On the mean spherical approximation for the Lennard–Jones fluid

Subtle details on the mean spherical approximation (MSA) theory for the Lennard–Jones potential [Fluid Phase Equilib. 134 (1997) 21] are presented. In order to enhance the appreciation of the theory, the accuracy of the mapping method and the contact approximation used in the theory are demonstrated by comparing with the exact results at certain extreme conditions. Technical derivation of internal energy of the MSA is also fully displayed. In addition, the typographic errors appeared in [Fluid Phase Equilib. 134 (1997) 21] are also corrected in this work.     

Analytic solution of the mean spherical approximation for a multi-component plasma

The mean spherical approximation for a mixture of charged hard spheres in a uniform neutralizing background is solved analytically. The factor correlation functions and the excess thermodynamic properties are explicitly expressed through a single parameter, which can be obtained by solving an algebraic equation.     

First-order mean spherical approximation for inhomogeneous fluids

The first-order mean-spherical approximation (FMSA) [Y. Tang, J. Chem. Phys., 118, 4140 (2003)] is extended to the studies of inhomogeneous fluids by combining with Rosenfeld's perturbative method [Y. Rosenfeld, J. Chem. Phys. 98, 8126 (1993)]. In the extension, the key input-direct correlation function of FMSA-is applied to constructing the free energy density functional. Preserving its high fidelity at the bulk limit, the FMSA shows satisfactory performance for Yukawa fluids near hard and attractive walls. The results are better than or comparable to several other theories reported before for the geometry. The FMSA is found, in particular, more satisfactory than the traditional mean-field theory for predicting density profiles around hard walls. The FMSA is also compared with the full MSA for inhomogeneous fluids, showing no appreciable differences. The inhomogeneous FMSA goes successfully through the self-consistency test for reproducing the radial distribution function of the bulk Yukawa fluid. As far as the computation is concerned, the FMSA can be executed much faster than any nonmean-field theories, and the speed is virtually identical to that of the mean-field theory.     

Phase coexistence in a polydisperse charged hard-sphere fluid: polymer mean spherical approximation

We have reconsidered the phase behavior of a polydisperse mixture of charged hard spheres (CHSs) introducing the concept of minimal size neutral clusters. We thus take into account ionic association effects observed in charged systems close to the phase boundary where the properties of the system are dominated by the presence of neutral clusters while the amount of free ions or charged clusters is negligible. With this concept we clearly pass beyond the simple level of the mean spherical approximation (MSA) that we have presented in our recent study of a polydisperse mixture of CHS [Yu. V. Kalyuzhnyi, G. Kahl, and P. T. Cummings, J. Chem. Phys. 120, 10133 (2004)]. Restricting ourselves to a 1:1 and possibly size-asymmetric model we treat the resulting polydisperse mixture of neutral, polar dimers within the framework of the polymer MSA, i.e., a concept that--similar as the MSA--readily can be generalized from the case of a mixture with a finite number of components to the polydisperse case: again, the model belongs to the class of truncatable free-energy models so that we can map the formally infinitely many coexistence equations onto a finite set of coupled, nonlinear equations in the generalized moments of the distribution function that characterizes the system. This allows us to determine the full phase diagram (in terms of binodals as well as cloud and shadow curves), we can study fractionation effects on the level of the distribution functions of the coexisting daughter phases, and we propose estimates on how the location of the critical point might vary in a polydisperse mixture with an increasing size asymmetry and polydispersity.     

Communication: rationale for a new class of double-hybrid approximations in density-functional theory

We provide a rationale for a new class of double-hybrid approximations introduced by Bre?mond and Adamo [J. Chem. Phys. 135, 024106 (2011)] which combine an exchange-correlation density functional with Hartree-Fock exchange weighted by λ and second-order M?ller-Plesset (MP2) correlation weighted by λ(3). We show that this double-hybrid model can be understood in the context of the density-scaled double-hybrid model proposed by Sharkas et al. [J. Chem. Phys. 134, 064113 (2011)], as approximating the density-scaled correlation functional E(c)[n(1/λ)] by a linear function of λ, interpolating between MP2 at λ = 0 and a density-functional approximation at λ = 1. Numerical results obtained with the Perdew-Burke-Ernzerhof density functional confirms the relevance of this double-hybrid model.     

Field induced anisotropy of charged magnetic colloids: a rescaled mean spherical approximation study

The liquidlike structure of colloidal suspensions with both electrostatic and magnetic interactions is investigated by means of small angle x-ray scattering (SAXS) dependent on an external magnetic field. For weak magnetic interactions, without external field, the magnetic dipoles are randomly oriented. Under this condition, isotropic structures are observed. In an external field, however, the magnetic momenta arrange parallel to the external field and induce anisotropic liquidlike structures. For weak magnetic interactions, the structure factor can be described within the framework of the rescaled mean spherical approximation. Due to the high experimental accuracy of synchrotron SAXS, from the anisotropic distortion of liquidlike structures, interparticle forces smaller than 10(-15) N can easily be detected.     

On a family of differential approximations of the radiative transfer equation

The radiative transfer equation (RTE) arises in a variety of applications and is challenging to solve numerically due to its integro-differential form and high dimension. For highly forward-peaked media, it is even more difficult to solve RTE since accurate numerical solutions require a high resolution of the direction variable. For this reason, various approximations of RTE have been proposed in the literature. In this paper, we study a family of differential approximations of the RTE in three spatial variables. We explain the idea of constructing the differential approximations, and comment on the usefulness of the approximations.     

Phase coexistence in polydisperse charged hard-sphere fluids: mean spherical approximation

Taking advantage of the availability of the analytic solution of the mean spherical approximation for a mixture of charged hard spheres with an arbitrary number of components we show that the polydisperse fluid mixture of charged hard spheres belongs to the class of truncatable free energy models, i.e., to those systems where the thermodynamic properties can be represented by a finite number of (generalized) moments of the distribution function that characterizes the mixture. Thus, the formally infinitely many equations that determine the parameters of the two coexisting phases can be mapped onto a system of coupled nonlinear equations in these moments. We present the formalism and demonstrate the power of this approach for two systems; we calculate the full phase diagram in terms of cloud and shadow curves as well as binodals and discuss the distribution functions of the coexisting daughter phases and their charge distributions.     

An efficiently extended class of unnatural base pairs

A third DNA base pair, which is synthesized efficiently and selectively, would have wide ranging applications from synthetic organisms to nucleic acids biotechnology. Hydrophobic unnatural nucleobases offer a promising route to such a pair, but are often limited by inefficient extension, defined as synthesis immediately following the unnatural pair. Here, we describe a simple screen which enables the characterization of large numbers of previously uncharacterized hetero base pairs. From this screen, we identified a class of unnatural base pairs which are extended more efficiently than any unnatural base pair reported to date. Screening, when complemented by further kinetic analysis, can improve the understanding of the determinants of efficient extension as well as identify viable hetero base pairs.     

The coupled perturbed electron propagator in the two-particle-hole and extended two-particle-hole Tamm-Dancoff approximations

The equations satisfied by the first-order perturbed electron propagator in an applied external field are examined at a level equivalent to the two-particle-hole Tamm-Dancoff and extended two-particle-hole Tamm-Dancoff approximations (2ph-TDA). These schemes are derived with the intention of evaluating linear and quadratic response properties through second and third order in correlation. Their derivation is based on a combination of the diagrammatic and algebraic superoperator methods. Both schemes account for the polarization of the 2p-1h and 2h-1p responses and bielectron interactions under an external field. The 2ph-TDA scheme is correct up to second order in electronic correlation and includes infinite geometric series of mixed RPA-ladder-type character. Its extended version is derived consistently through third order and accounts for a first-order screening of the external field and bielectron interaction by the effects of electronic correlation. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 483–509, 1997     

Liquid-vapor transition of systems with mean field universality class

We have considered a system where the interaction, v(r)=v(IS)(r)+xi(2)v(MF)(r), is given as a linear combination of two potentials, each of which being characterized with a well-defined critical behavior: for v(IS)(r) we have chosen the potential of the restricted primitive model which is known to belong to the three-dimensional Ising universality class, while for v(MF)(r) we have considered a long-range interaction in the Kac [J. Math. Phys. 4, 216 (1963)] limit, displaying mean field (MF) behavior. We study the performance of two theoretical approaches and of computer simulations in the critical region for this particular system and give a detailed comparison between theories and simulation of the critical region and the location of the critical point. Having shown by theoretical arguments that the system belongs to the MF universality class for any positive value of xi and shows nonclassical behavior only for xi=0, we examine to which extent theoretical approximations and simulation can reproduce this behavior. While in this limiting case theoretical approaches are known to fail, we find good agreement for the critical properties between the theoretical approaches and the simulations for xi(2) larger than 0.05.     

First-order mean spherical approximation for attractive, repulsive, and multi-Yukawa potentials

The first-order mean spherical approximation (FMSA) theory proposed by Tang et al. [Fluid Phase Equilib., 134, 21(1997)] is applied for studying several typical Yukawa fluids, including attractive, repulsive, and multi-Yukawa cases. The FMSA study is particularly advantageous in providing thermodynamics and structure information in a simple, analytical, and consistent manner. Comparisons with the latest reported computer simulation data for compressibility factor, internal energy, and radial distribution function show that FMSA performs very well and the performance is very close to the full MSA and to several other theories, developed individually for the above-mentioned cases or properties. The present study provides solid evidence to support FMSA applications to more complex fluids.     

Estimation of activity coefficients at different temperatures by using the mean spherical approximation

A method of estimating activity coefficients for a variety of electrolytes at different temperatures is presented. The MSA approximation is used to calculate the activity coefficients from experimental data available in the literature. This strategy provides suitable results within a wide range of temperatures, electrolyte stoichiometries and concentrations of investigated solutions.     

Theoretical calculations of the ionic strength dependence of the ionic product of water based on a mean spherical approximation

A modified version of the restricted primitive model for electrolyte solutions based on the mean spherical approximation (MSA) is applied to estimate the ionic strength dependence of the ionic product of water in aqueous solutions containing different salts, which are commonly used as background electrolytes (NaCl, KCl, KNO₃, and NaC10₄). The modification involves the use of permittivity of the solvent as concentration-dependent parameter and a single average effective diameter. This is a way of including effects originated from the solvent which do not exist in the primitive model. In the case of potassium nitrate and sodium perchlorate, a complete methodology to calculate the effective diameter and density dependence of the dielectric constant has been proposed and developed. Fits between calculated and experimental pK_w values are possible over wide concentration ranges using a single adjustable parameter, namely, the average hard core diameter of water.     

Lanthanide salts solutions: representation of osmotic coefficients within the binding mean spherical approximation

Osmotic coefficients of aqueous solutions of lanthanide salts are described using the binding mean spherical approximation (BIMSA) model based on the Wertheim formalism for association. The lanthanide(III) cation and the co-ion are allowed to form a 1-1 ion pair. Hydration is taken into account by introducing concentration-dependent cation size and solution permittivity. An expression for the osmotic coefficient, derived within the BIMSA, is used to fit data for a wide variety of lanthanide pure salt aqueous solutions at 25 degrees C. A total of 38 lanthanide salts have been treated, including perchlorates, nitrates, and chlorides. For most solutions, good fits could be obtained up to high ionic strengths. The relevance of the fitted parameters has been discussed, and a comparison with literature values has been made (especially the association constants) when available.     

On the origins of approximations for stochastic chemical kinetics

This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported. In addition, the derivation points out several weaknesses in previous justifications of both the hybrid and equilibrium systems and demonstrates the connection between the original and approximate master equations. Two simple examples illustrate situations in which these two approximate methods are applicable and demonstrate the two methods' efficiencies.     

Improved radial distribution functions for Coulomb charged fluid based on first-order mean spherical approximation

In this work, we solve the Ornstein-Zernike equation in a simple, analytical, and consistent manner to obtain the like and unlike radial distribution functions (RDFs) for charged fluids. To improve mean spherical approximation (MSA) solutions, the direct correlation functions both for the density and charge contributions are modified with the Yukawa potential, respectively. On the basis of the contact values of RDFs and excess internal energy of the system, we construct correlated equations to cope with the potential parameters. Thus obtained equations are solved with the first-order MSA method. The resulting like and unlike RDFs are in good agreement with molecular simulation data within a wide range of densities and temperatures.     

Equation of state for aqueous electrolyte systems based on the semirestricted non-primitive mean spherical approximation

The semirestricted non-primitive mean spherical approximation (npmsa) is used in combination with the PC-SAFT equation of state to model completely dissociating aqueous alkali halide systems. The salts are described using ion-specific parameters from tables and correlations. Upon analyzing aqueous electrolyte systems at infinite dilution of the salt it was concluded that for the arithmetic mean ion diameter of anion and cation, the semirestricted npmsa contribution gives no reliable results. Therefore, this parameter is adjusted in this work. The model was applied to aqueous alkali halide systems up to the solubility limit at T = 298.15 K. Mean ionic activity coefficients and osmotic coefficients were correlated with good results. The model was subsequently applied to temperatures up to T = 373.15 K and compared to liquid densities and to system pressures up to the solubility limit of the salts in water. The agreement between experimental data and the proposed equation of state is satisfactory for the liquid densities and excellent in case of the system pressures.