About one year ago, we reported the Frank-Kasper (F-K) Z phase in the single-component soft matter system for the first time.1 F-K phases, a family of ordered structures formed from tetrahedrally close-packing of particles with roughly spherical shape, are found in a host of materials such as metal alloys, inorganic colloids, and various types of soft matters. The formation of Z requires a relatively large volume asymmetry. The relatively volume of constructing polyhedra in a Z phase, defined as the ratio between the volume of a constructing polyhedron and the average volume of all the polyhedra, is 90.1%, 102.3%, and 112.6% based on Voronoi cell. The volume asymmetry in a Z phase is larger than the more ubiquitous body-centered cubic phase (volume symmetric), face-centered cubic phase (volume symmetric), F-K A15 phase (97.7%, 100.8%), and F-K σ phase (91.8%, 94.4%, 100.9%, 103.2%, 107.2%). The relatively large volume asymmetry in the Z phase can be one of the reasons why the Z phase is previously not observed in single-component soft matters.
Although the F-K C14 and C15 phases have an even larger volume asymmetry compared with the Z phase (92.8%, 92.8%, 113.9% for C14 phase; 92.2%, 114.2% for C15 phase), they are observed to be thermodynamically metastable in single-component soft matter.2 The volume asymmetry in a Z phase achieved in our work through shape amphiphile molecular design is perhaps close to the upper limit in the single-component soft matter system (Figure 1A). In order to realize even larger volume ratios to generate more complicated F-K phases, other kinds of metal alloy phases, or even some quasicrystal phase, multiple-component soft matter systems should be considered.
Several thermodynamically stable phases with large volume asymmetry (such as the F-K C14 and C15) were already reported recently based on multiple-component soft matter systems, including block copolymer/homopolymer blending systems reported by Bates et al.,3 small molecular surfactant/oil blending systems reported by Mahanthappa et al.,4 and giant molecule blending systems reported by our group.5
Motivated by the wealth of documented metal-alloy F-K phases, there are two main aspects need to be considered for generating other F-K phases. The first critical point is the large volume asymmetry among the constructing polyhedra. This can be achieved by block copolymer/homopolymer blending based on the “dry-brush” mechanism (Figure 1B), or by self-sorted self-assembly process in the blends of two or more types of giant molecules with different inner core structures (Figure 1C). Another point, which is electron orbital interactions in metal-alloy system, is reflected by the outside shells of polyhedra must have identical chemical structures. The identical shell structures of different components could prevent the phase separation and enable ordered nanostructure formation.
After the observation of the Z phase in single component soft matter in our work, more interesting open questions are in front of us. An important but not an easy task in further exploration is how to precisely control the volume asymmetry among the deformed spherical motifs for lattice structure tuning. One step further, could the limit of volume asymmetry degree be further pushed to seek other unprecedented metal alloy analog phases in polymers, not only constrained to the F-K phases? For example, decagonal quasicrystals with 10-fold rotational symmetry are often observed in the phase transition of metal alloys with the C15 phase.
Figure 1. (A) The schematic illustration of the Z phase formation mechanism based on nano-sized shape amphiphile. (B) The schematic illustration of the AB block copolymer/A’ homopolymer blends in the dry-brush model. After adding the homopolymer, a volume-symmetric bcc phase transforms into a volume-asymmetric C15 phase. (C) The schematic illustration of the C15 phase formed by giant molecules blending system.
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Complex self-assembled lattices in single/multiple-component soft matter systems
1 Su, Z. et al. Identification of a Frank–Kasper Z phase from shape amphiphile self-assembly. Nat. Chem. 11, 899-905,(2019).
2 Kim, K. et al. Thermal processing of diblock copolymer melts mimics metallurgy. Science 356, 520-523,(2017).
3 Mueller, A. J. et al. Emergence of a C15 Laves Phase in Diblock Polymer/Homopolymer Blends. ACS Macro Lett. 9, 576-582,(2020).
4 Baez-Cotto, C. M. & Mahanthappa, M. K. Micellar Mimicry of Intermetallic C14 and C15 Laves Phases by Aqueous Lyotropic Self-Assembly. ACS Nano 12, 3226-3234,(2018).
5 Liu, Y. et al. Mesoatom alloys via self-sorting approach of giant molecules blends. Giant 4, 100031,(2020).
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