Network simulation of the electrical response of ion-exchange membranes with fixed charge varying linearly with position

The steady-state and transient electrical properties of ion-exchange membrane systems with fixed charge distributions varying linearly with position inside the membrane have been investigated using the network simulation method, including the diffuse double layer effects. A network model for the Nernst–Planck and Poisson equations has been used to describe the ionic transport processes through an inhomogeneous cation-exchange membrane and the two diffusion boundary layers on both sides of the membrane. With this model and the electric circuit simulation program PSpice, the steady-state and transient responses of the system to an externally applied electric potential difference have been simulated. The steady-state current–voltage characteristic of the whole membrane system and the equilibrium and steady-state non-equilibrium profiles of the ionic concentrations, the electric potential and the electric charge density across the system, have been analyzed. The responses of the system to a step-function potential (chronoamperometric response) and to a square shaped periodic potential, have also been obtained. The time evolution of the counterion flux exiting from the system has been analyzed in order to establish the conditions in which the use of transient techniques in inhomogeneous ion-exchange membranes can lead to intensification of the efficiency of membrane processes such as electrodialysis.