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

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.

Enhanced dielectric permittivity of hierarchically double-gyroid nanocomposites via macromolecular engineering of block copolymers

It is a challenging task to realize the periodically bicontinuous gyroid nanostructures of flexible nanocomposites with high loading of functionalized nanoparticles, which could exhibit high dielectric permittivity for energy storage and electronic devices. Herein, with the aid of the concept of macromolecular engineering, we propose novel nanocomposites, composed of A'(A''B)_n miktoarm star copolymers and nanoparticles, to obtain a double-gyroid structure through self-consistent field theory coupled with density functional theory. By tailoring the architecture of this copolymer, a large window of the double-gyroid phase extending to a high loading concentration of nanoparticles is achieved, leading to a hierarchical structure of a percolation network of nanoparticles within the gyroid channels. Furthermore, the finite difference quasielectrostatic method is integrated to reveal an enhanced dielectric permittivity of the structured nanocomposites by increasing the loading concentration of nanoparticles. The simultaneous achievement of an ordered double-gyroid phase and high loading nanoparticles represents a crucial step toward the realization of fully three-dimensional network-like metamaterials via a rational molecular design of nanocomposites.

Phase Behaviors of ABA Star Polymer and Nanoparticles Confined in a Sphere with Soft Inner Surface

The phase behaviors of an ABA star polymer and nanoparticles confined in a sphere with soft inner surface, which is grafted with homopolymer brushes have been studied by the self-consistent field theory (SCFT). The morphologies of mixture in the center slice of sphere were focused. Two cases are considered: one is that the nanoparticles interact with the B blocks and the other is that the nanoparticles preferentially wet the B blocks. Under the two conditions, through changing the block ratio of the ABA star polymer, the concentration and radius of the nanoparticles, the phase behaviors of the mixtures confined the soft sphere are studied systematically. With increasing the concentration of nanoparticles, the entropy and the steric repulsive interaction of nanoparticles, and the nanoparticle density distributions along the perpendicular line through the center of sphere are plotted. The phase diagram is also constructed to analyze the effects of the nanoparticle volume fraction and radius on morphologies of ABA star polymers, and to study the effect of confinement on the phase behaviors. The results in this work provide a useful reference for controlling the ordered structures in experiment, which is an effective way to fabricate the newly multifunctional materials.

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.

Autonomous Construction of Phase Diagrams of Block Copolymers by Theory-Assisted Active Machine Learning

Equilibrium phase diagrams serve as blueprints for rational design of nanostructured materials of block copolymers, but their construction is time-consuming and requires profound expertise. Herein, by virtue of the knowledge of self-consistent field theory (SCFT), the active-learning method is developed to autonomously construct the phase diagrams of block copolymers. Without human intervention, the SCFT-assisted active-learning method can rapidly search the undetected phases and efficiently reproduce the complicated phase diagrams of diblock copolymers and multiblock terpolymers via decreasing the number of sampling points to about 20%. It is clearly demonstrated that the combined uncertainty sampling/random selection scheme in the active-learning method shows the outperformance in spite of a small amount of initial data set. This work highlights the promising integration of theoretical modeling with machine learning and represents a crucial step toward rational design of nanostructured materials.

Conformational and topological correlations in non-frustated triblock copolymers with homopolymers

The phase behavior of non-frustrated ABC block copolymers polymers, modeling poly(isoprene-b-styrene-b-ethylene oxide) (ISO), is studied using dissipative particle dynamic (DPD) simulations. The phase diagram showed a wide composition range for the alternating gyroid morphology, which can be transformed to a chiral metamaterial. A quantitative analysis of topology was developed, that correlates the location of a block relative to the interface with the block's end-to-end distance. This analysis showed that the A-blocks stretched as they were located deeper in the A-rich region. To further expand the stability of the alternating gyroid phase, A-selective homopolymers of different lengths were co-assembled with the ABC copolymer at several compositions. Topological analysis showed that homopolymers with lengths shorter than or equal to the A-block length filled the middle of the networks, decreasing packing frustration and stabilizing them, while longer homopolymers stretched across the network but allowed for the formation of stable, novel morphologies. Adding homopolymers to triblock copolymer melts increases tunability of the network, offering greater control over the final stable phase and bridging two separate regions in the phase diagram.

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.