Monovalent Counterions Research Articles

Structure of stable double‐ionic model water clusters of quaternary alkylammonium surfactants with some monovalent counterions as derived by the DFT method

AbstractWe have performed DFT calculations on stability of model water clusters of alkylammonium surfactants with different monovalent counterions, such as fluoride, chloride, bromide, hydroxide, nitrate, perchlorate, and tetrafluoroborate. We have found that stable water clusters are formed if they contain at least three molecules of water. We can distinguish two types of stable water clusters of ammonium salts: stable neutral water clusters and double‐ionic water clusters. According to the results of our DFT calculations, the first type of cluster is more stable by ca. 3–7 kcal/mol. We have found several types of stable double‐ionic water clusters of alkylammonium salts with different counterions. In each case, the stable structures have some element of symmetry and they are stabilized by hydrogen bonding. The computed energy of double‐ionic cluster formation of hydrated alkylammonium salts with different counterions correlates quite well with experimental data of the critical micelle concentration (CMC), indicating a role of hydration phenomena in the process of micelle formation. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Structure of polyelectrolytes in 3:1 salt solutions

Polyion conformation and the distribution of small ions near the polyion have been investigated using Monte Carlo simulations. The systems of interest contained one polyion and its monovalent counterions, and variable amount of a 3:1 salt. With monovalent counterions only, the polyion is strongly extended. As salt is added, the polyion folds, and the most compact and spherical-like structure appears at a three-fold excess of the trivalent counterions. The polyion exerts a strong influence on the nearest-neighbor distance among the trivalent ions, an effect being relevant for energy transfer reactions.

Probing charge inversion in model colloids: electrolyte mixtures of multi- and monovalentcounterions

Under certain conditions ion–ion correlations play a crucial role in the description of theelectrical double layer of colloidal particles. In fact, in many instances, the inclusion of theshort range correlations between ions in the study of the ionic distribution leads to quitedifferent results with respect to the classical treatment (where ions are assumed to bepoints). In particular, these discrepancies become more noticeable for highly chargedparticles in the presence of moderate or highly multivalent counterion concentrations.Moreover, it can be shown that the existence of an electrolyte mixture consisting ofmulti- and monovalent counterions may cause that system to become overcharged,a feature that cannot be predicted from a classical point of view based on theBoltzmann distribution function. Precisely this aspect has recently produced anenormous interest in the field of biophysics since small variations in the physiologicalconditions of biocolloidal systems (e.g. the addition of a multivalent salt) can induceimportant changes in their behaviour. In order to determine the relevance ofion correlations in electrolyte mixtures, we present some experimental resultson the electrophoretic mobility of latex particles in the presence of different 1:1and 3:1 salt mixtures. Likewise, these results are analysed within the so-calledhypernetted-chain/mean spherical approximation where ion size correlations are taken intoaccount.

Ion Pairing in Fast-Exchange Host−Guest Systems: Concentration Dependence of Apparent Association Constants for Complexes of Neutral Hosts and Divalent Guest Salts with Monovalent Counterions

An equilibrium treatment of complexation of neutral hosts with dicationic guests having univalent counterions includes two possible modes: (1) dissociation of the ion pair prior to interaction of the free dication with the host to produce a complex that is not ion paired and (2) direct complexation of the ion pair to produce an ion paired complex. This treatment is easily modified for complexation of neutral guests by dianionic hosts, or divalent hosts by neutral guests. The treatment was tested by a study of fast-exchange host-guest systems based on paraquats or viologens (G(2+)2X(-)) and crown ethers (H). The bis(hexafluorophosphate) salts of viologens are predominantly ion paired in acetone; the value of the dissociation constant of paraquat bis(hexafluorophosphate) was determined to be 4.64 (+/- 1.86) x 10(-4) M(2). The complex based on dibenzo-24-crown-8 and paraquat bis(hexafluorophosphate) is not ion paired in solution, resulting in concentration dependence of the apparent association constant K(a,exp), (= [complex]/[H][G(2+)2X(-)]) which is well fit by the treatment, according to mode (1), yielding K(ap) = 106 (+/-42) M(-1). However, the four complexes of two different bis(m-phenylene)-32-crown-10 derivatives and bis(p-phenylene)-34-crown-10 with paraquat derivatives are all ion paired in solution and therefore K(a,exp) is not concentration dependent for these systems, mode (2). X-ray crystal structures support these solution-based assessments in that there is clearly ion pairing of the cationic guest with its PF(6)(-) counterions in the solid states of the latter four examples in which access of the counterions to the guests is granted by the relatively large cavities of the hosts and dispositions of the guest species within them.

Monte Carlo Simulation of the Mean Force between Two Like-Charged Macroions with Simple 1:3 Salt Added

The mean force and the potential of the mean force between two like- harged macroions with monovalent counterions and added simple 1:3 salt described within the primitive model and confined in a cylindrical cell have been investigated by Monte Carlo simulations. Without additional salt, a strongly repulsive mean force was obtained at all macroion separations, consistent with a stable solution of macroions. At a trivalent counterion-to-macroion charge ratio of 0.4, the mean force became attractive at short separations but still possessed a substantial repulsion at longer separations. However, at a stoichiometric amount of trivalent counterions, no long-range repulsion remained and the attraction became substantial (approximate to5kT attraction at a short separation). In excess of salt, the magnitude of the attractive mean force was reduced. The attractive component of the mean force originates from spatial correlations between counterions residing near different macroions and is not captured by mean-field theories such as the Poisson-Boltzmann equation or any of its simplific tions. The observed sequence of mean forces is consistent with recent experimental observations on an aqueous solution of sodium dodecyl sulfate micelles as Al(NO3)(3) was added. (Less)

Effect of Counterion Binding on Micellar Solution Behavior: 2. Prediction of Micellar Solution Properties of Ionic Surfactant−Electrolyte Systems

A molecular−thermodynamic theory of micellization of ionic surfactants, developed in paper 1 of this series, is applied here to specific ionic surfactant−electrolyte systems in order to test its ability to quantitatively predict various micellar solution properties, including the effect of the counterion hydrated size, valence, and lipophilicity. With this goal in mind, the theory is utilized to model surfactant solutions containing (i) monovalent counterions (specifically, the alkali metal dodecyl sulfate series, MDS), (ii) multivalent counterions (specifically, the sodium dodecyl dioxyethylene sulfate surfactant, SDE2S, with added AlCl3 + NaCl and CaCl2 + NaCl), and (iii) organic counterions (specifically, the alkyl trimethylammonium salicylate series, CnTASal). The predicted micellar solution properties include (i) the optimal degree of binding of each counterion species onto the charged micelle surface, (ii) the surfactant critical micelle concentration, and (iii) the optimal micelle shape and average micelle aggregation numbers. In the MDS surfactant series, a decrease in the hydrated size of the alkali metal counterion leads to an increase in the degree of counterion binding and to an increase in the average sizes of the micelles formed. In the SDE2S−AlCl3−NaCl and the SDE2S−CaCl2−NaCl surfactant systems, the degrees of binding of the multivalent counterion (Al3+ or Ca2+) and of the monovalent counterion (Na+) vary with the individual concentrations of the two added electrolytes, even when the overall solution ionic strength is kept constant. Moreover, at fixed ionic strength, as the proportion of the multivalent-ion-carrying electrolyte is increased, the degree of binding of the multivalent counterion increases, and the resulting reduction in the micelle surface charge leads to a shape transition from spherical to cylindrical micelles. In the CnTASal surfactant system, the hydrophobicity of the salicylate counterion promotes a higher degree of counterion binding onto the micelle surface, as compared to that of its chloride analogue, CnTAC, and leads to the aggregation of the CnTASal surfactants into cylindrical micelles as compared to the aggregation of the CnTAC surfactants into spherical micelles. In addition to reproducing the experimentally observed qualitative trends, our theoretically predicted micellar solution properties are found to be in good quantitative agreement with the available experimental results.

Adsorption of DNA to Mica Mediated by Divalent Counterions: A Theoretical and Experimental Study

The adsorption of DNA molecules onto a flat mica surface is a necessary step to perform atomic force microscopy studies of DNA conformation and observe DNA-protein interactions in physiological environment. However, the phenomenon that pulls DNA molecules onto the surface is still not understood. This is a crucial issue because the DNA/surface interactions could affect the DNA biological functions. In this paper we develop a model that can explain the mechanism of the DNA adsorption onto mica. This model suggests that DNA attraction is due to the sharing of the DNA and mica counterions. The correlations between divalent counterions on both the negatively charged DNA and the mica surface can generate a net attraction force whereas the correlations between monovalent counterions are ineffective in the DNA attraction. DNA binding is then dependent on the fractional surface densities of the divalent and monovalent cations, which can compete for the mica surface and DNA neutralizations. In addition, the attraction can be enhanced when the mica has been pretreated by transition metal cations (Ni2+, Zn2+). Mica pretreatment simultaneously enhances the DNA attraction and reduces the repulsive contribution due to the electrical double-layer force. We also perform end-to-end distance measurement of DNA chains to study the binding strength. The DNA binding strength appears to be constant for a fixed fractional surface density of the divalent cations at low ionic strength (I<0.1M) as predicted by the model. However, at higher ionic strength, the binding is weakened by the screening effect of the ions. Then, some equations were derived to describe the binding of a polyelectrolyte onto a charged surface. The electrostatic attraction due to the sharing of counterions is particularly effective if the polyelectrolyte and the surface have nearly the same surface charge density. This characteristic of the attraction force can explain the success of mica for performing single DNA molecule observation by AFM. In addition, we explain how a reversible binding of the DNA molecules can be obtained with a pretreated mica surface.

Onset of DNA Aggregation in Presence of Monovalent and Multivalent Counterions

We address theoretically aggregation of DNA segments by multivalent polyamines such as spermine and spermidine. In experiments, the aggregation occurs above a certain threshold concentration of multivalent ions. We demonstrate that the dependence of this threshold on the concentration of DNA has a simple form. When the DNA concentration cDNA is smaller than the monovalent salt concentration, the threshold multivalent ion concentration depends linearly on cDNA, having the form αcDNA+β. The coefficients α and β are related to the density profile of multivalent counterions around isolated DNA chains, at the onset of their aggregation. This analysis agrees extremely well with recent detailed measurements on DNA aggregation in the presence of spermine. From the fit to the experimental data, the number of condensed multivalent counterions per DNA chain can be deduced. A few other conclusions can then be reached: 1), the number of condensed spermine ions at the onset of aggregation decreases with the addition of monovalent salt; 2), the Poisson-Boltzmann theory overestimates the number of condensed multivalent ions at high monovalent salt concentrations; and 3), our analysis of the data indicates that the DNA charge is not overcompensated by spermine at the onset of aggregation.

Direct Derivation of the Interfacial Free Energy of Charged Colloids from (N,V,T) Monte Carlo Simulations

(N,V,T) Monte Carlo simulations are used to simulate the equilibrium distribution of the neutralizing monovalent counterions condensed in the vicinity of two charged colloids of various shapes (spheres, disks, and cylinders). The corresponding configurational entropy is used, in addition to the total electrostatic energy, to estimate the free energy of a pair of colloids at different distances and relative orientations (in the case of nonspherical colloids). By calculating the balance between energetic and entropic contributions to the total free energy of charged colloids, this study illustrates the large influence of the entropy on the net repulsion between colloids carrying electric charges of the same sign and neutralized by monovalent counterions. This procedure leads also to an effective pair potential useful for describing dispersions of charged colloids in the one-component plasma framework, implicitly including the contribution of the labile counterions. The treatment is based on a pairwise additivity of the effective potential. The validity of this hypothesis is carefully examined for the case of three charged cylinders.

Monte Carlo Simulation of Defect-Free Cross-Linked Polyelectrolyte Gels

Model systems of cross-linked polyelectrolyte gels were investigated by means of Monte Carlo simulations. The model contained a charged defect-free th ee-dimensional network of a diamond-like topology and explicit counterions. Pressure vs volume relations and chain extensions were determined and compared to those of the corresponding polyelectrolyte solution. The structure of the gel was characterized by radial distribution functions. In the swollen state, the network particles and the counterions are inhomogeneously distributed in space. Also, the properties of the polyelectrolyte gels were investigated at different charge density, cross-linking density, chain flexibility, and counterion valence. An increase in the gel volume was observed for increasing charge density, decreasing cross-linking density, and increasing chain stiffness. The exchange of the monovalent counterions for divalent counterions reduced the equilibrium volume of the gel substantially. The affine assumption, which states that a linear relation exists between chain end-to-end separation and macroscopic gel size, was found to be only of limited validity, whereas the Gaussian chain appr ximation was never fulfilled for polyelectrolyte gels. (Less)

Polyelectrolyte solutions with added salt: A simulation study

Using Langevin dynamics simulations, we have investigated the distribution of counterions around a flexible polyelectrolyte chain as a function of polymer concentration (Cp), salt concentration (Cs), and valency of the counterion from the added salt. In the present simulations, the aqueous solutions are at room temperatures and polymer concentrations are either below or comparable to overlap concentrations. The net polymer charge and the radius of gyration (Rg) of a labeled chain are found to decrease with an increase in either Cp or Cs. We present details of the distribution of monovalent and divalent counterions inside the counterion worm surrounding a polymer chain, when a salt-free solution of polyelectrolytes with monovalent counterions is challenged by a salt with divalent counterions. The simulation results for the dependence of Rg on chain length (N), Cp and Cs are compared with the theory of Muthukumar [J. Chem. Phys. 86, 7230 (1987); 105, 5183 (1996)] which contains two parameters, viz., degree of ionization (α) and strength (w) of excluded volume interaction. Using the values of α and w as determined by simulations, there is a very good agreement between theoretical predictions and simulations for monovalent counterions. For the case of divalent counterions there is evidence for significant bridging between polymer segments mediated by counterions. This bridging leads to an enhanced shrinkage of polymer size beyond expected from averaged electrostatic screening. A mean-field counting of the bridging effect as an effective two-body attraction leads to a good agreement between theory and simulations.

Where the linearized Poisson–Boltzmann cell model fails: Spurious phase separation in charged colloidal suspensions

The Poisson–Boltzmann (PB) spherical Wigner–Seitz cell model—introduced to theoretically describe suspensions of spherical charged colloidal particles—is investigated at the nonlinear and linearized levels. The linearization of the mean-field PB functional yields linearized Debye–Hückel-type equations agreeing asymptotically with the nonlinear PB results in the weak-coupling (high-temperature) limit. Both the canonical (fixed number of microions) as well as the semigrand-canonical (in contact with an infinite salt reservoir) cases are considered and discussed in a unified linearized framework. In disagreement with the exact nonlinear PB solution inside a Wigner–Seitz cell, the linearized theory predicts the occurrence of a thermodynamical instability with an associated phase separation of the homogeneous suspension into dilute (gas) and dense (liquid) phases, being thus a spurious result of the linearization. We show that these artifacts, although thermodynamically consistent with quadratic expansions of the nonlinear functional and osmotic pressure, may be traced back to the nonfulfillment of the underlying assumptions of the linearization. This raises questions about the reliability of the prediction of gas/liquid-like phase separation in deionized aqueous suspensions of charged colloids mediated by monovalent counterions obtained by linearized theories.

Brownian dynamics simulations of polyelectrolyte solutions with divalent counterions

Brownian dynamics simulations are performed for salt-free polyelectrolyte solutions with divalent counterions. The polymer molecules are modeled as freely jointed charged chains and the counterions are incorporated explicitly. The conformational properties, static structure, and dynamic properties of salt-free polyelectrolyte solutions show interesting behavior that can be attributed to the correlations induced by the counterions. The size of polyelectrolyte chains and the counterion self-diffusion coefficient show a nonmonotonic concentration dependence. There is a sharp peak in the polyion pair correlation functions at short distances and an upturn in the partial static structure factors at low wave vectors. In semidilute solutions, the polyions contract in the presence of divalent counterions, when compared to solutions with monovalent counterions. This contraction is accompanied by the peak in the static structure moving to lower wave vectors. The self-diffusion of polyions is faster with divalent counterions than with monovalent counterions, whereas the collective diffusion at long length scale slows down with divalent counterions compared to the monovalent case. These results are consistent with experiments and suggest that primitive models with strong electrostatic correlations can explain many of the experimental observations.

Self‐Consistent Integral Equation Theory for Semiflexible Polyelectrolytes in Poor Solvent

AbstractSelf‐consistent hybrid MC/PRISM method is presented for calculating properties of polyelectrolytes in semidilute and more concentrated regimes in a poor solvent. The static structure and conformational behavior of salt‐free polyelectrolyte solutions composed of semiflexible polyions and monovalent counterions are studied using the approach which combines the traditional Monte‐Carlo (MC) simulation with the numerical solution of the polymer integral PRISM equation. The MC technique is applied to generate the configurations of a single chain molecule and obtain the averaged intrapolymer correlation function. The PRISM equation is then numerically solved for a given monomer density to obtain the various correlation functions and the medium‐induced intrapolymer potential. This is used in a single chain MC simulation, where the polymer sites interact via the bare Coulomb potential together with the short range attractive potential and a self‐consistently determined medium‐induced potential. The monomer‐monomer pair correlation functions and static structure factors are calculated for a large variety of parameters. Conformational properties such as the radius of gyration and visual images are obtained as a function of attractive short‐range interaction, monomer density, Bjerrum length, and chain stiffness. The MC/PRISM study predicts that there is a range of hydrophobicity and monomer density for which polyion chains can form the toroidal structure in a poor solvent. Nonmonotonic dependence of the chain size on monomer density is predicted over the entire range of parameters. Polyion structure factor peak position as a function of density is described. Two concentration regimes in which the polyion structure factors exhibit physically different peaks were found. Over the entire concentration regime considered polyelectrolyte chains undergo strong compression with Rg ∝ l.Conformation of a polyion chain for lB = 2, ε = 0.18 at ρ* = 0.2 and α = 10°.imageConformation of a polyion chain for lB = 2, ε = 0.18 at ρ* = 0.2 and α = 10°.

Phase Behavior of an Ionic Surfactant with Mixed Monovalent/Polymeric Counterions

A complex salt of cetyltrimethylammonium (CTA(+)) with short (30 repeating units) polyacrylate (PA(-)) counterions has been synthesized. The phase diagrams of its aqueous mixtures with either the surfactant cetyltrimethylammonium acetate (CTAAc), or the polyelectrolyte NaPA, have been studied by visual inspection through crossed polarizers and by small-angle X-ray scattering. Both of the ternary phase diagrams are strikingly simple, containing only micellar, cubic micellar, and hexagonal phases. In the CTAPA/CTAAc/water system, the surfactant forms essentially spherical micelles above ca. 50 wt % of water, regardless of the counterion composition, and the system may serve as a model for charged colloids with mixed monovalent/polymeric counterions. The interactions between micelles varies from repulsive to attractive as the fraction of monovalent counterions is dec eased. This results, first, in a liquid-liquid phase separation between a concentrated branch and a dilute branch of the micellar phase and, finally, a crystallization of micelles into a cubic (Pm3n) phase in equilibrium with essentially pure water. Small fractions of polymeric counterions melt the cubic phase. This is attributed to heterogeneity: A small proportion of micelle pairs that share polymeric counterions experience strong attractions. In CTAPA/NaPA/water mixtures, the micelle-micelle interactions switch from attractive to repulsive as the NaPA content is increased. A similar effect occurs with added NaAc. Monte Carlo simulations of interactions between surfactant aggregates neutralized by mixed polymeric and monovalent counterions qualitatively reproduce all experimental trends and show that the dominating source of the attraction between the aggregates is polyion bridging. (Less)

Polyelectrolyte Multilayering on a Charged Sphere

The adsorption of highly \textit{oppositely} charged flexible polyelectrolytes onto a charged spherical surface is investigated by means of Monte Carlo simulations in a fashion which resembles the layer-by-layer deposition technique introduced by Decher. Electroneutrality is insured at each step by the presence of monovalent counterions (anions and cations). We study in detail the structure of the \textit{equilibrium} complex. Our investigations of the first few layer formations strongly suggest that multilayering in spherical geometry is not possible as an equilibrium process with purely electrostatic interactions. We especially focus on the influence of specific (non-electrostatic) short range attractive interactions (e.g., Van der Waals) on the stability of the multilayers.

Structural characteristics of carrageenan gels: various types of counter ions

The gelation mechanism of κ- and ι-carrageenan with various types of monovalent counter ions are considered by means of small-angle X-ray scattering. The extent of chain aggregation was discussed with the cross-sectional radius of gyration estimated from cross-sectional Gunier plots. The gelation of κ-carrageenan found to involve the multiple aggregation of double helices except for Li + and Na +-type, while ι-carrageenan gel was consisted of just double helices.

Polyelectrolyte behaviour and calcium binding properties of sugar beet pectins differing in their degrees of methylation and acetylation

Five series of pectins with different levels and patterns of methyl esterification and/or different levels of acetyl esterification were produced by chemical or enzymatic treatment of an acid-extracted sugar beet pectin. The relationship between p K a and the degree of dissociation and the free fractions of monovalent and calcium counterions were determined on dilute pectin salt-free solutions. Calcium sensitivity was determined in more concentrated solutions. The presence of acetyl groups hindered the formation of calcium-pectinate precipitates in different manners according to the demethoxylation mode and the pectin concentration. The base-deesterified pectins appeared to have the most homogeneous methyl ester distribution. Pectins demethoxylated by fungus-PME exhibited a peculiar distribution of free galacturonic acid residues. Blocks of contiguous free galacturonic acid were generated by treatment of sugar beet pectin with a plant-PME. Those blocks were not long enough to induce abnormal polyelectrolyte behaviour or to promote dimerisation of pectic molecules in dilute solution but allow the formation of calcium-pectinate precipitates in concentrated medium for high DM.

Adsorption of proteins on spherical polyelectrolyte brushes in aqueous solution

We consider the adsorption of bovine serum albumin (BSA) on spherical polyelectrolyte brushes (SPB). The SPB consist of a solid polystyrene core of 100 nm diameter onto which linear polyelectrolyte chains [poly(acrylic acid), (PAA)] are grafted. The adsorption of BSA is studied at a pH of 6.1 at different concentrations of added salt and buffer. We observe strong adsorption of BSA onto the SPB despite the effect that the particles as well as the dissolved BSA are charged negatively. The adsorption of BSA is strongest at low salt concentration and decreases drastically with increasing amounts of added salt. Virtually no adsorption takes place at salt concentration of 0.1 M. Moreover, the adsorbed protein can be washed out again by raising the ionic strength from low to high values. A major driving force for the adsorption is located at a lower pH within the brush at low ionic strength. Thus, the isoelectric point of the protein may be approached or even reached. In this case strong interaction between the SPB and the protein results. Moreover, the negative charge of the polyelectrolyte interacts with the patches of positive charges on the protein. In this way the protein becomes a multivalent counterion within the brush and monovalent counterions will be released. All results demonstrate that the SPB present a new class of colloidal carrier particles whose interaction with proteins can be tuned in a well-defined fashion.

Reversible Binding of DNA on NiCl2-Treated Mica by Varying the Ionic Strength

The atomic force microscope is a key tool for investigating DNA conformation and DNA−protein interactions in liquid. The main advantage of this technique is that moving molecules can be studied in real time provided that molecules are sufficiently bound to the surface. Mg2+ ions with a very low concentration of monovalent salt are generally used to attach DNA on mica because monovalent counterions inhibit the DNA electrostatic attraction with the surface. However, monovalent counterions at physiological concentrations are necessary to obtain specific DNA/protein interactions. To solve this problem, we propose a new protocol to obtain a reversible binding of DNA on NiCl2-pretreated mica. This protocol uses Mg2+ ions for monitoring DNA attachment on NiCl2-pretreated mica, which allows the DNA molecules to remain bound to the surface even at high NaCl concentration thanks to Ni2+ ions adsorbed on the surface.