Diffusion and migration in polymer electrolytes

Mixtures of neutral polymers and lithium salts have the potential to serve as electrolytes in next-generation rechargeable Li-ion batteries. The purpose of this review is to expose the delicate interplay between polymer-salt interactions at the segmental level and macroscopic ion transport at the battery level. Since complete characterization of this interplay has only been completed in one system: mixtures of poly(ethylene oxide) and lithium bis(trifluoromethanesulfonyl)imide (PEO/LiTFSI), we focus on data obtained from this system. We begin with a discussion of the activity coefficient, followed by a discussion of six different diffusion coefficients: the Rouse motion of polymer segments is quantified by Dseg, the self-diffusion of cations and anions is quantified by Dself,+ and Dself,−, and the build-up of concentration gradients in electrolytes under an applied potential is quantified by Stefan-Maxwell diffusion coefficients, D0+, D0-, and D+-. The Stefan-Maxwell diffusion coefficients can be used to predict the velocities of the ions at very early times after an electric field is applied across the electrolyte. The surprising result is that D0- is negative in certain concentration windows. A consequence of this finding is that at these concentrations, both cations and anions are predicted to migrate toward the positive electrode at early times. We describe the controversies that surround this result. Knowledge of the Stefan-Maxwell diffusion coefficients enable prediction of the limiting current. We argue that the limiting current is the most important characteristic of an electrolyte. Excellent agreement between theoretical and experimental limiting current is seen in PEO/LiTFSI mixtures. What sequence of monomers that, when polymerized, will lead to the highest limiting current remains an important unanswered question. It is our hope that the approach presented in this review will guide the development of such polymers

Comparing Experimental Phase Behavior of Ion-Doped Block Copolymers with Theoretical Predictions Based on Selective Ion Solvation

The effects of salt-doping on the morphological behavior of block copolymers are well established but remain poorly understood, partially because of the challenge of resolving electrostatics in a heterogeneous medium with low average permittivity. By employing a recently developed field theory, we analyze the phase behavior of polystyrene-b-poly(ethylene oxide) (SEO) copolymers doped with lithium bis(trifluoromethanesulfonyl)imide salts (LiTFSI). Using a single fitting parameter, the ionic solvation radius, we obtain qualitative agreement between our theory and experimental data over a range of polymer molecular weights and copolymer compositions. Such agreement supports and highlights the need of solvation free energy to accurately describe the self-assembly of ion-doped block copolymers and demonstrates that experimentally observed dependence on molecular weight, not present in neutral block copolymers, can be rationalized by solvation effects. Overall, morphological variations are stronger than those predicted by the leading, linear order theory but can be captured by the full model

Polymer Dynamics in Block Copolymer Electrolytes Detected by Neutron Spin Echo

Polymer chain dynamics of a nanostructured block copolymer electrolyte, polystyrene-block-poly(ethylene oxide) (SEO) mixed with lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt, are investigated by neutron spin echo (NSE) spectroscopy on the 0.1-100 ns time scale and analyzed using the Rouse model at short times (t ≤ 10 ns) and the reptation tube model at long times (t ≥ 50 ns). In the Rouse regime, the monomeric friction coefficient increases with increasing salt concentration, as seen previously in homopolymer electrolytes. In the reptation regime, the tube diameters, which represent entanglement constraints, decrease with increasing salt concentration. The normalized longest molecular relaxation time, calculated from the NSE results, increases with increasing salt concentration. We argue that quantifying chain motion in the presence of ions is essential for predicting the behavior of polymer-electrolyte-based batteries operating at large currents

Segmental Dynamics Measured by Quasi-Elastic Neutron Scattering and Ion Transport in Chemically Distinct Polymer Electrolytes

We investigate the segmental dynamics and ion transport in two chemically distinct polymer electrolytes, poly(2-cyanoethyl acrylate) (PCEA) and poly(ethylene oxide) (PEO), and their mixtures with lithium bis(trifluoromethane)sulfonimide (LiTFSI) salt. Quasi-elastic neutron scattering experiments reveal slow dynamics in PCEA/LiTFSI relative to that in PEO/LiTFSI, translating to monomeric friction coefficients that are orders of magnitude different. In spite of the enhanced salt dissociation in PCEA due to the presence of polar groups, ion transport is largely dominated by the effect of increased monomeric friction in the pure polymer. Conductivity in these systems is quantified through a simple expression combining salt dissociation, the monomeric friction in the pure polymer, and the effect of added salt on the monomeric friction

Relationship between steady-state current in symmetric cells and transference number of electrolytes comprising univalent and multivalent ions

We derive a general relationship between the applied potential across a binary electrolyte in a symmetric cell and steady-state current density, iss. The relationship is applicable to salts comprising ions that are either univalent or multivalent. In concentrated solutions, iss depends on the electrolyte conductivity which governs i0, the initially recorded current density at time zero when the potential is applied, and a dimensionless parameter derived here in terms of multicomponent transport coefficients. In the dilute limit, the ratio iSS/i0 is the cation transference number, irrespective of the charge on the cation or the anion

High-Resolution Imaging of Unstained Polymer Materials

Electron microscopy has played an important role in polymer characterization. Traditionally, electron diffraction is used to study crystalline polymers while transmission electron microscopy is used to study microphase separation in stained block copolymers and other multiphase systems. We describe developments that eliminate the barrier between these two approaches - it is now possible to image polymer crystals with atomic resolution. The focus of this Review is on high-resolution imaging (30 Å and smaller) of unstained polymers. Recent advances in hardware allow for capturing numerous (as many as 105) low-dose images from an unperturbed specimen; beam damage is a significant barrier to high-resolution electron microscopy of polymers. Machine-learning-based software is then used to sort and average the images to retrieve pristine structural information from a collection of noisy images. Acknowledging the heterogeneity in polymer samples prior to averaging is essential. Molecular conformations in a wide range of amphiphilic block copolymers, polymerized ionic liquids, and conjugated polymers can be gleaned from two-dimensional projections (2D), three-dimensional (3D) tomograms, and four-dimensional (4D) scanning transmission electron microscopy (STEM) data sets where 2D diffraction patterns are taken as a function of position. Some methods such as phase contrast STEM have been used to image closely related materials such as metal-organic frameworks but not polymers. With improvements in hardware and software, such methods may soon be applied to polymers. Our goal is to provide a comprehensive understanding of the strategies toward the high-resolution imaging of radiation sensitive polymer materials at different length scales

Organizing thermodynamic data obtained from multicomponent polymer electrolytes: Salt-containing polymer blends and block copolymers

The objective of this review is to organize literature data on the thermodynamic properties of salt-containing polystyrene/poly(ethylene oxide) (PS/PEO) blends and polystyrene-b-poly(ethylene oxide) (SEO) diblock copolymers. These systems are of interest due to their potential to serve as electrolytes in all-solid rechargeable lithium batteries. Mean-field theories, developed for pure polymer blends and block copolymers, are used to describe phenomenon seen in salt-containing systems. An effective Flory–Huggins interaction parameter, χeff, that increases linearly with salt concentration is used to describe the effect of salt addition for both blends and block copolymers. Segregation strength, χeffN, where N is the chain length of the homopolymers or block copolymers, is used to map phase behavior of salty systems as a function of composition. Domain spacing of salt-containing block copolymers is normalized to account for the effect of copolymer composition using an expression obtained in the weak segregation limit. The phase behavior of salty blends, salty block copolymers, and domain spacings of the latter systems, are presented as a function of chain length, composition and salt concentration on universal plots. While the proposed framework has limitations, the universal plots should serve as a starting point for organizing data from other salt-containing polymer mixtures. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1177–1187

Electrochemical properties of poly(ethylene oxide) electrolytes above the entanglement threshold

Ion transport in electrolytes depends on three transport coefficients, conductivity (κ), salt diffusion coefficient (D), and the cation transference number with respect to the solvent velocity (t+0), and the thermodynamic factor (Tf). Current methods for determining these parameters involve four separate experiments, and the coupled nature of the equations used to determine them generally results in large experimental uncertainty. We present data obtained from 64 independent polymer electrolytes comprising poly(ethylene oxide) (PEO) and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt. The molecular weights of PEO ranged from 5 to 275 kg mol−1; these samples are all above the entanglement threshold. We minimize the experimental uncertainty in transport and thermodynamic measurements by exploiting the fact that ion transport in entangled polymer electrolytes should be independent of molecular weight. The dependence of κ, D, t+0, and Tf as a function of salt concentration in the range 0.035 ≤ r ≤ 0.30 are presented with a 95% confidence interval, where r is the molar ratio of lithium ions to ethylene oxide monomer units. While κ, D, and Tf are all positive as required by thermodynamic constraints, there is no constraint on the sign of t+0. We find that t+0 is negative in the salt concentration range of 0.093 ≤ r ≤ 0.189