A15, σ, and a Quasicrystal: Access to Complex Particle Packings via Bidisperse Diblock Copolymer Blends

Stabilizing hexagonally close-packed phase in single-component block copolymers through rational symmetry breaking

Despite being predicted to be a thermodynamically equilibrium structure, the absence of direct experimental evidence of hexagonally close-packed spherical phase in single-component block copolymers raises uncomfortable concerns regarding the existing fundamental phase principles. This work presents a robust approach to regulate the phase behavior of linear block copolymers by deliberately breaking molecular symmetry, and the hexagonally close-packed lattice is captured in a rigorous single-component system. A collection of discrete A1BA2 triblock copolymers is designed and prepared through an iterative growth method. The precise chemical composition and uniform chain length eliminates inherent size distribution and other molecular defects. Simply by tuning the relative chain length of two end A blocks, a rich array of ordered nanostructures, including Frank-Kasper A15 and σ phases, are fabricated without changing the overall chemistry or composition. More interestingly, hexagonally close-packed spherical phase becomes thermodynamically stable and experimentally accessible attributed to the synergistic contribution of the two end blocks. The shorter A blocks are pulled out from the core domain into the matrix to release packing frustration, while the longer ones stabilize the ordered spherical phase against composition fluctuation that tends to disrupt the lattice. This study adds a missing puzzle piece to the block copolymer phase diagram and provides a robust approach for rational structural engineering.

Frank-Kasper phases in charge transfer complexes enable tunable photoelectronic properties

Understanding how particles pack in space and the mechanisms underlying symmetry selection across soft matter is challenging. The Frank-Kasper (F-K) phase of complex spherical packing is amongst the most fascinating phases; however, it has not been observed in discotic liquid crystals until now. Herein, we report the first observation of F-K phases of charge transfer complexes (CTCs) obtained from triphenylene derivatives as donors and 2,4,7-trinitro-9-fluorenone as the acceptor. The CTCs were characterized using experimental and theoretical calculations, indicating that the F-K A15 cubic lattice possesses a unit cell containing 8 sphere-like supramolecules, each of which was self-assembled from 3 CTC complexes. The lattice constant was only 3.2 nm, which is by far the smallest for the A15 phase. Interestingly, the supramolecular assembly can be regarded as the molecular column splitting into isolated spherical fragments, impeding charge transfer and turning it into one insulator. This provides a simple and effective method for preparing asymmetric complex compounds for the design of unconventional self-assembled nanostructures.

Particle Dynamics in a Diblock-Copolymer-Based Dodecagonal Quasicrystal and Its Periodic Approximant by X-Ray Photon Correlation Spectroscopy

Temperature-dependent x-ray photon correlation spectroscopy (XPCS) measurements are reported for a binary diblock-copolymer blend that self-assembles into an aperiodic dodecagonal quasicrystal and a periodic Frank-Kasper σ phase approximant. The measured structural relaxation times are Bragg scattering wavevector independent and are 5 times faster in the dodecagonal quasicrystal than the σ phase, with minimal temperature dependence. The underlying dynamical relaxations are ascribed to differences in particle motion at the grain boundaries within each of these tetrahedrally close-packed assemblies. These results identify unprecedented particle dynamics measurements of tetrahedrally coordinated micellar block polymers, thus expanding the application of XPCS to ordered soft materials.

High-Density Packing of Spherical Microdomains from A(AB3)3 Dendron-like Miktoarm Star Copolymer

An A(AB3)3 dendron-like miktoarm star copolymer consisting of polystyrene (PS, A) and poly(2-vinylpyridine) (P2VP, B) was synthesized using a series of anionic polymerization, atom-transfer radical polymerization (ATRP), and click reaction. The morphology of A(AB3)3 changed greatly depending on the volume fraction of A and the chain asymmetry. Interestingly, a body-centered cubic spherical phase was found even at fA = 0.51 because the chain architecture of A(AB3)3 stabilizes the large interfacial curvature toward A domains. On the other hand, when the length difference between the end and middle A blocks decreased, a hexagonally packed cylindrical phase was formed at fA = 0.50. This is attributed to the fact that the middle A chains are arranged in a more relaxed way, resulting in a milder interfacial curvature toward A domains. The experimental observations are well-consistent with the predictions based on self-consistent-field theory.

Phase Behavior of Binary Blends of Diblock Copolymers: Progress and Opportunities

The phase behavior of binary blends of diblock copolymers has been examined extensively in the past decades. Experimental and theoretical studies have demonstrated that mixing two different block copolymers provides an efficient and versatile route to regulate their self-assembled morphologies. A good understanding of the principles governing the self-assembly of block copolymer blends has been obtained from the study of A1B1/A2B2 diblock copolymer blends. The second (A2B2) diblocks could act synergistically as fillers and cosurfactants to regulate the domain size and interfacial properties, resulting in the formation of ordered phases not found in the parent (A1B1 or A2B2) diblock copolymer melts. The study of A1B1/A2B2 block copolymer blends further provides a solid foundation for future research on more complex block copolymer blends.

Non-Equilibrium Block Copolymer Self-Assembly Based Porous Membrane Formation Processes Employing Multicomponent Systems

Porous polymer-derived membranes are useful for applications ranging from filtration and separation technologies to energy storage and conversion. Combining block copolymer (BCP) self-assembly with the industrially scalable, non-equilibrium phase inversion technique (SNIPS) yields membranes comprising periodically ordered top surface structures supported by asymmetric, hierarchical substructures that together overcome performance tradeoffs typically faced by materials derived from equilibrium approaches. This review first reports on recent advances in understanding the top surface structural evolution of a model SNIPS-derived system during standard membrane formation. Subsequently, the application of SNIPS to multicomponent systems is described, enabling pore size modulation, chemical modification, and transformation to non-polymeric materials classes without compromising the structural features that define SNIPS membranes. Perspectives on future directions of both single-component and multicomponent membrane materials are provided. This points to a rich and fertile ground for the study of fundamental as well as applied problems using non-equilibrium-derived asymmetric porous materials with tunable chemistry, composition, and structure.

Autonomous discovery of emergent morphologies in directed self-assembly of block copolymer blends

The directed self-assembly (DSA) of block copolymers (BCPs) is a powerful approach to fabricate complex nanostructure arrays, but finding morphologies that emerge with changes in polymer architecture, composition, or assembly constraints remains daunting because of the increased dimensionality of the DSA design space. Here, we demonstrate machine-guided discovery of emergent morphologies from a cylinder/lamellae BCP blend directed by a chemical grating template, conducted without direct human intervention on a synchrotron x-ray scattering beamline. This approach maps the morphology-template phase space in a fraction of the time required by manual characterization and highlights regions deserving more detailed investigation. These studies reveal localized, template-directed partitioning of coexisting lamella- and cylinder-like subdomains at the template period length scale, manifesting as previously unknown morphologies such as aligned alternating subdomains, bilayers, or a "ladder" morphology. This work underscores the pivotal role that autonomous characterization can play in advancing the paradigm of DSA.

Local Chain Feature Mandated Self-Assembly of Block Copolymers

This work demonstrates an effective and robust approach to regulate phase behaviors of a block copolymer by programming local features into otherwise homogeneous linear chains. A library of sequence-defined, isomeric block copolymers with globally the same composition but locally different side chain patterns were elaborately designed and prepared through an iterative convergent growth method. The precise chemical structure and uniform chain length rule out all inherent molecular defects associated with statistical distribution. The local features are found to exert surprisingly pronounced impacts on the self-assembly process, which have yet to be well recognized. While other molecular parameters remain essentially the same, simply rearranging a few methylene units among the alkyl side chains leads to strikingly different phase behaviors, bringing about (i) a rich diversity of nanostructures across hexagonally packed cylinders, Frank-Kasper A15 phase, Frank-Kasper σ phase, dodecagonal quasicrystals, and disordered state; (ii) a significant change of lattice dimension; and (iii) a substantial shift of order-to-disorder transition temperature (up to 40 °C). Different from the commonly observed enthalpy-dominated cases, the frustration due to the divergence between the native molecular geometry originating from side chain distribution and the local packing environment mandated by lattice symmetry is believed to play a pivotal role. Engineering the local chain feature introduces another level of structural complexity, opening up a new and effective pathway for modulating phase transition without changing the chemistry or composition.

Formation and fluctuation of two-dimensional dodecagonal quasicrystals

The self-assembly of two-dimensional dodecagonal quasicrystals (DDQCs) from patchy particles is investigated by Brownian dynamics simulations. The patchy particle has a five-fold rotational symmetry pattern described by the spherical harmonics Y₅₅. From the formation of the DDQC obtained by an annealing process, we find the following mechanism. The early stage of the dynamics is dominated by hexagonal structures. Then, nucleation of dodecagonal motifs appears by particle rearrangement, and finally the motifs span the whole system. The transition from the hexagonal structure into the dodecagonal motif is coincident with the collective motion of the particles. The DDQC consists of clusters of dodecagonal motifs, which can be classified into several packing structures. By the analyses of the DDQC under fixed temperature, we find that the fluctuations are characterised by changes in the network of the dodecagonal motifs. Finally we compare the DDQCs assembled from the patchy particle system and isotropic particle system. The two systems share a similar mechanism of the formation and fluctuation of DDQCs.

The Largest Quasicrystalline Tiling with Dodecagonal Symmetry from a Single Pentablock Quarterpolymer of the AB1CB2D Type

A quasicrystalline tiling pattern with tile size of ca. 60 nm has been discovered in the bulk state of a four-component pentablock polymer molecule of the AS₁IS₂P type, where A, S, I, and P denote poly(4-vinylbenzyldimethylamine), polystyrene, polyisoprene, and poly(2-vinylpyridine), respectively. The polymer samples used were prepared by anionic polymerizations and have narrow molecular weight distribution. The sample films were obtained by an extremely slow solvent-cast process from dilute solutions of tetrahydrofuran for 14 days. It has been found by TEM observation that the quarterpolymer, AS₁IS₂P-4 (M_n = 149 kg/mol, ϕ_A/ϕ_S1/ϕ_I/ϕ_S2/ϕ_P = 0.12/0.27/0.20/0.29/0.13), reveals two final stable structures, i.e., a 3.3.4.3.4 periodic tiling pattern as a minor component and a quasicrystalline (QC) tiling with dodecagonal symmetry as a major component, where the former includes a triangle/square number ratio of 2 and the latter has one of approximately 2.28, which is close enough to the ideal ratio, 4/ 3 ≑ 2.31, for the triangle/square random tiling of the dodecagonal QC tiling (DDQC). Two structures were also clearly proved by SAXS diffraction patterns. Here, it should be noted this QC structure having a tile side length of ca. 60 nm was created with a single block polymer molecule.

Expanding quasiperiodicity in soft matter: Supramolecular decagonal quasicrystals by binary giant molecule blends

The quasiperiodic structures in metal alloys have been known to depend on the existence of icosahedral order in the melt. Among different phases observed in intermetallics, decagonal quasicrystal (DQC) structures have been identified in many glass-forming alloys yet remain inaccessible in bulk-state condensed soft matters. Via annealing the mixture of two giant molecules, the binary system assemblies into an axial DQC superlattice, which is identified comprehensively with meso-atomic accuracy. Analysis indicates that the DQC superlattice is composed of mesoatoms with an unusually broad volume distribution. The interplays of submesoatomic (molecular) and mesoatomic (supramolecular) local packings are found to play a crucial role in not only the formation of the metastable DQC superlattice but also its transition to dodecagonal quasicrystal and Frank-Kasper σ superlattices.

Superlattice Engineering with Chemically Precise Molecular Building Blocks

Correlating nanoscale building blocks with mesoscale superlattices, mimicking metal alloys, a rational engineering strategy becomes critical to generate designed periodicity with emergent properties. For molecule-based superlattices, nevertheless, nonrigid molecular features and multistep self-assembly make the molecule-to-superlattice correlation less straightforward. In addition, single component systems possess intrinsically limited volume asymmetry of self-assembled spherical motifs (also known as "mesoatoms"), further hampering novel superlattices' emergence. In the current work, we demonstrate that properly designed molecular systems could generate a spectrum of unconventional superlattices. Four categories of giant molecules are presented. We systematically explore the lattice-forming principles in unary and binary systems, unveiling how molecular stoichiometry, topology, and size differences impact the mesoatoms and further toward their superlattices. The presence of novel superlattices helps to correlate with Frank-Kasper phases previously discovered in soft matter. We envision the present work offers new insights about how complex superlattices could be rationally fabricated by scalable-preparation and easy-to-process materials.

Transition pathways connecting crystals and quasicrystals

Due to structural incommensurability, the emergence of a quasicrystal from a crystalline phase represents a challenge to computational physics. Here, the nucleation of quasicrystals is investigated by using an efficient computational method applied to a Landau free-energy functional. Specifically, transition pathways connecting different local minima of the Lifshitz-Petrich model are obtained by using the high-index saddle dynamics. Saddle points on these paths are identified as the critical nuclei of the 6-fold crystals and 12-fold quasicrystals. The results reveal that phase transitions between the crystalline and quasicrystalline phases could follow two possible pathways, corresponding to a one-stage phase transition and a two-stage phase transition involving a metastable lamellar quasicrystalline state, respectively.

Open-source platform for block polymer formulation design using particle swarm optimization

Facile exploration of large design spaces is critical to the development of new functional soft materials, including self-assembling block polymers, and computational inverse design methodologies are a promising route to initialize this task. We present here an open-source software package coupling particle swarm optimization (PSO) with an existing open-source self-consistent field theory (SCFT) software for the inverse design of self-assembling block polymers to target bulk morphologies. To lower the barrier to use of the software and facilitate exploration of novel design spaces, the underlying SCFT calculations are seeded with algorithmically generated initial fields for four typical morphologies: lamellae, network phases, cylindrical phases, and spherical phases. In addition to its utility within PSO, the initial guess tool also finds generic applicability for stand-alone SCFT calculations. The robustness of the software is demonstrated with two searches for classical phases in the conformationally symmetric diblock system, as well as one search for the Frank-Kasper [Formula: see text] phase in conformationally asymmetric diblocks. The source code for both the initial guess generation and the PSO wrapper is publicly available.

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.

Dodecagonal quasicrystals of oil-swollen ionic surfactant micelles

A delicate balance of noncovalent interactions directs the hierarchical self-assembly of molecular amphiphiles into spherical micelles that pack into three-dimensional periodic arrays, which mimic intermetallic crystals. Herein, we report the discovery that adding water to a mixture of an ionic surfactant and n-decane induces aperiodic ordering of oil-swollen spherical micelles into previously unrecognized, aqueous lyotropic dodecagonal quasicrystals (DDQCs), which exhibit local 12-fold rotational symmetry and no long-range translational order. The emergence of these DDQCs at the nexus of dynamically arrested micellar glasses and a periodic Frank-Kasper (FK) σ phase approximant sensitively depends on the mixing order of molecular constituents in the assembly process and on sample thermal history. Addition of n-decane to mixtures of surfactant and water instead leads only to periodic FK A15 and σ approximants with no evidence for aperiodic order, while extended ambient temperature annealing of the DDQC also reveals its transformation into a σ phase. Thus, these lyotropic DDQCs are long-lived metastable morphologies, which nucleate and grow from a stochastic distribution of micelle sizes formed by abrupt segregation of varied amounts of oil into surfactant micelles on hydration. These findings indicate that molecular building block complexity is not a prerequisite for the formation of aperiodic supramolecular order, while also establishing the generic nature of quasicrystalline states across metal alloys and self-assembled micellar materials.

Softness-driven complexity in supercrystals of gold nanoparticles

Many soft matter systems are composed of roughly spherical objects that can self-assemble in ordered structures. Unlike hard spheres, at high volume fraction these soft spheres adapt their shape to the local geometrical constraints and the question of space filling needs to be entirely revisited. Hydrophobically coated gold nanocrystals self-assemble in supercrystals and are good candidates to explore this question. When the soft coating is thin compared to the rigid core, a FCC structure is obtained, with a behaviour similar to that of hard spheres. In the opposite case, for a thick soft coating, a BCC structure is found instead. This paper focus on the intermediate region between these two classical structures. By varying the gold core radius R and the ligand fully extended length L, we establish a structure diagram based on a large experimental data set. The hexagonal Frank-Kasper C14 structure is observed for various values of R and L and can coexist with a FCC phase. Depending on the structure, values of the minimum thickness e of the ligand shell compared to L are different. These experimental results confirm that the C14 Frank-Kasper phase is a solution to the problem of filling the space with soft particles even with a rigid core and should help to establish pertinent models in order to predict the structures of the superlattices built by gold nanoparticles.

Reevaluation of Poly(ethylene-alt-propylene)-block-Polydimethylsiloxane Phase Behavior Uncovers Topological Close-Packing and Epitaxial Quasicrystal Growth

Reanalysis of an asymmetric poly(ethylene-alt-propylene)-block-polydimethylsiloxane (PEP-PDMS) diblock copolymer first investigated in 1999 has revealed a rich phase behavior including a dodecagonal quasicrystal (DDQC), a Frank-Kasper σ phase, and a body-centered cubic (BCC) packing at high temperature adjacent to the disordered state. On subjecting the sample to large amplitude oscillatory shear well below the σ-BCC order-order transition temperature (T_OOT), small-angle X-ray scattering evidenced the emergence of a twinned BCC phase that, on heating, underwent a phase transition to an unusually anisotropic DDQC state. Surprisingly, we observe no evidence of this apparent epitaxy on heating or cooling through the equilibrium σ-BCC transition. We rationalize these results in terms of a shear-induced order-order transition and an apparent BCC-DDQC epitaxy favored by micelle translation-mediated ordering dynamics far below T_OOT.

Frustration in block copolymer assemblies

Frustration is ubiquitous in condensed matter systems and it provides a central concept to understand the self-assembly of soft matter. Frustration is found at multiple scales in polymeric systems containing block copolymers. At the molecular scale, frustration arises because the chemically distinct blocks repel each other whereas the chain connectivity prevents a macroscopic separation. At the mesoscopic scale, frustration occurs due to the competition between the tendency for the block copolymer assemblies to maintain their native shape and the requirement to fill the space. At an even larger scale, frustrations could be induced by external fields or spatial confinement. Recent theoretical and experimental studies provide a good understanding of the origin of various frustrations in the self-assembly of block copolymers. Furthermore, it has been demonstrated that designed block copolymer systems, either in the form of multiblock copolymers with different architectures or block copolymer blends, could be utilized to regulate frustrations resulting in the formation of complex ordered and hierarchically structured phases.

Shear-Modulated Rates of Phase Transitions in Sphere-Forming Diblock Oligomer Lyotropic Liquid Crystals

Hydration of the amphiphilic diblock oligomer C₁₆H₃₃(CH₂CH₂O)₂₀OH (C₁₆E₂₀) leads to concentration-dependent formation of micellar body-centered cubic (BCC) and Frank-Kasper A15 lyotropic liquid crystals (LLCs). Quiescent thermal annealing of aqueous LLCs comprising 56-59 wt % C₁₆E₂₀ at 25 °C after quenching from high temperatures established their ability to form short-lived BCC phases, which transform into long-lived, transient Frank-Kasper σ phases en route to equilibrium A15 morphologies on a time scale of months. Here, the frequency and magnitude of applied oscillatory shear show the potential to either dynamically stabilize the metastable BCC phase at low frequencies or increase the rate of formation of the A15 to minutes at high frequencies. Time-resolved synchrotron small-angle X-ray scattering (TR-SAXS) provides in situ characterization of the structures during shear and thermal processing. This work shows that the LLC morphology and order-order phase transformation rates can be controlled by tuning the shear strain amplitude and frequency.

Frank-Kasper Phases Self-Assembled from a Linear A1B1A2B2 Tetrablock Copolymer

The Frank-Kasper (FK) phases self-assembled from block copolymer systems have attracted abiding interest. In this work, the formation mechanism of the complex FK phases from the self-assembly of simple A₁B₁A₂B₂ tetrablock copolymers is investigated using self-consistent field theory (SCFT). For a typical set of parameter spaces, we utilize SCFT to construct a number of phase diagrams. In these phase diagrams, the FK phases exhibit a notable stability region. The stable region of the FK phases reveals that the distribution of A₁ and A₂ blocks can be precisely regulated by tuning the ratio of the A₁/A₂ block, wherein the long A₁ blocks can aggregate within the "core" while the short A₂ blocks can form the "shell" of a spherical domain in the FK phases, respectively, to accommodate the sizes and shapes of the spherical domains in the complex spherical packing phases. Besides, we also demonstrate that the existence of the B₂ block plays a crucial factor to stabilize the FK phases.

High-throughput morphology mapping of self-assembling ternary polymer blends

Multicomponent blending is a convenient yet powerful approach to rationally control the material structure, morphology, and functional properties in solution-deposited films of block copolymers and other self-assembling nanomaterials. However, progress in understanding the structural and morphological dependencies on blend composition is hampered by the time and labor required to synthesize and characterize a large number of discrete samples. Here, we report a new method to systematically explore a wide composition space in ternary blends. Specifically, the blend composition space is divided into gradient segments deposited sequentially on a single wafer by a new gradient electrospray deposition tool, and characterized using high-throughput grazing-incidence small-angle X-ray scattering. This method is applied to the creation of a ternary morphology diagram for a cylinder-forming polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) block copolymer blended with PS and PMMA homopolymers. Using “wet brush” homopolymers of very low molecular weight (∼1 kg mol⁻¹), we identify well-demarcated composition regions comprising highly ordered cylinder, lamellae, and sphere morphologies, as well as a disordered phase at high homopolymer mass fractions. The exquisite granularity afforded by this approach also helps to uncover systematic dependencies among self-assembled morphology, topological grain size, and domain period as functions of homopolymer mass fraction and PS : PMMA ratio. These results highlight the significant advantages afforded by blending low molecular weight homopolymers for block copolymer self-assembly. Meanwhile, the high-throughput, combinatorial approach to investigating nanomaterial blends introduced here dramatically reduces the time required to explore complex process parameter spaces and is a natural complement to recent advances in autonomous X-ray characterization.

Compositionally graded electrospray deposition combined with grazing incidence small angle X-ray scattering forms a high-throughput approach for mapping phase behavior in ternary mixtures as demonstrated here using block copolymer blends.

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.

Impact of Architectural Asymmetry on Frank-Kasper Phase Formation in Block Polymer Melts

In recent decades, the discoveries of complex low-symmetry phases in soft matter have inspired advances in molecular and materials design. However, understanding the mechanisms underlying symmetry selection across soft matter remains an important challenge in materials science. Block polymers represent attractive model materials because they permit wide synthetic tunability and provide access to multiple length scales (1-100 nm). However, to date the block polymer design space has been largely limited to variations in molecular weight, block volume fraction, and conformational asymmetry. The molecular architecture-the way in which chains are connected-offers rich potential but remains relatively unexplored in experimental block polymers. Our work bridges this gap, connecting molecular architecture, space-filling demands, and symmetry selection in block polymer self-assembly. Three series of block polymers were synthesized by living polymerization, tuning the architectural asymmetry across the linear-b-linear and linear-b-bottlebrush limits. The bottlebrush architecture amplifies two key ingredients for the formation of Frank-Kasper phases: high conformational asymmetry and high self-concentration. Analysis by small-angle X-ray scattering provides insight into the impact of architectural asymmetry on block polymer self-assembly. Increasing the asymmetry between blocks opens the complex phase window, expanding opportunities to tune symmetry selection in block polymer melts.

Discrete Block Copolymers with Diverse Architectures: Resolving Complex Spherical Phases with One Monomer Resolution

This work describes the first rigorous example of a single-component block copolymer system forming unconventional spherical phases. A library of discrete block polymers with uniform chain length and diverse architectures were modularly prepared through a combination of a step-growth approach and highly efficient coupling reactions. The precise chemical structure eliminates all the molecular defects associated with molar weight, dispersity, and compositional ratio. Complex spherical phases, including the Frank-Kasper phase (A15 and σ) and quasicrystalline phase, were experimentally captured by meticulously tuning the composition and architectures. A phase portrait with unprecedented accuracy was mapped out (up to one monomer resolution), unraveling intriguing details of phase behaviors that have long been compromised by inherent molecular weight distribution. This study serves as a delicate model system to bridge the existing gaps between experimental observations and theoretical assessments and to provide insights into the formation and evolution of the unconventional spherical phases in soft matter systems.