Thermodynamics of Ion-Containing Polymer Blends and Block Copolymers

We develop a theory for the thermodynamics of ion-containing polymer blends and diblock copolymers, taking polyethylene oxide (PEO), polystyrene and lithium salts as an example. We account for the tight binding of Li^+ ions to the PEO, the preferential solvation energy of anions in the PEO domain, the translational entropy of anions, and the ion-pair equilibrium between EO-complexed Li^+ and anion. Our theory is able to predict many features observed in experiments, particularly the systematic dependence in the effective χ parameter on the size of the anions. Furthermore, comparison with the observed linear dependence in the effective χ on salt concentration yields an upper limit for the binding constant of the ion pair

Thermodynamic Properties of Block Copolymer Electrolytes Containing Imidazolium and Lithium Salts

We report on the thermal properties, phase behavior, and thermodynamics of a series of polystyrene-block-poly(ethylene oxide) copolymers (SEO) mixed with the ionic species Li[N(SO_(2)CF_3)_2] (LiTFSI), imidazolium TFSI (ImTFSI), and an equimolar mixture of LiTFSI and ImTFSI (Mix). Differential scanning calorimetric scans reveal similar thermal behavior of SEO/LiTFSI and SEO/ImTFSI at the same salt concentrations. Phase behavior and thermodynamics were determined using a combination of small-angle X-ray scattering and birefringence. The thermodynamics of our mixtures can be mapped on to the theory of neat block copolymer phase behavior provided the Flory−Huggins interaction parameter, χ, between the blocks is replaced by an effective χ (χ_(eff)) that increases linearly with salt concentration. The phase behavior and the value of m, the slope of the χ_(eff) versus salt concentration data, were similar for SEO/LiTFSI, SEO/ImTFSI, and SEO/Mix blends. The theory developed by Wang [ J. Phys. Chem. B. 2008, 41, 16205] provides a basis for understanding the fundamental underpinnings of the measured value of m. We compare our experimental results with the predictions of this theory with no adjustable parameters

Measurement of Three Transport Coefficients and the Thermodynamic Factor in Block Copolymer Electrolytes with Different Morphologies.

The design and engineering of composite materials is one strategy to satisfy the materials needs of systems with multiple orthogonal property requirements. In the case of rechargeable batteries with lithium metal anodes, the system requires a separator with fast lithium ion transport and good mechanical strength. In this work, we focus on the system polystyrene-block-poly(ethylene oxide) (SEO) with bis(trifluoromethane)sulfonimide lithium salt (LiTFSI). Ion transport occurs in the salt-containing poly(ethylene oxide)-rich domains. Mechanical rigidity arises due to the glassy nature of polystyrene (PS). If we assume that the salt does not interact with the PS-rich domains, we can describe ion transport in the electrolyte by three transport parameters (ionic conductivity, κ, salt diffusion coefficient, D, and cation transference number, t+0) and a thermodynamic factor, Tf. By systematically varying the volume fraction of the conducting phase, ϕc between 0.29 and 1.0, and chain length, N between 80 and 8000, we elucidate the role of morphology on ion transport. We find that κ is the strongest function of morphology, varying by three full orders of magnitude, while D is a weaker function of morphology. To calculate t+0 and Tf, we measure the current fraction, ρ+, and the open circuit potential, U, of concentration cells. We find that ρ+ and U follow universal trends as a function of salt concentration, regardless of chain length, morphology, or ϕc, allowing us to calculate t+0 for any SEO/LiTFSI or PEO/LiTFSI mixture when κ and D are known. The framework developed in this paper enables predicting the performance of any block copolymer electrolyte in a rechargeable battery

Toward Establishing Uniqueness of Experimentally Determined Transference Numbers

The passage of current through a battery results in the development of concentration gradients in the electrolytic phase. For a fully characterized binary electrolyte, where the conductivity, salt diffusion coefficient, cation transference number, and the thermodynamic factor are known, concentration and potential gradients in the electrolytic phase can be modeled using Newman’s concentrated solution theory. We report two methods for measuring the transference number: the standard method based on electrochemical measurements ( t + , echem 0 ) and electrophoretic NMR ( t + , eNMR 0 ). The electrochemical approach requires combining measurements from multiple experiments; the equations used to determine the cation transference number and the thermodynamic factor are coupled, nonlinear algebraic equations. In the electrophoretic-NMR-based approach, however, the equations used to determine the cation transference number and the thermodynamic factor are decoupled. We find for a liquid electrolyte comprised of a lithium salt dissolved in tetraglyme, the values of the transference numbers obtained by these two methods are distinct. For example, at 30 °C, t + , echem 0 = −1.02 ± 1.11 and t + , eNMR 0 = 0.25 ± 0.04. The corresponding thermodynamic factors are also different. While the magnitude of the predicted concentration gradients based on the two sets of parameters are different, the predicted current-voltage relationships are similar

Phase Behavior of a Block Copolymer/Salt Mixture through the Order-to-Disorder Transition

Mixtures of block copolymers and lithium salts are promising candidates for lithium battery electrolytes. Structural changes that occur during the order-to-disorder transition (ODT) in a diblock copolymer/salt mixture were characterized by small-angle X-ray scattering (SAXS). In salt-free block copolymers, the ODT is sharp, and the domain size of the ordered phase decreases with increasing temperature. In contrast, the ODT of the diblock copolymer/salt mixture examined here occurs gradually over an 11 °C temperature window, and the domain size of the ordered phase is a nonmonotonic function of temperature. We present an approach to estimate the fraction of the ordered phase in the 11 °C window where ordered and disordered phases coexist. The domain spacing of the ordered phase increases with increasing temperature in the coexistence window. Both findings are consistent with the selective partitioning of salt into the ordered domains, as predicted by Nakamura et al. ( ACS Macro Lett. 2013, 2, 478−481)

Universal Relationship between Conductivity and Solvation-Site Connectivity in Ether-Based Polymer Electrolytes

We perform a joint experimental and computational study of ion transport properties in a systematic set of linear polyethers synthesized via acyclic diene metathesis (ADMET) polymerization. We measure ionic conductivity, σ, and glass transition temperature, T_g, in mixtures of polymer and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt. While T_g is known to be an important factor in the ionic conductivity of polymer electrolytes, recent work indicates that the number and proximity of lithium ion solvation sites in the polymer also play an important role, but this effect has yet to be systematically investigated. Here, adding aliphatic linkers to a poly(ethylene oxide) (PEO) backbone lowers T_g and dilutes the polar groups; both factors influence ionic conductivity. To isolate these effects, we introduce a two-step normalization scheme. In the first step, Vogel–Tammann–Fulcher (VTF) fits are used to calculate a temperature-dependent reduced conductivity, σ_r(T), which is defined as the conductivity of the electrolyte at a fixed value of T – T_g. In the second step, we compute a nondimensional parameter f_(exp), defined as the ratio of the reduced molar conductivity of the electrolyte of interest to that of a reference polymer (PEO) at a fixed salt concentration. We find that f_(exp) depends only on oxygen mole fraction, x_0, and is to a good approximation independent of temperature and salt concentration. Molecular dynamics simulations are performed on neat polymers to quantify the occurrences of motifs that are similar to those obtained in the vicinity of isolated lithium ions. We show that f_(exp) is a linear function of the simulation-derived metric of connectivity between solvation sites. From the relationship between σ_r and f_(exp) we derive a universal equation that can be used to predict the conductivity of ether-based polymer electrolytes at any salt concentration and temperature

Atomic-scale cryogenic electron microscopy imaging of self-assembled peptoid nanostructures

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.

Relationship between molecular structure and corrugations in self-assembled polypeptoid nanosheets revealed by cryogenic electron microscopy

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

Understanding the Conductivity and Transference Trade-Off in Polymer Electrolytes Using a Robeson-Inspired Upper Bound

The development of high-performance electrolytes is crucial for advancing next-generation lithium and sodium battery technologies. Since the cation is the working ion in both technologies, electrolytes exhibiting the rapid cation transport are essential for making progress. Pathways to optimize electrolytes are unclear due to the inherent trade-off between conductivity and cation transference. While this trade-off is sometimes recognized, there are no well-accepted methodologies for quantifying it. Inspired by the Robeson upper bound for the permeability-selectivity trade-off in gas separation membranes, we propose an approach for quantifying the trade-off in electrolytes using Newman’s concentrated solution theory. We suggest calling this the Newman upper bound. By analyzing published data from 30 polymer electrolytes containing univalent lithium and sodium salts, the Newman upper bound is expressed as κ = 2.0(1/ρ+ - 1) where κ (mS/cm) is conductivity and ρ+ is the current fraction measured in a symmetric cell as first described by Bruce et al. [J. Electroanal. Chem. Interfacial Electrochem. 1987, 225 (1), 1-17]. This formulation of the upper bound introduces a critical guiding metric for designing next-generation polymer electrolytes; it highlights factors underlying the trade-off, including the salt diffusion coefficient (D), cation transference number relative to solvent velocity ((Formula presented)), and thermodynamic factor (1 + (d lnγ+-)/(d lnm)), where γ+- is the mean molar activity coefficient and m is the molality. These parameters have been measured for very few electrolytes. We posit that establishing the molecular properties that govern these parameters will lead to improved electrolytes that greatly exceed the current upper bound

Exponential vs Gaussian Correlation Functions in the Characterization of Block Copolymer Grain Structure by Depolarized Light Scattering.

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