Fundamental understanding of ion sorption and transport in ion-exchange polymers is critical for development of high performance membranes. Despite the long history of literature on the subject, this topic is currently not well understood, making it difficult to build the appropriate connections between polymer structure and transport properties. Experimental techniques for characterizing ion sorption and transport in charged membranes have been established, however, a simple theoretical framework to describe the experimental findings is currently lacking. In this work, a model to predict ion sorption and permeability in ion-exchange membranes has been formulated and tested against experimental data. The model requires basic membrane information (chemical structure, fixed charge density, and water content). For the membranes used in this study, the model was completely predictive and no adjustable parameters were required.
Quantitative description of ion sorption in charged membranes equilibrated in salt solutions typically relies on a rigorous thermodynamic formalism (i.e., Donnan-type analysis). Previous studies have often overlooked the importance of including ion activity coefficients in such treatments, mainly because no reliable models or experimental techniques were available for obtaining these values in the polymer phase. In this work, Manning’s counter-ion condensation theory, originally developed for polyelectrolytes, was extended to ion-exchange membranes and used to estimate membrane ion activity coefficients. Solution activity coefficients were obtained by the Pitzer model. The results of the model were compared to ion sorption data obtained experimentally for various commercially available ion-exchange membranes. Good agreement was found between the predicted values for membrane co-ion concentration and those obtained experimentally when solution and membrane non-idealities were included in the model. The generality and shortcomings of the model, as well as the applicability of polyelectrolyte theories to charged membrane systems, are discussed.
The model was extended to predict salt permeability coefficients in charged membranes within the framework of the solution-diffusion mechanism. According to this model, the permeability of a penetrant across dense polymers is comprised of the product between partition and diffusion coefficients. Ion diffusion coefficients in the membrane were estimated using the Mackie and Meares model. This model has no adjustable parameters and requires knowledge of polymer volume fraction and solution diffusion coefficient of the penetrant. Ion sorption coefficients were estimated by the model presented in this work. Thus, predicted values for permeability coefficients were obtained, and these values were compared to those determined experimentally. Good agreement between model and experiment was found without use of adjustable parameters. General applicability and limitation of this treatment are discussed.