Abstract
Distribution of a two component electrolyte mixture between the model adsorbent and a bulk aqueous electrolyte solution was studied using the replica Ornstein-Zernike theory and the grand canonical Monte Carlo method. The electrolyte components were modelled to mimic the HCl/NaCl and HCl/CaCl_2 mixtures, respectively. The matrix, invaded by the primitive model electrolyte mixture, was formed from monovalent negatively charged spherical obstacles. The solution was treated as a continuous dielectric with the properties of pure water. Comparison of the pair distribution functions (obtained by the two methods) between the various ionic species indicated a good agreement between the replica Ornstein-Zernike results and machine calculations. Among thermodynamic properties, the mean activity coefficient of the invaded electrolyte components was calculated. Simple model for the ion-exchange resin was proposed. The selectivity calculations yielded qualitative agreement with the following experimental observations: (i) selectivity increases with the increasing capacity of the adsorbent (matrix concentration), (ii) the adsorbent is more selective for the ion having higher charge density if its fraction in mixture is smaller.
Highlights
A variety of phenomena of interest for basic science and technology occur when an electrolyte solution or a mixture of electrolytes is in equilibrium with a porous phase containing fixed charges
The two theoretical methods described above were established to be complementary in the sense that they yield consistent results for structural and thermodynamic properties of electrolyte solutions adsorbed in nanoporous materials [11, 37, 38, 40, 41]
While the replica Ornstein-Zernike (ROZ)/HNC theory is computationally less demanding, and is, faster to use for systematic investigations of different effects on the system properties, the grand canonical Monte Carlo (GCMC) method is more convenient in studying the equilibrium distribution of ions between the bulk and matrix phase
Summary
A variety of phenomena of interest for basic science and technology occur when an electrolyte solution or a mixture of electrolytes is in equilibrium with a porous phase containing fixed charges. In references [16, 17] and [20,21,22,23] the replica Ornstein-Zernike theory was proposed to calculate the thermodynamic properties and spatial distribution of particles in partly quenched systems with short-range forces. The system of quenched obstacles formed from the primitive model ions is negatively charged Within this system (matrix) the annealed ions are distributed; an excess of cations is present to maintain the electroneutrality condition. The concentration of the invading electrolyte is determined by the properties of the bulk solution of the same chemical composition Such a system can represent a crude model of the ion-exchange resin. The ion-exchange isotherms, reflecting the ion selectivity in HCl/NaCl and HCl/CaCl2 mixtures, are presented as functions of the model parameters
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