The self-consistent field theory (SCFT) predicted the existence of a close-packed sphere phase over a narrow window in the phase diagram of a block copolymer (bcp). It however remains unclear whether the face-centered cubic (FCC) or hexagonal close-packed (HCP) lattice represents the more stable close-packed lattice of the spherical micelles formed by the neat bcp in the quiescent melt. Here, we revisited this problem by exploring the stable close-packed lattice of conformationally symmetric poly(ethylene oxide)-block-poly(1,2-butadiene) (PEOb-PB). We disclosed that an HCP structure eventually formed in the ordered phase upon cooling from the micellar liquid phase. The micelle ordering was found to follow the Ostwald's step rule of the Alexander−McTague type, where a metastable BCC phase first developed followed by a transformation into the stable HCP structure. The higher thermodynamic stability of HCP relative to that of FCC was consistent with the prediction of a later SCFT calculation by Matsen and also demonstrated the generic difference between soft colloids and hard colloids in selecting their stable close-packed lattices.

Previous studies of the Frank−Kasper (FK) phase of block copolymer (bcp) have highlighted the significance of the mass transfer of constituent molecules in regulating the micelle size to fit in the volume asymmetry of the Voronoi cells comprising the lattice. Here, we present the transformation of a metastable liquidlike packing (LLP) phase into the Laves C14 phase of a conformationally symmetric bcp below the glass-transition temperature of the micelle core (T g core ), where the mass transfer during the phase transition was prohibited. The micelles composed of a hard core and a soft corona resembled fuzzy colloids, with their ordering process occurred under the particle number density and size distribution inherited from the LLP phase. We argue that the relatively high size dispersity of the particles drove the hard-core micelles to pack into the C14 phase to relieve the packing frustration of the coronal blocks and the intermicellar repulsion due to the large volume asymmetry and the small surface area, respectively, of the Voronoi cells constituting C14 phase. The present study identified a new regime in which FK phase could emerge from the LLP phase with adequately high polydispersity of particle size even for conformationally symmetric bcp and supported the significance of the LLP structure in directing the ordered packing of bcp micelles.

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The formation of a Frank–Kasper (FK) phase in a one-component block copolymer (bcp) has been attributed to the sufficiently large conformational asymmetry parameter that leads to the deformation of the micellar core into the polyhedral shape templated by the Voronoi cells for relieving the packing frustration of the coronal blocks. Here we present the insight into the evolution of body-centered cubic (BCC) and Laves C14 phases from the corresponding metastable liquidlike packing (LLP) phases in a conformationally symmetric poly(2-vinylpyridine)-block-poly(dimethylsiloxane) (P2VP-b-PDMS) forming the colloid-like micelle with a hard P2VP core and a soft PDMS corona at the temperature of micelle ordering (T g corona < T a < T g core). Different thermal processing conditions were applied to produce four distinct types LLP phase characterized by different average micelle size and size dispersity. The LLP phase was found to transform to BCC, C14 and a reorganized LLP phase with increasing polydispersity of particle size, showing the existence of a proper range of size dispersity for the formation of the Laves phase. The real-space analysis of the local environments of the particles revealed that the C14 phase can accommodate the particles with a broader range of interparticle distance and a less uniform local environment, such that the PDMS coronal blocks of the micelles with greater size dispersity suffered a lower degree of packing frustration when they organized into a C14 lattice. In view of the colloid-like nature of the micelle, a size fractionation process found in the crystallization of polydisperse colloidal particles was proposed as the mechanism for directing the effective development of C14 phase from the LLP phase. Due to the metastable nature of the ordered phases, their order–disorder transition temperatures were found to depend strongly on the structures of the LLP phases from which they developed and a strong memory effect underlying the phase transitions was identified.

The discovery of Frank-Kasper (FK) phase in block copolymer (bcp) has prompted the progress of the field of soft quasicrystals. In principle, the formation of FK phase from the supercooled liquid phase of the bcp micelles should involve the mass transport of constituent molecules to transform the unimodal distribution of micelle size into the multimodal distribution prescribed by the volume asymmetry of the Voronoi cells in the FK phase. Here we present a new regime in which the Laves C14 phase of bcp developed below the glass transition temperature of the micelle core, where the mass transport was inhibited by the immobile block chains forming the core. The bcp micelle comprising a glassy core and a soft corona resembles the fuzzy colloid and the strong van der Waals attraction between the cores directs their organization into C14 phase to minimize the interparticle interaction energy under the metastable condition.