Excluded volume driven counterion condensation inside nanotubes in a concave electrical double layer model

The physical properties of organic nanotubes attract increasing attention due to their potential benefit in technology, biology and medicine. We study the effect of ion size on the electrical properties of cylindrical nanotubes filled with electrolyte solution within a modified Poisson-Boltzmann (PB) approach. For comparison purposes, small hollow nanospheres filled with electrolyte solution are considered. The finite size of the particles in the inner electrolyte solution is described by the excluded volume effect within a lattice statistics approach. We found that an increased ion size reduces the number of counterions near the charged inner surface of the nanotube, leading to an enlarged electrostatic surface potential. The concentration of counterions close to the inner surface saturates for higher surface charge densities and larger ions. In the case of saturation, the closest counterion packing is achieved, all lattice sites near the surface are occupied and an actual counterion condensation is observed. By contrast, the counterion concentration at the axis of the nanotube steadily increases with increasing surface charge density. This growth is more pronounced for smaller nanotube radii and larger ions. At larger nanotube radii for small ion size counterion condensation may also be observed according to the Tsao criterion, i.e. the counterion concentration at the centre is independent of the number of counterions in the system. With decreasing radius the Tsao condensation effect is shifted towards physiologically unrealistic surface charge densities.     

Simulation of the electrical double layer of a macroion with different counterion charges

An electrical double layer of a spherical macroion with single-, double-, and triple-charged counterions in aqueous solution of 1: 1 background electrolyte at different concentrations are studied by the molecular dynamics method for models with discrete and continuous surface charge distribution. Radial profiles of ion partial densities and the electric potential distribution in the double layer are calculated. The degree of counterion binding with a macroion is determined. The effect of water permittivity on the structure of electrical double layer is studied.     

Explanation of Ionic Sequences in Various Phenomena. II. Reversal of Colloid Charge and Ion Binding

Abstract

Previous proposed models for the structure of hydrated ions and the calculated values of the effective dielectric constant of such hydrated ions were used to explain the reversal of colloid charge and ion binding phenomena. In contrast to the conclusions made by Bungenberg de Jong, it is shown that the more soluble the counter -cation or counter-anion of a colloid charge, the greater is the ability of the counterion to reverse the electrical charge of the colloid. The reversal of charge phenomenon is therefore associated with the counterions's solubility, not its insolubility. The solubility sequence is determined by whether or not the carboxylate, sulfate, or phosphate ion is positively (A regions) or negatively hydrated. The phosphate group of DNA or RNA must be associated with a base by means of ion-ion bonds in order to produce the observed reversal of charge sequence. Just as in the reversal of charge phenomenon, the ion-binding phenomenon involves the electrostatic attraction of a counterion with the polyelectrolyte rather than a binding or insolubilization of the counterion. The reverse ion-binding sequence can be obtained if one dialyzes extensively in the presence of sufficient salt before physical measurements are made. This is because the solubility of a counterion determines the true electrostatic charge of the polymer. In other words, different concentrations of salt arise in the dialysis bag when different counter-ions are added because the activity coefficient of the counterion is determined by the solubility of the ion-ion complex between the counterion and the colloid′s charged group.     

Molecular Dynamics Simulation of the Electrical Double Layer of Spherical Macroion

The structure of the electrical double layer (EDL) of a spherical macroion with a total charge of 60 elementary charges is studied by molecular dynamics methods. In calculations we used two models: continuous and discrete. In the continuous model, the total charge was concentrated in the center of the macroion; in the discrete model, elementary charges were randomly distributed over the surface of the macroion. The radial profiles of local densities and electric potential in EDL, as well as the degree of counterion binding by the macroion, are calculated with allowance for the Lennard-Jones and electrostatic interactions. It is established that the character of charge distribution significantly affects the EDL structure near the macroion, whereas its effect is much weaker at larger distances. The results obtained are compared with the experimental data on the surface potential and the diffuse part of EDL of sodium dodecyl sulfate micelles in aqueous solution, as well as on the micelle-bound charge. It is shown that even weak specific interaction between counterions and a macroion can substantially influence the structure of its EDL.     

How accurate is Poisson-Boltzmann theory for monovalent ions near highly charged interfaces?

Surface sensitive synchrotron X-ray scattering studies were performed to obtain the distribution of monovalent ions next to a highly charged interface. A lipid phosphate (dihexadecyl hydrogen-phosphate) was spread as a monolayer at the air-water interface to control surface charge density. Using anomalous reflectivity off and at the L3 Cs+ resonance, we provide spatial counterion (Cs+) distributions next to the negatively charged interfaces. Five decades in bulk concentrations are investigated, demonstrating that the interfacial distribution is strongly dependent on bulk concentration. We show that this is due to the strong binding constant of hydronium H3O+ to the phosphate group, leading to proton-transfer back to the phosphate group and to a reduced surface charge. The increase of Cs+ concentration modifies the contact value potential, thereby causing proton release. This process effectively modifies surface charge density and enables exploration of ion distributions as a function of effective surface charge-density. The experimentally obtained ion distributions are compared to distributions calculated by Poisson-Boltzmann theory accounting for the variation of surface charge density due to proton release and binding. We also discuss the accuracy of our experimental results in discriminating possible deviations from Poisson-Boltzmann theory.     

Counterion volume effects in mixed electrical double layers

When a monolayer of negatively charged surfactant molecules is brought in contact with an aqueous solution containing mixtures of counterions of different size and valency, very large deviations from Poisson-Boltzmann theory (PBT) develop at a high surface charge, with the smaller counterion outcompeting the larger one (even if divalent) near the interface, leading to counterion segregation [V.L. Shapovalov, G. Brezesinski, J. Phys. Chem. B 110 (2006) 10032]. We use a modified PBT that empirically includes an extended Carnahan-Starling equation-of-state to describe hard-sphere interactions in electrical double layers containing ions of different size and charge. Model calculations are made for ion concentration profiles, free energies, surface pressures, and differential capacities. At high surface charge, volume interactions become important, leading to significant deviations from PBT. In contrast to PBT, at high surface charge, contributions to energy and pressure are no longer mainly entropic, but instead volume and electrostatic field effects now dominate. When the hydrated size of the divalent ion is used as an adjustable parameter, the theory is in good agreement with the experimental data.     

Solution properties of ion-containing polymers in polar solvents

The placement of ionic groups within the molecular structure of a polymer produces marked modification in physical properties. A large number of studies have been performed on these ion-containing polymers, but few have focused on the effects of anion–cation interactions (i.e., counterion binding or ionization) on hydrodynamic volume, especially as the molecular structure of the solvent and nature of counterion are varied. In this study changes in hydrodynamic volume are followed through reduced viscosity measurements as a function of the abovementioned molecular parameters. The dilute solution properties of various polyelectrolytes that contain sulfonate and carboxylate groups were investigated as a function of the counterion structure, charge density, molecular weight, and solvent structure. The polymeric materials were selected because of their specific chemical structure and physical properties. In the first instance a (2-acrylamide-2 methylpropanesulfonic acid)-acrylamide-sodium vinyl sulfonate terpolymer was synthesized and subsequently neutralized with a series of bases. Viscometric measurements on these materials indicate that the nature of the cation affects the ability of the polyelectrolyte to expand its hydrodynamic volume at low polymer levels. The magnitude of the molecular expansion is shown to be due in part to the ability of the counterion to dissociate from the backbone chain, which, in turn, is directly related to the solvent structure. The changes in solution behaviour of these inomers lend support for the existence of ion pairs (i.e., site binding) and ionized moieties on the polymer chains. Measurements performed in a variety of solvent systems further confirm this interpretation. In addition, and acrylamide-sodium vinyl sulfonate copolymer was partially hydrolyzed with sodium hydroxide to study the effect of varying the charge density at a constant degree of polymerization and counterion structure. The results show that the charge density has a significant effect on the magnitude of the reduced viscosity and dilute solution behaviour. These observations, made in aqueous and nonaqueous solvents, are related to the interrelation of hydrodynamic volume, counterion concentration, and site binding. Again the controlling factor is the degree of site binding of the counterion onto the polymer backbone. Finally, we observe that the increased hydrodynamic volume affects viscosity behavior beyond the polyelectrolyte effect regime. If the average charge density on the macromolecule is relative high and/or the molecular weight is large (≥ 10⁶) sufficient intermolecular interactions will occur to produce rapid changes in reduced viscosity.     

A model for self-diffusion of guanidinium-based ionic liquids: a molecular simulation study

We propose a novel self-diffusion model for ionic liquids on an atomic level of detail. The model is derived from molecular dynamics simulations of guanidinium-based ionic liquids (GILs) as a model case. The simulations are based on an empirical molecular mechanical force field, which has been developed in our preceding work, and it relies on the charge distribution in the actual liquid. The simulated GILs consist of acyclic and cyclic cations that were paired with nitrate and perchlorate anions. Self-diffusion coefficients are calculated at different temperatures from which diffusive activation energies between 32-40 kJ/mol are derived. Vaporization enthalpies between 174-212 kJ/mol are calculated, and their strong connection with diffusive activation energies is demonstrated. An observed formation of cavities in GILs of up to 6.5% of the total volume does not facilitate self-diffusion. Instead, the diffusion of ions is found to be determined primarily by interactions with their immediate environment via electrostatic attraction between cation hydrogen and anion oxygen atoms. The calculated average time between single diffusive transitions varies between 58-107 ps and determines the speed of diffusion, in contrast to diffusive displacement distances, which were found to be similar in all simulated GILs. All simulations indicate that ions diffuse by using a brachiation type of movement: a diffusive transition is initiated by cleaving close contacts to a coordinated counterion, after which the ion diffuses only about 2 A until new close contacts are formed with another counterion in its vicinity. The proposed diffusion model links all calculated energetic and dynamic properties of GILs consistently and explains their molecular origin. The validity of the model is confirmed by providing an explanation for the variation of measured ratios of self-diffusion coefficients of cations and paired anions over a wide range of values, encompassing various ionic liquid classes as well as the simulated GILs. The proposed diffusion model facilitates the qualitative a priori prediction of the impact of ion modifications on the diffusive characteristics of new ionic liquids.     

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.     

Surface charge density and electrokinetic potential of highly charged minerals: experiments and Monte Carlo simulations on calcium silicate hydrate

In this paper, we are concerned with the charging and electrokinetic behavior of colloidal particles exhibiting a high surface charge in the alkaline pH range. For such particles, a theoretical approach has been developed in the framework of the primitive model. The charging and electrokinetic behavior of the particles are determined by the use of a Monte Carlo simulation in a grand canonical ensemble and compared with those obtained through the mean field theory. One of the most common colloidal particles has been chosen to test our theoretical approach. That is calcium silicate hydrate (C-S-H) which is the main component of hydrated cement and is known for being responsible for cement cohesion partly due to its unusually high surface charge density. Various experimental techniques have been used to determine its surface charge and electrokinetic potential. The experimental and simulated results are in excellent agreement over a wide range of electrostatic coupling, from a weakly charged surface in contact with a reservoir containing monovalent ions to a highly charged one in contact with a reservoir with divalent ions. The electrophoretic measurements show a charge reversal of the C-S-H particles at high pH and/or high calcium concentration in excellent agreement with simulation predictions. Finally, both simulation and experimental results clearly demonstrate that the mean field theory fails not only quantitatively but also qualitatively to describe a C-S-H dispersion under realistic conditions.     

The influence of an acid treatment on the surface charge density of silica gel

The influence of an acid treatment on the pore structure as well as on the surface charge density of porous silica was investigated. It is shown that this treatment causes only small changes of the pore structure. Positive values of the surface charge density at pH>4 are interpreted in terms of surface impurities consisting of Na⁺ ions resulting from the synthesis of the gel from sodium silicate solution. This effect is strongly influenced by the acid treatment. The surface charge density parameters were evaluated on the basis of the triple-layer model for the electrical double layer. Here two different mechanisms of counterion attachment in the inner Helmholtz plane are discussed.     

Investigation of the electrokinetic properties of paraffin suspension. 1. In inorganic electrolyte solutions

Although electrical properties of nonionogenic hydrophobic surface (solid or liquid) in water and/or electrolyte solutions have been studied for many decades, they are still not well recognized, especially as for the nature of the charge and potential origin. Similarly, water structure at such a surface is still extensively studied. One such system is paraffin wax/water (electrolyte). The zeta potentials and the particle diameters of this system were investigated in this paper. To obtain the suspension of paraffin in water or electrolyte solution (NaCl or LaCl3), the mixture was heated to ca. 70 degrees C and then stirred during cooling. For thus obtained suspensions, the zeta potential was determined as a function of time at 20 degrees C. Also the pH effect on the zeta potentials was investigated. The zeta potentials were calculated from Henry's equation. The results obtained by us are in agreement with those obtained earlier by others. They confirm that although H+/OH- are not surface charge creating ions, OH- ions to some extent are zeta potential determining for the paraffin surface. By use of the potentials and diameters, the electric charge for a spherical particle in the shear plane was calculated. These values are small in the range of 10(-3) C/m2. On the basis of the findings of water structure near hydrophobic surface and the calculated charges, it is concluded that in fact the potential may be created by immobilized and oriented water dipoles.     

Surface charge density/surface potential relationship for a spherical colloidal particle in a salt-free medium

On the basis of a theory of Imai and Oosawa (Busseiron Kenkyu52, 42 (1952); 59, 99 (1953)), approximate analytic expressions for the surface charge density/surface potential relationship for a spherical colloidal particle in a salt-free (aqueous or nonaqueous) medium containing only counterions are derived. There is a certain critical value of the surface charge density (or the total surface charge) separating two distinct cases: low surface charge density case and high surface charge density case. In the latter case counterion condensation occurs in the vicinity of the particle surface. The results are in excellent agreement with numerical calculations for the case of dilute suspensions.     

Self-doping of molecular quantum-dot cellular automata: mixed valence zwitterions

Molecular quantum-dot cellular automata (QCA) is a promising paradigm for realizing molecular electronics. In molecular QCA, binary information is encoded in the distribution of intramolecular charge, and Coulomb interactions between neighboring molecules combine to create long-range correlations in charge distribution that can be exploited for signal transfer and computation. Appropriate mixed-valence species are promising candidates for single-molecule device operation. A complication arises because many mixed-valence compounds are ions and the associated counterions can potentially disrupt the correct flow of information through the circuit. We suggest a self-doping mechanism which incorporates the counterion covalently into the structure of a neutral molecular cell, thus producing a zwitterionic mixed-valence complex. The counterion is located at the geometrical center of the QCA molecule and bound to the working dots via covalent bonds, thus avoiding counterion effects that bias the system toward one binary information state or the other. We investigate the feasibility of using multiply charged anion (MCA) boron clusters, specifically closo-borate dianion, as building blocks. A first principle calculation shows that neutral, bistable, and switchable QCA molecules are possible. The self-doping mechanism is confirmed by molecular orbital analysis, which shows that MCA counterions can be stabilized by the electrostatic interaction between negatively charged counterions and positively charged working dots.     

Thermodynamics of monolayers formed by mixtures of phosphatidylcholine/phosphatidylserine

In this work we obtain the thermodynamic properties of mixed (1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine) PC and (1-stearoyl-2-oleoyl-sn-glycero-3-phospho-l-serine (sodium salt)) PS monolayers. Measurements of compressibility (isotherms, bulk modulus, and excess area per molecule) and surface potential show that the properties of monolayers at the air-water interface depend on the concentration of ions (Na(+) and K(+)) and the proportion of PS in the mixture. The dependence on PS arises because the molecule is originally bound to a Na(+) counterion; by increasing the concentration of ions the entropy changes, creating a favorable system for the bound counterions of PS to join the bulk, leaving a negatively charged molecule. This change leads to an increase in electrostatic repulsions which is reflected by the increase in area per molecule versus surface pressure and a higher surface potential. The results lead to the conclusion that this mixture of phospholipids follows a non ideal behavior and can help to understand the thermodynamic behavior of membranes made of binary mixtures of a zwitterionic and an anionic phospholipid with a bound counterion.     

Phagostimulatory effect of uptake of PLGA microspheres loaded with rifampicin on alveolar macrophages

In this work we obtain the thermodynamic properties of mixed (1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine) PC and (1-stearoyl-2-oleoyl-sn-glycero-3-phospho-l-serine (sodium salt)) PS monolayers. Measurements of compressibility (isotherms, bulk modulus, and excess area per molecule) and surface potential show that the properties of monolayers at the air–water interface depend on the concentration of ions (Na⁺ and K⁺) and the proportion of PS in the mixture. The dependence on PS arises because the molecule is originally bound to a Na⁺ counterion; by increasing the concentration of ions the entropy changes, creating a favorable system for the bound counterions of PS to join the bulk, leaving a negatively charged molecule. This change leads to an increase in electrostatic repulsions which is reflected by the increase in area per molecule versus surface pressure and a higher surface potential. The results lead to the conclusion that this mixture of phospholipids follows a non ideal behavior and can help to understand the thermodynamic behavior of membranes made of binary mixtures of a zwitterionic and an anionic phospholipid with a bound counterion.     

Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

The equilibrium electric double layer (EDL) that surrounds colloidal particles is essential for the response of a suspension under a variety of static or alternating external fields. An ideal salt-free suspension is composed of charged colloidal particles and ionic countercharges released by the charging mechanism. Existing macroscopic theoretical models can be improved by incorporating different ionic effects usually neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann equation (PB). The influence of the finite size of the ions seems to be quite promising because it has been shown to predict phenomena like charge reversal, which has been out of the scope of classical PB approximations. In this work we numerically obtain the surface electric potential and the counterion concentration profiles around a charged particle in a concentrated salt-free suspension corrected by the finite size of the counterions. The results show the high importance of such corrections for moderate to high particle charges at every particle volume fraction, especially when a region of closest approach of the counterions to the particle surface is considered. We conclude that finite ion size considerations are obeyed for the development of new theoretical models to study non-equilibrium properties in concentrated colloidal suspensions, particularly salt-free ones with small and highly charged particles.