(272f) Thermodynamic Modeling of Ion Exchange Membranes with Enrtl Model
This work is able to model mobile ions in membranes in equilibrium with salt solutions. Manningâs limiting law is used to capture the âpoint-to-lineâ electrostatic interaction between mobile ions and charged functional group, as well as counterion condensation. Counterion condensation is a phenomenon happens in highly charged polymer solutions where counterions attach to the polyion to reduce its charge density to a critical value.  The Pitzer-Debye-HÃ¼ckel formulation is applied to account for the âpoint-to-pointâ electrostatic interactions between each charged particles in the solution. And the eNRTL theory is used to deal with the local short-range interactions between all molecular and ionic species. 
Sulfonated crosslinked hydrogel membranes, with Ion Exchange Capacity (IEC) values ranging from 0.01 to 1.93 meq/g(dry polymer) and water uptake levels ranging from 0.2 to 1.8 g(water)/g(dry polymer) are studied in this work. They were synthesized by UV-crosslinking. 2-acrylamido-2-methylpropane sulfonic acid (AMPS) was copolymerized into a hydrogel matrix based on poly (ethylene glycol) diacrylate (PEGDA). Anion sorption was measured using a desorption technique and ion chromatography and cation sorption was measured using a polymer ashing technique and atomic absorption spectrophotometry .
Dimensionless charge density of polymers and eNRTL short-range parameters are required to describe the membrane systems. The charge density of polymers can be either determined by the structure of the polymers or fitted from experimental data, while eNRTL short-range parameters have to be identified from data for species of significant concentrations. For membranes that have only one type of monomer with charged functional groups, the short-range parameter between water and the counterion-polyion ionic pair is necessary. In addition, the pair parameter between simple salts and the polyelectrolyte is needed when salt concentration is high. In a more interesting case where there are non-charged segments in the polymer, the neutral segments are treated as second solvent and its short range parameters with water have to be well identified.
This model is able to correlate and extrapolate the concentration of mobile ionsÂ in membranes equilibrated in external brine solutions. With limited number of parameters, this model represents the experimental data of different salt concentrations and IECs very well, with much higher accuracy compared to using Manningâs limiting law alone.
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