Mobile ion partitioning in ion exchange membranes immersed in saline solutions

doi:10.1016/j.memsci.2020.118760

Journal of Membrane Science

Volume 620, 15 February 2021, 118760

https://doi.org/10.1016/j.memsci.2020.118760 Get rights and content

Highlights

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Ion sorption behavior of ion exchange membranes in saline solutions is examined with an electrolyte thermodynamic model.
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For weakly charged membranes, the ion-ion electrostatic interactions and the van der Waals interactions dominate.
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For strongly charged membranes, the behavior can be interpreted with the ideal Donnan model or Manning’s limiting law.

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.

Graphical abstract

Introduction

Ion exchange membranes (IEMs), a special type of cross-linked polyelectrolyte with repeat units bearing charged functional groups distributed on the polymer backbone, are of great interest in the fields of separations, energy storage, and electrochemical systems [[1], [2], [3]]. The charged functional groups are electrostatically attached to counterions, which bear opposite charges. When IEMs are immersed in saline solutions, ions bearing the same charge as the charged functional groups are designated coions, and together, counterions and coions are called mobile ions. The long-range electrostatic and short-range van der Waals interactions between mobile ions, solvent molecules, and polymer repeat units (whether charged or uncharged) in the system contribute to the thermodynamic nonideality of IEMs and the mobile ions in them.

The thermodynamic nonideality of mobile ions in solution has often been ignored in IEM studies [4]. Recently, from salt partitioning measurements, Kamcev et al. reported activity coefficients of mobile ions in the cation exchange membrane CR61-CMP and anion exchange membranes AR103-QDP and AR204-SZRA where the external NaCl salt concentration ranged from 0.01 to 1 mol/L [4,5]. In addition, they correlated these activity coefficients with Manning's limiting law [6] for the IEM phase and with the Pitzer ion-specific model [7] for the external salt solution. The correlation quantitatively described the increasing activity coefficients of mobile ions in the membranes for external salt concentrations between 0.1 and 1 mol/L. However, their study failed to quantitatively interpret the mobile ion activity coefficients for external salt concentrations lower than 0.1 mol/L. In fact, as the external salt concentration drops, the model extrapolations for activity coefficients asymptotically approach constant values, in contrast to the monotonic decreasing trend obtained from their actual measurements. Kamcev et al. attributed this deficiency to a “breakdown in one or more assumptions,” such as “ignorance of interactions between distant chains or different segments on the same chain,” in Manning's limiting law [4]. Later they also applied Manning's limiting law in their interpretation of ion diffusion and salt permeability coefficient data in IEMs. Similar to the activity coefficient results, their theoretical interpretation departs from the experimental measurements for low external salt concentrations [8,9].

In parallel to Kamcev's work [4,5], an experimental study [10] systematically examined the relationship between polymer structure, external salt concentration, water uptake, and mobile ion partitioning for cross-linked hydrogel membranes of poly (ethylene glycol diacrylate) (PEGDA) randomly copolymerized with 2-acrylamido-2-methylpropanesulfonic acid (AMPS). Fig. 1 shows the molecular structure of the copolymer. Different ion exchange capacities (IECs) were achieved by changing the mass ratio of AMPS to PEGDA. IEC is one measure of the charge density of IEMs, with units of milli-equivalents of charged segments per dry polymer weight (meq/g dry polymer). This study reported experimental results of ion sorption, i.e., mobile ion partitioning, as well as mobile ion activity coefficients, as functions of IEC and external salt concentration. In addition, they attempted to describe the ion sorption data with the ideal Donnan equilibrium model [11], which assumes unity activity coefficients for the mobile ions in both the membrane phase and the external salt solution phase. While the model captured the mobile ion partitioning data qualitatively for a dilute external NaCl concentration of 0.01 M, it failed for the case with external NaCl concentration of 1 M [10]. Suggesting strong nonideality of the mobile ions in the membrane phase, their data show that the activity coefficients are strong functions of IEC and external salt concentration. The ideal Donnan equilibrium model ignores the nonideality, while Manning's limiting law fails to describe the nonideality for both very low and high salt concentrations at a fixed charge density for the membrane [10,12]. The authors concluded that “there is a strong need for validation of fundamental theoretical models … to describe ionic activity coefficients in a wide range of membranes,” in order to interpret the mobile ion partitioning behavior between IEMs and external salt solutions.

Recently, Yu and Chen [12] proposed a comprehensive thermodynamic model to describe nonideality of mobile ions in aqueous polyelectrolyte solutions. Their model integrates Manning's limiting law with the electrolyte nonrandom two-liquid (eNRTL) model that is well established for electrolyte thermodynamics [13]. Manning's limiting law is used to capture the long-range “point-to-line” or “ion-polyion” electrostatic interactions between mobile ions and charged segments on the polymer backbone, as well as the counterion condensation phenomenon in highly charged polymers where the counterions attach to the polyions and reduce the polyion charge density to a critical value [6]. The eNRTL model is composed of the Pitzer-Debye-Hückel formulation for the long-range “point-to-point” or “ion-ion” electrostatic interactions between charged species in solution and, for the short-range van der Waals interactions between all molecular and ionic species, a local composition expression derived from the nonrandom two-liquid theory [13].

This work presents a rigorous thermodynamic treatment for the experimental study of ion sorption as functions of IEC and external salt concentration for cross-linked (XL) PEGDA and AMPS copolymer membranes [10]. Both Manning's limiting law and the polyelectrolyte NRTL model are considered in addition to the ideal Donnan equilibrium model. With its limited number of adjustable model parameters, the polyelectrolyte NRTL model quantitatively represents the ion sorption data of different IECs and salt concentrations and the ion sorption behavior is further explained from the perspective of the polyelectrolyte NRTL model.

Section snippets

Thermodynamic Framework

When thermodynamic equilibrium is established between ion exchange membranes and external salt solutions, the chemical potential of the salt should be equal between the two phases: $μ_{s a l t}^{m} = μ_{s a l t}^{s}$ where $μ_{s a l t}^{m}$ and $μ_{s a l t}^{s}$ are the chemical potential of salts in the membrane phase (superscript m) and salt solution (superscript s) phase, respectively. Alternatively, Eq. (1) can be written in terms of mean ionic activity, $a_{\pm}$ . $a_{\pm}^{m} = a_{\pm}^{s}$

NaCl is the only salt considered in this work. Mean ionic activity can

Experimental Data

Yan et al. reported experimental results of mobile ion partitioning as functions of IEC and external NaCl concentration for uncharged XL PEGDA membranes and charged XL (PEGDA/AMPS) membrane samples, with corresponding IEC values of 0, 0.01, and 1.93 respectively [10]. In addition, they reported the activity coefficient product of Na⁺ ion and Cl⁻ ion in eight membrane samples with IECs ranging from 0 to 1.93. The mobile ion concentrations in the membranes equilibrated with external NaCl

Modeling Results

From the mobile ion partitioning data of Yan et al. for the uncharged XL PEGDA membrane and the charged XL (PEGDA/AMPS) membrane samples, we regressed the Manning parameter $ξ$ for each XL (AMPS-PEGDA) sample and the eNRTL binary interaction parameters $τ_{i j}$ . The results are given in Table 3, Table 4. Note that the PEGDA segment in the membrane phase is treated as a second solvent. Therefore, the Born correction term is required to transfer the thermodynamic reference state of the membrane phase

Conclusion

We have modeled the ion sorption behavior for a series of AMPS/PEGDA ion exchange membranes equilibrated with external aqueous NaCl solutions by using ideal Donnan equilibrium model, Manning's limiting law, and the polyelectrolyte NRTL model. The ion sorption behavior in ion exchange membranes is highly complex. While theoretical treatments such as ideal Donnan equilibrium model and Manning's limiting law may qualitatively describe the ion sorption data in the strongly charged membranes, they

Disclaimer

Funding support is provided by the U. S. Department of Energy under the grant DE-EE0007888. The authors gratefully acknowledge the financial support of the Jack Maddox Distinguished Engineering Chair Professorship in Sustainable Energy sponsored by the J.F Maddox Foundation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific

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Mobile ion partitioning in ion exchange membranes immersed in saline solutions

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Thermodynamic Framework

Experimental Data

Modeling Results

Conclusion

Disclaimer

Declaration of competing interest

Acknowledgments

J. Membr. Sci.

Polymer

Fluid Phase Equil.

J. Membr. Sci.

J. Membr. Sci.

Polymer

Moon Hee Han, Dong Kook Kim. Desalination via a new membrane capacitive deionization process utilizing flow-electrodes

Energy Environ. Sci.

High performance of lithium-ion polymer battery based on non-aqueous lithiated perfluorinated sulfonic ion-exchange membranes

Energy Environ. Sci.