Asymmetry of current-voltage characteristics of ion-exchange membranes: Model of charge density of fixed groups linear by membrane thickness

The model of a finely porous membrane with a linear distribution of charges of its fixed groups along its depth is used in the work to explain the phenomenon of asymmetry of current-voltage characteristics of perfluorinated MF-4SK membranes surface–modified by polyaniline or halloysite nanotubes. A new exact analytical method of solution of a system of transport equations is suggested that is based on the assumption of the monotonous behavior of the electric potential inside the membrane and allows finding current- voltage characteristics (CVCs) of the membrane using a system of two implicit algebraic equations. Algebraic equations for limiting currents are obtained for the first time for different orientations of the anisotropic membrane in an electrodyalisis cell and existence of two inflection points in CVCs is explained when its less charge side is oriented towards the anode.