Morphology Transitions of Linear A1B1A2B2 Tetrablock Copolymers at Symmetric Overall Volume Fraction

Theoretical Study of Phase Behaviors of Symmetric Linear B1A1B2A2B3 Pentablock Copolymer

The nanostructures that are self-assembled from block copolymer systems have attracted interest. Generally, it is believed that the dominating stable spherical phase is body-centered cubic (BCC) in linear AB-type block copolymer systems. The question of how to obtain spherical phases with other arrangements, such as the face-centered cubic (FCC) phase, has become a very interesting scientific problem. In this work, the phase behaviors of a symmetric linear B₁A₁B₂A₂B₃ (f_A1 = f_A2, f_B1 = f_B3) pentablock copolymer are studied using the self-consistent field theory (SCFT), from which the influence of the relative length of the bridging B₂-block on the formation of ordered nanostructures is revealed. By calculating the free energy of the candidate ordered phases, we determine that the stability regime of the BCC phase can be replaced by the FCC phase completely by tuning the length ratio of the middle bridging B₂-block, demonstrating the key role of B₂-block in stabilizing the spherical packing phase. More interestingly, the unusual phase transitions between the BCC and FCC spherical phases, i.e., BCC → FCC → BCC → FCC → BCC, are observed as the length of the bridging B₂-block increases. Even though the topology of the phase diagrams is less affected, the phase windows of the several ordered nanostructures are dramatically changed. Specifically, the changing of the bridging B₂-block can significantly adjust the asymmetrical phase regime of the Fddd network phase.

Fabrication of Ultrafine, Highly Ordered Nanostructures Using Carbohydrate-Inorganic Hybrid Block Copolymers

Block copolymers (BCPs) have garnered considerable interest due to their ability to form microphase-separated structures suitable for nanofabrication. For these applications, it is critical to achieve both sufficient etch selectivity and a small domain size. To meet both requirements concurrently, we propose the use of oligosaccharide and oligodimethylsiloxane as hydrophilic and etch-resistant hydrophobic inorganic blocks, respectively, to build up a novel BCP system, i.e., carbohydrate-inorganic hybrid BCP. The carbohydrate-inorganic hybrid BCPs were synthesized via a click reaction between oligodimethylsiloxane with an azido group at each chain end and propargyl-functionalized maltooligosaccharide (consisting of one, two, and three glucose units). In the bulk state, small-angle X-ray scattering revealed that these BCPs microphase separated into gyroid, asymmetric lamellar, and symmetric lamellar structures with domain-spacing ranging from 5.0 to 5.9 nm depending on the volume fraction. Additionally, we investigated microphase-separated structures in the thin film state and discovered that the BCP with the most asymmetric composition formed an ultrafine and highly oriented gyroid structure as well as in the bulk state. After reactive ion etching, the gyroid thin film was transformed into a nanoporous-structured gyroid SiO₂ material, demonstrating the material’s promising potential as nanotemplates.

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.

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.

Effect of chain architectures on the domain spacing of block copolymers with equivalent segregation degrees

It is crucial to lower the domain spacing in the application of directed self-assembly (DSA) of block copolymers. Architectural design of block copolymers provides a possible route. However, the change of the segregation degree is always coupled with that of domain spacing. Therefore, we rescale the segregation degrees of different multiblock copolymers with reference to that of the AB diblock using self-consistent field theory (SCFT), including the [AB]n linear multiblock, AnBn multi-arm star and Ad,nBd,n dendron-like, such that the density profiles of the lamellar morphology are consistent. Then we compare the lamellar periods of these different copolymers under the condition of equivalent segregation degrees. We find that the star and dendron-like architectures can significantly lower the domain spacing relative to that of the AB diblock, especially when the arm number or the generation number is large. On one hand, our work presents a simple criterion for quantifying the reduction of domain spacing of a specific multiblock architecture relative to that of the AB diblock. On the other hand, our conclusion provides a useful guide for the application of directed self-assembly.