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Counterion-Dependent Access to Low-Symmetry Lyotropic Sphere Packings of Ionic Surfactant Micelles

The water-driven self-assembly of homologous dianionic surfactants into lyotropic liquid crystals (LLCs) is investigated, with a focus on understanding how surfactant headgroup and counterion identities guide supramolecular spherical mesophase selection. Using temperature-dependent small-angle X-ray scattering (SAXS), we demonstrate that 2-alkylmalonate surfactants (CnMal-M2) with n = 8 (octyl) or 10 (decyl) and M = K + , Cs + , or (CH 3 ) 4 N + form both simple and complex micelle packings. Observed spherical morphologies include body-centered cubic (BCC), hexagonally closest-packed (HCP), and tetrahedrally closest-packed Frank–Kasper (FK) A15 and σ phases (Pm3(–)n and P4 2 /mnm symmetries, respectively). Previously observed in only one other minimally hydrated surfactant, the σ phase is a rare LLC morphology comprising a low-symmetry unit cell containing 30 sub-2-nm quasispherical micelles, each of which belongs to one of five symmetry-equivalent classes with discrete aggregation numbers. Temperature versus water concentration phase maps for C n Mal-M 2 LLCs reveal that σ-phase formation depends sensitively on the size and polarizability of the surfactant counterion and the length of the surfactant alkyl tail. Furthermore, these observations are rationalized in terms of a delicate interplay between global packing symmetry and local particle symmetry, and the extent to which counterion–headgroup correlations enforce the latter structures in these LLC phases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Conventional and Stuffed Bergman-Type Phases in the Na-Au-T (T = Ga, Ge, Sn) Systems: Syntheses, Structures, Coloring of Cluster Centers, and Fermi Sphere–Brillouin Zone Interactions

Bergman-type phases in the Na-Au-T (T = Ga, Ge, and Sn) systems were synthesized by solid-state means and structurally characterized by single-crystal X-ray diffraction studies. Two structurally related (1:1) Bergman phases were found in the Na-Au-Ga system: (a) a conventional Bergman-type (CB) structure, Na 26 Au x Ga 54-x , which features empty innermost icosahedra, as refined with x = 18.1 (3), Im$\overline{3}$ a = 14.512(2) Å, and Z = 2; (b) a stuffed Bergman-type (SB) structure, Na 26 Au y Ga 55-y , which contains Gacentered innermost icosahedra, as refined with y = 36.0 (1), Im$\overline{3}$, a = 14.597(2) Å, and Z = 2. Although these two subtypes have considerable phase widths along with respective tie lines at Na ≈ 32.5 and 32.1 atom %, they do not merge into a continuous solid solution. Rather, a quasicrystalline phase close to the Au-poor CB phase and an orthorhombic derivative near the Au-rich SB phase lie between them. In contrast, only Au-rich SB phases exist in the Ge and Sn systems, in which the innermost icosahedra are centered by Au rather than Ge or Sn. These were refined for Na26Au40.93(5)Ge14.07(5) (Im$\overline{3}$, a = 14.581(2) Å, and Z = 2) and Na 26 Au 39.83(6) Sn 15.17(6) (Im$\overline{3}$, a = 15.009(2) Å, and Z = 2), respectively. Occupations of the centers of Bergman clusters are rare. Such centering and coloring correlate with the sizes of the neighboring icosahedra, the size ratios between electropositive and electronegative components, and the values of the average valence electron count per atom (e/a). Theoretical calculations revealed that all of these phases are Hume-Rothery phases, with evident pseudogaps in the density of states curves that arise from the interactions between Fermi surface and Brillouin zone boundaries corresponding to a strong diffraction intensity.

36 MATERIALS SCIENCE↗