sizes of the objects and to examine conformational transitions in the polymer chains. Received: 15 May 1998 / Revised: 11 June 1998 / Accepted: 12 June 1998     

Density functional study of one- and two-component bottlebrush molecules in solvents of varying quality

Modified inhomogeneous statistical associating fluid theory (iSAFT) density functional theory is extended to bottlebrush polymers in both good and poor solvent. The detailed structures of side chains in the implicit solvent are calculated and have a semi-quantitative agreement with simulation. The average brush heights calculated from the theory agree with well-established scaling theories. iSAFT is easily extended to model bottlebrush polymers with two or more components. For an amphiphilic core-shell bottlebrush polymer, if the solvent-phobic block is much shorter than the solvent-philic block, it will fold towards the backbone even though it resides at the free end of the side chain. Similarly, for an amphiphilic mixed-type bottlebrush polymer, the chain length of different components has a great impact on the structure and properties of the molecule. The molecule may not have the response (the switch of outer layer) towards the solvent treatment if one component is significantly longer than the other. Our results provide insight into the conformation of bottlebrush polymers as well as guidance in practical applications.     

Simulation of the Critical Adsorption of Semi-Flexible Polymers

The critical adsorption of semi-flexible pol.ymer chains on attractive surfaces is studied using Monte Carlo simulations.The results reveal that the critical adsorption point of a free polymer chain is the same as that of an end-grafted one.For the end-grafted polymer,we find that the finite-size scaling relation and the maximum fluctuation of adsorbed monomers are equivalent in estimating the critical adsorption point.The effect of chain stiffness on the critical adsorption is also investigated.The surface attraction strength for the critical adsorption of semi-flexible polymer chain decreases exponentially with an increase in the chain stiffness;In other words,lower adsorption energy is needed to adsorb a stiffer polymer chain.The result is explained from the viewpoint of the free energy profile for the adsorption.