The C36 Laves phase in diblock polymer melts

Abstract

The C14 and C15 Laves phases form as micelle packing structures in many types of soft matter, but the related C36 phase, which consists of alternating C14-type and C15-type layers,...

Emergence and Stability of Exotic “Binary” HCP-Type Spherical Phase in Binary AB/AB Blends

“…At the beginning, we just considered the similar candidate phases as those considered in the previous work by Liu et al, , including the BCC, C14, C15, σ, A15, and hexagonal cylinder (C 6 ) phases (Figure ). Though there is another Laves phase named as C36, Magruder, and Dorfman have verified that the C36 phase cannot be stable in neat AB or AB/A blending systems . In our SCFT calculations, we have confirmed that the stability of C36 is intermediate between C14 and C15, and thus, it does not have a stable region in the AB/AB blending system.…”

Laves Phase Field in a Diblock Copolymer Alloy

“…These bcc phases are composed of micelles of the majority component at the lattice sites, with the minority component at the interstitial sites. The choice of C15 (vs C14) for the present purposes is arbitrary as these two phases are nearly degenerate in free energy as shown in prior work, 17,18,32,59 and that proves to be the case here, too (Figure S10).…”

“…This near-degeneracy between C14 and C15 is expected from prior work. 17,18,32,59 Ultimately, distinguishing between these two very similar Laves phase particle packings is of little relevance in practice because fluctuation effects 12 and uncertainties in the experimental data (polydispersity, precision in measuring the degree of polymerization, mapping multiple χ parameters to experiments 64,65 ) make it challenging to translate such subtle SCFT predictions into experimental realizations. For this reason, we will simply refer to the stable state as the "Laves" phase in what follows, with the understanding that SCFT predicts C14 but it is very plausible that C15 could be realized in practice.…”

“…Here, the selection of the ordered state is governed by a competition between chain stretching and interfacial tension subject to the constraint of constant density and thus exposes the geometric role of particle packing on the selection of ordered state symmetry. While bcc is the most commonly observed particle packing in block polymer melts, various Frank–Kasper phases have been observed as well, − consistent with their emergence in other forms of soft matter. − However, Laves phases are much less commonly observed in diblock copolymer melts − than other Frank–Kasper phases, and theory predicts that only the C14 and C15 Laves phases are likely to be stable . Moreover, the Laves phases seen to date appear in block polymer phase diagrams as stability windows rather than the line compounds that emerge for intermetallic compounds.…”

“…23−31 However, Laves phases are much less commonly observed in diblock copolymer melts 17−22 Laves phases are likely to be stable. 32 Moreover, the Laves phases seen to date appear in block polymer phase diagrams as stability windows rather than the line compounds that emerge for intermetallic compounds. In the present contribution, we describe an approach, inspired by metallic alloys and supported by self-consistent field theory (SCFT) calculations, that promotes the formation of block copolymer Laves phases as a phase field (i.e., a nonideal line compound) within a eutectic phase diagram that closely mimics that observed for metal alloys.…”