Cooling disordered compositionally asymmetric diblock copolymers leads to the formation of nearly spherical particles, each containing hundreds of molecules, which crystallize upon cooling below the order–disorder transition temperature (T_ODT). Self-consistent field theory (SCFT) reveals that dispersity in the block degrees of polymerization stabilizes various Frank–Kasper phases, including the C14 and C15 Laves phases, which have been accessed experimentally in low-molar-mass poly(isoprene)-b-poly(lactide) (PI-PLA) diblock copolymers using thermal processing strategies. Heating and cooling a specimen containing 15% PLA above and below the T_ODT from the body-centered cubic (BCC) or C14 states regenerates the same crystalline order established at lower temperatures. This memory effect is also demonstrated with a specimen containing 20% PLA, which recrystallizes to either C15 or hexagonally ordered cylinders (HEX_C) upon heating and cooling. The process-path–dependent formation of crystalline order shapes the number of particles per unit volume, n/V, which is retained in the highly structured disordered liquid as revealed by small-angle X-ray scattering (SAXS) experiments. We hypothesize that symmetry breaking during crystallization is governed by the particle number density imprinted in the liquid during ordering at lower temperature, and this metastable liquid is kinetically constrained from equilibrating due to prohibitively large free energy barriers for micelle fusion and fission. Ordering at fixed n/V is enabled by facile chain exchange, which redistributes mass as required to meet the multiple particle sizes and packing associated with specific low-symmetry Frank–Kasper phases. This discovery exposes universal concepts related to order and disorder in self-assembled soft materials.

The phase behavior of B₁AB₂C tetrablock terpolymer melts is systematically studied using the self-consistent field theory, focusing on the emergence and stability of the complex Frank–Kasper σ-phase. Our study starts with an investigation of the stability region of the σ phase for a generic model of B₁AB₂C terpolymers, in which the C-blocks form spherical domains immersed in the A/B matrix. Then, we examine the stability of the σ phase for a model system with a specific set of parameters mimicking poly(styrene-b-isoprene-b-styrene-b-ethylene oxide) (SISO) block copolymers which were examined in recent experiments. Our results reveal that the formation of the σ phase is mainly governed by two factors. The first factor is the conformational asymmetry between the A/B-blocks and the C-block, similar to that in conformationally asymmetric AB-type block copolymers. The second factor is the specific chain architecture of B₁AB₂C. The tetrablock architecture with a specific set of interaction parameters and compositions leads to the formation of large core–shell spherical domains, which amplifies the effect of interfacial energy and thereby stabilizes the σ phase.