Extended Mean Spherical Approximation Research Articles

Physical interpretation of theories of homogeneous electrolytes in the primitive model

The primitive model of ions is an important model system of electrolytes and ionic liquids because it is the simplest one to include both electrostatic and ion size effects. Here, two recent theories of the electrostatic excess chemical potential of homogeneous electrolytes modeled in the primitive model are analyzed. Both the Mean Countershell Approximation (MCSA) and the Extended Mean Spherical Approximation (MSAX) theories were already known to be accurate when compared to Grand Canonical Monte Carlo simulation results. The analysis here uncovers why these two seemingly very different theories agree very closely numerically. Moreover, knowledge of the physical meaning of the MCSA theory is used to define the MSAX theory’s terms as electrostatic interactions of ionic screening clouds. Lastly, a mathematical analysis of MCSA, MSAX, and a third theory is performed. This shows how all these theories—despite using very different mathematical and physical approximations—couple the distinct physical regimes of the low- and high-density limits to get accurate results at intermediate ion densities.

Electrical Conductivity of Concentrated Al2(SO4)3−MgSO4−H2SO4 Aqueous Solutions up to 250 °C

The extended mean spherical approximation (MSA) model was applied to previously published electrical conductivity data for H2SO4−H2O, Al2(SO4)3−H2SO4−H2O, and MgSO4−H2SO4−H2O solutions. It was foun...

Electrical Conductivity of Concentrated MgSO4−H2SO4 Solutions up to 250 °C

A conductivity cell, developed previously, was employed to investigate the speciation of MgSO4−H2SO4 solutions particularly at high temperatures. These solutions were measured from 15 to 250 °C at the equilibrium vapor pressures. The maximum measured concentrations of MgSO4 and H2SO4 were 0.30 m and 0.45 m, respectively. At 250 °C and constant H2SO4 concentration, the solution conductivity drops with the increase of MgSO4 concentration. It is postulated that this drop is caused by a decrease in the concentration of H+ due to bisulfate formation. However, the limiting equivalent conductivity of H+ was not significantly affected by MgSO4. Application of the extended mean spherical approximation (MSA) theory to the experimental data allowed the coefficients that determine the ionic strength dependence of the average effective radius to be obtained. With these coefficients, the conductivity of the MgSO4−H2SO4 aqueous system can be reproduced up to 250 °C with an average absolute difference of 2.47%.

Density profiles of associating fluid near a hard wall: PY/EMSA and HNC/EMSA singlet theory

A two-component model of hard spheres with a spherically symmetric associative interaction between the particles of different species near a hard wall is studied by suing the integral equation method. It is shown that the extended mean spherical approximation for the bulk associating fluid in conjunction with the Percus-Yevick closure of the singlet level theory of inhomogeneous fluid leads to very good agreement of theoretical density profiles with simulation data for highly associated fluid at a high bulk density.

Primitive models of chemical association. I. Theory and simulation for dimerization

The structure and thermodynamic properties of a model of associating particles that dimerize into fused-sphere dumbbells are investigated by MC simulation and by integral-equation theory. The model particles, introduced by Cummings and Stell, associate as a result of shielded attractive shells. The integral equation theories are of two types. The first is an extension of Wertheim’s associative Percus–Yevick (APY) equation to the case of the shielded sticky shell model, which is the limiting case of the shielded attractive shell model that can be handled analytically. The second is the extended mean spherical approximation (EMSA) of Zhou and Stell applied to the shielded sticky shell model. In the case of partially associated systems, the EMSA requires as input the equilibrium association constant, which is obtained here using an exact relation between monomer density and a cavity correlation function, together with an equation of state due to Boublik. The structure obtained from the EMSA is in good agreement with the predictions of the MC simulation over a substantial density range that includes liquid-state densities, while the thermodynamic input from Boublik’s equation is in excellent agreement with the simulation results for all densities. Predictions of the APY approximation are also in good agreement with the simulation results as long as the density of the system is relatively low or, at high density, when the hard-core volume of a dimer is not substantially less than that of the two free monomers from which it is formed. There is an intermediate density range in which neither integral-equation theory gives correlation functions of high quantitative accuracy.

Analytical approach to molecular liquids. V. Symmetric dissociative dipolar dumbbells with the bonding length σ/3≤L≤σ/2 and related systems

The exact asymptotic behavior of the particle–particle direct correlation function for dissociative dipolar dumbbells is discussed. It reveals the sense in which the complete association limit is like a critical point and suggests several approximations as well as the conditions under which they can be expected to be useful. The simplest of these is an extended mean spherical approximation (EMSA) that can be solved analytically for a model liquid of symmetric dissociative dipolar dumbbells with two centers (each bearing a point charge of opposite sign) a distance L apart, when σ/3≤L≤σ/2, where σ is the diameter of the spheres that consistute the dumbbells. The analytical expressions for the Born solvation free energy of a symmetric dipolar dumbbell in a symmetric dipolar dumbbell solvent and in a dipolar hard-sphere solvent are also obtained. Such expressions can be expected to be useful in investigating intramolecular electron-transfer reactions. Results for σ/2≤L≤σ that have a somewhat different conceptual status are obtained as well. They suggest a new interpretation of the Percus–Yevick solution to the sticky-sphere model considered by Baxter.

Ion solvation dynamics in an interaction-site model solvent

The molecular theory of the frequency-dependent and wavevector-dependent longitudinal dielectric function ϵ L( k, ω) is derived for fluids comprising interaction-site model molecules in which point charges are located on the interaction sites. We find that ϵ L( k, ω) is a simple functional of a particular charge susceptibility χ μϕ 0 ( k, ω), which in turn is related to a collective charge-charge equilibrium time correlation function. The electrostatic part F Born ( t) of the time-dependent free energy of solvation of a solute that instantaneously changes its charge state is, on the other hand, determined by a charge susceptibility χ μϕ 0 (1) ( k, k t́, ω) of the solvent in the presence of the solute molecule in its initial charge state. Using an approximate relation between χ μϕ 0 (1) and χ μϕ 0 we express F Born( t) in terms of χ μϕ 0 . The resulting theory is applied to calculate the solvation time correlation function of the solute immersed in a dipolar hard sphere (DS) and in dipolar dumbbell (DD) model solvent; the mean spherical approximation and an extended mean spherical approximation are used to compute the structure of the DS and DD solvent models, respectively. With parameters chosen so that the two models have the same molecular volume and the same electric dipole moment, it is found that they have very nearly the same ϵ L( k, ω) except at large wavevector, but significantly different solvation time correlation functions.

On the calculation of single-ion activity coefficients by the Kirkwood-Buff theory

An expression which applies for single-ion activity coefficients is obtained from the theory of Kirkwood and Buff by introduction of a single plausible assumption. When this expression is used in connection with the extended mean spherical approximation for the primitive model of electrolyte solutions, the limiting law of Debye and Hückel is recovered in the limit of low ionic concentration.

Analytical approach to molecular liquids. I. Site–site interaction model using an extended mean-spherical approximation

The observation that the intramolecular direct-correlation-function matrix is very closely approximated by its large-r form for rigid diatomics suggests an approximation such that the site–site Ornstein–Zernike equation becomes analytically solvable for several molecular models of interest. Alternatively, approximation of the particle–particle direct correlation function by its asymptotic form directly yields the same approximation, in particle–particle (in contrast to site–site) language. Applications of this approximation, which can be regarded as an extended mean spherical approximation when viewed in particle–particle terms, are made to rigid hard diatomics, dipolar diatomics, and a tetrahedral molecular model. The close but subtle connections between our approximation procedure and earlier approximations are discussed.

Eigenmodes of the quantized polarizable fluid

The equilibrium properties of a polarizable fluid that consists of interacting quantized Drude oscillators have recently been evaluated in an extended mean spherical approximation (MSA). Here we show that the thermodynamic properties that come from this result may be interpreted in terms of a set of quantized harmonic oscillators whose frequency distribution may be determined.

An extended mean spherical approximation for Coulombic systems

A systematic series of extensions of the mean spherical approximation is presented and is used to calculate the structural and thermodynamic properties of the restricted primitive model at reduced temperatures and densities comparable to the molten salt region.

An extended mean spherical approximation calculation of the potential of an electrified interface

An extended mean spherical approximation is formulated and used to calculate the density and charge profiles and the potential difference of a fluid of charged hard spheres near a charged planar wall. The results are nearly identical to those of the hypernetted chain approximation provided that the same correlation functions for the bulk fluid are used.

On a class of extended mean spherical approximations

The extended mean spherical approximation of Martina B, and del Rio is solved variationally for the restricted primitive model of 1—1 and 2—2 electrolyte solutions. Thermodynamic properties are calculated and compared to Monte Carlo results for the same model. A modification of the extended mean spherical approximation is presented that is more internally self-consistent and is in better agreement with Monte Carlo data.

Extended mean spherical approximation for electrolyte solutions

The range of applicability of the mean spherical approximation to a primitive-model electrolyte is extended to allow for stronger Coulomb coupling. The new terms in the approximation are extracted from the HNC formalism, which is adequate for strongly coupled Coulomb systems. The new approximation satisfies the Stillinger-Lovett conditions. The new integral equation thus obtained is presented.