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.

Stabilizing Differential Interfacial Curvatures by Mismatched Molecular Geometries: Toward Polymers with Percolating 1 nm Channels of Gyroid Minimal Surfaces

Soft materials with self-assembled networks possess saddle-shaped interfaces with distributed negative Gaussian curvatures. The ability to stabilize such a geometry is critically important for various applications but can be challenging due to the possibly "deficient" packing of the building blocks. This nontrivial challenge has been manifested, for example, by the limited availability of cross-linkable bicontinuous cubic (Q) liquid crystals (LCs), which can be utilized to fabricate compelling polymers with networked nanochannels uniformly sized at ∼1 nm. Here, we devise a facile approach to stabilizing cross-linkable Q mesophases by leveraging the synergistic self-assembly from pairs of scalably synthesized polymerizable amphiphiles. Hybridization of the molecular geometries by mixing significantly increases the propensity of the local deviations in the interfacial curvature specifically required for Q assemblies. "Normal" (type 1) double gyroid LCs possessing 1 nm ionic channels conforming to minimal surfaces can be formulated by simultaneous hydration of the amphiphile mixtures, as opposed to the formation of hexagonal or lamellar mesophases exhibited by the single-amphiphile systems, respectively. Fixation of the bicontinuous network in polymers via radical polymerization has been efficaciously facilitated by the presence of the bifunctional polymerizable groups in one of the employed amphiphiles. High-fidelity lock-in of the ordered continuous 1 nm channels has been unambiguously confirmed by the observation of single-crystal-like diffraction patterns from synchrotron small-angle X-ray scattering and large-area periodicities by transmission electron microscopy. The produced polymeric materials exhibit the required mechanical integrity as well as chemical robustness in a variety of organic solvents that benefit their practical applications for selective transport of ions and molecules.

Double Gyroid Morphologies in Precise Ion-Containing Multiblock Copolymers Synthesized via Step-Growth Polymerization

The double gyroid structure was first reported in diblock copolymers about 30 years ago, and the complexity of this morphology relative to the other ordered morphologies in block copolymers continues to fascinate the soft matter community. The double gyroid microphase-separated morphology has co-continuous domains of both species, and the minority phase is subdivided into two interpenetrating network structures. In addition to diblock copolymers, this structure has been reported in similar systems including diblock copolymers blended with one or two homopolymers and ABA-type triblock copolymers. Given the narrow composition region over which the double gyroid structure is typically observed (∼3 vol %), anionic polymerization has dominated the synthesis of block copolymers to control their composition and molecular weight. This perspective will highlight recent studies that (1) employ an alternative polymerization method to make block copolymers and (2) report double gyroid structures with lattice parameters below 10 nm. Specifically, step-growth polymerization linked precise polyethylene blocks and short sulfonate-containing blocks to form strictly alternating multiblock copolymers, and these copolymers produce the double gyroid structure over a dramatically wider composition range (>14 vol %). These new (AB) _n multiblock copolymers self-assemble into the double gyroid structure by having exceptional control over the polymer architecture and large interaction parameters between the blocks. This perspective proposes criteria for a broader and synthetically more accessible range of polymers that self-assemble into double gyroids and other ordered structures, so that these remarkable structures can be employed to solve a variety of technological challenges.

Stabilizing a Double Gyroid Network Phase with 2 nm Feature Size by Blending of Lamellar and Cylindrical Forming Block Oligomers

Molecular dynamics simulations are used to study binary blends of an AB-type diblock and an AB₂-type miktoarm triblock amphiphiles (also known as high-χ block oligomers) consisting of sugar-based (A) and hydrocarbon (B) blocks. In their pure form, the AB diblock and AB₂ triblock amphiphiles self-assemble into ordered lamellar (LAM) and cylindrical (CYL) structures, respectively. At intermediate compositions, however, the AB₂-rich blend (0.2 ≤ x _AB ≤ 0.4) forms a double gyroid (DG) network, whereas perforated lamellae (PL) are observed in the AB-rich blend (0.5 ≤ x _AB ≤ 0.8). All of the ordered mesophases present domain pitches under 3 nm, with 1 nm feature sizes for the polar domains. Structural analyses reveal that the nonuniform interfacial curvatures of DG and PL structures are supported by local composition variations of the LAM- and CYL-forming amphiphiles. Self-consistent mean field theory calculations for blends of related AB and AB₂ block polymers also show the DG network at intermediate compositions, when A is the minority block, but PL is not stable. This work provides molecular-level insights into how blending of shape-filling molecular architectures enables network phase formation with extremely small feature sizes over a wide composition range.

Medial packing and elastic asymmetry stabilize the double-gyroid in block copolymers

Triply-periodic networks are among the most complex and functionally valuable self-assembled morphologies, yet they form in nearly every class of biological and synthetic soft matter building blocks. In contrast to simpler assembly motifs – spheres, cylinders, layers – networks require molecules to occupy variable local environments, confounding attempts to understand their formation. Here, we examine the double-gyroid network phase by using a geometric formulation of the strong stretching theory of block copolymer melts, a prototypical soft self-assembly system. The theory establishes the direct link between molecular packing, assembly thermodynamics and the medial map, a generic measure of the geometric center of complex shapes. We show that “medial packing” is essential for stability of double-gyroid in strongly-segregated melts, reconciling a long-standing contradiction between infinite- and finite-segregation theories. Additionally, we find a previously unrecognized non-monotonic dependence of network stability on the relative entropic elastic stiffness of matrix-forming to tubular-network forming blocks. The composition window of stable double-gyroid widens for both large and small elastic asymmetry, contradicting intuitive notions that packing frustration is localized to the tubular domains. This study demonstrates the utility of optimized medial tessellations for understanding soft-molecular assembly and packing frustration via an approach that is readily generalizable far beyond gyroids in neat block copolymers.

Double-gyroid networks assemble in diverse soft materials, yet the molecular packing that underlies their complex structure remains obscure. Here, authors advance a theory that resolves a long-standing puzzle about their formation in block copolymers.