Counterion-counterion correlation in the double layer around cylindrical polyions: counterion size and valency effects

Monte Carlo simulation and Poisson-Boltzmann results on some aspects of structure and thermodynamics of aqueous polyelectrolyte solutions are presented. The polyelectrolyte solution is described by an infinitely long cylindrical polyion surrounded by counterions modeled as rigid ions moving in a continuum dielectric. Ion-ion correlations in the form of volume average of the counterion-counterion distribution function in the double layer surrounding the polyion are reported for mono- and divalent counterions and for a range of polyion concentrations and charge density parameters in each case. These results confirm again strong influence of the charge density parameter of polyions on properties of polyelectrolyte solutions. The structural information is supplemented by the calculated thermodynamic properties such as osmotic coefficients and heats of dilutions; the latter quantity has not been examined yet in detail by computer simulations. The results are discussed in view of the existing experimental data from the literature for these properties.     

Phenomenological surface characterization of cationic-lipid monolayers in the presence of oppositely charged polyions

The thermodynamic properties of monolayers of double chain cationic lipids DOTAP at the air–water interface have been investigated by means of surface pressure and surface potential measurements. We studied the interfacial properties of the film in the liquid-expanded regime during the isothermal compression in the presence of oppositely charged linear polyions (poly(acrylate)sodium salt, [NaPA]) of different molecular weights. The influence of the ionic character of the aqueous subphase on the polyion adsorption has been studied in different environmental conditions, considering different subphase compositions, ranging from a polyion solution at different concentrations to a salty polyion solution, containing different amount of simple added salt [NaCl]. The data are compared to the ones when only NaCl salt is present in the subphase. The results have been analyzed according to an osmotic-type equation of state and the characteristic parameter associated with the water activity has been evaluated as a function the different molecular weight polyion content. The influence of the simple salt in the adsorption process has been discussed in the light of current scaling theories of polyelectrolyte solutions and the critical salt concentrations inducing a polyion desorption in the different experimental conditions investigated have been estimated.     

Structural properties of star-shaped polyions: Entropic sampling

The method of entropic sampling within the Wang–Landau algorithm (a modern variant of the Monte Carlo method) is used to determine the densities of energy states of a strongly charged star-shaped polyelectrolyte within the framework of the lattice model. The equilibrium thermal and structural properties of the polyelectrolyte with the number of arms f ≤ 6 and the length of arms N _arm ≤ 73 in a wide temperature range are determined from the density of states. Such characteristics as the free energy, the mean-squared radius of gyration, its components, and the parameters characterizing the shape of a polyion are calculated. It is found that the concentration, length, and number of arms affect the thermal and structural properties. The main attention is focused on the effect of temperature on these properties. The coil-to-globule transition is detected, while for the polyion with the highest length of arms (N _arm = 24) the transition from the liquid globule to the crystal-like one is observed. Differences in the properties of the star-shaped and corresponding linear polyions are characterized.     

Increased layer interdiffusion in polyelectrolyte films upon annealing in water and aqueous salt solutions

As-deposited films of multilayered polyelectrolytes are considered to be non-equilibrium structures. Due to the strong attraction between oppositely charged polyions, polyelectrolyte interdiffusion is thought to be suppressed during the adsorption process. Equilibration is promoted by a decrease of the electrostatic attraction between polyion pairs. We have used neutral impact collision ion scattering spectroscopy to investigate the influence of polyelectrolyte multilayer annealing in water and aqueous 1 M NaCl solutions at different temperatures (20 and 70 degrees C) on the increase in interpenetration of a single polyelectrolyte layer throughout the whole film. The multilayers were composed of poly(4-vinylpyridinium) and poly(4-styrenesulfonate). Contrast between neighboring layers was established by labelling the layer in question with the heavy atom ruthenium. It is found that both temperature and salt increase layer interpenetration, whereas salt has a stronger influence than temperature. From numerical simulations polyelectrolyte diffusion coefficients were evaluated for the different annealing conditions. The influence of temperature and salt on the equilibration of the film is interpreted in terms of increased screening of polyion charges and binding of small counterions to polyion monomeric units.     

无盐聚电解质溶液的分子热力学模型

聚电解质在水处理和胶体领域应用广泛 ,在生物系统中 ,蛋白质和 DNA等均是聚电解质 .文献中已发表了不少聚电解质溶液的理论和模型 ,如基于柱型胞腔模型的 Poison- Boltzmann( PB)方程理论[1]及其改进型 ( MPB) [2 ] 、Manning反离子凝聚理论 [3 ] 、积分方程理论 [4] 及适合于工程应用的半经验模型 [5 ]等 ,但离工程实际应用的要求还相差较远 .最近 ,姜建文等 [6]建立的分子热力学模型 ,其预测结果与 MD模拟数据非常吻合 .本文在此基础上进一步考虑聚离子与反离子间的缔合作用 ,可以在中高浓度范围内很好地关联实验数据 .1　模　　型…     

Polyion interchange reactions of interpolyelectrolyte complexes in aqueous solutions and gels

Cooperative coupling reaction between two opposite charged polyelectrolytes results in formation of polyelectrolyte complexes (IPEC). This reaction is very fast and diffusion controlled. Whether IPECs formed by linear polyions are soluble or limitary swellable in aqueous media is decided by their composition, namely, by a ratio of oppositely charged polyions as well as by a water phase composition (the nature and the concentration of a simple salt, pH, the presence and the concentration of organic additives etc.). The most important intrinsic property of IPECs is their ability to participate in interchange (exchange and substitution) reactions with competing polyions. The kinetics and the position of equilibria in these reactions are controlled by the low molecular salt concentration, the nature of small counterions, DP of interaction polyelectrolytes, as well as by their linear charge density. IPECs can be formed also by interacting linear and opposite charged networks. It is shown that linear polyelectrolytes dissolved in aqueous solution can penetrate unexpectedly fast into oppositely charged cross-linked polyelectrolyte gels to form “snake-in-cage” composites representing IPECs of corresponding polyion segments. It is proved that the mechanism consists in “relay-race” transfer of linear polyion segments from one segment of the polyelectrolyte network to the other via interpolyelectrolyte exchange reaction. The driving force for the fast transport of linear polyions into the gel is produced by coupling reaction between two polyelectrolytes proceeding on solution/gel interface.     

Stoichiometric polyelectrolyte complexes of ionic block copolymers and oppositely charged polyions

Micellization in dilute solutions of diblock copolymers with a polyelectrolyte and a hydrophilic nonionic blocks and oppositely charged polyions is studied using mean-field theory. In aqueous solutions the micelle core consists of the polyelectrolyte complex (PEC) while the corona is formed by hydrophilic blocks of the block copolymers. Describing PEC as a globule in the framework of the Lifshitz [Zh. Eksp. Teor. Fiz. 55, 2408 (1968)] globule theory we calculate the surface tension of the micellar core/solvent interface as a function of the polyion degree of ionization, solvent quality, and concentration of low-molecular-mass salt. The equilibrium aggregation number of starlike micelles formed by block copolymers and homopolymers of opposite charge at stoichiometric mixture compositions is found as a function of the system parameters. It is shown that micelles disintegrate upon addition of salt.     

Determination of the concentration dependence of polyelectrolyte diffusion coefficients by application of the Boltzmann gradient method

The concentration dependence of a polyelectrolyte diffusion coefficient in aqueous low salt solution (KCl, 1 mM) is determined from a single dynamic gradient experiment. The Boltzmann method is applied to calculate the diffusion coefficient. A special diffusion cell is constructed that minimizes aberrations in the optical detection of the polyion concentration profile. Bovine serum albumin (BSA) is chosen as a model polyion. To get information about the diffusion process down to very small polyion concentrations, the BSA molecule is fluorescently labeled. The fluorescence intensity is used as a measure of the polyion concentration. The change of the polyion net charge caused by labeling is discussed. The cell is illuminated by an LED, and the fluorescence intensity profile is detected by a CCD camera. Experiments at 5 and 17 degrees C show that the diffusion coefficient of labeled BSA remains constant in the very low polyion concentration range below a threshold of about 1.5 g/l. This is in contradiction to the linear concentration dependence of polyion diffusion coefficients at very low concentrations often postulated in the literature without reference to direct experimental evidence. Our finding is confirmed by dynamic light scattering experiments published recently. An explanation for this behavior based on a modified Donnan osmotic compressibility approach is given.     

Dynamics and Structure of Biopolyelectrolytes Characterized by Dielectric Spectroscopy

Structural properties of Na-DNA and Na-HA aqueous solutions can be quantified using dielectric spectroscopy in the frequency range 100 Hz–100 MHz. Two relaxation modes are typically detected that can be attributed to diffusive motion of polyion counterions. The overall study as a function of polyion length, concentration and added salt concentration demonstrates that the motion of polyion counterions detected at MHz frequencies probes collective properties, whereas the motion at kHz range probes single-chain properties of polyelectrolytes. Fundamental length scales found to characterize the polyelectrolyte structure differ for the dilute and semidilute regime and also depend on the strength of electrostatic interactions and the flexibility. Characteristic length scales detected in the dielectric spectroscopy measurements compare well with the fundamental length scales predicted by theory and comply with those extracted from small-angle X-ray scattering.     

Distribution of counterions in the double layer around a cylindrical polyion

The modified Poisson-Boltzmann (MPB) equation, and the Monte Carlo (MC) method, were applied to the cell model of a polyelectrolyte solution in order to calculate the distribution of counterions around a cylindrical polyion. Both methods suggest stronger binding of counterions to the polyion than predicted by the ordinary Poisson-Boltzmann (PB) equation. The inclusion of counterion-counterion correlation being neglected in the PB equation, leads to a better agreement of the calculated osmotic coefficients with those measured.     

Ionic effects in collapse of polyelectrolyte brushes

We investigated the effect of counterion valence on the structure and swelling behavior of polyelectrolyte brushes using a nonlocal density functional theory that accounts for the excluded-volume effects of all ionic species and intrachain and electrostatic correlations. It was shown that charge correlation in the presence of multivalent counterions results in collapse of a polyelectrolyte brush at an intermediate polyion grafting density. At high grafting density, the brush reswells in a way similar to that in a monovalent ionic solution. In the presence of multivalent counterions, the nonmonotonic swelling of a polyelectrolyte brush in response to the increase of the grafting density can be attributed to a competition of the counterion-mediated electrostatic attraction between polyions with the excluded-volume effect of all ionic species. While a polyelectrolyte brush exhibits an "osmotic brush" regime at low salt concentration and a "salted brush" regime at high salt concentration regardless of the counterion valence, we found a smoother transition as the valence of the counterions increases. As observed in recent experiments, a quasi-power-law dependence of the brush thickness on the concentration ratio can be identified when the monovalent counterions are replaced with trivalent counterions at a fixed ionic strength.     

End effects for a rodlike polyelectrolyte molecule in salt solution

Electrostatic potentials around a single rodlike polyelectrolyte molecule are calculated by solving the nonlinear Poisson–Boltzmann equation numerically in the presence of externally added salt. The polyion is regarded as a cylinder with a finite length whose side surface is uniformly charged and end surfaces uncharged. The calculations show that the distance to which end effects extend is about half the Debye screening length and is almost independent of the surface charge density and concentration of added salt. For a long polyion whose length is much greater than the Debye length, the end effects can be neglected even for a polyelectrolyte with high surface charges, whereas they play an important role for a short polyion with a length of the same order as the Debye length. In addition, a strong charge condensation is found in the direction of the axis of the cylinder for a long polyion.     

Polyion complex nanomaterials from block polyelectrolyte micelles and linear polyelectrolytes of opposite charge: 1. Solution behavior

The present study investigates whether block polyelectrolyte micelles can form soluble complexes upon interaction with oppositely charged linear polyelectrolytes. The phase behavior and molecular characteristics of the complexes were examined by turbidimetry, phase analysis, dynamic light scattering, and sedimentation velocity techniques. At an excess of polyelectrolyte micelles, soluble complexes were formed either independently on the route of preparation or, for select linear polyelectrolytes, through routes that avoided macrophase separation. Such soluble complexes are in a thermodynamic equilibrium state for all polyion pairs. The hydrodynamic sizes and sedimentation coefficients did not depend on the chemical nature of the linear polyelectrolyte, but were determined by the charge ratios and the hydrodynamic properties of the initial micelles. At an excess of linear polyelectrolyte, complex solubility and molecular characteristics depended on the chemical nature of the linear polyelectrolyte. In this region, linear polyelectrolytes formed soluble complexes with micelles if soluble complexes could be formed with the corresponding linear analogues of the block polyelectrolyte.     

Phénomènes de transport dans les solutions de polyélectrolytes—II. Vitesse de sédimentation limite de polyélectrolytes en solution saline

Equations are derived for the sedimentation transport coefficient of polyelectrolyte systems comprising a macromolecular component and an added simple electrolyte component (salt) present in excess. The equations are discussed with respect to previous results and the validity of some of the assumptions usually made in the interpretation of transport data is questioned. It is shown that since some of the small ions are not randomly distributed through the solution, the macro-ion undergoes electrostatic retention from its non-electroneutral environment and the motion of the polyion does not proceed identically to that of an uncharged particle for which only hydro- dynamical interactions are occuring.     

A unified analytical treatment of the acid-dissociation equilibria of weakly acidic linear polyelectrolytes and the conjugate acids of weakly basic linear polyelectrolytes

 The influence of added sodium chloride concentration levels on the acid-dissociation equilibria of a weakly acidic linear polyelectrolyte and a conjugate acid of weakly basic linear polyelectrolyte has been investigated potentiometrically by use of polyacrylic acid (PAA) and poly(N-vinylimidazole) (PVIm) as examples of polyelectrolytes. Both equilibria are strongly influenced by the degree of dissociation of the polyacids as well as the concentration levels of sodium chloride due to an electrostatic effect originating from the negatively or positively charged polymer surfaces. These have been analyzed in a unified manner by taking accounts of two-phase properties of the charged linear polyions. Distribution of counterions and coions between a polyelectrolyte phase formed around the polymer skeleton and a bulk solution phase has been rationalized by a Donnan’s relation. Introduction of a volume term for the polyelectrolyte phase permits definition of averaged concentrations of mobile ions in the vicinity of the polyion molecules, which enables us to define hypothetical intrinsic acid-dissociation constants in the polyion domain. The intrinsic constants estimated by extrapolation of apparent acid-dissociation constants at zero-charge state are in good agreement with the acid-dissociation constants of the monomer analogs of the polymers, i.e., acetic acid for PAA and imidazole for PVIm, respectively. The difference between the apparent and intrinsic acid-dissociation constants for PVIm was much higher than that for PAA at defined degree of dissociation of the polyacids, even though the separations of the functionalities fixed on the linear polymers are approximately equal to each other. Received: 4 February 1997 Accepted: 26 May 1997     

Potentiometric detection of polyions based on functionalized magnetic nanoparticles

A novel potentiometric detection strategy based on functionalized magnetic nanoparticles has been developed for rapid and sensitive sensing of polyions. Highly dispersed magnetic nanoparticles coated with ion exchanger and plasticizer could promote an in situ cooperative ion-pairing interaction between the ion exchanger and the polyion analyte in sample solution by dramatically reducing the mass-transfer distance. With applying a magnetic field, the nanoparticles can be attached to the surface of ion exchanger free polymeric membrane. The observed potential signals are related to the polyion concentrations. The proposed polymeric membrane electrode exhibits a linear relationship between the greatest potential response slope (dE/dt) and the logarithm of protamine concentration in the range of 0.05−5 μg/mL with a lower detection limit of 0.033 μg/mL.     

Self-assembly in ternary systems: cross-linked polyelectrolyte,linear polyelectrolyte and surfactant

The competitive interactions in ternary systems consisting of a slightly cross-linked polyelectrolyte hydrogel and the mixture of linear polyelectrolyte and micelle forming surfactant both oppositely charged relative to the polyelectrolyte network were studied. It was shown that the equilibrium in the competitive reactions depends on the linear polyion charge density and the length of the surfactant aliphatic radical. Dependency on these characteristics the interpolyelectrolyte complex formed by cross-linked and linear polyelectrolytes can uptake surfactant ions from water solution transforming into the cross-linked polyelectrolyte-surfactant complex and releasing the linear polyelectrolyte or vice versa. The ternary systems of this kind are perspective to design the novel family of delivery constructs.     

Linear polyelectrolytes in tetravalent salt solutions

The effect of adding tetravalent salt of different sizes to a solution of linear and flexible polyelectrolytes is investigated by molecular dynamics simulations. Upon the addition of salt, a chain reexpansion takes place, following a well-known collapsed conformation. The degrees of collapse and reexpansion increase with ion size. In the solution, tetravalent counterions replace monovalent ones and condense onto the chains. The condensation for small ions displays a profile different from that for large ones. In a high-salt region, ions can form layering orders around a polyelectrolyte and locally overcompensate the charge inside. Consequently, the integrated charge distribution reveals an oscillatory behavior away from a chain. By studying the radial distribution function between monomers on different polyelectrolytes, like-charge attraction between chains is demonstrated. This attraction is a prerequisite to chain aggregation or precipitation. The results show a strong dependence of salt concentration and ion size on the properties of polyelectrolyte solutions.     

Complexation of anionic polyelectrolytes with cationic liposomes: evidence of reentrant condensation and lipoplex formation

We have studied the complexation process taking place in cationic liposomes in the presence of anionic polyelectrolytes, in the polyion concentration range from the dilute to the concentrated regime, by combining dynamic light scattering and transmission electron microscopy techniques. We employed as the cationic lipid a two-chained amphiphile (Dioleoyltrimethylammoniumpropane) and sodium polyacrylate salt as the flexible anionic polyelectrolyte. The results evidence a variety of different structures, mainly depending on the liposome-polyion charge ratio, whose peculiar dynamical and structural features are briefly described. In particular, three different polyion concentration regions are found, within which a monomodal or bimodal distribution of aggregates, with a well-defined time evolution, is present. At low polyion content, close to the isoelectric point, large aggregates are formed, deriving from the collapse of the liposomal bilayers into extended charged surfaces, where adsorbed polyions form a two-dimensional strongly correlated array and organize into a two-dimensional Wigner liquid. At high polyion content, above a critical concentration, the size distributions of the complexes are clearly bimodal and a large-component aggregate, continuously increasing with time, coexists with a population of smaller-size aggregates. At an intermediate polyion concentration, spherical, small-size vesicular structures are reformed, connected in a network by polymer chains. A brief discussion tries to summarize our results into a consistent picture.