M. Holovko

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...

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 agreem...

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.

Integral equation theory for the four bonding sites model of I. Structure factor and compressibility associating fluids

The Wertheim integral equation theory for associating fluids is reformulated for the study of associating hard spheres with four bonding sites. The association interaction is described as a square well saturable attraction between these sites. The associative version of the OrnsteinZernike integral equation is supplemented by the Percus-Yevick-like closure relation and solved analytically within an ideal network approximation, in which the network is the result of the crossing of ideal polymer chains. The structure factor S(k) is obtained for both symmetrical network and polymer chain cases. It is shown that S(k) exhibits a peculiarity (a socalled pre-peak) at small wavenumbers, connected with the formation of relatively large molecular aggregates due to highly directional saturable bonds. The magnitude and location of the pre-peak as functions of density theta and association Ks are analysed. Based on the analysis of the S(k = 0) limit, the behaviour of the isothermal compressibility χ T is studied and t...

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...

Solution of the associative Percus—Yevick approximation for the n-component mixture of dimerizing hard spheres

Abstract An analytical solution of Wertheims associative Percus-Yevick (APY) approximation for the n -component mixture of dimertizing hard spheres is presented. The solution is illustrated by the numerical results obtained for the two-component mixture with associative interaction only between particles of a different sort. In the limiting case of complete dimerization the results of the APY approximation are in good agreement with the predictions of the Monte Carlo simulation performed for the corresponding system of heteronuclear hard dumbbells. In this limit the present solution can be used as a simple analytical approach in the description of the system of heteronuclear hard dumbbells and their mixtures.

Highly Asymmetric Electrolytes in the Associative Mean-Spherical Approximation

The associate mean-spherical approximation (AMSA) is used to derive the closed-form expressions for the thermodynamic properties of an (n+m)-component mixture of sticky charged hard spheres, with m components representing polyions and n components representing counterions. The present version of the AMSA explicitly takes into account association effects due to the high asymmetry in charge and size of the ions, assuming that counterions bind to only one polyion, while the polyions can bind to an arbitrary number of counterions. Within this formalism an extension of the Ebeling–Grigo choice for the association constant is proposed. The derived equations apply to an arbitrary number of components; however, the numerical results for thermodynamic properties presented here are obtained for a system containing one counterion and one macroion (1+1 component) species only. In our calculation the ions are pictured as charged spheres of different sizes (primitive model) embedded in a dielectric continuum. Asymmetries in charge of −10:+1, −10:+2, −20:+1, and −20:+2 and asymmetries in diameter of 2:0.4nm and 3:0.4nm are studied. Monte Carlo simulations are performed for the same model solution. By comparison with new and existing computer simulations it is demonstrated that the present version of the AMSA provides semiquantitative or better predictions for the excess internal energy and osmotic coefficient in the range of parameters where the regular hypernetted chain (HNC) and improved (associative) HNC do not yield convergent solutions. The AMSA liquid–gas phase diagram in the limit of complete association (infinitely strong sticky interaction) is calculated for models with different degrees of asymmetry.

SOLUTION OF THE POLYMER MEAN SPHERICAL APPROXIMATION FOR THE TOTALLY FLEXIBLE STICKY TWO-POINT ELECTROLYTE MODEL

Abstract The general solution of the polymer MSA (mean spherical approximation) for an arbitrary mixture of charged hard spheres with multiple bonding obtained recently by Blum, Holovko and Protsykevytch [J. Stat. Phys,] is applied to the case of totally flexible linear polymer chains. The approximation is an extension of the associative MSA proposed by M.Holovko and Yu.Kalyuzhnyi, [Mol.Phys., 73, 1145(1991)] to study the effects of association in ionic systems. The model is defined by adding charges to the multicomponent version of the totally-flexible sticky two-point model of associating monomers introduced by Wertheim.

Cytochrome-c in reverse micelles: Small angle x-ray scattering measurements, percolation process, and critical behavior: An interpretation with an association model

It has been shown that solubilization of cytochrome-c in water in oil reverse micellar systems induces a change in the small angle x-ray scattering (SAXS) spectrum which suggests an increase in the attractive part of the intermicellar potential. In addition, from conductivity measurements a percolation threshold appears for a micellar concentration which is smaller than that observed without protein. Finally, for the liquid–liquid phase transition, a decrease in the critical temperature and concentration is observed. To explain these results, we introduce a pairing sticky hard sphere model. In this approach, the empty micelles are described by the sticky hard sphere model as is usually done. The presence of cytochrome-c is represented by an additional attractive potential characterized by an association parameter that leads to the pair formation of micelles. The association parameter was determined by fitting the experimental structure factors and from this parameter the decrease in the percolation thresh...