Influence of Cation Type on Ionic Aggregates in Precise Ionomers

Binding of Li+ to Negatively Charged and Neutral Ligands in Polymer Electrolytes

Conceptually, single-ion polymer electrolytes (SIPE) with the anion bound to the polymer could solve major issues in Li-ion batteries, but their conductivity is too low. Experimentally, weakly interacting anionic groups have the best conductivity. To provide a theoretical basis for this result, density functional theory calculations of the optimized geometries and energies are performed for charged ligands used in SIPE. Comparison is made to neutral ligands found in dual-ion conductors, which demonstrate higher conductivity. The free energy differences between adding and subtracting a ligand are small enough for the neutral ligands to have the conductivity seen experimentally. However, charged ligands have large barriers, implying that lithium transport will coincide with the slow polymer diffusion, as observed in experiments. Overall, SIPE will require additional solvent to achieve a sufficiently high conductivity. Additionally, the binding of mono- and bidentate geometries varies, providing a simple and clear reason that polarizable force fields are required for detailed interactions.

Binding of carboxylate and water to monovalent cations

The interactions of carboxylate anions with water and cations are important for a wide variety of systems, both biological and synthetic. To gain insight on properties of the local complexes, we apply density functional theory, to treat the complex electrostatic interactions, and investigate mixtures with varied numbers of carboxylate anions (acetate) and waters binding to monovalent cations, Li+, Na+ and K+. The optimal structure with overall lowest free energy contains two acetates and two waters such that the cation is four-fold coordinated, similar to structures found earlier for pure water or pure carboxylate ligands. More generally, the complexes with two acetates have the lowest free energy. In transitioning from the overall optimal state, exchanging an acetate for water has a lower free energy barrier than exchanging water for an acetate. In most cases, the carboxylates are monodentate and in the first solvation shell. As water is added to the system, hydrogen bonding between waters and carboxylate O atoms further stabilizes monodentate structures. These structures, which have strong electrostatic interactions that involve hydrogen bonds of varying strength, are significantly polarized, with ChelpG partial charges that vary substantially as the bonding geometry varies. Overall, these results emphasize the increasing importance of water as a component of binding sites as the number of ligands increases, thus affecting the preferential solvation of specific metal ions and clarifying Hofmeister effects. Finally, structural analysis correlated with free energy analysis supports the idea that binding to more than the preferred number of carboxylates under architectural constraints are a key to ion transport.

Accurate Calculation of Solvation Properties of Lithium Ions in Nonaqueous Solutions

We perform all-atom molecular dynamics simulations of lithium triflate in 1,2-dimethoxyethane using six different literature force fields. This system is representative of many experimental studies of lithium salts in solvents and polymers. We show that multiple historically common force fields for lithium ions give qualitatively incorrect results when compared with those from experiments and quantum chemistry calculations. We illustrate the importance of correctly selecting force field parameters and give recommendations on the force field choice for lithium electrolyte applications.

Ion Solvation Cage Structure in Polymer Electrolytes Determined by Combining X-ray Scattering and Simulations

Solvation structure plays a crucial role in determining ion transport in electrolytes. We combine wide-angle X-ray scattering (WAXS) and molecular dynamics (MD) simulation to identify the solvation cage structure in two polymer electrolytes, poly(pentyl malonate) (PPM) and poly(ethylene oxide) (PEO) mixed with lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt. As the salt concentration increases, the amorphous halo in the pure polymers is augmented by an additional peak at low scattering angles. The location of this peak and its height are, however, different in the two electrolytes. By decoupling the total intensity into species contributions and mapping scattering peaks to position-space molecular correlations, we elucidate distinct origins of the additional peak. In PPM, it arises from long-range charge-ordering between solvation cages and anions, while in PEO it is dominated by correlations between anions surrounding the same cage. TFSI- ions are present in the PPM solvation cage, but expelled from the PEO solvation cage.

Decoupling Ion Transport and Matrix Dynamics to Make High Performance Solid Polymer Electrolytes

Transport of ions through solid polymeric electrolytes (SPEs) involves a complicated interplay of ion solvation, ion-ion interactions, ion-polymer interactions, and free volume. Nonetheless, prevailing viewpoints on the subject promote a significantly simplified picture, likening ion transport in a polymer to that in an unstructured fluid at low solute concentrations. Although this idealized liquid transport model has been successful in guiding the design of homogeneous electrolytes, structured electrolytes provide a promising alternate route to achieve high ionic conductivity and selectivity. In this perspective, we begin by describing the physical origins of the idealized liquid transport mechanism and then proceed to examine known cases of decoupling between the matrix dynamics and ionic transport in SPEs. Specifically we discuss conditions for "decoupled" mobility that include a highly polar electrolyte environment, a percolated path of free volume elements (either through structured or unstructured channels), high ion concentrations, and labile ion-electrolyte interactions. Finally, we proceed to reflect on the potential of these mechanisms to promote multivalent ion conductivity and the need for research into the interfacial properties of solid polymer electrolytes as well as their performance at elevated potentials.

Carboxylate binding prefers two cations to one

Almost all studies of specific ion binding by carboxylates (-COO^-) have considered only a single cation, but clustering of ions and ligands is a common phenomenon. We apply density functional theory to investigate how variations in the number of acetate ligands in binding to two monovalent cations affects ion binding preferences. We study a series of monovalent (Li⁺, Na⁺, K⁺, Cs⁺) ions relevant to experimental work on many topics, including ion channels, battery storage, water purification and solar cells. We find that the preferred optimal structure has 3 acetates except for Cs⁺, which has 2 acetates. The optimal coordination of the cation by the carboxylate O atoms is 4 for both Na⁺ and K⁺, and 3 for Li⁺ and Cs⁺. There is a 4-fold coordination minimum just a few kcal mol^-1 higher than the optimal 3-fold structure for Li⁺. For two cations, multiple minima occur in the vicinity of the lowest free energy state. We find that, for Li, Na and K, the preferred optimal structure with two cations is favored over a mixture of single cation complexes, providing a basis for understanding ionic cluster formation that is relevant for engineering proteins and other materials for rapid, selective ion transport.

Structure and Diffusion of Ionic PDMS Melts

Ionic polymers exhibit mechanical properties that can be widely tuned upon selectively charging them. However, the correlated structural and dynamical properties underlying the microscopic mechanism remain largely unexplored. Here, we investigate, for the first time, the structure and diffusion of randomly and end-functionalized ionic poly(dimethylsiloxane) (PDMS) melts with negatively charged bromide counterions, by means of atomistic molecular dynamics using a united atom model. In particular, we find that the density of the ionic PDMS melts exceeds the one of their neutral counterpart and increases as the charge density increases. The counterions are condensed to the cationic part of end-functionalized cationic PDMS chains, especially for the higher molecular weights, leading to a slow diffusion inside the melt; the counterions are also correlated more strongly to each other for the end-functionalized PDMS. Temperature has a weak effect on the counterion structure and leads to an Arrhenius type of behavior for the counterion diffusion coefficient. In addition, the charge density of PDMS chains enhances the diffusion of counterions especially at higher temperatures, but hinders PDMS chain dynamics. Neutral PDMS chains are shown to exhibit faster dynamics (diffusion) than ionic PDMS chains. These findings contribute to the theoretical description of the correlations between structure and dynamical properties of ion-containing polymers.

Polycation radius of gyration in a polymeric ionic liquid (PIL): the PIL melt is not a theta solvent

The conformation of the polycation in the prototypical polymeric ionic liquid (PIL) poly(3-methyl-1-aminopropylimidazolylacrylamide) bis(trifluoromethylsulfonyl)imide (poly(3MAPIm)TFSI) was probed using small-angle neutron scattering (SANS) and ultra-small-angle neutron scattering (USANS) at 25 °C and 80 °C. Poly(3MAPIm)TFSI contains microvoids which lead to intense low q scattering that can be mitigated using mixtures of hydrogen- and deuterium-rich materials, allowing determination of the polycation conformation and radius of gyration (R_g). In the pure PIL, the polycation adopts a random coil conformation with R_g = 52 ± 0.5 Å. In contrast to conventional polymer melts, the pure PIL is not a theta solvent for the polycation. The TFSI^- anions, which comprise 48% v/v of the PIL, are strongly attracted to the polycation and act like small solvent molecules which leads to chain swelling analogous to an entangled, semi-dilute, or concentrated polymer solution in a good solvent.

Theory of ionic conductivity with morphological control in polymers

We present a general theory of ionic conductivity in polymeric materials consisting of percolated ionic pathways. Identifying two key length scales corresponding to inter-path permeation distance ξ and one-dimensional hopping conduction path length mλ, we have derived closed-form formulas in terms of the energy U required to unbind a conductive ion from its bound state and the partition ratio ξ/mλ between the three-dimensional permeation and one-dimensional hopping pathways. The results provide design strategies to significantly enhance ionic conductivity in single-ion conductors. For large barriers to dissociate an ion, corrections to the Arrhenius law are presented. The predicted dependence of ionic conductivity on the unbinding time is in agreement with results in the literature based on simulations and experiments. This theory is generally applicable to conductive systems where the two mechanisms of permeation and hopping occur concurrently.

Ion Pairing and the Structure of Gel Coacervates

A scaling model for the structure of coacervates is presented for mixtures of oppositely-charged polyelectrolytes of both symmetric and asymmetric charge-densities for different degrees of electrostatic strength and levels of added salt. At low electrostatic strengths, weak coacervates, with the energy of electrostatic interactions between charges less than the thermal energy, k B T, are liquid. At higher electrostatic strengths, strong coacervates are gels with crosslinks formed by ion pairs of opposite charges bound to each other with energy higher than k B T. Charge-symmetric coacervates are formed for mixtures of oppositely-charged polyelectrolytes with equal and opposite charge-densities. While charge-symmetric weak coacervates form a semidilute polymer solution with a correlation length equal to the electrostatic blob size, charge-symmetric strong coacervates form reversible gels with a correlation length on the order of the distance between bound ion pairs. Charge-asymmetric coacervates are formed from mixtures of oppositely-charged polyelectrolytes with different charge-densities. While charge-asymmetric weak coacervates form double solutions with two correlation lengths and qualitatively different chain conformations of polycations and polyanions, charge-asymmetric strong coacervates form bottlebrush and star-like gels. Unlike liquid coacervates, for which an increase in the concentration of added salt screens electrostatic interactions, causing structural rearrangement and eventually leads to their dissolution, the salt does not affect the structure of strong coacervates until ion pairs dissociate and the gel disperses.

Inside the Ionic Aggregates Constrained by Covalently Attached Polymer Chain Segments: Order or Disorder?

When a small-molecule ionic crystal is group-substituted with polymer chain-segments to form an ionomer, do its constrained ionic aggregates maintain ordered internal structures? This work presents, for a Na-salt sulfonated-polystyrene ionomer, reconciled TEM electron-diffraction schlieren textures and WAXS Bragg-type reflections from the ionic-aggregate nanodomains, which solidly prove the aggregates' internal (mono)crystalline order. The observed DSC endotherm of the ionomer, identified by WAXS as an order-disorder transition interior to its aggregates, gradually becomes enhanced over a 3-month, room-temperature physical aging process, indicating that the aggregates' ordering is a slow relaxation process in which the degree of order increases with time. This work corroborates an uncommon form of order, i.e., polymer-bound small-molecule ionic (quasi)crystal, which is supplementary to the order phenomena in small molecules, polymers, and liquid crystals.

The evolution of acidic and ionic aggregates in ionomers during microsecond simulations

We performed microsecond-long, atomistic molecular dynamics simulations on a series of precise poly(ethylene-co-acrylic acid) ionomers neutralized with lithium, with three different spacer lengths between acid groups on the ionomers and at two temperatures. Ionic aggregates form in these systems with a variety of shapes ranging from isolated aggregates to percolated aggregates. At the lower temperature of 423 K, the ionic aggregate morphologies do not reach a steady-state distribution over the course of the simulations. At the higher temperature of 600 K, the aggregates are sufficiently mobile that they rearrange and reach steady state after hundreds of nanoseconds. For systems that are 100% neutralized with lithium, the ions form percolated aggregates that span the simulation box in three directions, for all three spacer lengths (9, 15, and 21). In the partially neutralized systems, the morphology includes lithium ion aggregates that may also include some unneutralized acid groups, along with a coexisting population of acid group aggregates that form through hydrogen bonding. In the lithium ion aggregates, unneutralized acid groups tend to be found on the ends or sides of the aggregates.

Self-assembled highly ordered acid layers in precisely sulfonated polyethylene produce efficient proton transport

Recent advances in polymer synthesis have allowed remarkable control over chain microstructure and conformation. Capitalizing on such developments, here we create well-controlled chain folding in sulfonated polyethylene, leading to highly uniform hydrated acid layers of subnanometre thickness with high proton conductivity. The linear polyethylene contains sulfonic acid groups pendant to precisely every twenty-first carbon atom that induce tight chain folds to form the hydrated layers, while the methylene segments crystallize. The proton conductivity is on par with Nafion 117, the benchmark for fuel cell membranes. We demonstrate that well-controlled hairpin chain folding can be utilized for proton conductivity within a crystalline polymer structure, and we project that this structure could be adapted for ion transport. This layered polyethylene-based structure is an innovative and versatile design paradigm for functional polymer membranes, opening doors to efficient and selective transport of other ions and small molecules on appropriate selection of functional groups.

Influence of a nanoparticle on the structure and dynamics of model ionomer melts

We simulate a single spherical nanoparticle (NP) surrounded by partially neutralized ionomers. The coarse-grained ionomers consist of a linear backbone of neutral monomer beads with charged pendant beads and counterions, along with pendant 'sticker' beads that represent unneutralized acid groups. Two different NP interactions are considered; one in which the NP interacts uniformly with all beads in the system (neutral NP) and another in which the NP has higher cohesive interactions with ions and stickers (sticky NP). Ions are depleted around the neutral NP relative to the bulk, but are denser around the surface of the sticky NP. The bond vector autocorrelation function was computed as a function of distance from the NP. For the neutral NP, due to the absence of ions, there is an increase in bond rotational dynamics near the surface relative to the bulk, while the reverse trend is observed in the case of the sticky NP. These analyses were done systematically for differing mole content of pendants, levels of neutralization, and NP sizes; lower pendant content causes a significantly larger difference in the bond dynamics near and far from the NP surface.

High Morphological Order in a Nearly Precise Acid-Containing Polymer and Ionomer

Linear polyethylenes with functional groups at precise intervals along the backbone possess a number of remarkable properties, but the current synthetic methods that produce these precise polymers are difficult to scale up beyond the laboratory setting. When evaluating alternative synthetic routes, a critical question is how precise must the polymer microstructure be to achieve the properties of interest? As a first step in answering this question, we present morphological characterization of a nearly precise polymer-that is, an acid-containing polymer wherein the acid groups are separated by either n or n + 1 methylene groups. We find that the size scale and uniformity of the amorphous morphologies of the nearly precise acid-containing polymer and its sodium-neutralized ionomer are essentially indistinguishable from the precise polymers based on X-ray scattering. Meanwhile, the nearly precise polymer is strikingly distinct from a pseudorandom copolymer with similar average composition. This result suggests that the properties of nearly precise polymers could likewise be quite similar to truly precise polymers and beckons future work to explore their properties.

Nanoscale Aggregation in Acid- and Ion-Containing Polymers

In this review we summarize recent efforts in understanding nano-aggregation in acid- and ion-containing polymer systems. The acid and ionic groups have specific interactions that drive aggregation and alter polymer behavior at the nano-, micro-, and bulk length scales. Advancements in synthetic methods, characterization techniques, and computer simulations have enabled researchers to better understand the morphologies and dynamics, particularly at the nanoscale. This overview of recent advancements in nano-aggregated polymer systems highlights the current understanding of the field and presents promising directions for future investigations and new applications.

Depletion attraction of sheet-like ion aggregates in low-dielectric ionomer melts

Ionomers are polymers in which an ionic group is covalently bonded to the polymer backbone. Ion aggregates in ionomers have morphologies that allow for the packing of the attached polymer backbone. Using ion-only coarse-grained molecular dynamics, we observe that string-like ion aggregates become flat and sheet-like at lower dielectric constants. A consequence of the changing morphology is that the sheet-like aggregates self-assemble to form ordered, lamellar structures. We use a simple thermodynamic model to demonstrate that depletion attraction mediated by small aggregates can explain the observed order. Our results suggest that depletion attraction can drive ions to form structures that have the size scale suggested by direct visualization, produce the commonly observed experimental correlation peak from X-ray and neutron scattering, and satisfy chain-packing constraints that have been demonstrated to be important in simulations.

Ion-Specific Effects in Carboxylate Binding Sites

Specific ion binding by carboxylates (-COO^-) is a broadly important topic because -COO^- is one of the most common functional groups coordinated to metal ions in metalloproteins and synthetic polymers. We apply quantum chemical methods and the quasi-chemical free-energy theory to investigate how variations in the number of -COO^- ligands in a binding site determine ion-binding preferences. We study a series of monovalent (Li⁺, Na⁺, K⁺, Cs⁺) and divalent (Zn²⁺, Ca²⁺) ions relevant to experimental work on ion channels and ionomers. Of two competing hypotheses, our results support the ligand field strength hypothesis and follow the reverse Hofmeister series for ion solvation and ion transfer from aqueous solution to binding sites with the preferred number of ligands. New insight arises from the finding that ion-binding sequences can be manipulated and even reversed just by constraining the number of carboxylate ligands in the binding sites. Our results help clarify the discrepancy in ion association between molecular ligands in aqueous solutions and ionomers, and their chemical analogues in ion-channel binding sites.

Role of Tethered Ion Placement on Polymerized Ionic Liquid Structure and Conductivity: Pendant versus Backbone Charge Placement

The role of ion placement was systematically investigated in imidazolium bis(trifluoromethane)sulfonimide (ImTFSI) polymerized ionic liquids (PILs) containing pendant charges and charges in the backbone (sometimes called ionenes). The backbone PILs were synthesized via a facile step growth route, and pendant PILs were synthesized via RAFT. Both PILs were designed to have nearly identical charge density, and the conductivity was found to be substantially enhanced in the backbone PIL systems even after accounting for differences in the glass transition temperature (T_g). Wide-angle X-ray scattering (WAXS) revealed an invariance in the location of the amorphous halo between the two systems, while the anion-anion correlation peak was shifted to lower scattering wavevector (q) in the backbone PILs. This indicates an increase in the correlation length of ions and is consistent with charge transport along a more correlated pathway following the polymer backbone. Due to the linear nature of the backbone PILs, crystallization was observed and correlated with changes in conductivity. Upon crystallization, the conductivity dropped, and eventually, two populations of mobile ions were observed and attributed to ions in the amorphous and near-crystallite regions. The present work demonstrates the important role of ion placement on local structure and conductivity as well as the ability of backbone PILs to be used as controllable optical or dielectric materials based on crystallization or processing history.

Cluster Morphology-Polymer Dynamics Correlations in Sulfonated Polystyrene Melts: Computational Study

Reaching exceptionally long times up to 500 ns in equilibrium and nonequilibrium molecular dynamics simulations studies, we have attained a fundamental molecular understanding of the correlation of ionomer clusters structure and multiscale dynamics, providing new insight into one critical, long-standing challenge in ionic polymer physics. The cluster structure in melts of sulfonated polystyrene with Na^{+} and Mg^{2+} counterions are resolved and correlated with the dynamics on multiple length and time scales extracted from measurements of the dynamic structure factor and shear rheology. We find that as the morphology of the ionic clusters changes from ladderlike for Na^{+} to disordered structures for Mg^{2+}, the dynamic structure factor is affected on the length scale corresponding to the ionic clusters. Rheology studies show that the viscosity for Mg^{2+} melts is higher than for Na^{+} ones for all shear rates, which is well correlated with the larger ionic clusters' size for the Mg^{2+} melts.

Molecular relaxation and dynamic rheology of “cluster phase”-free ionomers based on lanthanum(iii)-neutralized low-carboxylated poly(methyl methacrylate)

La(iii)-neutralized low-carboxylated poly(methyl methacrylate)-based ionomers free of cluster phase exhibit a fluid-to-solid transition assigned to an interconnected multiplets network.

Ionomer-like structure in mature oil paint binding media

We use ATR-FTIR and SAXS to demonstrate that oil paint binding media go through an ionomer-like state during ageing.