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

Abstract

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 (CMal-M) with n = 8 (octyl) or 10 (decyl) and M = K, Cs, or (CH)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/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 CMal-M 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. 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.

Role of Chain Length in the Formation of Frank-Kasper Phases in Diblock Copolymers

“…The conclusions of this work are consistent with the recent explosion in the number of reports describing Frank-Kasper phases in surfactant systems [5][6][7], which conform to the N b < N x limit. These findings also explain why tetrahedral packing has not been encountered in diblock copolymers until recently.…”

“…Recent discoveries involving mesoscopic particles formed by self-assembled dendrimers [1][2][3][4], surfactants [5][6][7], and block polymers [8][9][10] have revealed a variety of low-symmetry periodic and aperiodic states of order with particle dimensions ranging from several to tens of nanometers. These tetrahedrally coordinated Frank-Kasper [11,12] and quasicrystalline phases are strikingly similar to those found in many types of metals [13,14] and alloys [15], offering enticing opportunities to establish the universal principles that govern the organization of dense arrays of particles in condensed matter [16].…”

Path-Dependent Preparation of Complex Micelle Packings of a Hydrated Diblock Oligomer

“…While the (002) reflection for the A15 phase is distinct from the (002) peak for the σ phase, the relatively close values are consistent with the observed epitaxial relationship between these tetrahedrally close packed FK phases. 19,29,30,35 Over a period of 150 days of isothermal annealing at 25 °C, the sample continues to evolve and eventually transforms into a pure A15 phase (Figure 5). Note that the unit cell parameter for this A15 phase is identical to that of the initially prepared LLC ( a = 14.7 nm), indicating the apparent metastability of the σ phase with respect to the thermodynamically preferred A15 phase at 25 °C.…”

Frank–Kasper Phases Identified in PDMS‐b‐PTFEA Copolymers with High Conformational Asymmetry

“…Since the pioneering recognition of fascinating atomic or molecular geometries by Frank and Kasper, the Frank–Kasper (FK) phases were originally discovered in hard materials such as inter‐metallic alloys . However, these intricate structural orders have also been identified in a host of soft materials, including dendrimers, surfactants, and block copolymers …”