Elucidating conductivity-permselectivity tradeoffs in electrodialysis and reverse electrodialysis by structure-property analysis of ion-exchange membranes

Highlights

• Integration of counterion condensation theory with Nernst-Planck transport framework.

• Higher bulk concentration lowers permselectivity but improves conductivity.

• Increasing ion-exchange capacity enhances both conductivity and permselectivity.

• Raising swelling degree improves conductivity but compromises permselectivity.

• Reducing membrane thickness lowers resistance while preserving permselectivity.

Abstract

Ion-exchange membranes (IEMs) are used in environmental and energy technologies of electrodialysis (ED) desalination and reverse electrodialysis (RED) power generation, respectively. Recent studies reported empirical evidence that the conductivity and permselectivity of IEMs are bound by a tradeoff relationship, where an increase in ionic conductivity is accompanied by a decrease in counterion selectivity over co-ion. A fundamental understanding of this conductivity-permselectivity tradeoff is principal to inform membrane development. This study presents an IEM transport model to analytically relate conductivity and permselectivity to intrinsic membrane chemical and structural properties. The model employs the Nernst-Planck transport framework and incorporates counterion condensation theory to simulate the performance of IEMs in a range of ED and RED operations. The analysis revealed the mechanism for the tradeoff induced by bulk solution concentration: a higher salinity suppresses IEM charge-exclusion, thus lowering permselectivity, but elevates mobile ion concentration within the membrane matrix to improve conductivity. As such, IEM applications are practically confined to sub-seawater salinities, i.e., RED using hypersaline streams will not be efficient. In another tradeoff driven by IEM water sorption, increasing membrane swelling enhances effective ion diffusivity to raise conductivity, but diminishes permselectivity due to dilution of fixed charges. The transport model indicates that increasing membrane ion-exchange capacity and reducing thickness can yield highly selective and conductive IEMs.

Introduction

Ion-exchange membranes (IEMs) are charged polymeric films that allow the selective transport of oppositely-charged species (counterions), while retaining the like-charged ions (co-ions) and water [1]. IEMs are employed in environmental and energy technologies, such as desalination, fuel cells, and salinity gradient power generation [2], [3], [4], [5], and also chemical production by the chloralkali process [6]. In electrodialysis (ED) desalination, the application of an electric current drives the separation of ions from saline brackish water, across the IEMs, to produce freshwater [2], [7]. Reverse electrodialysis (RED), the power generation analog of ED, converts the chemical potential energy stored in salinity gradients to useful electrical work by the directional permeation of ions across the charge-selective membranes [8], [9]. In both ED and RED, permeability of the IEM to ions and charge selectivity are principal parameters that determine performance.

A tradeoff relationship between permeability and selectivity exists for membrane processes of gas separation, reverse osmosis, and ultrafiltration [10], [11], [12], [13], [14]. Empirical evidence from recent studies indicates IEMs are also bound by a similar constraint — an increase in ionic conductivity (i.e., permeability) is almost inevitably accompanied by a decrease in selectivity for counterions over co-ions, termed permselectivity [5], [15], [16]. Because of this conductivity-permselectivity tradeoff for ion-exchange membranes, any efforts to improve separation will be at the expense of reduced kinetics, thus restricting overall ED and RED performance and energy efficiency [5], [15], [16], [17]. As such, the tradeoff phenomenon has profound impacts on ED, RED, and other IEM-based processes.

Fundamental understanding of the tradeoff and its intrinsic relation to membrane properties is crucial to inform the development of better membranes. However, while theoretical explanations for the tradeoff of other membrane processes are available [10], [11], [12], [13], [14], a complete fundamentals-based framework to describe the IEM conductivity-permselectivity relationship is lacking. Although recent experimental studies demonstrated that membrane water uptake and bulk solution concentrations can induce the tradeoff between IEM conductivity and permselectivity, the qualitative explanations provided do not give a rigorous mechanistic explanation of the phenomenon [15], [18]. Analytical approaches to describe the effects of membrane property on IEM transport are almost always focused on quantifying isolated property-performance relationships [19], [20], [21] (such as, ionic conductivity dependence on bulk concentrations) and oftentimes adopt semi-empirical models, i.e., employ fitting parameters [18], [19], [22], [23]. Hence, such approaches are unable to elucidate the intrinsic relationship between membrane properties and the intertwined performance parameters of permselectivity and conductivity. The Nernst-Planck framework is commonly used to describe IEM transport [21], [24], [25], [26], [27], but requires the activity and diffusion coefficient of ions within the charged IEM matrix, which are anticipated to deviate significantly from bulk solution due to non-idealities and are also not readily accessible by experiments [24], [25]. Recently, studies showed that counterion condensation theory, originally established for aqueous polyelectrolyte solutions, can be applied to IEM to predict ion activity and diffusivity with reasonable accuracy [28], [29], thus highlighting the potential to overcome the present limitations of Nernst-Planck transport models.

This study analyzes ion transport across IEMs to elucidate the dependence of key performance parameters, ionic conductivity and charge selectivity, on intrinsic membrane chemical and structural properties. Firstly, the working principles of ion-exchange membranes, electrodialysis, and reverse electrodialysis are described. The IEM model is presented and principal governing equations are discussed. In the model, ion transport is driven by chemical and electrostatic potential, i.e., the Nernst-Planck equation, and counterion condensation theory is incorporated to account for ion activity and diffusivity within the membrane matrix. Computational codes numerically solve for the system of nonlinear differential equations. After the model is validated with literature data, the effects of operating parameters, electric potential difference and external solution concentrations, on current efficiency and resistance to ion fluxes are examined. The analysis then assessed the dependence of permselectivity and conductivity in ED and RED on the intrinsic membrane properties of ion-exchange capacity, degree of swelling, and membrane thickness. The underpinning phenomena relating operating conditions and membrane properties to IEM performance are highlighted and the principal factors governing the observed conductivity-permselectivity tradeoff are elucidated. Lastly, the implications for ED desalination, RED salinity gradient power generation, and membrane development are discussed.