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.     

Adsorption of the associative fluid onto the lattice of sticky sites

The liquid-solid interface is modelled by a system consisting of dimerizing hard spheres and a wall with an array of sticky sites. The results for the fraction of occupied sites, θ, calculated in the mean-field approximation are given. The dependence of θ on the bulk number density η and on the fraction of dimerized particles 1-x₅, is investigated. The effect of the dimerization on the exact result for θ, obtained for the hard-spheres model, is studied.     

A solution of the multiple-binding mean spherical approximation for ionic mixtures

The mean spherical approximation (MSA) for an arbitrary mixture of charged hard spheres with saturating bonds is solved in the Wertheim formalism. Any number of bonds is allowed. It is shown that the general solution is given in terms of a screening MSA-like parameter ^T , a cross-interaction parameter that will depend on the binding association equations, the set of binding association fractions, and an additional algebraic equation. The equation for ^T is given for the general case. The equation for , however, depends strongly on the particular closure that is used to compute the contact pair correlation function. The full solution requires, as in the dimer case recently solved by Blum and Bernard, solvingm+2 equations and additionally the inversion of a matrix of size [(–1)m] for a system withm components and bonds. We recall that when =1, only dimers are allowed; for =2, only linear chains are formed: and when 3, branching of the polymers occurs. It can be shown that the excess entropy for the polymer case is as before,S ^MSA=( ^T )³/3 + sticky terms, where the sticky terms depend on the model and will be given in future work.     

On the contact conditions for the charge profile in the theory of the electrical double layer for nonsymmetrical electrolytes

In this paper, we generalize a recently derived expression of the contact value of the charge profile for the case of nonsymmetrical electrolytes. For the electrolytes with a single type of cation and anion, this relation can be presented as the sum of three contributions. One of them is the normal component of the Maxwell electrostatic stress tensor. The second one is the surface electrostatic property, which is defined as the integral of the product of the gradient of the electrical potential and the density distribution function of coions. The third term is the bulk contribution, which is defined by the sum for anions and for cations of the product of their charge and their partial pressure. For noncharged surfaces, only the last two terms are present and have the same sign in the case of size asymmetry. In the case of charge asymmetry, the contact value of the charge profile is the result of the competitions of bulk and surface terms in which the bulk term is dominant. Using both the contact theorems for the density and the charge profiles, the exact expressions for the contact values of the profiles of coions and counterions are obtained and some related properties are discussed. A semiempirical expression of the contact value of the charge profile is discussed in relation to our exact result.     

On the quantum properties of adsorbed particles within the model of a hydrogen atom near a hard wall

A hydrogen molecule near a hard wall was considered within the Heiteler–London method using the atomic orbits in the presence of the wall. Rapidly converging expansions of the atomic wave functions were proposed. The asymptotics were obtained and studied. The atomic dipole moment induced by the surface gave rise to a long-range interatomic interaction. The covalent bond length increased near the wall. Depending on the orientation relative to the wall, the potential well can vanish. It is interpreted as an interaction between the atomic dipole moments. An approximation of the interatomic potential was proposed.     

Contact conditions for the charge in the theory of the electrical double layer

In this paper, from the Born-Green-Yvon equations of the liquid-state theory, we derive a general expression for the charge-density contact value at charged interfaces. This relation is discussed, in particular, for symmetrical electrolytes. We emphasize an essential coupling between the electric properties and the density profile. Limiting behavior at small and large charges at the interface is discussed.     

Analytic solution of the RISM equation forn s-atomic symmetric molecules

A general method of an analytic solution of the RISM equation based on the Baxter factorization is explicitly extended to three- and four-atomic symmetric homonuclear molecules. Results of higher order approximations (beyond the zero pole approximation) are compared with numerical results and it is shown that the analytic solution converges to the numerical one for allL}<1. The role of poles of the intramolecular structural function 1/W(k) depending on the number of sites, site-site span, and density is discussed.     

Mercedes-Benz water molecules near hydrophobic wall: integral equation theories vs Monte Carlo simulations

Associative version of Henderson-Abraham-Barker theory is applied for the study of Mercedes-Benz model of water near hydrophobic surface. We calculated density profiles and adsorption coefficients using Percus-Yevick and soft mean spherical associative approximations. The results are compared with Monte Carlo simulation data. It is shown that at higher temperatures both approximations satisfactory reproduce the simulation data. For lower temperatures, soft mean spherical approximation gives good agreement at low and at high densities while in at mid range densities, the prediction is only qualitative. The formation of a depletion layer between water and hydrophobic surface was also demonstrated and studied.     

Network Forming Fluids: Yukawa Square-Well <Emphasis Type="Italic">m</Emphasis>-Point Model

Thermal and connectivity properties of the Yukawa square-well m-point (YSWmP) model of the network forming fluid are studied using solution of the multidensity Ornstein-Zernike and connectedness Ornstein-Zernike equations supplemented by the associative mean spherical approximation (AMSA). The model is represented by the multicomponent mixture of Yukawa hard spheres with m_s^am_{s}^{a} square-well sites, located on the surface of each hard sphere. To validate the accuracy of the theory, computer simulation is used to calculate the structure, thermodynamic and connectivity properties of the one-component YSW4P version of the model which is compared against corresponding theoretical data. In addition, connectivity properties of the model were studied using Flory-Stockmayer (FS) theory. Predictions of the AMSA for the thermal properties of the model (radial distribution functions (RDF), internal energy, pressure, fractions of the particles in different bonding states) are in good agreement with computer simulation predictions. Similarly, good agreement was found for the connectedness RDF (CRDF), except for the statepoints located close to the percolation threshold, where the theory fails to reproduce the long-range behavior of the CRDF. Results of both theories (AMSA and FS) for the mean cluster size are reasonably accurate only at low degrees of association. Predictions of the FS theory for the percolation lines are in a good agreement with computer simulation predictions. AMSA predictions of percolation are much less accurate, where corresponding percolation lines are located at a temperatures approximately 25% lower then those calculated using computer simulation.