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Cryogenic transmission electron microscopy (cryo-TEM) combined with single particle analysis (SPA) is an emerging imaging approach for soft materials. However, the accuracy of SPA-reconstructed nanostructures, particularly those formed by synthetic polymers, remains uncertain due to potential packing heterogeneity of the nanostructures. In this study, the combination of molecular dynamics (MD) simulations and image simulations is utilized to validate the accuracy of cryo-TEM 3D reconstructions of self-assembled polypeptoid fibril nanostructures. Using CryoSPARC software, image simulations, 2D classifications, ab initio reconstructions, and homogenous refinements are performed. By comparing the results with atomic models, the recovery of molecular details is assessed, heterogeneous structures are identified, and the influence of extraction location on the reconstructions is evaluated. These findings confirm the fidelity of single particle analysis in accurately resolving complex structural characteristics and heterogeneous structures, exhibiting its potential as a valuable tool for detailed structural analysis of synthetic polymers and soft materials.

The functioning of a wide variety of charged macromolecules, from DNA to fuel cell membranes, is dependent on how the counterions surrounding them are arranged. In order to decrease Coulombic repulsion, some of the fixed charges on these molecules are neutralized by a fraction of the counterions─this phenomenon is called counterion condensation. The nature of counterion condensation can be only be inferred indirectly from traditional experiments such as X-ray scattering and modern experiments such as single molecule electrometry. The prevalent conclusion in the literature, based on both theory and experiment, is that the distribution of counterions is peaked right next to the macromolecule, i.e., condensation results in the formation of contact ion pairs. In this study, cryogenic electron microscopy (cryo-EM) was used to study the arrangement of condensed halide counterions near a positively charged polypeptoid nanofiber. The locations of both condensed and fixed charges were determined directly from atomic-scale images. Our experimentally determined counterion distributions were peaked at distances of about 5 Å away from the fixed positive charge, indicating the presence of a layer of water molecules between condensed ion pairs. We posit that this distribution is driven by the entropy of the condensed ions.

The arrangement of crystalline domains in semicrystalline polymers is key to understanding how to optimize the nanostructured morphology for enabling better properties. For example, in polystyrene-b-poly(ethylene oxide) (PS-b-PEO), the degree of crystallinity and arrangement of the crystallites within the PEO phase plays a crucial role in determining the physical properties of the electrolyte. Here, we used four-dimensional scanning transmission electron microscopy to directly visualize the crystal domains within the PEO-rich region of the PS-b-PEO block copolymer and show the relative angle of the domain with respect to the PEO-PS interface. As demonstrated here, our analysis method is applicable to other electron-beam sensitive materials, especially semicrystalline polymers, to unveil their local phase condition and distribution.

Rechargeable batteries exhibit poor performance at low temperatures due to sluggish ion transport through the electrolytic phase. Ion transport is governed by three transport parameters—conductivity, diffusion coefficient, and the cation transference number with respect to the solvent velocity—and the thermodynamic factor. Understanding how these parameters change with temperature is necessary for designing improved electrolytes. In this work, we combine electrochemical techniques with electrophoretic NMR to determine the temperature dependence of these parameters for a liquid electrolyte, LiTFSI salt dissolved in tetraglyme between −20 and 45 °C. At colder temperatures, all species in the electrolyte tend to move more slowly due to increasing viscosity, which translates to a monotonic decrease in conductivity and diffusion coefficient with decreasing temperature. Surprisingly, we find that the field-induced velocity of solvent molecules at a particular salt concentration is a nonmonotonic function of temperature. The cation transference number with respect to the solvent velocity thus exhibits a complex dependence on temperature and salt concentration. The measured thermodynamic and transport properties are used to predict concentration gradients that will form in a lithium-lithium symmetric cell under a constant applied potential as a function of temperature using concentrated solution theory. The calculated steady current at −20 °C is lower than that at 45 °C by roughly two orders of magnitude.

Designing conformationally dynamic molecules that self-assemble into predictable nanostructures remains an important unmet challenge. This paper describes how atomic-scale cryogenic transmission electron microscopy (cryo-TEM) can be used to explore the relationship between molecular structure and self-assembly of block copolymers. We examined sheetlike micelles formed in water using a series of diblock copolypeptoids with the same hydrophilic block and three distinct crystalline hydrophobic blocks. Our cryo-TEM images revealed all the structures share nansoscale features, but differ in their intermolecular packing geometries. Different molecular arrangements, parallel and antiparallel V-shaped crystal motifs, were revealed by two-dimensional atomic-scale through-plane images. However, images from tilted samples revealed an unexpected feature when the hydrophobic polypeptoid block comprised phenyl rings with substituted bromine atoms at the para position. The nanosheets contained atomic-scale corrugations that were absent in the other systems which comprised unsubstituted aliphatic and aromatic side chains. We hypothesize that these corrugations are due to the dipolar characteristics of the brominated phenyl group and interactions between this group and water molecules.

Block copolymer (BCP) grain structure affects the mechanical, optical, and electrical properties of BCP materials, making the accurate characterization of this grain structure an important goal. In this study, improved BCP grain parameters were obtained by employing an exponentially decaying correlation function within the ellipsoidal grain model, instead of the Gaussian correlation function that was used in previous work. The exponential correlation function provides a better fit to the experimental depolarized light scattering data, which outweighs the disadvantage that it requires numerical integration to obtain the model scattered intensity.

Concentration polarization in an electrolyte comprising dissociated ions and a solvent is often modeled using concentrated solution theory developed by Newman. This theory is built upon two differential equations for electrolyte concentration and solvent velocity fields. We characterize the concentration and solvent velocity fields in a polystyrene-block-polyethylene oxide (SEO) block copolymer electrolyte using operando X-ray transmission measurements and X-ray photon correlation spectroscopy, respectively. Using calculations based on the assumption that the SEO chain behaves as a single species, we show that the experimental data are consistent with a cation transference number, t+0, ≈ 0.7. Previously published electrochemical experiments using small polarizations led to the conclusion that t+0 is less than 0.3. The discrepancy indicates that the block copolymer electrolyte cannot be approximated as a three-component system (cation, anion, and a single solvent), and frictional interactions involving the glassy polystyrene cannot be lumped with those involving rubbery poly(ethylene oxide) segments.

We compare the electrochemically measured Sand’s time, the time required for the cell potential to diverge when the applied current density exceeds the limiting current, with theoretical predictions for a 0.47 M poly(ethylene oxide) (5 kg mol−1)/LiTFSI electrolyte. The theoretical predictions are made using concentrated solution theory which accounts for both concentration polarization and polymer motion, using independently measured parameters that depend on concentration, c: conductivity (κ), salt diffusion coefficient (D), cationic transference number with respect to the solvent velocity ( t + 0 ), thermodynamic factor 1 + dln f ± dln c , and partial molar volume of the salt ( V ̅ ); f ± is the mean molar activity coefficient of the salt. We find quantitative agreement between experimental data and theoretical predictions. We derive a generalized analytical expression for Sand’s time for electrolytes based on dilute solution theory. This expression correctly predicts the divergence of the Sand’s time at the limiting current, in agreement with experimental data and concentrated solution theory predictions. When the applied current is large compared to the limiting current, the analytical expression approaches the standard expression for Sand’s time used in the literature.

Amphiphilic polypeptoids with defined sequences, versatile in forming various nanostructures, are ideal for mimicking biomacromolecular structures. The predictive design of nanostructures depends on our understanding of the relationship between molecular structure and the locations of atoms in the nanostructure. Factors of importance include chain conformation, crystal motifs, and the arrangement of the molecules within the nanostructure. This review introduces the cryogenic transmission electron microscopy (cryo-TEM) method, sorting and averaging unit cells in nanosheets for resolution enhancement and identifying structural heterogeneity. The resulting atomic-scale images reveal the presence of two types of crystal motifs. The impact of processing conditions, capping group chemistry, and side chain chemistry on structural heterogeneity and crystal motifs can be quantified. The 3D reconstruction of nanosheets, wherein atomic-scale corrugations were revealed, is introduced in this review. New developments in cryo-TEM, such as phase retrieval reconstruction, hold great promise for atomic-scale imaging of soft nanostructures. Graphical abstract: [Figure not available: see fulltext.]

Concentrated solution theory has furthered our understanding of ion transport in electrolytes. This theory can be used to predict salt concentration profiles under an applied current if the transport properties of the electrolyte (conductivity (κ), restricted diffusion coefficient (D), and the cation transference number with respect to the solvent velocity ( t + 0 )), and the thermodynamic factor (T f ) are known. In this work, we provide the first study comparing the predicted salt concentration profiles with measurements based on operando Raman spectroscopy. Concentration polarization is asymmetrical; the increase in salt concentration near the positive electrode is a factor of two greater than the decrease in salt concentration near the negative electrode. We find qualitative agreement between theory and experiment. Further work is needed to resolve the quantitative differences.

One approach for improving lithium transference in electrolytes is through the use of bulky multivalent anions. We have studied a multivalent salt containing a bulky star-shaped anion with a polyhedral oligomeric silsesquioxane (POSS) center and lithium counterions dissolved in a solvent. The charge on each anion, z-, is equal to -20. The self-diffusion coefficients of all species were measured by pulsed field gradient NMR (PFG-NMR). As expected, anion diffusion was significantly slower than cation diffusion. An approximate transference number, also referred to as the current fraction (measured by Bruce, Vincent and Watanabe method), was higher than those expected from PFG-NMR. However, the rigorously defined cation transference number with respect to the solvent velocity measured by electrophoretic NMR was negative at all salt concentrations. In contrast, the approximate transference numbers based on PFG-NMR and current fractions are always positive, as expected. The discrepancy between these three independent approaches for characterizing lithium transference suggests the presence of complex cation-anion interactions in solution. It is evident that the slow self-diffusion of bulky multivalent anions does not necessarily lead to an improvement of lithium transference.

Electrolytes in lithium-ion batteries comprise solvent mixtures, but analysis of ion transport is always based on treating the solvents as a single-entity. We combine electrophoretic NMR (eNMR) measurements and molecular dynamics (MD) simulations to quantify electric-field-induced transport in a concentrated solution containing LiPF6 salt dissolved in an ethylene carbonate/ethyl methyl carbonate (EC/EMC) mixture. The selective transport of EC relative to EMC is reflected in the difference between two transference numbers, defined as the fraction of current carried by cations relative to the velocity of each solvent species. This difference arises from the preferential solvation of cations by EC and its dynamic consequences. The simulations reveal the presence of a large variety of transient solvent-containing clusters which migrate at different velocities. Rigorous averaging over different solvation environments is essential for comparing simulated and measured transference numbers. Our study emphasizes the necessity of acknowledging the presence of four species in mixed-solvent electrolytes.

Amphiphilic molecules that can crystallize often form molecularly thin nanosheets in aqueous solutions. The possibility of atomic-scale corrugations in these structures has not yet been recognized. We have studied the self-assembly of amphiphilic polypeptoids, a family of bio-inspired polymers that can self-assemble into various crystalline nanostructures. Atomic-scale structure of the crystals in these systems has been inferred using both X-ray diffraction and electron microscopy. Here we use cryogenic electron microscopy to determine the in-plane and out-of-plane structures of a crystalline nanosheet. Data were collected as a function of tilt angle and analyzed using a hybrid single-particle crystallographic approach. The analysis reveals that adjacent rows of peptoid chains, which are separated by 4.5 Å in the plane of the nanosheet, are offset by 6 Å in the direction perpendicular to the plane of the nanosheet. These atomic-scale corrugations lead to a doubling of the unit cell dimension from 4.5 to 9 Å. Our work provides an alternative interpretation for the observed Å X-ray diffraction peak often reported in polypeptoid crystals.

The ability to engineer synthetic polymers with the same structural precision as biomacromolecules is crucial to enable the de novo design of robust nanomaterials with biomimetic function. Peptoids, poly(N-substituted) glycines, are a highly controllable bio-inspired polymer family that can assemble into a variety of functional, crystalline nanostructures over a wide range of sequences. Extensive investigation on the molecular packing in these lattices has been reported; however, many key atomic-level details of the molecular structure remain underexplored. Here, we use cryo-TEM 3D reconstruction to directly visualize the conformation of an individual polymer chain within a peptoid nanofiber lattice in real space at 3.6 Å resolution. The backbone in the N-decylglycine hydrophobic core is shown to clearly adopt an extended, all-cis-sigma strand conformation, as previously suggested in many peptoid lattice models. We also show that packing interactions (covalent and noncovalent) at the solvent-exposed N-termini have a dominant impact on the local chain ordering and hence the ability of the chains to pack into well-ordered lattices. Peptoids in pure water form fibers with limited growth in the a direction (

Accurate measurement of the cation transference number is critical for designing batteries with a given electrolyte. A promising approach for measuring this parameter is electrophoretic NMR (eNMR). In the standard approach, the average cation, anion, and solvent velocities under an applied electric field are used to estimate the cation transference number with respect to the solvent velocity, t + 0 . In this study, we show that t + 0 can be determined from measurements of the electric-field-induced velocities of individual species. The t + 0 values obtained from eNMR experiments on a model electrolyte (LiTFSI/tetraglyme) based on single species velocities are consistent with the standard approach. An important parameter that enters into the analysis is the velocity of the electrode-electrolyte interface which must be finite in an eNMR experiment. Agreement is only obtained after accounting for this velocity. The single-species approach is particularly valuable when one or more components of the electrolytic mixture are not easily accessible by NMR, for example zinc and magnesium cations.

Mixed conductors-materials that can efficiently conduct both ionic and electronic species-are an important class of functional solids. Here we demonstrate an organic nanocomposite that spontaneously forms when mixing an organic semiconductor with an ionic liquid and exhibits efficient room-temperature mixed conduction. We use a polymer known to form a semicrystalline microstructure to template ion intercalation into the side-chain domains of the crystallites, which leaves electronic transport pathways intact. Thus, the resulting material is ordered, exhibiting alternating layers of rigid semiconducting sheets and soft ion-conducting layers. This unique dual-network microstructure leads to a dynamic ionic/electronic nanocomposite with liquid-like ionic transport and highly mobile electronic charges. Using a combination of operando X-ray scattering and in situ spectroscopy, we confirm the ordered structure of the nanocomposite and uncover the mechanisms that give rise to efficient electron transport. These results provide fundamental insights into charge transport in organic semiconductors, as well as suggesting a pathway towards future improvements in these nanocomposites.

The rate at which rechargeable batteries can be charged and discharged is governed by the selective transport of the working ions through the electrolyte. Conductivity, the parameter commonly used to characterize ion transport in electrolytes, reflects the mobility of both cations and anions. The transference number, a parameter introduced over a century ago, sheds light on the relative rates of cation and anion transport. This parameter is, not surprisingly, affected by cation-cation, anion-anion, and cation-anion correlations. In addition, it is affected by correlations between the ions and neutral solvent molecules. Computer simulations have the potential to provide insights into the nature of these correlations. We review the dominant theoretical approaches used to predict the transference number from simulations by using a model univalent lithium electrolyte. In electrolytes of low concentration, one can obtain a quantitative model by assuming that the solution is made up of discrete ion-containing clusters-neutral ion pairs, negatively and positively charged triplets, neutral quadruplets, and so on. These clusters can be identified in simulations using simple algorithms, provided their lifetimes are sufficiently long. In concentrated electrolytes, more clusters are short-lived and more rigorous approaches that account for all correlations are necessary to quantify transference. Elucidating the molecular origin of the transference number in this limit remains an unmet challenge.

Solid polymer and perovskite-type ceramic electrolytes have both shown promise in advancing solid-state lithium metal batteries. Despite their favorable interfacial stability against lithium metal, polymer electrolytes face issues due to their low ionic conductivity and poor mechanical strength. Highly conductive and mechanically robust ceramics, on the other hand, cannot physically remain in contact with redox-active particles that expand and contract during charge-discharge cycles unless excessive pressures are used. To overcome the disadvantages of each material, polymer-ceramic composites can be formed; however, depletion interactions will always lead to aggregation of the ceramic particles if a homopolymer above its melting temperature is used. In this study, we incorporate Li0.33La0.56TiO3 (LLTO) nanoparticles into a block copolymer, polystyrene-b-poly (ethylene oxide) (SEO), to develop a polymer-composite electrolyte (SEO-LLTO). TEMs of the same nanoparticles in polyethylene oxide (PEO) show highly aggregated particles whereas a significant fraction of the nanoparticles are dispersed within the PEO-rich lamellae of the SEO-LLTO electrolyte. We use synchrotron hard x-ray microtomography to study the cell failure and interfacial stability of SEO-LLTO in cycled lithium-lithium symmetric cells. Three-dimensional tomograms reveal the formation of large globular lithium structures in the vicinity of the LLTO aggregates. Encasing the SEO-LLTO between layers of SEO to form a "sandwich" electrolyte, we prevent direct contact of LLTO with lithium metal, which allows for the passage of seven-fold higher current densities without signatures of lithium deposition around LLTO. We posit that eliminating particle clustering and direct contact of LLTO and lithium metal through dry processing techniques is crucial to enabling composite electrolytes.

We have studied ion transport in electrolytes created by blending two different polymers and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI). The polymers covered in this study are poly(ethylene oxide) (PEO), poly(1,3,6-trioxocane) (P(2EO-MO)), and poly(1,3-dioxolane) (P(EO-MO)). Ion transport is quantified by the product κρ+which is defined as the efficacy of the electrolytes, where κ is conductivity and ρ+is the current fraction determined by the Bruce-Vincent method. Polymer blends can be either one-phase or macrophase-separated. We used small-angle neutron scattering (SANS) to distinguish between these two possibilities. The random phase approximation (RPA) was used to interpret SANS data from one-phase blends. The effect of added salt on polymer blend thermodynamics is quantified by an effective Flory-Huggins interaction parameter. All polymer blends were one-phase in the absence of salt. Adding salt in small concentrations results in macrophase separation in all cases. One-phase systems were observed in the PEO/P(EO-MO)/LiTFSI blends at high salt concentrations. In most of the polymer blend electrolytes, the measured κρ+was either lower than or comparable to that of the homopolymer electrolytes. An exception to this was one-phase PEO/P(EO-MO)/LiTFSI blends electrolytes at high salt concentrations.

Molecular dynamics (MD) simulations, density functional theory (DFT) calculations, and 1H NMR spectroscopy were performed to gain a complementary understanding of the concentrated Li-ion electrolyte system, lithium bis(trifluoromethanesulfonyl)imide (Li[TFSI]) dissolved in tetraglyme. The computational methods provided the concentration dependence of differing solvation structure motifs by reference to changes in the corresponding NMR spectra. By combining both the computational and experimental methodologies, we show that the various solvation structures, dominated by the coordination between the tetraglyme (G4) solvent and lithium cation, directly influence the chemical shift separation of resonances in the 1H NMR spectra of the solvent. Thus, the 1H NMR spectra can be used to predict the fraction of tetraglyme involved in the solvation process, with quantitative agreement with solvation fraction predictions from MD simulation snapshots. Overall, our results demonstrate the reliability of a hybrid computational and experimental methodology to understand the solvation structure and hence transport mechanism of LiTFSI-G4 electrolytes in the low concentration region.

Improving transport properties of electrolytes is important for developing lithium-ion batteries for future energy storage applications. In Newman's concentrated solution theory, electrolytes are characterized by three transport parameters, conductivity, diffusion coefficient, and transference number, in addition to the thermodynamic factor. In this work, these parameters are all determined for an exemplar liquid electrolyte, lithium bis(trifluoromethanesulfonyl)imide mixed in tetraethylene glycol dimethyl ether, using electrochemical methods. The intrinsic coupling between parameters obtained by electrochemical methods results in large error bars in the transference number that obscure the transport behavior of the electrolyte. Here, we use electrophoretic NMR (eNMR) to measure the electric-field-induced ion and solvent velocities to obtain the transference number directly, which enables determination of the thermodynamic factor with greater certainty. Our work indicates that the combination of eNMR and electrochemical methods provides a robust approach for complete characterization of battery electrolytes.

Performant solid polymer electrolytes for battery applications usually have a low glass transition temperature and good ion solvation. Recently, to understand the success of PEO for solid-sate battery applications and explore alternatives, we have studied a series of polyacetals along with PEO, both from an experimental and a computational standpoint. We observed that even though the mechanism of transport may be more optimal in polyacetals, the lower glass transition temperature of the PEO-salt electrolyte system still makes it the best option, in this class of polymers, for battery applications. In this work, we explored the free-energy landscape of PEO and P(EO-MO) at various compositions and temperatures using metadynamics simulations to gain deeper insights into the various factors that affect the glass transition temperatures in these systems. In particular, we study the competition between intra- and inter-chain coordination of the cation in these systems that we had hypothesized in our previous work was responsible for the differences in the glass transition temperature. We observe that in PEO, the single-chain binding motif is thermodynamically more stable than the multi-chain binding motif, unlike P(EO-MO), where the opposite is true. We also show that multi-chain coordination, and the associated higher glass transition temperature, in P(EO-MO) is due to a larger strain energy for single-chain coordination that originates in the introduced OCO linkages (relative to PEO's consistent OCCO linkages). Furthermore, the type of pathways to move from one transition state to another in the various systems do not change at higher concentrations though the relative probability of cation-anion coordinated states increases. Calculations at different temperatures to understand the entropic effect on the stability of these coordination environments reveal that as we increase the temperature, single-chain coordination becomes relatively more stable due to the entropic cost of multi-chain coordination, reducing the number of accessible states for the polymer. The various insights into the factors that affect glass transition temperature in these systems suggest design principles for polymer electrolyte systems with lower glass transition temperatures that need further research to compete with PEO at the same absolute battery working temperatures.

Human pluripotent stem cells (hPSCs) are an exciting and promising source to enable cell replacement therapies for a variety of unmet medical needs. Though hPSCs can be successfully derived into numerous physiologically relevant cell types, effective translation to the clinic is limited by challenges in scalable production of high-quality cells, cellular immaturity following the differentiation process, and the use of animal-derived components in culture. To address these limitations, we have developed a fully defined, reproducible, and tunable thermoreversible polymer for high-quality, scalable 3D cell production. Our reproducible synthesis method enables precise control of gelation temperature (24°C-32°C), hydrogel stiffness (100-4000 Pa), and the prevention of any unintended covalent crosslinking. After material optimization, we demonstrated hPSC expansion, pluripotency maintenance, and differentiation into numerous lineages within the hydrogel. Overall, this 3D thermoreversible hydrogel platform has broad applications in scalable, high-quality cell production to overcome the biomanufacturing burden of stem cell therapy.

Bottom-up understanding of transport describes how molecular changes alter species concentrations and electrolyte voltage drops in operating batteries. Such an understanding is essential to predictively design electrolytes for desired transport behavior. We herein advocate building a structure-property-performance relationship as a systematic approach to accurate bottom-up understanding. To ensure generalization across salt concentrations as well as different electrolyte types and cell configurations, the property-performance relation must be described using Newman's concentrated solution theory. It uses Stefan-Maxwell diffusivity, ij , to describe the role of molecular motions at the continuum scale. The key challenge is to connect ij to the structure. We discuss existing methods for making such a connection, their peculiarities, and future directions to advance our understanding of electrolyte transport.

While electric fields primarily result in migration of charged species in electrolytic solutions, the solutions are dynamically heterogeneous. Solvent molecules within the solvation shells of the cation will be dragged by the field while free solvent molecules will not. We combine electrophoretic NMR measurements of ion and solvent velocities under applied electric fields with molecular dynamics simulations to interrogate different solvation motifs in a model liquid electrolyte. Measured values of the cation transference number (t_{+}^{0}) agree quantitatively with simulation-based predictions over a range of electrolyte concentrations. Solvent-cation interactions strongly influence the concentration-dependent behavior of t_{+}^{0}. We identify a critical concentration at which most of the solvent molecules lie within solvation shells of the cations. The dynamic heterogeneity of solvent molecules is minimized at this concentration where t_{+}^{0} is approximately equal to zero.

We use concentrated solution theory to derive an equation governing solvent velocity in a binary electrolyte when a current passes through it. This equation, in combination with the material balance equation, enables the prediction of electrolyte concentration profiles and species velocities as a function of space and time. This framework is used to predict ion velocities in Li-Li symmetric cells containing a mixture of lithium bis(trifluoromethanesulfonyl)imide and poly(ethylene oxide) (LiTFSI/PEO), for which the cation transference number relative to the solvent velocity, + t0, can be either positive or negative, depending on salt concentration. Accounting for the solvent motion is increasingly important at higher concentrations. Especially for negative + t0, if solvent velocity is set to zero, the cation velocity, based on the electrode-electrolyte interface reference frame, is pointed opposite to the current flow. However, when solvent motion is taken into account, the cation velocity, based on the same reference frame, is in the same direction as the current. This analysis demonstrates the importance of accounting for solvent velocity rigorously in seemingly simple systems such as symmetric cells.

The limiting current density of a conventional polymer electrolyte (PS-PEO/LiTFSI) and a single-ion-conducting polymer electrolyte (PSLiTFSI-PEO) was measured using a new approach based on the fitted slopes of the potential obtained from lithiumpolymer-lithium symmetric cells at a constant current density. The results of this method were consistent with those of an alternative framework for identifying the limiting current density taken from the literature. We found the limiting current density of the conventional electrolyte is inversely proportional to electrolyte thickness as expected from theory. The limiting current density of the single-ion-conducting electrolyte was found to be independent of thickness. There are no theories that address the dependence of the limiting current density on thickness for single-ion-conducting electrolytes.

Optimizing electrolyte performance is crucial for the widespread adoption of electrochemical energy storage. We demonstrate that limiting current provides a robust criterion for determining the optimum electrolyte. Experiments were conducted on rigid block copolymer electrolytes comprising mixtures of polystyrene-block-poly(ethylene oxide) copolymer (SEO) and lithium bis(trifluoromethanesulfonyl) imide salt (LiTFSI) over a salt concentration range from rav = 0.04 to rav = 0.20 (rav is the molar ratio of lithium ions to ethylene oxide). We show that the maximum limiting current density is 4.3 mA cm−2 at rav = 0.12. The dependence of limiting current on salt concentration is in good agreement with predictions from Newman's concentrated solution theory with no adjustable parameters.

We investigate a polyacetal-based electrolyte, poly(1,3,6-Trioxocane) (P(2EO-MO)) mixed with lithium bis(trifluoromethanesulfonyl) imide (LiTFSI) salt, and report full electrochemical characterization of the transport parameters and a thermodynamic property in comparison to the previously reported poly(ethylene oxide) (PEO) electrolyte data [D. Gribble et al., J. Electrochem. Soc., 166, A3228 (2019)]. While the steady-state current fraction (?+) of P(2EO-MO) electrolyte is greater than that of PEO electrolyte in the entire salt concentration window we explored, the rigorously defined transference number using Newman s concentrated solution theory ( + t 0) appears to be similar to that of PEO electrolyte. On the basis of full electrochemical characterization, we calculate the salt concentration profile as a function of position in the cell and predict limiting current density (iLL) as a function of salt concentration. Experimental data were compared to the predicted values. The non-monotonic behaviors were observed both in prediction and experimental results with offset peak positions. We find that the limiting current density of P (2EO-MO) electrolyte is systematically lower than that of PEO electrolyte in most of the salt concentrations with the exception of rav = 0.05. It is noteworthy that even though one measure of electrolyte efficacy (?+) is superior in P(2EO-MO) electrolyte, the limiting current density, which is another metric of electrolyte efficacy at high currents, is not greater in P(2EO-MO).

Even though batteries operate at different temperatures depending on their use and state of charge, little work has been done to understand the effects of temperature on the ionic transport properties of the electrolyte. The temperature dependence of these properties is important for predicting how the performance of the battery will change as a function of temperature, along with gaining fundamental insights into the underpinnings of ion transport in these electrolytes. In this study we provide the first investigation of the effect of temperature on ionic conductivity, salt diffusion coefficient, transference number, and the thermodynamic factor of a model polymer electrolyte: lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt dissolved in poly(ethylene oxide) (PEO). These properties were measured at 70, 90, and 110 °C. As expected, we see monotonic increases in conductivity and diffusion with increasing temperature. Additionally, monotonic dependencies on temperature were obtained for the transference number and the thermodynamic factor. One presumes that concentration polarization decreases with increasing temperature due to more rapid ion transport. We use concentrated solution theory to predict concentration polarization in lithium-PEO/LiTFSI‑lithium symmetric cells and thereby quantify the effect of temperature on concentration polarization.

Hybrid organic-inorganic block copolymer electrolytes are of interest to enable batteries containing lithium metal anodes. The conductive block is a standard polymer electrolyte of poly(ethylene oxide) and the mechanically rigid block is an inorganic poly(acryloisobutyl polyhedral oligomeric silsesquioxane) polymer. In this paper, we compare a poly(acryloisobutyl polyhedral oligomeric silsesquioxane)-b-poly(ethylene oxide)-b-poly(acryloisobutyl polyhedral oligomeric silsesquioxane) (POSS-PEO-POSS) triblock copolymer and a poly(ethylene oxide)-b- poly(acryloisobutyl polyhedral oligomeric silsesquioxane) (PEO-POSS) diblock copolymer mixed with lithium bis(trifluoromethanesulfonyl)imide salt. We have experimentally measured the limiting current density in lithium symmetric cells containing hybrid organic-inorganic electrolytes at 90 °C. The cells were polarized at a large range of applied current density. The diblock copolymer electrolyte exhibited a clear plateau in cell potential at all current densities below the limiting current density. At low applied current density, the triblock copolymer electrolyte also exhibited a clear plateau in cell potential. At currents approaching the limiting current density, the triblock copolymer electrolyte exhibited an underdamped potential profile. The cell potential did not reach a plateau at current densities above the limiting current in both systems. The diblock and triblock copolymer electrolytes were fully characterized using electrochemical methods to determine the ionic conductivity, cation current fraction, salt diffusion coefficient, and open circuit voltage as a function of salt concentration. Cell potential and salt concentration as functions of position in the cell at various current densities were calculated using Newman's concentrated solution theory. The theoretical limiting current density was calculated to be the current density at which salt is depleted at the cathode. We see quantitative agreement between experimental measurements and theoretical predictions for the limiting current density in the diblock copolymer electrolyte which has an ordered structure at all salt concentrations, while the experimental limiting current density is lower than the theoretical prediction for the triblock copolymer electrolyte, which exhibits a disordered morphology at high salt concentrations.

Electrolytes used in rechargeable batteries must enable rapid translation of the working ion between macroscopically separated electrodes. These electrolytes are, however, usually designed and synthesized using atomic-level insights. Whether the ideal electrolyte for a particular battery is a solid or a liquid remains an important unresolved question, especially as solids with conductivities comparable with liquids are discovered. To help resolve such questions, we present the first steps toward a unified framework for relating atomic and continuum scale phenomena. Solvation shells in liquids are entities that translate with the working ion for a short while before they break up due to Brownian motion. By contrast, solvation cages in classical solids and polymers cannot not translate with the working ion. Mobility of the entities that make up the cages and shells, which is quantified by an order parameter, is shown to influence translation of the working ion on continuum length scales.

The success of poly(ethylene oxide) (PEO) in solid-state polymer electrolytes for lithium-ion batteries is well established. Recently, in order to understand this success and to explore possible alternatives, we studied polyacetal electrolytes to deepen the understanding of the effect of the local chemical structure on ion transport. Advanced molecular dynamics techniques using newly developed, tailored interaction potentials have helped elucidate the various coordination environments of ions in these systems. In particular, the competition between cation-anion pairing and coordination by the polymer has been explored using free-energy sampling (metadynamics). At equivalent reduced temperatures, with respect to the polymer-specific glass-transition temperature, two-dimensional free-energy plots reveal the existence of multiple coordination environments for the lithium (Li) ions in these systems and their relative stabilities. Furthermore, we observe that the Li-ion movement in PEO follows a serial, stepwise pathway when moving from one coordination state to another, whereas this happens in a more continuous and concerted fashion in a polyacetal such as poly(1,3-dioxalane) [P(EO-MO)]. The implication is that interconversion between coordination states of the Li ions may be easier in P(EO-MO). However, the overarching observation from our free-energy analysis is that Li-ion coordination is dominated by the polymer (in either case) and contact-ion pairs are rare. We rationalize the observed higher increase in glass-transition temperature (Tg) with salt loading in polyacetals as due to intermolecular Li-ion coordination involving multiple polymer chains, rather than just one chain for PEO-based electrolytes. This interchain coupling in the polyacetals, resulting in the higherTg, works against any gains due to variations in Li-ion coordination that might enhance transport processes over PEO. Further research is required to overcome the interdependence between local coordination and macroscopic properties to compete with PEO electrolytes at the same absolute working temperature.

Lithium-salt-doped block copolymers have the potential to serve as solid electrolytes in rechargeable batteries with lithium metal anodes. In this work, we use small-angle X-ray scattering (SAXS) to study the structure of polystyrene-block-poly(ethylene oxide) (PS-b-PEO) doped with bis-(trifluoromethylsulfonyl)amine lithium salt (LiTFSI) during direct current (dc) polarization experiments in lithium-lithium symmetric cells. The block copolymer studied is nearly symmetric in composition, has a total molecular weight of 39 kg mol-1, and exhibits a lamellar morphology at all studied salt concentrations. When ionic current is passed through the electrolyte, a salt concentration gradient forms that induces a spatial gradient in the domain spacing, d. The dependence of d on distance from the positive electrode, x, was determined experimentally by scanning the incident X-ray beam from one lithium electrode to the other. By studying the two-dimensional (2D) SAXS patterns as a function of azimuthal scattering angle, we find that lamellae with PS/PEO interfaces oriented perpendicular to the flow of ionic current (LAM∥) swell and contract to a greater degree than those with interfaces oriented parallel to the current direction (LAM||). While domains with the LAM∥ do not provide direct conducting pathways between the electrodes, our analysis suggests that they play an important role in establishing the salt concentration gradient necessary for sustaining a large ionic current through greater expansion and contraction.

We introduce a novel composite holey gold support that prevents cryo-crinkling and reduces beam-induced motion of soft specimens, building on the previously introduced all-gold support. The composite holey gold support for high-resolution cryogenic electron microscopy of soft crystalline membranes was fabricated in two steps. In the first step, a holey gold film was transferred on top of a molybdenum grid. In the second step, a continuous thin carbon film was transferred onto the holey gold film. This support (Au/Mo grid) was used to image crystalline synthetic polymer membranes. The low thermal expansion of Mo is not only expected to avoid cryo-crinkling of the membrane when the grids are cooled to cryogenic temperatures, but it may also act to reduce whatever crinkling existed even before cooling. The Au/Mo grid exhibits excellent performance with specimens tilted to 45°. This is demonstrated by quantifying beam-induced motion and differences in local defocus values. In addition, images of specimens on the Au/Mo grids that are tilted at 45° show high-resolution information of the crystalline membranes that, after lattice-unbending, extends beyond 1.5 Å in the direction perpendicular to the tilt axis.

Polyacetal electrolytes have been demonstrated as promising alternatives to liquid electrolytes and poly(ethylene oxide) (PEO) for rechargeable lithium-ion batteries; however, the relationship between polymer structure and ion motion is difficult to characterize. Here, we study structure-property trends in ion diffusion with respect to polymer composition for a systematic series of five polyacetals with varying ratios of ethylene oxide (EO) to methylene oxide (MO) units, denoted as P(xEO-yMO), and PEO. We first use 7Li and 19F pulsed-field-gradient NMR spectroscopy to measure cation and anion self-diffusion, respectively, in polymer/lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt mixtures. At 90 °C, we observe modest changes in Li+ diffusivity across all polymer compositions, while anion (TFSI-) self-diffusion coefficients decrease significantly with increasing MO content. At a given reduced temperature (T - Tg), all polyacetal electrolytes exhibit faster Li+ self-diffusion than PEO. Intriguingly, P(EO-MO) and P(EO-2MO) also show slower TFSI- anion self-diffusion than PEO at a given reduced temperature. Molecular dynamics simulations reveal that shorter distances between acetal oxygen atoms (O-CH2-O) compared to ether oxygens (O-CH2-CH2-O) promote more diverse, often asymmetric, Li+ coordination environments. Raman spectra reveal that anion-rich ion clusters in P(EO-MO) and P(EO-2MO) lead to decreased anion diffusivity, which along with increased cation diffusivity, support the viability of polyacetals as high-performance polymer electrolytes.

Growing demand for rechargeable batteries with higher energy densities has motivated research focused on enabling the lithium metal anode. A prominent failure mechanism in such batteries is short circuiting due to the uncontrolled propagation of lithium protrusions that often have a dendritic morphology. In this paper, the electrodeposition of metallic lithium through a rigid polystyrene-b-poly(ethylene oxide) (PS-b-PEO or SEO) block copolymer electrolyte was studied using hard X-ray microtomography. In this system, protrusions were approximately ellipsoidal globules: we take advantage of this simple geometry to quantify their growth as a function of polarization time and electrolyte salt concentration. The growth of 47 different globules was tracked with time to obtain average velocities of globule growth into the electrolyte. The globule diameter was a linear function of globule height in the electrolyte with a slope of about 6, independent of time and electrolyte salt concentration.

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.

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.

Polymer electrolytes mitigate safety concerns surrounding flammable liquid electrolytes in lithium-ion batteries. Poly(ethylene oxide) (PEO) electrolytes demonstrate viable conductivity values (∼1 × 10-3 S/cm) at elevated temperatures (>70 °C) but a relatively low Li+ current fraction (≤0.2) because strong Li+ coordination inhibits cation mobility. We have developed a series of polyacetal electrolytes by systematically varying methylene oxide (MO) and ethylene oxide (EO) units in the polymer backbone. These materials maintain high oxygen-to-carbon ratios like PEO but offer improved ion transport, revealing trends of decreasing conductivity and increasing current fraction with respect to polymer composition. In particular, the increasing current fraction measured via the Bruce-Vincent method suggests that MO units improve Li+ mobility relative to anion mobility. We calculate an overall efficacy (product of conductivity and current fraction) for each polymer/salt composition and identify two polymers - P(EO-MO) and P(EO-2MO) - that outperform PEO at high and low salt concentrations, respectively.

Next-generation electrolytes for lithium batteries must be able to conduct ions at sufficiently high current densities; yet this regime is rarely studied directly. The limiting current density of an electrolyte quantifies the highest possible rate of ion transport under an applied dc potential. Herein, we report on the limiting current density in twelve nanostructured polystyrene-block-poly(ethylene oxide) (PS-b-PEO, or SEO) copolymer electrolytes. We find that the limiting current at a given salt concentration increases systematically with increasing volume fraction of the PEO block (φEO). In contrast, the effective-medium theory, commonly used to analyze conductivity in block copolymer electrolytes, predicts that limiting current is independent of φEO. To resolve this conundrum, the ionic conductivity, the mutual diffusion coefficient of the salt, and the steady-state current fraction of the block copolymer electrolytes were measured. These measurements enable predictions of limiting current with no adjustable parameters using the concentrated solution theory. We found quantitative agreement between experimentally measured limiting current densities and predictions based on the concentrated solution theory. This work sheds light on how to reliably measure and predict limiting current density in composite electrolytes.

The morphological changes of phosphonate polypeptoid electrolyte membranes, poly-N-(2-ethyl)hexylglycine-block-poly-N-phosphonomethylglycine (pNehm-b-pNpmn), in hydrated and dry states were characterized by cryogenic transmission electron microscopy (cryo-TEM) and cryogenic electron tomography (cryo-ET). The analysis of 3D tomograms revealed that the pNeh9-b-pNpm9 thin films absorbed a large amount of water, resulting in the formation of membranes that were nearly flat and giant multicompartment vesicles dispersed in the water phase. A simple lamellar phase appeared when the films were dried. In contrast, pNeh18-b-pNpm18 thin films absorbed little water and formed small highly curved unilamellar and multilamellar vesicles. Water was located mainly outside the closely-packed vesicles. When water was removed by drying, the walls of adjacent vesicles collapsed to form honeycomb-like capsules. The changes in domain size reflected changes in chain conformations. The pNpm9 blocks were saturated by water and fully extended, while pNpm18 blocks were neither saturated by water nor fully extended. In addition, the thicknesses of hydrophobic blocks in the hydrated films of both pNeh9-b-pNpm9 and pNeh18-b-pNpm18 were smaller than those in the dry films, reflecting an increase of the average distance between the neighboring junctions of polypeptoid molecules.

We studied the effect of salt addition on a diblock copolymer system with a negative Flory-Huggins interaction parameter, χ, indicative of attractive interactions between the two blocks. The system studied is poly(ethylene oxide)-block-poly(methyl methacrylate) (PEO-PMMA) with added lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt. We studied two asymmetric block copolymers, PEO-PMMA(10-33) and PEO-PMMA(10-64), where the numbers refer to the molar masses of the blocks in kg mol-1. The small-angle X-ray scattering (SAXS) profiles for PEO-PMMA(10-33) were featureless at all salt concentrations. In contrast, PEO-PMMA(10-64) exhibited SAXS peaks when the salt concentration was between 0.22 ≤ m (mol Li/kg polymer) ≤ 0.44. The appearance of SAXS peaks only in PEO-PMMA(10-64) is consistent with the predictions of ionic self-consistent field theory developed by de la Cruz and co-workers, which predicts that in systems with negative χ, ordered phases are only found when the volume fraction of the ionic block is about 10%.