Self-diffusion coefficients of ions in the presence of charged obstacles

Abstract

The self-diffusion coefficient of ions of the charge- and size-symmetric +1:-1 (or +2:-2) electrolyte was studied in the presence of ionic obstacles (matrix) representing disordered media. For this purpose the Brownian dynamics method was used, complemented with the replica Ornstein-Zernike theory for the partly-quenched systems. The matrix was prepared by a rapid quench of the size-symmetric +1:-1 (in few cases also of +2:-2) electrolyte solution being in equilibrium at (temperature, relative permittivity) T0, epsilon. Within the matrix the charge- and size-symmetric (+1:-1 or +2:-2) electrolyte at T1, epsilon1 was distributed. This component was fully mobile (annealed) and in thermodynamic equilibrium with the matrix. In this study a special attention was paid to the self-diffusion of the annealed ions. The ratio D/D degrees, where D degrees is the self-diffusion coefficient of ions at infinite dilution, has been studied for various model parameters varying the concentration of all species in the system. The presence of charged obstacles decreases the self-diffusion of the annealed electrolyte; the D/D degrees values are lower in the partly-quenched mixtures than in the fully annealed electrolyte of the same concentration. In the investigated range of concentrations and solvent dielectric constants, the D/D degrees values first increased with the increased concentration of annealed electrolyte present and then decreased. An increase of the strength of the Coulomb interaction between annealed ions, or between annealed and quenched charges, yielded a decrease of the self-diffusion. In the range of concentrations investigated in this work, the decrease is mainly due to the Coulomb interaction with the matrix, since the presence of neutral obstacles did not modify the diffusion properties with respect to the situation without obstacles.

Sodium chloride diffusion in sulfonated polymers for membrane applications

“…The activation energy for salt diffusion in a polyphosphazene cation exchange material is $1.4 times higher than that in a similar uncharged polyphosphazene polymer doped with salt to maintain similar ion concentrations in both polymers, and this result suggests that the fixed nature of the polymer's charge acts to hinder salt diffusion [91]. Additionally, molecular dynamics simulations suggest that ion self-diffusion coefficients in a nano-porous matrix of charged obstacles (similar, in principle, to the charged polymers considered in the present work) tend to increase with increasing salt concentration, provided that the mobile salt concentration is sufficiently less than the fixed charge concentration (a condition obeyed by the materials considered in this study [44]) [92].…”

Modelling the ion-exchange equilibrium in nanoporous materials

“…Very good agreement between the theory and simulations was obtained for both, thermodynamic parameters and for the pair distribution functions (see, for example, [37][38][39]). More recently, good agreement was confirmed by the independent Brownian Dynamics simulations based on the same model [9].…”

“…In such cases the calculations are, due to the known geometry, relatively simple (see, for example, [5]) and the Poisson-Boltzmann theory is most often accurate enough to make viable predictions of measurable properties. Alternatively, the Monte Carlo or Brownian Dynamics methods may be used for this purpose [6][7][8][9][10].…”

“…The porous material (matrix) is pictured as a set of charged obstacles. Distribution of the obstacles is obtained by a certain recipe (see, for example, [9,11]). Inhomogeneity that causes the field in which mobile ions are distributed is given on a molecular level.…”

Application of Replica Ornstein-Zernike equations in studies of the adsorption of electrolyte mixtures in disordered matrices of charged particles

“…The thermodynamic and structural properties of these systems can be calculated using the computer simulations and/or the replica integral equation theories. This work presents the continuation of our previous studies of partly quenched systems containing charges [18][19][20][21][22][23][24][25]. The quenched "phase" (we shall call it the matrix) is some frozen (quenched) equilibrium distribution of a symmetric model +1:−1 electrolyte.…”