title: Partitioning of mobile ions between ion exchange polymers and aqueous salt solutions: importance of counter-ion condensation.
abstract: Equilibrium partitioning of ions between a membrane and a contiguous external solution strongly influences transport properties of polymeric membranes used for water purification and energy generation applications. This study presents a theoretical framework to quantitatively predict ion sorption from aqueous electrolytes (e.g., NaCl, MgCl2) into charged (i.e., ion exchange) polymers. The model was compared with experimental NaCl, MgCl2, and CaCl2 sorption data in commercial cation and anion exchange membranes. Ion sorption in charged polymers was modeled using a thermodynamic approach based on Donnan theory coupled with Manning's counter-ion condensation theory to describe non-ideal behavior of ions in the membrane. Ion activity coefficients in solution were calculated using the Pitzer model. The resulting model, with no adjustable parameters, provides remarkably good agreement with experimental values of membrane mobile salt concentration. The generality of the model was further demonstrated using literature data for ion sorption of various electrolytes in charged polymers, including HCl sorption in Nafion.
authors: McKetta Department of Chemical Engineering, Center for Energy and Environmental Resources, and Texas Materials Institute, The University of Texas at Austin, 10100 Burnet Road Building 133 (CEER), Austin, TX 78758, USA. freeman@che.utexas.edu.
authors: Jovan
authors: J
authors: Kamcev
authors: McKetta Department of Chemical Engineering, Center for Energy and Environmental Resources, and Texas Materials Institute, The University of Texas at Austin, 10100 Burnet Road Building 133 (CEER), Austin, TX 78758, USA. freeman@che.utexas.edu.
authors: Michele
authors: M
authors: Galizia
authors: McKetta Department of Chemical Engineering, Center for Energy and Environmental Resources, and Texas Materials Institute, The University of Texas at Austin, 10100 Burnet Road Building 133 (CEER), Austin, TX 78758, USA. freeman@che.utexas.edu.
authors: Francesco M
authors: FM
authors: Benedetti
authors: McKetta Department of Chemical Engineering, Center for Energy and Environmental Resources, and Texas Materials Institute, The University of Texas at Austin, 10100 Burnet Road Building 133 (CEER), Austin, TX 78758, USA. freeman@che.utexas.edu.
authors: Eui-Soung
authors: ES
authors: Jang
authors: McKetta Department of Chemical Engineering, Center for Energy and Environmental Resources, and Texas Materials Institute, The University of Texas at Austin, 10100 Burnet Road Building 133 (CEER), Austin, TX 78758, USA. freeman@che.utexas.edu.
authors: Donald R
authors: DR
authors: Paul
authors: McKetta Department of Chemical Engineering, Center for Energy and Environmental Resources, and Texas Materials Institute, The University of Texas at Austin, 10100 Burnet Road Building 133 (CEER), Austin, TX 78758, USA. freeman@che.utexas.edu.
authors: Benny D
authors: BD
authors: Freeman
authors: Department of Chemistry and Chemical Biology, Rutgers University, 610 Taylor Road, Piscataway, NJ 08854-8087, USA.
authors: Gerald S
authors: GS
authors: Manning