四臂星型聚电解质刷在外加三价盐离子和电场下的塌缩

本文采用Langevin动力学模拟的方法,研究存在三价盐离子时,接枝在带相反电荷的极板上的部分带电的四个臂星型链呈现出的塌缩现象. 结果表明,在电场作用下,接枝星型链的平均带电分数和盐浓度在带电单体和三价盐离子的竞争性吸附中起关键作用. 对于接枝在带相反电荷的极板上的带电分数较高的星型链,刷子会塌缩到接枝极板上,并会产生极板表面电荷的过度补偿现象. 当带电分数较低时,如果星型链所带电荷数与三价盐离子电荷数相同,即使在很低的盐浓度下,极板对三价盐离子的吸引能力也高于对星型链中的带电单体的吸引. 结果表明,星型链在带电分数较低的情况下,三价盐离子的加入不会导致接枝电极表面电荷的过度补偿. 此外,本文还研究了三价盐离子对电场作用下星型刷的拉伸的影响.     

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.     

Polyelectrolyte brushes with specific charge distribution: Mean-field lattice theory

A novel polymer system containing charged diblock polymers grafted onto a planar surface, simple salt and solvent has been considered in the framework of a mean-field lattice theory. On the basis of predicted volume fraction profiles of polymer segments, free ends, block junctions, and small ions, a detailed picture of the system has emerged. It is found that the structure of the polymer brush is decisively dependent of the relative charge of the blocks. For certain conditions, bimodal profiles appear which demonstrate the simultaneous presence of two types of chain conformations, one coiled and one stretched. Received 30 August 2000     

Counterion distribution in a spherical charged sparse brush

The counterion distribution within a spherical polyelectrolyte sparse brush was measured by small-angle X-ray scattering using contrast variation with different counterions by means of ion dialysis. The brush was made by self-association of charged diblock copolymers. Thanks to the contrast variation method, we were able to separate the signal due to the monomers and the signal due to the counterions. At a small length scale, it is demonstrated that the system behaves as independent charged rods whose counterion distribution follows the Poisson-Boltzmann model. Received 14 February 2001 and Received in final form 2 May 2001     

Polyelectrolytes tethered to a free surface

Several attempts have been already carried out in order to tether charged chains by an end at a free fluctuating surface. We review here most of these attempts and focus on how close the physics of charged brushes can be investigated by such an approach. We first describe results about films of charged-neutral diblock copolymers spread at the surface of water. Results can be mostly rationalized in terms of charged brushes although additional structurations and fluctuations of the interface can be observed. The latter deformations are also observed when adsorbed layers of charged-neutral diblock copolymers are considered. At last, we examine how free suspended films of charged-neutral diblock copolymers can be viewed as two opposing charged brushes, both in terms of thickness and pressure. Received 9 May 2000     

Scaling theory of mixed amphiphilic monolayers

We predict the elastic properties of mixed amphiphilic monolayers in the swollen state within the blob model using scaling arguments. First the elastic moduli and the spontaneous curvature of a bimodal brush are determined as a function of the composition and the relative chain length. We obtain simple and useful scaling functions which interpolate between the elastic moduli of a pure short-chain brush and a pure long-chain brush. By using the analogy between block copolymer interfaces and polymeric brushes, the effect of mixing on self-assembled diblock copolymer monolayers is investigated in the swollen state. We calculate various interfacial properties, such as the equilibrium surface coverage, interface curvature, and the mixing free energy as a function of the composition. In general, we find a nonlinear dependence on the composition, which deviates from the simple linear averaging of the properties of pure components. Our results are used to discuss a recent experiment on the effect of amphiphilic block copolymers on the efficiency of microemulsions. Received 29 December 2000 and Received in final form 19 March 2001     

Adsorption of hydrophobic polyelectrolytes onto oppositely charged surfaces

We present a scaling theory for the adsorption of a weakly charged polyelectrolyte chain in a poor solvent onto an oppositely charged surface. Depending on the fraction of charged monomers and on the solvent quality for uncharged monomers, the globule in the bulk of the solution has either a spherical conformation or a necklace structure. At sufficiently high surface charge density, a chain in the globular conformation adsorbs in a flat pancake conformation due to the Coulombic attraction to the oppositely charged surface. Different adsorption regimes are predicted depending on two screening lengths (the Debye screening length monitored by the salt concentration and the Gouy-Chapman length monitored by the surface charge density), on the degree of ionization of the polymer and on the solvent strength. At low bulk ionic strength, an increase in the surface charge density may induce a transition from an adsorbed necklace structure to a uniform pancake due to the enhanced screening of the intra-chain Coulombic repulsion by the counterions localized near the surface. Received 12 April 2001     

Vesicle-to-micelle transition induced by grafted diblock copolymers

We study by small-angle neutron scattering the vesicle-to-micelle transition induced by anchoring diblock copolymers on the surfactant membranes. Vesicles are made using the ternary system SDS (sodium dodecyl sulfate)/octanol/PS-POE (polystyrene-polyoxyethylene), chosen as a model of more complex biological systems. The anchored polymer chains destabilize the membranes and lead to the formation of mixed polymer-surfactant micelles. We show that there is no influence of the polymer mass on the membranes destabilization. We compare this experimental result with recent theoretical predictions concerning the polymer-grafted membranes. We have a good agreement with predictions involving membrane curvature effects, and also with predictions focusing on more local deformations of membranes created by the grafted chains. Received 12 June 2001 and Received in final form 18 March 2002     

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.     

Structure and frustration in liquid crystalline polyacrylates I. Bulk behaviour

The phase behaviour and structure are reported of a new type of frustrated side-chain liquid crystalline (LC) polymer, a polyacrylate with phenylbenzoate mesogenic side groups and a narrow polydispersity. At a high degree of polymerisation the LC polymers show a nematic, a smectic-A_d, a re-entrant nematic and a C phase, for shorter chains only a nematic and a C phase. This constitutes a new example of nematic re-entrance for which the driving field is the length of the polymer chain. The smectic-A_d layers consist of partially overlapped side groups while in the C phase the side chains are rearranged into chevron-like blocks of bilayers. We propose an explanation of the frustrated phase behaviour in terms of these two different competing length scales and their coupling to the backbone conformations. Received 28 February 2001 and Received in final form 6 August 2001     

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     

Rayleigh instability of charged droplets in the presence of counterions

The classical instability of a charged spherical droplet is reconsidered in the presence of counterions. An ensemble of such droplets is studied within a simplified cell model. Screening of the electric field by the counterions is found to increase the equilibrium droplet size. Furthermore, if the ions can enter the droplet, a first-order phase transition occurs upon increasing Bjerrum length, surface tension or droplet density, leading to a phase separation. Simple scaling properties of the free energy give the shape of the phase boundary and show the system to be scale-invariant there. Pearl-necklace structures of hydrophobic polyelectrolytes are discussed as an application. Received 30 August 2001     

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.     

On the fragmentation of multiply charged sodium clusters

The fragmentation of multiply charged atomic sodium clusters of mass 200 is investigated using the Micro-canonical Metropolis Monte Carlo (MMMC) statistical technique for excitation energies up to 200 eV and for cluster charges up to +9e. In this work we present caloric curves and charged and uncharged fragment mass distributions for clusters with charges 0, 2, and 4. The caloric curves show a dip at the critical point implying a negative specific heat, as expected for finite systems, while the fragment mass distributions corroborate the picture of a phase transition from one dominant liquid-like cluster to complete vaporization. Received 7 November 2001 / Received in final form 4 April 2002 Published online 28 June 2002     

Scaling concepts for polymer brushes and their test with computer simulation

After a brief review of the scaling concepts for static and dynamic properties of polymer brushes in good solvents and Theta solvents, the Monte Carlo evidence is discussed. It is shown that under typical conditions the diameter of the last blob is of the order of 10-20% of the brush height, and therefore pronounced deviations from the self-consistent field predictions occur. In bad solvents, lateral microphase separation occurs leading to an irregular pattern of “dimples”. Particularly interesting is the response of brushes to shear deformation, and the interaction between two interpenetrating brushes. Recent attempts to understand the resulting shear forces via molecular-dynamics simulations are briefly described, and an outlook on related experiments is given. Dedicated to Prof. H.E. Stanley on the occasion of his 60th birthday Received 11 March 2002 and Received in final form 3 June 2002     

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.     

Molecular dynamics simulation of the response of bi-disperse polyelectrolyte brushes to external electric fields

Langevin dynamics simulations have been performed to investigate the response of bi-disperse and strong polyacid chains grafted on an electrode to electric fields generated by opposite surface charges on the polyelectrolyte(PE)-grafted electrode and a second parallel electrode. Simulation results clearly show that, under a negative external electric field, the longer grafted PE chains are more strongly stretched than the shorter ones in terms of the relative change in their respective brush heights. Whereas under a positive external electric field, the grafted shorter chains collapse more significantly than the longer ones. It was found that, under a positive external electric field, the magnitude of the total electric force acting on one shorter PE chain is larger than that on one longer PE chain, or vice versa. The effects of smeared and discrete charge distributions of grafted PE chains on the response of PE brushes to external electric fields were also examined.     

Decoupling and coherence in E1 and E2 moments in drip line nuclei

I discuss first the effect of decoupling of extended wave functions and the coherence in the low-energy E1 strength in drip line nuclei ¹²Be and ¹³O, which are studied by large-scale shell model calculations including 3 ?ω configuration space. The calculated results are compared to recent experimental data of Coulomb excitations. The quenching of the core polarization charges in drip line nuclei is also discussed in relation to recent observations of quadrupole moments in B-isotopes. Received: 1 May 2001 / Accepted: 4 December 2001     

On exact singular wave functions of two identical particles

We discuss the occurrence and properties of exact singular anyonic wave functions describing stationary states of two identical charged particles moving on a plane and under the influence of a perpendicular uniform magnetic field. Received 25 September 2001 / Received in final form 4 December 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: truong@u-cergy.fr     

Partitioning of a heterotelechelic polystyrene to separate interfaces of thin films

Heterotelechelic deuteropolystyrenes have been synthesised with a tertiary amine functionality at one end and a fluorocarbon group at the other end of the polymer chain. A layer of this polymer, circa 120 ? thick, has been attached to the surface of a silicon substrate and subsequently covered with a much thicker layer of hydrogenous polystyrene. The combination has then been annealed at 413 K under vacuum for defined times and the subsequent distribution of the deutero heterotelechelic polymer determined using nuclear reaction analysis and neutron reflectometry. The influences of annealing time, molecular weight and thickness of the hydrogenous polymer have been examined. Nuclear reaction analysis showed that an excess of the heterotelechelic polymer formed at both interfaces with a larger excess remaining at the substrate-polymer interface. When the molecular weight of the hydrogenous polymer is lower than that of the deuteropolymer, the deutero layer is initially swollen by the hydrogenous polymer but the thickness then decreases as deutero polymer becomes detached from the silicon substrate and an additional excess layer is eventually formed at the vacuum-polymer surface. When the molecular weight of the hydrogenous polymer is higher, there is an initial shrinkage of the deuteropolymer layer, but the original thickness (∼ radius of gyration of the deuteropolymer) is regained on prolonged annealing. There is no evidence for bridging between the two interfaces by the heterotelechelic polymer. After five days annealing the volume fraction distribution of the deuteropolymer at the silicon substrate was well described by a self-consistent field model where the only adjustable parameter was the sticking energy of the tertiary amine group to the silicon substrate for which a value of 8k _B T was obtained. Comparison of the dependence of the equilibrium layer thickness of the deuteropolymer on the equilibrium grafting density at the silicon surface with the predictions of scaling theory for brush-like polymer layers suggested that the grafted molecules were in the ideal, unperturbed brush region. Received 12 October 2000 and Received in final form 27 March 2001