Thermodynamics of Block Copolymers with and without Salt

Poly(ethylene oxide)- and Polyzwitterion-Based Thermoplastic Elastomers for Solid Electrolytes

In this article, ABA triblock copolymer (tri-BCP) thermoplastic elastomers with poly(ethylene oxide) (PEO) middle block and polyzwitterionic poly(4-vinylpyridine) propane-1-sulfonate (PVPS) outer blocks were synthesized. The PVPS-b-PEO-b-PVPS tri-BCPs were doped with lithium bis-(trifluoromethane-sulfonyl) imide (LiTFSI) and used as solid polyelectrolytes (SPEs). The thermal properties and microphase separation behavior of the tri-BCP/LiTFSI hybrids were studied. Small-angle X-ray scattering (SAXS) results revealed that all tri-BCPs formed asymmetric lamellar structures in the range of PVPS volume fractions from 12.9% to 26.1%. The microphase separation strength was enhanced with increasing the PVPS fraction (fPVPS) but was weakened as the doping ratio increased, which affected the thermal properties of the hybrids, such as melting temperature and glass transition temperature, to some extent. As compared with the PEO/LiTFSI hybrids, the PVPS-b-PEO-b-PVPS/LiTFSI hybrids could achieve both higher modulus and higher ionic conductivity, which were attributed to the physical crosslinking and the assistance in dissociation of Li+ ions by the PVPS blocks, respectively. On the basis of excellent electrical and mechanical performances, the PVPS-b-PEO-b-PVPS/LiTFSI hybrids can potentially be used as solid electrolytes in lithium-ion batteries.

Solvent-Tailored Reversible Self-Assembly: Unveiling Ionic Transport Nanochannels in Block Copolymer Composite Electrolytes

Block copolymer composite electrolytes have gained extensive attention for their promising performance in ionic conductivity and mechanical properties, making them valuable for future technologies. The control of the ionic conductivity through the self-assembly of block copolymers, however, remains a great challenge, especially in confined environments. In this study, we prepare block copolymer composite electrolytes using polystyrene-block-poly(ethylene oxide) (PS-b-PEO, SEO) as the polymer matrix and anodic aluminum oxide (AAO) templates as the ceramic skeleton. The self-assembly of SEO creates nanoscale ion transport pathways in the PEO regions through ionic interactions with lithium salts. The nanopores of the AAO templates provide a confined environment for complex phase separation of SEO controlled by selective solvent vapor annealing. Our findings demonstrate that transforming self-assembled SEO structures allows for precise control of ion transport pathways with cylindrical structures exhibiting 20 times higher ionic conductivities than those of helical structures. For AAO templates with pore diameters of 20 nm (SEO-LiTFSI@AAO-20), the ionic conductivities are approximately 410 times higher than those with pore diameters of 200 nm (SEO-LiTFSI@AAO-200), owing to the larger specific surface areas within the smaller nanopores. Utilizing the self-assembly of SEO not only enables the construction of vertically aligned ion transport channels on various scales but also offers a fascinating approach to tailor the conductive capabilities of composite electrolytes, enhancing the ion transport efficiency and allowing for the flexible design of block copolymer composite electrolytes.

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.

Double Gyroid Morphologies in Precise Ion-Containing Multiblock Copolymers Synthesized via Step-Growth Polymerization

The double gyroid structure was first reported in diblock copolymers about 30 years ago, and the complexity of this morphology relative to the other ordered morphologies in block copolymers continues to fascinate the soft matter community. The double gyroid microphase-separated morphology has co-continuous domains of both species, and the minority phase is subdivided into two interpenetrating network structures. In addition to diblock copolymers, this structure has been reported in similar systems including diblock copolymers blended with one or two homopolymers and ABA-type triblock copolymers. Given the narrow composition region over which the double gyroid structure is typically observed (∼3 vol %), anionic polymerization has dominated the synthesis of block copolymers to control their composition and molecular weight. This perspective will highlight recent studies that (1) employ an alternative polymerization method to make block copolymers and (2) report double gyroid structures with lattice parameters below 10 nm. Specifically, step-growth polymerization linked precise polyethylene blocks and short sulfonate-containing blocks to form strictly alternating multiblock copolymers, and these copolymers produce the double gyroid structure over a dramatically wider composition range (>14 vol %). These new (AB) _n multiblock copolymers self-assemble into the double gyroid structure by having exceptional control over the polymer architecture and large interaction parameters between the blocks. This perspective proposes criteria for a broader and synthetically more accessible range of polymers that self-assemble into double gyroids and other ordered structures, so that these remarkable structures can be employed to solve a variety of technological challenges.

Effects of Local Order Parameter Dependent Transport Coefficient in Diblock Copolymers Under Applied Electric Fields

We present an approach for constructing thermodynamically consistent time-dependent models relevant to thin films of diblock copolymers in applied electric fields. The approach is based on the principles of linear irreversible thermodynamics and in this work, it is applied to study the effects of electric  fields on thin  films of incompressible diblock copolymers. Enforcement of local incompressibility constraint at all times leads to a local order parameter dependent transport coefficient in the model for the diblock copolymers. The dependence of transport coefficient on the local order parameter is used to relate it with diffusion constant of Rouse chains and leads to sensitivity of the model to initial conditions. Also, transient behavior is found to be a affected when compared with an ad hoc model assuming a constant transport coefficient. Numerical results such as electric  field induced alignment of lamellae domains due to the  field are found to be in qualitative agreements with experiments.This approach opens up a systematic way of developing kinetic models for simulating effects of electrolytes added to thin  films containing diblock copolymers in the presence of applied electric  fields.

para-Fluoro/thiol click chemistry-driven pentafluorostyrene-based block copolymer self-assembly: to mimic or not to mimic the solubility parameter?

This investigation reports the controlled transition from disordered/nano-segregated poly(styrene-b-pentafluorostyrene) (PS-b-PPFS)-based block copolymers after a subsequent para-fluoro/thiol click reaction with different functional thiol agents.

Nanostructured Block Polymer Electrolytes: Tailoring Self-Assembly to Unlock the Potential in Lithium-Ion Batteries

ConspectusIon-containing solid block polymer (BP) electrolytes can self-assemble into microphase-separated domains to facilitate the independent optimization of ion conduction and mechanical stability; this assembly behavior has the potential to improve the functionality and safety of lithium-ion batteries over liquid electrolytes to meet future demands (e.g., large capacities and long lifetimes) in various applications. However, significant enhancements in the ionic conductivity and processability of BPs must be realized for BP-based electrolytes to become robust alternatives in commercial devices. Toward this end, the controlled modification of BP electrolytes' intra-domain (nanometer-scale) and multi-grain (micrometer-scale) structure is one viable approach; intra-domain ion transport and segmental compatibility (related to the effective Flory-Huggins parameter, χ_eff) can be increased by tuning the ion and monomer-segment distributions, and the morphology can be selected such that the multi-grain transport is less sensitive to grain size and orientation.To highlight the characteristics of intra-domain structure that promote efficient ion transport, this Account begins by describing the relationship between BP thermodynamics (namely, χ_eff and the statistical segment length, b, which is indicative of chain stiffness) and local ion concentration. These thermodynamic insights are vital because they inform the selection of synthesis and formulation variables, such as polymer and ion chemistry, polymer molecular weight and composition, and ion concentration, which boost electrolyte performance. In addition to its relationship with local ion transport, χ_eff is also an important factor with respect to electrolyte processability. For example, a reduced χ_eff can allow BP electrolytes to be processed at lower temperatures (i.e., lower energy input), with less solvent (i.e., reduced waste), and/or for shorter times (i.e., higher throughput) yet still form desired nanostructures. This Account also examines the impact of electrolyte preparation and processing on the ion transport across nanostructured grains because of grain size and orientation. As morphologies with a 3D-connected versus 2D-connected conducting phase show different sensitivities to conductivity losses that can occur because of the fabrication methods, it is necessary to account for electrolyte processing effects when probing ion transport.The intra-domain and micrometer-scale structure also can be tuned using either tapered BPs (macromolecules with modified monomer-segment composition profiles between two homogeneous blocks) or blends of BPs and homopolymers, independent of the BP molecular weight and composition, as detailed herein. The application of TBPs or BP/HP blends as ion-conducting materials leads to improved ion transport, reduced χ_eff, and greater availability of morphologies with 3D connectivity relative to traditional (non-tapered and unblended) BP electrolytes. This feature results from the fact that ion transport is related more closely to the monomer-segment distributions within a domain than the overall nanoscale morphology or average polymer/ion mobilities. Taken together, this Account describes how ion transport and processability are influenced by BP architecture and nanostructural features, and it provides avenues to tune nanoassemblies that can contribute to improved lithium-ion battery technologies to meet future demands.

Block copolymers as (single-ion conducting) lithium battery electrolytes

Solid-state batteries are considered the next big step towards the realization of intrinsically safer high-energy lithium batteries for the steadily increasing implementation of this technology in electronic devices and particularly, electric vehicles. However, so far only electrolytes based on poly(ethylene oxide) have been successfully commercialized despite their limited stability towards oxidation and low ionic conductivity at room temperature. Block copolymer (BCP) electrolytes are believed to provide significant advantages thanks to their tailorable properties. Thus, research activities in this field have been continuously expanding in recent years with great progress to enhance their performance and deepen the understanding towards the interplay between their chemistry, structure, electrochemical properties, and charge transport mechanism. Herein, we review this progress with a specific focus on the block-copolymer nanostructure and ionic conductivity, the latest works, as well as the early studies that are fr"equently overlooked by researchers newly entering this field. Moreover, we discuss the impact of adding a lithium salt in comparison to single-ion conducting BCP electrolytes along with the encouraging features of these materials and the remaining challenges that are yet to be solved.

Sub-3-Nanometer Domain Spacings of Ultrahigh-χ Multiblock Copolymers with Pendant Ionic Groups

We investigated the temperature-dependent phase behavior and interaction parameter of polyethylene-based multiblock copolymers with pendant ionic groups. These step-growth polymers contain short polyester blocks with a single Li⁺SO₃^- group strictly alternating with polyethylene blocks of x-carbons (PESxLi, x = 12, 18, 23). At room temperature, these polymers exhibit layered morphologies with semicrystalline polyethylene blocks. Upon heating above the melting point (∼130 °C), PES18Li shows two order-to-order transitions involving Ia3̅d gyroid and hexagonal morphologies. For PES12Li, an order-to-disorder transition accompanies the melting of the polyethylene blocks. Notably, a Flory-Huggins interaction parameter was determined from the disordered morphologies of PES12Li using mean-field theory: χ(T) = 77.4/T + 2.95 (T in Kelvin) and χ(25 °C) ≈ 3.21. This ultrahigh χ indicates that the polar ionic and nonpolar polyethylene segments are highly incompatible and affords well-ordered morphologies even when the combined length of the alternating blocks is just 18-29 backbone atoms. This combination of ultrahigh χ and short multiblocks produces sub-3-nm domain spacings that facilitate the control of block copolymer self-assembly for various fields of study, including nanopatterning.

Influence of Charge Fraction on the Phase Behavior of Symmetric Single-Ion Conducting Diblock Copolymers

A series of symmetric poly[(oligo(ethylene glycol) methyl ether methacrylate-co-oligo(ethylene glycol) propyl sodium sulfonate methacrylate)]-block-polystyrene (PsOEGMA-PS) diblock copolymers were synthesized as a model system to probe the effect of charge fraction on the phase behavior of charged-neutral single-ion conducting diblock copolymers. Small-angle X-ray scattering (SAXS) experiments showed that increasing the charge fraction does not alter the ordered phase morphology (lamellar) but increases the order-disorder transition temperature (T_ODT) significantly. Additionally, the effective Flory-Huggins interaction parameter (χ_eff) was found to increase linearly with the charge fraction, similar to the case of conventional salt-doped diblock copolymers. This indicates that the effect of counterion solvation, attributed to the significant mismatch between the dielectric constant of each block, provides the dominant effect in tuning the phase behavior of this charged diblock copolymer. We therefore infer that electrostatic cohesion (local charge ordering induced by Coulombic interactions), which is predicted to suppress microphase separation and lead to asymmetric phase diagrams, only plays a minor role in this model system.

Enhancing ion transport in charged block copolymers by stabilizing low symmetry morphology: Electrostatic control of interfaces

Recently, the interest in charged polymers has been rapidly growing due to their uses in energy storage and transfer devices. Yet, polymer electrolyte-based devices are not on the immediate horizon because of the low ionic conductivity. In the present study, we developed a methodology to enhance the ionic conductivity of charged block copolymers comprising ionic liquids through the electrostatic control of the interfacial layers. Unprecedented reentrant phase transitions between lamellar and A15 structures were seen, which cannot be explained by well-established thermodynamic factors. X-ray scattering experiments and molecular dynamics simulations revealed the formation of fascinating, thin ionic shell layers composed of ionic complexes. The ionic liquid cations of these complexes predominantly presented near the micellar interfaces if they had strong binding affinity with the charged polymer chains. Therefore, the interfacial properties and concentration fluctuations of the A15 structures were crucially dependent on the type of tethered acid groups in the polymers. Overall, the stabilization energies of the A15 structures were greater when enriched, attractive electrostatic interactions were present at the micellar interfaces. Contrary to the conventional wisdom that block copolymer interfaces act as "dead zone" to significantly deteriorate ion transport, this study establishes a prospective avenue for advanced polymer electrolyte having tailor-made interfaces.

Weakening of Solvation-Induced Ordering by Composition Fluctuation in Salt-Doped Block Polymers

The spontaneous ordering of block polymers doped with ions is affected by both selective solvation and long-range Coulombic interaction. The mean-field treatment was recently shown to overestimate the solvation-induced ordering, requiring a large solvation radius to fit experimental phase diagrams, which may be relieved by including composition fluctuations. Treating the composition fluctuations in such systems is challenging because of the need of resolving heterogeneous dielectric profile that couples with the ordering itself. Starting from a minimal model, we develop a Landau-Brazovskiĭ expansion for the free energy of salt-doped block polymer near the ordering transition. It is found that the wavelength for typical composition fluctuations first decreases with salt doping, due to Coulombic interaction, then increases due to ionic solvation. Two mechanisms that weaken the solvation-enhanced ordering are identified: the Brazovskiĭ-type composition fluctuation that stabilizes disordered phase, and the coupling between mismatch in dispersion interaction and the dielectric permittivity through monomeric polarizability.

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.

Formation of a C15 Laves Phase with a Giant Unit Cell in Salt-Doped A/B/AB Ternary Polymer Blends

Salt-doped A/B/AB ternary polymer blends, wherein an AB copolymer acts as a surfactant to stabilize otherwise incompatible A and B homopolymers, display a wide range of nanostructured morphologies with significant tunability. Among these structures, a bicontinuous microemulsion (BμE) has been a notable target. Here, we report the surprising appearance of a robust C15 Laves phase, at compositions near where the BμE has recently been reported, in lithium bis(trifluoromethane) sulfonimide (LiTFSI)-doped low-molar-mass poly(ethylene oxide) (PEO)/polystyrene (PS)/symmetric PS-b-PEO block copolymer blends. The materials were analyzed by a combination of small-angle X-ray scattering (SAXS), ¹H NMR spectroscopy, and impedance spectroscopy. The C15 phase emerges at a high total homopolymer volume fraction ϕ_H = 0.8 with a salt composition r = 0.06 (Li⁺/[EO]) and persists as a coexisting phase across a large area of the isothermal phase diagram with high PS homopolymer compositions. Notably, the structure exhibits a huge unit cell size, a = 121 nm, with an unusually high micelle core volume fraction (f_core = 0.41) and an unusually low fraction of amphiphile (20%). This unit cell dimension is at least 50% larger than any previously reported C15 phase in soft matter, despite the low molar masses used, unlocking the possibility of copolymer-based photonic crystals without compromising processability. The nanostructured phase evolution from lamellar to hexagonal to C15 along the EO60 isopleth (ϕ_{PEO,homo-LiTFSI}/ϕ_H = 0.6) is rationalized as a consequence of asymmetry in the homopolymer solubility limit for each block, which leads to exclusion of PS homopolymer from the PS-b-PEO brush prior to exclusion of the PEO homopolymer, driving increased interfacial curvature and favoring the emergence of the C15 Laves phase.

Intrinsic Ion Transport Properties of Block Copolymer Electrolytes

Knowledge of intrinsic properties is of central importance for materials design and assessing suitability for specific applications. Self-assembling block copolymer electrolytes (BCEs) are of great interest for applications in solid-state energy storage devices. A fundamental understanding of ion transport properties, however, is hindered by the difficulty in deconvoluting extrinsic factors, such as defects, from intrinsic factors, such as the presence of interfaces between the domains. Here, we quantify the intrinsic ion transport properties of a model BCE system consisting of poly(styrene-block-ethylene oxide) (SEO) and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt using a generalizable strategy of depositing thin films on interdigitated electrodes and self-assembling fully connected parallel lamellar structures throughout the films. Comparison between conductivity in homopolymer poly(ethylene oxide) (PEO)-LiTFSI electrolytes and the analogous conducting material in SEO over a range of salt concentrations (r, molar ratio of lithium ion to ethylene oxide repeat units) and temperatures reveals that between 20% and 50% of the PEO in SEO is inactive. Using mean-field theory calculations of the domain structure and monomer concentration profiles at domain interfaces-both of which vary substantially with salt concentration-the fraction of inactive PEO in the SEO, as derived from conductivity measurements, can be quantitatively reconciled with the fraction of PEO that is mixed with greater than a few volume percent of polystyrene. Despite the detrimental interfacial effects for ion transport in BCEs, the intrinsic conductivity of the SEO studied here (ca. 10^-3 S/cm at 90 °C, r = 0.085) is an order of magnitude higher than reported values from bulk samples of similar molecular weight SEO (ca. 10^-4 S/cm at 90 °C, r = 0.085). Overall, this work provides motivation and methods for pursuing improved BCE chemical design, interfacial engineering, and processing.

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.

The Influence of Additives on the Interfacial Width and Line Edge Roughness in Block Copolymer Lithography

The challenges of patterning next generation integrated circuits have driven the semiconductor industry to look outside of traditional lithographic methods in order to continue cost effective size scaling. The directed self-assembly (DSA) of block copolymers (BCPs) is a nanofabrication technique used to reduce the periodicity of patterns prepared with traditional optical methods. BCPs with large interaction parameters (χ eff), provide access to smaller pitches and reduced interface widths. Larger χ eff is also expected to be correlated with reduced line edge roughness (LER), a critical performance parameter in integrated circuits. One approach to increasing χ eff is blending the BCP with a phase selective additive, such as an Ionic liquid (IL). The IL does not impact the etching rates of either phase, and this enables a direct interrogation of whether the change in interface width driven by higher χ eff translates into lower LER. The effect of the IL on the layer thickness and interface width of a BCP are examined, along with the corresponding changes in LER in a DSA patterned sample. The results demonstrate that increased χ eff through additive blending will not necessarily translate to a lower LER, clarifying an important design criterion for future material systems.