Low-Symmetry Sphere Packings of Simple Surfactant Micelles Induced by Ionic Sphericity
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Low-symmetry sphere packings of simple surfactant micelles induced by ionic sphericity Sung A Kima, Kyeong-Jun Jeongb, Arun Yethirajb, and Mahesh K. Mahanthappaa,1 aDepartment of Chemical Engineering & Materials Science, University of Minnesota, Minneapolis, MN 55455; and bDepartment of Chemistry and Theoretical Chemistry Institute, University of Wisconsin–Madison, Madison, WI 53706 Edited by Michael L. Klein, Temple University, Philadelphia, PA, and approved March 9, 2017 (received for review January 29, 2017) Supramolecular self-assembly enables access to designer soft mate- and lipidic LLCs were identified over 30 y ago, yet the principles rials that typically exhibit high-symmetry packing arrangements, governing their formation remain poorly understood (17). More which optimize the interactions between their mesoscopic constitu- recently, FK A15 and σ phases were documented in thermotropic ents over multiple length scales. We report the discovery of an ionic LCs of wedge-shaped dendrons (18–20), linear diblock and mul- small molecule surfactant that undergoes water-induced self- tiblock polymers (21, 22), and giant shape amphiphiles (2, 23). assembly into spherical micelles, which pack into a previously These studies culminated in the discovery of soft, dodecagonal unknown, low-symmetry lyotropic liquid crystalline Frank–Kasper σ QCs (23–26), for which the A15 and σ phases are 3D periodic phase. Small-angle X-ray scattering studies reveal that this complex approximants. phase is characterized by a gigantic tetragonal unit cell, in which Many of the previously reported soft matter FK phases optimize 30 sub-2-nm quasispherical micelles of five discrete sizes are arranged the van der Waals packing of hairy, uncharged particles that fill into a tetrahedral close packing, with exceptional translational order space at constant density, while minimizing unfavorable interfacial over length scales exceeding 100 nm. Varying the relative concentra- interactions between the particle cores and coronae (2, 17, 19, 21). tions of water and surfactant in these lyotropic phases also triggers In this paper, we describe the spontaneous formation of a new, – formation of the related Frank Kasper A15 sphere packing as well as direct LLC FK σ phase by simple ionic surfactant micelles in water. a common body-centered cubic structure. Molecular dynamics simu- Complementary molecular dynamics (MD) simulations reveal a lations reveal that the symmetry breaking that drives the formation σ previously unrecognized mechanism for forming low-symmetry, of the andA15phasesarisesfromminimization of local deviations periodic materials from charged self-assembled particles. in surfactant headgroup and counterion solvation to maintain a nearly spherical counterion atmosphere around each micelle, while Results and Discussion maximizing counterion-mediated electrostatic cohesion among the Synchrotron small-angle X-ray scattering (SAXS) was used to in- ensemble of charged particles. vestigate the aqueous LLC phase diagram of bis(tetramethy- lammonium) decylphosphonate (DPA-TMA )between25–100 °C, self-assembly | liquid crystals | surfactants | Frank–Kasper phases | lyotropic 2 with water contents w = (moles H O)/(moles DPA-TMA ) = phase 0 2 2 0–44 (Fig. 1A). Aqueous LLCs were produced by thoroughly mixing measured amounts of DPA-TMA2 with ultrapure water (Materials olecular self-assembly provides a facile means of con- and Methods and SI Appendix). Samples with w0 ≥ 44 are freely Mstructing a plethora of multifunctional soft materials, with flowing fluids, indicative of disordered micellar solutions. When mesoscopic structures that dictate their tailored properties and w0 = 31–42, we observe SAXS peaks at q/q* = √2, √4, √6, and performance applications. Driven by noncovalent interactions between constituents, block polymers (1), giant shape amphiphiles Significance (2), thermotropic liquid crystals (LCs) (3), lyotropic liquid crystals (LLCs) (4), and colloids (5) exemplify soft matter systems that “ ” spontaneously form periodic 1D lamellar phases, 2D columnar Surfactants ( soaps ) spontaneously self-assemble into spher- structures, and 3D packings of spherical particles. Columnar and ical micelles in water, which pack into ordered crystalline spherical phases are useful as templates for mesoporous hetero- states. Such soft particles have long been assumed to adopt geneous catalysts (6) and as microscale photonic bandgap mate- the same closest-packed configurations observed with hard rials (7). Manipulating supramolecular self-assembly to achieve spheres (e.g., billiard balls). Here, we show that surfactant micelles also form complex, tetrahedrally closest-packed Frank– specific materials morphologies and functions requires a funda- Kasper (FK) phases. Surprisingly, the low-symmetry unit cells of mental understanding of the interplay between the structure and these structures comprise multiple particle types with discrete symmetry of the constituents and their multibody interactions. size distributions. We demonstrate that these unexpected Although the packing of spherical objects (e.g., oranges and structures arise from simultaneous optimization of interparticle billiard balls) seems intuitively simple, point particles form a diz- electrostatic interactions and the spherical symmetry of the zying array of periodic crystals, quasicrystals (QCs), and structurally charged ion clouds around each micelle. This discovery bridges disordered glasses. Metallic elements typically form high-symmetry previous reports of FK phases in neutral soft materials such as body-centered cubic (BCC), hexagonally closest-packed, and face- block polymers, dendrimers, and giant shape amphiphiles and centered cubic (FCC) structures, due to the isotropy of metallic in metal alloys. cohesion mediated by itinerant electrons (8). A few pure elements (e.g., Mn and U) form low-symmetry crystals with large and Author contributions: S.K., K.-J.J., A.Y., and M.K.M. designed research; S.K., K.-J.J., and complex unit cells that maximize metallic cohesion against local M.K.M. performed research; S.K., K.-J.J., A.Y., and M.K.M. analyzed data; and S.K., K.-J.J., constraints, such as maximization of Fermi surface sphericity (9). A.Y., and M.K.M. wrote the paper. Sphere-forming soft materials tend to prefer different packing The authors declare no conflict of interest. symmetries from those of metallic solids (10). Although squishy This article is a PNAS Direct Submission. spheres do form BCC and FCC crystals, they also form tetrahe- Freely available online through the PNAS open access option. drally closest-packed Frank–Kasper (FK) phases that contain 1To whom correspondence should be addressed. Email: [email protected]. – combinations of 12-, 14-, 15-, and 16-coordinate lattice sites (11 This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 14). The first FK A15 (15) and C15 (16) phases in ionic surfactant 1073/pnas.1701608114/-/DCSupplemental. 4072–4077 | PNAS | April 18, 2017 | vol. 114 | no. 16 www.pnas.org/cgi/doi/10.1073/pnas.1701608114 Downloaded by guest on September 28, 2021 reversibly melt into disordered micellar solutions at elevated A temperatures. Decreasing the surfactant hydration to w0 = 20–31 yields an LLC that exhibits at least 50 instrument resolution-limited SAXS peaks (Fig. 1B and SI Appendix, Fig. S1), inconsistent with any known lyotropic phase. Crystallographic analyses of the w0 = 24.0 LLC reveal a tetragonal unit cell with P42/mnm symmetry and lattice parameters a = 13.36 nm and c = 7.02 nm (SI Ap- pendix, Table S1). The numerous sharp SAXS reflections in- dicate exceptional translational ordering of sub-2-nm-diameter micelles in a water matrix on length scales ≥ 100 nm. The re- semblance between this remarkable diffraction pattern and those of thermotropic LC and block polymer FK σ phases (19, 21), coupled with the lattice symmetry and characteristic unit cell parameter ratio c/a = 0.526, strongly imply the formation of the first LLC σ phase. Le Bail SAXS data refinement combined with charge-flipping algorithms (27, 28) enabled electron density map reconstruction forthisLLCσ phase (Fig. 2 A–C). The water-filled unit cell contains 30 quasispherical micelles arranged into alternating sparsely and densely populated layers, consistent with other σ phase structures (19, 21). The micelles apparently have different volumes and exhibit soft facets, with the facets of neighboring micelles facing one another (Figs. 2 B and C and 3A). In contrast to previously reported soft matter σ phases wherein the particles make van der Waals contacts, the ionic micelles in this LLC σ phase sit in a water matrix and make no apparent physical contacts. LLCs formed at w0 = 10–18 typically display at least 18 SAXS peaks at q/q* = √2, √4, √5, √6, √8,andsoon(Fig.1B), which B conform to cubic Pm3(–)n symmetry with unit cell parameters a ∼ 6.95 nm. The electron density reconstruction for this phase in Fig. 2D is consistent with known soft matter A15 phases (15, 18). The corner and center micelles are somewhat facetted in the 90% isosurface plots, and the pairs of larger particles in each unit cell face are severely distorted despite their spatial CHEMISTRY separation by water (Fig. 2 E and F). At the lowest hydrations studied (w0 = 6), we observed a hexagonally packed cylinders morphology (SI Appendix,Fig.S2). The σ and A15 LLC electron density maps reveal that they comprise squashed micelles with different volumes, instead of the uniform spherical particles intuitively