Yu. V. Kalyuzhnyi

On the effects of association in the statistical theory of ionic systems. Analytic solution of the PY-MSA version of the Wertheim theory

The statistical mechanical approach to a fluid of dimerizing hard spheres proposed recently by Wertheim is extended to a two-component mixture of oppositely charged hard spheres. The pair potential is represented as a sum of the short-range hard-sphere potential, an intermediate-range square-well potential between the oppositely charged spheres, and a long-range Coulomb potential. The square-well potential, which is responsible for association, results from a single auxiliary site. If the site is located in such a way that only dimers are formed, the model presented here can be viewed as a model of chemical association in a fluid consisting of molecular ions. The model with the site located in the centre of hard sphere can be used to describe the formation of contact ion pairs in ionic systems. An analytical solution of the Ornstein-Zernike-like integral equation is obtained within a mixed Percus-Yevick and mean spherical approximation closure. The fraction of unbonded ions and the radial distribution fun...

Integral equation theory for associating liquids: Weakly associating 2–2 electrolytes

Formation of ion pairs in a 2–2 aqueous electrolyte is studied using a generalization of Wertheim’s formalism, designed to treat explicitly association between molecules. The ions in the model electrolyte interact via a continuous potential energy (unlike previous studies), which combines the long‐range Coulomb interaction with a soft repulsive potential at short distances. Both the derivation of new equations, including approximately the formation of trimers, and numerical solution of the resultant equations are presented here. The predictions of the theory are in excellent agreement with new molecular dynamics (MD) simulations of the same electrolyte. Explicit predictions are made for the fraction of monomers, dimers, and trimers in the electrolyte, over the full range of concentrations of interest for association, from 0.001 to 0.2 M.

Multidensity integral equation theory for highly asymmetric electrolyte solutions

Integral equation theory based on a recently developed multidensity formalism [Mol. Phys. 78, 1247 (1993)] is proposed to study highly asymmetric electrolyte (polyelectrolyte) solutions. The system studied consists of large and highly charged polyions and small counterions having one or two elementary charges. The potential energy of interaction between counterions and polyions is separated into two parts, a strongly attractive part responsible for the association and a nonassociative part. Due to the strong asymmetry in size we can treat each counterion as bondable to a limited number of polyions n, while each polyion can bond arbitrary number of counterions. In our cluster expansion appropriate to the problem the diagrams appearing in the activity expansion of the one‐point counterion density are classified in terms of the number of associating bonds incident upon the labeled white counterion circle. The corresponding diagrams for the one‐point polyion density are classified in the usual way. A generali...

An analytical study of the effects of association in a 2-2 electrolyte solution. I: Associative mean spherical approximation

An analytical theory of the effects of association in a 2-2 electrolyte solution, modelled by the restricted primitive model, is presented. Our approach is based on Wertheims integral equation theory for associating fluids, reformulated to describe the effects of association in fluids with spherically symmetric interactions. We consider the simplest two-density version, coinciding with the corresponding orientationally averaged version of Wertheims theory. An analytical solution of the associative mean spherical approximation (AMSA) is obtained, the latter being the two-density analogue of the regular MSA. It is demonstrated that the AMSA substantially extends the range of applicability of the MSA. The AMSA results for thermodynamic properties are as good as or slightly worse than the hypernetted chain results. A similar statement holds for the pair correlation function of unlike charged ions in the region of the low (0·0001 M) and intermediate (0·005 M) concentrations. Predictions of the present versio...

A two-dimensional model of water: Theory and computer simulations

We develop an analytical theory for a simple model of liquid water. We apply Wertheim’s thermodynamic perturbation theory (TPT) and integral equation theory (IET) for associative liquids to the MB model, which is among the simplest models of water. Water molecules are modeled as 2-dimensional Lennard-Jones disks with three hydrogen bonding arms arranged symmetrically, resembling the Mercedes-Benz (MB) logo. The MB model qualitatively predicts both the anomalous properties of pure water and the anomalous solvation thermodynamics of nonpolar molecules. IET is based on the orientationally averaged version of the Ornstein-Zernike equation. This is one of the main approximations in the present work. IET correctly predicts the pair correlation function of the model water at high temperatures. Both TPT and IET are in semi-quantitative agreement with the Monte Carlo values of the molar volume, isothermal compressibility, thermal expansion coefficient, and heat capacity. A major advantage of these theories is that...

A two-dimensional model of water: Solvation of nonpolar solutes

We recently applied a Wertheim integral equation theory (IET) and a thermodynamic perturbation theory (TPT) to the Mercedes–Benz (MB) model of pure water. These analytical theories offer the advantage of being computationally less intensive than the Monte Carlo simulations by orders of magnitudes. The long-term goal of this work is to develop analytical theories of water that can handle orientation-dependent interactions and the MB model serves as a simple workbench for this development. Here we apply the IET and TPT to the hydrophobic effect, the transfer of a nonpopular solute into MB water. As before, we find that the theories reproduce the Monte Carlo results quite accurately at higher temperatures, while they predict the qualitative trends in cold water.

Orientation-dependent integral equation theory for a two-dimensional model of water

We develop an integral equation theory that applies to strongly associating orientation-dependent liquids, such as water. In an earlier treatment, we developed a Wertheim integral equation theory (IET) that we tested against NPT Monte Carlo simulations of the two-dimensional Mercedes Benz model of water. The main approximation in the earlier calculation was an orientational averaging in the multidensity Ornstein–Zernike equation. Here we improve the theory by explicit introduction of an orientation dependence in the IET, based upon expanding the two-particle angular correlation function in orthogonal basis functions. We find that the new orientation-dependent IET (ODIET) yields a considerable improvement of the predicted structure of water, when compared to the Monte Carlo simulations. In particular, ODIET predicts more long-range order than the original IET, with hexagonal symmetry, as expected for the hydrogen bonded ice in this model. The new theoretical approximation still errs in some subtle properti...

Solution of the polymer Percus-Yevick approximation for the multicomponent totally flexible sticky two-point model of polymerizing fluid

The analytic solution of the polymer Percus–Yevick approximation for the multicomponent version of the totally flexible sticky two‐point model of Wertheim is obtained in closed form. The model consists of an n‐component mixture of hard spheres with two sticky points of the type A and B randomly placed on the surface of each hard sphere. The solution of the problem has been reduced to solving a set of 5n algebraic equations. An iterative scheme of the solution of this set of equations is proposed.

Solution of the polymer MSA for the polymerizing primitive model of electrolytes

Abstract An analytical solution of the polymer MSA (mean spherical approximation) for the polymerizing primitive model of electrolytes is obtained. The approximation is an extension of the associative MSA proposed recently [M. Holovko and Yu. Kalyuzhnyi, Mol. Phys. 73 (1991) 1145] to study the effects of association in ionic systems. The model is defined by adding charges to the totally flexible sticky two-point model of associating monomers introduced by Wertheim. In the limiting case of an uncharged system, our solution reduces to the solution of the Wertheim polymer PY approximation solved recently [J. Chang and S.I. Sandler, J. Chem. Phys. 102 (1995) 437].

Phase diagram for the Lennard-Jones fluid modelled by the hard-core Yukawa fluid

The liquid-gas phase diagram for the Lennard-Jones (LJ) fluid model is obtained using the mean spherical approximation (MSA) for the corresponding hard-core Yukawa fluid. The calculated phase diagram is compared with the phase diagrams for the LJ fluid predicted by the Gibbs ensemble Monte Carlo simulation, and by the Percus-Yevick (PY) and reference hypernetted chain (RHNC) theories. The accuracy of the MSA is comparable with the accuracy of the PY approximation. Although the MSA is less accurate than the RHNC approximation, it has an important advantage of being solvable along the whole liquid-gas coexistence curve, including the vicinity of the critical point.