**Electrolyte Rejection from Charged Nanoporous Material†**

**Miha Lukšič, Barbara Hribar-Lee and Vojko Vlachy***

*Faculty of Chemistry and Chemical Technology, University of Ljubljana,
Aškerčeva c. 5, SI-1000 Ljubljana, Slovenia
e-mail: vojko.vlachy@fkkt.uni-lj.si*

**Abstract**

RAdsorption of the charge and size symmetric +1 : –1 primitive model electrolyte
in disordered media (matrix) with charged (or neutral) obstacles was studied
using the Replica Ornstein-Zernike theory and Grand Canonical Monte Carlo
computer simulation. The charged matrix was prepared by a rapid quench of the +1
: z^{0} – (z^{0} – = –1, –2, –3, and –4) electrolyte solution
being in equilibrium at temperature T_{0}, and relative permittivity ε_{0}.
Than the positive ions were allowed to anneal and mix with the invading +1 : –1
electrolyte at T, ε_{1}, while the anions were left quenched and
represented the collection of obstacles, called here matrix, to which the
external electrolyte was adsorbed. To complement the data for charged adsorbent
we also considered the adsorption of the same +1 : –1 electrolyte in the matrix
prepared from hard sphere fluid and in the electroneutral matrix formed by
quenched +1:–1 electrolyte. In the latter case, the (electroneutral) matrix was
represented as an equilibrium distribution (T_{0}, ε_{0}) of
monovalent cations and anions being quenched during the adsorption of an
invading model electrolyte. Special attention was paid to the thermodynamic
properties of the adsorbed fluid. We were particularly interested in the mean
activity coefficient of the adsorbed electrolyte and in the Donnan exclusion
coefficient as a function of the charge density of the matrix. At higher
concentrations of the invading electrolyte the adsorption was dominated by the
excluded volume effect of the matrix, whereas at low electrolyte concentrations
the adsorption was governed by the combined effect of the matrix charge density
and the excluded volume. These findings are in good qualitative agreement with
those obtained previously for the electrolyte adsorbed in charged cylindrical
micropores.

**Keywords:** Disordered charged matrix, adsorption, Donnan equilibrium,
electrolyte, replica Ornstein-Zernike equation, Grand Canonical Monte Carlo
simulation.