Spherical polyelectrolyte block copolymer micelles: Structural change in presence of monovalent salt

Spherical polyelectrolyte block copolymer micelles were investigated as a function of added NaCl salt concentration using Small-Angle Neutron Scattering (SANS) and Light Scattering (LS). The micelles are formed by the self-association of charged-neutral copolymers made of a long deuterated polyelectrolyte moiety (NaPSS_d)₂₅₁ and a short hydrophobic moiety (PEP)₅₂. In presence of salt, the core shape and the aggregation number of the micelles are not affected. The hydrodynamic radius of the micelle is found to be identical to the radius of the whole micelle deduced from neutron scattering and thus the hydrodynamic radius is a valid measure of the corona thickness. At the lowest salt concentrations investigated the thickness of the corona, R_s, remains essentially constant and a contraction is observed above an added-salt concentration c_s of 2×10^-2 M where this crossover concentration corresponds to the average ionic strength of the free counterions in the corona. The contraction takes place while maintaining a rod-like behavior of the chains at short scale and obeys to: R_s c_s^-0.18. The exponent 0.18 suggests an electrostatic persistence length proportional to the Debye screening length.     

Small-angle X-ray scattering from salt-free solutions of star-branched polyelectrolytes

The dispersion state of sodium-sulphonated polystyrene ( NaPSS) star-branched polyelectrolytes was investigated in salt-free aqueous solutions, by use of the small-angle X-ray scattering technique. With respect to polystyrene (PS) star-branched polymers of identical functionality, the ordering phenomenon occurring in the neighborhood of the overlap concentration c^* is reinforced and observed in a larger range of concentrations. Moreover, the degree of order is no longer maximum at c^* and is improved as the concentration decreases. The dispersion state is then mainly controlled by the electrostatic interaction. A crystalline order should therefore be achieved with stars of lower functionality, provided the electrostatic interaction is added to the osmotic repulsion. On the other hand, unusual scattering patterns are measured for aqueous solutions of NaPSS star polyelectrolytes. Indeed, a diffuse scattering is revealed at high angles, in addition to the regular diffraction rings related to preferred interstar distances. It is similar to the broad scattering peak produced by semidilute solutions of NaPSS linear polyelectrolytes and associated to the electrostatic correlation hole within the isotropic model. In the dilute regime (c < c ^*), it is just an intramolecular characteristic and represents the electrostatic repulsion between arms belonging to the same star. In the semidilute regime (c > c ^*), it also reflects the electrostatic repulsion between arms of distinct stars. So, as the concentration increases, it is mainly caused by the interpenetration of NaPSS stars. Such an observation is in agreement with the composite structure earlier proposed by Daoud and Cotton for star semidilute solutions. For c > c ^*, NaPSS star aqueous solutions can therefore be pictured as effective stars immersed in a matrix formed by the overlap of the arm ends. With respect to the dilute regime, the effective stars are smaller; the higher the concentration the smaller the size. Received 14 May 1999 and Received in final form 15 March 2000     

Micelles of poly(isoprene-b-2-vinylpyridine-b-ethylene oxide) terpolymers in aqueous media and their interaction with surfactants

Well-defined poly(isoprene-b-2-vinylpyridine-b-ethylene oxide) (PI-P2VP-PEO) triblock terpolymers were synthesized by anionic polymerization high-vacuum techniques. The terpolymers formed spherical three-layer (onion-type) micelles in neutral and acidic pH aqueous media as evidenced by static and dynamic light scattering. In pure water, kinetically frozen micelles with a core composed of a soft PI inner part and a hard P2VP outer shell and protected by a neutral PEO corona were formed. In acidic media the core was formed by the soft PI hydrophobic segment, whereas the corona consisted of an inner cationic polyelectrolyte P2VPH⁺ part and an outer PEO shell. The aggregation numbers were found to be high in all cases, due to the high hydrophobicity of the core-forming blocks. In the latter case an increase in size was observed due to the electrostatic repulsions between the P2VPH⁺ chains in the inner part of the corona, which is also responsible for the lower aggregation numbers observed in the acidic solutions. The interaction of these onion-type micelles with cationic (DTMAB) and anionic (SDS) surfactants led to the formation of mixed polymer/surfactant aggregates. Their structural characteristics could be varied by combining changes in surfactant type and concentration, solution pH and type of electrostatic interaction, leading to interesting, block-copolymer-based, environmentally responsive colloidal systems.     

Amphiphilic telechelic poly(N-isopropylacrylamide) in water: From micelles to gels<Superscript>⋆</Superscript>

We report the first study of aqueous solutions (0.025 gL^-1 to 46 gL^-1) of a telechelic poly(N-isopropylacrylamide) with octadecyl termini (C₁₈-PNIPAM-C₁₈, M_w: 37000, 320 NIPAM units, M_w/ M_n = 1.07) obtained by reversible addition-fragmentation chain transfer (RAFT) free radical polymerization of N-isopropylacrylamide. Static and dynamic light scattering measurements and fluorescence spectroscopy, using 8-anilino-1-naphthalenesulfonic acid (ANS) as probe, yielded the concentration dependence of the size and aggregation number of C₁₈-PNIPAM-C₁₈ micelles in cold ( 20^°C) dilute aqueous solutions. Concentrated solutions ( c > 20gL^-1) form transient gels exhibiting an oscillatory shear behavior that can be approximated by a single-relaxation Maxwellian model. Aqueous solutions of C₁₈-PNIPAM-C₁₈ undergo a phase transition upon heating to 31.5^°C as determined by microcalorimetry. The heat-induced phase separation of dilute (0.025 gL^-1) C₁₈-PNIPAM-C₁₈ solutions yields a fluid that is colloidally stable at temperatures higher than 33^°C. The overall results are consistent with a model assuming the formation of flowerlike micelles in the dilute regime and a network of micelles connected by telechelic chains in the concentrated regime.     

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.     

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.     

Study of radiative leptonic events with hard photons and search for excited charged leptons at GeV

During the last 1995 data acquisition period at LEP, the DELPHI experiment collected an integrated luminosity of 5.9 pb⁻¹ at centre-of-mass energies of 130 GeV and 136 GeV. Radiative leptonic events (e, μ, τ) with high energy photons were studied and compared to Standard Model predictions. The data were used to search for charged excited leptons decaying through an electromagnetic transition. No significant signal was found. From the search for pair produced excited leptons, the limits m_e^* > 62.5 GeV/c², m_μ^* > 62.6 GeV/c² and m_τ^* > 62.2 GeV/c² at 95% confidence level were established. For single excited lepton production, upper limits on the ratio λ/m_l^* of the coupling of the excited charged lepton to its mass were derived.     

Compression induced phase transitions in PEO brushes: the n-cluster model

The compression of brushes of terminally anchored chain within the de Gennes n-cluster model is analysed. This model was developed for Poly(ethylene oxide) in water but may apply to other systems. Brushes described by this model exhibit discontinuous concentration profile associated with the coexistence of an inner dense “phase” and an outer, dilute, one. The compression induces growth of the dense, weakly compressible region. This, in turn, gives rise to distinctive force profiles associated with changes of slope. When the dilute region disappears, the compression of two brushes can give rise to a transient attraction. Received: 4 November 1997 / Revised: 29 January 1998 / Accepted: 24 March 1998     

Salt-modulated structure of polyelectrolyte-macroion complex fibers

The structure and stability of strongly charged complex fibers, formed by complexation of a single long semi-flexible polyelectrolyte chain and many oppositely charged spherical macroions, are investigated numerically at the ground-state level using a chain-sphere cell model. The model takes into account chain elasticity as well as electrostatic interactions between charged spheres and chain segments. Using a numerical optimization method based on a periodically repeated unit cell, we obtain fiber configurations that minimize the total energy. The optimal fiber configurations exhibit a variety of helical structures for the arrangement of macroions including zig-zag, solenoidal and beads-on-a-string patterns. These structures result from the competition between attraction between spheres and the polyelectrolyte chain (which favors chain wrapping around the spheres), chain bending rigidity and electrostatic repulsion between chain segments (which favor unwrapping of the chain), and the interactions between neighboring sphere-chain complexes which can be attractive or repulsive depending on the system parameters such as salt concentration, macroion charge and chain length per macroion (linker size). At about physiological salt concentration, dense zig-zag patterns are found to be energetically most stable when parameters appropriate for the DNA-histone system in the chromatin fiber are adopted. In fact, the predicted fiber diameter in this regime is found to be around 30 nanometers, which roughly agrees with the thickness observed in in vitro experiments on chromatin. We also find a macroion (histone) density of 5–6 per 11nm which agrees with results from the zig-zag or cross-linker models of chromatin. Since our study deals primarily with a generic chain-sphere model, these findings suggest that structures similar to those found for chromatin should also be observable for polyelectrolyte-macroion complexes formed in solutions of DNA and synthetic nano-colloids of opposite charge. In the ensemble where the mean linear density of spheres on the chain is fixed, the present model predicts a phase separation at intermediate salt concentrations into a densely packed complex phase and a dilute phase.     

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.     

Optimal cell approach to osmotic properties of finite stiff-chain polyelectrolytes

We propose a self-consistent geometry optimized cell model approach to study osmotic properties of stiff-chain polyelectrolyte solutions. In contrast with the usual monotonic Poisson-Boltzmann prediction, the cell model predicts the correct nonmonotonic dependence of the osmotic coefficient on concentration. A lower degree of polymerization is found to reduce significantly the counterion condensation in a typical dilute strong polyelectrolyte. The results agree quantitatively with simulations of a corresponding many-body bulk system up to a dense semidilute regime.     

Nanostructures of colloidal complexes formed in oppositely charged polyelectrolyte/surfactant dilute aqueous solutions

Small-angle neutron scattering measurements were performed on dilute solutions of carboxymethylcellulose/DTAB complexes in water in order to determine their size, shape and internal structures. At low polymer content, the complexes are spherical, rather monodisperse and probably made of polymer chains intercalated between surfactant micelles. Moreover, we show that these micelles have a similar cubic arrangement than found in polymer/surfactant precipitates formed at higher surfactant concentrations. At larger polymer content, in the semi-dilute polyelectrolyte regime, the complexes are larger, softer and polydisperse. However, they possess a similar internal structure in both regimes. Carboxymethylcellulose/CTAB complexes are also large, soft and polydisperse but do not seem to exhibit well-defined internal structures.     

Towards a structural characterization of charge-driven polymer micelles

Light scattering and small-angle neutron scattering experiments were performed on comicelles of several combinations of oppositely charged (block co)polymers in aqueous solutions. Fundamental differences between the internal structure of this novel type of micelle --termed complex coacervate core micelle (C3Ms), polyion complex (PIC) micelle, block ionomer complex (BIC), or interpolyelectrolyte complex (IPEC)-- and its traditional counterpart, i.e., a micelle formed via self-assembly of polymeric amphiphiles, give rise to differences in scaling behaviour. Indeed, the observed dependencies of micellar size and aggregation number on corona block length, N _corona , are inconsistent with scaling predictions developed for polymeric micelles in the star-like and crew-cut regime. Generic C3M characteristics, such as the relatively high core solvent fraction, the low core-corona interfacial tension, and the high solubility of the coronal chains, are causing the deviations. A recently proposed scaling theory for the cross-over regime, as well as a primitive first-order self-consistent field (SCF) theory for obligatory co-assembly, follow our data more closely.     

Polyelectrolytes in the presence of multivalent ions: gelation versus segregation

We analyze solutions of strongly charged chains bridged by linkers such as multivalent ions. The gelation induced by the strong short range electrostatic attractions is dramatically suppressed by the long range electrostatic correlations due to the charge along the non-cross-linked monomers and ions. A modified Debye-Hückel approach of cross-linked clusters of charged chains is used to determine the mean field gelation transition self-consistently. Highly dilute polyelectrolyte solutions tend to segregate macroscopically. Semidilute solutions can form gels if the Bjerrum length l(B) and the distance between neighboring charged monomers along the chain b are both greater than the ion size a.     

Collapse of sodium polyacrylate chains in calcium salt solutions

The sodium salt of polyacrylic acid (NaPA) precipitates in the presence of Ca²⁺-ions. This phase behaviour can be represented by a phase diagram where the critical NaPA concentration is plotted versus the critical Ca²⁺ concentration resulting in a straight line as a phase boundary. The location of this phase boundary is influenced by the presence of an inert monovalent salt like NaCl. The present contribution focuses on the coil dimensions of NaPA chains in dilute aqueous solution corresponding to the one phase region of such a phase diagram. A variety of parameters with which the size and shape of the polyelectrolyte chains can be modulated are revealed. Approaching the phase boundary by decreasing the NaPA concentration at a constant Ca²⁺ content leads to a collapse of the NaPA chains. Combined static and dynamic light scattering suggests a compact spherical shape as the final state of this transition, both in 0.1 M NaCl and in 0.01 M NaCl. In the lower NaCl concentration, indication is presented for the existence of a cigar or pearl necklace like intermediate. Most strikingly, the collapsed chains can be reexpanded by increasing the concentration of inert NaCl at constant content of NaPA and Ca²⁺. Clearly, excessive Na⁺-ions displace the Ca²⁺-ions from the NaPA chains. Received 18 July 2000 and Received in final form 24 August 2000     

Pseudogap and precursor superconductivity in underdoped cuprate high temperature superconductors: A far-infrared ellipsometry study

With the technique of infrared ellipsometry we performed a detailed study of the temperature- and doping dependence of the c-axis response of a series of YBa₂Cu₃O_7−δ single crystals. In particular, we explored the anomalous electronic properties at temperatures above the macroscopic superconducting transition temperature, T _c, whose conflicting explanations range from a precursor superconducting state to electronic correlations that compete with superconductivity. We show that the c-axis spectra provide evidence that both kinds of correlations are present and that their contributions can be disentangled based on an analysis with a so-called multilayer-model. We find that the onset temperature, T ^*, and the energy scale, Δ_PG, of the competing pseudogap increase rapidly towards the underdoped side whereas they vanish on the overdoped side. In addition, we provide evidence that in a strongly underdoped sample the precursor superconducting correlations develop below an onset temperature, T ^ons, that is considerably lower than T ^* but still much higher than T _c.     

Do spherical polyelectrolyte brushes interdigitate?

The structure of spherical micelles of the diblock copolymer poly(styrene-block-acrylic acid) in water was investigated with small angle neutron scattering and contrast matching. We have monitored intermicelle correlation and the extension of the polyelectrolyte chains in the coronal layer through the overlap concentration. Irrespective of ionic strength, the corona shrinks with increasing packing fraction. Furthermore, at high charge and minimal screening conditions, the corona layers interpenetrate once the volume fraction exceeds the critical value 0.53+/-0.02.     

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.     

Transport theory of multiterminal hybrid structures

We derive a microscopic transport theory of multiterminal hybrid structures in which a superconductor is connected to several spin-polarized electrodes. We discuss the non-perturbative physics of extended contacts, and show that such contacts can be well represented by averaging out the phase of the electronic wave function. The intercontact Andreev reflection and elastic cotunneling conductances are identical if the phase can be averaged out, namely in the presence of at least one extended contact. The maximal conductance of a two-channel contact is proportional to (e ²/h)(a ₀/D)²exp[-D/ξ(ω^*)], where D is the distance between the contacts, a₀ the lattice spacing, ξ(ω) is the superconducting coherence length, and ω^* is the cross-over frequency between a perturbative regime ( ω < ω^*) and a non perturbative regime ( ω^* < ω < Δ). Received 18 June 2001 and Received in final form 17 January 2002