Dynamics of Model Ionomer Melts of Various Architectures

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.

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.

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.

Structures of cationic and anionic polyelectrolytes in aqueous solutions: the sign effect

In this study, we use molecular dynamics simulation to explore the structures of anionic and cationic polyelectrolytes in aqueous solutions. We first confirm the significantly stronger solvation effects of single anions compared to cations in water at the fixed ion radii, due to the reversal orientations of asymmetric dipolar H₂O molecules around the ions. Based on this, we demonstrate that the solvation discrepancy of cations/anions and electrostatic correlations of ionic species can synergistically cause the nontrivial structural difference between single anionic and cationic polyelectrolytes. The cationic polyelectrolyte shows an extended structure whereas the anionic polyelectrolyte exhibits a collapsed structure, and their structural differences decline with increasing the counterion size. Furthermore, we corroborate that multiple cationic polyelectrolytes or multiple anionic polyelectrolytes can exhibit largely differential molecular architectures in aqueous solutions. In the solvation dominant regime, the polyelectrolyte solutions exhibit uniform structures; whereas, in the electrostatic correlation dominant regime, the polyelectrolyte solutions exhibit heterogeneous structures, in which the likely charged chains microscopically aggregate through counterion condensations. Increasing the intrinsic chain rigidity causes polyelectrolyte extension and hence moderately weakens the inter-chain clustering. Our work highlights the various, unique structures and molecular architectures of polyelectrolytes in solutions caused by the multi-body correlations between polyelectrolytes, counterions and asymmetric dipolar solvent molecules, which provides insights into the fundamental understanding of ion-containing polymers.

Glass transition of ion-containing polymer melts in bulk and thin films

Ion-containing polymers often are good glass formers, and the glass transition temperature is an important parameter to consider for practical applications, which prescribes the working temperature range for different mechanical and dynamic properties. In this work, we present a systematic molecular dynamics simulation study on the coupling of ionic correlations with the glass transition, based on a generic coarse-grained model of ionic polymers. The variation of the glass transition temperature is examined concerning the influence of the electrostatic interaction strength, charge fraction, and charge sequence. The interplay with the film thickness effect is also discussed. Our results reveal a few typical features about the glass transition process that are in qualitative agreement with previous studies, further highlighting the effects of counterion entropy at weak ionic correlations and physical crosslinking of ionic aggregates at strong ionic correlations. Detailed parametric dependencies are displayed, which demonstrate that introducing strong ionic correlations promotes vitrification while adopting a precise charge sequence and applying strong confinement with weak surface affinity reduce the glass transition temperature. Overall, our investigation provides an improved picture towards a comprehensive understanding of the glass transition in ion-containing polymeric systems from a molecular simulation perspective.

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.

A Perspective on the Design of Ion-Containing Polymers for Polymer Electrolyte Applications

Ion-containing polymers have numerous potential applications as energy storage and conversion devices, water purification membranes, and gas separation membranes, to name a few. Given the low dielectric constant of the media, ions and charges on polymers in a molten state interact strongly producing large effects on chain statistics, thermodynamics, and diffusion properties. Here, we discuss recent research accomplishments on the effects of ionic correlation and dielectric heterogeneity on the phase behavior of ion-containing polymers. Progress made in studying ion transport properties in these material systems is also highlighted. Charged block copolymers (BCPs), among all kinds of ion-containing polymers, have a particular advantage owing to their robust mechanical support and ion conducting paths provided by the segregation of the neutral and charged blocks. Coulombic interactions among the charges play a critical role in determining the phase segregation in charged BCPs and the domain size of charge-rich regions. We show that strongly charged BCPs display ordered phases as a result of electrostatic interactions alone. In addition, bulky charge-containing side groups attached to the charged block lead to the formation of morphologies that provide continuous channels and better dissociation for ion conduction purposes. Finally, a few avenues for designing ion-containing polymers for energy applications are discussed.

Effects of interaction strength of associating groups on linear and star polymer dynamics

A small number of associating groups incorporated onto a polymer backbone have dramatic effects on the mobility and viscoelastic response of the macromolecules in melts. These associating groups assemble, driving the formation of clusters, whose lifetime affects the properties of the polymers. Here, we probe the effects of the interaction strength on the structure and dynamics of two topologies, linear and star polymer melts, and further investigate blends of associative and non-associating polymers using molecular dynamics simulations. Polymer chains of approximately one entanglement length are described by a bead-spring model, and the associating groups are incorporated in the form of interacting beads with an interaction strength between them that is varied from 1 to 20 k_BT. We find that, for all melts and blends, interaction of a few k_BT between the associating groups drives cluster formation, where the size of the clusters increases with increasing interaction strength. These clusters act as physical crosslinkers, which slow the chain mobility. Blends of chains with and without associating groups macroscopically phase separate for interaction strength between the associating groups of a few k_BT and above. For weakly interacting associating groups, the static structure function S(q) is well fit by functional form predicted by the random phase approximation where a clear deviation occurs as phase segregation takes place, providing a quantitative assessment of phase segregation.

Ion transport in small-molecule and polymer electrolytes

Solid-state polymer electrolytes and high-concentration liquid electrolytes, such as water-in-salt electrolytes and ionic liquids, are emerging materials to replace the flammable organic electrolytes widely used in industrial lithium-ion batteries. Extensive efforts have been made to understand the ion transport mechanisms and optimize the ion transport properties. This perspective reviews the current understanding of the ion transport and polymer dynamics in liquid and polymer electrolytes, comparing the similarities and differences in the two types of electrolytes. Combining recent experimental and theoretical findings, we attempt to connect and explain ion transport mechanisms in different types of small-molecule and polymer electrolytes from a theoretical perspective, linking the macroscopic transport coefficients to the microscopic, molecular properties such as the solvation environment of the ions, salt concentration, solvent/polymer molecular weight, ion pairing, and correlated ion motion. We emphasize universal features in the ion transport and polymer dynamics by highlighting the relevant time and length scales. Several outstanding questions and anticipated developments for electrolyte design are discussed, including the negative transference number, control of ion transport through precision synthesis, and development of predictive multiscale modeling approaches.

Quantifying Single-Ion Transport in Percolated Ionic Aggregates of Polymer Melts

Single-ion conducting polymers such as ionomers are promising battery electrolyte materials, but it is critical to understand how rates and mechanisms of free cation transport depend on the nanoscale aggregation of cations and polymer-bound anions. We perform coarse-grained molecular dynamics simulations of ionomer melts to understand cation mobility as a function of polymer architecture, background relative permittivity, and corresponding ionic aggregate morphology. In systems exhibiting percolated ionic aggregates, cations diffuse via stepping motions along the ionic aggregates. These diffusivities can be quantitatively predicted by calculating the lifetimes of continuous association between oppositely charged ions, which equal the time scales of the stepping (diffusive) motions. In contrast, predicting cation diffusivity for systems with isolated ionic aggregates requires another time scale. Our results suggest that to improve conductivity the Coulombic interaction strength should be strong enough to favor percolated aggregates but weak enough to facilitate ion dissociation.

100th Anniversary of Macromolecular Science Viewpoint: Opportunities in the Physics of Sequence-Defined Polymers

Polymer science has been driven by ever-increasing molecular complexity, as polymer synthesis expands an already-vast palette of chemical and architectural parameter space. Copolymers represent a key example, where simple homopolymers have given rise to random, alternating, gradient, and block copolymers. Polymer physics has provided the insight needed to explore this monomer sequence parameter space. The future of polymer science, however, must contend with further increases in monomer precision, as this class of macromolecules moves ever closer to the sequence-monodisperse polymers that are the workhorses of biology. The advent of sequence-defined polymers gives rise to opportunities for material design, with increasing levels of chemical information being incorporated into long-chain molecules; however, this also raises questions that polymer physics must address. What properties uniquely emerge from sequence-definition? Is this circumstance-dependent? How do we define and think about sequence dispersity? How do we think about a hierarchy of sequence effects? Are more sophisticated characterization methods, as well as theoretical and computational tools, needed to understand this class of macromolecules? The answers to these questions touch on many difficult scientific challenges, setting the stage for a rich future for sequence-defined polymers in polymer physics.

Control of Ionic Mobility via Charge Size Asymmetry in Random Ionomers

Solid polymer electrolytes are considered a promising alternative to traditional liquid electrolytes in energy storage applications because of their good mechanical properties, and excellent thermal and chemical stability. A gap, however, still exists in understanding ion transport mechanisms and improving ion transport in solid polymer electrolytes. Therefore, it is crucial to bridge composition-structure and structure-property relationships. Here, we demonstrate that size asymmetry, λ, represented by the ratio of counterion to charged monomer size, plays a key role both in the nanostructure and in the ionic dynamics. More specifically, when the nanostructure is modified by an external electric field such that the mobility cannot be described by linear response theory, two situations arise. The ionic mobility increases as λ decreases (small counterions) in the weak electrostatics (high dielectric constant) regime, whereas in systems with strong electrostatic interactions, ionomers with higher size symmetry (λ ≈ 1) display higher ionic mobility. Moreover, ion transport is found to be dominated by the hopping of the ions and not by moving ionic clusters (also known as "vehicular" charge transport). These results serve as a guide for designing ion-containing polymers for ion transport related applications.

Non-solvating, side-chain polymer electrolytes as lithium single-ion conductors: synthesis and ion transport characterization

Non-solvating, side-chain polymer electrolytes with more dissociable pendent anion chemistries exhibit a dielectric relaxation dominated lithium ion transport mechanism.

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.

Boosting Rechargeable Batteries R&D by Multiscale Modeling: Myth or Reality?

This review addresses concepts, approaches, tools, and outcomes of multiscale modeling used to design and optimize the current and next generation rechargeable battery cells. Different kinds of multiscale models are discussed and demystified with a particular emphasis on methodological aspects. The outcome is compared both to results of other modeling strategies as well as to the vast pool of experimental data available. Finally, the main challenges remaining and future developments are discussed.

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.

Covalently Crosslinked 1,2,3-Triazolium-Containing Polyester Networks: Thermal, Mechanical, and Conductive Properties

Azide-alkyne "click" cyclization was used to prepare a series of polymerizable acetoacetate monomers containing a 1,2,3-trizolium ionic liquid group. The monomers were subsequently polymerized using base-catalyzed Michael addition chemistry, producing a series of covalently crosslinked 1,2,3-triazolium poly(ionic liquid) (TPIL) networks. Structure-activity relationships were conducted to gauge how synthetic variables, such as counteranion ([Br], [NO3], [BF4], [OTf], and [NTf2]), and crosslink density (acrylate/acetoacetate ratio) effected thermal, mechanical, and conductive properties. TPIL networks were found to exhibit ionic conductivities in the range of 10-6-10-9 S/cm (30 °C, 30% relative humidity), as determined from dielectric relaxation spectroscopy, despite their highly crosslinked nature. Temperature-dependent conductivities demonstrate a dependence on polymer glass transition, with free-ion concentrations impacted by various ions' Lewis acidity/basicity and ion mobilities impacted by freely mobile anion size.

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.

Ionic Correlations in Random Ionomers

Understanding the electrostatic interactions in ion-containing polymers is crucial to better design shape memory polymers and ion-conducting membranes for multiple energy storage and conversion applications. In molten polymers, the dielectric permittivity is low, generating strong ionic correlations that lead to clustering of the charges. Here, we investigate the influence of electrostatic interactions on the nanostructure of randomly charged polymers (ionomers) using coarse-grained molecular dynamics simulations. Densely packed branched structures rich in charged species are found as the strength of the electrostatic interactions increases. Polydispersity in charge fraction and composition combined with ion correlations leads to percolated nanostructures with long-range fluctuations. We identify the percolation point at which the ionic branched nanostructures percolate and offer a rigorous investigation of the statistics of the shape of the aggregates. The extra degree of freedom introduced by the charge polydispersity leads to bicontinuous structures with a broad range of compositions, similar to neutral A-B random copolymers, as well as to desirable percolated ionic structure in randomly charged-neutral diblock copolymers. These findings provide insight into the design of conducting and robust nanostructures in ion-containing polymers.

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.