Morphology Reentry with a Change in Degree of Chain Asymmetry in Neat Asymmetric Linear A1BA2 Triblock Copolymers

Stabilizing hexagonally close-packed phase in single-component block copolymers through rational symmetry breaking

Despite being predicted to be a thermodynamically equilibrium structure, the absence of direct experimental evidence of hexagonally close-packed spherical phase in single-component block copolymers raises uncomfortable concerns regarding the existing fundamental phase principles. This work presents a robust approach to regulate the phase behavior of linear block copolymers by deliberately breaking molecular symmetry, and the hexagonally close-packed lattice is captured in a rigorous single-component system. A collection of discrete A1BA2 triblock copolymers is designed and prepared through an iterative growth method. The precise chemical composition and uniform chain length eliminates inherent size distribution and other molecular defects. Simply by tuning the relative chain length of two end A blocks, a rich array of ordered nanostructures, including Frank-Kasper A15 and σ phases, are fabricated without changing the overall chemistry or composition. More interestingly, hexagonally close-packed spherical phase becomes thermodynamically stable and experimentally accessible attributed to the synergistic contribution of the two end blocks. The shorter A blocks are pulled out from the core domain into the matrix to release packing frustration, while the longer ones stabilize the ordered spherical phase against composition fluctuation that tends to disrupt the lattice. This study adds a missing puzzle piece to the block copolymer phase diagram and provides a robust approach for rational structural engineering.

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.

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.

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.

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.

Mesoscopic Detection of the Influence of a Third Component on the Self-Assembly Structure of A2B Star Copolymer in Thin Films

The most common self-assembly structure for A2B copolymer is the micellar structure with B/A segments being the core/corona, which greatly limits its application range. Following the principle of structure deciding the properties, a reformation in the molecular structure of A2B copolymer is made by appending three segments of a third component C with the same length to the three arms, resulting (AC)2CB 3-miktoarm star terpolymer. A reverse micellar structure in self-assembly is expected by regulating the C length and the pairwise repulsive strength of C to A/B, aiming to enrich its application range. Keeping both A and B lengths unchanged, when the repulsion strength of C to A is much stronger than C to B, from the results of mesoscopic simulations we found, with a progressive increase in C length, (AC)2CB terpolymer undergoes a transition in self-assembled structures, from a cylindrical structure with B component as the core, then to a deformed lamellar structure, and finally to a cylindrical structure with A component as the core. This reverse micellar structure is formed with the assistance of appended C segments, whose length is longer than half of B length, enhancing the flexibility of three arms, and further facilitating the aggregation of A component into the core. These results prove that the addition of a third component is a rational molecular design, in conjunction with some relevant parameters, enables the manufacturing of the desired self-assembly structure while avoiding excessive changes in the involved factors.

Emergence and Stability of a Hybrid Lamella-Sphere Structure from Linear ABAB Tetrablock Copolymers

The self-assembly of linear A₁B₁A₂B₂ tetrablock copolymers is studied using the self-consistent field theory, aiming to target the formation of stable hybrid structures composed of lamellar and spherical domains of the same component, i.e., the lamella-sphere (LS) phase. Two types of lamellar morphologies, regular (L) and sandwich-like (L'), are observed, and their transition is identified as first-order. The formation of L' is a prior condition for the formation of LS because the disordered short A₂-blocks sandwiched in the B domain in L' aggregate into spheres as χN increases, leading to the formation of LS. The separation of A₂-blocks from A₁-blocks in L' or LS causes extra interfacial energy, which is compensated by the gain of configurational entropy. The tail B₂-block is demonstrated to play a critical role in enlarging the gain of configurational entropy. In a word, the formation of L' is driven by entropy, while the transition from L' to LS is driven by enthalpy.

Versatile Controls of Microdomain Morphologies and Temperature Dependencies in Lamellar Spacing by Blending Diblock Copolymers Bearing Antisymmetric Compositions

The morphologies of the microphase-separated structures in the binary blends of diblock copolymers (AB/AB) have been studied intensively for the case of diblock copolymers bearing antisymmetric compositions with similar molecular weights. Here, the two diblock copolymers 1 and 2, of which compositions are 0.5 - x and 0.5 + x (0 < x < 0.5), respectively, were blended, and the morphology diagram was constructed in the plot of χZ vs the average composition of the A component, where χ is the interaction parameter between A and B segments and Z is the average degree of polymerization of the two AB diblock copolymers. The temperature-dependent morphologies were analyzed by synchrotron small-angle X-ray scattering (SAXS) measurements. It was found that the morphology diagram agrees in principle with the theoretical one for the neat AB diblocks by Matsen and Bates (Macromolecules 1996, 29, 1091-1098), although the disordered phase was a bit expanded in the experimentally determined morphology diagram. Anomalous temperature dependencies in the lamellar spacing have been also comprehensively studied for the binary blends of antisymmetric diblock copolymers as a function of the degree of compositional asymmetry by closely adjusting the average composition in the blend specimen at 0.50. For this purpose, more than 20 neat diblock copolymers have been synthesized with a wide range of compositions from 0.20 to 0.87 and a range of molecular weight of 12 000-33 800. The temperature dependencies of the lamellar spacing were also analyzed by synchrotron SAXS measurements. As a result, the following things were found. The scaling exponent α in D ∼ T α was still negative but slightly larger than the usual value (i.e., α = -0.33) for the smaller degree of asymmetry in the composition (i.e., x is small), while α became positive for the higher degree of asymmetry. The latter result is very anomalous because the temperature dependence is opposite (i.e., the lamellar spacing increases with an increase of temperature). The value of α was found to be linearly rationalized with the degree of asymmetry τ (which is especially introduced in the current paper for this purpose), for the binary blends with the average composition of 0.50. Based on this result, one can prepare lamellar microdomains, of which spacing does not change with temperature, by blending two diblock copolymers with τ = 1.33 (corresponding to 0.3 and 0.7 of compositions) having similar molecular weights. This would be important for manufacturing materials with properties (for instance, the optical property) independent of temperature. From the current study, the binary blends of the antisymmetric diblock copolymers are concluded to be versatile such that the precise controls of the morphologies and the temperature dependencies of the lamellar microdomains are plausible.