Partly-quenched systems containing charges. Structure and dynamics of ions in nanoporous materials

Abstract

Disordered porous materials filled with liquid or solution may be considered as partly-quenched, i.e., as systems in which some of the degrees of freedom are quenched and others annealed. In such cases, the statistical-mechanical averages used to calculate the system's thermodynamical properties become double ensemble averages: first over the annealed degrees of freedom and then over all possible values of the quenched variables. In this respect, the quenched-annealed systems differ from regular mixtures. The multi-faceted applications of the partly-quenched systems to a kaleidoscope of technological and biological processes make the understanding of these systems important and of interest. Present contribution reviews recent developments in theory and simulation of partly-quenched systems containing charges. Specifically, two different models of such systems are discussed: (a) the model in which the nanoporous system (matrix subsystem) formed by charged obstacles is electroneutral, and (b) the model, where the subsystem of obstacles has some net charge. The latter model resembles, for example, the situation in ion exchange resins etc. Various theoretical methods are applied to investigate structural and dynamical peculiarities of such systems. One is the replica Ornstein-Zernike theory, especially adapted for charged systems, and the other is the Monte Carlo computer simulation method. These two approaches are well suited to study thermodynamical parameters, such as the mean activity coefficient of the annealed electrolyte or Donnan's exclusion parameter. Highly relevant issue of dynamics of ions in partly-quenched systems is also addressed. For this purpose, the Brownian dynamic method is used: the self-diffusion coefficients of ions are calculated for various model parameters and discussed in light of the experimental data. These results, together with the thermodynamical data mentioned above, provide additional evidence that properties of the adsorbed fluid substantially differ from those of its bulk counterpart.