(272f) Thermodynamic Modeling of Ion Exchange Membranes with Enrtl Model

Ion Exchange Membranes are of great importance in the fields of separations, energy storage, electrochemical reaction et al. [1, 2] They are a special type of polyelectrolytes that have charged functional groups distributed on the backbone polymers. The charged functional groups are electrostatically attached with counterions that carry opposite charges. The counterions are able to dissociate in solutions. The interactions between counterions and other particles in the system might cause high nonidealities of mobile ions’ behavior. Such nonidealities have often been ignored in membrane studies. [3] And there is no successful modeling work dealing with such nonidealities in membrane systems yet. Kamcev tried to calculate the activity coefficients of mobile ions in the highly charged membranes with Manning’s limiting law, however, it does not work for less charged polymers and has not been examined beyond certain concentrations of the electrolyte solutions. [3, 4]

This work is able to model mobile ions in membranes in equilibrium with salt solutions. Manning’s limiting law is used to capture the “point-to-line” 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. [4] The Pitzer-Debye-Hückel formulation is applied to account for the “point-to-point” 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. [6]

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 [7].

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 ions 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 Manning’s limiting law alone.

1. Jeon, Sung-il, et al. "Desalination via a new membrane capacitive deionization process utilizing flow-electrodes." Energy & Environmental Science 6.5 (2013): 1471-1475.
2. Cai, Zhijun, et al. "High performance of lithium-ion polymer battery based on non-aqueous lithiated perfluorinated sulfonic ion-exchange membranes." Energy & Environmental Science 5.2 (2012): 5690-5693.
3. Kamcev, Jovan, Donald R. Paul, and Benny D. Freeman. "Ion activity coefficients in ion exchange polymers: applicability of Manning’s counterion condensation theory." Macromolecules 48.21 (2015): 8011-8024.
4. Kamcev, Jovan, et al. "Partitioning of Mobile Ions Between Ion Exchange Polymers and Aqueous Salt Solutions: Importance of Counter-ion Condensation." Physical Chemistry Chemical Physics (2016).
5. Manning, Gerald S. "Limiting laws and counterion condensation in polyelectrolyte solutions I. Colligative properties." The Journal of Chemical Physics 51.3 (1969): 924-933.
6. Song, Yuhua, and Chau-Chyun Chen. "Symmetric electrolyte nonrandom two-liquid activity coefficient model." Industrial & Engineering Chemistry Research 48.16 (2009): 7788-7797.
7. G.M. Geise, L.P. Falcon, B.D. Freeman, D.R. Paul, Sodium chloride sorption in sulfonated polymers for membrane applications, Journal of Membrane Science, 423-424 (2012) 195-208.