Effect of proton concentration on membrane potential across a weak amphoteric polymer membrane

An amphoteric membrane consists of both positively and negatively fixed charge groups chemically bound to the polymer chains. If the external solution is changed from alkali to acid, it is possible to obtain an experimental result in which the membrane potential changes from positive to negative through the isoelectric point. It was characterized by examining the relationship between membrane potential and proton concentration (pH) obtained from both experimental and theoretical considerations. The Nernst-Planck flux equation and the Donnan equilibrium theory were also solved for a four-component system combined with the dissociation constant, in order to discuss the pH dependence of membrane potential in a weak amphoteric membrane by comparing the experimental results with the calculated results. It was proven that the calculated results substantially deviated from the theoretical results despite a similar tendency. Such a deviation was caused by the fact that the original theory disregarded the activity coefficient and the ionic mobility, which were dependent on the fixed charge concentration in a membrane. The original theoretical model was modified by adding the effect of a fixed charge group to the activity coefficient and ionic mobility. The calculated results using the modified model explained well the experimental results if the parameter called charge effectiveness, phi, was introduced into the equations. Introduction of phi into the prediction of membrane potential was already done by Kobatake et al. in a system of a strong polyelectrolyte monopolar membrane/salt aqueous solution. In this study, it was proved that phi can also be introduced into a weak amphoteric polymer membrane/salt aqueous solution system. Finally it was also concluded that the Donnan equilibrium and the Nernst-Planck flux equation were still applicable for examining the transport phenomena for the system of a weak amphoteric charged membrane and electrolyte solutions at various pH.