Impact of Ionic Correlations on Selective Salt Transport in Ligand-Functionalized Polymer Membranes

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 ligandagnostic (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.

Automated summary

We present a theoretical formalism that quantifies the interplay between cation-ligand interaction strength and dynamical ionic correlations on salt diffusivities in ligand-functionalized polymer membranes. Our results show that ionic correlations speed up the diffusivities of both ligand-selective and ligand-agnostic salts compared to the ideal, uncorrelated case. The speedup is due to positively correlated motion among mobile ions at low interaction strengths and correlated hopping of cations bound to ligands at high interaction strengths.