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.     

Bipolar reverse osmosis membrane for separating mono-and divalent ions

Bipolar reverse osmosis membranes that have both negatively and positively charged layers have been prepared to enhance the selectivity towards mono- and divalent ions in respect of both cations and anions. Positively charged layers are formed on low pressure reverse osmosis membranes having negative charge (NTR-7410 and 7450) by an adsorption method using polyethyleneimine (PEI) or a quaternary ammonium polyelectrolyte (QAP). These layers attach to the membrane's dense layer, which is made of sulfonated polyether sulfone. The selectivity of mono- and divalent ions is proven by experimental results for single electrolytes (NaCl, Na₂SO₄ and MgCl₂). Although negatively charged membranes repulse divalent anions more strongly than cations and monovalent anions, bipolar reverse osmosis membranes reject both divalent cations and divalent anions better than monovalent ions. An optimal preparation method for bipolar membranes showing selectivity towards mono- and divalent ions were developed. The bipolar membranes showed good ion selectivity for artificial sea water.     

Monte Carlo simulations of the hydrophobic effect in aqueous electrolyte solutions

The hydrophobic interaction between two methane molecules in salt-free and high salt-containing aqueous solutions and the structure in such solutions have been investigated using an atomistic model solved by Monte Carlo simulations. Monovalent salt representing NaCl and divalent salt with the same nonelectrostatic properties as the monovalent salt have been used to examine the influence of the valence of the salt species. In salt-free solution the effective interaction between the two methane molecules displayed a global minimum at close contact of the two methane molecules and a solvent-separated secondary minimum. In 3 and 5 M monovalent salt solution the potential of mean force became slightly more attractive, and in a 3 M divalent salt solution the attraction became considerably stronger. The structure of the aqueous solutions was determined by radial distribution functions and angular probability functions. The distortion of the native water structure increased with ion valence. The increase of the hydrophobic attraction was associated with (i) a breakdown of the tetrahedral structure formed by neighboring water molecules and of the hydrogen bonds between them and (i) the concomitant increase of the solution density.     

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.     

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.     

Monte Carlo simulations of a polyelectrolyte chain with added salt: effect of temperature and salt valence

Using the cooperative motion algorithm, the effect of salt valence z(s) and of the reduced temperature T* on a single polyelectrolyte chain as well as on counterions and salt ions themselves is studied. The calculations show that both parameters strongly influence the polymer, causing it to undergo conformational changes. For a given number of the added salt cations (anions) n(s) and temperature T*, the chain takes more and more compact forms as z(s) increases (z(s) > 0). For fixed z(s), in turn, the polymer size reduces sharply as T* drops down from intermediate to low. For high T* configurational the entropy dominates the chain statistics and the mean-square radius of gyration (s2)1/2(T*,n(s),z(s)) approaches its athermal value. The low-temperature polymer collapse is also accompanied by a drop in the effective mean charge per monomer q*(T*,n(s),z(s)) (condensation of ions onto the chain) and the total inner energy e*(T*,n(s),z(s)). Furthermore, the local structure of the system is analyzed by means of pair-correlation functions g(ab)(r,T*,n(s),z(s)). At lower T* they possess sharp local maxima at small interparticle distances r that disappear as T* grows. The former observation indicates that at lower T* the ions tend to group themselves close to each other. In particular, it is concluded that the condensation is dominated by the multivalent salt ions carrying charges of opposite sign to that of monomers.     

Lattice Monte Carlo simulations of a charged polymer chain: effect of valence and concentration of the added salt

The configurational properties of a single polyelectrolyte chain accompanied by counterions and added salt are simulated using the cooperative motion algorithm on the face-centered cubic lattice. In particular, a greater emphasis is put on the effect of valence z(s) and concentration of the added positive (negative) salt ions n(s) on the polymer behavior. This is achieved by inspecting two families of systems with widely varying numbers n(s) of monovalent (z(s)=1) or multivalent (z(s)=4) salt ions at two fixed reduced temperatures T*=0.5, 1. The calculations indicate that especially at the lower temperature the addition of some amount of multivalent salt has a tremendous impact on chain conformations compared to the situation with monovalent salt. Even for relatively low concentrations of the former, the mean radius of gyration (1/2) and the mean end-to-end distance (1/2) decrease sharply, i.e., the polymer exists in strongly collapsed forms. This reduction of polymer size is also accompanied by a drop in the system inner energy e* and the effective mean charge per monomer q*. The analysis of various pair-correlation functions g(ab)(r) indicates that the latter effect-caused by condensation of ions onto the chain-is dominated by the multivalent ones. Furthermore, it is found that for z(s)=4, the uncondensed salt ions tend to group themselves into small clusters.     

Influence of divalent ions on composition and viscoelasticity of polyelectrolyte complexes

The addition of monovalent salts to polyelectrolyte complexes (PECs) comprising oppositely charged polyelectrolytes results in diminishing propensity for complexation, leading to complexes with higher water contents and lower moduli. However, the corresponding influence of multivalent ions on polyelectrolyte complexation has not yet been explored beyond enhanced screening effects. Here, we elucidate the significant impact of the valency of the salt cation on the composition, ion partitioning, and viscoelasticity of charge-matched PECs comprising sodium salt of poly(acrylic acid) and poly(allylamine hydrochloride). Notably, preferential partitioning of divalent cations (Ca²⁺ and Sr²⁺) into the complexes is observed, in stark contrast to the depletion of monovalent ions (Na⁺) from the complexes. Concomitantly, electrostatic bridging of polyanion chains by divalent ions is found to hinder their relaxation, manifesting as a non-monotonic evolution of the shear moduli of the complexes with increasing divalent salt concentrations. Relatedly, a failure of time-salt and time-ionic strength superposition approaches in presence of divalent ions is demonstrated, highlighting the nontrivial influence of these ions on chain relaxation behavior.     

Influence of ion size on the stability of chloroplumbates containing PbCl<Stack><Subscript>5</Subscript><Superscript>−</Superscript></Stack> or PbCl<Stack><Subscript>6</Subscript><Superscript>2−</Superscript></Stack>

The enthalpies of formation of PbCl₄, PbCl₅⁻ and PbCl₆²⁻, originating from quantum mechanics, have enabled the thermodynamic behaviour of these ions with respect to Cl-detachment to be assessed. The stability of salts containing PbCl₅⁻ and PbCl₆²⁻ as a function of the dimensions of these anions and complementary cations was studied using an approach combining the Kapustinskii-Yatsimirskii equation with basic thermochemical relationships. It was found that hexachloroplumbates of monovalent metal cations will not dissociate into metal chlorides and PbCl₄, provided the complementary cations are suitably large in size. Hexachloroplumbates of divalent metal cations have not yet been synthesised since no known metal cations attain the requisite large size. Such salts will not dissociate if the divalent metal cations are able to complex suitably large electron-donating ligands. The pentachloroplumbates of both monovalent and divalent metal cations are unstable, since no known metal cations have appropriately large ionic radii. The approach adopted appears to be useful for the examination of the thermal behaviour, stability and reactivity of chloroplumbates.     

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.     

Monte Carlo simulations of charged dendrimer-linear polyelectrolyte complexes and explicit counterions

We study complexes composed of one dendrimer of generation G = 4 (G4 dendrimer) with N(t) = 32 charged terminal groups and an oppositely charged linear polyelectrolyte accompanied by neutralizing counterions in an athermal solvent using Monte Carlo simulations based on the bond fluctuation model. In our study both the full Coulomb potential and the excluded volume interactions are taken into account explicitly with the reduced temperature τ and the chain length N(ch) as the main simulation parameters. Our calculations indicate that there exist three temperature ranges that determine the behavior of such complexes. At τ(complex) stable charged dendrimer-linear polyelectrolyte complexes are formed first, which are subsequently accompanied by selective counterion localization within the complex interior at τ(loc) ≤ τ(complex), and counterion condensation as temperature is further decreased below τ(cond) < τ(loc). In particular, we observe that condensation takes place exclusively on the excess charges in the complex and thus no condensation is observed at the compensation point (N(ch) = N(t)), irrespective of τ. For N(ch) ≠ N(t) the complex is overally charged. Furthermore, we discuss the size and structure of the dendrimer and the linear polyelectrolyte within the complex, as well as spatial distributions of monomers and counterions. Conformations of the chain in the bound state are analysed in terms of loops, trains, and tails.     

Interaction study of a lysozyme‐binding aptamer with mono‐ and divalent cations by ACE

Binding between an aptamer and its target is highly dependent on the conformation of the aptamer molecule, this latter seeming to be affected by a variety of cations. As only a few studies have reported on the interactions of monovalent or divalent cations with aptamers, we describe herein the use of ACE in its mobility shift format for investigating interactions between various monovalent (Na⁺, K⁺, Cs⁺) or divalent (Mg²⁺, Ca²⁺, Ba²⁺) cations and a 30‐mer lysozyme‐binding aptamer. This study was performed in BGEs of different natures (phosphate and MOPS buffers) and ionic strengths. First, the effective charges of the aptamer in 30 mM ionic strength phosphate and MOPS (pH 7.0) were estimated to be 7.4 and 3.6, respectively. Then, corrections for ionic strength and counterion condensation effects were performed for all studies. The effective mobility shift was attributed not only to these effects, but also to a possible interaction with the buffer components (binary or ternary complexes) as well as possible conformational changes of the aptamer. Finally, apparent binding constants were calculated for divalent cations with mathematical linearization methods, and the influence of the nature of the BGE was evidenced.     

Explicit ions condensation around strongly charged polyelectrolytes and spherical macroions: the influence of salt concentration and chain linear charge density. Monte Carlo simulations

The condensation of monovalent counterions and trivalent salt particles around strong rigid and flexible polyelectrolyte chains as well as spherical macroions is investigated by Monte Carlo simulations. The results are compared with the condensation theory proposed by Manning. Considering flexible polyelectrolyte chains, the presence of trivalent salt is found to play an important role by promoting chain collapse. The attraction of counterions and salt particles near the polyelectrolyte chains is found to be strongly dependent on the chain linear charge density with a more important condensation at high values. When trivalent salt is added in a solution containing monovalent salt, the trivalent cations progressively replace the monovalent counterions. Ion condensation around flexible chains is also found to be more efficient compared with rigid rods due to monomer rearrangement around counterions and salt cations. In the case of spherical macroions, it is found that a fraction of their bare charge is neutralized by counterions and salt cations. The decrease of the Debye length, and thus the increase of salt concentration, promotes the attraction of counterions and salt particles at the macroion surface. Excluded volume effects are also found to significantly influence the condensation process, which is found to be more important by decreasing the ion size.     

A Two Phase Model for the Binding of Cations To Long-Chain Polyphosphate Anions

Abstract

Binding of uni- and divalent cations to long-chain polyphosphate anions was investigated in the presence of excess uni-univalent salt. It was concluded that the binding occurs mainly in a “territorial binding” mode, i.e., most of the bound cations move freely within a specified volume around the polymer. Intrinsic complex formation (site binding) should be expressed as an equilibrium in the polymer phase.     

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.     

HYDROPHOBIZING EFFECT OF CATIONS ON ACIDIC PHOSPHOLIPID MEMBRANES

By means of contact angle measurements with water and aqueous salt solutions, it is shown that plurivalent cations increase the hydrophobicity of negatively charged phospholipid vesicle membranes (consisting of phosphatidic acid, PA, or of phosphatidylserine, PS), but does not influence the hydrophobicity of neutral phospholipid membranes, (e.g., phosphatidylcholine, PC, at up to 200 mM of CaCl₂). The hydrophobizing action of cations on PA and PS membranes is concomitant with the reduction in (negative) zeta potential with increasing cation concentrations. Trivalent cations, La³⁺, showed more effective in hydrophobizing negatively charged phospholipid membranes than divalent and monovalent cations. Except for hydrogen ions, monovalent cations do not show any appreciable hydrophobizing effect on lipid vesicle membranes at concentrations less than 1 M. The hydrophobizing effect on phospholipid membranes can also be used to explain the induction of lateral phase separation into patches of different phospholipids as well as cell fusion.     

The non-selective voltage-activated cation channel in the human red blood cell membrane: reconciliation between two conflicting reports and further characterisation

Using the patch-clamp technique, the non-selective, voltage-activated cation channel in the human red blood cell (RBC) membrane was further characterised. Activity of the cation channel could be demonstrated at a range of salt concentrations with the current-voltage characteristics for monovalent cations going from linear to superlinear functions, depending on the cation concentration in the range of 100-500 mM. The non-selective voltage-activated cation channel was demonstrated to be permeable to the divalent cations Ca2+ and Ba2+, and even Mg2+. The current-voltage relations for the divalent cations were superlinear even at 75 mM salt concentration, but indicated outward rectification in contrast to the I-V curve for monovalent cations. The degree of activation at a given membrane potential depended strongly on the prehistory of the channel. The gating exhibited hysteretic-like behaviour, since the quasi steady-state deactivation and activation curves were displaced by approximately 25 mV. This result fully explains apparent discrepancies between V0.5-values previously obtained by slightly different experimental protocols. The possible physiological/pathophysiological role of the channel is discussed in the context of the demonstrated permeability for divalent cations.     

Colloidal metal dispersions and metal complexes in hydrocarbons

Stable dispersions of colloidal metals in hydrocarbons have been prepared by a novel phase-transfer method. The metals were gold, silver, palladium and ruthenium; the hydrocarbons were n-hexane, cyclohexane and benzene. The phase transfer of colloidal metal particles from an aqueous phase to a hydrocarbon phase was achieved by adding salt to the emulsion of hydrocarbon in the aqueous suspension of metal with sodium oleate. The salts were sodium chloride, magnesium chloride, sodium sulfate, etc. The size distributions of the metal particles in the resulting hydrocarbon suspensions were almost the same as that of the original aqueous suspension. The dispersions of colloidal metals in hydrocarbons were stable for a long period of time without the addition of hydrocarbon-soluble stabilizer. The critical phase-transfer concentrations of various salts were determined. The phase-transfer powers of cations were larger than those of anions. Those of divalent and trivalent cations were exceedingly larger than that of the monovalent cation. The concentration of colloidal metal dispersed in hydrocarbon was achieved by using the phase-transfer method.     

Detection of metal ions using ion-channel sensor based on self-assembled monolayer of thioctic acid

Gold electrodes were chemically modified with thioctic acid monolayer designed to mimic biological ion-channel membranes. The technique was then used in the determination of alkali, alkaline earth, thallium(I), and lanthanum metal cations as analytes. Cyclic voltammograms (CV) of [Fe(CN)6]³⁻ an electroactive marker, were measured in the presence of the various types of analyte cations. In the absence of the analyte cation, electrostatic repulsion between the marker anions and the carboxylate groups of the receptor monolayer hindered the approach of the marker anion to the electrode surface and hence hindered its reduction. The modified electrodes responded well to the metal cations except the alkali metal cations. The sensors could detect the trivalent cation La³⁺ at concentrations as low as 10⁻⁸ M. The response of the sensor to the metal cations increase in the order alkali metal3+ can be discriminated in the ratio 1:100. This makes it possible to determine the trivalent ion in a sample matrix containing monovalent and divalent cations. Thallium(I) ion showed marked deviation in its response as compared to monovalent ions of the alkali metals. The ion-channel sensor based on self-assembled monolayer of thioctic acid therefore offers a potential alternative technique for the selective determination of metal ions.     

Salt‐induced formation of DNA double helices from single stranded DNA investigated by analytical ultracentrifugation

The effect of monovalent and divalent cations on the ssDNA to dsDNA transformation was systematically examined. For salts containing monovalent cations (LiCl, NaC1, KCl, CsCl), the conversion of ssDNA to dsDNA increased with ionic strength up to a value of I = 0.01 M and then plateaued, confirming that all four of the monovalent cations behaved similarly and promoted the formation of dsDNA. The monovalent cation type influenced the equilibrium constant for the conversion of ssDNA to dsDNA, indicating a degree of ion‐specificity in dsDNA formation. In the case of salts containing divalent cations (e.g., MgCl₂), the conversion of ssDNA to dsDNA also increased with increasing ionic strength, though the plateau region was reached at a much lower ionic strength (I = 5.0 × 10⁻⁴ M), which can be attributed to the higher electrostatic screening efficiency of Mg²⁺ cations and thus their superior ability to link DNA chains. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 501–508