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The Faraday Discussions article delves into the equilibrium behavior of ionic fluids, covering topics such as thermodynamics, nanostructure, phase behavior, and activity. Researchers engage in a discussion on phase separation, ion size differences, and temperature effects, exploring the impact of ion pairing, solvation properties, and polymer conformation on the phase separation of salt solutions. The study aims to understand the driving forces behind liquid-liquid phase separation and its practical applications in electrochemical devices and batteries, emphasizing the need for diverse datasets and molecular structure correlations to enhance predictive models for deep eutectic solvents. [Extracted from the article]

The document delves into the properties of dense ionic fluids, particularly the viscoelastic characteristics influenced by charge-charge correlations. Researchers shared their findings on topics like charge alternation peaks relaxation and micelle behavior in deep eutectic solvents. Interactions between hydrogenated and fluorinated moieties in ionic liquid mixtures were examined, revealing no phase separation. Additionally, the use of machine learning potentials in molecular dynamics simulations to study transport coefficients in complex charged solutions was explored, with discussions on the choice of potentials, treatment of long-range Coulomb interactions, and the accuracy of DFT calculations. The study focuses on a specific ionic liquid but hints at future exploration of more complex systems. [Extracted from the article]

A unified treatment of oscillatory and monotonic exponential decays of interactions in electrolytes is displayed, which highlights the role of dielectric response of the fluid in terms of renormalized (effective) dielectric permittivity and charges. An exact, but physically transparent statistical mechanical formalism is thereby used, which is presented in a systematic, pedagogical manner. Both the oscillatory and monotonic behaviors are given by an equation for the decay length of screened electrostatic interactions that is very similar to the classical expression for the Debye length. The renormalized dielectric permittivities, which have similar roles for electrolytes as the dielectric constant has for pure polar fluids, consist in general of several entities with different physical meanings. They are connected to dielectric response of the fluid on the same length scale as the decay length of the screened interactions. Only in cases where the decay length is very long, these permittivities correspond approximately to a dielectric response in the long-wavelength limit, like the dielectric constant for polar fluids. Experimentally observed long-range exponentially decaying surface forces are analyzed as well as the oscillatory forces observed for short to intermediate surface separations. Both occur in some ionic liquids and in concentrated as well as very dilute electrolyte solutions. The coexisting modes of decay are in general determined by the bulk properties of the fluid and not by the solvation of the surfaces; in the present cases, they are given by the behavior of the screened Coulomb interaction of the bulk fluid. The surface-fluid interactions influence the amplitudes and signs or phases of the different modes of the decay, but not their decay lengths and wavelengths. The similarities between some ionic liquids and very dilute electrolyte solutions as regards both the long-range monotonic and the oscillatory decays are analyzed. [ABSTRACT FROM AUTHOR]

Screened electrostatic interactions in ionic liquids are investigated by means of exact statistical mechanical analysis combined with physical arguments that enhance the transparency and conceptual accessibility of the analysis and results. The constituent ions and immersed particles in the liquid can have arbitrary shapes and any internal charge distributions. The decay of the screened electrostatic potential and the free energy of interaction in ionic liquids can be exponentially damped oscillatory (like in molten simple salts) as well as plain exponential and long-ranged (like in dilute electrolyte solutions). Both behaviors are in agreement with the exact statistical mechanical analysis and reasons for their appearances are investigated. Exact but surprisingly simple expressions for the decay parameter k of the screened electrostatics are obtained, which replace the classical expression for the Debye-Hückel parameter kDH (the reciprocal Debye length). The expressions are applicable both for cases with plain exponential and oscillatory behaviors. The key importance of nonlocal electrostatics is thereby demonstrated explicitly. Dielectric properties of ionic liquids and other electrolytes are investigated, in particular the static dielectric function ∊(k) and some effective relative permittivities (εreff and εr*), which take roles that the dielectric constant εr has for polar liquids consisting of electroneutral molecules. The dielectric constant in the latter case, which is the limit of ∊(k) when the wave number k → 0, can be expressed solely in terms of dipolar features of the molecules. In contrast to this, the effective dielectric permittivities of ionic liquids have contributions also from quadrupolar, octupolar, and higher multipolar features of the constituent ions. The "dielectric constant" of electrolytes does not exist since ∊(k) → ∞ when k → 0, a well-known effect of perfect screening. The effective relative permittivities, εreff, and εr* of ionic liquids are obtained from the non-diverging part of ∊(k), but not as a k → 0 limit. Influences of ion associations, especially pairing, are investigated for screened electrostatics and these permittivities. A general, multipolar expansion of ∊(k) is derived and used to analyze dielectric properties of ionic liquids and other electrolytes. [ABSTRACT FROM AUTHOR]

Packing frustration for confined fluids, i.e., the incompatibility between the preferred packing of the fluid particles and the packing constraints imposed by the confining surfaces, is studied for a dense hard-sphere fluid confined between planar hard surfaces at short separations. The detailed mechanism for the frustration is investigated via an analysis of the anisotropic pair distributions of the confined fluid, as obtained from integral equation theory for inhomogeneous fluids at pair correlation level within the anisotropic Percus-Yevick approximation. By examining the mean forces that arise from interparticle collisions around the periphery of each particle in the slit, we calculate the principal components of the mean force for the density profile -- each component being the sum of collisional forces on a particle's hemisphere facing either surface. The variations of these components with the slit width give rise to rather intricate changes in the layer structure between the surfaces, but, as shown in this paper, the basis of these variations can be easily understood qualitatively and often also semi-quantitatively. It is found that the ordering of the fluid is in essence governed locally by the packing constraints at each single solid-fluid interface. A simple superposition of forces due to the presence of each surface gives surprisingly good estimates of the density profiles, but there remain nontrivial confinement effects that cannot be explained by superposition, most notably the magnitude of the excess adsorption of particles in the slit relative to bulk. [ABSTRACT FROM AUTHOR]

The Poisson–Boltzmann and Debye–Hückel approximations for the pair distributions and mean electrostatic potential in electrolytes predict that these entities have one single decay mode with a decay length equal to the Debye length 1/κD, that is, they have a characteristic contribution that decays with distance r like e−κDr/r. However, in reality, electrolytes have several decay modes e−κr/r, e−κ′r/r etc. with different decay lengths, 1/κ, 1/κ′ etc., that in general are different from the Debye length. As an illustration of the significance of multiple decay modes in electrolytes, the present work uses a very simple extension of the Debye–Hückel approximation with two decay lengths, which predicts oscillatory modes when appropriate. This approach gives very accurate results for radial distribution functions and thermodynamic properties of aqueous solutions of monovalent electrolytes for all concentrations investigated, including high ones. It is designed to satisfy necessary statistical mechanical conditions for the distributions. The effective dielectric permittivity of the electrolyte plays an important role in the theory and each mode has its own value of this entity. Electrolytes with high electrostatic coupling, like those with multivalent ions and/or with solvent of low dielectric constant, have decay lengths in dilute solutions that substantially deviate from the Debye length. It is shown that this is caused by nonlinear ion–ion correlation effects and the origin of under-screening, i.e., 1/κ > 1/κD, in dilute symmetric electrolytes is analyzed. The under-screening is accompanied by an increase in the effective dielectric permittivity that is also caused by these correlations. The theoretical results for the decay length are successfully compared with recent experimental data for simple electrolytes in various solvents. The paper includes background material on electrolyte theory and screening in order to be accessible for nonexperts in the field. [ABSTRACT FROM AUTHOR]

The interaction pressure between two uncharged planar walls immersed in various electrolyte solutions containing mono- and/or divalent ions is investigated. The solution is treated as a primitive model electrolyte, and the wall surfaces constitute dielectric discontinuities. Ionic image charge and ion-wall dispersion interactions are included. The interaction parameters are appropriate for hydrocarbon (polystyrene)/water interfaces, and the electrolyte concentrations considered lie between 0.250M and 1.00M. The anisotropic hypernetted chain method is used to self-consistently calculate the ion density profiles and the ion-ion correlation functions in the inhomogeneous electrolyte. Thereby, the effects of image charge interactions and dispersion interactions on the pressure and the electrolyte structure are included in a fully consistent manner. The explicit consideration of correlations between the ions in the presence of image charges ensures that the screening of the zero-frequency van der Waals interaction is taken into account. Of special interest are the effects of asymmetries between anions and cations with respect to valency and/or dispersion interaction with the walls. Such asymmetries create an electric double layer in the electrolyte outside each electroneutral surface. This causes the wall-wall interaction for large surface separations to be similar to the interaction between charged surfaces. For intermediate separations, around 1–2 nm, a substantial repulsive peak appears in the ionic pressure. In some cases the repulsion is larger than the van der Waals attraction between the walls, which implies that there is a repulsive barrier in the total pressure despite that the surfaces are uncharged. The strongest repulsion is found for 2:1 electrolytes where the monovalent anions interact strongly with the walls via dispersion forces. In general, ion-wall dispersion forces acting on ions of lower valency have a much greater effect than equally strong dispersion forces acting on ions of higher valency. This is mainly due to the more strongly repulsive image charge forces on ions of higher valency that counteract the attractive dispersion forces. Effects of confinement on the ion-ion correlations also contribute to this difference. For all electrolytes the interaction pressure from the ions is attractive for small surface separations. The main cause is a depletion of ions between the walls from the self-image repulsion and confinement effects. For totally symmetric electrolytes the attractive pressure extends to large separations in most cases. [ABSTRACT FROM AUTHOR]

Two effects of interactions between polarizable ions and polarizable walls in electric double layers are investigated: ionic image charge forces and ion-wall dispersion forces. The first must be included for a consistent treatment of the wall-wall van der Waals (vdW) interaction, since it contains the effect of screening of the static part of the vdW interaction. The second has been suggested to give rise to ion specificity in double layer interactions. The strength of the ion-wall dispersion forces are estimated from quantum mechanical calculations of ionic polarizability and from experimental data for the dielectric functions of the media. The ion density profiles and the anisotropic ion-ion distribution functions in the double layer are calculated in the highly accurate anisotropic hypernetted chain approximation, which allows the correct treatment of the image charge forces. The double layer interactions are evaluated from these distribution functions. It is found that it is important to include both kinds of ion-wall forces. Quantitative and sometimes even qualitative differences occur in the double layer interactions depending on the ionic species of the electrolyte due to different strengths of the ion-wall dispersion interactions. [ABSTRACT FROM AUTHOR]

In this paper we derive the multipolar expansion of the screened Coulomb potential in electrolyte solutions with molecular solvent. The solute and solvent molecules can have arbitrary sizes, shapes, and internal charge distributions. We use the exact statistical mechanical definition of renormalized charge distributions coming from “dressed molecule theory” to determine the effective multipoles of a molecule immersed in an electrolyte. The effects of many-body correlations are fully included in our formally exact theory. We restrict ourselves to sufficiently dilute solutions so the screened Coulomb potential decays for large distances like a Yukawa function, exp(-κr)/r, where r is the distance and 1/κ is the decay length (it is normally different from the Debye length). The resulting “Yukawa electrostatics” differ in many respects from ordinary, unscreened electrostatics. The “Yukawa charge” of a molecule (the lowest order moment in the multipolar expansion) is in general not equal to its Coulombic charge and it is not the integral of the renormalized charge distribution of the molecule. Moreover, as shown in this paper, the multipolar expansion of the Yukawa potential does not correspond, contrary to the case of the Coulomb potential, to its asymptotic expansion for large r. As a consequence, the charge term in the multipolar expansion is not the leading term in the asymptotic expansion. Instead, for large r values, multipoles of all orders contribute to the leading asymptotic term. Thus, the electrostatic potential from, for example, an electroneutral solvent molecule in an electrolyte solution has generally the same range as that from an ion. The proper asymptotic expansion for electrostatic interactions in electrolytes is derived. It is briefly shown how the multipole expansion formalism can also be applied in the Poisson-Boltzmann approximation for primitive model electrolytes. [ABSTRACT FROM AUTHOR]

The effects of ionic size asymmetry on long-range electrostatic interactions in electrolyte solutions are investigated within the primitive model. Using the formalism of dressed ion theory we analyze correlation functions from Monte Carlo simulations and the hypernetted chain approximation for size asymmetric 1:1 electrolytes. We obtain decay lengths of the screened Coulomb potential, effective charges of ions, and effective permittivity of the solution. It is found that the variation of these quantities with the degree of size asymmetry depends in a quite intricate manner on the interplay between the electrostatic coupling and excluded volume effects. In most cases the magnitude of the effective charge of the small ion species is larger than that of the large species; the difference increases with increasing size asymmetry. The effective charges of both species are larger (in absolute value) than the bare ionic charge, except for high asymmetry where the effective charge of the large ions can become smaller than the bare charge. [ABSTRACT FROM AUTHOR]

An exact statistical mechanical theory for fluid mixtures of rigid molecules with arbitrary charge distributions, sizes, and shapes is presented. It deals with many-body effects in electrostatic interactions between molecules in fluids and can, for example, be applied to mixtures of polar molecules and to solutions of electrolytes or colloidal dispersions in polar molecular solvents. All solute and solvent molecules are treated on the same fundamental level in statistical mechanics. The exact screened Coulomb potential [lowercase_phi_synonym][sup 0](r) for the solution is given a general definition. A renormalized charge distribution ρ[sub i][sup 0] for each molecule of any species i is uniquely defined such that the total electrostatic potential from each i molecule is exactly given by [lowercase_phi_synonym][sup 0] with ρ[sub i][sup 0] as the source. By using ρ[sub i][sup 0] when calculating the interaction between the molecule and the total electrostatic potential from any source, one includes the indirect effects from the surrounding polarizable molecular medium on the electrostatic part of the potential of mean force for the molecule. In general, all kinds of molecules (charged, polar, and apolar ones) acquire renormalized charges in electrolyte solutions. The dielectric function and other fundamental properties of the mixture can be expressed in terms of ρ[sub i][sup 0] for all species. The formally exact theory is expressed in a Poisson–Boltzmann (PB)-type manner by using the renormalized rather than actual (bare) charges and it is shown that the total electrostatic potential due to a molecule satisfies an equation that is the exact version of the linear PB equation. The decay behaviors of [lowercase_phi_synonym][sup 0], the pair potential of mean force and pair distribution functions are investigated. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We analyze the decay of structural correlation functions for 1:1, 1:2, and 2:2 electrolyte solutions obtained from Monte Carlo simulations. It is found that by the use of dressed ion theory and a simple Picard iteration scheme one can extract the leading decay parameters with high accuracy, even from simulations with a rather limited number of ions in the simulation cell. The extraction scheme consists of replacing in a self-consistent manner the tails of the simulated pair distribution functions by analytical expressions evaluated by residue analysis of short-ranged parts of the correlation functions. Numerical results in this work are restricted to primitive model electrolytes where the solvent only enters as a dielectric continuum. The leading decay parameters of the simulated correlation functions are compared to results obtained from the hypernetted chain (HNC) approximation. For 1:1 and 1:2 electrolytes in aqueous solution the simulation results confirm predictions from the HNC approximation. For 2:2 electrolytes the HNC results agree qualitatively with the simulations but deviate quantitatively. To investigate artifacts induced by boundary conditions used in the simulations we analyze correlation functions obtained from simulations in a spherical cell as well as with cubic periodic boundary conditions. The results and method of analysis presented are restricted to electrolyte concentrations at which the leading decay terms of the pair distribution functions exhibit monotonic exponential decay. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Examines the screening and asymptotic decay of pair distributions in asymmetric electrolytes. Use of the dressed ion theory; Effect of dielectric response function on asymptotic behavior; Relationship between the asymptotic behavior of charge-charge, density-density and charge-density correlation.

Investigates the charge inversion in electric double layer with statistical mechanical methods. Interactions of the double-layer between charged surfaces; Induction of larger coions in charge inversion phenomena; Occurrence of charge inversion at low surface charge density.

The correlation functions of bulk symmetric electrolytes in the restricted primitive model are analyzed using the formalism of the dressed ion theory of Kjellander and Mitchell [Chem. Phys. Lett. 200, 76 (1992), J. Chem. Phys. 101, 603 (1994)]. An important result of this analysis is that the exact theory for the pair correlation functions can be cast in a form that is virtually identical to that of the Debye–Hückel theory provided one uses the renormalized charges of the ions—‘‘dressed ions’’—instead of bare ion charges. In the current work the (state dependent) charges of these dressed ions are investigated using the HNC approximation. The asymptotic decay of the pair correlation functions are analyzed in terms of the effective point charges of the ions and the effective permittivity of the electrolyte solution, concepts which are given rigorous and physically transparent definitions in the dressed ion theory. Several transitions between regimes with different qualitative behavior of the pair correlation functions are demonstrated, in addition to the well-known transition between monotonic and oscillatory damped decay. By means of an analysis of the singularities of the correlation functions in complex Fourier space, dressed ion theory provides a general method to determine these transitions from numerical pair correlation data and in this paper results are given for symmetric electrolytes with monovalent and divalent ions. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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–Hückel (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 the general case and is found to be intimately related to the dressed-ion charge distributions. A close relationship is also demonstrated between these charge distributions and the electrostatic susceptibility of the electrolyte solution. The theory gives a rigorous definition of the concept of effective point charges for ions. Except at high coupling, the long-range asymptotic behavior of the pair distribution functions is of the Debye–Hückel form, but with effective values of the ionic charges (qi*) and a decay length (κ-1) different from the Debye length (κ-1D). A simple formula relating qi* and κ is derived. Explicit formulae for qi* and κ in terms of κD are given in the limit of low electrolyte concentrations. The long range asymptotic behaviors of the bridge function and the short range parts of the direct and total correlation functions are... [ABSTRACT FROM AUTHOR]

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 approximation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The electrostatic fluctuation interactions between two surfaces which carry charged or dipolar, laterally mobile particles, are investigated using both a formally exact theory and approximate methods. Each surface constitutes the boundary between two dielectric continua and has no net charge. The exact analysis demonstrates the interdependence of the van der Waals interaction between the dielectric media and the electrostatic image interactions of the particles. General asymptotic laws for the pressure between the surfaces, valid at large separations, are extracted from the exact equations. Even at relatively small separations, the asymptotic expressions give surprisingly good estimates of the actual interactions, as calculated using the hypernetted chain equation and Monte Carlo techniques. A simple mean field perturbation approximation is also investigated and is shown to give good results, provided accurate pair distributions are known for the corresponding isolated, single surface. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The anisotropic hypernetted chain approximation is used to calculate the one- and two-particle distribution functions for an ionic fluid confined between two charged surfaces. Particular attention is given to the anisotropic distribution functions g(R,R’), c(R,R’), and ρ(R)g(R,R’) (where g, c, and ρ are the pair distribution, direct correlation, and density functions, respectively). They are plotted for various cases and are used to illustrate the mechanisms of the double-layer interaction and other aspects of the system. The effects of image charges (when each surface is a dielectric boundary) and discrete surface charges are investigated. [ABSTRACT FROM AUTHOR]

Screened electrostatic surface forces, also called double layer forces, between surfaces in ionic liquids can, depending on the circumstances, decay in an exponentially damped, oscillatory manner or in a plain exponential way (the latter as in dilute electrolyte solutions where ion–ion correlations are very weak). The occurrence of both of these behaviors in dense ionic liquids, where ion–ion correlations are very strong, is analyzed in the current work using exact statistical mechanics formulated in a manner that is physically transparent. A vital ingredient in understanding the decay behaviors is the fact that electrostatics in dense electrolytes have a non-local nature caused by the strong correlations. It is shown that the effects of non-locality can be elucidated by a remarkably simple, general expression for the decay parameter κ that replaces the classical expression for the inverse Debye length κDH of the Debye–Hückel (DH) and non-linear Poisson–Boltzmann approximations. This exact expression is valid for both the plain exponential and the oscillatory cases. It shows how strong correlations can give rise to plain exponential decay with a long decay length. Such a decay can arise from anion–cation associations of various kinds, for instance transient ion pairing or association caused by many-body correlations; ion pairing is a possibility but not a necessity for this to occur. Theoretical analysis is done for systems consisting of ions with an arbitrary shape and internal charge density and immersed planar walls with arbitrary internal charge distribution and any short-range ion–surface interaction. The screened electrostatic surface force between two walls is at large separations proportional to the product of effective surface charge densities of each wall. For the oscillatory case, each wall contributes with a phase shift to the oscillations of the interaction. [ABSTRACT FROM AUTHOR]

The concept of effective charges of charged particles in electrolyte solutions is discussed and defined in a general and exact way for cases with 'exponential' screening. The effective charges thus obtained are equivalent to those used in dressed ion theory (DIT) (Kjellander, R., and Mitchell, D. J., 1992, Chem. Phys. Lett., 200, 76; 1994, J. chem. Phys., 101, 603), which is an exact reformulation of the statistical mechanics of electrolytes, DIT is particularly suited for use in analyses of screening phenomena in electrolytes, and the reasons why it has this property are discussed in some detail. The DIT formalism is applied to obtain effective ionic charges q *, effective permittivity E, and screening length 1/ kappa , of 1:2 aqueous electrolyte solutions in the hypernetted chain approximation. In the limit of infinite dilution q * the actual charge, E the permittivity of the solvent and 1/kappa ~ the Debye length. The values of these quantities deviate much more from these limiting values compared with similar 1:1 and 2:2 electrolytes, and this is the case even at quite low concentrations. [ABSTRACT FROM AUTHOR]

Anisotropic ion-ion distribution functions g ( R , R ), where R and R are the positions of ions of species i and j respectively, and various other properties of electric double layer systems have been calculated by simulation and integral equation methods. The system is composed of a 1 : 1 or 2 : 1 electrolyte solution between two planar walls with rather high surface charge - 2 density (0.267 C m ) and in equilibrium with a bulk electrolyte solution with a certain concentration (1.0 m or 2.0 m). In the integral equation calculations, the hypernetted chain (HNC) or the reference hypernetted chain (RHNC) closure has been applied for the ion-ion distribution functions in the inhomogeneous electrolyte (the so-called anisotropic HNC or RHNC approximations). The Widom test particle technique has been used to calculate the ion-ion distribution functions in the simulations. The results of the anisotropic RHNC calculations and the simulations are in almost perfect agreement throughout (they virtually coincide). The HNC approximation is almost as good as the RHNC approximation for 2 : 1 electrolytes, but it is not as good for 1 : 1 electrolytes due to the higher packing density of the monovalent counterions near the surfaces. The excellent results for the pair distributions ensures that thermodynamic properties calculated in the RHNC approximation will be very good. The double layer interaction pressure, which is sensitive to details of the distributions, is indeed in excellent agreement with the simulations. The results also show that the Widom technique is successful for calculating pair distributions for inhomogeneous electrolytes by simulation. ij 1 2 1 2. [ABSTRACT FROM AUTHOR]

Dressed ion theory, an exact statistical mechanical formalism for electrolyte systems in the primitive model, is extended to electric double layer systems in various geometries. In this theory an exact equation that has the same form as the linearized Poisson-Boltzmann (PB ) equation is set up, in which 'dressed ions' take the same role in the exact theory as the bare ions have in the PB approximation. Various distribution functions are expressed in terms of the dressed ion charges. Exact asymptotic results for large particle separations are obtained for the distribution functions, the average electrostatic potential and the interaction free energies in colloid dispersions and for planar double layer systems. A practical method is derived for evaluating the effective surface charge densities of the particles. The question of whether double layer interactions between equally charged colloid particles must be repulsive at large separations (as suggested by the PB approximation ) or whether they can be attractive there is treated in some detail. [ABSTRACT FROM AUTHOR]

The anisotropic ion-ion correlation function g(Rl,R2), where Rl and R2 are the coordinates of ions 1 and 2, is calculated for double layer systems composed of counterions between two charged, planar walls. The primitive model of the electrolyte is used. The Widom formula for the excess chemical potential is applied in the neighbourhood of a confined particle in the double layer to obtain g(Rl,R2) from Monte Carlo (MC) simulations. The pair correlations are also calculated in the anisotropic RHNC approximation, where the reference hypernetted chain (RHNC) closure is applied at the pair (ion-ion) level and where the anisotropic bridge function is taken from an inhomogeneous reference system composed of a hard sphere fluid with the same density profile as the double-layer system. The results of the MC simulations and RHNC calculations are generally in very good agreement with each other. This demonstrates the fact that the anisotropic RHNC approximation is a very accurate method for calculating the various double-layer properties. It also follows that the Widom technique is a very versatile tool in simulation studies of double-layer systems. To obtain 15 points for the pair correlation function by simulation takes about 60 times longer than to obtain 200000 points by anisotropic RHNC calculations (the latter takes a few minutes on an IBM RS-6000/590 workstation). [ABSTRACT FROM AUTHOR]

Pair distributions of fluids confined between two surfaces at close distance are of fundamental importance for a variety of physical, chemical, and biological phenomena, such as interactions between macromolecules in solution, surface forces, and diffusion in narrow pores. However, in contrast to bulk fluids, properties of inhomogeneous fluids are seldom studied at the pair-distribution level. Motivated by recent experimental advances in determining anisotropic structure factors of confined fluids, we analyze theoretically the underlying anisotropic pair distributions of the archetypical hard-sphere fluid confined between two parallel hard surfaces using first-principles statistical mechanics of inhomogeneous fluids. For this purpose, we introduce an experimentally accessible ensemble-averaged local density correlation function and study its behavior as a function of confining slit width. Upon increasing the distance between the confining surfaces, we observe an alternating sequence of strongly anisotropic versus more isotropic local order. The latter is due to packing frustration of the spherical particles. This observation highlights the importance of studying inhomogeneous fluids at the pair-distribution level. [ABSTRACT FROM AUTHOR]

We show that the screening of the electrostatic potential in electrolytes can in exact theory be expressed in terms of a generalized screened Colomb potential, analogous to the Yukawa potential from the Debye–Hu¨ckel approximation, provided the source charge of the potential is renormalized. The renormalized charge distribution is identical to that of a “dressed particle” in dressed ion theory, DIT, of Kjellander and Mitchell. Using DIT we analyze the leading terms of the decay of density profiles and electrostatic potential outside a charged planar wall in contact with 1:2 electrolytes. The formalism leads in a natural manner to the definition of a primary and a secondary effective charge of an object immersed in an electrolyte. These charges are associated with the leading and second leading decay modes of the potential, which have different decay lengths. It is found that both leading terms in the decay are important; together, they give in many cases a very good representation of the density profiles and the potential for distances larger than about a couple of ionic diameters from the wall. When varying the actual (bare) surface charge density σ of the wall, two points of zero effective surface charge density are found: one at low (but nonzero) and one at high value of σ. The former occurs when the counterions are monovalent and the latter when the counterions are divalent and the electrolyte concentration is sufficiently high. Both are associated with effective charge reversals where the surface appears to attain a charge of opposite sign compared to its bare charge. The double layer interaction between two equally charged particles is attractive at large separations at a point of zero effective surface charge. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We demonstrate how to use the McMillan-Mayer theory to include solvent effects in effective solute-solute interactions for inhomogeneous systems, extending a recent derivation [S. Marcelja, Langmuir 16, 6081 (2000)] for symmetric planar double layers to the general case. In the exact treatment, the many-body potential of mean force between the solute molecules can be evaluated for an inhomogeneous reference system in equilibrium with pure bulk solvent. The reference system contains only solvent and a finite number, n, of fixed solute molecules and it has an external potential that in some cases is different from that of the original system. It is discussed how the n-body potential of mean force between the ions for the relevant cases of large n values can be approximated by a sum of effective singlet and pair interactions evaluated in the presence of, on average, all n ions, i.e., at finite concentration. In examples considered in this work we use effective interionic pair potentials evaluated from bulk electrolyte calculations at finite electrolyte concentrations. We calculate the contribution to the double layer interaction pressure arising from the interaction between ions dissolved in aqueous electrolyte. In cases of moderate or high surface charge, calculations show several new effects. At small surface separations one finds attractive and then strongly repulsive contributions. For surface charge density around one negative charge per 70 Å2 the full results for pressures resemble "secondary hydration force" measured in classical experiments in 1980s. When there is a tendency for ions to adsorb at the surfaces there is a marked change in behavior. The force is then oscillatory, reminiscent of results obtained with the surface force apparatus at low electrolyte concentration. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Presents a correction to the article 'Inhomogeneous Coulomb Fluids with Image Interactions Between Planar Surfaces. II. On the Anisotropic Hypernetted Chain Approximation,' by Roland Kjellander, which appeared in the 1988 issue of the 'Journal of Chemical Physics.'