Theoretical and Experimental Study of the Voltage–Current Characteristic of an Asymmetric Cellulose Acetate Membrane

Abstract

The voltage–current characteristic of an asymmetric cellulose acetate (KP96) membrane in NaCl solutions (0.005–0.1 M) has been studied both experimentally and theoretically. The theoretical analysis was carried out within the context of a bilayer model, thereby taking into account ion transport across the interfaces of the active layer and the effect of concentration polarization at the selective layer/nonselective layer boundary. The transport process was treated mathematically by applying the Nernst–Planck–Poisson equations. Image forces affecting ion transport across the surfaces of the active layer have been incorporated into the theoretical description by means of a mathematical simulation of the profile of the image force potential. Most of the parameters characterizing the model membrane were estimated from literature data, from the known value of the final rejection coefficient of an asymmetric KP96 cellulose acetate membrane, and from our experimental results on the NaCl concentration dependency of the small-current resistance of an asymmetric KP96 membrane. The thickness of the active layer, however, was considered as an adjustable parameter in our analysis. The theoretical predictions, obtained by numerically solving the Nernst–Planck–Poisson equations, have been compared with the experimental results to obtain insight into the factors underlying the observed nonlinear and asymmetric features of the voltage–current characteristic. For the case of a relatively thick active layer, the nonequilibrium state of the interfaces was also investigated theoretically. Our analysis indicates that ion transport across the interfacial regions of the active layer plays a crucial role in the explanation of the observed phenomena, whereas the influence of concentration polarization in the porous support layer is of minor importance.