Effects of Chain Topology on the Self-Assembly of AB-Type Block Copolymers

Tailored Solid-State Carbohydrate Nanostructures Based on Star-Shaped Discrete Block Co-Oligomers

Carbohydrates are key building blocks for advanced functional materials owing to their biological functions and unique material properties. Here, we propose a star-shaped discrete block co-oligomer (BCO) platform to access carbohydrate nanostructures in bulk and thin-film states via the microphase separation of immiscible carbohydrate and hydrophobic blocks (maltooligosaccharides with 1-4 glucose units and solanesol, respectively). BCOs with various star-shaped architectures and saccharide volume fractions were synthesized using a modular approach. In the bulk, the BCOs self-assembled into common lamellar, cylindrical, and spherical carbohydrate microdomains as well as double gyroid, hexagonally perforated lamellar, and Fddd network morphologies with domain spacings of ∼7 nm. In thin films, long-range-ordered periodic carbohydrate microdomains were fabricated via spin coating. Such controlled spatial arrangements of functional carbohydrate moieties on the nanoscale have great application potential in biomedical and nanofabrication fields.

Medial packing and elastic asymmetry stabilize the double-gyroid in block copolymers

Triply-periodic networks are among the most complex and functionally valuable self-assembled morphologies, yet they form in nearly every class of biological and synthetic soft matter building blocks. In contrast to simpler assembly motifs – spheres, cylinders, layers – networks require molecules to occupy variable local environments, confounding attempts to understand their formation. Here, we examine the double-gyroid network phase by using a geometric formulation of the strong stretching theory of block copolymer melts, a prototypical soft self-assembly system. The theory establishes the direct link between molecular packing, assembly thermodynamics and the medial map, a generic measure of the geometric center of complex shapes. We show that “medial packing” is essential for stability of double-gyroid in strongly-segregated melts, reconciling a long-standing contradiction between infinite- and finite-segregation theories. Additionally, we find a previously unrecognized non-monotonic dependence of network stability on the relative entropic elastic stiffness of matrix-forming to tubular-network forming blocks. The composition window of stable double-gyroid widens for both large and small elastic asymmetry, contradicting intuitive notions that packing frustration is localized to the tubular domains. This study demonstrates the utility of optimized medial tessellations for understanding soft-molecular assembly and packing frustration via an approach that is readily generalizable far beyond gyroids in neat block copolymers.

Double-gyroid networks assemble in diverse soft materials, yet the molecular packing that underlies their complex structure remains obscure. Here, authors advance a theory that resolves a long-standing puzzle about their formation in block copolymers.

Effect of Molecular Architecture and Symmetry on Self-Assembly: A Quantitative Revisit Using Discrete ABA Triblock Copolymers

The inherent statistical heterogeneities associated with chain length, composition, and architecture of synthetic block copolymers compromise the quantitative interpretation of their self-assembly process. This study scrutinizes the contribution of molecular architecture on phase behaviors using discrete ABA triblock copolymers with precise chemical structure and uniform chain length. A group of discrete triblock copolymers with varying composition and symmetry were modularly synthesized through a combination of iterative growth methods and efficient coupling reactions. The symmetric ABA triblock copolymers self-assemble into long-range ordered structures with expanded domain spacings and enhanced phase stability, compared with the diblock counterparts snipped at the middle point. By tuning the relative chain length of two end blocks, the molecular asymmetry reduces the packing frustration, and thus increases the order-to-disorder transition temperature and enlarges the domain sizes. This study would serve as a quantitative model system to correlate the experimental observations with the theoretical assessments and to provide quantitative understandings for the relationship between molecular architecture and self-assembly.

Periodic Patchy Spheres Self-Assembled by AmBCAn' Multiblock Terpolymers

We have designed A_mBCA_n^' multiblock terpolymers and studied their self-assembly using self-consistent field theory, aiming to generate the periodically arranged patchy spheres and thus to clarify the regulation mechanism of the number of patches. A number of two-dimensional phase diagrams are constructed for three typical architectures A₂BCA₂^', A₂BCA₃^', and A₃BCA₂^'. Four kinds of stable patchy spheres with the number of patches as 2 (S₂), 4 (S₄), 5 (S₅), and 6 (S₆) are obtained. These phases follow a common transition sequence of S₂ → S₄ → S₅ → S₆ along with the increasing of the volume fraction of C-block (f_C), which forms the core sphere patched with B-domains. Moreover, the S₆ phase exhibits the widest stability window, while S₅ has the narrowest one. The increased arms of A'-blocks in A₂BCA₃^' architecture deflect the phase boundaries toward large f_C and accordingly expand the regions of these patchy spheres due to the amplified effect of spontaneous curvature. In contrast, the increased arms of A-blocks in A₃BCA₂^' remarkably expands the window of S₆ but narrows those of the other patchy spheres, which is mainly caused by increased packing frustration resulting from the reduced extension of the more divided A-blocks. The widest window of the S₆ phase reaches Δf_C ∼ 0.13, which is readily accessed by experiment. Our work not only demonstrates a self-assembly strategy to engineer the patchy spheres, but also sheds light on the regulation mechanism of the patchy number.

Single Gyroid Self-Assembled by Linear BABAB Pentablock Copolymer

Although the double-gyroid (DG) structure has been commonly formed from the self-assembly of block copolymers, the single-gyroid (SG) structure is rarely reported. Moreover, the SG structure even shows better performance than DG in some optical applications. How to prepare the SG structure has become an attractive but challenging topic. We speculate that the SG structure can be stabilized by the synergistic effect of released packing frustration and stretched bridging block in AB-type block copolymers. Accordingly, we propose the minimum conditions for the design of architecture that enables the two mechanisms simultaneously. Following these conditions, a simple linear BABAB pentablock copolymer is successfully devised. SCFT calculations confirm that the SG phase can be stabilized by tailoring the architecture. Our work is hopeful to promote relevant experimental studies for engineering the unusual SG structure.

Integration of Machine Learning and Coarse-Grained Molecular Simulations for Polymer Materials: Physical Understandings and Molecular Design

In recent years, the synthesis of monomer sequence-defined polymers has expanded into broad-spectrum applications in biomedical, chemical, and materials science fields. Pursuing the characterization and inverse design of these polymer systems requires our fundamental understanding not only at the individual monomer level, but also considering the chain scales, such as polymer configuration, self-assembly, and phase separation. However, our accessibility to this field is still rudimentary due to the limitations of traditional design approaches, the complexity of chemical space along with the burdened cost and time issues that prevent us from unveiling the underlying monomer sequence-structure-property relationships. Fortunately, thanks to the recent advancements in molecular dynamics simulations and machine learning (ML) algorithms, the bottlenecks in the tasks of establishing the structure-function correlation of the polymer chains can be overcome. In this review, we will discuss the applications of the integration between ML techniques and coarse-grained molecular dynamics (CGMD) simulations to solve the current issues in polymer science at the chain level. In particular, we focus on the case studies in three important topics—polymeric configuration characterization, feed-forward property prediction, and inverse design—in which CGMD simulations are leveraged to generate training datasets to develop ML-based surrogate models for specific polymer systems and designs. By doing so, this computational hybridization allows us to well establish the monomer sequence-functional behavior relationship of the polymers as well as guide us toward the best polymer chain candidates for the inverse design in undiscovered chemical space with reasonable computational cost and time. Even though there are still limitations and challenges ahead in this field, we finally conclude that this CGMD/ML integration is very promising, not only in the attempt of bridging the monomeric and macroscopic characterizations of polymer materials, but also enabling further tailored designs for sequence-specific polymers with superior properties in many practical applications.

A3B-type miktoarm star polymer nanoassemblies prepared by reversible addition–fragmentation chain transfer (RAFT) dispersion polymerization

The investigation on a series of A3B-type miktoarm star polymer assemblies by RAFT PISA has revealed the role of A3B architecture in delaying morphological transitions, and the formation of larger vesicles as well as other interesting morphologies.

Emergence of Hexagonally Close-Packed Spheres in Linear Block Copolymer Melts

The hexagonally close-packed (HCP) sphere phase is predicted to be stable across a narrow region of linear block copolymer phase space, but the small free energy difference separating it from face-centered cubic spheres usually results in phase coexistence. Here, we report the discovery of pure HCP spheres in linear block copolymer melts with A = poly(2,2,2-trifluoroethyl acrylate) ("F") and B = poly(2-dodecyl acrylate) ("2D") or poly(4-dodecyl acrylate) ("4D"). In 4DF diblocks and F4DF triblocks, the HCP phase emerges across a substantial range of A-block volume fractions (circa f_A = 0.25-0.30), and in F4DF, it forms reversibly when subjected to various processing conditions which suggests an equilibrium state. The time scale associated with forming pure HCP upon quenching from a disordered liquid is intermediate to the ordering kinetics of the Frank-Kasper σ and A15 phases. However, unlike σ and A15, HCP nucleates directly from a supercooled liquid or soft solid without proceeding through an intermediate quasicrystal. Self-consistent field theory calculations indicate the stability of HCP is intimately tied to small amounts of molar mass dispersity (Đ); for example, an HCP-forming F4DF sample with f_A = 0.27 has an experimentally measured Đ = 1.04. These insights challenge the conventional wisdom that pure HCP is difficult to access in linear block copolymer melts without the use of blending or other complex processing techniques.

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.

Simplicity in mean-field phase behavior of two-component miktoarm star copolymers

Using self-consistent field theory, we systematically explore the microphase separation in the class of two-component miktoarm star copolymers containing a single conjunction point between different blocks by considering an extended list of candidate microphases. We plot mean-field phase diagrams in the plane of segregation strength and composition for an array of representative star copolymers. Three principal phase diagram topologies, dictated by different phase stabilities, are exposed, displaying a hierarchy in complexity by increasing the molecular asymmetry. Our investigation indicates that the phase diagram topology depends on the ratios of arm numbers and Kuhn segment lengths, which highlights the role of the coordination number ratio between different polymers at the domain interface. These findings reveal the simplicity of the general phase behavior and suggest a complete list of stable microphases for the entire class, which provide useful insight into studying copolymers with more complicated architectures and conformational properties.

Synergistic Effect of Stretched Bridging Block and Released Packing Frustration Leads to Exotic Nanostructures

The self-assembly of amphiphilic macromolecules into various mesocrystals has attracted abiding interest. Although many interesting mesocrystals have been achieved, mesocrystals of a low coordination number (CN) such as simple cubic are rarely reported. Here we purposely design an AB-type multiblock copolymer to target exotic spherical phases of low CNs. Self-consistent field theory reveals that two sophisticated mechanisms are realized in the copolymer, that is, stretched bridging block and released packing frustration, synergistically leading to the formation of three spherical phases with extremely low CNs, including the simple cubic spheres (CN = 6), the cubic diamond spheres (CN = 4), and normally aligned hexagonal-packing spheres (6 < CN < 8) in a considerable parameter region. Moreover, we demonstrate that these exotic phases are hard to be stabilized by either of the two mechanisms individually.

Ionic complexation of endblock-sulfonated thermoplastic elastomers and their physical gels for improved thermomechanical performance

Thermoplastic elastomers (TPEs) composed of nonpolar triblock copolymers constitute a broadly important class of (re)processable network-forming macromolecules employed in ubiquitous commercial applications. Physical gelation of these materials in the presence of a low-volatility oil that is midblock-selective yields tunably soft TPE gels (TPEGs) that are suitable for emergent technologies ranging from electroactive, phase-change and shape-memory responsive media to patternable soft substrates for flexible electronics and microfluidics. Many of the high-volume TPEs used for these purposes possess styrenic endblocks that are inherently limited by a relatively low glass transition temperature. To mitigate this shortcoming, we sulfonate and subsequently complex (and physically crosslink) the endblocks with trivalent Al³⁺ ions. Doing so reduces the effective hydrophilicity of the sulfonated endblocks, as evidenced by water uptake measurements, while concurrently enhancing the thermomechanical stability of the corresponding TPEGs. Chemical modification results, as well as morphological and property development, are investigated as functions of the degree of sulfonation, complexation and TPEG composition.

Regulate the Stability of Gyroids of ABC-Type Multiblock Copolymers by Controlling the Packing Frustration

We propose to regulate the stability of gyroids of ABC-type multiblock copolymers by controlling the packing frustration of majority-component B-blocks. Accordingly, we investigate the self-assembly behaviors of the BABCB linear terpolymer with a variable length ratio τ of the middle B-block relative to the total B-blocks using self-consistent field theory. It is observed that the gyroid region exhibits a maximal width with respect to τ, which is attributed by the nonmonotonical change of the packing frustration of three B-blocks in the morphology of discrete domains, for example, cylinders. Then we further purposely design another ABC-type copolymer composed of an ABC linear triblock tethered by another B-block at the middle of the B-block. In contrast, the packing frustration of B-blocks of the second terpolymer drops down continuously as the middle B-block shortens, thus, expanding the stable regions of cylinders and spheres while contracting those of lamella and gyroid.

Tunable helical structures formed by ABC triblock copolymers under cylindrical confinement

Block copolymers confined in nanopores provide unique achiral systems for the formation of helical structures. With AB diblock copolymers, stable single and double helical structures are observed. Aiming to obtain more different helical structures, we replace the AB diblock copolymer with linear ABC triblock copolymers. We speculate that a core-shell superstructure is formed within the nanopore, which is composed of a C-core cylinder wrapped by B-helices within the A-shell. Accordingly, the pore surface is set to be most attractive to the majority A-block and a typical set of interaction parameters is chosen as χACN ≪ χABN = χBCN = 80 to generate the frustrated interfaces. Furthermore, the volume fraction of B-block is fixed as fB = 0.1 to form helical cylinders. A number of helical structures with strands ranging from 1 to 5 are predicted by self-consistent field theory, and in general, the number of strands decreases as the volume fraction of C-block fC increases in a given nanopore. More surprisingly, the variation of helical strand in the confined system has an opposite trend to that in the bulk, which mainly results from the constraint of the cylindrical confinement on the change of the curvature between the outer A-layer and the inner B/C-superdomain. Our work demonstrates a facile way to fabricate different helical superstructures.

Surface-Induced Nanostructures and Phase Diagrams of ABC Linear Triblock Copolymers under Spherical Confinement: A Self-Consistent Field Theory Simulation

We investigate the nanostructures and phase diagrams of ABC linear triblock copolymers confined in spherical cavities by using real-space self-consistent field theory. Various 3D morphologies, such as spherical concentric lamellae, dumbbell-like cylinder, and rotational structures, are identified in the phase diagrams, which are constructed on the basis of the diameters of spherical cavities and the interaction between the polymers and preferential surfaces. We designate specific monomer-monomer interactions and block compositions, with which the polymers spontaneously form a cylindrical morphology in bulk, and firstly study morphology transformation with a neutral surface when a confining radius progressively increases. We then focus on phase morphologies under the preferential surfaces and consolidate them into phase diagrams. The spherical radius and the degree of preferential interactions can obviously induce the formation of a cylindrical morphology. Theoretical results correspond to an amount of recent experimental observations to a high degree and contribute to synthesising functional materials.