Collapse of spherical polyelectrolyte brushes in the presence of multivalent counterions

We consider the interaction of multivalent counterions with spherical polyelectrolyte brushes (SPB). The SPB result if linear polyelectrolyte (PE) chains (contour length: 60 nm) are densely grafted to colloidal spheres of 116 nm in diameter. Dispersed in water, the surface layer consisting of chains of the strong PE poly(styrene sulfonic acid) (PSS) will swell. We demonstrate that successive addition of trivalent ions (La3+) leads to a collapse in which the surface layer is shrinking drastically. All findings are discussed on the base of a theoretical mean-field approach using the Donnan equilibrium. The ion exchange and a strong binding of trivalent ions by PE chains is followed up by a drop in the osmotic pressure inside the brush. This reduction is the driving force for the collapse. The strong ion-chain correlation is discussed with results obtained from molecular dynamics simulations.     

The distribution of counterions around synthetic rod-like polyelectrolytes in solution

An investigation of the radial distribution of the counterions of a synthetic rodlike polyelectrolyte in aqueous solution is presented. The cationic polyelectrolyte used here has a poly(p-phenylene) backbone. For typical molecular weights the macroion comprises approximately one persistence length (ca. 20 nm) and effects of finite stiffness may be disregarded. Each repeating unit bears four charges which leads to a charge parameter of ξ = 6.65. The distribution of the iodide counterions around this highly charged macroion is studied by small-angle X-ray scattering (SAXS) in dilute aqueous solution. These investigations are supplemented by measurements using anomalous small-angle X-ray scattering (ASAXS) that furnishes additional information about the contrast of the macroion. Data taken at high scattering angles give indication for contributions caused by the longitudinal fluctuations of the counterions. After correction for this effect the experimental results are compared to intensities calculated by use of the Poisson-Boltzmann (PB)-cell model. It is found that the PB-cell model describes the corrected data at intermediate and high scattering angles. Deviations at low scattering angle are attributed to the mutual interaction of the rod-like polyelectrolyte that can be described in terms of an effective structure factor. Data taken at lowest scattering angles point to a weak attraction between the rod-like macroions. Received: 27 July 2001 and Received in final form 27 March 2002     

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.     

Molecular dynamics study of linear and comb-like polyelectrolytes in aqueous solution: effect of Ca2+ ions

All-atom molecular dynamics simulations were employed to provide microscopic mechanism for the salt tolerance of polyelectrolytes dispersants. The conformational variation of polyelectrolytes and interactions between COO^? groups and counterions/water molecules were also studied via radius of gyration and pair correlations functions. Sodium polyacrylate (NaPA) and sodium salts of poly(acrylic acid)–poly(ethylene oxide) (NaPA–PEO) were selected as the representative linear and comb-like polyelectrolyte, respectively. The results show that Ca²⁺ ions interact with COO^? groups much stronger than Na⁺ ions and can bring ion-bridging interaction between intermolecular COO^? groups in the NaPA systems. While in the NaPA–PEO systems, the introduced PEO side chains can prevent backbone chains from ion-bridging interactions and weaken the conformational changes. The present results can help in selecting and designing new-type efficient polyelectrolyte dispersants with good salt tolerance.     

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.     

Polyelectrolyte multilayer formation: Electrostatics and short-range interactions

We investigate the phenomenon of multilayer formation via layer-by-layer deposition of alternating charged polyelectrolytes. Using mean-field theory, we find that a strong short-range attraction between the two types of polymer chains is essential for the formation of multilayers. For strong enough short-range attraction, the adsorbed amount per layer increases (after an initial decrease), and finally it stabilizes in the form of a polyelectrolyte multilayer that can be repeated hundreds of times. For weak short-range attraction between any two adjacent layers, the adsorbed amount (per added layer) decays as the distance from the surface increases, until the chains stop adsorbing altogether. The dependence of the threshold value of the short-range attraction as function of the polymer charge fraction and salt concentration is calculated.     

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.     

Swelling behavior and viscoelasticity of ultrathin grafted hyaluronic acid films

In this paper we study the effect of monovalent and divalent ions on the swelling behavior and viscoelastic parameters of ultrathin layers of the natural polyelectrolyte hyaluronic acid covalently coupled to glass substrates. A colloidal probe technique is applied for this purpose based on latex beads, hovering over the polymer cushion. By analyzing the vertical Brownian motion of these beads with reflection interference contrast microscopy (RICM) we determined the equilibrium layer thickness (with 3 nm vertical resolution), the interfacial interaction potential, and the characteristic mesh size limiting the hydrodynamic flow within the polyelectrolyte film as a function of the ionic strength. The experimental results are interpreted in terms of three different theoretical models: the polyelectrolyte brush approximation of Pincus [#!ref1!#], a modified polyelectrolyte brush approximation in the high salt concentration limit of Ross and Pincus [#!ref2!#] and the simple scaling approximation for neutral adsorbed polymers of de Gennes [#!ref3!#]. Within experimental error all of these different models fit our experimental data and yield comparable results for the equilibrium layer thickness. Moreover we determine a thickness dependent, effective surface coverage from both brush models. The hydrodynamic properties of the films are interpreted in terms of the Brinkmann model of elastic porous media by assuming an effective mesh size, which depends linearly on the Debye screening length. The salt induced condensation of the polyelectrolyte films can be described microscopically in terms of a progressive contraction of the mesh size with increasing salt concentration. Received 10 September 1998 and Received in final form 30 November 1998     

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.     

Conformation of poly(L-lysine)-graft-poly(ethylene glycol) molecular brushes in aqueous solution studied by small-angle neutron scattering

Small-angle neutron scattering (SANS) has been employed for the analysis of conformations of poly(L-lysine)-graft-poly(ethylene glycol) (PLL-g -PEG) molecular bottle brushes in aqueous solutions. The degree of polymerisation of the PEG chains was systematically varied in order to unravel dependence of the conformational properties of the bottle brushes on the molecular weight of the grafted chains. The grafting density was kept constant and high enough to ensure strong overlap of the PEG chains. The scattering spectra were fitted on the basis of the model of an effective worm-like chain with the account of average radial distribution and local fluctuations of the PEG density in the bottle brush. The results of the fits indicate that molecular brushes retain weakly bent configuration on the length scale of the order of (or larger than) the brush thickness. This finding is in agreement with earlier simulation and recent theoretical results.     

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.     

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.     

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.     

Structure of colloidal complexes obtained from neutral/poly- electrolyte copolymers and oppositely charged surfactants

We report on the phase behavior and scattering properties of colloidal complexes made from block copolymers and surfactants. The copolymer is poly(sodium acrylate)-b-poly(acrylamide), hereafter abbreviated as PANa-PAM, with molecular weight 5000 g/mol for the first block and 30000 g/mol for the second. In aqueous solutions and neutral pH, poly(sodium acrylate) is a weak polyelectrolyte, whereas poly(acrylamide) is neutral and in good-solvent conditions. The surfactant is dodecyltrimethylammonium bromide (DTAB) and is of opposite charge with respect to the polyelectrolyte block. Combining dynamical light scattering and small-angle neutron scattering, we show that in aqueous solutions PANa-PAM diblocks and DTAB associate into colloidal complexes. For surfactant-to-polymer charge ratios Z lower than a threshold (Z(C) approximately 0.3), the complexes are single surfactant micelles decorated by few copolymers. Above the threshold, the colloidal complexes reveal an original core-shell microstructure. We have found that the core of typical radius 100-200 A is constituted from densely packed surfactant micelles connected by the polyelectrolyte blocks. The outer part of the colloidal complex is a corona and is made from the neutral poly(acrylamide) chains. Typical hydrodynamic sizes for the whole aggregate are around 1000 A. The aggregation numbers expressed in terms of numbers of micelles and copolymers per complex are determined and found to be comprised between 100-400, depending on the charge ratio Z and on the total concentration. We have also shown that the sizes of the complexes depend on the exact procedure of the sample preparation. We propose that the driving mechanism for the complex formation is similar to that involved in the phase separation of homopolyelectrolyte/surfactant systems. With copolymers, the presence of the neutral blocks prevents the macroscopic phase separation from occurring.     

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.     

Polyelectrolyte Multilayers Studied by Electron Paramagnetic Resonance (EPR) Spin-Label Technique

A nitroxide spin label has been covalently attached to the polyelectrolyte poly(ethylene-alt-maleic acid) (P(E-alt-MA)) to study the interaction between this weak polyanion, the oppositely charged strong polycation poly(diallyldimethylammonium chloride) (PDADMAC) and water in swollen polyelectrolyte multilayers (PEM) by electron paramagnetic resonance (EPR) spectroscopy. If the spin-labeled polyanion has been used for the preparation of every double layer, the growth of the PEM film can be monitored by quantitative EPR. On the other hand, if the spin-labeled polyanion has been selectively placed in different layers in the PEM film the influence of the environment such as pH of the swelling medium of the mobility of the polyelectrolyte molecules positioned in the selected layer can be investigated.     

Stretching and collapse of neutral polymer layers under association with ionic surfactants

We provide experimental evidence for stretching and collapse of neutral polymer layers, already adsorbed at an oil-in-water interface, due to its interaction with surfactants. Upon stretching, the first interaction length (2L(0)) follows a power law dependence on surfactant concentration ( proportional, variant C(x)(s), where x approximately 0.5 for cationic surfactants) and collapses in the presence of salt, as a relatively weak power law (C(-y)(s), where y=0.17), in good agreement with brush length decay for polyelectrolyte brushes.     

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.     

水蒸气诱导聚电解质刷的构象转变

我们把Flory-Huggins模型(association models)推广应用到暴露于水蒸气中的聚电解质刷体系,考虑聚电解质-水氢键(P-W氢键)与水-水氢键(W-W氢键)、形成氢键与聚电解质链构象的耦合特性,研究水蒸气诱导的聚电解质刷构象转变的机理.研究发现,当P-W氢键效应起主导作用时,随着水蒸气浓度的增加,聚电解质刷会单调溶胀;P-W和W-W两种氢键效应,则会导致随着水蒸气浓度的增加,聚电解质刷的构象首先塌缩,然后开始溶胀的反常转变行为.基于本文的分析,可以预言,由于P-W氢键效应,聚电解质刷可以吸附水蒸气,吸附能力随聚电解质链长的增加而增强;当聚电解质链接枝密度足够高时,由于P-W和W-W两种氢键效应,增加体系中的水蒸气,会在聚电解质刷体系中形成由P-W氢键和W-W氢键交错链接的三维网络状凝胶结构.     

水蒸气诱导聚电解质刷的构象转变

我们把 Flory−Huggins 模型(association models)推广应用暴露于水蒸气中的聚电解质刷体系,考虑聚电解质-水氢键(P-W氢键)与水-水氢键(W-W氢键)、形成氢键与聚电解质链构象的耦合特性,研究水蒸气诱导的聚电解质刷构象转变的机理.研究发现,当 P-W 氢键效应起主导作用时,随着水蒸气浓度的增加,聚电解质刷会单调溶胀;P-W 和 W-W 两种氢键效应,则会导致随着水蒸气浓度的增加,聚电解质刷的构象首先塌缩,然后开始溶胀的反常转变行为。基于本文的分析,可以预言,由于 P-W 氢键效应,聚电解质刷可以吸附水蒸气,吸附能力随聚电解质链长的增加而增强;当聚电解质链接枝密度足够高时,由于 P-W 和 W-W 两种氢键效应,增加体系中的水蒸气,会在聚电解质刷体系中形成由 P-W 氢键和 W-W 氢键交错链接的三维网络状凝胶结构。