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.     

Elasticity of hollow polyelectrolyte capsules prepared by the layer-by-layer technique

Osmotically induced deformations (invaginations) of polyelectrolyte capsules were observed in poly(styrene sulfonate, sodium salt) (PSS) solution since PSS of Mw 70 000 is excluded from the capsule interior. It was found that there is a critical osmotic pressure difference at which the initial spherical capsule shape becomes unstable and invaginations are formed. This critical osmotic pressure was obtained as a function of the wall thickness and the capsule size. A theoretical model is provided which describes the relationship between the critical osmotic pressure, the elasticity modulus, the capsule wall thickness, and the capsule radius. The model was verified by measuring the invagination onset as a function of particle radius and wall thickness. The elasticity modulus of the PSS/PAH (polyallylamine hydrochloride) polyelectrolyte multilayer was measured as a function of wall thickness and capsule diameter. The modulus ranges between 500 and 750 MPa, which indicates a relatively strongly interconnected polyelectrolyte multilayer structure. With higher molecular weight PAH the elasticity modulus of the PSS/PAH multilayer was slightly enhanced. Received 25 January 2000 and Received in final form 18 May 2000     

Self-consistent field theory investigation of the behavior of hyaluronic acid chains in aqueous salt solutions

In this work we continue to develop a field-theoretic methodology, which combines the technique of Gaussian equivalent representation for the calculation of functional integrals with the continuous Gaussian thread model of flexible polymers for solving statistical–mechanical problems of polyelectrolyte solutions. We present new analytic expressions for the osmotic pressure, the potential of mean force, and the monomer–monomer pair distribution function, and employ them to investigate the structural and thermodynamic quantities of the polyelectrolyte system. We demonstrate the applicability of the method for systems of polyelectrolyte chains in which the monomers interact via a Yukawa-type pair potential. As a specific example, the present work focuses on aqueous solutions of hyaluronic acid with added salts NaCl and CaCl₂. Hyaluronic acid is a high molecular weight linear polysaccharide, which has a multitude of roles in biological tissues. We conclude that the effect of sodium chloride and calcium chloride on the osmotic properties of hyaluronic acid solutions can be accounted for by their contributions to the ionic strength. Nevertheless, the effects of coiling and self-association can be stimulated in solution by added salt.     

Theory and simulations of rigid polyelectrolytes

Theoretical and numerical studies are reported on stiff, linear polyelectrolytes within the framework of the cell model, first reviewing analytical results obtained on a mean-field Poisson—Boltzmann level, and then using molecular dynamics simulations to show the circumstances under which these fail quantitatively and qualitatively. For the hexagonally packed nematic phase of the polyelectrolytes the osmotic coefficient is computed as a function of density. In the presence of multivalent counterions it can become negative, leading to effective attractions. This is shown to result from a reduced contribution of the virial part to the pressure. The osmotic coefficient and ionic distribution functions are computed from Poisson—Boltzmann theory with and without a recently proposed correlation correction. Simulation results for the case of poly(p-phenylene) are presented and compared with recently obtained experimental data on this stiff polyelectrolyte. Ion—ion correlations in the strong coupling regime are studied and compared with the predictions of the recently advocated Wigner crystal theories.     

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.     

Scaling equations for a biopolymer in salt solution

The effect of the simultaneous presence of monovalent and divalent cations on the thermodynamics of polyelectrolyte solutions is an incompletely solved problem. In physiological conditions, combinations of these ions affect structure formation in biopolymer systems. Dynamic light scattering measurements of the collective diffusion coefficient D and the osmotic compressibility of semidilute hyaluronan solutions containing different ratios of sodium and calcium ions are compared with simple polyelectrolyte models. Scaling relationships are proposed in terms of polymer concentration and ionic strength J of the added salt. Differences in the effects of sodium and calcium ions are found to be expressed only through J.     

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.     

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.     

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.     

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.     

Insensitivity to salt of assembly of a rigid biopolymer aggrecan

Many polyelectrolytes, ranging from sulfonated polystyrene to DNA, exhibit a strong sensitivity of their phase behavior to salt concentration, especially to higher valence salts, which often lead to phase separation. We show that the stiff polyelectrolyte aggrecan exhibits a qualitatively different behavior. Specifically, the scattering properties of aggrecan solutions are exceptionally insensitive to the addition of calcium salt, conferring on aggrecan the role of an ion reservoir mediating calcium metabolism in cartilage and bone, and also providing osmotic resilience to compressive load.     

The effect of cell size distribution on predicted osmotic responses of cells

An understanding of the kinetics of the osmotic response of cells is important in understanding permeability properties of cell membranes and predicting cell responses during exposure to anisotonic conditions. Traditionally, a mathematical model of cell osmotic response is obtained by applying mass transport and Boyle-vant Hoff equations using numerical methods. In the usual application of these equations, it is assumed that all cells are the same size equal to the mean or mode of the population. However, biological cells (even if they had identical membranes and hence identical permeability characteristics--which they do not) have a distribution in cell size and will therefore shrink or swell at different rates when exposed to anisotonic conditions. A population of cells may therefore exhibit a different average osmotic response than that of a single cell. In this study, a mathematical model using mass transport and Boyle-van't Hoff equations was applied to measured size distributions of cells. Chinese hamster fibroblast cells (V-79W) and Madin-Darby canine kidney cells (MDCK), were placed in hypertonic solutions and the kinetics of cell shrinkage were monitored. Consistent with the theoretical predictions, the size distributions of these cells were found to change over time, therefore the selection of the measure of central tendency for the population may affect the calculated osmotic parameters. After examining three different average volumes (mean, median, and mode) using four different theoretical cell size distributions, it was determined that, for the assumptions used in this study, the mean or median were the best measures of central tendency to describe osmotic volume changes in cell suspensions.     

Ion-Exchange selectivity coefficients in the exchange of calcium,strontium, cobalt,nickel, zinc,and cadmium ions with hydrogen ion in variously cross-linked polystyrene sulfonate cation exchangers at 25°C

The ion-exchange selectivity parameters for the exchange of trace calcium, strontium, cobalt, nickel, zinc, and cadmium ions with hydrogen ion in cross-linked polystyrene-sulfonic acid cation exchangers have been determined from equilibrium ionic distribution measurements at 25°C in dilute solutions of perchloric acid and polystyrene-sulfonic acid. The selectivity behavior in perchloric acid solutions shows that the divalent ion is always preferred by the resin phase. The selectivity coefficients are a smooth function of resin phase concentration, increasing with concentration for Sr²⁺ more than for Ca²⁺ and Cd²⁺ and being practically independent of resin phase concentration for Co²⁺, Ni²⁺, and Zn²⁺. The selectivity coefficients measured in salt-free solutions of polystyrene-sulfonic acid show a marked dependence on the polyelectrolyte concentration, the divalent ion being preferred by the aqueous phase. This preference diminishes with the concentration of polyelectrolyte. These results are interpreted by resort to the Gibbs-Duhem equation. This thermodynamic analysis has been facilitated by the availability of osmotic coefficient data for the pure polyelectrolyte ion forms over a large concentration range. Ion-exchange selectivity predictions by using this approach accurately reflect the observed ion-exchange selectivity behavior.     

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。     

Swelling of cross-linked polyelectrolyte gels

A model of a cross-linked polyelectrolyte gel has been examined using Monte Carlo simulations. The simple model contained a charged defect-free network represented by linked charged beads and explicit counterions. Pressure-density relations for the polyelectrolyte gel, a corresponding non-ionic polymer gel, and several partly or fully degraded gels have been determined. The polyelectrolyte gel displayed a very large swelling capacity, in agreement with experiments. The swelling mechanism and chain properties are discussed and foundations of current theories on gel swelling are examined.     

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     

A model of electrodiffusion and osmotic water flow and its energetic structure

We introduce a model for ionic electrodiffusion and osmotic water flow through cells and tissues. The model consists of a system of partial differential equations for ionic concentration and fluid flow with interface conditions at deforming membrane boundaries. The model satisfies a natural energy equality, in which the sum of the entropic, elastic and electrostatic free energies is dissipated through viscous, electrodiffusive and osmotic flows. We discuss limiting models when certain dimensionless parameters are small. Finally, we develop a numerical scheme for the one-dimensional case and present some simple applications of our model to cell volume control.