The emergence of the complex Frank-Kasper phases from binary mixtures AB diblock copolymers is studied using self-consistent field theory. relative stability different ordered phases, including σ and A15 containing nonspherical minority domains with sizes, examined by a comparison their free energy. resulting phase diagrams reveal that occupies large region in space system. formation mechanism elucidated distribution two lengths compositions. In particular, segregation types copolymers,...

It is generally believed that the spherical domains self-assembled from AB-type block copolymers are composed of minority A blocks with a volume fraction fA < 1/2. Breaking this generic rule so formed by majority (fA > 1/2) requires mechanisms to drastically expand stable region packing phases. Self-consistent field theory predicts dendron-like copolymers, G - 1 generations connected outermost generation B blocks, exhibit phases extending ∼ 0.7. The extremely expanded regions shed light on...

The effects of chain topology on the self-assembly block copolymers are examined using an ABAT copolymer, composed AB diblock copolymer with extra A tethered onto B block, as a model system. is regulated by tethering point, such that changes continuously from linear ABA triblock to A2B miktoarm star position moves end junction. phase diagrams different positions constructed self-consistent field theory. theoretical results reveal behavior system depends sensitively copolymers. In particular,...

Although the double-gyroid (DG) structure has been commonly formed from self-assembly of block copolymers, single-gyroid (SG) is rarely reported. Moreover, SG even shows better performance than DG in some optical applications. How to prepare become an attractive but challenging topic. We speculate that can be stabilized by synergistic effect released packing frustration and stretched bridging AB-type copolymers. Accordingly, we propose minimum conditions for design architecture enables two...

The self-assembly behavior of (B1AB2)5 star copolymers, composed five asymmetric BAB-triblock arms joined at the end B2-blocks, has been investigated using self-consistent field theory. special architecture enables a few different sophisticated mechanisms such as conformational asymmetry from topology, effect combinatorial entropy multiple that enhances formation bridging configurations for core local segregation between two B-blocks, and solubilization short B2-block in majority A-domain,...

Quasicrystalline (QC) phases have been observed in various condensed matter systems including self-assembling block copolymer (BCP) melts. Theoretical study of the thermodynamic stability QC presents a long-standing unsolved problem because aperiodic nature structures. Here, we report combination method to two-dimensional dodecagonal quasicrystalline (DDQC) phase with both ideal tiling and random patterns formed by ABCB tetrablock terpolymers. This applies self-consistent field theory...

The self-assembly of amphiphilic macromolecules into various mesocrystals has attracted abiding interest. Although many interesting have been achieved, 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 CNs. Self-consistent field theory reveals that two sophisticated mechanisms realized in the copolymer, is, stretched bridging block and released packing frustration,...

We propose to regulate the stability of gyroids ABC-type multiblock copolymers by controlling packing frustration majority-component B-blocks. Accordingly, we investigate self-assembly behaviors BABCB linear terpolymer with a variable length ratio τ middle B-block relative total B-blocks using self-consistent field theory. It is observed that gyroid region exhibits maximal width respect τ, which attributed nonmonotonical change three in morphology discrete domains, for example, cylinders....

Recent experiments demonstrated the emergence of regular mesoscopic patterns when liquid droplets form in an elastic gel after cooling. These appeared via a continuous transition and were smaller stiffer systems. We capture these observations with phenomenological equilibrium model describing density field component to account for phase separation. show that local elasticity theories are insufficient, even if they allow large shear deformations. Instead, we can key using nonlocal theory...

Phase separation, crucial for spatially segregating biomolecules in cells, is well-understood the simple case of a few components with pairwise interactions. Yet, biological cells challenge picture at least two ways: First, biomolecules, like proteins and nucleic acids, exhibit complex, higher-order interactions, where single molecule may interact multiple others simultaneously. Second, comprise myriad different that form various droplets. Such multicomponent phase separation has been...

Block copolymers with different architectures can possibly generate innumerable stable or metastable structures and thus provide an irreplaceable platform for theoretically exploring novel structures. Self-consistent field theory (SCFT) is a powerful tool to predict the ordered of block copolymers; however, it sensitively dependent on its initial condition. Here we propose use multiple symmetry-adapted basis functions conditions SCFT then apply Bayesian optimization search by navigating...

Self-consistent field theory (SCFT) has been proven as one of the most successful methods for studying phase behavior block copolymers. In past decades, a number numerical have developed solving SCFT equations. Recently, pseudo-spectral method based on fast Fourier transform (FFT) become frequently used due to its versatility and high efficiency. However, computational cost is still rather high, especially some complex structures or in strong-segregation case. To accelerate calculation, we...

Soft spherical domains assembled from block copolymers can pack into Frank-Kasper phases, reminiscent of those found in alloys. As a special subcategory Laves phases are particularly challenging to obtain. So far, the most stable have been realized copolymer blends, where mixing different polymers accommodates size discrepancy between two types spheres. Here, we propose an intramolecular blending strategy stabilize neat AB-type melts. By designing multiblock with separate A blocks...

Linear ABC triblock copolymers with frustrated interactions of χACN ≪ χABN ∼ χBCN can self-assemble into double- and triple-helical superstructures, where the B blocks form helical domains wrapping around hexagonally packed A core cylinders in a C matrix. It has been argued that larger length ratio between helices cylinder tends to number on each cylinder. On basis this argument, we propose branch block enlarge domain relative thus reduce ratio, i.e., altering linear branching ABC2...

Although the general mechanism of block copolymer self-assembly has been well established, behaviors multiblock copolymers are still hard to understand and even quite counterintuitive. Herein, we investigate a relatively simple copolymer, i.e., symmetric ABCA linear tetrablock composed equal B C blocks as two end A blocks, focusing on emergence stability Janus-like superspherical (JS) supercylindrical (JC) morphologies. Intuitively, JS JC superstructures could be formed by this with proper...

Chiral selection has attracted tremendous attention from the scientific communities, especially biologists, due to mysterious origin of homochirality in life. The self-assembly achiral block copolymers confined nanopores offers a simple but useful model forming helical structures, where structures possess random chirality selection, i.e. equal probability left-handedness and right-handedness. Based on this model, we study stimulus-response chiral external conditions by introducing designed...

Although self-consistent field theory (SCFT) has been become one of the most successful methods for study block copolymers, its application to ring copolymers hindered years, especially three-dimensional structures. Here, we have developed an accelerated pseudospectral algorithm solve SCFT equations by taking advantage symmetry ordered By combining various advanced techniques, speed-up orders magnitude achieved, making construction a complete phase diagram affordable. This applied...

The self-assembly of binary blends composed AB diblock and ABC triblock copolymers is investigated using self-consistent field theory. Specifically, the miscibility mixture studied by tuning concentration ϕ2 length ratio γ between triblock. It predicted that sphere-forming can be compatible coassembling into new spherical phases, even when close to 50%. For relatively low (0.48 < 1.13), two different are accommodated an asymmetric phase, Li3Bi, where A-sphere coformed A-blocks with similar...

Mixtures with many components can segregate into coexisting phases, e.g., in biological cells and synthetic materials such as metallic glass. The interactions between dictate what phases form equilibrium, but quantifying this relationship has proven difficult. We derive scaling relations for the number of multicomponent liquids random compositions, which we verify numerically. Our results indicate that only need to increase logarithmically liquid phases. In contrast, a stability analysis...

Biomolecular condensates are complex droplets comprising many different types of molecules that interact using various mechanisms. Condensation is often driven by short-ranged attraction, but net charges can also mediate long-ranged repulsion. Using molecular dynamics simulations and an equilibrium field theory, we show such opposing interactions suppress coarsening so equal size coexist at equilibrium. This control depends strongly on the charge asymmetry between constituents, while...

The phase behavior of binary blends composed AB diblock and (A′B)_nstar copolymers is studied using the polymeric self-consistent field theory, focusing on formation stability stable tetragonal cylinders.

The inability to synthesize hierarchical structures with independently tailored nanoscale and mesoscale features limits the discovery of next-generation multifunctional materials. We present a programmable molecular self-assembly strategy craft nanostructured materials variety phase-in-phase morphologies. compositionally anisotropic building blocks employed in assembly process are formed by multi-component graft block copolymers (GBCPs) containing sequence-defined side chains. judicious...