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.     

Resiliently spherical micelles of alkyltrimethylammonium surfactants with multivalent, hydrolyzable counterions

A series of C(12)-C(16) alkyltrimethylammonium surfactants with hydrolyzable phosphate (PO(4)(3-), HPO(4)(2-), and H(2)PO(4)(-)), oxalate (HC(2)O(4)(-) and C(2)O(4)(2-)), and carbonate (HCO(3)(-) and CO(3)(2-)) counterions have been prepared, and their micellar solution behavior has been characterized. Critical micelle concentrations were measured using electrical conductivity and were found to depend on both the counterion and its hydrolysis state. All monovalent counterions bind less strongly to the micelle surface than does bromide or chloride, whereas multivalent species bind more strongly. Small-angle neutron scattering reveals that, unlike alkyltrimethylammonium bromides and chlorides, micelles are small and spherical in the presence of hydrolyzable counterions of all valences and remain spherical even in the presence of added electrolyte. This is consistent with the strong solvation of even strongly bound hydrolyzable counterions, which prevents the screening of repulsions between adjacent headgroups necessary for sphere-cylinder transformations. Salts of multivalent hydrolyzable counterions could thus be used to control the micelle structure in novel ways.     

Conformational transitions of flexible hydrophobic polyelectrolytes in solutions of monovalent and multivalent salts and their mixtures

Conformations of cationic polyelectrolytes (PEs), a weak poly(2-vinylpyridine) (P2VP) and a strong poly(N-methyl-2-vinylpyridinium iodide) (qP2VP), adsorbed on mica from saline solutions in the presence of counterions of different valences are studied using in situ atomic force microscopy (AFM). Quantitative characteristics of chain conformations are analyzed using AFM images of the adsorbed molecules. The results of the statistical analysis of the chain contour reveal collapse of the PE coils when ionic strength is in a range from tens to hundreds of millimoles per kilogram and re-expansion of the coils with a further increase of ionic strength up to a region of the saturated saline solutions. The competition between monovalent and multivalent counterions simultaneously present in solutions strongly affects conformations of PE chains even at a very small fraction of multivalent counterions. Shrinkage of PE coils is steeper for multivalent counterions than for monovalent counterions. However, the re-expansion is only incremental in the presence of multivalent counterions. Extended adsorbed coils at low salt concentrations and at very high concentrations of monovalent salt exhibit conformation corresponding to a 2D coil with 0.95 fraction of bound segments (segments in "trains") in the regime of diluted surface concentration of the PE. Shrunken coils in the intermediate range of ionic strength resemble 3D-globules with 0.8 fraction of trains. The incrementally re-expanded PE coils at a high ionic strength remain unchanged at higher multivalent salt concentrations up to the solubility limit of the salt. The formation of a strong PE complex with multivalent counterions at high ionic strength is not well understood yet. A speculative explanation of the observed experimental result is based on possible stabilization of the complex due to hydrophobic interactions of the backbone.     

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.     

The effect of counterions on the chain conformation of polyelectrolytes,as assessed by extensibility in elongational flow: The influence of multiple valency

An elongational flow technique was used to determine the effect of counterions on the chain conformation of polyelectrolyte molecules in solution, by means of the extensibility of the chains in the flow field. It is demonstrated that adding excess cations of seven low molecular weight salts, NaCl, CaCl₂, BaCl₂, SrCl₂, MgCl₂, AlCl₃, and SnCl₄, to a very dilute solution of fully sulphonated polystyrene (NaPSS) reduces the extensibility of the chains, that is, the facility by which a chain can be extended to varying degrees, an effect associated with chain contractions. In the case of multivalent counterions, these contractions, which with monovalent counterions are primarily due to screening of charges by excess counterions, are greatly enhanced, which we attribute to the formation of intramolecular ionic bridges. When, in the case of multivalent counterions, the polymer concentration is increased, in inversion of the effect, namely increase in chain extensibility on addition of ions, is observed. We attribute this latter effect to the ionic bridges becoming increasingly intermolecular, leading to effectively large molecules, and eventually to a gel. All these effects were accentuated with increase in valency. They could also be accompanied by precipitation which were of two kinds: one due to formation of insoluble ionic associations and a second attributable to enhanced hydrophobic interaction within the contracted chain itself. © 1994 John Wiley & Sons, Inc.     

Ion condensation behavior and dynamics of water molecules surrounding the sodium poly(methacrylic acid) chain in water: a molecular dynamics study

All-atom molecular dynamics simulations are used to study the condensation behavior of monovalent (Na(+)) and multivalent (Ca(2+)) salt counterions associated with the co-ions (Cl(-)) surrounding the charged poly(methacrylic acid) (PMAA) chain in water. The study is extended to the influences on chain conformation, local arrangement, and dynamics of water in the highly diluted aqueous solutions. We find that even when the salt ions are monovalent, they attract more than one charged monomer and act as a bridging agent within the chain, as the multivalent salt ions. In principle, the salt ions bridge between not only the "non-adjacent" but also the "adjacent" charged monomers, leading to a more coil-like and a locally stretched conformation, respectively. With an increase in the salt concentration, the amount of coiled-type condensed ions increase and reach a maximum when the chain conformation becomes the most collapsed; whereas, the stretched-type shows an opposite trend. Our results show that the attractive interactions through the condensed salt ions between the non-adjacent monomers are responsible for the conformational collapse. When the salt concentration increases high enough, a significant increase for the stretched-type condensed ions makes an expansion effect on the chain. These stretched-type salt ions, followed by the adsorption of the co-ions and water molecules, tend to form a multilayer organization outside surrounding the PMAA chain. Thus, the expansion degree of the chain conformation is greatly limited. When only the monovalent Na(+) ions are present in the solutions, water molecules are primarily adsorbed into either the condensed Na(+) ions or the COO(-) groups. These adsorbed water molecules form hydrogen bonds with each other and enhance the local bridging behavior associated with the Na(+) condensation on the resultant chain conformation. With an increase in the amount of multivalent Ca(2+) salt ions, more water molecules are bonded directly with the condensed Ca(2+) ions. In this case, only the condensed Ca(2+) ions provide a strong bridging effect within the polymer chain. We observe a significant shift towards a higher frequency of the oxygen vibration spectrum and only a slight shift towards a higher frequency of the hydrogen spectrum for the water molecules associated with the ion condensation.     

Onset of cohesion in cement paste

It is generally agreed that the cohesion of cement paste occurs through the formation of a network of nanoparticles of a calcium-silicate-hydrate ("C-S-H"). However, the mechanism by which these particles develop this cohesion has not been established. Here we propose a dielectric continuum model which includes all ionic interactions within a dispersion of C-S-H particles. It takes into account all co-ions and counterions explicitly (with pure Coulomb interactions between ions and between ions and the surfaces) and makes no further assumptions concerning their hydration or their interactions with the surface sites. At high surface charge densities, the model shows that the surface charge of C-S-H particles is overcompensated by Ca2+ ions, giving a reversal of the apparent particle charge. Also, at high surface charge densities, the model predicts that the correlations of ions located around neighboring particles causes an attraction between the particle surfaces. This attraction has a range of approximately 3 nm and a magnitude of 1 nN, values that are in good agreement with recent AFM experiments. These predictions are stable with respect to small changes in surface-surface separation, hydrated ion radius, and dielectric constant of the solution. The model also describes the effect of changes in cement composition through the introduction of other ions, either monovalent (Na) or multivalent (aluminum or iron hydroxide).     

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.     

Simulation of electric double layers undergoing charge inversion: mixtures of mono- and multivalent ions

In this paper, the electric double layer (EDL) of a charged plane in the presence of mixtures of 1:1 and 3:1 electrolytes has been investigated through Monte Carlo (MC) simulations using a nonrestrictive primitive model of EDL. In particular, the charge inversion in colloids (attributable to an accumulation of counterions on the surface) can be better understood by means of the simulations performed here. Moreover, two mechanisms proposed for charge inversion are probed: The formation of a strongly correlated layer (SCL) of multivalent counterions and excluded volume effects (to which we will also refer as ion size correlations). Our results are in agreement with the behavior found experimentally for some model colloids with increasing the concentration of monovalent salt in the presence of trivalent ions, which clearly supports the relevance of ion size correlations. In contrast, certain disagreement with predictions of SCL theories is reported.     

Repulsion between oppositely charged macromolecules or particles

The interaction of two oppositely charged surfaces has been investigated using Monte Carlo simulations and approximate analytical methods. When immersed in an aqueous electrolyte containing only monovalent ions, two such surfaces will generally show an attraction at large and intermediate separations. However, if the electrolyte solution contains divalent or multivalent ions, then a repulsion can appear at intermediate separations. The repulsion increases with increasing concentration of the multivalent salt as well as with the valency of the multivalent ion. The addition of a second salt with only monovalent ions magnifies the effect. The repulsion between oppositely charged surfaces is an effect of ion-ion correlations, and it increases with increasing electrostatic coupling and, for example, a lowering of the dielectric permittivity enhances the effect. An apparent charge reversal of the surface neutralized by the multivalent ion is always observed together with a repulsion at large separation, whereas at intermediate separations a repulsion can appear without charge reversal. The effect is hardly observable for a symmetric multivalent salt (e.g., 2:2 or 3:3).     

Reentrant behavior of grafted poly(sodium styrenesulfonate) chains investigated with a quartz crystal microbalance

Poly(sodium styrenesulfonate) (PSSNa) chains have been grafted onto a SiO(2)-coated resonator surface. The conformational changes of grafted chains have been investigated using a quartz crystal microbalance with dissipation (QCM-D) in the presence of monovalent or multivalent salts as a function of ionic strength. In the case of monovalent counterions, the changes in frequency (Δf) and dissipation (ΔD) indicate that the highly extended PSSNa chains first shrink into a loose and inhomogeneous layer as the ionic strength increases. As the ionic strength increases further, the chains will collapse and form a denser and more homogeneous layer. In the case of divalent or trivalent counterions, the grafted PSSNa chains also collapse into a dense layer as the ionic strength increases. However, when the ionic strength is above a critical value, the chains would re-expand so that the layer becomes partially extended due to the charge inversion. Additionally, the effect of ion-specificity on the conformational changes of the chains has also been examined.     

Competition between Monovalent and Divalent Counterions in Surfactant Systems

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

The wall and multivalent counterion effects on the electrostatic force between like-charged spherical particles confined in a charged pore

The effect of wall confinement (wall charge and wall-sphere separation distance) on the electrostatic force between two charged spheres confined in a long charged pore in symmetric and asymmetric electrolytes have been quantified by solving the nonlinear Poisson-Boltzmann equation (PBE), using adaptive finite elements combined with error minimization techniques. The computed force indicated the strong effect of the wall potential on the reduction of the repulsive force for all type of electrolytes. The influence of the wall effect was reduced when the valence of the electrolyte was increased. A significant reduction in the repulsive force between the two spheres was also observed when the distance between the pore wall and the sphere surface was reduced. A smaller long-range repulsive interaction was observed between spheres when the solutions contained multivalent counterions as compared with a monovalent solution. However, at short ranges of separation distances multivalent counterions increase the electrostatic repulsive force between the spheres. The effect of the dimensionless radius of the spheres on the electrostatic force between them has been determined and a significant reduction observed as the dimensionless radius was reduced.     

Ion aggregation in polymer gels

This brief review deals with our early experimental studies of ion aggregation in polymer gels proceeding via the condensation of counterions on the oppositely charged monomer units of the network with the formation of ion pairs and their clustering into multiplets. The two particular cases of the emergence of ion aggregates are considered: (a) for monovalent counterions in media of low polarity and (b) for multivalent counterions in water.     

Molecular dynamics simulations of end‐grafted polymers with charged side chains

We report molecular dynamics simulations on bottle‐brush polyelectrolytes end‐grafted to a planar surface. For each bottle‐brush polyelectrolyte, flexible charged side chains are anchored to one neutral main chain. The effects of the counterion valence and the grafting density on the density profiles and the structural characteristics of the brush were studied in this work. It is found that the electrostatic repulsion between charged monomers in the side chains leads an extended conformation of the brush in a solution containing monovalent counterions, while strong electrostatic binding of multivalent counterions to the side chains has a significant contribution to the collapse of the brush. For the trivalent case, the distribution of end monomers in the main chains becomes broader upon decreasing the grafting density, as compared with the monovalent case. However, the position of the distribution for the monovalent case is relatively insensitive to the change of the grafting density. Additionally, with increased counterion valence, enhanced electrostatic correlation between counterions and charged side chains also weakens the diffusive ability of counterions. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Effects of image charges, interfacial charge discreteness, and surface roughness on the zeta potential of spherical electric double layers

We investigate the effects of image charges, interfacial charge discreteness, and surface roughness on spherical electric double layer structures in electrolyte solutions with divalent counterions in the setting of the primitive model. By using Monte Carlo simulations and the image charge method, the zeta potential profile and the integrated charge distribution function are computed for varying surface charge strengths and salt concentrations. Systematic comparisons were carried out between three distinct models for interfacial charges: (1) SURF1 with uniform surface charges, (2) SURF2 with discrete point charges on the interface, and (3) SURF3 with discrete interfacial charges and finite excluded volume. By comparing the integrated charge distribution function and the zeta potential profile, we argue that the potential at the distance of one ion diameter from the macroion surface is a suitable location to define the zeta potential. In SURF2 model, we find that image charge effects strongly enhance charge inversion for monovalent interfacial charges, and strongly suppress charge inversion for multivalent interfacial charges. For SURF3, the image charge effect becomes much smaller. Finally, with image charges in action, we find that excluded volumes (in SURF3) suppress charge inversion for monovalent interfacial charges and enhance charge inversion for multivalent interfacial charges. Overall, our results demonstrate that all these aspects, i.e., image charges, interfacial charge discreteness, their excluding volumes, have significant impacts on zeta potentials of electric double layers.     

Stability of dispersions in polar media

The stability of dispersions in polar organic media was reviewed comparing with that of in aqueous and non-polar media. Structure and properties of the double layer of AgI in water-ethylene glycol were studied and the stability of the dispersions was related to the study of the double layer.Coagulation concentrations of Ag,AgI and α-FeOOH dispersions in methanol, ethanol 1,2-propanol and acetone by the addition of electrolytes were determined.Coagulation by monovalent counterions is due to double layer compression. With bi- and multivalent counterions or in low dielectric constant-solvents coagulation is primarily caused by charge neutralization.The effect of an ionic surfactant, AOT on the stability of TiO₂ or α-Fe₂O₃ in water-p-dioxane mixtures was studied. AOT behaved as a coagulating agent in polar media ( ϵ = 10–50) , though it worked as a dispersing agent in non-polar (dioxane) and water rich media. AOT accordingly coagulated the dispersion a carbon black in 2-butanone, though a nonionic surfactant did not so. Desolvation from the particle surface is considered to be an important origin of coagulation by AOT in polar media, because AOT is not adsorbed on particles and comsiderably dissociates into ions in 2-butanone.