Abstract Ion exchange membranes (IEMs) are extensively used in separation and energy storage systems. Prior studies have suggested that rigorous thermodynamic modeling is essential to describe mobile ion partitioning in IEMs, especially weakly charged ionic membranes, immersed in aqueous salt solutions. Based on a recently developed polyelectrolyte nonrandom two-liquid (NRTL) activity coefficient model, this work presents a thermodynamic analysis for the mobile ion partitioning between external salt solutions with ionic strength from 0.01 to 1 molal and membranes of poly (ethylene glycol diacrylate) (PEGDA) copolymerized with 2-acrylamido-2-methylpropanesulfonic acid (AMPS). We show that mobile ion partitioning in the uncharged membranes and the weakly charged membranes immersed in saline solutions is controlled by the long-range “point-to-point” electrostatic interactions and the short-range van der Waals interactions in the membrane phase. For the strongly charged membrane samples, the long-range “point-to-line” electrostatic interactions also play a role, the mobile ion mean ionic activity coefficients are close to unity, and the ion sorption data may be qualitatively interpreted with either the ideal Donnan equilibrium model or Manning's limiting law.

中文翻译：

---

浸在盐溶液中的离子交换膜中的移动离子分配

摘要 离子交换膜 (IEM) 广泛用于分离和储能系统。先前的研究表明，严格的热力学模型对于描述 IEM 中的移动离子分配至关重要，尤其是浸入盐水溶液中的带弱电的离子膜。基于最近开发的聚电解质非随机两液体 (NRTL) 活性系数模型，这项工作对离子强度为 0.01 至 1 摩尔的外部盐溶液和聚（乙二醇二丙烯酸酯）膜之间的移动离子分配进行了热力学分析。 PEGDA) 与 2-丙烯酰胺基-2-甲基丙磺酸 (AMPS) 共聚。我们表明，在不带电的膜和浸没在盐溶液中的带弱电的膜中的移动离子分配是由膜相中的长程“点对点”静电相互作用和短程范德华相互作用控制的。对于带强电荷的膜样品，长距离的“点对线”静电相互作用也起作用，移动离子平均离子活度系数接近统一，离子吸附数据可以用理想的唐南均衡模型或曼宁极限定律。