Physical Review Materials

Supramolecular crystal phases of self-assembled soft matter share the symmetries of atomic and molecular crystals, but with vastly larger unit cells occupied by huge numbers of flexible molecules. Recent progress in understanding the formation of complex crystals of quasi-spherical soft matter domains derives from a mesoatomic analogy. In this analogy, the ultimate structure is broken down into micelle-like motifs, whose shape, size, and packing dictate thermodynamics. This begs a basic question for complex network phases, such as the double-gyroid: what are the mesoatomic “building blocks” of crystals with non-convex, polycontinuous, and inter-catenated domains? Here, the authors propose generic principles for divining the mesoatomic building blocks of network crystals and illustrate these principles for double-networks of diblock copolymers. They also propose and explore a minimal physical model for how mesoatomic shapes and packing can template a rich dynamics for the assembly and link formation of inter-catenating soft matter crystals.

The beautiful colors we observe in nature, such as butterfly wing scales, reveal how nature precisely controls the propagation of light by creating photonic crystals, such as the single gyroid network. Recreating these chiral networks in synthetic materials, especially self-assembled block polymers, offers great potential applications as next-generation optical devices. However, single gyroid is thermodynamically unfavorable in linear diblock copolymers owing to the molecular packing mechanisms. This study uses self-consistent field theory to elucidate the design principles for stabilizing single gyroid in a synthetically tractable block copolymer architecture.

The latest complex network phase to be discovered in diblock copolymer melts is the orthorhombic $Fddd$ phase. Mean-field theory predicts it to be stable, but only at weak segregations where ordered phases are typically destroyed by thermal fluctuations. Indeed, Landau-Brazovskii theory confirmed this expectation, raising the question of how $Fddd$ survives in experiments. However, this problem was recently resolved by accurate field-theoretic simulations, which found that $Fddd$ is simply more resilient to fluctuations than other ordered phases. Here, the authors find that this is also true for the family of (AB)${}_M$ starblock copolymer architectures. This resilience may very well extend to numerous other architectures, and thus it would be prudent to keep our eyes open for $Fddd$.

Unlocking the Frank-Kasper phase in block copolymers represents a significant breakthrough, shedding light on the fundamental principles governing versatile particle arrangements across various size scales. Nevertheless, achieving this intricate phase is a challenging task that demands precise control of factors such as molecular weight, molecular architecture, and conformational asymmetry. Furthermore, the compositional window for this intricate packing is quite narrow. This study contributes a facile method for expanding the window of Frank-Kasper σ phase. By introducing a minute quantity of metal salt into the core of the micelle, the compositional and thermal windows of the Frank-Kasper phase is broadened significantly due to the collective effects of core enlargement and shift of the spherical phase boundary to higher core volume fraction.

Close-packed structures of spherical particles describe the ordered lattices of many systems, such as oranges stacked on grocery stands, densely packed colloids, and solid elements. However, stabilizing a target close-packed structure of a material system has been a puzzling problem. This research update overviews the early and recent progress on the close-packed structures in block copolymer materials and attempts to identify the unrealized role of polymer chains as a structure director in polytypic crystal systems. The polymer chains stabilize polytypes with larger local interstitial space groups, allowing higher conformational entropy of the chains.

Ordered nanostructures arising from block copolymer self-assembly, such as three-dimensional bicontinuous network phases with percolating and interpenetrating microdomain structures, are attractive in thin films for photonic crystals, optical metamaterials, size-selective separation membranes, and components in hybrid solar cells. This study describes the thin-film self-assembly behavior of a diblock copolymer, which undergoes melt-self-assembly in the bulk into a double gyroid (DG) network phase. The authors discovered film-thickness-dependent formation of topographical terraces, including islands, holes, and bicontinuous features. The occurrence of these terraces sensitively depends on the incommensurability of the as-prepared film thickness with the (211)-interplanar spacing of the DG unit cell.

Blending block copolymers with homopolymers and other block copolymers provides control over self-assembly kinetics, and unlocks a diversity of non-native morphologies. The authors review this emerging paradigm, focusing on the thin film regime, providing examples of enhanced ordering kinetics, control of morphology orientation, and even the formation of non-native structures that do not appear in the bulk equilibrium phase diagram.

Mesoatoms, micelle-like supramolecular clusters, play a crucial role as intermediate building blocks in the formation of self-assembled superlattices. This Research Update highlights giant molecules (GMs) for their precision at the molecular level, enabling a focused examination of mesoatomic characteristics. It systematically explores practical guidelines in molecular design, with the goal of achieving controlled fabrication of molecule-based superlattices. The categorization of phases based on structural features, ranging from simple spherical packing to quasicrystalline and crystalline arrangements, allows the unraveling of tunable mesoatomic traits like individual size, size difference, stoichiometry, and shape distributions. These traits emerge as pivotal considerations in the strategic design of spherical superlattice phases.

This study sheds new light on the blend properties of block copolymers with different topologies. The phase diagrams of homologous ABA and BAB linear symmetric triblock copolymers are similar, with a slight difference due to their topologies. The authors discover that this slight difference is greatly amplified with the addition of A homopolymers, leading to distinct phase behaviors in ABA/A and BAB/A blends. BAB/A exhibit much poorer miscibility than ABA/A, resulting in much smaller stable windows for the Frank-Kasper phases. The Lifshitz point of these two blends has different characteristics, changing from continuous in ABA/A to discontinuous in BAB/A.

Block copolymers spontaneously self-assemble into well-defined nanostructures, but the vast and ever-growing design space of these intriguing materials complicates studying and anticipating useful structure–property relationships a $priori$. This study reports a versatile and efficient strategy to accelerate materials discovery by building expansive and high-quality block copolymer libraries through a combination of controlled polymerization and automated chromatographic separation. The power of this method was highlighted through the rapid generation of over 300 distinct and well-defined samples, yielding comprehensive phase diagrams with exceptional compositional and structural resolution.

Block copolymer self-assembly offers access to functional nanostructured materials with properties that depend on the underlying microphase-separated morphologies. While linear A/B block copolymer phase behavior is well-studied, that of architecturally complex, nonlinear copolymers is less well-understood. This study describes the melt microphase separation of A/B core-shell bottlebrush polymers, made by linking the midpoints of ABA triblock copolymers. These core-shell bottlebrushes form tetrahedrally close-packed Frank-Kasper A15 and σ phases. Changes in the preferred brush molecular conformations as a function of backbone length suggest a star-to-bottlebrush transition, which enables subtle manipulation of the preferred interfacial curvature and consequent supramolecular morphology.

ABC-type block copolymers can self-assemble into a great variety of complex ordered structures due to their large parameter space as well as highly designable architectures. However, due to their complexity, the potential of ABC-type block copolymers is far from being fully explored. A starting point in unlocking the potential of ABC-type block copolymers is to speculate on what structures they can form. In this work, the authors propose a useful rule to systematically assume ordered structures possibly formed by ABC-type block copolymers. Through this strategy, they construct a series of ABCtype structures. Some of these fascinating novel structures are expected to have special properties, which may be obtained by properly designing the architecture of ABC-type block copolymers. Finally, the authors verify the effectiveness of this strategy by SCFT calculations.

Designing conformationally dynamic molecules that self-assemble into predictable nanostructures remains a significant unmet challenge. This work describes the application of atomic-scale cryogenic transmission electron microscopy (cryo-TEM) to elucidate the relationship between molecular structure and self-assembly of block copolymers. Cryo-TEM images revealed the presence of atomic-scale corrugations in sheet-like micelles that are not anticipated by theories which assume that the surfaces of micelles are smooth. The authors propose that the atomic-scale corrugations are due to the dipolar nature of the monomers and interactions between the monomers and water molecules.

Unlocking complex nanostructures like triply periodic minimal surfaces in block copolymer systems poses a crucial hurdle in creating multiscale functional materials. Despite ingenious methods such as interface manipulation, introduction of conformational asymmetry, and chain connectivity regulation, achieving block copolymer self-assembly into nanostructures with high packing frustration remains elusive. In this research update, the authors spotlight the use of end-group chemistry as an effective strategy for stabilizing diverse complex network morphologies beyond the gyroid. Particularly, they redefine phase diagrams by introducing robust end-to-end interactions through end-group and linker chemistry, unveiling unprecedented network structures.

Various phases from the self-assembly of block copolymer (BCP) as the outcome of microphase separation thermodynamically have been studied for decades. This review proposed a facile approach for creating metastable network phases with triply periodic minimal surface (TPMS) by using selective solvent with controlled evaporation for casting. The combination of BCP/solvent equilibrium state and kinetic control for solvent evaporation offers the opportunity to capture the local minimum metastable states with high packing frustration, giving the formation of double primitive and double diamond as well as double gyroid phases from controlled self-assembly of high-$\chi$ BCPs. The controlled windows for those network phases can be further expanded by using star-block copolymers due to the topological effect on self-assembly.

Self-assembly of blends consisting of linear and cyclic block copolymers is a potential route to obtain nanostructures needed for soft nanolithography. Blending offers an attractive strategy to modulate the feature size of the ordered morphology by controlling the relative fraction of blend components of dissimilar molecular weights. At the same time, knowledge of the blend order-disorder transition (ODT) is essential to ensure self-assembly. This study shows that polymer size and topology mismatch affect the blend ODT. Specifically, clustering of blend components in the disordered phase near the transition is an important feature of the ODT and can be used to explain why topological blends exhibit ODTs at higher segregation strengths than one might expect based on the ODTs of individual components.

ABC miktoarm triblock terpolymer melts (or simply stars) are unique due to their tendency to self-assemble into nanostructures rarely found in other block copolymer systems, such as the various tiling patterns. Several discrepancies, however, exist among previous self-consistent field (SCF) calculations of symmetrically interacting stars, where the repulsion between different types of segments is the same. These are resolved with the authors’ high-accuracy SCF calculations that include all known tiling patterns, as well as several lamellar-type phases known to bound the regions occupied by the tiling patterns in the parameter space of block volume fractions $f$${}_P$ ($P$=A,B,C). Both the (3.4.6.4) tiling pattern and the 3D phase of hierarchical-hexagonal lamellae (HHL) are found to be stable for the first time, and their stability mechanisms including the important (3${}^2$.4.3.4) tiling pattern are revealed.

Coil-helix block copolymers, i.e. blocks with different chemistries and different conformations, are versatile building blocks due to the diverse range of conformational properties that the helical block (pitch, helical radius, persistence length) can adopt. This study uses coarse-grained molecular dynamics simulations to bridge the gap between geometrical and experimental studies of helical polymers by examining the effects of helical conformation on the lamellar phase. In particular, helical blocks with higher molecular aspect ratio and higher stiffness are found to enlarge domain sizes and to produce anisotropic effects such as nematic ordering and enhanced local helicity.