Streaming potentials and conductivities of latex plugs. Influence of the valency of the counterion

Plugs consisting of polystyrene particles with sulphonate surface groups have been investigated in the presence of mono-, di- and trivalent counterions. The streaming potentials and conductivities of the plug and bulk solution have been measured. From the latter, the overall surface conductivity has been estimated. It is shown that for this system, accounting for the surface conductivity in the hydrodynamically stagnant layer is crucial to convert the streaming potentials into zeta potentials. The overall surface conductivity clearly depends on the charge of the counterion, and so do the ionic mobilities in the stagnant layer. The higher the valency of the counterion, the lower is the ionic mobility in the stagnant layer, but for all counterions, the ionic mobility in the stagnant layer is of the same order of magnitude as in the bulk. For the divalent counterions, no indications of specific interactions with the surface groups have been found.     

Overcharging of nanoparticles in electrolyte solutions

Monte Carlo simulations are performed to investigate the effects of salt concentration, valence and size of small ions, surface charge density, and Bjerrum length on the overcharging of isolated spherical nanoparticles within the framework of a primitive model. It is found that charge inversion is most probable in solutions containing multivalent counterions at high salt concentrations. The maximum strength of overcharging occurs near the nanoparticle surface where counterions and coions have identical local concentrations. The simulation results also suggest that both counterion size and electrostatic correlations play major roles for the occurrence of overcharging.     

Simulation of electric double layers with multivalent counterions: ion size effect

In this paper, the structure of the electric double layer in the presence of (mostly) multivalent counterions is investigated through Monte Carlo simulations. Unlike previous similar studies addressing this matter, the difference of this study lies in the use of realistic hydrated ion sizes. Additionally, two different methods for calculating energies in the Metropolis algorithm are applied. The obtained results show that the conclusions of preceding papers must be revised. In particular, our simulations suggest the existence of certain ion layering effects at high surface charge densities, which are not accounted for by integral equation theories in the case of divalent counterions. These layering effects could justify why the overcharging phenomena due to ion size correlations are hardly observable in real colloids with divalent counterions. The existence of charge inversion due to ion size correlations (and without requiring specific counterion adsorption) is probed for trivalent counterions. Moreover, the hypernetted-chain/mean-spherical-approximation is tested under conditions not studied yet.     

Molecular dynamics simulation of discontinuous volume phase transitions in highly-charged crosslinked polyelectrolyte networks with explicit counterions in good solvent

The volumetric properties of highly-charged defect-free polyelectrolyte networks with tetrafunctional crosslinks are studied through molecular dynamics simulations in the canonical ensemble. The network backbone monomers, which are monovalent, and the counterions, which are mono-, di-, or trivalent, are modeled explicitly in the simulations, but the solvent is treated implicitly as a dielectric medium of good solvation quality. The osmotic pressure of the network-solvent system is found to depend greatly on the strength of electrostatic interactions. Discontinuous volume phase transitions are observed when the electrostatic interactions are strong, and the onset of these transitions shifts to higher solvent dielectricity as the counterion valency increases. The roles of the various virial contributions to the osmotic pressure are examined. The network elasticity entropy is found to behave nearly classically. As the network contracts and collapses with increasing strength of electrostatic interactions, the loss of counterion entropy leads to increased counterion osmotic pressure contributions via two mechanisms. The reduction in available configurational space increases the counterion translational entropy contribution to the ideal part of the osmotic pressure, and the greater number of counterion-monomer contacts formed due to counterion condensation and confinement increases the counterion excluded-volume entropy contribution to the excess part of the osmotic pressure. These observations contrast the decrease in the single ideal-gas-like counterion translational entropy contribution to the osmotic pressure predicted by the counterion condensation-charge renormalization theory. An accompanying decrease in the total electrostatic energy balances the loss of counterion excluded-volume entropy as the polyelectrolyte networks collapse in low-dielectric solvents. This interplay between the electrostatic energy and the counterion excluded-volume entropy appears to be responsible for the discontinuous volume phase transitions that are observed in polyelectrolyte networks. The structure of the polyelectrolyte network is also found to be affine in the swollen state, with constituent chains nearly fully extended, and nonaffine in the collapsed state, with the chains adopting a Gaussian conformation.     

Langevin dynamics of semiflexible polyelectrolytes: rod-toroid-globule-coil structures and counterion distribution

We have investigated the nature of counterion condensation on uniformly charged semiflexible polyelectrolyte chains and the concomitant configurations by monitoring the role of chain stiffness, chain length, counterion valency, and the strength of electrostatic interaction. The counterion condensation is seen to follow the adsorption process and the effective polymer charge increases with chain stiffness. Size and shape, as calculated through the radius of gyration, effective persistence length, and hydrodynamic radius, are studied. Stable coil-like, globular, folded-chain, toroidal, and rodlike configurations are possible at suitable combinations of values of chain stiffness, chain length, electrostatic interaction strength, and the valency of counterion. For high strengths of electrostatic interactions, sufficiently stiff polyelectrolytes form toroids in the presence of multivalent counterions, whereas flexible polyelectrolytes form disordered globules. The kinetic features of the nucleation and growth of toroids are monitored. Several metastable structures are found to frustrate the formation of toroids. The generic pathway involves the nucleation of one primary loop somewhere along the chain contour, followed by a growth process where the rest of the chain is folded continuously on top of the primary loop. The dependence of the average radii of toroids on the chain length is found to be roughly linear, in disagreement with existing scaling arguments.     

Molecular dynamics and neutron scattering study of the dependence of polyelectrolyte dendrimer conformation on counterion behavior

Atomistic molecular dynamics (MD) simulations and contrast variation small angle neutron scattering (SANS) have been combined to investigate the Generation-5 polyelectrolyte polyamidoamine starburst dendrimer. This work reveals the dendrimer conformational dependence on counterion association at different levels of molecular charge. The accuracy of the simulations is verified through satisfactory comparison between modeled results, such as excess intra-dendrimer scattering length density distribution and hydration level, and their experimental counterparts. While the counterion distributions are not directly measureable with SANS, the spatial distribution of the counterions and their dendrimer association are extracted from the validated MD equilibrium trajectories. It is found that the conformation of the charged dendrimer is strongly dependent on the counterion association. Sensitivity of the distribution of counterions around charged amines to the counterion valency is qualitatively explained by adopting Langmuir adsorption theory. Moreover, via extending the concept of electrical double layer for compact charged colloids, we define an effective radius of a charged dendrimer including the spatial distribution of counterions in its vicinity. Within the same framework, the correlation between the strength of intra-dendrimer electrostatic repulsion and the counterion valency and dynamics is also addressed.     

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.     

Phase behavior of cetyltrimethylammonium surfactants with oligo carboxylate counterions mixed with water and decanol: attraction between charged planes or spheres with oligomeric counterions

Cetyltrimethylammonium surfactants with a range of oligo carboxylate anions bearing 2, 3, or 4 negative charges have been synthesized, and their respective behaviors in binary mixtures with water and in ternary mixtures with added decanol have been investigated. In binary mixtures with water, all surfactants formed nearly spherical micelles at high water contents; however, the interactions between micelles varied strongly with the number of charges in the counterion. Micelles with divalent counterions were generally miscible with water, whereas micelles with tri- or tetravalent counterions demixed in one concentrated and one dilute phase. Addition of decanol resulted in all cases in the appearance of a lamellar phase, and all investigated oligo carboxylate anions (di-, tri-, and tetravalent) gave rise to a strong attraction between the lamellar planes, resulting in a limited swelling (up to 35-40 wt % water) of the lamellar phase in contact with excess water. These experiments confirm the theoretically predicted influence of aggregate geometry (spheres or planes) on the attraction between colloidal aggregates neutralized by multivalent counterions. Further addition of decanol resulted in the appearance of a second birefringent phase in equilibrium with the lamellar phase. SWAXS showed this phase to be lamellar and to display short-range order that disappeared upon heating. This phase is identified as a lamellar gel phase (Lbeta-phase).     

Aggregation and adsorption of sodium dioctylsulfosuccinate in aqueous ammonium chloride solution: role of mixed counterions

The critical micelle concentration (cmc) of sodium dioctylsulfosuccinate (AOT) was determined at 25 °C from surface tension and fluorescence methods in aqueous NH(4)Cl solution for assessing the influence of mixed counterions on the special counterion binding behavior (SCB) of AOT. The SCB of AOT refers to a sudden twofold increase in the value of the counterion binding constant (β) in aqueous medium when the concentration (c(*)) of the added 1:1 sodium salt is about 0.015 mol kg(-1), and it has been tested so far for sodium ion only. In the presence of sodium and ammonium mixed counterions also the SCB of AOT exist, but with lower c(*) (0.009 mol kg(-1) NH(4)Cl). Synergism in the cmc occurs due to mixed counterions. In the case of inorganic counterions, unlike the case with organic counterions, the cmc is dependent on the total counterion concentration in solution and negligibly on the specific type of counterion. Na(+) and NH(4)(+) bind almost equally to the micelle in the region of low β (below c(*)), but in the region of high β (above c(*)) NH(4)(+) binds predominantly. It has been shown that the theoretical expression for the surface excess of ionic surfactant+electrolyte system containing a single counterion can also be used to evaluate the surface excess in the presence of mixed counterions if the two counterions are considered to undergo Henry-type adsorption at the air-solution interface.     

Experimental study of electrostatically stabilized colloidal particles: colloidal stability and charge reversal

We consider the interaction of colloidal spheres in the presence of mono-, di-, and trivalent ions. The colloids are stabilized by electrostatic repulsion due to surface charges. The repulsive part of the interaction potential Ψ(d) is deduced from precise measurements of the rate of slow coagulation. These "microsurface potential measurements" allow us to determine a weak repulsion in which Ψ(d) is of the order of a few k(B)T. These data are compared to ζ potential measured under similar conditions. At higher concentrations both di- and trivalent counterions accumulate at the very proximity of the particle surface leading to charge reversal. The salt concentration c(cr) at which charge reversal occurs is found to be always above the critical coagulation concentration c(ccc). The analysis of Ψ(d) and of the ζ potential demonstrates, however, that adsorption of multivalent counterions starts far below c(cr). Hence, colloid stability in the presence of di- and trivalent ions cannot be described in terms of a DLVO ansatz assuming a surface charge that is constant with regard to the ionic strength.     

Influence of the diffuse layer overcharging or undercharging on the stability of charged interfaces: a restricted grand canonical Monte Carlo study

We have applied a restricted grand canonical Monte Carlo procedure to describe, in the framework of the primitive model, the counterion exchange mechanism between diffuse layers of counterions surrounding segregated charged lamellae. The net charge transfer between the dense and dilute domains is shown to vary as a function of the valence of the neutralizing counterions: undercharging of the dense interlayer is detected in the presence of monovalent counterions and overcharging with divalent counterions. Furthermore, no net reduction of the swelling pressure is detected for monovalent counterions, while a large enhancement of the net interlamellar attraction is found for charged lamellae neutralized by divalent counterions.     

Interaction of similarly charged surfaces mediated by nanoparticles

We study the interaction between two like charged surfaces embedded in a solution of oppositely charged multivalent rod-like counterions.The counterions consist of two rigidly bonded point charges,each of valency Z.The strength of the electrostatic coupling increases with increasing surface charge density or valency of the charges.The system is analyzed by employing a self-consistent field theory,which treats the short and long range interactions of the counterions within different approximations.We find that in the weak coupling limit,the interactions are only repulsive.In the intermediate coupling regime,the multivalent rod-like counterions can mediate attractive interactions between the surfaces. For sufficiently long rods,bridging contributes to the attractive interaction.In the strong coupling limit,the charge correlations can contribute to the attractive interactions at short separations between the charged surfaces.Two minima can then appear in the force curve between surfaces.     

Chain stiffness, salt valency, and concentration influences on titration curves of polyelectrolytes: Monte Carlo simulations

Monte Carlo simulations have been used to study two different models of a weak linear polyelectrolyte surrounded by explicit counterions and salt particles: (i) a rigid rod and (ii) a flexible chain. We focused on the influence of the pH, chain stiffness, salt concentration, and valency on the polyelectrolyte titration process and conformational properties. It is shown that chain acid-base properties and conformational properties are strongly modified when multivalent salt concentration variation ranges below the charge equivalence. Increasing chain stiffness allows to minimize intramolecular electrostatic monomer interactions hence improving the deprotonation process. The presence of di and trivalent salt cations clearly promotes the chain degree of ionization but has only a limited effect at very low salt concentration ranges. Moreover, folded structures of fully charged chains are only observed when multivalent salt at a concentration equal or above charge equivalence is considered. Long-range electrostatic potential is found to influence the distribution of charges along and around the polyelectrolyte backbones hence resulting in a higher degree of ionization and a lower attraction of counterions and salt particles at the chain extremities.     

Testing one component plasma models on colloidal overcharging phenomena

In this paper, the mechanisms of overcharging of a colloidal macroion in the presence of multivalent counterions are investigated by means of Monte Carlo simulations. This computational technique appears as a powerful tool for probing the validity of semianalytical models developed for this issue. In particular, the simulations performed are compared with the predictions of two different models based on the one component plasma (OCP) theory. Therein, the multivalent ionic atmosphere confined at the macroion surface is approximated by a two-dimensional Wigner crystal. These kinds of models are largely used in the literature since (in some cases) they present quite simple equations to describe the electric double layer (EDL) of macroions with different geometries in the presence of much smaller (but still multivalent) ions. In this sense, charge inversion phenomena of membranes, polyelectrolytes, DNA molecules, etc., are straightforwardly predicted in terms of these expressions. Unfortunately, comparisons between these predictions and experimental results are scarce, mostly due to the difficulty to reproduce the experimental conditions in the laboratory. Accordingly, the goal of the present paper is to simulate EDLs under real conditions (in which overcharging phenomena are expected to happen) and use the results obtained in this way for comparing with those obtained from OCP models.     

Probing multivalent interactions in a synthetic host-guest complex by dynamic force spectroscopy

Multivalency is present in many biological and synthetic systems. Successful application of multivalency depends on a correct understanding of the thermodynamics and kinetics of this phenomenon. In this Article, we address the stability and strength of multivalent bonds with force spectroscopy techniques employing a synthetic adamantane/β-cyclodextrin model system. Comparing the experimental findings to theoretical predictions for the rupture force and the kinetic off-rate, we find that when the valency of the complex is increased from mono- to di- to trivalent, there is a transition from quasi-equilibrium, with a constant rupture force of 99 pN, to a kinetically dependent state, with loading-rate-dependent rupture forces from 140 to 184 pN (divalent) and 175 to 210 pN (trivalent). Additional binding geometries, parallel monovalent ruptures, single-bound divalent ruptures, and single- and double-bound trivalent ruptures are identified. The experimental kinetic off-rates of the multivalent complexes show that the stability of the complexes is significantly enhanced with the number of bonds, in agreement with the predictions of a noncooperative multivalent model.     

Micellization and interfacial properties of alkyloxyethylene sulfate surfactants in the presence of multivalent counterions

Alkyloxyethylene sulfates are a special class of surfactants that are unusually stable in the presence of multivalent counterions and are not as prone to precipitation as anionic surfactants without intermediate ethoxy groups in the molecule. However, formation of micelles, their structure, and the properties of monolayers of these surfactants exhibit very interesting and sometimes unexpected properties depending on the nature of the ions dissolved in the solution. This paper presents a brief overview of our recent efforts to reveal the nature of these properties, including some new results. We show that the strong binding of multivalent (and particularly trivalent counterions) triggers a sphere-to-cylinder shape transition of the micelles and facilitates their further growth, even at very low ionic strength. The properties of surfactant monolayers are coupled to those of the micelles in the bulk and are governed also by multivalent counterion binding. The effect of multivalent counterions on the aggregation and structure formation in anionic surfactant solutions has both fundamental and practical importance.     

Kinetics study of the binding of multivalent ligands on size-selected gold nanoparticles

The effect of ligand multivalency and nanoparticle size on the binding kinetics of thiol ligands on gold nanoparticles is investigated by exchanging monovalently bound pyrene on gold nanoparticles against flexible mono- and multivalent thiol ligands. Variable-sized gold nanoparticles of 2.2 ± 0.4, 3.2 ± 0.7, and 4.4 ± 0.9 nm diameter are used as substrates. The particles are coated by thiol functionalized pyrene ligands and the binding kinetics of the thiol ligands is studied by time-resolved fluorescence spectroscopy. The effect of multivalency on the binding kinetics is evaluated by comparing the rate constants of ligands of different valency. This comparison reveals that the multivalent ligands are exchanging substantially more rapidly than the monovalent ones. A particle size dependence of the rate constants is also observed, which is used to derive structural information on the binding of the mono- and multivalent ligands to the nanoparticle surface.     

Counterion binding behaviour of micelles of sodium dodecyl sulphate and bile salts in the pure state,in mutually mixed states and mixed with a nonionic surfactant

The counterion binding behaviour of micelles of sodium dodecyl sulphate (SDS) and several bile salts in the pure state have been studied, as well as in mutually mixed states, and in a mixed state with polyoxyethylene sorbitan monolaurate (PSML) as a nonionic surfactant. Electrochemical measurements have shown no counterion binding by the pure bile salt micelles and their mixtures with PSML; they can bind counterions when mixed with SDS, whereas the surfactant anions of SDS micelles bind counterions in the pure state and/or in mixed states with PSML. In the SDS-PSML and SDS-bile salts combinations, the counterion association is decreased by the increased proportions of the second component. The extent of counterion binding by the different systems is presented.