Effect of polymer architecture and ionic aggregation on the scattering peak in model ionomers

Bead-Spring Simulation of Ionomer Melts-Studying the Effects of Chain-Length and Associating Group Fraction on Equilibrium Structure and Extensional Flow Behavior

Ionomers are associative polymers with diverse applications ranging from selective membranes and high-performance adhesives to abrasion- and chemical-resistant coatings, insulation layers, vacuum packaging, and foamed sheets. Within equilibrium melt, the ionic or associating groups are known to form thermally reversible, associative clusters whose presence can significantly affect the system's mechanical, viscoelastic, and transport properties. It is, thus, of great interest to understand how to control such clusters' size distribution, shape, and stability through the designed choice of polymer architecture and the ionic groups' fraction, arrangement, and interaction strength. In this work, we represent linear associating polymers using a Kremer-Grest type bead-spring model and perform large-scale MD simulations to explore the effect of polymer chain-length (l) and fraction (fs) of randomly placed associating groups on the size distribution and stability of formed clusters. We consider different chain-lengths (below and above entanglement), varying fractions of associating groups (represented by 'sticky' beads) between 5 and 20%, and a fixed sticky-sticky nonbond interaction strength of four times that between regular non-associating beads. For all melts containing associating groups the equilibrium structure factor S(q) displays a signature ionomer peak at low wave vector q whose intensity increases with increasing fs and l. The average cluster size Nc increases with fs. However, the effect of chain-length on Nc appears to be pronounced only at higher values of fs. Under extensional flows, the computed stress (and viscosity) is higher at higher fs and l regardless of strain rate. Beyond a critical strain rate, we observe fragmentation of the associative clusters, which has interesting effects on the stress/viscous response.

Polymer Architecture-Induced Trade-off between Conductivities and Transference Numbers in Salt-Doped Polymeric Ionic Liquids

Recent experiments have demonstrated that polymeric ionic liquids that share the same cation and anion but possess different architectures can exhibit markedly different conductivity and transference number characteristics when doped with lithium salt. In this study, we used atomistic molecular simulations on polymer chemistries inspired by the experiments to probe the mechanistic origins underlying the competition between conductivity and transference numbers. Our results indicate that the architecture of the polycationic ionic liquid plays a subtle but crucial role in modulating the anion-cation interactions, especially their dynamical coordination characteristics. Chemistries leading to longer-lived anion-cation coordinations relative to lithium-anion coordinations lead to lower conductivities and higher transference numbers. Our results suggest that higher conductivities are accompanied by lower transference numbers and vice versa, revealing that alternative approaches may need to be considered to break this trade-off in salt-doped polyILs.

Probing the size-dependent polarizability of mesoscopic ionic clusters and their induced-dipole interactions

Mesoscopic clusters composed of oppositely charged particles are ubiquitous in synthetic and biological soft materials. The effective interaction between these clusters is influenced by their polarizability, that is, the ability of their constituent charges to re-arrange in response to an external electrical field. Here, using coarse-grained simulations, we show that the polarizability of electrically neutral ionic clusters decreases as the number of constituent charges increases and/or their Coulombic interaction strength increases for various ion valencies, ion densities, and degrees of cluster boundary hardness. For clusters of random ionomers and their counterions, their polarizability is shown to depend on the number of polymer chains. The variation of the cluster polarizability with the cluster size indicates that throughout the assembly, the induced-dipole interactions between the clusters may be reduced substantially as they acquire more charges while maintaining zero net charge. Under certain conditions, the induced-dipole interactions may become repulsive, as inferred from our simulations with a polarizable solvent. As a result, the dipole-induced related interactions can serve as a counterbalancing force that contributes to the self-limiting aggregation of charge-containing assemblies.

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.

Coarse-grained simulations of ionic liquid materials: from monomeric ionic liquids to ionic liquid crystals and polymeric ionic liquids

Ionic liquid (IL) materials are promising electrolytes with striking physicochemical properties for energy and environmental applications. Heterogeneous structures and transport quantities of monomeric and polymeric ILs are intrinsically intercorrelated and span multiple spatiotemporal scales, which is more feasible for coarse-grained (CG) simulations than atomistic modelling. Herein we constructed a novel CG model for ethyl-imidazolium tetrafluoroborate ILs with varied cation alkyl chains ranging from C₂ to C₂₀, and the interaction parameters were validated against representative static and dynamic properties that were obtained from atomistic reference simulations and experimental characterizations at relevant thermodynamic states. This CG model was extended to study thermotropic phase behaviors of monomeric ILs and to explore ion association structures and ion transport quantities in polymeric ILs with different architectures. A systematic analysis of structural and dynamical quantities identifies an evolution of liquid morphology from homogeneous to nanosegregated structures and then a smectic mesomorphism via a gradual lengthening of cation alkyl chains, and thereafter a distinct structural transition characterized by a monotonic decrease in orientational and translational order parameters in a sequential heating cascade. Backbone and pendant polymeric ILs exhibit evident anion association structures with cation monomers and polymer chains, and striking intra- and interchain coordinations between cation monomers owing to an intrinsic polymer architecture effect. Such a peculiar ion pairing association leads to a progressive increase in anion intrachain hopping probabilities, and a concomitant decrease in anion interchain hopping events with a gradual lengthening of polymeric ILs. The anion diffusivities in polymeric ILs are intrinsically correlated with ion pairing association lifetimes and ion structural relaxation times via a universal power law correlation D ∼ τ^-1, irrespective of polymer architectures.

Structure and dynamics of ions in dipolar solvents: a coarse-grained simulation study

We employ the coarse-grained molecular dynamics simulation to investigate the fundamental structural and dynamic properties of the ionic solution with and without the application of an external electric field. Our simulations, in which the solvent molecules are treated as Stockmayer fluids and the ions are modeled as spheres, can effectively account for the multi-body correlations between ion-ion, ion-dipole, and dipole-dipole interactions, which are often ignored by the mean-field theories or coarse-grained simulations based on a dielectric continuum. By focusing on the coupling between effects of ion solvation, electrostatic correlations and applied electric field, we highlight some nontrivial microscopic molecular features of the systems, such as the reorganization of the dipolar solvent, clustering of the ions, and diffusions of ions and dipolar solvent molecules. Particularly, our simulation indicates the nonmonotonic dependence of the ionic clustering and ion diffusion rates on the dipolar nature of the solvent molecules, as well as the amplification of these tendencies caused by the electric field application. This work provides insights into the fundamental understanding of physicochemical properties for ion-containing liquids and contributes to the design and development of ion-containing materials.

The influence of spacer composition on thermomechanical properties, crystallinity, and morphology in ionene segmented copolymers

A series of segmented ammonium ionenes with varying weight fractions of 2000 g mol-1 poly(ethylene glycol) (PEG) or poly(tetramethylene oxide) (PTMO) soft segments were synthesized, and a simplified coarse-grained model of these materials was implemented using molecular dynamics simulations. In addition to varying soft segment type (PTMO vs. PEG), charge density and soft segment content were varied to create a comprehensive series of segmented ammonium ionenes; thermogravimetric analysis reveals that all segmented ionenes in the series are thermally stable up to 240 °C. Differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) show the formation of phase separated microdomains at low soft segment content. In particular, DSC shows that the hard and soft domains have distinct glass transition temperatures. Similarly, simulations show that reduced soft segment content induces stronger microphase separation, reduces soft segment mobility, and increases ionic aggregate connectivity and size. These increased ionic associations result in elastomeric behavior, as evidenced by the higher rubbery plateau moduli observed at lower soft segment contents through DMA. Moreover, simulations show that ionic aggregation increases when switching from PEG to the less polar PTMO repeat units, which is consistent with DMA results showing higher plateau moduli for PTMO-based ionenes relative to PEG ionenes. DSC and X-ray diffraction determined that the degree of crystallinity increased with soft segment content regardless of segment type. Overall, these results suggest a semi-crystalline microphase-separated morphology strongly influenced by charge density, the degree of ionic aggregation, and the resulting level of confinement and mobility of the soft segments.

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.

Modulating Microphase Separation of Lamellae-Forming Diblock Copolymers via Ionic Junctions

We present a molecular dynamics simulation study investigating the phase behavior of lamellae-forming diblock copolymers with a single ionic junction on the backbone. Our results show qualitative agreement with experimental findings regarding enhanced microphase separation with the introduction of an ionic junction at the conjunction point, while further revealing nonmonotonic changes in domain spacing and order-disorder transition as a function of the electrostatic interaction strength. This highlights the dominant roles of entropic and binding effects of counterions under weak and strong ionic correlations, respectively. The location of the ionic junction is found to effectively modulate the charge distribution and chain conformation in the ordered domains; its presence in the middle of a block promotes folding of the block, leading to a smaller domain size. These findings demonstrate the interplay of ionic coupling with steric hindrance and chain end effects, which enhances our understanding of the delicate control over the microphase domain features.

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.

A comprehensive review of the structures and properties of ionic polymeric materials

This review focuses on the mechanistic approach, the structure–property relationship and applications of ionic polymeric materials.

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.

High aspect ratio nanotubes assembled from macrocyclic iminium salts

One-dimensional nanostructures such as carbon nanotubes and actin filaments rely on strong and directional interactions to stabilize their high aspect ratio shapes. This requirement has precluded making isolated, long, thin organic nanotubes by stacking molecular macrocycles, as their noncovalent stacking interactions are generally too weak. Here we report high aspect ratio (>10³), lyotropic nanotubes of stacked, macrocyclic, iminium salts, which are formed by protonation of the corresponding imine-linked macrocycles. Iminium ion formation establishes cohesive interactions that, in organic solvent (tetrahydrofuran), are two orders of magnitude stronger than the neutral macrocycles, as explained by physical arguments and demonstrated by molecular dynamics simulations. Nanotube formation stabilizes the iminium ions, which otherwise rapidly hydrolyze, and is reversed and restored upon addition of bases and acids. Acids generated by irradiating a photoacid generator or sonicating chlorinated solvents also induced nanotube assembly, allowing these nanostructures to be coupled to diverse stimuli, and, once assembled, they can be fixed permanently by cross-linking their pendant alkenes. As large macrocyclic chromonic liquid crystals, these iminium salts are easily accessible through a modular design and provide a means to rationally synthesize structures that mimic the morphology and rheology of carbon nanotubes and biological tubules.

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.

Morphology of Anion-Conducting Ionenes Investigated by X-ray Scattering and Simulation

We have studied the morphology of a novel series of benzimidazole-based ionenes, methylated poly(hexamethyl-p-terphenylbenzimidazolium) (HMT-PMBI), in halide form. Materials with anion-exchange capacities ranging from 0 to 2.5 mequiv/g were studied. X-ray scattering reveals three length scales in the materials: ion-polymer spacing (4 Å), polymer-polymer interchain spacing (6 Å), and an intrachain repeat distance (20 Å). No long-range structure is apparent above the monomer length, which is rare in ion-conducting polymer membranes. In preliminary molecular dynamics simulations, water molecules were observed forming chains between ions, even at a modest level of hydration, providing an interpenetrating network where conductivity can occur.

Effect of Rubber Polarity on Cluster Formation in Rubbers Cross-Linked with Diels-Alder Chemistry

Diels–Alder chemistry has been used for the thermoreversible cross-linking of furan-functionalized ethylene/propylene (EPM) and ethylene/vinyl acetate (EVM) rubbers. Both furan-functionalized elastomers were successfully cross-linked with bismaleimide to yield products with a similar cross-link density. NMR relaxometry and SAXS measurements both show that the apolar EPM-g-furan precursor contains phase-separated polar clusters and that cross-linking with polar bismaleimide occurs in these clusters. The heterogeneously cross-linked network of EPM-g-furan contrasts with the homogeneous network in the polar EVM-g-furan. The heterogeneous character of the cross-links in EPM-g-furan results in a relatively high Young’s modulus, whereas the more uniform cross-linking in EVM-g-furan results in a higher tensile strength and elongation at break.

Two regions of microphase separation in ion-containing polymer solutions

The phenomenon of spinodal decomposition in weakly charged polyelectrolyte solutions is studied theoretically within the random phase approximation. A novel feature of the theoretical approach is that it accounts for the effects of ionic association, i.e. ion pair and multiplet formation between counterions and ions in polymer chains, as well as the dependence of local dielectric permittivity on the polymer volume fraction Φ. The main focus is on the spinodal instability of polyelectrolyte solutions towards microscopic phase separation. It has been shown that increasing the binding energy of ions decreases the classical microphase separation region (possible at low polymer concentrations) due to the effective neutralization of the chains. A qualitatively new type of microphase separation is found in the presence of a dielectric mismatch between polymer and solvent. This new branch of microphase separation is realized at high polymer concentrations where ion association processes are the most pronounced. Typical microstructures are shown to have a period of a few nanometers like in ionomers. The driving force for the microphase formation of a new type is more favourable ion association in polymer-rich domains where ionomer-type behavior takes place. Effective attraction due to ion association promotes microscopic as well as macroscopic phase separation, even under good solvent conditions for uncharged monomer units of polymer chains. Polyelectrolyte-type behavior at low Φ and ionomer-type behavior at high Φ result in the presence of two critical points on the phase diagrams of polyelectrolyte solutions as well as two separate regions of possible microscopic structuring. Our predictions on the new type of microphase separation are supported by experimental data on polymer solutions, membranes and gels.

Polymerized Ionic Liquids: Correlation of Ionic Conductivity with Nanoscale Morphology and Counterion Volume

The impact of the chemical structure on ion transport, nanoscale morphology, and dynamics in polymerized imidazolium-based ionic liquids is investigated by broadband dielectric spectroscopy and X-ray scattering, complemented with atomistic molecular dynamics simulations. Anion volume is found to correlate strongly with T_g-independent ionic conductivities spanning more than 3 orders of magnitude. In addition, a systematic increase in alkyl side chain length results in about one decade decrease in T_g-independent ionic conductivity correlating with an increase in the characteristic backbone-to-backbone distances found from scattering and simulations. The quantitative comparison between ion sizes, morphology, and ionic conductivity underscores the need for polymerized ionic liquids with small counterions and short alkyl side chain length in order to obtain polymer electrolytes with higher ionic conductivity.

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.