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

Study of the electrochemical impedance and the linearity of the current–voltage relationship in inhomogeneous ion-exchange membranes

“…The numerical results are obtained by using the network simulation method [15] and they are presented by using dimensionless variables. Thus, the following relations are used:…”

“…The values chosen for the parameters of the systems are similar to those used in previous papers, in which we have studied the electrical properties of homogeneous [7] and inhomogeneous [15] ion-exchange membrane systems. In this paper, the results are presented in two sections: (i) electrochemical impedance; and (ii) linearity of the current-voltage relationship.…”

“…From the results obtained in these theoretical studies, it is well known that the non-linear distortion which is present in the current-voltage relationship of a homogeneous ion-exchange membrane system increases as the fixed charge concentration of the membrane increases. However, the study of the electrical properties of inhomogeneous ion-exchange membranes have also received considerable attention in the literature because it has been demonstrated that the particular distribution of the fixed charge groups inside the membrane play a significant role determining the behaviour of the system [9][10][11][12][13][14][15]. It is well known that an increase in the permselectivity of a membrane system can be obtained by redistributing the fixed charge groups asymmetrically inside the membrane.…”

“…It is well known that an increase in the permselectivity of a membrane system can be obtained by redistributing the fixed charge groups asymmetrically inside the membrane. In particular, it has been established that a fixed charge distribution varying linearly with position inside the membrane lead to higher permselectivity than an homogeneous membrane with the same value of the average charge concentration when the coions enter the membrane through the highly charged side [11,15]. It is the main purpose of this paper to contribute to this area and to extend our previous work in this field [15] by investigating the electrochemical impedance and the effect of non-linearity on the validity of impedance measurements of an inhomogeneous ion-exchange membrane system.…”

“…In particular, it has been established that a fixed charge distribution varying linearly with position inside the membrane lead to higher permselectivity than an homogeneous membrane with the same value of the average charge concentration when the coions enter the membrane through the highly charged side [11,15]. It is the main purpose of this paper to contribute to this area and to extend our previous work in this field [15] by investigating the electrochemical impedance and the effect of non-linearity on the validity of impedance measurements of an inhomogeneous ion-exchange membrane system. The system under study is constituted by an inhomogeneous membrane with negative fixed charge varying linearly with position and two diffusion boundary layers on both sides of the membrane, ionic transport being described by the Nernst-Planck and Poisson equations.…”