Ion Conductivity and Correlations in Model Salt-Doped Polymers: Effects of Interaction Strength and Concentration

Dynamic density functional theory of polymers with salt in electric fields

We present a dynamic density functional theory for modeling the effects of applied electric fields on the local structure of polymers with added salt (polymer electrolytes). Time-dependent equations for the local electrostatic potential and volume fractions of polymer, cation, and anion of added salt are developed using the principles of linear irreversible thermodynamics. For such a development, a field theoretic description of the free energy of polymer melts doped with salts is used, which captures the effects of local variations in the dielectric function. Connections of the dynamic density functional theory with experiments are established by relating the three phenomenological Onsager's transport coefficients of the theory to the mutual diffusion of electrolyte, ionic conductivity, and transference number of one of the ions. The theory is connected with a statistical mechanical model developed by Bearman and Kirkwood [J. Chem. Phys. 28, 136 (1958)] after relating the three transport coefficients to friction coefficients. The steady-state limit of the dynamic density functional theory is used to understand the effects of dielectric inhomogeneity on the phase separation in polymer electrolytes. The theory developed here provides not only a way to connect with experiments but also to develop multi-scale models for studying connections between local structure and ion transport in polymer electrolytes.

Understanding Ion Distribution and Diffusion in Solid Polymer Electrolytes

Solid polymer electrolytes (SPEs)─polymer melts with added salts─exhibit ion conduction and high mechanical properties, and are thus promising materials for future energy storage devices. The ion conductivity in an SPE is intricately connected to the salt ion distribution in the polymer matrix. The relationship between ion diffusion and ion distribution in SPEs remains unresolved. Here, we conduct coarse-grained molecular dynamics simulations and establish correlations between ion distribution and transport for a phenomenological SPE model. We propose phase diagrams of SPEs as a function of ion pair size, ion concentration, and the Bjerrum length of the material. A crossover from a discrete ion aggregate to a percolated ion aggregate is demonstrated as a function of ion pair size for low ion concentration in the SPE. The ion diffusion shows a strong correlation with its size, as has been found experimentally. The work provides important design strategies for controlling the ion distribution and enhancing ion conductivity in a polymer matrix.

A transferable classical force field to describe glyme based lithium solvate ionic liquids

A non-polarizable force field for lithium (Li+) and bis(trifluoromethanesulfonyl)imide (TFSI-) ions solvated in diglyme at around 0.2 mol fraction salt concentration was developed based on ab initio molecular dynamics (AIMD) simulations and a modified polymer consistent force field model. A force-torque matching based scheme, in conjunction with a genetic algorithm, was used to determine the Lennard-Jones (LJ) parameters of the ion-ion and ion-solvent interactions. This force field includes a partial charge scaling factor and a scaling factor for the 1-4 interactions. The resulting force field successfully reproduces the radial distribution function of the AIMD simulations and shows better agreement compared to the unmodified force field. The new force field was then used to simulate salt solutions with glymes of increasing chain lengths and different salt concentrations. The comparison of the MD simulations, using the new force field, with experimental data at different salt concentrations and AIMD simulations on equimolar concentrations of the triglyme system demonstrates the transferability of the force field parameters to longer glymes and higher salt concentrations. Furthermore, the force field appears to reproduce the features of the experimental x-ray structure factors, suggesting accuracy beyond the first solvation shell, for equimolar salt solutions using both triglyme and tetraglyme as the solvent. Overall, the new force field was found to accurately reproduce the molecular descriptions of LiTFSI-glyme systems not only at various salt concentrations but also with glymes of different chain lengths. Thus, the new force field provides a useful and accurate tool to perform in silico studies of this family of systems at the atomistic level.

Ion Conductivity in Salt-Doped Polymers: Combined Effects of Temperature and Salt Concentration

We construct a coarse-grained molecular dynamics model based on poly(ethylene oxide) and lithium bis(trifluoromethane)sulfonimide salt to examine the combined effects of temperature and salt concentration on the transport properties. Salt doping notably slows the dynamics of polymer chains and reduces ion diffusivity, resulting in a glass transition temperature increase proportional to the salt concentration. The polymer diffusion is shown to be well represented by a modified Vogel-Fulcher-Tamman (M-VFT) equation that accounts for both the temperature and salt concentration dependence. Furthermore, we find that, at any temperature, the concentration dependence of the conductivity is well described by the product of its infinite dilution value and a correction factor accounting for the reduced segmental mobility with increasing salt concentration. These results highlight the important role of polymer segmental mobility in the salt concentration dependence of ion conductivity for temperatures near and above the glass transition.

Toward a molecular understanding of the conductivity of lithium-ion conducting polyanion polymer electrolytes by molecular dynamics simulation

With the improved lithium-ion transference number near unity, the low conductivity of single lithium-ion conducting solid polymer electrolytes (SLIC-SPEs) still hinders their application in high-rate batteries. Though some empirical conclusions on the conducting mechanism of SLIC-SPEs have been obtained, a more comprehensive study on the quantitative relationship between the molecular structure factors and ionic conduction performance is expected. In this study, a model structure that contains adjustable main chain and anion groups in the polyethylene oxide (PEO) matrix was used to clarify the influence of molecular structural factors on ionic conductivity and electrochemical stability of SLIC-SPEs. The anionic group was further disassembled into the intermediate group and end group while the main chain structure was distinguished into different degrees of polymerization and various lengths of the spacers between anions. Therefore, a well-defined molecular structure was employed to describe its relationship with ionic conductivity. In addition, the dissociation degree of salts and mobility of ions changing with the molecular structure were also discussed to explore the fundamental causes of conductivity. It can be concluded that the anion group affects the conductivity mainly via the dissociation degree, while the main chain structure impacts the conductivity by both dissociation degree and mobility.

Nanoscale Confinement Effects on Ionic Conductivity of Solid Polymer Electrolytes: The Interplay between Diffusion and Dissociation

Solid polymer electrolytes (SPEs) are attractive for next-generation lithium metal batteries but still suffer from low ionic conductivity. Nanostructured materials offer design concepts for SPEs with better performance. Using molecular dynamics simulation, we examine SPEs under nanoscale confinement, which has been demonstrated to accelerate the transport of neutral molecules such as water. Our results show that while ion diffusion indeed accelerates by more than 2 orders of magnitude as the channel diameter decreases from 15 to 2 nm, the ionic conductivity does not increase significantly in parallel. Instead, the ionic conductivity shows a nonmonotonic variation, with an optimal value above, but on the same order as, its bulk counterparts. This trend is due to enhanced ion association with decreasing channel size, which reduces the number of effective charge carriers. This effect competes with accelerated ion diffusion, leading to the nonmonotonicity in ion conductivity.

Charge Transport in Water-NaCl Electrolytes with Molecular Dynamics Simulations

A systematic description of microscopic mechanisms is necessary to understand mass transport in solid and liquid electrolytes. From Molecular Dynamics (MD) simulations, transport properties can be computed and provide a detailed view of the molecular and ionic motions. In this work, ionic conductivity and transport numbers in electrolyte systems are computed from equilibrium and nonequilibrium MD simulations. Results from the two methods are compared with experimental results, and we discuss the significance of the frame of reference when determining and comparing transport numbers. Two ways of computing ionic conductivity from equilibrium simulations are presented: the Nernst-Einstein approximation or the Onsager coefficients. The Onsager coefficients take ionic correlations into account and are found to be more suitable for concentrated electrolytes. Main features and differences between equilibrium and nonequilibrium simulations are discussed, and some potential anomalies and critical pitfalls of using nonequilibrium molecular dynamics to determine transport properties are highlighted.

Perspective: Morphology and ion transport in ion-containing polymers from multiscale modeling and simulations

Ion-containing polymers are soft materials composed of polymeric chains and mobile ions. Over the past several decades they have been the focus of considerable research and development for their use as the electrolyte in energy conversion and storage devices. Recent and significant results obtained from multiscale simulations and modeling for proton exchange membranes (PEMs), anion exchange membranes (AEMs), and polymerized ionic liquids (polyILs) are reviewed. The interplay of morphology and ion transport is emphasized. We discuss the influences of polymer architecture, tethered ionic groups, rigidity of the backbone, solvents, and additives on both morphology and ion transport in terms of specific interactions. Novel design strategies are highlighted including precisely controlling molecular conformations to design highly ordered morphologies; tuning the solvation structure of hydronium or hydroxide ions in hydrated ion exchange membranes; turning negative ion-ion correlations to positive correlations to improve ionic conductivity in polyILs; and balancing the strength of noncovalent interactions. The design of single-ion conductors, well-defined supramolecular architectures with enhanced one-dimensional ion transport, and the understanding of the hierarchy of the specific interactions continue as challenges but promising goals for future research.

Coarse-Grained Modeling of Ion-Containing Polymers

Ion-containing polymers have continued to be an important research focus for several decades due to their use as an electrolyte in energy storage and conversion devices. Elucidation of connections between the mesoscopic structure and multiscale dynamics of the ions and solvent remains incompletely understood. Coarse-grained modeling provides an efficient approach for exploring the structural and dynamical properties of these soft materials. The unique physicochemical properties of such polymers are of broad interest. In this review, we summarize the current development and understanding of the structure-property relationship of ion-containing polymers and provide insights into the design of such materials determined from coarse-grained modeling and simulations accompanying significant advances in experimental strategies. We specifically concentrate on three types of ion-containing polymers: proton exchange membranes (PEMs), anion exchange membranes (AEMs), and polymerized ionic liquids (polyILs). We posit that insight into the similarities and differences in these materials will lead to guidance in the rational design of high-performance novel materials with improved properties for various power source technologies.

Effects of off-axis translocation through nanopores on the determination of shape and volume estimates for individual particles

Resistive pulses generated by nanoparticles that translocate through a nanopore contain multi-parametric information about the physical properties of those particles. For example, non-spherical particles sample several different orientations during translocation, producing fluctuations in blockade current that relate to their shape. Due to the heterogenous distribution of electric field from the center to the wall of a nanopore while a particle travels through the pore, its radial position influences the blockade current, thereby affecting the quantification of parameters related to the particle's characteristics. Here, we investigate the influence of these off-axis effects on parameters estimated by performing finite element simulations of dielectric particles transiting a cylindrical nanopore. We varied the size, ellipsoidal shape, and radial position of individual particles, as well as the size of the nanopore. As expected, nanoparticles translocating near the nanopore wall produce increase current blockades, resulting in overestimates of particle volume. We demonstrated that off-axis effects also influence estimates of shape determined from resistive pulse analyses, sometimes producing a multiple-fold deviation in ellipsoidal length-to-diameter ratio between estimates and reference values. By using a nanopore with the minimum possible diameter that still allows the particle to rotate while translocating, off-axis effects on the determination of both volume and shape can be minimized. In addition, tethering the nanoparticles to a fluid coating on the nanopore wall makes it possible to determine an accurate particle shape with an overestimated volume. This work provides a framework to select optimal ratios of nanopore to nanoparticle size for experiments targeting free translocations.

The effect of explicit counterion binding on the transference number of polyelectrolyte solutions

Polyelectrolyte solutions have been proposed as a method to improve the efficiency of lithium-ion batteries by increasing the cation transference number because the polymer self-diffusion coefficient is much lower than that of the counterion. However, this is not necessarily true for the polymer mobility. In some cases, negative transference numbers have been reported, which implies that the lithium ions are transporting to the same electrode as the anion, behavior that is often attributed to a binding of counterions to the polyion. We use a simple model where we bind some counterions to the polymer via harmonic springs to investigate this phenomenon. We find that both the number of bound counterions and the strength of their binding alter the transference number, and, in some cases, the transference number is negative. We also investigate how the transference number depends on the Manning parameter, the ratio of the Bjerrum length to charge separation along the chain. By altering the Manning parameter, the transference number can almost be doubled, which suggests that charge spacing could be a way to increase the transference number of polyelectrolyte solutions.

Association-Dissociation Dynamics of Ionic Electrolytes in Low Dielectric Medium

Ionic electrolytes are known to form various complexes which exist in dynamic equilibrium in a low dielectric medium. However, structural characterization of these complexes has always posed a great challenge to the scientific community. An additional challenge is the estimation of the dynamic association-dissociation time scales (lifetime of the complexes), which are key to the fundamental understanding of ion transport. In this work, we have used a combination of infrared absorption spectroscopy, two-dimensional infrared spectroscopy, molecular dynamics simulations, and density functional theory calculations to characterize the various ion complexes formed by the thiocyanate-based ionic electrolytes as a function of different cations in a low dielectric medium. Our results demonstrate that thiocyanate is an excellent vibrational reporter of the heterogeneous ion complexes undergoing association-dissociation dynamics. We find that the ionic electrolytes exist as contact ion pairs, dimers, and clusters in a low dielectric medium. The relative ratios of the various ion complexes are sensitive to the cations. In addition to the interactions between the thiocyanate anion and the countercation, the solute-solvent interactions drive the dynamic equilibrium. We have estimated the association-dissociation dynamics time scales from two-dimensional infrared spectroscopy. The exchange time scale involving the cluster is faster than that between a dimer and an ion pair. Moreover, we find that the dynamic equilibrium between the cluster and another ion complex is correlated to the solvent fluctuations.

Importance of the Ion-Pair Lifetime in Polymer Electrolytes

Ion pairing is commonly considered as a culprit for the reduced ionic conductivity in polymer electrolyte systems. However, this simple thermodynamic picture should not be taken literally, as ion pairing is a dynamical phenomenon. Here we construct model poly(ethylene oxide)-bis(trifluoromethane)sulfonimide lithium salt systems with different degrees of ion pairing by tuning the solvent polarity and examine the relation between the cation-anion distinct conductivity σ+-d and the lifetime of ion pairs τ+- using molecular dynamics simulations. It is found that there exist two distinct regimes where σ+-d scales with 1/τ+- and τ+-, respectively, and the latter is a signature of longer-lived ion pairs that contribute negatively to the total ionic conductivity. This suggests that ion pairs are kinetically different depending on the solvent polarity, which renders the ion-pair lifetime highly important when discussing its effect on ion transport in polymer electrolyte systems.

Relationship between Ionic Conductivity, Glass Transition Temperature, and Dielectric Constant in Poly(vinyl ether) Lithium Electrolytes

We report a partial elucidation of the relationship between polymer polarity and ionic conductivity in polymer electrolyte mixtures comprising a homologous series of nine poly(vinyl ether)s (PVEs) and lithium bis(trifluoromethylsulfonyl)imide. Recent simulation studies have suggested that low dielectric polymer hosts with glass transition temperatures far below ambient conditions are expected to have ionic conductivity limited by salt solubility and dissociation. In contrast, high dielectric hosts are expected to have the potential for high ion solubility but slow segmental dynamics due to strong polymer-polymer and polymer-ion interactions. We report results for PVEs in the low polarity regime with dielectric constants of about 1.3 to 9.0. Ionic conductivity measured for the PVE and salt mixtures ranged from about 10^-10 to 10^-3 S/cm. In agreement with the predictions from computer simulations, the ionic conductivity increased with dielectric constant and plateaued as the dielectric approached 9.0, comparable to the dielectric constant of the widely used poly(ethylene oxide).

Dynamic Structure and Phase Behavior of a Block Copolymer Electrolyte under dc Polarization

An important consideration when designing lithium battery electrolytes for advanced applications is how the electrolyte facilitates ion transport at fast charge and discharge rates. Large current densities are accompanied by large salt concentration gradients across the electrolyte. Nanostructured composite electrolytes have been proposed to enable the use of high energy density lithium metal anodes, but many questions about the interplay between the electrolyte morphology and the salt concentration gradient that forms under dc polarization remain unanswered. To address these questions, we use an in situ small-angle X-ray scattering technique to examine the nanostructure of a polystyrene-block-poly(ethylene oxide) copolymer electrolyte under dc polarization with spatial and temporal resolution. In the quiescent state, the electrolyte exhibits a lamellar morphology. The passage of ionic current in a lithium symmetric cell leads to the formation of concurrent phases: a disordered morphology near the negative electrode, lamellae in the center of the cell, and coexisting lamellae and gyroid near the positive electrode. The most surprising result of this study was obtained after the applied electric field was turned off: a current-induced gyroid phase grows in volume for 6 h in spite of the absence of an obvious driving force. We show that this reflects the formation of localized pockets of salt-dense electrolyte, termed concentration hotspots, under dc polarization. Our methods may be applied to understand the dynamic structure of composite electrolytes at appreciable current densities.

Effects of Solvent Polarity on Li-ion Diffusion in Polymer Electrolytes: An All-Atom Molecular Dynamics Study with Charge Scaling

We herein report an all-atom molecular dynamics study on the role of solvent polarity for Li+ diffusion in polymer electrolytes using PEO-LiTFSI (poly(ethylene oxide)-lithium bis(trifluoromethane)sulfonimide) as a model system. By separating the effect of Tg and the effect of solvent polarity in our simulations, we show that the maximum in the diffusion coefficient of Li+ with respect to the dielectric constant of polymer solvent εp is due to transitions in the transport mechanism. In particular, it is found that the frequent interchain hopping involves the coordination of both PEO and TFSI. This optimal solvating ability of PEO at an intermediate value of εp leads to the fast ion conduction. These findings highlight the synergetic effect of solvent polarity and bond polarity on Li-ion diffusion in solid polymer electrolytes.