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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]

The free energy perturbation method is employed to study the free energy of solvation of a drug molecule in its pure drug melt, which is supposed to be considered the second step in predicting the solubility of drugs in water. The analysis reveals contradictory results, revealing that the Coulomb interactions are much weaker in pure drug systems, whereas the van der Waals interactions are extremely important and highly influence the interaction.

The study uses the free energy of the perturbation method and the optimized potential for the liquid simulations to take the first step for the computational prediction of drug solubility by measuring the free energy of hydration. The analysis provides an accurate demonstration of the macroscopic surface tension of water, which is not in agreement with the surface tension for water around a spherical cavity that normally is supposed to be dependent on the size of the cavity.

A method is suggested to construct good bias potentials ('balancing factors') to be used in expanded ensemble (EE) calculations of chemical potential of solution. The method uses a coupling parameter pathway that avoids large variations in free energy, and a bias potential construction that approximately eliminates the remaining free energy variations along the path.

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]

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]

The calculation results of the interaction pressure between two planar charged walls for a range of surface charge densities, strengths of the anion-wall dispersion interaction and bulk electrolyte concentrations are presented. The image charge interactions are observed to show considerable depletion attraction between the walls for low surface charge densities.

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 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]

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]

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.

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]