Impact of Confinement and Zwitterionic Ligand Chemistry on Ion-Ion Selectivity of Functionalized Nanopores.

Membranes incorporating zwitterionic chemistries have recently emerged as promising candidates for facilitating challenging ion-ion separations. Transport of ions in such membranes predominantly occurs in hydrated nanopores lined with zwitterionic monomers. To shed light on the physics of ion-ion selectivity underlying such materials, we conducted molecular dynamics simulations of sodium halide transport in model nanopores grafted with sulfobetaine methacrylate molecules. Our results reveal that in both functionalized and unfunctionalized nanopores smaller ions prefer to reside near the pore center, while the larger ions tend to reside near the pore walls. An enhancement in the selective transport of larger anions is observed within the unfunctionalized nanopores relative to that in salt-in-water solutions. Upon functionalization of the nanopores with zwitterions (ZIs), the disparities in the anionic distribution profiles within the pores coupled with differences in the anion-ZI interactions result in a slowdown of larger anions relative to smaller anions. Increasing the ZI grafting density exacerbates these effects, further promoting the selective transport of smaller anions. Our results suggest that selectivity toward large anions can be realized by using nanoporous membranes with ZI content that is high enough to facilitate ion/water partitioning into the pores while preserving the characteristic tendency of the unfunctionalized pores to facilitate faster transport of the larger anions. On the other hand, selectivity toward smaller anions can be achieved by targeting ZI content within the pores that is high enough to significantly slow down the transport of large anions but not high enough to hinder the partitioning of ions/water molecules into the pore due to steric effects.

Mechanisms of ion transport in lithium salt-doped zwitterionic polymer-supported ionic liquid electrolytes.

Recent experimental results have demonstrated that zwitterionic ionogel comprised of polyzwitterion (polyZI)-supported lithium salt-doped ionic liquid exhibits improved conductivities and lithium transference numbers than the salt-doped base ionic liquid electrolyte (ILE). However, the underlying mechanisms of such observations remain unresolved. In this work, we pursued a systematic investigation to understand the impact of the polyZI content and salt concentration on the structural and dynamic properties of the poly(MPC) ionogel of our model polyZI ionogel, poly(2-methacryloyloxyethyl phosphorylcholine) [poly(MPC)] supported LiTFSI/N-butyl-N-methylpyrrolidinium TFSI base ionic liquid electrolyte. Our structural analyses show strong lithium-ZI interaction consistent with the physical network characteristic observed in the experiments. An increase in polyZI content leads to an increased fraction of Li+ ions coordinated with the polyZI. In contrast, an increase in salt concentration leads to a decreased fraction of Li+ ions coordinated with the polyZI. The diffusivities of the mobile ions in the poly(MPC) ionogel were found to be lower than the base ILE in agreement with experiments at T > 300 K. Analysis of ion transport mechanisms shows that lithium ions within the poly(MPC) ionogel travel via a combination of structural, vehicular diffusion, as well as hopping mechanism. Finally, the conductivity trend crossover between the poly(MPC) ionogel and the base ILE was rationalized via a temperature study that showed that the base ILE ions are influenced more by the variation of temperature when compared to the poly(MPC) ions.

Engineering Li/Na selectivity in 12-Crown-4-functionalized polymer membranes.

Lithium is widely used in contemporary energy applications, but its isolation from natural reserves is plagued by time-consuming and costly processes. While polymer membranes could, in principle, circumvent these challenges by efficiently extracting lithium from aqueous solutions, they usually exhibit poor ion-specific selectivity. Toward this end, we have incorporated host-guest interactions into a tunable polynorbornene network by copolymerizing 1) 12-crown-4 ligands to impart ion selectivity, 2) poly(ethylene oxide) side chains to control water content, and 3) a crosslinker to form robust solids at room temperature. Single salt transport measurements indicate these materials exhibit unprecedented reverse permeability selectivity (∼2.3) for LiCl over NaCl-the highest documented to date for a dense, water-swollen polymer. As demonstrated by molecular dynamics simulations, this behavior originates from the ability of 12-crown-4 to bind Na+ ions more strongly than Li+ in an aqueous environment, which reduces Na+ mobility (relative to Li+) and offsets the increase in Na+ solubility due to binding with crown ethers. Under mixed salt conditions, 12-crown-4 functionalized membranes showed identical solubility selectivity relative to single salt conditions; however, the permeability and diffusivity selectivity of LiCl over NaCl decreased, presumably due to flux coupling. These results reveal insights for designing advanced membranes with solute-specific selectivity by utilizing host-guest interactions.

Mechanism of monovalent and divalent ion mobility in Nafion membrane: An atomistic simulation study.

Polymer cation exchange membranes (CEMs) are widely used in water treatment processes. The fundamental factors that control the separation and selectivity of cations with different valences in CEMs are not fully understood. In this study, we use atomistic molecular dynamics simulations to investigate the underlying molecular mechanisms that control the mobility of cations with different valences in Nafion membranes. Our results indicate structural differences in binding of monovalent and divalent cations, which gives rise to differences in ion diffusion in Nafion. Monovalent cations are shown to be "territorially" bound, i.e., bound while partially hydrated, to the fixed charge groups whereas divalent cations are shown to be "site" bound, i.e., bound while fully dehydrated, to the charge groups on the polymer. This difference in binding structure gives rise to differences in transport characteristics of cations in Nafion.

The influence of counterion structure identity on conductivity, dynamical correlations, and ion transport mechanisms in polymerized ionic liquids.

We used equilibrium and non-equilibrium atomistic simulations to probe the influence of anion chemistry on the true conductivity, dynamical correlations, and ion transport mechanisms in polymeric ionic liquids. An inverse correlation was found between anion self-diffusivities, ionic mobilities, and the anion size for spherical anions. While some larger asymmetric anions had higher diffusivities than smaller spherical anions, their diffusivities and mobilities did not exhibit a direct correlation to the anion volumes. The conductivity and anion dynamical correlations also followed the same trends as displayed by the diffusivity and mobility of anions. All the systems we examined displayed positively correlated motion among anions, suggesting a contribution that enhances the conductivity beyond the ideal Nernst-Einstein value. Analysis of ion transport mechanisms demonstrated very similar hopping characteristics among the spherical anions despite differences in their sizes.

Multiscale modeling of solute diffusion in triblock copolymer membranes.

We develop a multiscale simulation model for diffusion of solutes through porous triblock copolymer membranes. The approach combines two techniques: self-consistent field theory (SCFT) to predict the structure of the self-assembled, solvated membrane and on-lattice kinetic Monte Carlo (kMC) simulations to model diffusion of solutes. Solvation is simulated in SCFT by constraining the glassy membrane matrix while relaxing the brush-like membrane pore coating against the solvent. The kMC simulations capture the resulting solute spatial distribution and concentration-dependent local diffusivity in the polymer-coated pores; we parameterize the latter using particle-based simulations. We apply our approach to simulate solute diffusion through nonequilibrium morphologies of a model triblock copolymer, and we correlate diffusivity with structural descriptors of the morphologies. We also compare the model's predictions to alternative approaches based on simple lattice random walks and find our multiscale model to be more robust and systematic to parameterize. Our multiscale modeling approach is general and can be readily extended in the future to other chemistries, morphologies, and models for the local solute diffusivity and interactions with the membrane.

Influence of pore morphology on the diffusion of water in triblock copolymer membranes.

Understanding the transport properties of water in self-assembled block copolymer morphologies is important for furthering the use of such materials as water-purifying membranes. In this study, we used coarse-grained dissipative particle dynamics simulations to clarify the influence of pore morphology on the self-diffusion of water in linear-triblock-copolymer membranes. We considered representative lamellar, cylindrical, and gyroid morphologies and present results for both the global and local diffusivities of water in the pores. Our results suggest that the diffusivity of water in the confined, polymer-coated pores differs from that in the unconfined bulk. Explicitly, in confinement, the mobility of water is reduced by the hydrodynamic friction arising from the hydrophilic blocks coating the pore walls. We demonstrate that in lamella and cylindrical morphologies, the latter effects can be rendered as a universal function of the pore size relative to the brush height of the hydrophilic blocks.

Ion transport in backbone-embedded polymerized ionic liquids.

We use atomistic computer simulations to examine ion-transport phenomena for backbone polymerized cationic liquids with bistrifluoromethylesulfonylimide (TFSI-) counterions. We consider a system in which the polymerized cation moiety is the imidazolium ring and study the structural characteristics and ion mobilities for cases in which the cations are separated by four, six, and eight methylene units on the backbone. A pendant polymerized ionic liquid, 1-butyl-3-vinylimidazolium, is compared to the backbone series across ion coordination and hopping features. The anion diffusivity in backbone polymerized cationic liquids is found to decrease with increasing spacer length, which is shown to result from a decrease in intramolecular and intermolecular hopping frequencies due to an increasing distance separating imidazolium moieties. In comparison with pendant polymerized ionic liquids, we observe that the participation rates of intermolecular hopping events in the backbone polymers far exceed that of the pendant, and the intrapolymeric ionic coordination profile shows the TFSI- of the pendant polymer with a high propensity for coordination by multiple imidazolium, compared with one monomer from a given polymer for the backbone series. Despite these differences, backbone polymerized ionic liquids are seen to possess correlated diffusivity and ion-association relaxation times, in a manner similar to the results observed in past studies for pendant variants.

Influence of morphology of colloidal nanoparticle gels on ion transport and rheology.

We develop a simple model to probe the ion transport and mechanical properties of low volume fraction colloidal nanoparticle gels. Specifically, we study the influence of the morphology of gels on ion diffusion and the corresponding roles of affinity to and enhanced ion transport along nanoparticle surfaces. We employ kinetic Monte Carlo simulations to simulate ion transport in the colloidal gels, and we perform nonequilibrium molecular dynamics to study their viscoelastic behavior. Our results indicate that in the presence of enhanced diffusion pathways for ions along the particle surface, morphology has a significant influence on the diffusivity of ions. We demonstrate that some gel morphologies can exhibit simultaneously enhanced ion transport and mechanical properties, thus illustrating a strategy to decouple ion transport and mechanical strength in electrolytes.

Influence of protein charge patches on the structure of protein-polyelectrolyte complexes.

We employ a combination of the single chain in mean field simulation approach with the solution of Poisson's equation to study the influence of charge heterogeneities on the structure of protein-polyelectrolyte complexes. By adopting a coarse-grained model of representing proteins as charged nanoparticles, we studied the influence of the pattern of charge heterogeneities, net charge, ratio of positive to negative charges on the patches, and the volume fraction of the particles on the structural and aggregation characteristics of proteins in polyelectrolyte solutions. Our results demonstrate that the pattern of charge heterogeneities can exert a significant influence on the resulting characteristics of the aggregates, in some cases leading to a transformation from polymer-bridged complexes into direct particle aggregates driven by the attraction between oppositely charged patches.

Influence of dielectric inhomogeneities on the structure of charged nanoparticles in neutral polymer solutions.

We study the structural characteristics of a system of charged nanoparticles in a neutral polymer solution while accounting for the differences in the dielectric constant between the particles, polymer and the solvent. We use a hybrid computational methodology involving a combination of single chain in mean-field simulations and the solution of the Poisson's equation for the electrostatic field. We quantify the resulting particle structural features in terms of radial distribution function among particles as a function of the dielectric contrast, particle charge, particle volume fraction and polymer concentration. In the absence of polymers, charged macroions experience increased repulsion with a lowering of the ratio of particle to solvent dielectric constant. The influence of the dielectric contrast between the particle and the solvent however diminishes with an increase in the particle volume fraction and/or its charge. In the presence of neutral polymers, similar effects manifest, but with the additional physics arising from the fact that the polymer-induced interactions are influenced by the dielectric contrast of the particle and solvent.

Impact of cross-linking of polymers on transport of salt and water in polyelectrolyte membranes: A mesoscopic simulation study.

Our recent atomistic simulation studies demonstrated that the transport properties of salt ions and water in non-crosslinked polymer electrolyte membrane exhibit an intriguing dependence on salt concentration that is opposite to that seen in electrolyte solutions. Here, we extend our study to probe the influence of the degree of cross-linking of the polymer on the transport properties of salt and water in polymer electrolyte membranes. Towards this objective, we use a coarse-grained model embedded within dissipative particle dynamics (DPD) mesoscale simulations, which allows us to access time scales necessary for studying crosslinked polymer systems. Our DPD simulations on non-crosslinked membranes reproduce results that are in qualitative agreement with our atomistic simulations. For the case of crosslinked membranes, our results demonstrate that the diffusion of salt ions and water is reduced significantly relative to crosslinked systems. However, the trends exhibited by the salt concentration dependence of diffusivities and the coordination of the cations with anions and with the polymer backbone remain qualitatively similar to those observed in non-crosslinked membranes.

Mechanisms Underlying Ion Transport in Polymerized Ionic Liquids.

We report the results of atomistic molecular dynamics simulations informed by quantum-mechanically parametrized force fields, which identify the mechanisms underlying ion motion and diffusivities in poly(1-butyl-3-vinylimidazolium-hexafluorophosphate) polymerized ionic liquid (polyIL) electrolytes. Our results demonstrate that anion transport in polyILs occurs through a mechanism involving intra- and intermolecular ion hopping through formation and breaking of ion-associations involving four polymerized cationic monomers bonded to two different polymer chains. The resulting ion mobilities are directly correlated to the average lifetimes of the ion-associations. Such a trend is demonstrated to contrast with the behavior in pure ILs, wherein structural relaxations and the associated times are dominant mechanism. Our results establish the basis for experimental findings that reported ion transport in polyILs to be decoupled from polymer segmental relaxations.

Ion transport mechanisms in lamellar phases of salt-doped PS-PEO block copolymer electrolytes.

We use a multiscale simulation strategy to elucidate, at an atomistic level, the mechanisms underlying ion transport in the lamellar phase of polystyrene-polyethylene oxide (PS-PEO) block copolymer (BCP) electrolytes doped with LiPF6 salts. Explicitly, we compare the results obtained for ion transport in the microphase separated block copolymer melts to those for salt-doped PEO homopolymer melts. In addition, we also present results for dynamics of the ions individually in the PEO and PS domains of the BCP melt, and locally as a function of the distance from the lamellar interfaces. When compared to the PEO homopolymer melt, ions were found to exhibit slower dynamics in both the block copolymer (overall) and in the PEO phase of the BCP melt. Such results are shown to arise from the effects of slower polymer segmental dynamics in the BCP melt and the coordination characteristics of the ions. Polymer backbone-ion residence times analyzed as a function of distance from the interface indicate that ions have a larger residence time near the interface compared to that near the bulk of lamella, and demonstrates the influence of the glassy PS blocks and microphase segregation on the ion transport properties. Ion transport mechanisms in BCP melts reveal that there exist five distinct mechanisms for ion transport along the backbone of the chain and exhibit qualitative differences from the behavior in homopolymer melts. We also present results as a function of salt concentration which show that the mean-squared displacements of the ions decrease with increasing salt concentration, and that the ion residence times near the polymer backbone increase with increasing salt concentration.

Influence of molecular weight on ion-transport properties of polymeric ionic liquids.

We report the results of atomistic molecular dynamics simulations on polymerized 1-butyl-3-vinylimidazolium-hexafluorophosphate ionic liquids, studying the influence of the polymer molecular weight on the ion mobilities and the mechanisms underlying ion transport, including ion-association dynamics, ion hopping, and ion-polymer coordinations. With an increase in polymer molecular weight, the diffusivity of the hexafluorophosphate (PF6-) counterion decreases and plateaus above seven repeat units. The diffusivity is seen to correlate well with the ion-association structural relaxation time for pure ionic liquids, but becomes more correlated with ion-association lifetimes for larger molecular weight polymers. By analyzing the diffusivity of ions based on coordination structure, we unearth a transport mechanism in which the PF6- moves by "climbing the ladder" while associated with four polymeric cations from two different polymers.

On the relationship between the local segmental dynamics and the tagged monomer dynamics in lamellar phases of diblock copolymers.

In this brief article, we present results from coarse-grained molecular dynamics simulations which probed the relationship between the local segmental dynamics and the tagged monomer dynamics in lamellar phases of diblock copolymers. Our results demonstrate that monomer relaxation times do not provide directly a quantitatively accurate measure of the spatial variations in segmental dynamics. However, a convolution of the monomer density distributions with their corresponding relaxation times is shown to provide an approximate, but accurate, quantitative characterization of the average local segmental dynamics.

Structure and mechanisms underlying ion transport in ternary polymer electrolytes containing ionic liquids.

We use all atom molecular dynamics simulations to investigate the influence of 1-butyl-3-methylimidazolium hexafluorophosphate (BMIMPF6) ionic liquid on the structure and transport properties of poly(ethylene oxide) (PEO) polymer electrolytes doped with LiPF6 salt. We observe enhanced diffusivities of the Li+, PF6-, and BMIM+ ions with increasing loading of the ionic liquid. Interplay between the different ion-ion and ion-polymer interactions is seen to lead to a destabilization of the Li-PF6 coordination and increase in the strength of association between the Li+ cations and the polymer backbone. As a consequence, the polymer segmental relaxation times are shown to be only moderately affected by the addition of ionic liquids. The ionic-liquid induced changes in the mobilities of Li+ ions are seen to be correlated to polymer segmental relaxation times. However, the mobilities of BMIM+ ions are seen to be more strongly correlated to the BMIM-PF6 ion-pair relaxation times.

Perspective: Outstanding theoretical questions in polymer-nanoparticle hybrids.

This topical review discusses the theoretical progress made in the field of polymer nanocomposites, i.e., hybrid materials created by mixing (typically inorganic) nanoparticles (NPs) with organic polymers. It primarily focuses on the outstanding issues in this field and is structured around five separate topics: (i) the synthesis of functionalized nanoparticles; (ii) their phase behavior when mixed with a homopolymer matrix and their assembly into well-defined superstructures; (iii) the role of processing on the structures realized by these hybrid materials and the role of the mobilities of the different constituents; (iv) the role of external fields (electric, magnetic) in the active assembly of the NPs; and (v) the engineering properties that result and the factors that control them. While the most is known about topic (ii), we believe that significant progress needs to be made in the other four topics before the practical promise offered by these materials can be realized. This review delineates the most pressing issues on these topics and poses specific questions that we believe need to be addressed in the immediate future.

Segmental dynamics in lamellar phases of tapered copolymers.

Recent experiments have reported that the lamellar phase of salt-doped tapered copolymers exhibit higher ionic conductivity compared to those seen in similar morphologies of diblock copolymers. Such observations were in turn rationalized by invoking the corresponding glass transition temperature of the segregated copolymers. In this work we report the results of coarse-grained molecular dynamics simulations to identify the mechanisms underlying such characteristics. Explicitly, we probe the combined influences of the degree of segregation and the disparity in mobilities of the segments of the two blocks, upon the local relaxation dynamics of tapered copolymers segregated in lamellar phases. Our results show that the local dynamics of tapered copolymers depend on two independent factors, viz., the degree of segregation of such copolymers relative to their order-disorder transition temperature, and the relative mobilities (glass transition temperatures) of the two blocks. In qualitative correspondence with experiments, we find that for appropriate combinations of mobility ratios and degree of segregation, the lamellar phases of tapered copolymers can exhibit faster local segmental dynamics compared to diblock copolymers.

Influence of nanoparticle-ion and nanoparticle-polymer interactions on ion transport and viscoelastic properties of polymer electrolytes.

We use atomistic simulations to probe the ion conductivities and mechanical properties of polyethylene oxide electrolytes containing Al2O3nanoparticles. We specifically study the influence of repulsive polymer-nanoparticle and ion-nanoparticle interactions and compare the results with those reported for electrolytes containing the polymorph ß-Al2O3nanoparticles. We observe that incorporating repulsive nanoparticle interactions generally results in increased ionic mobilities and decreased elastic moduli for the electrolyte. Our results indicate that both ion transport and mechanical properties are influenced by the polymer segmental dynamics in the interfacial zones of the nanoparticle in the ion-doped systems. Such effects were seen to be determined by an interplay between the nanoparticle-polymer,nanoparticle-ion, and ion-polymer interactions. In addition, such interactions were also observed to influence the number of dissociated ions and the resulting conductivities. Within the perspective of the influence of nanoparticles on the polymer relaxation times in ion-doped systems, our results in the context of viscoelastic properties were consistent with the ionic mobilities. Overall, our results serve to highlight some issues that confront the efforts to use nanoparticle dispersions to simultaneously enhance the conductivity and the mechanical strength of polymer electrolyte.