Comparative Study of Scattering and Osmotic Properties of Synthetic and Biopolymer Gels

Summary: The effect of monovalent/divalent cation exchange on the structure and osmotic properties of chemically cross-linked polyacrylate and DNA gels swollen in near physiological salt solutions has been investigated. Both systems exhibit a reversible volume phase transition in the presence of calcium ions. The small-angle neutron scattering spectra of these gels display qualitatively similar features. At low values of q surface scattering is observed, while in the intermediate q range the signal is characteristic of scattering from rod-like elements. At high values of q the scattering intensity is governed by the local (short-range) geometry of the polymer chains. The competition between monovalent and divalent cations has been studied by anomalous small-angle X-ray scattering (ASAXS). The ASAXS results reveal that the local concentration of the divalent counter-ions in the vicinity of the polymer chains significantly exceeds that of the monovalent counter-ions.     

Ion‐exchange induced change in the structure and osmotic properties of sodium polyacrylate hydrogels

The swelling and volume transition of fully neutralized sodium polyacrylate gels were investigated in salt solutions using osmotic and small angle neutron scattering measurements. The volume transition was induced by monovalent/divalent cation exchange. The overall salt concentration and the ratio of monovalent to divalent cations were varied in the biologically significant range. The neutron scattering response of fully neutralized polyacrylate gels in the presence of excess salt is described by the sum of a dynamic and a static component. The thermal correlation length determined from the intensity of the dynamic component displays a maximum at the transition.     

Simulation Study of the Conformational Properties of Diblock Polyelectrolytes in Salt Solutions

Coarse-grained molecular dynamics simulations are performed to understand the behavior of diblock polyelectrolytes in solutions of divalent salt by studying the conformations of chains over a wide range of salt concentrations. The polymer molecules are modeled as bead spring chains with different charged fractions and the counterions and salt ions are incorporated explicitly. Upon addition of a divalent salt, the salt cations replace the monovalent counterions, and the condensation of divalent salt cations onto the polyelectrolyte increases, and the chains favor to collapse. The condensation of ions changes with the salt concentration and depends on the charged fraction. Also, the degree of collapse at a given salt concentration changes with the increasing valency of the counterion due to the bridging effect. As a quantitative measure of the distribution of counterions around the polyelectrolyte chain, we study the radial distribution function between monomers on different polyelectrolytes and the counterions inside the counterion worm surrounding a polymer chain at different concentrations of the divalent salt. Our simulation results show a strong dependence of salt concentration on the conformational properties of diblock copolymers and indicate that it can tune the self-assembly behaviors of such charged polyelectrolyte block copolymers.     

Competitive binding of Na<Superscript>+</Superscript> and Ca<Superscript>2+</Superscript> ions to teichoic acid analogues

The competitive binding of monovalent and divalent counterions to poly(alkylene phosphate) related to bacterial teichoic acids and poly(styrenesulfonate) was studied experimentally by potentiometry with ion-selective electrodes. The binding of calcium ions and the release of sodium ions accompanying calcium ions binding in aqueous solutions of the polyelectrolytes was analysed and the mean exchange ratio Na⁺/Ca²⁺ was estimated. It was found that in the process of addition of calcium ions to sodium poly(alkylene phosphate) and sodium poly(styrenesulfonate) solutions all the Ca²⁺ ions added are bound to polyions and the initially condensed Na⁺ ions are released proportionally to the concentration of the added Ca²⁺ ions up to the critical concentration of the Ca²⁺ ions added. For a molar concentration ratio of calcium counterions to charged groups on the polyion up to 0.20 the exchange ratio was approximately equal to 1 or 2 for the sodium poly(alkylene phosphate)/CaCl₂ and sodium poly(styrenesulfonate)/CaCl₂ systems, respectively.     

Effect of the steric accessibility of the exchange site in long-chain quaternary ammonium salts on the anion-exchange extraction of divalent ions

The constants of anion-exchange extraction of divalent ions by quaternary ammonium salts of various structures were determined. The exchange constants depend significantly on steric accessibility of the exchange site. For the exchange of small-size anions, the affinity of the ion exchanger for divalent ions is higher than for monovalent ions. For large divalent anions, the exchange constant may increase or decrease, depending on the size of a monovalent anion. The obtained results are explained by the specifics of the ion-pair association of monovalent and divalent anions with quaternary ammonium cations.     

Theory of competitive counterion adsorption on flexible polyelectrolytes: divalent salts

The counterion distribution around an isolated flexible polyelectrolyte in the presence of a divalent salt is evaluated using the adsorption model [M. Muthukumar, J. Chem. Phys. 120, 9343 (2004)] that considers the Bjerrum length, salt concentration, and local dielectric heterogeneity as physical variables in the system. Self-consistent calculations of effective charge and size of the polymer show that divalent counterions replace condensed monovalent counterions in competitive adsorption. The theory further predicts that at modest physical conditions for a flexible polyelectrolytes such as sodium polystyrene sulfonate in aqueous solutions polymer charge is compensated and reversed with increasing divalent salt. Consequently, the polyelectrolyte shrinks and reswells. Lower temperatures and higher degrees of dielectric heterogeneity between chain backbone and solvent enhance condensation of all species of ions. Complete diagrams of states for the effective charge calculated as functions of the Coulomb strength and salt concentration suggest that (a) overcharging requires a minimum Coulomb strength and (b) progressively higher presence of salt recharges the polymer due to either electrostatic screening (for low Coulomb strengths) or coion condensation (for high Coulomb strengths). Consideration of ion-bridging by divalent counterions leads to a first-order collapse of polyelectrolytes in modest presence of divalent salts and at higher Coulomb strengths. The authors' theoretical predictions are in agreement with the generic results from experiments and simulations.     

Competition between Monovalent and Divalent Counterions in Surfactant Systems

Competition between mono- and divalent ions in the association of counterions to the headgroups of amphiphiles was studied in one surfactant system with organic counterions (piperidine⁺/piperazine²⁺octanesulfonate) and one with inorganic counterions (Na⁺/Ca²⁺octyl sulfate). By conductivity and¹³C NMR chemical shift measurements the critical micelle concentration (CMC) was found to decrease drastically when small amounts of divalent counterions were present in the system. Self-diffusion coefficients of surfactant ions and organic counterions were measured in the micellar phase by the Fourier transform pulsed-gradient spin-echo (FT-PGSE) NMR method. The degree of counterion binding in the micellar system with piperidine⁺/piperazine²⁺counterions was obtained from FT-PGSE NMR measurements. It was observed that the divalent counterions were more strongly bound than the monovalent counterions. The experimental results were compared with theoretical Poisson–Boltzmann calculations. The cell model was used to study the electrostatic effects. Good agreement between electrostatic theory and experiment was observed; however, an attractive force exists between the monovalent piperidine counterions and the micelle, probably because of hydrophobic interactions.     

Influence of the diffuse layer overcharging or undercharging on the stability of charged interfaces: a restricted grand canonical Monte Carlo study

We have applied a restricted grand canonical Monte Carlo procedure to describe, in the framework of the primitive model, the counterion exchange mechanism between diffuse layers of counterions surrounding segregated charged lamellae. The net charge transfer between the dense and dilute domains is shown to vary as a function of the valence of the neutralizing counterions: undercharging of the dense interlayer is detected in the presence of monovalent counterions and overcharging with divalent counterions. Furthermore, no net reduction of the swelling pressure is detected for monovalent counterions, while a large enhancement of the net interlamellar attraction is found for charged lamellae neutralized by divalent counterions.     

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.     

P-mSA/mCS双极膜的制备及其在一价、二价离子分离中的应用

以五氧化二磷、磷酸三乙酯和磷酸为反应剂, 制备了磷酸化海藻酸钠(P-SA), 经二茂铁离子改性后作为阳膜层(P-mSA); 用乙酰基二茂铁改性壳聚糖制备了阴膜溶胶(mCS). 将阴膜溶胶流延于阳膜层上, 制备了P-二茂铁-SA/乙酰基二茂铁-CS双极膜(P-mSA/mCS BPM). 测定了双极膜的红外光谱、接触角、电荷密度、离子交换容量与交流阻抗. IR与接触角的分析结果表明, SA经磷酸化后, 亲水性能得到了显著提高. 将P-mSA/mCS BPM应用于一价、二价离子的分离, 当压力差为0.3 MPa时, 二价离子的截留率(双极膜截留的离子百分数)为95%, 一价离子的截留率为22%左右.     

Ion condensation in a polyelectrolyte gel

Anomalous small angle X-ray scattering is used to determine the distribution of divalent ions in a neutralized polyelectrolyte gel of sodium polyacrylate in the vicinity of the volume transition. At the five different energies of the incident beam used to vary the contrast, the scattering curves have similar shapes, and are separated only by constant multiplying factors. This result, in conjunction with SANS results from the same sample, indicates that the divalent ion (strontium) is confined on the polymer backbone.     

Influence of various monovalent cations and calcium ion on the colloidal fouling potential

The influence of various monovalent cations and of divalent calcium ions on colloidal fouling strength was investigated quantitatively on a bench-scale ultrafiltration device. A higher colloidal fouling potential (k) was consistently observed with lithium chloride compared to the same ionic strengths of chlorides of other monovalent cations (Na+, K+, and Cs+). This observation was attributed to the formation of an impervious layer around the colloidal particle by lithium ions that prevented the repulsive forces due to the interaction of the silica hairs formed on the particles in the presence of water. The impact of the divalent calcium ion on the fouling potential was more complex. The fouling potential first increased with calcium ion concentration and then decreased. The maximum value of fouling potential occurred at the ionic strength corresponding to the critical coagulation concentration, which decreased with increasing colloid concentration. The colloidal fouling potential was well correlated by a bilinear relationship with colloid concentration and ionic strength for all salts tested under the critical coagulation concentration.     

Light,Small Angle Neutron and X-Ray Scattering from Gels

This paper gives two examples of experiments that demonstrate the power of small angle scattering techniques in the study of swollen polymer networks. First, it is shown how the partly ergodic character of these systems is directly detected by neutron spin echo experiments. The observed total field correlation function of the intensity scattered from a neutral gel allows the ergodic contribution to be directly distinguished from the non ergodic part, at values of transfer wave vector q that lie well beyond the range of dynamic light scattering. The results can be compared with those obtained at much lower q from visible light scattering. Second, a recent application of small angle X-ray (SAXS) and neutron (SANS) scattering is described for a polyelectrolyte molecule, DNA, in semi-dilute solutions under near-physiological conditions. For these observations, the divalent ion normally present, calcium, is replaced by an equivalent ion, strontium. The comparison between SANS and SAXS yields a quantitative picture of the cloud of divalent counter-ions around the central DNA core. At physiological conditions, the cloud is thinner than that predicted on the basis of the Debye screening length but thicker than if the counter-ions were condensed on the DNA chain.     

Nuclear magnetic relaxation of 23Na in polyelectrolytes with mono/divalent ion clouds

The nuclear magnetic relaxation rate of ²³Na ions in polyelectrolyte solutions containing both monovalent and divalent counter-ions is investigated to obtain information on the nature of the divalent ion/poly-ion interaction.     

Correlation of counterions with rodlike macroions as assessed by anomalous small-angle X-ray scattering

We consider the analysis of a rodlike synthetic polyelectrolyte in solution by anomalous small-angle X-ray scattering (ASAXS) in order to elucidate the correlation of the counterions with the highly charged macroion. ASAXS can be applied to these systems because the absorption edge of typical counterions, for example, bromine or iodine ions can be attained by synchrotron radiation. Model calculations using the Poisson–Boltzmann cell model show that ASAXS furnishes two terms caused by the anomalous dispersion of the counterions. The leading terms is a cross-term between the ordinary scattering amplitude of the polyelectrolyte and the real part of the scattering length f ′ of the counterions. A second term refers solely to the anomalous contribution of the counterions, i.e., to f ′ and f ′′ ( f ′′: imaginary part of scattering length). Preliminary data obtained from rodlike synthetic macroions having iodine counterions corroborate the theoretical deductions. They demonstrate that ASAXS is capable of furnishing information that is not available by the ordinary SAXS experiment. Received: 11 December 2000/Accepted: 22 February 2001     

Explicit water molecular dynamics study of the mobility of halide ions in presence of ionene oligocations

We present explicit water molecular dynamics simulations of solutions of aliphatic 3,3- and 6,6-ionene oligocations neutralized with (i) fluoride, chloride, bromide, or iodide counterions, respectively, or (ii) with a 1:1 mixture of chloride and bromide anions in presence of a low molecular weight salt at 298 K. The SPC/E model was used to describe water molecules. Results of the simulation are presented in form of the pair distribution functions between various atoms on the ionene oligoion and counterions in solution. In addition, we were interested in the dynamics of counterions around model ionenes. We showed that counterions residing in the vicinity of the oligoion exchange rapidly with those in the bulk solution, with the frequency depending on the nature of the counterion and on the charge density of the oligoion. We calculated the average residence times of the various counterion species to the oligoions and proposed the model which divides the counterions into "free" and "bound" and calculated the fraction of "free" counterions. In the second part of the study, we investigated interaction of the sodium chloride and sodium bromide, being simultaneously present in the solution, with differently charged ionenes in water. The selectivity effect was clearly observed: bromide ions tend to replace chloride ions in the immediate vicinity of the ionene oligoions. Simulation results are discussed in light of our recent measurements of thermodynamic and transport properties of aqueous ionene solutions.     

Anionic polyelectrolyte adsorption on mica mediated by multivalent cations: a solution to DNA imaging by atomic force microscopy under high ionic strengths

Adsorption of DNA molecules on mica, a highly negatively charged surface, mediated by divalent or trivalent cations is considered. By analyzing atomic force microscope (AFM) images of DNA molecules adsorbed on mica, phase diagrams of DNA molecules interacting with a mica surface are established in terms of concentrations of monovalent salt (NaCl) and divalent (MgCl2) or multivalent (spermidine, cobalt hexamine) salts. These diagrams show two transitions between nonadsorption and adsorption. The first one arises when the concentration of multivalent counterions is larger than a limit value, which is not sensitive to the monovalent salt concentration. The second transition is due to the binding competition between monovalent and multivalent counterions. In addition, we develop a model of polyelectrolyte adsorption on like-charged surfaces with multivalent counterions. This model shows that the correlations of the multivalent counterions at the interface between DNA and mica play a critical role. Furthermore, it appears that DNA adsorption takes place when the energy gain in counterion correlations overcomes an energy barrier. This barrier is induced by the entropy loss in confining DNA in a thin adsorbed layer, the entropy loss in the interpenetration of the clouds of mica and DNA counterions, and the electrostatic repulsion between DNA and mica. The analysis of the experimental results provides an estimation of this energy barrier. We then discuss some important issues, including DNA adsorption under physiological conditions.     

纳滤膜对电解质溶液分离特性的理论研究(II): 混合电解质溶液

假定纳滤膜具有狭缝状孔, 使用纯水透过系数、膜孔径及膜表面电势来表征纳滤膜的分离特征, 用流体力学半径和无限稀释扩散系数表征了离子特性. 采用扩展Nernst-Planck方程、Donnan平衡模型和Poisson-Boltzmann理论描述了混合电解质溶液中离子在膜孔内的传递现象, 计算了三种商用纳滤膜(ESNA1-LF, ESNA1和LES90)对同阴离子、同阳离子和含四种离子的混合电解质体系中离子的截留率, 并与实验数据进行了比较. 计算结果表明, 电解质溶液中离子在纳滤膜孔内传递的主要机理是离子的扩散和电迁移, 纳滤膜对混合电解质溶液中离子的分离效果主要由空间位阻和静电效应决定. 该模型在低浓度时对含一价离子的混合电解质溶液通过纳滤膜的截留率计算结果比较准确, 但对高浓度或含高价离子的混合电解质溶液则偏差较大.     

Counterion Exchange Selectivity in Detergent–Polymer Aggregates

In aqueous solution, the interaction between sodium dodecyl sulfate (SDS) and poly(ethylene glycol) (PEG) results in the formation of small aggregates or clusters of SDS attached to the PEG polymer chain. Selectivity coefficients for exchange of two monovalent (N-methyl-4-cyanopyridinium cation and Tl⁺) and two divalent (methylviologen cation and Cu²⁺) counterions at the surface of SDS–PEG clusters, determined employing photophysical techniques, are similar, but not identical, to those for exchange at the surface of SDS micelles in the absence of PEG. The principal factor affecting ion exchange selectivity in SDS–PEG clusters does not appear to be aggregate size or surface charge density but rather the presence of poly(oxyethylene) subunits at the aggregate surface.