Monovalent Counterions Research Articles

Counterion and pH‐Mediated Structural Changes in Charged Biopolymer Gels

DNA solutions and gels exhibit a wide range of phenomena, many of which have not yet been fully understood. In the presence of multivalent counterions, attraction between charged DNA strands occurs. Increasing the concentration of multivalent ions leads to a decrease of the osmotic pressure, and a sufficiently high ion concentration results in the precipitation of the polymer. Replacing the monovalent counterions by hydrogen ions (decreasing the pH) also produces a marked decrease of the osmotic pressure, and at low pH a phase transition takes place. In this paper we analyze osmotic swelling pressure measurements and small-angle neutron scattering (SANS) measurements made on chemically cross-linked DNA gels swollen in near physiological salt solutions. The effect of calcium ions is compared with that of decreasing the pH of the equilibrium salt solution. We demonstrate that both the concentration dependence of the osmotic pressure and the SANS response of DNA gels display significant differences in the two cases.

Selective Monovalent Cation Association and Exchange around Keplerate Polyoxometalate Macroanions in Dilute Aqueous Solutions

The interaction between water-soluble Keplerate polyoxometalate {Mo(72)Fe(30)} macroions and small countercations is explored by laser light scattering, anomalous small-angle X-ray scattering (ASAXS), and isothermal titration calorimetry (ITC) techniques. The macroions are found to be able to select the type of associated counterions based upon the counterions' valence state and hydrated size, when multiple types of additional cations are present in solution (even among different monovalent cations). The preference goes to the cations with higher valences or smaller hydrated sizes if the valences are identical. This counterion exchange process changes the magnitude of the macroion-counterion interaction and, thus, is reflected in the dimension of the self-assembled {Mo(72)Fe(30)} blackberry supramolecular structures. The hydrophilic macroions exhibit a competitive recognition of various monovalent counterions in dilute solutions. A critical salt concentration (CSC) for each type of cation exists for the blackberry formation of {Mo(72)Fe(30)} macroions, above which the blackberry size increases significantly with the increasing total ionic strength in solution. The CSC values are much smaller for cations with higher valences and also decrease with the cations' hydrated size for various monovalent cations. The change of blackberry size corresponding to the change of ionic strength in solution is reversible.

Membrane filtration of fullerene nanoparticle suspensions: Effects of derivatization, pressure, electrolyte species and concentration

Particle aggregation is induced in derivatized fullerene (fullerol) suspensions by introducing different counter-ion species (Na + Ca 2+ and Mg 2+) and concentrations. The suspensions are filtered through 20 nm ceramic membranes under different transmembrane pressures, and the removal efficiency is compared. In all cases, the average hydrodynamic radius far exceeded the average pore diameter of the membrane. In the case of mono-valent counter-ions, removal efficiency is influenced by transmembrane pressure, with higher removal efficiencies achieved at lower pressures. In contrast, removal efficiencies of fullerol suspensions destabilized with di-valent ions are insensitive to transmembrane pressure, similar to what was found in the case of non-derivatized fullerene. Scanning Electron Microscope (SEM) images of post-filtration membranes indicate that fullerol aggregates destabilized with Mg 2+ ions deform and partially penetrate the membrane, but are ultimately trapped. The proposed mechanism suggests that di-valent ions act as bridges between fullerol aggregates, forming strong bonds that were not broken under the experimental conditions. These strong bonds may allow aggregated fullerol particles to deform under high pressure, and partially penetrate the membrane. Mono-valent ions are incapable of functioning as bridges, and subsequently, when sufficient pressure is applied, fullerol aggregates will break apart and pass through the membrane.

Estimating vertical and lateral pressures in periodically structured montmorillonite clay particles

Given a montmorillonitic clay soil at high porosity and saturated by monovalent counterions, we investigate the particle level responses of the clay to different external loadings. As analytical solutions are not possible for complex arrangements of particles, we employ computational micromechanical models (based on the solution of the Poisson-Nernst-Planck equations) using the finite element method, to estimate counterion and electrical potential distributions for particles at various angles and distances from one another. We then calculate the disjoining pressures using the Van't Hoff relation and Maxwell stress tensor. As the distance between the clay particles decreases and double-layers overlap, the concentration of counterions in the micropores among clay particles increases. This increase lowers the chemical potential of the pore fluid and creates a chemical potential gradient in the solvent that generates the socalled 'disjoining' or 'osmotic' pressure. Because of this disjoining pressure, particles do not need to contact one another in order to carry an 'effective stress'. This work may lead towards theoretical predictions of the macroscopic load deformation response of montmorillonitic soils based on micromechanical modelling of particles.

Two Types of Block Copolymer Micelles with Ion-Containing Cores

We report a combined experimental and theoretical study of micellization of block copolymer with hydrophilic nonionic corona-forming blocks and weak polyelectrolyte (wPE) core-forming blocks with pH-triggered solubility in aqueous solutions. We demonstrate that in addition to micelles with neutral cores, there exist two other types of micelles with PE- or ionomer-like cores, in which monovalent counterions are released or condensed on core wPE block, respectively. The transition between the two types of micelles occurred upon changes in ionization of the PE core block and resulted in nonmonotonous changes of aggregation number as a function of pH. Such micelles with stimulus responsive cores represent promising nanocarriers for controlled delivery applications.

Effect of chain stiffness on ion distributions around a polyelectrolyte in multivalent salt solutions

Ion distributions in dilute polyelectrolyte solutions are studied by means of Langevin dynamics simulations. We show that the distributions depend on the conformation of a chain while the conformation is determined by the chain stiffness and the salt concentration. We observe that the monovalent counterions originally condensed on a chain can be replaced by the multivalent ones dissociated from the added salt due to strong electrostatic interaction. These newly condensed ions give an important impact on the chain structure. At low and at high salt concentrations, the conformation of a semiflexible chain is rodlike. The ion distributions show similarity to those for a rigid chain, but difference to those for a flexible chain whose conformation is a coil. In the midsalt region, the flexible chain and the semiflexible chain collapse but the collapsed chain structures are, respectively, disordered and ordered structures. The ion distributions, hence, show different profiles for this three chain stiffness with the curves for the semiflexible chain lying between those for the flexible and the rigid chains. The number of the condensed multivalent counterions, as well as the effective chain charge, also shows similar behavior, demonstrating a direct connection with the chain morphology. Moreover, we find that the condensed multivalent counterions form triplets with two adjacent monomers and are localized on the chain axis at intermediate salt concentration when the chain stiffness is semiflexible or rigid. The microscopic information obtained here provides a valuable insight to the phenomena of DNA condensation and is very useful for researchers to develop new models.

Conformational behaviors of a charged-neutral star micelle in salt-free solution

The conformational behaviors of charged brushes on a micelle self-assembled by charged-neutral diblock copolymers in salt-free solution are extensively analyzed using a coarse-grained dissipative particle dynamic (DPD) simulation. When only monovalent counterions exist, the brush conformation of the corona in the micelle is exactly consistent with the predictions from the blob-scaling theory based on the spherical polyelectrolyte brush model, which differentiates the system into three distinct regimes: (I) quasi-neutral regime, (II) "Pincus" regime, and (III) osmotic regime. For multivalent counterions such as divalence and trivalence, however, the strong electrostatic correlations lead the micelle structures to deviate obviously from those of scaling predictions. The collapse of the brush appears to be due to the drop in the osmotic pressure inside the corona region of the micelle.

A Molecular Dynamics Study of Two Apposing Polyelectrolyte Brushes with Mono‐ and Multivalent Counterions

AbstractThe conformational characteristics of polyelectrolytes end‐grafted on two apposing walls are studied. The monovalent and multivalent counterions are explicitly treated. It is found that the polyelectrolyte brushes undergo a collapse transition in the presence of multivalent counterions at large wall separations. Moreover, the brush thickness is linearly proportional to the grafting density and independent of the counterion valence. The effects of normal compression on the density profiles of monomers and counterions, the pressure, the net charge density and the degree of interpenetration are also studied. The density profiles of counterions exhibit an asymmetrical distribution in systems with a mixture of monovalent and trivalent counterions.magnified image

Ion distributions, exclusion coefficients, and separation factors of electrolytes in a charged cylindrical nanopore: A partially perturbative density functional theory study

The structural and thermodynamic properties for charge symmetric and asymmetric electrolytes as well as mixed electrolyte system inside a charged cylindrical nanopore are investigated using a partially perturbative density functional theory. The electrolytes are treated in the restricted primitive model and the internal surface of the cylindrical nanopore is considered to have a uniform charge density. The proposed theory is directly applicable to the arbitrary mixed electrolyte solution containing ions with the equal diameter and different valences. Large amount of simulation data for ion density distributions, separation factors, and exclusion coefficients are used to determine the range of validity of the partially perturbative density functional theory for monovalent and multivalent counterion systems. The proposed theory is found to be in good agreement with the simulations for both mono- and multivalent counterion systems. In contrast, the classical Poisson-Boltzmann equation only provides reasonable descriptions of monovalent counterion system at low bulk density, and is qualitatively and quantitatively wrong in the prediction for the multivalent counterion systems due to its neglect of the strong interionic correlations in these systems. The proposed density functional theory has also been applied to an electrolyte absorbed into a pore that is a model of the filter of a physiological calcium channel.

Molecular Dynamics Simulations of a Charged Dendrimer in Multivalent Salt Solution

The multivalent salt dependent behaviors of a charged dendrimer in solution are investigated by molecular dynamics simulations with explicit free ions. We find that the charged dendrimers show a dense-core conformation together with the back-folding of terminal monomers to the interior under all the conditions studied. We also observe an interesting ion exchange phenomenon, the replacement of the condensed monovalent counterions by multivalent salt ions due to a strong electrostatic attraction. Furthermore, we find that the dendrimer adopts an extended conformation in the absence of salt. Upon addition of salt, the dendrimer collapses as a result of a drop in the osmotic pressure inside the dendrimer. With an additional increase in the salt concentration, the dendrimer weakly swells due to an enhanced excluded volume effect of the adsorbed salt ions. The overcharge phenomenon also appears in our system. Consequently, our findings show a strong dependence of the conformation of charged dendrimers on salt concentration and give valuable insight into their behaviors at various salt concentrations at the molecular level.

Numerical particle-scale study of swelling pressure in clays

The particle level responses to different external loadings of a montmorillonitic clay soil are investigated numerically. The soil is saturated by a solution of monovalent counterions, of varying concentrations. We use finite element micromechanical models (based on the Poisson-Nernst-Planck equations) to estimate counterion and electrical potential distributions around individual clay particles at various distances from one another, since analytical solutions are not possible for these complex arrangements of particles. Disjoining pressures are then estimated using the Van’t Hoff relation and Maxwell stress tensor. As the distance between the clay particles decreases and double-layers overlap, the concentration of counterions in the micropores between clay particles increases. This increase lowers the chemical potential of the pore fluid and creates a chemical potential gradient in the solvent that generates the so-called “disjoining” or “osmotic” pressure. Because of this disjoining pressure, it is clear that particles need not contact one another in order to carry an “effective stress”. This work may lead towards theoretical predictions of the macroscopic load deformation response of montmorillonitic soils based on micro-electro-chemo-mechanical modelling of particles.

Counterion specificity of surfactants based on dicarboxylic amino acids

The behavior in solution of a series of amino acid-based surfactants having two carboxyl groups separated by a spacer of one, two, or three carbon atoms has been investigated. All three surfactants precipitated on addition of acid, but the aspartate surfactant (with a two-carbon spacer) was considerably more resistant to precipitation than the aminomalonate surfactant (one-carbon spacer) and the glutamate surfactant (three-carbon spacer). The interactions with the monovalent counterions lithium, sodium, and potassium were investigated by conductivity. It was found that lithium ions bound the strongest and potassium ions the weakest to the surfactant micelles. These results were interpreted using the hard and soft acid-base theory. Comparing the three surfactants with respect to binding of one specific counterion, sodium, showed that the aminomalonate surfactant, which has the shortest spacer, bound sodium ions the strongest and the glutamate surfactant, which has the longest spacer, had the lowest affinity for the counterion. Also that could be explained by the hard and soft acid-base concept. The glutamate surfactant was found to be considerably more resistant to calcium ions than the two other surfactants. This was attributed to this surfactant forming an intermolecular complex with the calcium ion at the air–water interface while the aminomalonate and the aspartate surfactants, with shorter distance between the carboxylate groups could form six- and seven-membered intramolecular calcium complexes.

Dynamics of counterions in dendrimer polyelectrolyte solutions

Molecular dynamics simulations were employed in models of peripherally charged dendrimers in solutions of explicit solvent and monovalent counterions in order to explore aspects of the dynamic behavior of counterions. The present study explores the effects of varying strength of electrostatic interactions for models of two dendrimer generations, in explicit solvent solutions below the dendrimer overlap concentration. Counterion diffusional motion as well as residence lifetimes of pairs formed by charged dendrimer beads and condensed counterions is monitored in the different electrostatic regimes. Spatiotemporal characteristics of self- and collective counterion motion are explored by means of space-time Van Hove correlation functions. A characteristic scaling law is found to describe the counterion diffusion coefficient as a function of Bjerrum length in the strong electrostatic regime, independent of the size of the dendrimer molecules at the examined volume fractions. The change noted in the diffusional motion of counterions in the range of strong Coulombic interactions is also reflected to their relevant residence times. Development of dynamic heterogeneities in counterion self-motion is observed during the gradual increase in the strength of electrostatic interactions, characterized by the emergence of distinct counterion populations in terms of their mobility. The time scale for the development of such a mobility contrast in the self-motion of the counterions can be correlated with that describing their collective motion as well. The latter increases with Bjerrum length but remains shorter compared to the time scale at which free diffusional motion sets in. Findings from the present study provide further insight on the mechanisms pertinent to ion migration in macroion dispersions and may serve as a basis for the interpretation of ionic motion in a broader range of polyelectrolyte systems.

Dissipative Particle Dynamics Simulations of Complexes Comprised of Cylindrical Polyelectrolyte Brushes and Oppositely Charged Linear Polyelectrolytes

Dissipative particle dynamics (DPD) approach is used to investigate the conformational behaviors and interactions of the complex between a cylindrical polyelectrolyte brush (CPB) and linear polyelectrolytes (LPs) with opposite charges. The effective complex between CPB and LPs and its dependence on the amount and length of LPs are examined. It is found that the CPB conformation presents collapse and reswelling with the increasing amount of LPs. The collapse is caused by the replacement of monovalent CPB counterions by LPs and the condensation of LPs on the CPB which reduce the osmotic pressure inside the brush. The swelling of the collapsed CPB is induced by the excluded volume effects of additionally absorbed LPs and LP counterions. The results show that the addition of LPs can not enhance the effective complex between the CPB and LPs when the total charge of LPs exceeds that of CPB. Our simulation also demonstrates that the increase of the LP length leads to a shrinking of the CPB which consequently exhibits rod-like or spherical conformations. The most effective complex between a CPB and LPs can be reached only when the contour length of LPs is not less than that of the CPB side chain.

Redox, Ionic Strength, and pH Sensitive Supramolecular Polymer Assemblies.

Supramolecular complex of a cationic surfactant and oppositely charged disulfide containing polyelectrolyte was found to form micelle type aggregates at concentration much lower than the critical aggregate concentration (CAC) of the surfactant itself. We show that this difference can be utilized to generate stimulus-sensitive disassembly of these structures. This can be achieved either by converting the polyelectrolyte counterions to monovalent counterions in response to a stimulus or by simply weakening the interaction between the polymer and the surfactant in the presence of a stimulus. We have utilized three different stimuli to demonstrate these possibilities.

Probing the supramolecular interaction synthons of 1-benzofuran-2,3-dicarboxylic acid in its monoanionic form

1-Benzofuran-2,3-dicarboxylic acid (C(10)H(6)O(5)) is a dicarboxylic acid ligand which can readily engage in organometallic complexes with various metal ions. This ligand is characterized by an intramolecular hydrogen bond between the two carboxyl residues, and, as a monoanionic species, readily forms supramolecular adducts with different organic and inorganic cations. These are a 1:1 adduct with the dimethylammonium cation, namely dimethylammonium 3-carboxy-1-benzofuran-2-carboxylate, C(2)H(8)N(+).C(10)H(5)O(5)(-), (I), a 2:1 complex with Cu(2+) ions in which four neutral imidazole molecules also coordinate the metal atom, namely bis(3-carboxy-1-benzofuran-2-carboxylato-kappaO(3))tetrakis(1H-imidazole-kappaN(3))copper(II), [Cu(C(10)H(5)O(5))(2)(C(3)H(4)N(2))(4)], (II), and a 4:1 adduct with [La(H(2)O)(7)](3+) ions, namely heptaaquabis(3-carboxy-1-benzofuran-2-carboxylato-kappaO(3))lanthanum 3-carboxy-1-benzofuran-2-carboxylate 1-benzofuran-2,3-dicarboxylic acid solvate tetrahydrate, [La(C(10)H(5)O(5))(2)(H(2)O)(7)](C(10)H(5)O(5)).C(10)H(6)O(5).4H(2)O, (III). In the crystal structure, complex (II) resides on inversion centres, while complex (III) resides on axes of twofold rotation. The crystal packing in all three structures reveals pi-pi stacking interactions between the planar aromatic benzofuran residues, as well as hydrogen bonding between the components. The significance of this study lies in the first crystallographic characterization of the title framework, which consistently exhibits the presence of an intramolecular hydrogen bond and a consequent monoanionic-only nature. It shows further that the anion can coordinate readily to metal cations as a ligand, as well as acting as a monovalent counter-ion. Finally, the aromaticity of the flat benzofuran residue provides an additional supramolecular synthon that directs and facilitates the crystal packing of compounds (I)-(III).

Effects of binding of counterions on adsorption and coalescence

In many industrial applications, ionic surfactants are used in aqueous media in the presence of a mixture of salts. The surface activity of a surfactant in such solutions depends strongly on the ions of different valence. In the present study, surface tensions of aqueous solutions of cetyltrimethylammonium bromide (CTAB) were measured in the presence of sodium bromide and potassium sulfate. The interfacial tension between water and toluene was also measured in the presence of CTAB and these salts. The effects of monovalent (bromide) and divalent (sulfate) counterions on the adsorption of CTAB at air–water and water–toluene interfaces were studied. Coalescence of air bubbles and toluene drops at flat interfaces was studied in these surfactant–salt systems. A stochastic model was used to fit the coalescence time distributions. The significance of the model parameters was discussed. The difference between air–water and water–hydrocarbon interfaces was analyzed in terms of the effects of counterion-binding on adsorption and coalescence. The mean values of the coalescence time distributions were compared with the predictions from seven film-drainage models.

Molecular simulation of the swelling of polyelectrolyte gels by monovalent and divalent counterions.

Permanently crosslinked polyelectrolyte gels are known to undergo discontinuous first-order volume phase transitions, the onset of which may be caused by a number of factors. In this study we examine the volumetric properties of such polyelectrolyte gels in relation to the progressive substitution of monovalent counterions by divalent counterions as the gels are equilibrated in solvents of different dielectric qualities. We compare the results of coarse-grained molecular dynamics simulations of polyelectrolyte gels with previous experimental measurements by others on polyacrylate gels. The simulations show that under equilibrium conditions there is an approximate cancellation between the electrostatic contribution and the counterion excluded-volume contribution to the osmotic pressure in the gel-solvent system; these two contributions to the osmotic pressure have, respectively, energetic and entropic origins. The finding of such a cancellation between the two contributions to the osmotic pressure of the gel-solvent system is consistent with experimental observations that the swelling behavior of polyelectrolyte gels can be described by equations of state for neutral gels. Based on these results, we show and explain that a modified form of the Flory-Huggins model for nonionic polymer solutions, which accounts for neither electrostatic effects nor counterion excluded-volume effects, fits both experimental and simulated data for polyelectrolyte gels. The Flory-Huggins interaction parameters obtained from regression to the simulation data are characteristic of ideal polymer solutions, whereas the experimentally obtained interaction parameters, particularly that associated with the third virial coefficient, exhibit a significant departure from ideality, leading us to conclude that further enhancements to the simulation model, such as the inclusion of excess salt, the allowance for size asymmetric electrolytes, or the use of a distance-dependent solvent dielectricity model, may be required. Molecular simulations also reveal that the condensation of divalent counterions onto the polyelectrolyte network backbone occurs preferentially over that of monovalent counterions.

Bound pairs: Direct evidence for long-range attraction between like-charged colloids

We report observations of stable bound pairs in very dilute deionized aqueous suspensions of highly charged polystyrene colloidal particles, with monovalent counterions, using a confocal laser scanning microscope. Through an analysis of several thousands of time series of confocal images recorded deep inside the bulk suspension, we find that the measured pair-potential, U ( r ) has a long-range attractive component with well depths larger than the thermal energy. These observations provide direct and unequivocal evidence for the existence of long-range attraction in U ( r ) of like-charged colloidal particles.

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.