Mean Spherical Approximation Research Articles

Prediction of Viscosity of Liquid Alkali Metals Using an Improved Mean Spherical Approximation

Prediction of Viscosity of Liquid Alkali Metals Using an Improved Mean Spherical Approximation

Closure to the PRISM equation derived from nonlinear response theory.

Nonlinear response theory is employed to derive a closure to the polymer reference interaction site model equation. The closure applies to a liquid of neutral polymers at melt densities. It can be considered a molecular generalization of the mean spherical approximation (MSA) closure of Lebowitz and Percus to the atomic Ornstein-Zernike (OZ) equation and is similar in some aspects to the reference "molecular" MSA (R-MMSA) closure of Schweizer and Yethiraj to PRISM. For a model binary blend of freely-jointed chains, the new closure predicts an unmixing critical temperature, Tc, via the susceptibility route that scales linearly with molecular weight, N, in agreement with Flory theory. Predictions for Tc of the new closure differ greatest from those of the R-MMSA at intermediate N, the latter being about 40% higher than the former there, but at large N, both theories give about the same values. For an isotopic blend of polyethylene, the new and R-MMSA closures predict a Tc about 25% higher than the experimental value, which is only moderately less accurate than the prediction of atomic OZ-MSA theory for Tc of methane. In this way, the derivation and its consequences help to identify the ingredients in a theory needed to properly model the equilibrium properties of a polymeric liquid at both short and long lengthscales.

Comment on "Binding Debye-Hückel theory for associative electrolyte solutions" [J. Chem. Phys. 159, 154503 (2023)

It is argued that the Binding Debye-Hückel (BiDH) model proposed by Naseri Boroujeni et al. [J. Chem. Phys. 159, 154503 (2023)] might not be appropriate for the description of Monte Carlo simulation data obtained for primitive model electrolytes. The first reason is that the original Debye-Hückel (DH) theory is of low accuracy for describing deviations from ideality in concentrated solutions of strong salts. The DH framework is thus a poor basis for building a model including association. The second reason is that the mean-spherical approximation, without assumption of association, apparently predicts Monte Carlo (MC) data for primitive electrolytes better than BiDH. Thus, the BiDH model seems to be simply a way of compensating for the deficiencies of DH theory by assuming association.

Response to "Comment on 'Binding Debye-Hückel theory for associative electrolyte solutions'" [J. Chem. Phys. 159, 154503 (2023)

This Response addresses critiques raised about the Binding Debye-Hückel (BiDH) theory [Naseri Boroujeni et al., J. Chem. Phys. 159, 154503 (2023)] by Simonin and Bernard [J.-P. Simonin and O. Bernard, J. Chem. Phys. (2024)]. The critiques questioned the foundational framework of the Debye-Hückel (DH) theory, the relevance of ion pairing in primitive model fluids, and the accuracy of the BiDH model compared to mean spherical approximation model. Through a systematic rebuttal, supported by extensive literature review and comparison with Monte Carlo simulation data, this Response addresses these concerns. It demonstrates the efficacy of DH theory in describing real electrolyte solutions, validates the relevance of ion pairing in primitive model fluids, and establishes the BiDH model's accuracy in describing electrolyte properties.

Simplified Versions of the Mean Spherical Approximation (MSA) for the Prediction of Activity Coefficients in Electrolytes

Simplified Versions of the Mean Spherical Approximation (MSA) for the Prediction of Activity Coefficients in Electrolytes

Measurement and modeling of the electrical conductivity of organic electrolyte solutions and their mixtures with compressed CO2

The electrochemical carbon dioxide reduction reaction (CO2RR) is of increasing importance for the development of a closed carbon cycle. Here, electrolytes are often used to increase the electrical conductivity and thus the current density. In addition, the use of compressed CO2 and electrolyte-containing organic solvents suppresses hydrogen evolution. However, the electrical conductivity of CO2-saturated electrolyte solutions is mostly unknown. Therefore, their electrical conductivity was investigated in this work at different electrolyte concentrations, pressures (up to 150 bar) and temperatures (298.15 K and 343.15 K). In addition, the simplified Mean Spherical Approximation (MSA-simple) model, supported by ePC-SAFT for density modeling, was used to successfully model the conductivity. The results show that CO2-saturated electrolyte solutions generally exhibit lower conductivities than CO2-free electrolyte solutions. However, at very low electrolyte and CO2 concentrations, the conductivities were higher in CO2-saturated electrolyte solutions than in CO2-free electrolyte solutions, which is a new finding in the literature.

A Theoretical and Computational Study of Structure‐Property Relationship in Five Binary Liquid Alloys

AbstractA theoretical model is proposed in this work for the evaluation of composition‐dependent thermophysical properties such as the isothermal compressibility, velocity of sound and Debye temperature of liquid binary alloys. Using a square‐well (SW) model potential function under mean spherical model approximation, the composition‐dependent atomic‐level structural functions of Al1‐xCux, Ag1‐xCux, Au1‐xCux, Ag1‐xAlx, and Au1‐xAgx alloys have been determined and compared with available experimental data. An extensive computation was done to calculate the composition‐dependent isothermal compressibility through the structure factor in the long wavelength limit (k→0), and then we employed this data to investigate the velocity of sound in the considered melts. This yields the fundamental maximum frequency with which the constituent particles are vibrating in the melts and is used to determine the composition‐dependent Debye temperature, ΘD. The computed Debye temperature of considered melts using the Square‐well potential function is found to be in satisfactory agreement with the available DFT and MD simulation results.

Dependence temperature on effective mass and susceptibility in quantum well-wires

In this study, we investigated the simulation impact of carrier density and temperature on properties such as susceptibility and effective mass of electrons in GaAs/Al x Ga1−x As quantum-well wires, involving the treatment of Coulomb interaction and the interaction between electrons and holes with longitudinal optical phonons (LO-phonon) on an equal basis. The susceptibility and effective mass were calculated and compared with the results when no phonon coupling was considered. Furthermore, the key findings were compared with results from the sum-rule version of the Singwi-Tosi-Land-Sj ö lander (STLS) theory, mean-spherical approximation (MSA) theory, and there is a high level of concordance between this formula and experimental values obtained by other researchers. Our results reveal that carrier concentration and temperature significantly affect susceptibility and effective mass of the quantum well-wires in both cases, with LO-phonon contributions. These results contribute to illuminating how Coulomb interactions and exchange-correlation energies influence the susceptibility and effective mass of GaAs/Al x Ga1−x As across a broad range of temperature and carrier density conditions.

Step-wise ion hydration modeling of aqueous solutions of 1:1 acid neutral electrolytes at different temperatures

In a previous work, we showed that the current stepwise ion hydration framework was promising for modeling electrolyte activities at 298.15 K. Briefly, the model assumes that (1) ions are hydrated in solution and this hydration is governed by an equilibrium between the bound and free water, (2) the mean spherical approximation (MSA) models the long range electrostatic interactions in the solution sufficiently well, and (3) this solution behaves ideally. In this work, we continue developing this model by exploring its temperature dependence. MSA has no temperature-dependent adjustable parameters. The hydration equilibrium constants are temperature dependent due to non-zero enthalpy and specific heat of the hydration equilibrium. Their values were adjusted. The calculated osmotic coefficients from the model are in good agreement with measured values.

Theoretical investigation of collective motion in some liquid metals using pseudopotential approach

The collective motions are studied using a recently created pseudopotential and some elastic constants. This paper involves the calculations of the collective motions like phonon dispersion curves (PDCs) for longitudinal and transverse frequencies ([Formula: see text] and [Formula: see text]), longitudinal sound velocity ([Formula: see text]), transverse sound velocity ([Formula: see text]), isothermal bulk modulus (B), modulus of rigidity (G), Young’s modulus (Y), Poisson’s ratio [Formula: see text], Debye temperature ([Formula: see text]) of some monovalent (Na), divalent (Mg) and polyvalent liquid metals (Al, Pb, Bi). This investigation is based upon the theory of pseudopotential of second-order approach via the equations of Hubbard and Beeby (HB). [Formula: see text] The pair correlation function is calculated from the different mean spherical approximation (MSA), one-component plasma (OCP) and optimized random phase approximation (ORPA) structure factors employed in this work. Three different types of local field correction (screening) functions proposed by Hartree (H), Taylor (T) and Nagy (N) are utilized in this paper. The current findings are found to be in qualitative accord with experimental and theoretical data.

Comparative studies of role of different structure factors in various physical properties of some simple liquid metals

In the current work, the comparison of the structure factors and pair correlation functions produced by using eight different theoretical models based on the Perckus-Yevick Hard Sphere (PYHS), Hard Sphere Yukawa (HSY), Mean Spherical Approximation (MSA), Generalized Mean Spherical Approximation (GMSA), Soft Sphere (SS), One-Component Plasma (OCP), Optimized Random Phase Approximation (ORPA) and Charged Hard Sphere (CHS) models for liquid metals viz. Li, Na, K, Rb, Cs, Mg, Zn, Ca, Al, Ga, In, Pb, Sn, Bi and Sb are carried out. Our own model potential is used with the Taylor (TY) screening function in the present computation. With this, certain physical properties such as electrical transport (electrical resistivity), vibrational property (phonon dispersion), dynamical property (velocity autocorrelation function (VACF)) and static (long wavelength of structure factor) properties has also been calculated. When the several theoretical models of the structure factors of the researched simple liquid metals are compared, it is discovered that the experimental data is consistent and in good agreement with the theoretical models.

Toward Modeling the Structure of Electrolytes at Charged Mineral Interfaces Using Classical Density Functional Theory.

The organization of water molecules and ions between charged mineral surfaces determines the stability of colloidal suspensions and the strength of phase-separated particulate gels. In this article, we assemble a density functional that measures the free energy due to the interaction of water molecules and ions in electric double layers. The model accounts for the finite size of the particles using fundamental measure theory, hydrogen-bonding between water molecules using Wertheim's statistical association theory, long-range dispersion interactions using Barker and Henderson's high-temperature expansion, electrostatic correlations using a functionalized mean-spherical approximation, and Coulomb forces through the Poisson equation. These contributions are shown to produce highly correlated structures, aptly rendering the layering of counterions and co-ions at highly charged surfaces and permitting the solvation of ions and surfaces to be measured by a combination of short-range associations and long-ranged attractions. The model is tested in a planar geometry near soft, charged surfaces to reproduce the structure of water near graphene and mica. For mica surfaces, explicitly representing the density of the outer oxygen layer of the exposed silica tetrahedra allows water molecules to hydrogen-bond to the solid. When electrostatic interactions are included, water molecules assume a hybrid character, being accounted for implicitly in the dielectric constant but explicitly otherwise. The disjoining pressure between approaching like-charged surfaces is calculated, demonstrating the model's ability to probe pressure oscillations that arise during the expulsion of ions and water layers from the interfacial gap and predict strong interattractive stresses that form at narrow interfacial spacing when the surface charge is overscreened. This interattractive stress arises not due to in-plane correlations under strong electrostatic coupling but due to the out-of-plane structuring of associating ions and water molecules.

Modeling of dilution enthalpies within implicit-solvent models for electrolytes

This work deals with the calculation of dilution enthalpies for strong aqueous electrolyte solutions when their thermodynamic properties are described within implicit-solvent models. The solution is modeled as a collection of charged hard spheres in a continuum solvent. A new general expression is obtained that accounts for the variation of the solution permittivity, of the size of the ions, and of the specific volume of the solution, with temperature and concentration. This expression is used to compute the enthalpies of LiCl aqueous solutions at temperatures in the range of 25∘C to 100∘C for concentrations up to 6 mol kg−1. The mean spherical approximation (MSA) model with implicit continuum solvent is employed to describe the thermodynamic properties of these solutions.

Description of electrolytes at high temperatures within the binding mean spherical approximation (BiMSA)

In this work, the binding mean spherical approximation (BiMSA) theory is used to describe osmotic and activities coefficients for electrolytes solutions up to high temperatures. Four salts are analysed: NaCl, LiCl, MgCl2 and CaCl2, in the temperature range of 25∘C to 300∘C and molalities from 0.05 to 6 molal. A good representation of experimental data is obtained for all salts and temperatures considered by introducing temperature-dependent cation size and permittivity in a suitable way. The proportion of ion pairs (that are formed at sufficiently high temperature in these solutions) for each salt is predicted from the theory, showing a pronounced increase for temperatures above 100∘C. A good agreement is found between the values of optimised and experimental association constants given in the literature.

Calculation of specific loss power of magnetic fluids by mean spherical approximation (MSA) model

According to various theoretical models the heating performance, i.e. the volumetric power dissipation of magnetic fluids under alternating magnetic field is proportional to the imaginary part of the complex susceptibility. However, the magnetic field strength dependence of the susceptibility is usually taken into account only by the Langevin theory. The main goal of our work was to propose a theoretical model based on the series expansion of the mean spherical approximation (MSA) theory to calculate the magnetic properties, and derive the power dissipation by including the dipole-dipole interactions. The predictions of the theory for the field strength dependence of the power dissipation was verified by comparison with experimental data. It was shown that compared to the MSA theory the generally used Langevin limiting case underestimates the power dissipation. The contribution of the higher-order terms in the approximated dynamic susceptibility at different field strengths was also investigated.

On analytical theories for conductivity and self-diffusion in concentrated electrolytes.

Describing analytically the transport properties of electrolytes, such as their conductivity or the self-diffusion of the ions, has been a central challenge of chemical physics for almost a century. In recent years, this question has regained some interest in light of Stochastic Density Field Theory (SDFT) - an analytical framework that allows the approximate determination of density correlations in fluctuating systems. In spite of the success of this theory to describe dilute electrolytes, its extension to concentrated solutions raises a number of technical difficulties, and requires simplified descriptions of the short-range repulsion between the ions. In this article, we discuss recent approximations that were proposed to compute the conductivity of electrolytes, in particular truncations of Coulomb interactions at short distances. We extend them to another observable (the self-diffusion coefficient of the ions) and compare them to earlier analytical approaches, such as the mean spherical approximation and mode-coupling theory. We show how the treatment of hydrodynamic effects in SDFT can be improved, that the choice of the modified Coulomb interactions significantly affects the determination of the properties of the electrolytes, and that comparison with other theories provides a guide to extend SDFT approaches in this context.

Association in electrolyte solution: Implementing inner sphere ion pairing into the mean spherical approximation

In many electrolyte solutions, ions of opposite signs can be paired due to electrostatic or more specific interactions. The pairing may occur in competition with the individual solvation of the ions. Some of the solvent molecules, initially present around each of the ions, may be excluded between pairing ions. The resulting complexes can be seen as dumbbells with a strong overlap between the spheres representing each of the hydrated ions involved in the association. The thermodynamic description of electrolyte solutions containing such pairing ions is described in this paper with a variational generalisation of the binding mean spherical approximation.

Mean ionic activity coefficient of associative electrolyte solutions: A comparison study

The performance of four implicit solvent models for associative and two models for non-associative electrolyte solutions has been compared and analyzed for the mean ionic activity coefficient (MIAC) of electrolytes in the solution. Two of these models for associative electrolyte solutions are based on a chemical approach (Fisher-Levin-Guillot-Guissani (FLGG) and Ebeling-Grigo (EG)), and one of them is based on the reference cavity approximation (Zhou-Yeh-Stell (ZYS)). The last one is based on the thermodynamic perturbation theory (Binding mean spherical approximation, BiMSA). Models without ion-pairing also consist of hard sphere (HS) contribution in addition to the electrostatic contribution from the Debye-Hückel (HS + DH) and the mean spherical approximation (HS + MSA) theories. To this aim, the models’ predictions are compared with the numerical solution of the Poisson-Boltzmann equation, the Monte Carlo simulations, and the experimental data. We have shown that considering the ion pairing results in a better agreement of the predicted MIAC against both simulations and experimental data of 2:2 electrolytes. We have also adjusted the ionic diameter and the distance between ion pairs to the MIAC experimental data and validated the estimated fractions of free ions with the electrical conductivity measurements. We have shown that the FLGG model captures the physics of the system more accurately compared to other models.

The Connection between the Debye and Güntelberg Charging Processes and the Importance of Relative Permittivity: The Ionic Cloud Charging Process

The Debye and Güntelberg Charging Processes are essential tools for deriving electrolyte solutions’ activity coefficient models. The Debye–Hückel, Born, and Mean Spherical Approximation are among some famous theories derived via charging processes. How they relate to each other, or if both charging processes are equivalent, or even if both are consistent, has been a matter of discussion in the literature for many years. In this work, we evaluate the results from both charging processes using the Debye–Hückel and the Born equations, using different dependencies of the relative permittivity concerning salt concentration, temperature, and partial charging variable. Our results show that both charging processes are connected through a charging process here called the Ionic Cloud Charging Process. We show how these three charging processes relate to each other, verifying the magnitude of the derivatives of relative permittivity on the final models and their origin from the Ionic Cloud Charging Process.

Asphaltene precipitation described with a Yukawa SAFT-VR/MSA equation of state

We combine the Statistical Associating Fluid Theory for Potentials of Variable Range (SAFT-VR) and the Mean Spherical Approximation (MSA) to develop an equation of state to model asphaltene precipitation in petroleum fluids including the measured asphaltene onset pressures (AOP’s) of a reservoir live oil. In this model, dispersive solvent–solvent and asphaltene–solvent interactions in reservoir fluid mixtures are represented by Yukawa potentials. The approach is based in the modeling of polar and ionic interactions via Yukawa potentials, as originally proposed by the Generalized Mean Spherical Approximation Theory, and also in recent studies in molecular simulation of charged fluids using non-Ewald effective pair interactions, as in the Wolf method.