Monovalent Counterions Research Articles

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.

Spherical polyelectrolyte brushes in the presence of multivalent counterions: The effect of fluctuations and correlations as determined by molecular dynamics simulations

We consider the interaction of multivalent counterions with spherical polyelectrolyte brushes (SPBs). SPBs result if linear polyelectrolyte chains (contour length 60 nm) are densely grafted to colloidal spheres of 116 nm in diameter. When dispersed in water the surface layer, consisting of chains of the strong polyelectrolyte poly(styrene sulfonic acid), will swell. Recent work [Mei, Phys. Rev. Lett. 97, 158301 (2006)] has demonstrated that spherical polyelectrolyte brushes undergo a collapse in the presence of a mixture of monovalent and multivalent counterions. The collapse crossover could be well described by a mean-field approach. Here we demonstrate that the application of a mean-field approach is well founded by simulation results done with molecular dynamics (MD). MD simulations show that over a wide range of multivalent counterion concentration the effects of ion correlation and fluctuations can be neglected. Higher-valent counterions are shown to interact strongly with the polyelectrolyte chains of the SPBs and thus exhibit a much reduced osmotic activity in the system. This reduction is the driving force for the collapse.

When, why, and how does like like like?: Electrostatic attraction between similarly charged species.

In the Derjaguin-Landau-Verwey-Overbeek (DLVO) framework of the past 60 years, colloidal interaction between similarly charged particles has been claimed to be simply repulsive, and an attraction such as the van der Waals interaction is attached to the Coulombic repulsion. Statistical-thermodynamic considerations show that the electrostatic Helmholtz free energy ΔFel is generally not equal to the electrostatic Gibbs free energy ΔGel for simple ionic solutions, and the difference ΔGel–ΔFel (corresponding to the electrostatic osmotic pressure pel) becomes larger with increasing charge number. Thus, it is expected that ΔGel–ΔFel be large for highly charged macroions. In the DLVO framework, however, ΔGel = ΔFel was postulated. Sogami showed that a mean field approach reproduced repulsion at the level of ΔFel but resulted in (repulsion and) attraction at the level of ΔGel. Overbeek’s critique of Sogami theory is shown to be in error. If this criticism were correct, then not only the Sogami theory but also the Debye-Hückel theory would be wrong. The attraction is thus confirmed to exist not only for multi-valent but also mono-valent counterions.

Forces between single pairs of charged colloids in aqueous salt solutions

Forces between single pairs of negatively charged micrometer-sized colloids in aqueous solutions of monovalent, divalent, or trivalent counter-ions at varying concentrations have been measured by employing optical tweezers. The experimental data have been analyzed by using the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory and a numerical solution of the Poisson-Boltzmann (PB) equation. With monovalent counterions, the data are well described by the DLVO and PB theories, suggesting that the DLVO theory is adequate to describe the colloidal forces at these conditions. At higher counter-ion valence, the approximations within the two theories become evident.

Crystal Structure Determination of Thallium Carbodiimide, Tl2NCN

AbstractOrange‐red single crystals of thallium carbodiimide, Tl2NCN, have been grown from an aqueous solution of cyanamide and thallium carbonate under strongly basic conditions. Tl2NCN crystallizes in space group with a = 5.338(1), b = 6.626(2), c = 9.645(3) Å, α = 98.765(4)°, β = 98.685(4)°, γ = 113.178(4)°, and Z = 3; the structure can be considered a strongly distorted anti‐CdI2 type. One finds two crystallographically different and irregular [NCN]Tl6 octahedra in which the Tl–N distances of the three‐coordinate monovalent thallium ions lie between 2.52 and 2.72Å. The two symmetry‐inequivalent NCN2− units adopt the carbodiimide shape, and the course of its molar volume as a function of the monovalent counter cation is analyzed.

Study on physical and electrostatic interactions of counterions in poly(perfluorosulfonic) acid matrix: Characterization of diffusion properties of membrane using radiotracers

The self-diffusion coefficients of water and ions were used to study the physical (tortuosity) and electrostatic interactions of counterions in poly(perfluorosulfonic) acid membrane (Nafion-117) matrix. The self-diffusion coefficients of water ( D H 2 O m ) were measured in the water swollen Nafion-117 membrane with Zn 2+, Ca 2+, Sr 2+, and Fe 2+ counterions by analyzing the experimental exchange rates between tritium tagged water (HTO) in membrane and equilibrating water. In order to study the effects of equilibrating solution, the HTO-desorption rate profiles between the membrane samples in H + or Cs + forms and equilibrating solution containing CsCl or HCl (0.25 mol/L) were measured. It was observed that the HTO-exchange rate profile was slower in case of membrane sample in Cs +-from equilibrated with salt/acid solution than that equilibrated with deionized water in same ionic form. However, HTO-exchange rate profile did not alter in case of H +-form of membrane on equilibration with salt or acid solution. The variation of ln D H 2 O m with polymer volume function V p/(1 − V p), where V p is polymer volume fraction, indicated that: (i) D H 2 O m in the membrane with multivalent counterions was lower than that reported for membrane with monovalent counterions at same V p, and (ii) the linear trends observed in variation of ln D H 2 O m with V p/(1 − V p) for multivalent and monovalent counterions were significantly different. The values of D H 2 O m in membrane normalized with D H 2 O m at V p = 0 were taken as an estimate of the tortuosity factor for self-diffusion of ions in the membrane matrix. The self-diffusion coefficients of ions reported in the literature along with tortuosity factor obtained from D H 2 O m in the corresponding ionic forms of the membrane were analyzed to obtain the charge ( Z i ) independent electrostatic interaction parameter g( φ) of monovalent and divalent ions in the membrane. This analysis indicated that g( φ) also vary exponentially as a function of V p/(1 − V p) irrespective of charge on counterions. In order to study the influence of V p on diffusional transport rates of Na + and Cs + ions in membrane, a permeation experiment was carried out using H +-form of membrane having high water volume fraction. The diffusional transport rates of Cs + and Na + in H +-form of membrane were found to be similar indicating that the water volume fraction in membrane has strong influence on the parameters that govern the diffusion across the Nafion-117 membrane.

Europium ion as a probe for binding sites to carrageenans

Carrageenans, sulfated polysaccharides extracted from red algae, present a coil-helix transition and helix aggregation dependence on the type and concentration of counterions. In this study, we focus attention on a mixed valence counterion system: Eu 3+/Na + or K + with different gel-forming carrageenans: kappa, iota, and kappa-2. Results of stationary and time-dependent luminescence showed to be a suitable tool to probe ion binding to both the negatively charged sulfate group and the hydroxyl groups present in the biopolymer. For lower europium ion concentrations, a single longer decay emission lifetime was detected, which was attributed to the binding of europium ion to the carrageenan sulfate groups. An additional decay ascribed to europium binding to hydroxyl groups was observed above a threshold concentration, and this decay was dependent on the carrageenan charge density. Symmetry of the europium ion microenvironment was estimated by the ratio between the intensities of its emission bands, which has been shown to depend on the concentration of europium ions and on the specificity of the monovalent counterion bound to the carrageenan.

Experimental and theoretical evidence of overcharging of calcium silicate hydrate

Electrokinetic measurements such as electrophoresis may show an inversion of the effective surface charge of colloidal particle called overcharging. This phenomenon has been studied by various theoretical approaches but up to now very few attempts of confrontation between theory and experiment have been conducted. In this work we report electrophoretic measurements as well as Monte Carlo simulations of the electrokinetic potential for the surface of calcium silicate hydrate (C S H), which is the major constituent of hydrated cement. In the simulations, the surface charge of C S H nanoparticles in equilibrium with the ionic solution is determined by a single site characteristic and electrostatic interactions between all explicit charges at the surface and in the electric double layer. We will show that ordinary electrostatic interactions are enough to describe all experimental observations. Actually, an excellent agreement is found between experimental and simulated results without any fitting parameter, both with respect to surface titration and electrokinetic behaviour. The agreement extends over a wide range of electrostatic coupling, from a weakly charged surface with mainly monovalent counter-ions to a highly charged one with divalent counter-ions.

When, why, and how does like like like?

In the Derjaguin-Landau-Verwey-Overbeek (DLVO) framework of the past 60 years, colloidal interaction between similarly charged particles has been claimed to be simply repulsive, and an attraction such as the van der Waals interaction is attached to the Coulombic repulsion. Statistical-thermodynamic considerations show that the electrostatic Helmholtz free energy ΔFel is generally not equal to the electrostatic Gibbs free energy ΔGel for simple ionic solutions, and the difference ΔGel–ΔFel (corresponding to the electrostatic osmotic pressure pel) becomes larger with increasing charge number. Thus, it is expected that ΔGel–ΔFel be large for highly charged macroions. In the DLVO framework, however, ΔGel=ΔFel was postulated. Sogami showed that a mean field approach reproduced repulsion at the level of ΔFel but resulted in (repulsion and) attraction at the level of ΔGel. Overbeek’s critique of Sogami theory is shown to be in error. If this criticism were correct, then not only the Sogami theory but also the Debye-Hückel theory would be wrong. The attraction is thus confirmed to exist not only for multi-valent but also mono-valent counterions.(Communicated by Hiroo INOKUCHI, M.J.A.)

Potentiometric Titrations of Maleic Acid Copolymers in Dilute Aqueous Solution: Experimental Results and Theoretical Interpretation

AbstractSummary: The paper reports a study on the flexibility of a family of 1:1 hydrolysed maleic anhydride (maleic acid, MA)–olefin copolymers in dilute aqueous solution. The copolymers were MA–ethene, MA–propene and MA–isobutene. The study was carried out in the absence and in the presence of monomonovalent salts and at different polymer concentrations. Experimental data showing the negative logarithm of the ‘apparent’ dissociation constant, pKa versus the degree of dissociation, α, experimental data were obtained from potentiometric titrations using NaOH, KOH or tetramethylammonium hydroxide as the base. The pKa data were fully described with calculated curves obtained using an extension of the counterion condensation theory of linear polyelectrolytes, in which a semiflexible model for the polymers was introduced. Under the present experimental condition, no relevant specificity of the monovalent counterions was apparently observed for the different copolymers. The calculated pKa versus α curves allowed the derivation of both the intrinsic dissociation constants of the first and the second dissociation steps for the different copolymers and the corresponding stiffness parameters built into the model. The agreement between the experimental and calculated data shows an appreciable success of the model. The results pointed to an increase of stiffness parallel to the increase of size of the olefin comonomer, in qualitative agreement with already published findings. Furthermore, for all copolymers the chain rigidity was larger in the α range of the first dissociation than in that of the second one. The former rigidity was attributed to the formation of intramolecular hydrogen bonds upon the first ionisation of the MA repeating units, followed by an increase of rotational freedom upon breaking of the H‐bond in the second dissociation step. Comparison of the rigidity parameters of the MA copolymers with the data obtained for other polyelectrolytes, both natural—poly(L‐glutamic acid) and pectic acid—and synthetic—poly(acrylic acid) and poly(methacrylic acid)—was also performed. magnified image

Effect of Counterion Condensation on Rigidity of Semiflexible Polyelectrolytes

I have calculated the effect of counterion condensation on the electrostatic persistence length of semiflexible polyelectrolytes. There are two contributions to the electrostatic persistence length. The first contribution is due to neutralization of the ionized groups by condensed ions that changes the effective linear charge density along the polymer backbone, weakening intrachain electrostatic repulsion. In the case of the monovalent counterions this contribution to the chain persistence length is proportional to the Debye screening length, underlining the fact of the exponential screening of electrostatic interactions on the length scales of the order of Debye screening length. The second contribution is due to correlation/fluctuation-induced attractive interactions between condensed counterions that result in a negative contribution to the chain persistence length. In the case of multivalent ions these interactions are assumed to be due to strong lateral correlations between condensed multivalent ions and were accounted for in the framework of the strongly correlated Wigner liquid approximation.

Complex Polyion−Surfactant Ion Salts in Equilibrium with Water: Changing Aggregate Shape and Size by Adding Oil

The phase behavior of ternary mixtures containing an alkyltrimethylammonium polyacrylate complex salt, water, and a nonpolar "oil" (n-decanol, p-xylene or cyclohexane) is investigated. The complex salts were prepared with short or long polyacrylates (30 or 6000 repeating units) and with hexadecyltrimethylammonium or dodecyltrimethylammonium surfactant ions. Phase diagrams and structures were determined by visual inspection and small-angle X-ray scattering analyses. Systems containing decanol display a predominance of lamellar phases, while hexagonal phases prevail in systems containing p-xylene or cyclohexane. The difference is interpreted as a result of the different locations of the oils within the surfactant aggregates. Decanol is incorporated at the aggregate interface, leading to a decrease in its curvature, which favors the appearance of lamellar structures. p-Xylene and cyclohexane, on the other hand, are mostly incorporated in the interior of the cylindrical aggregate, as reflected by its swelling as the oil content increases. The comparison of these results with those reported for similar systems with monovalent (bromide) counterions indicates a much more limited swelling of the lamellar phases with polymeric counterions by water. This limited swelling behavior is predominantly ascribed to bridging due to the polyions.

Electrostatic, Steric, and Hydration Interactions Favor Na+ Condensation around DNA Compared with K+

Condensation of monovalent counterions around DNA influences polymer properties of the DNA chain. For example, the Na(+) ions show markedly stronger propensity to induce multiple DNA chains to assemble into compact structures compared with the K(+) ions. To investigate the similarities and differences in the sodium and potassium ion condensation around DNA, we carried out a number of extensive all-atom molecular dynamics simulations of a DNA oligomer consisting of 16 base pairs, [d(CGAGGTTTAAACCTCG)](2), in explicit water. We found that the Na(+) ions penetrate the DNA interior and condense around the DNA exterior to a significantly larger degree compared with the K(+) ions. We have provided a microscopic explanation for the larger Na(+) affinity toward DNA that is based on a combination of steric, electrostatic, and hydration effects. Unexpectedly, we found that the Cl(-) co-ions provide more efficient electrostatic screening for the K(+) ions than for the Na(+) ions, contributing to the larger Na(+) condensation around DNA. To examine the importance of the discrete nature of water and ions, we also computed the counterion distributions from the mean-field electrostatic theory, demonstrating significant disagreements with the all-atom simulations. Prior experimental results on the relative extent of the Na(+) and K(+) condensation around DNA were somewhat contradictory. Recent DNA compaction experiments may be interpreted to suggest stronger Na(+) condensation around DNA compared to K(+), which is consistent with our simulations. We also provide a simple interpretation for the experimentally observed increase in DNA electrophoretic mobility in the alkali metal series, Li(+) < Na(+) < K(+) < Rb(+). We compare the DNA segment conformational preferences in various buffers with the proposed NMR models.

Understanding Electron Attachment to the DNA Double Helix: The Thymidine Monophosphate−Adenine Pair in the Gas Phase and Aqueous Solution

Electron attachment to the 2'-deoxythymidine-5'-monophosphate-adenine pairs (5'-dTMPH-A and 5'-dTMP(-)-A) has been investigated at a carefully calibrated level of theory (B3LYP/DZP++) to investigate the electron-accepting properties of thymine (T) in the DNA double helix under physiological conditions. All molecular structures have been fully optimized in vacuo and in solution. The adiabatic electron affinity of 5'-dTMPH-A in the gas phase has been predicted to be 0.67 eV. Solvent effects greatly increase the electron capture ability of 5'-dTMPH-A. In fact, the adiabatic electron affinity increases to 2.04 eV with solvation. The influence of the solvent environment on the electron-attracting properties of 5'-dTMPH-A arises not only from the stabilization of the corresponding radical anion through charge-dipole interactions, but also by changing the distribution of the unpaired electron in the molecular system. The unpaired electron is covalently bound even during vertical attachment, due to the solvent effects. Solvent effects also weaken the pairing interaction in the thymidine monophosphate-adenine complexes. The phosphate deprotonation is found to have a relatively minor influence on the capture of electrons by the 5'-dTMPH-A species in aqueous solution. The electron distributions, natural population analysis, and geometrical features of the models examined illustrate that the influence of the phosphate deprotonation is limited to the phosphate moiety in aqueous solution. Therefore, it is reasonable to expect that electron attachment to nucleotides will be independent of monovalent counterions in the vicinity of the phosphate group in aqueous solution.

Rayleigh instability of charged aggregates: Role of the dimensionality, ionic strength, and dielectric contrast

We extended a previous analysis of the classical Rayleigh instability of spherical charged droplets in the presence of neutralizing monovalent counterions [M. Deserno, Eur. Phys. J. E 6, 163 (2001)], by generalizing the problem for suspensions of aggregates with D-dimensional symmetry, corresponding for D = 2 to infinite (rodlike) cylindrical charged bundles and for D = 3 to spherical charged droplets. In addition, we include the effects of added monovalent salt and of dielectric contrast between the charged aggregate and the surrounding solvent. The electrostatic energy taking the microion screening into account is estimated using uniform profiles within the framework of the cell model. We verify the robustness of these results by also considering Debye-Hückel-type microion profiles that are obtained by the minimization of a linearized Poisson-Boltzmann free-energy functional. In the case when the microions can enter inside the charged aggregates, we confirm the occurrence of a discontinuous phase change between aggregates of finite size and an infinite aggregate, which takes place at a collapse temperature that depends on their volume fraction phi and on the salt content. Decrease of phi shifts the phase-change temperature toward higher values, while salt addition has an opposite effect. We obtain analytical expressions for the phase-separation line in the asymptotic limit of infinite dilution (phi-->0), showing that the collapse temperature depends logarithmically on phi . As an application for D = 3 we discuss the stability of the pearl-necklace structures of flexible polyelectrolytes in poor solvents. The case D = 2 is applied to the problem of finite bundle sizes of stiff polyelectrolytes that attract each other-via, e.g., multivalent counterions-leading to an effective surface tension.

Wheel-Shaped Polyoxotungstate [Cu20Cl(OH)24(H2O)12(P8W48O184)]25- Macroanions Form Supramolecular “Blackberry” Structure in Aqueous Solution

The hydrophilic polyoxotungstate [Cu20Cl(OH)24(H2O)12(P8W48O184)]25- ({Cu20P8W48}) self-assembles into single-layer, hollow, spherical "blackberry"-type structures in aqueous solutions, as studied by dynamic light scattering (DLS), static light scattering (SLS), zeta potential analysis, and scanning electron microscopy (SEM) techniques. This represents the first report of blackberry formation for a non-Mo-containing polyoxometalate. There is no obvious change in the shape and size of the blackberries during the slow blackberry formation process, neither with macroionic concentration nor with temperature. Our results suggest that the blackberry-type structure formation is most likely a general phenomenon for hydrophilic macroions with suitable size and charge in a polar solvent, and not a specific property of polyoxomolybdates and their derivatives. The {Cu20P8W48} macroions are thus far the smallest type of macroions to date (equivalent radius < 2 nm) showing the unique self-assembly behavior, helping us to move one step closer toward identifying the transition point from simple ions (can be described by the Debye-Hückel theory) to macroions in very dilute solutions. Moreover, by using {Cu20P8W48} blackberry-type structures as the model system, the electrophoretic properties of macroionic supramolecular structures are studied for the first time via zeta-potential analysis. The mobility of blackberry-type structures is determined and used for understanding the state of small cations in solution. We notice that the average charge density on each {Cu20P8W48} macroanion in a blackberry is much lower than that of discrete "free" {Cu20P8W48} macroions. This result suggests that some small alkali counterions are closely associated with, or even incorporated into, the blackberry-type structures and thus do not contribute to solution conductivity. This model is fully consistent with our speculation that monovalent counterions play an important role in the self-assembly of macroions, possibly providing an attractive force contributing to blackberry formation.

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.

Role of Monovalent Counterions in the Ultrafast Dynamics of DNA

This paper examines the contribution of counterion motion to the electric-field dynamics in the interior of DNA. The electric field is measured by a coumarin fluorophore that is synthetically incorporated into an oligonucleotide, where it replaces a native base pair. The DNA is a 17-base-pair oligomer with no A- or G-tracts. Time-resolved Stokes-shift measurements on the coumarin are made from 40 ps to 40 ns with each of the alkali ions and or one of several tetraalkylammonium ions as the DNA counterion. With the possible exception of rubidium, there are no indications of site-specific binding of the counterions. For sodium and other ions with a smaller hydrodynamic radius, the dynamics are identical and are fit to a power law. For larger ions, there is a progressive increase in the rate of shifting after 1 ns. This effect correlates with the hydrodynamic radius of the counterion. The lack of change in the spectral shape of the emission shows that neither the broadly distributed power-law relaxation nor the extra nanosecond dynamics are due to heterogeneity in the relaxation rates of different helices.

Measuring Inter-DNA Potentials in Solution

Interactions between short strands of DNA can be tuned from repulsive to attractive by varying solution conditions and have been quantified using small angle x-ray scattering techniques. The effective DNA interaction charge was extracted by fitting the scattering profiles with the generalized one-component method and inter-DNA Yukawa pair potentials. A significant charge is measured at low to moderate monovalent counterion concentrations, resulting in strong inter-DNA repulsion. The charge and repulsion diminish rapidly upon the addition of divalent counterions. An intriguing short range attraction is observed at surprisingly low divalent cation concentrations, approximately 16 mM Mg2+. Quantitative measurements of inter-DNA potentials are essential for improving models of fundamental interactions in biological systems.

Ion Adsorption and Lamellar−Lamellar Transitions in Charged Bilayer Systems

Using a primitive model approach, we analyze the influence of ion specific adsorption on the phase behavior of charged lamellar systems. The presence of a weak short-ranged surface potential, attracting monovalent counterions, induces a phase separation, where the separate phases have different repeat distance. If the adsorption potential is very weak, the more narrow phase never forms. An opposite behavior is found for strong surface affinities. Both Monte Carlo simulations and a recently developed correlation-corrected Poisson-Boltzmann theory are adopted, with a nearly quantitative agreement between the approaches. Different counterions are discriminated by the adsorption potential strength, and with physically reasonable values, experimental observations on these systems are well reproduced. The study highlights the importance of electrostatic correlations, even though only monovalent ions are present.