Nonelectrostatic interactions between ions with anisotropic ab initio dynamic polarisabilities

Influence of Sodium Salts on the Swelling and Rheology of Hydrophobically Cross-linked Hydrogels Determined by QCM-D

Hydrophobically modified copolymers provide a versatile platform of hydrogel materials for diverse applications, but the influence of salts on the swelling and material properties of this class of hydrogels has not been extensively studied. Here, we investigate model hydrogels with three different sodium salts with anions chosen from the classic Hofmeister series to determine how these counterions influence the swelling and mechanical properties of neutral hydrogels. The gel chosen was based on a statistical copolymer of dimethylacrylamide and 2-(N-ethylperfluorooctane sulfonamido) ethyl acrylate (FOSA). Our measurements utilize a quartz crystal microbalance with dissipation (QCM-D) to quantify both swelling and rheological properties of these gels. We find that a 1 mol/L solution of Na₂SO₄, corresponding to a kosmotropic anion, leads to nearly a 2.6-fold gel deswelling and correspondingly, the complex modulus increases by an order of magnitude under these solution conditions. In contrast, an initial increase in swelling and then a swelling maximum is observed for a 0.02 mol/L concentration in the case of a chaotropic anion, NaClO₄, but the changes in the degree of gel swelling in this system are not directly correlated with changes in the gel shear modulus. The addition of NaBr, an anion salt closer to the middle of the chaotropic to kosmotropic range, leads to hydrogel deswelling where the degree of deswelling and the shear modulus are both nearly independent of salt concentration. Overall, the observed trends are broadly consistent with more kosmotropic ions causing diminished solubility ("salting out") and strongly chaotropic ions causing improved solubility ("salting in"), a trend characteristic of the Hoffmeister series governing the solubility of many proteins and synthetic water-soluble polymers, but trends in the shear stiffness with gel swelling are clearly different from those normally observed in chemically cross-linked gels and are correspondingly difficult to interpret. The salt specificity of swelling and mechanical properties of nonionic hydrogels is important for any potential application in which a wide range of salt concentrations and types are encountered.

Origin of Hofmeister Effects for Complex Systems

Hofmeister effects have been recognized as important as Mendel’s work was to genetics while remain largely controversial, especially for the mechanistic aspects. Here we demonstrated that complex colloids in electrolyte solutions show resembling aggregation kinetics as model colloid, and then quantitatively evaluated the resulting Hofmeister effects. Mechanism for the aggregation of complex colloids has been proposed that is closely associated with the charges of their constituents; despite that, electrostatic interactions play a minor role while polarization effect is evidenced to be the driving force for the aggregation processes. Polarization effect is further ascribed to arouse the resulting Hofmeister effects, which is supported by the fine correlation of activation energies vs. polarizability data of different alkali ions and the calculations of dipole moments for minerals with different charges and adsorbed alkali ions. Because of neglecting polarization effect, the prevailing DLVO theory is not sufficient to describe Hofmeister effects that are ubiquitous in nature. We speculate that polarization effect should also be responsible for Hofmeister effects of other charged systems such as proteins and membranes.

Models and mechanisms of Hofmeister effects in electrolyte solutions, and colloid and protein systems revisited

Specific effects of electrolytes have posed a challenge since the 1880's. The pioneering work was that of Franz Hofmeister who studied specific salt induced protein precipitation. These effects are the rule rather the exception and are ubiquitous in chemistry and biology. Conventional electrostatic theories (Debye-Hückel, DLVO, etc.) cannot explain such effects. Over the past decades it has been recognised that additional quantum mechanical dispersion forces with associated hydration effects acting on ions are missing from theory. In parallel Collins has proposed a phenomenological set of rules (the law of matching water affinities, LMWA) which explain and bring to order the order of ion-ion and ion-surface site interactions at a qualitative level. The two approaches appear to conflict. Although the need for inclusion of quantum dispersion forces in one form or another is not questioned, the modelling has often been misleading and inappropriate. It does not properly describe the chemical nature (kosmotropic/chaotropic or hard/soft) of the interacting species. The success of the LMWA rules lies in the fact that they do. Here we point to the way that the two apparently opposing approaches might be reconciled. Notwithstanding, there are more challenges, which deal with the effect of dissolved gas and its connection to 'hydrophobic' interactions, the problem of water at different temperatures and 'water structure' in the presence of solutes. They take us to another dimension that requires the rebuilding of theoretical foundations.

Modeling of the effects of ion specificity on the onset and growth of ionic micelles in a solution of simple salts

A new version of the molecular thermodynamic model has been developed that takes into account the effect of ion specificity on the free energy of aggregation. The specificity of salt is reflected by differences in the bare ionic sizes and polarizabilities leading to the difference in the dispersion interaction of ions with the aggregate. The model also contains parameters that characterize the compactness of ionic pairs formed between a mobile ion and surfactant's headgroup. The values of these parameters show that more chaotropic heads form tighter pairs with chaotropic ions whereas more cosmotropic heads form more compact pairs with cosmotropic ions. The formation of compact pairs in the micelle corona diminishes the preferable curvature of the aggregates and promotes their growth. The model has been applied to aqueous solutions of cationic (alkyltrimethylammonium, alkyldimethylammonium, and alkylpyridinium) and anionic (alkylsulfate and alkylcarboxylate) surfactants in the presence of simple 1:1 salts. With a single set of parameter values, the model reproduces the critical micelle concentration-salinity curves and the sphere-to-rod transitions or the absence of thereof and describes the aggregate growth for different simple salts, in good agreement with experiment.

A continuum solvent model of the multipolar dispersion solvation energy

The dispersion energy is an important contribution to the total solvation energies of ions and neutral molecules. Here, we present a new continuum model calculation of these energies, based on macroscopic quantum electrodynamics. The model uses the frequency dependent multipole polarizabilities of molecules in order to accurately calculate the dispersion interaction of a solute particle with surrounding water molecules. It includes the dipole, quadrupole, and octupole moment contributions. The water is modeled via a bulk dielectric susceptibility with a spherical cavity occupied by the solute. The model invokes damping functions to account for solute-solvent wave function overlap. The assumptions made are very similar to those used in the Born model. This provides consistency and additivity of electrostatic and dispersion (quantum mechanical) interactions. The energy increases in magnitude with cation size, but decreases slightly with size for the highly polarizable anions. The higher order multipole moments are essential, making up more than 50% of the dispersion solvation energy of the fluoride ion. This method provides an accurate and simple way of calculating the notoriously problematic dispersion contribution to the solvation energy. The result establishes the importance of using accurate calculations of the dispersion energy for the modeling of solvation.

Measurements and theoretical interpretation of points of zero charge/potential of BSA protein

The points of zero charge/potential of proteins depend not only on pH but also on how they are measured. They depend also on background salt solution type and concentration. The protein isoelectric point (IEP) is determined by electrokinetical measurements, whereas the isoionic point (IIP) is determined by potentiometric titrations. Here we use potentiometric titration and zeta potential (ζ) measurements at different NaCl concentrations to study systematically the effect of ionic strength on the IEP and IIP of bovine serum albumin (BSA) aqueous solutions. It is found that high ionic strengths produce a shift of both points toward lower (IEP) and higher (IIP) pH values. This result was already reported more than 60 years ago. At that time, the only available theory was the purely electrostatic Debye-Hückel theory. It was not able to predict the opposite trends of IIP and IEP with ionic strength increase. Here, we extend that theory to admit both electrostatic and nonelectrostatic (NES) dispersion interactions. The use of a modified Poisson-Boltzmann equation for a simple model system (a charge regulated spherical colloidal particle in NaCl salt solutions), that includes these ion specific interactions, allows us to explain the opposite trends observed for isoelectric point (zero zeta potential) and isoionic point (zero protein charge) of BSA. At higher concentrations, an excess of the anion (with stronger NES interactions than the cation) is adsorbed at the surface due to an attractive ionic NES potential. This makes the potential relatively more negative. Consequently, the IEP is pushed toward lower pH. But the charge regulation condition means that the surface charge becomes relatively more positive as the surface potential becomes more negative. Consequently, the IIP (measuring charge) shifts toward higher pH as concentration increases, in the opposite direction from the IEP (measuring potential).

Possible origin of the inverse and direct Hofmeister series for lysozyme at low and high salt concentrations

Protein solubility studies below the isoelectric point exhibit a direct Hofmeister series at high salt concentrations and an inverse Hofmeister series at low salt concentrations. The efficiencies of different anions measured by salt concentrations needed to effect precipitation at fixed cations are the usual Hofmeister series (Cl(-) > NO(3)(-) > Br(-) > ClO(4)(-) > I(-) > SCN(-)). The sequence is reversed at low concentrations. This has been known for over a century. Reversal of the Hofmeister series is not peculiar to proteins. Its origin poses a key test for any theoretical model. Such specific ion effects in the cloud points of lysozyme suspensions have recently been revisited. Here, a model for lysozymes is considered that takes into account forces acting on ions that are missing from classical theory. It is shown that both direct and reverse Hofmeister effects can be predicted quantitatively. The attractive/repulsive force between two protein molecules was calculated. To do this, a modification of Poisson-Boltzmann theory is used that accounts for the effects of ion polarizabilities and ion sizes obtained from ab initio calculations. At low salt concentrations, the adsorption of the more polarizable anions is enhanced by ion-surface dispersion interactions. The increased adsorption screens the protein surface charge, thus reducing the surface forces to give an inverse Hofmeister series. At high concentrations, enhanced adsorption of the more polarizable counterions (anions) leads to an effective reversal in surface charge. Consequently, an increase in co-ion (cations) adsorption occurs, resulting in an increase in surface forces. It will be demonstrated that among the different contributions determining the predicted specific ion effect the entropic term due to anions is the main responsible for the Hofmeister sequence at low salt concentrations. Conversely, the entropic term due to cations determines the Hofmeister sequence at high salt concentrations. This behavior is a remarkable example of the charge-reversal phenomenon.

Specific ion effects on adsorption at the solid/electrolyte interface: a probe into the concentration limit

Adsorption of organic acid at the mineral oxide-electrolyte interface has been explored. The adsorption of 2,4-dihydroxybenzoic acid onto α-alumina illustrates that specific ion effects show up at very low salt concentration (<0.05 mM). These surprising Hofmeister effects occur at salt concentrations an order of magnitude lower than in a previous study ( J. Colloid Interface Sci. 2010, 344, 482 ). Salts enhance adsorption and specifically at ≤0.05 mM. With increasing concentration of ion, the adsorption density decreases. The results are accounted for by incorporating the ion size and dispersion forces in the theoretical modeling based on ab initio calculations of polarizabilities. The order appears to be governed by ion size, determining the maximum concentration that ions can attain near the surface due to close packing.

Charge heterogeneity of surfaces: mapping and effects on surface forces

The DLVO theory treats the total interaction force between two surfaces in a liquid medium as an arithmetic sum of two components: Lifshitz-van der Waals and electric double layer forces. Despite the success of the DLVO model developed for homogeneous surfaces, a vast majority of surfaces of particles and materials in technological systems are of a heterogeneous nature with a mosaic structure composed of microscopic and sub-microscopic domains of different surface characteristics. In such systems, the heterogeneity of the surface can be more important than the average surface character. Attractions can be stronger, by orders of magnitude, than would be expected from the classical mean-field DLVO model when area-averaged surface charge or potential is employed. Heterogeneity also introduces anisotropy of interactions into colloidal systems, vastly ignored in the past. To detect surface heterogeneities, analytical tools which provide accurate and spatially resolved information about material surface chemistry and potential - particularly at microscopic and sub-microscopic resolutions - are needed. Atomic force microscopy (AFM) offers the opportunity to locally probe not only changes in material surface characteristic but also charges of heterogeneous surfaces through measurements of force-distance curves in electrolyte solutions. Both diffuse-layer charge densities and potentials can be calculated by fitting the experimental data with a DLVO theoretical model. The surface charge characteristics of the heterogeneous substrate as recorded by AFM allow the charge variation to be mapped. Based on the obtained information, computer modeling and simulation can be performed to study the interactions among an ensemble of heterogeneous particles and their collective motions. In this paper, the diffuse-layer charge mapping by the AFM technique is briefly reviewed, and a new Diffuse Interface Field Approach to colloid modeling and simulation is briefly discussed.

Charge reversal of surfaces in divalent electrolytes: the role of ionic dispersion interactions

Surface potentials of alkali earth nitrates at a mica surface are calculated using a modified Poisson-Boltzmann approach that includes nonelectrostatic ion-surface dispersion interactions. New ab initio dynamic polarizabilities are used to determine dispersion interactions. A hydration model describing the hydration shell of cations is presented. Excellent agreement with experiment is achieved, including charge reversal at high electrolyte concentration without the need for site binding models. This suggests that specific ionic dispersion forces provide the mechanism for ion surface binding. An asymptotic surface potential is found in the limit of very high concentration. A Hofmeister series is predicted according to the strength of charge reversal, with Mg > Ca > Sr > Ba. The ion-surface dispersion adsorption energies of hydrated ions appear to explain the apparent repulsive secondary hydration forces observed experimentally between mica surfaces when taken with a surface hydration layer.

Quasichemical and structural analysis of polarizable anion hydration

Quasichemical theory is utilized to analyze the relative roles of solute polarization and size in determining the structure and thermodynamics of bulk anion hydration for the Hofmeister series Cl(-), Br(-), and I(-). Excellent agreement with experiment is obtained for whole salt hydration free energies using the polarizable AMOEBA force field. The total hydration free energies display a stronger dependence on ion size than on polarizability. The quasichemical approach exactly partitions the solvation free energy into inner-shell, outer-shell packing, and outer-shell long-ranged contributions by means of a hard-sphere condition. The inner-shell contribution becomes slightly more favorable with increasing ion polarizability, indicating electrostriction of the nearby waters. Small conditioning radii, even well inside the first maximum of the ion-water(oxygen) radial distribution function, result in Gaussian behavior for the long-ranged contribution that dominates the ion hydration free energy. This in turn allows for a mean-field treatment of the long-ranged contribution, leading to a natural division into first-order electrostatic, induction, and van der Waals terms. The induction piece exhibits the strongest ion polarizability dependence, while the larger-magnitude first-order electrostatic piece yields an opposing but weaker polarizability dependence. The van der Waals piece is small and positive, and it displays a small ion specificity. The sum of the inner-shell, packing, and long-ranged van der Waals contributions exhibits little variation along the anion series for the chosen conditioning radii, targeting electrostatic effects (influenced by ion size) as the largest determinant of specificity. In addition, a structural analysis is performed to examine the solvation anisotropy around the anions. As opposed to the hydration free energies, the solvation anisotropy depends more on ion polarizability than on ion size: increased polarizability leads to increased anisotropy. The water dipole moments near the ion are similar in magnitude to bulk water, while the ion dipole moments are found to be significantly larger than those observed in quantum mechanical studies. Possible impacts of the observed over-polarization of the ions on simulated anion surface segregation are discussed.

Why direct or reversed Hofmeister series? Interplay of hydration, non-electrostatic potentials, and ion size

A modified Poisson-Boltzmann analysis is made of the double layer interaction between two silica surfaces and two alumina surfaces in chloride electrolyte. The analysis incorporates nonelectrostatic ion-surface dispersion interactions based on ab initio ionic excess polarizabilities with finite ion sizes. A hydration model for the tightly held hydration shell of kosmotropic ions is introduced. A direct Hofmeister series (K > Na > Li) is found at the silica surface while the reversed series (Li > Na > K) is found at alumina, bringing theory in line with experiment for the first time. Calculations with unhydrated ions also suggest that surface-induced dehydration may be occurring at the alumina surface.

Ion specific surface charge density of SBA-15 mesoporous silica

Potentiometric titrations were used to estimate the surface charge density of SBA-15 mesoporous silica in different salt solutions. It was found that surface charge depends both on cation type, following a Hofmeister series (Cs(+) < Guanidinium(+) < K(+) < Na(+) < Li(+)), and on salt concentration (in the range 0.05-1 M). The surface charge series is reproduced by theoretical calculations performed using a modified Poisson-Boltzmann equation that includes ionic dispersion forces with ab initio ion polarizabilities and hydrated ions. The hydration model assigns an explicit hydration shell to kosmotropic (strong hydrated) ions only. The Hofmeister series appears to be due to the combination of ion-surface dispersion interactions and ion hydration.

Importance of accurate dynamic polarizabilities for the ionic dispersion interactions of alkali halides

Ab initio quantum mechanical calculations of the dynamic polarizability of alkali metal and halide ions are performed as a function of imaginary frequency. Electron correlation is shown to provide a significant correction to ionic polarizabilities. Ab initio ion-surface dispersion coefficients are compared with single- and multimode London approximations. The commonly employed single-mode model with the characteristic frequency taken from the ionization potential of the ion is shown to be inadequate, underestimating dispersion forces with an average error around 40% or as high as 80% for halide ions. Decomposition of the polarizability data into five modes covers the major modes of each ion adequately (four modes for Li(+)). Illustrative calculations of surface potentials at the mica surface in aqueous alkali halide electrolytes are made. Charge reversal is obtained with the more polarizable cations, K(+) and Rb(+). The error in the single-mode ionization potential models is seen as a strong shift in the surface potential from negative toward positive values.