Ion specific forces between charged self-assembled monolayers explained by modified DLVO theory

We recently investigated specific ion effects near a single charged self-assembled monolayer (SAM) in a salt solution by exploiting a modified Poisson–Boltzmann equation that accounts for both water profile and ion-surface potential profiles inferred from molecular dynamics simulations. In the present contribution we extend this work to consider two charged SAMs interacting across different salt solution. Our results demonstrate one important reason why the double layer force between charged colloidal surfaces in electrolytes could be highly ion specific.     

Hofmeister effects: interplay of hydration, nonelectrostatic potentials, and ion size

The classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of colloids, and corresponding theories of electrolytes, are unable to explain ion specific forces between colloidal particles quantitatively. The same is true generally, for surfactant aggregates, lipids, proteins, for zeta and membrane potentials and in adsorption phenomena. Even with fitting parameters the theory is not predictive. The classical theories of interactions begin with continuum solvent electrostatic (double layer) forces. Extensions to include surface hydration are taken care of with concepts like inner and outer Helmholtz planes, and "dressed" ion sizes. The opposing quantum mechanical attractive forces (variously termed van der Waals, Hamaker, Lifshitz, dispersion, nonelectrostatic forces) are treated separately from electrostatic forces. The ansatz that separates electrostatic and quantum forces can be shown to be thermodynamically inconsistent. Hofmeister or specific ion effects usually show up above ≈10(-2) molar salt. Parameters to accommodate these in terms of hydration and ion size had to be invoked, specific to each case. Ionic dispersion forces, between ions and solvent, for ion-ion and ion-surface interactions are not explicit in classical theories that use "effective" potentials. It can be shown that the missing ionic quantum fluctuation forces have a large role to play in specific ion effects, and in hydration. In a consistent predictive theory they have to be included at the same level as the nonlinear electrostatic forces that form the skeletal framework of standard theory. This poses a challenge. The challenges go further than academic theory and have implications for the interpretation and meaning of concepts like pH, buffers and membrane potentials, and for their experimental interpretation. In this article we overview recent quantitative developments in our evolving understanding of the theoretical origins of specific ion, or Hofmeister effects. These are demonstrated through an analysis that incorporates nonelectrostatic ion-surface and ion-ion dispersion interactions. This is based on ab initio ionic polarisabilities, and finite ion sizes quantified through recent ab initio work. We underline the central role of ionic polarisabilities and of ion size in the nonelectrostatic interactions that involve ions, solvent molecules and interfaces. Examples of mechanisms through which they operate are discussed in detail. An ab initio hydration model that accounts for polarisabilities of the tightly held hydration shell of "cosmotropic" ions is introduced. It is shown how Hofmeister effects depend on an interplay between specific surface chemistry, surface charge density, pH, buffer, and counterion with polarisabilities and ion size. We also discuss how the most recent theories on surface hydration combined with hydrated nonelectrostatic potentials may predict experimental zeta potentials and hydration forces.     

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.     

Approaches to hydration, old and new: Insights through Hofmeister effects

Hydration effects in colloidal interactions or problems involving electrolytes are usually taken care of by effective electrostatic potentials that subsume notions like hydrated ion size, Gurney potentials, soft and hard, chaotropic and cosmotropic ions, and inner and outer Helmholtz planes. Quantum fluctuation (dispersion) forces between ions and between ions and surfaces are missing from classical theories, at least not explicit in standard approaches to hydration. This paper outlines an evolving back-to-basics approach that allows these ion specific forces to be included in theories quantitatively. In this approach ab initio quantum mechanics is used to calculate dynamic polarisabilities of ions and to quantify bare ion radii. The ionic dispersion potentials between ions, and between ions and surfaces in water can then be given explicit analytic form from an extension of Lifshitz theory. They are included in the theory along with electrostatic potentials. In a first stage the primitive (continuum solvent) model provides a skeletal theory on which to build in hydration. Extension of the ab initio calculations to include “dressed” ions, i.e. water hydration shells for cosmotropic ions, quadrupolar and octupolar polarisability contributions and; for colloids, allowance for a surface hydration layer, permits quantification of Hofmeister effects and Gurney potentials. With these extensions, primary hydration forces (short range repulsion) arise due to an interplay between surface hydration layers and specific ion interactions. Apparent longer range “secondary hydration forces” are shown to be a consequence of ion-surface dispersion interactions and are not true “hydration forces”.     

Specific ion effects: Interaction between nanoparticles in electrolyte solutions

Dependence of colloidal interactions on salt identity, observed frequently in experiments, can be accounted for once ion specific non-electrostatic forces are included in the theory. Ability to predict the effect of added salt on the phase diagram of colloid dispersions is essential for the design of processes involving nanocolloids. The Ornstein–Zernike equation with hypernetted chain closure approximation provides a viable first estimate for the potential of mean force between ionized nanoparticles like alumina aggregates in aqueous electrolytes subject to dispersion interactions with hydrated simple ions. Calculated potentials of mean force enable the prediction of osmotic second virial coefficients and phase diagrams showing a dramatic dependence on ion type. The choice of salt therefore provides an efficient, non-intrusive way to tune the phase behavior of nanoparticle dispersions.     

Effect of ionic van der Waals forces on the diffuse potential of model colloids

In this work, the role of ionic dispersion forces in specific ion effects is evaluated through Monte Carlo simulations in the primitive model. More specifically, we assess the effect of such forces on the diffuse potential, since this property is essential to understand the electrokinetic behavior of colloids. In this way, ion specificity arises naturally since ion dispersion forces depend on ionic polarizability, which differs for ions with the same valence. This property is included in the primitive model by means of the Lifshitz theory. The results for different ions are summarized with the help of a nondimensional parameter characterizing the relative weight of ionic van der Waals interactions. Our data reveal that for small ions with high polarizability the ionic dispersion forces can considerably contribute to the specificity of the diffuse potential. In any case, the specific ion effects due to ion polarizability are strongly influenced by ion size.     

Hydration energy or hydration force? Origin of ion-specificity in ion selective electrodes

The origin of ion-specificity (also known as Hofmeister effect) in potentiometric ion selective electrodes (ISE) with polymeric membranes has been traditionally assigned to the differences in lipophilicities of ions, with hydration energies described in the framework of Born theory as being of purely electrostatic nature. This is in clear contrast to the current understanding of the Hofmeister effect in colloid and interface science, where it is viewed as resulting from an interplay between the electrostatic and non-electrostatic interactions, the latter often referred to as “hydration” forces. The two approaches to ion-specificity in ISE, simplistically termed “hydration energy” (ion partitioning between an aqueous phase and the ISE membrane) and “hydration force” (ion adsorption from an aqueous phase to the electrically charged ISE membrane) are described and compared. Two major conclusions are drawn: i) ion-specificity can be included in both approaches, although it is more natural within the “hydration force” approach with ion-surface interactions; ii) both ion partitioning into, and ion adsorption onto the ISE membrane should be considered in order to fully understand the origin of ion-specificity in ISE.     

Effective interaction between two ion-adsorbing plates: Hofmeister series and salting-in/salting-out phase diagrams from a global mean-field analysis

Interactions between ions and solutes are key to ion-specificity. A generic model in which ions interact via square well potentials of finite range with charged plates is solved analytically on the Poisson-Boltzmann level and analyzed globally for varying surface charge, salt concentration, and ion-surface affinity. Ion adsorption as well as depletion can lead to stably bound plates at finite separation, relevant for the equilibrium salting-out of small solutes such as proteins. The interplate pressure at large plate separation, relevant for aggregation kinetics of large solutes, exhibits direct as well as indirect Hofmeister ordering, depending on surface charge and salt concentration. A simple method for mapping explicit ion-surface potentials of mean force as obtained from solvent-explicit molecular dynamics simulations onto square-well potential parameters is demonstrated.     

Electrolytes in a nanometer slab-confinement: ion-specific structure and solvation forces

We study the liquid structure and solvation forces of dense monovalent electrolytes (LiCl, NaCl, CsCl, and NaI) in a nanometer slab-confinement by explicit-water molecular dynamics (MD) simulations, implicit-water Monte Carlo (MC) simulations, and modified Poisson-Boltzmann (PB) theories. In order to consistently coarse-grain and to account for specific hydration effects in the implicit methods, realistic ion-ion and ion-surface pair potentials have been derived from infinite-dilution MD simulations. The electrolyte structure calculated from MC simulations is in good agreement with the corresponding MD simulations, thereby validating the coarse-graining approach. The agreement improves if a realistic, MD-derived dielectric constant is employed, which partially corrects for (water-mediated) many-body effects. Further analysis of the ionic structure and solvation pressure demonstrates that nonlocal extensions to PB (NPB) perform well for a wide parameter range when compared to MC simulations, whereas all local extensions mostly fail. A Barker-Henderson mapping of the ions onto a charged, asymmetric, and nonadditive binary hard-sphere mixture shows that the strength of structural correlations is strongly related to the magnitude and sign of the salt-specific nonadditivity. Furthermore, a grand canonical NPB analysis shows that the Donnan effect is dominated by steric correlations, whereas solvation forces and overcharging effects are mainly governed by ion-surface interactions. However, steric corrections to solvation forces are strongly repulsive for high concentrations and low surface charges, while overcharging can also be triggered by steric interactions in strongly correlated systems. Generally, we find that ion-surface and ion-ion correlations are strongly coupled and that coarse-grained methods should include both, the latter nonlocally and nonadditive (as given by our specific ionic diameters), when studying electrolytes in highly inhomogeneous situations.     

Interaction forces in bitumen extraction from oil sands

Water-based extraction process (WBEP) has been successfully applied to bitumen recovery from Athabasca oil sand ore deposits in Alberta. In this process, two essential steps are involved. The bitumen first needs to be "liberated" from sand grains, followed by "aeration" with air bubbles. Bitumen "liberation" from the sand grains is controlled by the interaction between the bitumen and sand grains. Bitumen "aeration" is dependent, among other mechanical and hydrodynamic variables, on the hydrophobicity of the bitumen surface, which is controlled by water chemistry and interactions between bitumen and fine solids. In this paper, the interaction force measured with an atomic force microscope (AFM) between bitumen-bitumen, bitumen-silica, bitumen-clays and bitumen-fines is summarized. The measured interaction force barrier coupled with the contacted adhesion force allows us to predict the coagulative state of colloidal systems. Zeta potential distribution measurements, in terms of heterocoagulation, confirmed the prediction of the measured force profiles using AFM. The results show that solution pH and calcium addition can significantly affect the colloidal interactions of various components in oil sand extraction systems. The strong attachment of fines from a poor processing ore on bitumen is responsible for the corresponding low bitumen flotation recovery. The identification of the dominant non-contact forces by fitting with the classical DLVO or extended DLVO theory provides guidance for controlling the interaction behavior of the oil sand components through monitoring the factors that could affect the non-contact forces. The findings provide insights into megascale industrial operations of oil sand extraction.     

电喷雾离子源中样品离子化能量转移理论的初探

电喷雾离子源（electrospray ionization,ESI）不仅可以用于小分子的检测,也能够用于蛋白质、多肽等大分子的研究。本文通过对离子化过程的系统分析,提出了基于能量最低原理的离子化过程能量转移理论。样品分子在由液相转移到气相形成离子化气体的过程中受到静电力、分子间的范德华力等多种力的作用。样品的离子化是多种力共同作用的结果,在不同的离子化阶段,不同形式的力的作用也不尽相同。电荷在样品表面蒸发和多电荷离子的形成之间存在竞争。对不同结构的分子,分子形态、构象改变导致的两相间转移Gibbs自由能变化不同,可能导致离子蒸发、大分子形成多电荷离子、产生链弹射等行为。离子化能量转移理论不仅能够对已有的3种理论加以简化统一,也可以说明溶剂、电解质离子等在离子化过程中的作用,为优化不同结构与形态样品的质谱检测、了解离子化的真实过程提供了一种可能的依据。     

Fabrication of oriented crystals as force measurement tips via focused ion beam and microlithography methods

Detailed knowledge of the forces between nanocrystals is very crucial for understanding many generic (eg, random aggregation/assembly and rheology) and specific (eg, oriented attachment) phenomena at macroscopic length scales, especially considering the additional complexities involved in nanocrystals such as crystal orientation and corresponding orientation‐dependent physicochemical properties. Because there are a limited number of methods to directly measure the forces, little is known about the forces that drive the various emergent phenomena. Here, we report on two methods of preparing crystals as force measurement tips used in an atomic force microscope: the focused ion beam method and microlithography method. The desired crystals are fabricated using these two methods and are fixed to the atomic force microscope probe using platinum deposition, ultraviolet epoxy, or resin, which allows for the orientation‐dependent force measurements. These two methods can be used to attach virtually any solid particles (from the size of a few hundreds of nanometers to millimeters). We demonstrate the force measurements between aqueous media under different conditions such as pH.     

Isoelectric point of fluorite by direct force measurements using atomic force microscopy

Interaction forces between a fluorite (CaF2) surface and colloidal silica were measured by atomic force microscopy (AFM) in 1 x 10(-3) M NaNO3 at different pH values. Forces between the silica colloid and fluorite flat were measured at a range of pH values above the isoelectric point (IEP) of silica so that the forces were mainly controlled by the fluorite surface charge. In this way, the IEP of the fluorite surface was deduced from AFM force curves at pH approximately 9.2. Experimental force versus separation distance curves were in good agreement with theoretical predictions based on long-range electrostatic interactions, allowing the potential of the fluorite surface to be estimated from the experimental force curves. AFM-deduced surface potentials were generally lower than the published zeta potentials obtained from electrokinetic methods for powdered samples. Differences in methodology, orientation of the fluorite, surface carbonation, and equilibration time all could have contributed to this difference.     

The quest for the best nonpolarizable water model from the adaptive force matching method

The recently introduced adaptive force matching (AFM) method is used to develop a significantly improved pair‐wise nonpolarizable potential for water. A rigid version of the potential is also presented to enable larger time steps for biological simulations. In this work, it is demonstrated that the AFM method can be used to systematically assess the importance of each functional term during the construction of a force field. For a water potential, it is established that a single off‐atom charge center (M) in the plane of water outperforms two out‐of‐plane charge sites for reproducing intermolecular forces. The four‐site pair‐wise nonpolarizable force field developed in this work rivals some of the most sophisticated polarizable models in terms of reproducing accurate ab initio forces. The force fields are parameterized to perform best in the temperature range from 0 to 40°C. Equilibrium and dynamical properties calculated with the flexible and rigid force fields are in good agreement with experimental results. For the flexible model, the agreement improves when path integral simulation is performed. These force fields provide high‐quality results at a very low computational cost and are thus well suited to atomistic scale biological simulations. The AFM method provides a mechanism for selecting important terms in force field expressions and is a very promising tool for producing accurate force fields in condensed phases. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Electronic quantum motions in hydrogen molecule ion

The hydrogen molecule ion is a two‐center force system expressed under the prolate spheroidal coordinates, whose quantum motions and quantum trajectories have never been addressed in the literature before. The momentum operators in this coordinate system are derived for the first time from the Hamilton equations of motion and used to construct the Hamiltonian operator. The resulting Hamiltonian comprises a kinetic energy T and a total potential V_Total consisting of the Coulomb potential and a quantum potential. It is shown that the participation of the quantum potential and the accompanied quantum forces in the force interaction within H₂⁺ is essential to develop an electronic motion consistent with the prediction of the probability density function |Ψ|². The motion of the electron in H₂⁺ can be either described by the Hamilton equations derived from the Hamiltonian H = T_K + V_Total or by the Lagrange equations derived from the Lagrangian H = T_K ? V_Total. Solving the equations of motion with different initial positions, we show that the solutions yield an assembly of electronic quantum trajectories whose distribution and concentration reconstruct the σ and π molecular orbitals in H₂⁺. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Direct surface force measurement in water using a nanosize colloidal probe technique

The direct force measurement between colloidal surfaces has been an essential topic in both theories and applications of surface chemistry. As particle size is decreased from micron size down to true nano size (<10 nm), surface forces are increasingly important. Nanoparticles at close proximity or high solids loading are expected to show a different behavior than what can be estimated from continuum and mean field theories. The current tools for directly measuring interaction forces such as a surface force apparatus or atomic force microscopy (AFM) are limited to particles much larger than nanosize. Here a modified colloidal probe technique is suggested using a multiwalled carbon nanotube (MWNT) to overcome this problem. Determination of zero separation in AFM is critical to extract a reliable force-separation curve when MWNT is used as a probe. Hence, a systematic approach to the data collection for a nanosize colloidal probe is proposed and a sample of a direct surface force measurement curve obtained with the MWNT probe is presented.     

Applying a dynamic method to the measurement of ion mobility

A dynamic method is applied to measure the mobility of gas-phase ions in the dual ion funnel interface of the electrospray source of a quadrupole orthogonal time-of-flight mass spectrometer. In a new operational mode, a potential barrier was formed in the second ion funnel of the mass spectrometer and then progressively increased. In this region, a flow of gas drags the ions into the mass spectrometer while the electric force applied by the potential barrier decelerates them. Ions with lower mobility can be carried by the gas flow more easily than those with high mobility. Thus, electrical forces can block the more mobile ions more easily. Hence, the electric barrier formed in the ion funnel permits only ions below a certain mobility threshold to enter the mass spectrometer. When the barrier voltage is increased, this threshold moves from high to low mobilities. Ions with mobilities above the threshold cannot enter the mass spectrometer, and their signal decreases to zero. Thus, in a barrier voltage scan, mass spectrometric signals of ions sequentially disappear. Differentiation of these decreasing ion signal curves produces peaks from which an ion mobility spectrum can be reconstructed. Blocking voltages, i.e., the positions of the peaks on the barrier voltage scale are directly related to the mobility of these ions. An internal calibration using ions with known mobility values helps determine the unknown ion mobilities and allows calculation of ionic cross sections.     

Molecular hydrophobic attraction and ion-specific effects studied by molecular dynamics

Much is written about "hydrophobic forces" that act between solvated molecules and nonpolar interfaces, but it is not always clear what causes these forces and whether they should be labeled as hydrophobic. Hydrophobic effects roughly fall in two classes, those that are influenced by the addition of salt and those that are not. Bubble adsorption and cavitation effects plague experiments and simulations of interacting extended hydrophobic surfaces and lead to a strong, almost irreversible attraction that has little or no dependence on salt type and concentration. In this paper, we are concerned with hydrophobic interactions between single molecules and extended surfaces and try to elucidate the relation to electrostatic and ion-specific effects. For these nanoscopic hydrophobic forces, bubbles and cavitation effects play only a minor role and even if present cause no equilibration problems. In specific, we study the forced desorption of peptides from nonpolar interfaces by means of molecular dynamics simulations and determine the adsorption potential of mean force. The simulation results for peptides compare well with corresponding AFM experiments. An analysis of the various contributions to the total peptide-surface interactions shows that structural effects of water as well as van der Waals interactions between surface and peptide are important. Hofmeister ion effects are studied by separately determining the effective interaction of various ions with hydrophobic surfaces. An extension of the Poisson-Boltzmann equation that includes the ion-specific potential of mean force yields surface potentials, interfacial tensions, and effective interactions between hydrophobic surfaces. There, we also analyze the energetic contributions to the potential of mean force and find that the most important factor determining ion-specific adsorption at hydrophobic surfaces can best be described as surface-modified ion hydration.     

Surface induced dissociation of chromium hexacarbonyl on fluorinated alkanethiolate surface in ion cyclotron resonance mass spectrometer: studies of energetics of the process using recursive internal energy distribution search method

Energy transfer in ion-surface collisional activation is characterized for 0–30 eV collisions of chromium hexacarbonyl molecular cations with a monolayer of fluorinated alkanethiolate self-assembled onto a solid gold surface. This surface was mounted on the back trapping plate of the Infinity® cell of a Bruker BioApex 7T ion cyclotron resonance mass spectrometer on the B-field axis orthogonal to the ion beam direction. Internal energy deposition was deduced from fragmentation spectra using a recursive internal energy distribution search method. The efficiency of energy transfer into the ion slowly increases with incident ion energy to a maximum value of 20% at about 23 eV collision energy. Approximate kinetic energy distributions of the fragments were measured by deducing the dependence of ion abundance on trapping potential. From the kinetic energy dependence on mass we infer that rapid decomposition of the molecular cation occurs after it recoils from the surface. Knowledge of both internal and kinetic energy distributions of collisionally activated ions enabled us to deduce the energy deposited into the self-assembled monolayer as a function of collision energy.