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, ε. Within the matrix the charge- and size-symmetric (+1 : –1 or +2 : –2) electrolyte at T₁, ε₁ 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°, where D° 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° 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° 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.