Single Gyroid Self-Assembled by Linear BABAB Pentablock Copolymer

Highly Ordered Gyroid Nanostructured Polymers: Facile Fabrication by Polymerizable Pluronic Surfactants

Highly ordered, network-nanostructured polymers offer compelling geometric features and application potential. However, their practical utilization is hampered by the restricted accessibility. Here, we address this challenge using commercial Pluronic surfactants with a straightforward modification of tethering polymerizable groups. By leveraging lyotropic self-assembly, we achieve facile production of double-gyroid mesophases, which are subsequently solidified via photoinduced cross-linking. The exceptionally ordered periodicities of Ia3d symmetry in the photocured polymers are unambiguously confirmed by synchrotron small-angle X-ray scattering (SAXS), which can capture single-crystal-like diffraction patterns. Electron density maps reconstructed from SAXS data complemented by transmission electron microscopy analysis further elucidate the real-space gyroid assemblies. Intriguingly, by tuning the cross-linking through thiol-acrylate chemistry, the mechanical properties of the polymer are modulated without compromising the integrity of Ia3d assemblies. The 3-D percolating gyroid nanochannels demonstrate an ionic conductivity that surpasses that of disordered structures, offering promising prospects for scalable fabrication.

The permeability of diamond and other microphase-separated morphologies in copolymer films

A method is proposed for the theoretical assessment of potential membrane properties in materials based on microphase-separated block copolymer films subjected to the etching of one of the components. The concepts of topological permeability and connectivity contrast introduced by the authors are used to compare the percolation characteristics of simple cubic, diamond, and diamond-like morphologies compatible with the slit geometry and specified by a given distribution of the order parameter. The diamond-like morphology, which has the most promising transport characteristics, can be formed in a thin film of diblock copolymer AB placed on a chemically structured substrate. For this case, the quantitative analysis of permeability for certain parameters of the model system is carried out using the local distribution of A and B units calculated with the self-consistent field theory of microphase separation. The results obtained may be useful for the design of isoporous membranes based on block copolymers.

Gaming self-consistent field theory: Generative block polymer phase discovery

Block polymers are an attractive platform for uncovering the factors that give rise to self-assembly in soft matter owing to their relatively simple thermodynamic description, as captured in self-consistent field theory (SCFT). SCFT historically has found great success explaining experimental data, allowing one to construct phase diagrams from a set of candidate phases, and there is now strong interest in deploying SCFT as a screening tool to guide experimental design. However, using SCFT for phase discovery leads to a conundrum: How does one discover a new morphology if the set of candidate phases needs to be specified in advance? This long-standing challenge was surmounted by training a deep convolutional generative adversarial network (GAN) with trajectories from converged SCFT solutions, and then deploying the GAN to generate input fields for subsequent SCFT calculations. The power of this approach is demonstrated for network phase formation in neat diblock copolymer melts via SCFT. A training set of only five networks produced 349 candidate phases spanning known and previously unexplored morphologies, including a chiral network. This computational pipeline, constructed here entirely from open-source codes, should find widespread application in block polymer phase discovery and other forms of soft matter.

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.

Alternating Gyroid in Block Polymer Blends

Alternating gyroid is a lower symmetry variant of the double gyroid morphology, where the left-handed and right-handed chiral networks are physically distinct. This structure is of particular interest for photonic applications owing to predictions of a complete photonic band gap subject to the requirement of a large dielectric contrast between the individual networks and sufficient optical matching between one of the networks and the matrix. We provide evidence, via self-consistent field theory (SCFT), that stoichiometric blends of double-gyroid-forming AB and BC diblock copolymers with relatively immiscible A and C blocks should form an alternating gyroid morphology with complementary three-dimensional A and C networks that have a free energy that is nearly degenerate with two phase-separated double gyroid states. Solvent casting offers the potential for trapping this binary mixture of diblock copolymers in this metastable alternating gyroid phase. Theory further predicts that the addition of a minuscule amount (<1%) of ABC triblock terpolymer will open an alternating gyroid stability window in the resulting ternary-phase diagram. The surfactant-like stabilization produced by the triblock is relatively insensitive to its exact composition provided the B-block forms a sufficiently long bridge between the A-rich and C-rich networks. This blending strategy provides significant synthetic and material processing advantages compared to prevailing methods to produce an alternating gyroid phase in block polymers.