Modelling of anion-exchange membrane transport properties with taking into account the change in exchange capacity and swelling when varying bathing solution concentration and pH

In this paper we take into account the variation of anion-exchange membrane swelling and effective exchange capacity with changing the concentration and/or pH of the bathing solution when simulating membrane transport characteristics (the electric conductivity, diffusion permeability and ion transport numbers). Two main structural elements of the membrane are distinguished: a microporous polyelectrolyte gel assumed homogeneous, and macropores including structural defects and voids. It is supposed that only microporous gel exerts osmotic pressure, which causes membrane swelling described in our model by the Gregor equation, which employs the mole fractions of free and bound water. Three types of ion-exchange functional groups, namely, the secondary, tertiary and quaternary amino groups are taken into account. The degree of dissociation of these groups depends on the internal solution pH, which is described by equilibriums between protonated and de-protonated forms. The Donnan equations and electroneutrality condition are used to calculate the ion concentration in the membrane. The microheterogeneous model based on the Nernst-Planck equations is used to describe the ion transport. We take into account that the ion diffusion coefficients depend on the degree of gel swelling, this dependence is described by the Mackie-Meares equation. The model parameters include the equivalent volume of dry polyelectrolyte gel, the volume fraction of macropores, the structural parameters and others. The results of calculations are compared with experimental data on the electric conductivity, diffusion permeability and ion transport numbers for two heterogeneous anion-exchange membranes MA-40 and MA-41 (Shchekinoazot, Russia) differed by the fractions of the weakly basic functional groups. A good quantitative agreement between the theory and experiment is found for both membranes using the same set of ion hydration numbers and chemical equilibrium constants for secondary and tertiary amino groups. In particular, it is shown that with increasing pH of the bathing solution, the membrane diffusion permeability passes through a maximum, which is explained by the corresponding maximum of water content. A higher water content results in larger membrane pores, which leads to higher values of ion diffusion coefficients and higher amount of sorbed electrolyte. Together with varying water content, the variation in membrane effective exchange capacity as a function of external solution pH, determines a non-trivial behavior of electric conductivity, diffusion permeability and ion transport numbers in the membrane equilibrated with NaCl solutions of different concentration and pH.