The influence of ion binding and ion specific potentials on the double layer pressure between charged bilayers at low salt concentrations

Measurements of surface forces between double-chained cationic bilayers adsorbed onto molecularly smooth mica surfaces across different millimolar salt solutions have revealed a large degree of ion specificity [Pashley et al., J. Phys. Chem. 90, 1637 (1986)]. This has been interpreted in terms of highly specific anion binding to the adsorbed bilayers. We show here that inclusion in the double layer theory of nonspecific ion binding and ion specific nonelectrostatic potentials acting between ions and the two surfaces can account for the phenomenon. It also gives the right Hofmeister series for the double layer pressure.     

Dispersion self-free energies and interaction free energies of finite-sized ions in salt solutions

The role for many-body dipolar (dispersion) potentials in ion-solvent and ion-solvent-interface interactions is explored. Such many-body potentials, accessible in principle from measured dielectric data, are necessary in accounting for Hofmeister specific ion effects. Dispersion self-energy is the quantum electrodynamic analogue of the Born electrostatic self-energy of an ion. We here describe calculations of dispersion self-free energies of four different anions (OH-, Cl-, Br-, and I-) that take finite ion size into account. Three different examples of self-free energy calculations are presented. These are the self-free energy of transfer of an ion to bulk solution, which influences solubility; the dispersion potential acting between one ion and an air-water interface (important for surface tension calculations); and the dispersion potential acting between two ions (relevant to activity coefficient calculations). To illustrate the importance of dispersion self-free energies, we compare the Born and dispersion contributions to the free energy of ion transfer from water to air (oil). We have also calculated the change in interfacial tension with added salt for air (oil)-water interfaces. A new model is used that includes dispersion potentials acting on the ions near the interface, image potentials, and ions of finite size that are allowed to spill over the solution-air interface. It is shown that interfacial free energies require a knowledge of solvent profiles at the interface.     

Observation of Ion Electrosorption in Metal–Organic Framework Micropores with In Operando Small‐Angle Neutron Scattering

A molecular‐level understanding of transport and adsorption mechanisms of electrolyte ions in nanoporous electrodes under applied potentials is essential to control the performance of double‐layer capacitors. Here, in operando small‐angle neutron scattering (SANS) is used to directly detect ion movements into the nanopores of a conductive metal–organic framework (MOF) electrode under operating conditions. Neutron‐scattering data reveals that most of the void space within the MOF is accessible to the solvent. Upon the addition of the electrolyte sodium triflate (NaOTf), the ions are adsorbed on the outer surface of the protrusions to form a 30 Å layer instead of entering the ionophobic pores in the absence of an applied charging potential. The changes in scattering intensity when potentials are applied suggests the ion rearrangement in the micropores following different mechanisms depending on the electrode polarization. These observations shed insights on ion electrosorption in electrode materials.     

Ionic liquid near a charged wall: structure and capacitance of electrical double layer

We study the effects of ion size asymmetry and short-range correlations on the electrical double layer in ionic liquids: we perform molecular dynamics simulations of a model ionic liquid between two "electrodes" and calculate the differential capacitance of each as a function of the electrode potential. The capacitance curve has an asymmetric "bell-shape" character, in qualitative agreement with recent experiments and the mean- field theory (MFT) which takes into account the limitation on the maximal local density of ions. The short-range ionic correlations, not included in the MFT, lead to an overscreening effect which changes radically the structure of the double layer at small and moderate charging. With the radius of cations taken to be twice as large as anions, the position of the main capacitance maximum is shifted positively from the potential of zero charge (PZC), as predicted by MFT. An extension of the theory (EMFT), however, reproduces the simulated capacitance curve almost quantitatively. Capacitance curves for real ionic liquids will be affected by nonspherical shape of ions and sophisticated pair potentials, varying from liquid to liquid. But understanding the capacitance behavior of such model system is a basis for rationalizing those more specific features.     

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.     

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”.     

Ion specific surface forces between membrane surfaces

Entities such as ion distributions and forces between lipid membranes depend on effects due to the intervening salt solution that have not been recognized previously. These specific ion or Hofmeister effects influence membrane fusion. A typical illustrative example is this: measurements of forces between double-chained cationic bilayers adsorbed onto molecularly smooth mica surfaces across different 0.6-2 mM salt solutions have revealed a large degree of ion specificity [Pashley et al. J. Phys. Chem. 1986, 90, 1637]. This has been interpreted in terms of very specific anion "binding" to the adsorbed bilayers, as it would too for micelles and other self-assembled systems. However, we show here that inclusion of nonelectrostatic (NES) or ionic dispersion potentials acting between ions and the two surfaces explains such "ion binding". The observed Hofmeister sequence for the calculated pressure without any direct ion binding is given correctly. This demonstrates the importance of a source of ion specificity that has been ignored. It is due to ionic physisorption caused by attractive NES ionic dispersion potentials. There appear to be some far reaching consequences for interpretations of membrane intermolecular interactions in salt solutions.     

Electrostatic properties of aqueous salt solution interfaces: a comparison of polarizable and nonpolarizable ion models

The effects of ion force field polarizability on the interfacial electrostatic properties of approximately 1 M aqueous solutions of NaCl, CsCl, and NaI are investigated using molecular dynamics simulations employing both nonpolarizable and Drude-polarizable ion sets. Differences in computed depth-dependent orientational distributions, "permanent" and induced dipole and quadrupole moment profiles, and interfacial potentials are obtained for both ion sets to further elucidate how ion polarizability affects interfacial electrostatic properties among the various salts relative to pure water. We observe that the orientations and induced dipoles of water molecules are more strongly perturbed in the presence of polarizable ions via a stronger ionic double layer effect arising from greater charge separation. Both anions and cations exhibit enhanced induced dipole moments and strong z alignment in the vicinity of the Gibbs dividing surface (GDS) with the magnitude of the anion induced dipoles being nearly an order of magnitude larger than those of the cations and directed into the vapor phase. Depth-dependent profiles for the trace and z z components of the water molecular quadrupole moment tensors reveal 40% larger quadrupole moments in the bulk phase relative to the vapor which mimics a similar observed 40% increase in the average water dipole moment. Across the GDS, the water molecular quadrupole moments increase nonmonotonically (in contrast to the water dipoles) and exhibit a locally reduced contribution just below the surface due to both orientational and polarization effects. Computed interfacial potentials for the nonpolarizable salts yield values 20-60 mV more positive than pure water and increase by an additional 30-100 mV when ion polarizability is included. A rigorous decomposition of the total interfacial potential into ion monopole, water and ion dipole, and water quadrupole components reveals that a very strong, positive ion monopole contribution is offset by negative contributions from all other potential sources. Water quadrupole components modulated by the water density contribute significantly to the observed interfacial potential increments and almost entirely explain observed differences in the interfacial potentials for the two chloride salts. By lumping all remaining nonquadrupole interfacial potential contributions into a single "effective" dipole potential, we observe that the ratio of quadrupole to "effective" dipole contributions range from 2:1 in CsCl to 1:1.5 in NaI, suggesting that both contributions are comparably important in determining the interfacial potential increments. We also find that oscillations in the quadrupole potential in the double layer region are opposite in sign and partially cancel those of the "effective" dipole potential.     

Electrostatic interactions between double layers: influence of surface roughness, regulation, and chemical heterogeneities

Electrostatic interactions between two surfaces as measured by atomic force microscopy (AFM) are usually analyzed in terms of DLVO theory. The discrepancies often observed between the experimental and theoretical behavior are usually ascribed to the occurrence of chemical regulation processes and/or to the presence of surface chemical or morphological heterogeneities (roughness). In this paper, a two-gradient mean-field lattice analysis is elaborated to quantifying double layer interactions between nonplanar surfaces. It allows for the implementation of the aforementioned sources of deviation from DLVO predictions. Two types of ion-surface interaction ensure the adjustment of charges and potentials upon double layer overlap, i.e., specific ionic adsorption at the surfaces and/or the presence of charge-determining ions for the surfaces considered. Upon double layer overlap, charges and potentials are adjusted via reequilibrium of the different ion adsorption processes. Roughness is modeled by grafting asperities on supporting planar surfaces, with their respective positions, shapes, and chemical properties being assigned at will. Local potential and charge distributions are derived by numerically solving the nonlinear Poisson-Boltzmann equation under the boundary conditions imposed by the surface profiles and regulation mechanism chosen. Finite size of the ions is taken into account. A number of characteristic situations are briefly discussed. It is shown how the surface irregularities are reflected in the Gibbs energy of interaction.     

Co-ion and ion competition effects: ion distributions close to a hydrophobic solid surface in mixed electrolyte solutions

We consider within a modified Poisson-Boltzmann theory an electrolyte, with different mixtures of NaCl and NaI, near uncharged and charged solid hydrophobic surfaces. The parametrized potentials of mean force acting on Na+, Cl-, and I- near an uncharged self-assembled monolayer were deduced from molecular simulations with polarizable force fields. We study what happens when the surface presents negative charges. At moderately charged surfaces, we observe strong co-ion adsorption and clear specific ion effects at biological concentrations. At high surface charge densities, the co-ions are pushed away from the interface. We predict that Cl- ions can also be excluded from the surface by increasing the concentration of NaI. This ion competition effect (I- versus Cl-) may be relevant for ion-specific partitioning in multiphase systems where polarizable ions accumulate in phases with large surface areas.     

On the effects of ion-wall chemical association on the electric double layer: a density functional approach for the restricted primitive model at a charged wall

We describe a density functional theory for the restricted primitive model of ionic fluid at a charged wall with active sites to which ions can bond. The theory is an extension of our recent approach [Pizio et al., J. Chem. Phys. 121, 11957 (2004)] and is focused in the effects of specific adsorption of ions on the wall, besides the electrostatic phenomena. In order to solve the problem, we use the first-order thermodynamic perturbation theory of chemical association developed by Wertheim [J. Chem. Phys. 87, 7323 (1987)]. The microscopic structure of the electric double layer and the amount of adsorbed charge are investigated. Also, the temperature dependence of capacitance is analyzed. The capacitance depends on the kind of ions that form associative bonds with the surface sites and is determined by a net charge acting on the diffuse layer. The shape of the temperature dependence of capacitance essentially depends on the association energy and the density of bonding sites.     

An approach to the method for determination of surface potential on solid/liquid interface: theory

The electrochemical properties on solid particle surfaces in an aqueous system have found wide application in many fields. However, for some of them there are no reliable methods of determination. What is particularly worth mentioning is the surface potentials of solid particles. Though this is a most important property and a most basic parameter in colloid interface electrochemistry, no reliable method for its determination is available yet. In the present paper, based on the diffuse double-layer theory, mathematical relations are constructed between the average concentration of ions positively adsorbed in the diffuse double layer and the surface potential of solid particles, thus transforming the determination of surface potential of solid particles into that of the average concentration of ions in the diffuse double layer, and then by applying the standard relationships of Gouy-Chapman theory, the mathematical relations of the average concentration of ions in the diffuse double layer with surface charge density, electrical field strength at surface, and specific surface area of solid particles are constructed.     

Polarization of a diffuse soft particle subjected to an alternating current field

The polarization of a diffuse soft particle submerged in an aqueous electrolyte and subjected to a uniform alternating electric field is theoretically analyzed with the standard electrokinetic model (the Poisson-Nernst-Planck equations). The particle consists of a rigid uncharged core and a charged diffuse polyelectrolytic shell (soft layer) permeable to ions and solvent. Our focus is on the impact of the characteristics of the soft layer including the Donnan potential, the soft layer thickness, and the friction coefficient of the soft layer on the dipole coefficient, characterizing the strength of the polarization. Under the limits of thin double layers and thin polyelectrolytic shells, approximate analytical expressions to evaluate the dipole moment coefficients are derived for high-frequency and low-frequency ranges, respectively. The analytical results are compared and agree favorably with those numerically computed by the standard model. Interestingly, we discover that when the double layer is comparable to the soft layer the dipole moment behaves qualitatively differently at different Donnan potentials. When the Donnan potential is small, the dipole moment decreases as the double layer increases. In contrast, at large Donnan potentials, the dipole moment increases with the increase in the double layer. The distinct responses to Donnan potentials are attributed to the impact of the associated double layer on the charge distribution of mobile ions inside the soft layer. The theoretical model provides a fundamental basis for interpreting the polarization of heterogeneous systems, including environmental or biological colloids or microgel particles.     

Mechanisms behind concentration profiles illustrated by charge and concentration distributions around ions in double layers

The mechanisms behind the behaviour of concentration and charge density profiles in diffuse electric double layers are investigated quantitatively for 1:1 and 2:2 electrolytes. This is done by analysing various contributions to the mean force that acts on each ion. The forces are obtained from the calculated ionic charge and concentration distributions around individual ions at various positions in the double layer. These distributions are presented graphically which allows an immediate visual illustration of the mechanisms in action. Some features studied are charge inversion in double layers for divalent aqueous electrolytes, overcompensation of surface charge due to large amounts of physisorbed counterions, ion size effects in the double layer structure and various mechanisms that cause deviations from the predictions of the Poisson–Boltzmann approximation. A major objective of the paper is to present the results in a visual form and explain aspects of modern double layer theory in a simple manner.     

Direct measurement of ion accumulation at the electrode electrolyte interface under an oscillatory electric field

The ionic charge accumulation at the metal-electrolyte interface is directly measured by using differential interferometry as a function of magnitude and frequency (2-50 kHz) of external electric field. The technique developed probes the ion dynamics confined to the electrical double layer. The amplitude of modulation of the ions is linearly proportional to the amplitude of applied potential. The linearity is observed up to high electrode potentials and salt concentrations. The frequency response of the ion dynamics at the interface is interpreted in terms of the classical RC model.     

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.     

Chemical composition and structure of the surface layers-products of interaction between steel 3 and hostile aqueous environment: The effect of the environment

The composition and structure of layers formed by corrosion products at the open-circuit and passive potentials on the surface of steel 3 in aqueous media containing sulfate ions, borate ions, or their mixtures are studied by X-ray photoelectron spectroscopy and secondary ion mass spectrometry. The composition and structure of both the phase surface layers and the adsorption surface layers are found to depend on the solution nature. The composition and structure of a corrosion product layer; the composition of the double layer, in particular, the surface charge and potential; and the anion role as a corrosion inhibitor or activator depend on the way the anion coordinates with the corroding-metal surface. The coordination may be strong, in an inner coordination sphere (borate ions), or less strong, in an outer coordination sphere (sulfate ions) of a cation on the surface.     

Surface Raman Study of Cyanide Adsorption at Platinum Surface

Cyanide, a pseudohalide ion,is a very important anion with both practical and fundamental significance. It is advantageous to employ pseudohalide ions as specific adsorbates on an electrode surface to provide a wider double layer region, and it therefore becomes easier to probe the potential-dependent dynamics of the interface in the absence of complications from electrode-mediated reactions.     

The influence of crystallographic inhomogeneity of a polycrystalline electrode surface on the behavior of the electric double-layer

The specific features of the electric double-layer structure at polycrystalline electrodes in the absence of specific ion adsorption have been examined for two different models: Model I and Model II. In the case of Model I each of the faces showing on the surface of a polycrystalline electrode retains its own Helmholtz and diffuse double layers. In the case of Model II the faces retain only their own Helmholtz layer, whereas the diffuse layer is common to the entire electrode surface. The difference of zero charge potentials of the faces is defined both by their dissimilar hydrophilic properties and by different work functions. The experimental data available at present on the electric double-layer structure at polycrystalline electrodes for which the potentials of zero charge of the faces differ significantly are described by Model I.