The Multi-Density Integral Equation Approach in the Theory of Complex Liquids

Abstract

Recent development of the multi-density integral equation approach and its application to the statistical mechanical modelling of a different type of association and clusterization in liquids are reviewed. The effects of pairing, polymerization, solvation, formation of the network bonds and selfassembling are discussed. The numerical and analytical solutions of the integral equations in the multi-density formalism are used for the description of the association phenomena in the electrolyte and polyelectrolyte solutions, water, polymers, microemulsions and other fluids. The application of the multi-density integral equation approach for the treatment of the percolation phenomena, the adsorption of fluids in porous media and the description of electronic structure of associative fluids are illustrated.

The Application of the Associative Mean Spherical Approximation in the Theory of Nonaqueous Electrolyte Solutions

“…where α is the degree of dissociation, c = ρ/2N A is the analytical electrolyte concentration, ρ = ρ + + ρ − is the total number density, N A is the Avogadro constant, K A is the equilibrium constant of ion-pair formation, y ′ ± is the mean activity coefficient of the free ions in solution, and y ′ 0 is that of the ion pairs. The MAL (2) is written in the form [12][13][14] 1 − α…”

“…Another route [10] starts from the associative mean spherical approximation (AMSA) [11] based on the theory of associating fluids [12][13][14]. It was shown that this approach coincides with the traditional approach of weak association, but also is correct in the regime of strong association.…”

Dimerizing hard spherocylinders in porous media

“…For the isotropic phase, 𝑓 1 (Ω) = 𝑓 10 (Ω) = 1. The free energy of the system within the approximation obtained in the framework of the first-order thermodynamic perturbation theory [15,20,[51][52][53][54] can be written as the sum of three contributions:…”

Simple Model of Hydrophobic Hydration

“…Promising modern theories of water have been proposed on the basis of thermodynamic perturbation methods and the associative Ornstein–Zernike integral equation theory. − For example, these approaches have been explored in 2-dimensional water models, called Mercedes–Benz-like models. ,, Recently, this type of model has been also explored in 3D. ,, However, these integral-equation methods have the limitations that (1) although they are much more efficient than computer simulations, they, too, can be computationally expensive; (2) they are mathematically demanding for angle-dependent potentials; and (3) they treat cold water (around room temperature and biological temperatures) less accurately than hot water (near the boiling point), because the important angular dependences are only approximated. Here, we are particularly interested in treating cold water, because of its practical importance and because this is where experiments are commonly performed.…”