Roland Kjellander

Inhomogeneous Coulomb fluids with image interactions between planar surfaces. I

Description of Coulomb particles near a surface is complicated by the effect of the surface on the ion–ion correlations, the electrostatic images (if the surface is a dielectric boundary), and the long range of the correlations in the lateral direction. We formulate the problem of the ion distribution for inhomogeneous Coulomb fluids with an arbitrary core potential and confined between two planar surfaces, with which the particles can interect via any short‐ranged potential. All orders of image interactions are included into an effective position‐dependent pair potential. The problem is solved by mapping the inhomogeneus three‐dimensional system into a homogeneous two‐dimensional one. The system is subdivided into M layers, and then shown to be isomorphic to an M‐component fluid mixture in two dimensions. The mapping becomes exact as the number of layers (‘‘components’’) M→∞, and is accordingly an excellent approximation for finite, but large M. The correlations and other statistical mechanical functions can now be obtained with any conventional closure scheme. This forms the basis for a numerical method to solve the complete integral equations for the one‐ and two‐particle distribution functions, using, e.g., the hypernetted chain (HNC) closure for the inhomogeneous pair correlations as the sole approximation. The associated numerical procedures are briefly described. The method could also be applied to study various problems for solute particles interacting via other pair potentials.

Double layer interactions in mono‐ and divalent electrolytes: A comparison of the anisotropic HNC theory and Monte Carlo simulations

The interaction between charged surfaces in 1:1, 1:2, and 2:2 electrolyte solutions at various concentrations have been calculated using the anisotropic hypernetted chain (HNC) theory and Monte Carlo (MC) simulations. For divalent counterions, the surface interaction has an attractive minimum at short separations. This minimum turns more attractive at increasing electrolyte concentration, while the interaction at somewhat larger separations becomes oscillatory. The agreement between the HNC and the MC results is excellent for the 1:2 and 2:2 electrolyte systems. For 1:1 electrolytes the surface interaction is repulsive except at high concentrations at which it shows a weak attractive minimum. The HNC and the MC results agree quantitatively except in a few angstroms wide region at short separations, where the agreement is only qualitative due to a slight difference in the contributions from the hard core interactions. This is a consequence of the neglect of the short‐range bridge function in the HNC approx...

A theoretical and experimental study of forces between charged mica surfaces in aqueous CaCl2 solutions

The interaction between two mica surfaces immersed in CaCl2 solutions has been directly measured. Accurate theoretical calculations, including the anisotropic hypernetted chain (HNC) theory used in this work, predict that at reasonably high surface charge densities the electrical double layer interactions in the presence of divalent counterions should be attractive at short surface separations (in the range 0.6–2 nm). Under most conditions investigated, the experimental results indicate that this indeed is the case. The attraction is a consequence of the correlation between the ions. In addition to the double layer interaction, in most cases the measured force contains an oscillatory contribution. At low CaCl2 concentrations and small surface separations, Ca2+ ions between the surfaces are exchanged for H3O+ ions, which decreases the oscillatory interaction and the ion‐correlation attraction. At high concentrations the force is dominated by a strong hydration repulsion, which is related to the adoration o...

Dressed‐ion theory for electrolyte solutions: A Debye–Hückel‐like reformulation of the exact theory for the primitive model

A detailed derivation of the dressed‐ion theory—a formally exact theory for primitive model Coulomb fluids—is presented for the case of bulk electrolyte solutions. It is shown that the exact average electrostatic potential, ψ av(r), in the ion atmosphere around each ion satisfies a linear Poisson–Boltzmann (PB) equation for ‘‘dressed ions,’’ each of which consists of a central ion together with a specific part of the surrounding ion cloud. The dressed‐ion charge distribution—a renormalized charge for each ion—takes the role that the bare ionic charge has in the usual PB equation. Apart from this, virtually the only difference between the exact dressed‐ion and the approximate Debye–Huckel (DH) theories for the pair distribution function is that the former theory is nonlocal; the spread‐out nature of the dressed‐ion charge distribution gives rise to a nonlocal polarization response to the average potential. The linear response function relating the polarization and the average potential is investigated in t...

CHARGE INVERSION IN ELECTRIC DOUBLE LAYERS AND EFFECTS OF DIFFERENT SIZES FOR COUNTERIONS AND COIONS

The molecular mechanisms behind the phenomena of charge inversion in the diffuse electric double layer (i.e., inversion of sign in the charge distribution profile) and attractive double-layer interactions between equally charged surfaces have been investigated with statistical mechanical methods. In aqueous systems with monovalent electrolytes these phenomena can, for example, be induced by having larger coions than counterions, while for divalent electrolytes they occur primarily for electrostatic reasons. We have identified several different mechanisms for the charge inversion. In one of the mechanisms, which only occurs at low surface charge density, the different distances of closest approach to the surface for the ions are crucial, while in some other mechanisms active in the monovalent systems the different size in the ion–ion interaction is the important factor. For divalent electrolytes the electrostatic part of the ion–ion correlations is the dominating effect and ion sizes are not as important, ...

Interaction of charged surfaces in electrolyte solutions

Abstract We report a restricted primitive model calculation of the double-layer interaction between two uniformly charged surfaces immersed in an electrolyte solution, where the anisotropic hypernetted chain approximation is utilized for the pair correlations. The strong, attractive pressure contribution resulting from ion-ion correlations is very similar to that found earlier for double layers with only counterions present. Consequently, the Poisson-Boltzmann equation, which neglects ion-ion correlations, significantly overestimates the double-layer repulsion in most situations. Some ion concentration profiles are presented, and for large separations between the surfaces the profiles close to each surface agree with grand canonical simulation results for a single wall.

Perturbation of hydrogen bonding in water near polar surfaces

Abstract We report the results of a molecular dynamics simulation of water between polar molecular surfaces. Hydrogen bonding between water molecules is decreased in the first few layers of water, although the number of nearest neighbours to each water molecule is increased. The results indicate that near a polar surface, electric fields associated with discrete surface charges strongly orient neighbouring water molecules, thus weakening the hydrogen-bond network.

An exact but linear and Poisson-Boltzmann-like theory for electrolytes and colloid dispersions in the primitive model

Abstract It is shown that the exact theory for electrolyte solutions and colloid dispersions in the primitive model can be reformulated in terms of quasiparticles, constituting “dressed” ions or colloid particles, where parts of the ion cloud around each bare particle are included in the quasiparticle. The resulting exact theory for the dressed particles is virtually identical to the linear Poisson—Boltzmann (PB) theory, where the bare particle charges in the PB theory are replaced by the internal charge distributions of the quasiparticles. Nonlinearities and many-body correlations only contribute to the internal charge distributions of the quasiparticles. The long-range asymptotic behaviour of the pair correlations is analyzed.

The chemical potential of simple fluids in a common class of integral equation closures

An explicit formula for the chemical potential (μ) of simple fluids is derived for a whole class of integral equation theories, including the Percus–Yevick approximation and some other, more recently proposed closures. This formula only requires the pair correlation functions for one single state of the system, and applies to both homogeneous and inhomogeneous fluids. The coupling parameter integration method to calculate the chemical potential—where one particle is gradually coupled to the rest—is also investigated. It is shown that the μ value obtained in the approximate theories is not unique, but depends on the integration path. This behavior is due to inconsistencies of the approximation, which are discussed in some detail. For a certain choice of integration path the μ values obtained using the latter method agree with those from the explicit formula. Numerical results for the different closures are presented for a hard sphere fluid. The accuracy of μ depends strongly on the quality of the bridge function inside the hard core diameter.

Inhomogeneous Coulomb fluids with image interactions between planar surfaces. II. On the anisotropic hypernetted chain approximation

The physical assumptions underlying the anisotropic hypernetted chain (HNC) closure for the pair correlations in inhomogeneous fluids and the accompanying equation for the density distribution are discussed, treating the implications and limitations of the approximation. The theory is capable of incorporating image charge interactions (due to dielectric discontinuities at the surfaces) and discreteness of surface charges without further approximations. The computational implementation of the theory is described in some detail.