The influence of dynamical ion–ion correlations and ion pairing on salt transport in ion exchange membranes remain poorly understood. In this study, we use the framework of Onsager transport coefficients within atomistic molecular dynamics simulations to study the impact of ion–ion correlated motion on salt transport in hydrated polystyrene sulfonate membranes and compare with the results from aqueous salt solutions. At sufficiently high salt concentrations, cation–anion dynamical correlations exert a significant influence on both salt diffusivities and conductivities. Anion–anion distinct correlations, arising from the imbalance between the concentration of free (mobile) cations and anions, and the retarding effect of the fixed charge groups on cations, proves to be an additional important feature for polymer membranes. Our results demonstrate that dynamical correlations should become an important consideration in experimental measurements of salt diffusivities and conductivities for non-dilute salt solutions in polymer membranes.

We conduct molecular dynamics simulations to study the effects of cation–ligand interactions on salt permeation in ligand-functionalized polymer membranes. Our results indicate that salt partitioning into the membrane increases while the salt diffusivity decreases with enhancement in the cation–ligand interaction strength. Moreover, the increase in partitioning dominates the decline in salt diffusivity, leading to a net enhancement in salt permeation at higher cation–ligand interaction strengths. Equimolar binary mixed salt systems (having a common anion) generally exhibit much more selective partitioning of salts into the membrane as compared to their single salt counterparts. However, single salt systems exhibit much higher ratio of salt diffusivities than their mixed salt analogues. The permselectivity data closely resemble the trends in selective partitioning for both single and mixed salt systems, indicating that salt diffusivity selectivity plays a weaker role than salt partitioning selectivity in dictating the selective permeation of salts across the membrane.

Membranes are an attractive alternative to current thermal separations due to their scalability and energy efficiency in desalinating water. Unfortunately, many of the conventional membrane materials available today are unable to differentiate between ionic solutes, especially alkali cations, compromising their use in ion−ion separations. Inspired by the ion-specific interactions exhibited by biological ion channels, recent research efforts have focused on synthesizing and characterizing new polymeric materials that incorporate ligands into polymer networks to bias solubility and/or diffusivity of one cationic species over another. Despite these efforts, little is known about the influence of incorporating ligands into polymer membranes on solubility and diffusivity of the complexing species. In this study, we first build a qualitative model of salt partitioning, diffusivity, and permeability in generic cationcomplexing ligand-functionalized polymer membranes. Next, to validate our model and hypotheses, we perform atomistic molecular dynamics simulations of a 12-crown-4-functionalized membrane in the presence of alkali halide salts at low concentration. Generally, cation complexation enhances cation solubility but decreases diffusivity. Interestingly, the reduction in diffusivity is predicted to be larger than the enhancement in solubility for materials which operate by the mechanisms proposed in our physical picture, ultimately resulting in a reduction in the permeability of the selectively complexing ion.

No abstract

We present a theoretical formalism quantifying the interplay between cation–ligand interaction strength and dynamical ionic correlations on salt diffusivities in the transport of single salt and binary (mixed) salts through ligand-functionalized polymer membranes. The Onsager framework is utilized to capture the effect of correlated ionic motions on salt diffusivities. Such a framework is implemented in the context of a coarse-grained model of systems involving ligand-selective (LS) and/or ligand-agnostic (LA) salts in ligand-functionalized polymer membranes. Our results indicate that ionic correlations speed up the diffusivities of both LS and LA salts relative to the ideal, uncorrelated case. At small values of cation–ligand interaction strength, such a speedup arises from a general trend of positively correlated motion among the mobile ions. On the other hand, ionic correlation-mediated speedup in salt diffusivities at large values of cation–ligand interaction strength can be attributed to the correlated hopping of the cations bound to the ligands in both single and mixed salt systems. At low cation–ligand interaction strengths, ionic correlations reduce the ratio of salt diffusivities of LS to LA salts (relative to the uncorrelated case) in single salt systems. Disparately, ionic correlations enhance the ratio of salt diffusivities of LS to LA salts (relative to the uncorrelated case) at large values of the cation–ligand interaction strengths in both single and mixed salt systems. We observe that single salt systems exhibit higher LS to LA salt diffusivity ratios than their mixed salt analogs up to a certain value of the cation–ligand interaction strength, beyond which the salt diffusivity ratios for the two systems converge.