The self-assembly behavior of multiblock (ABC-type) and star-block copolymers represents a complex yet highly tunable approach to generating nanostructured materials with diverse morphologies. Unlike linear diblock copolymers, these architectures introduce additional variables such as sequence arrangement, arm number, and junction point constraints, leading to richer phase behavior and domain connectivity. Understanding these systems requires an examination of how molecular architecture influences packing frustration, interfacial curvature, and ultimately, the resulting nanostructures.

Multiblock copolymers, particularly ABC-type terpolymers, consist of three chemically distinct blocks arranged in linear or nonlinear sequences. The presence of a third block introduces two additional interaction parameters (χ_AB, χ_BC, χ_AC) and compositional variables, significantly expanding the phase space. For linear ABC triblock copolymers, the sequence order plays a critical role. ABC, ACB, and BAC sequences yield different morphologies due to varying interfacial tensions and chain stretching penalties. For instance, an ABC linear terpolymer with symmetric interaction parameters and compositions may form core-shell gyroid or lamellar structures, where the B domain mediates A and C interfaces. In contrast, ACB sequences often produce more complex architectures like knitting patterns or helical domains due to the mid-block’s connectivity constraints.

The phase behavior of ABC terpolymers is often represented using ternary phase diagrams, where each vertex corresponds to a pure block. Regions of stability for morphologies such as lamellae, hexagonally packed cylinders, and spheres are influenced by the relative volume fractions and χ parameters. For example, at roughly equal volume fractions and strong segregation (high χN), three-color lamellae dominate. As asymmetry increases, perforated layers or tetragonally packed core-shell cylinders emerge. The additional complexity of ABC systems allows for non-equilibrium trapping of metastable states, which can be leveraged to create hierarchical or defect-rich structures for specialized applications.

Star-block copolymers, where multiple arms radiate from a central junction, introduce topological constraints that alter self-assembly. A star architecture with ABC arms (3-arm star terpolymer) exhibits different behavior compared to linear analogs due to the forced proximity of all three blocks at the core. The junction point imposes packing frustration, often leading to curved interfaces and reduced domain sizes. For symmetric star terpolymers with equal arm lengths and compositions, the equilibrium morphology may transition from a three-color lamella to a hexagonal lattice of core-shell disks as the arm number increases. The increased crowding at the core favors higher curvature, stabilizing phases like the double gyroid or Frank-Kasper σ phase at intermediate compositions.

Domain connectivity in these systems is critical for functional properties. In ABC star-blocks, the central junction forces all three domains to meet at a single point, creating a tricontinuous structure if the interfaces are balanced. This is observed in systems where χ_AB ≈ χ_BC ≈ χ_AC, leading to interconnected networks useful for transport applications. As the interaction parameters diverge, one block may become increasingly isolated, breaking the tricontinuity. For example, if χ_AC ≫ χ_AB and χ_BC, the A and C domains will avoid contact, resulting in a B-mediated interface resembling a diblock-like morphology with an additional tethered block.

Architectural variations, such as miktoarm stars (e.g., A_2B_2C_2), further expand the design space. Miktoarm stars with unequal arm lengths or numbers introduce asymmetry in chain stretching, favoring non-uniform domain distributions. A 2A-2B-2C star may form a hexagonal array of alternating A and C rings around a B matrix, while a 1A-1B-2C system could produce a mixed morphology of C spheres and A/B lamellae. The number of arms also affects the critical micelle concentration and aggregation behavior in solution, with higher arm counts generally lowering the CMC due to increased hydrophobicity or interaction energy per molecule.

Experimental studies on poly(isoprene-b-styrene-b-ethylene oxide) (ISO) star terpolymers have demonstrated the formation of complex phases like the core-shell double gyroid, where the I and S domains form interpenetrating networks surrounded by an O matrix. Small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM) reveal lattice parameters scaling with arm molecular weight, confirming the strong dependence of domain spacing on architecture. Similarly, ABC linear terpolymers like polystyrene-b-polybutadiene-b-poly(methyl methacrylate) (SBM) exhibit a rich palette of morphologies, including knitting patterns and helical ribbons, depending on annealing conditions and solvent selectivity.

Theoretical frameworks, including self-consistent field theory (SCFT) and molecular dynamics simulations, have been employed to predict phase behavior in these systems. SCFT calculations for ABC stars show that the phase diagram is highly sensitive to the angle between arms, with 120° separation favoring three-fold symmetric morphologies. Simulations also reveal that kinetic pathways during self-assembly can trap non-equilibrium states, such as perforated lamellae or disordered micellar aggregates, depending on quenching rates and solvent evaporation profiles.

Practical implications of these morphologies are evident in applications ranging from nanoporous membranes to photonic crystals. The tricontinuous networks formed by balanced ABC stars enable efficient ion transport in battery electrolytes, while the tunable domain sizes in miktoarm systems allow for precise control over optical bandgaps. The architectural versatility of these copolymers provides a powerful toolkit for designing next-generation nanomaterials with tailored properties, underscoring the importance of continued research into their self-assembly mechanisms.