Dodecagonal tiling in mesoporous silica

Chen, Xiao; Fujita, Nobuhisa; Miyasaka, Keiichi; Sakamoto, Yasuhiro; Terasaki, Osamu

doi:10.1038/nature11230

Cited by 155 publications

(150 citation statements)

References 24 publications

Supporting

Mentioning

136

Contrasting

Unclassified

Order By: Relevance

“…Because these FK phases are also 3D periodic approximants to dodecagonal QCs, our observations suggest design principles for driving colloidal materials to form soft QCs at various length scales. Reports of surfactant-templated mesoporous silicate FK phases and 12-and 18-fold block polymer lyotropic QCs reflect initial discoveries in this exciting direction (26,33,34).…”

Section: Discussionmentioning

confidence: 88%

Low-symmetry sphere packings of simple surfactant micelles induced by ionic sphericity

Kim

Jeong

Yethiraj

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

118

137

View full text Add to dashboard Cite

Supramolecular self-assembly enables access to designer soft materials that typically exhibit high-symmetry packing arrangements, which optimize the interactions between their mesoscopic constituents over multiple length scales. We report the discovery of an ionic small molecule surfactant that undergoes water-induced selfassembly into spherical micelles, which pack into a previously unknown, low-symmetry lyotropic liquid crystalline Frank-Kasper σ phase. Small-angle X-ray scattering studies reveal that this complex phase is characterized by a gigantic tetragonal unit cell, in which 30 sub-2-nm quasispherical micelles of five discrete sizes are arranged into a tetrahedral close packing, with exceptional translational order over length scales exceeding 100 nm. Varying the relative concentrations of water and surfactant in these lyotropic phases also triggers formation of the related Frank-Kasper A15 sphere packing as well as a common body-centered cubic structure. Molecular dynamics simulations reveal that the symmetry breaking that drives the formation of the σ and A15 phases arises from minimization of local deviations in surfactant headgroup and counterion solvation to maintain a nearly spherical counterion atmosphere around each micelle, while maximizing counterion-mediated electrostatic cohesion among the ensemble of charged particles.self-assembly | liquid crystals | surfactants | Frank-Kasper phases | lyotropic phase M olecular self-assembly provides a facile means of constructing a plethora of multifunctional soft materials, with mesoscopic structures that dictate their tailored properties and performance applications. Driven by noncovalent interactions between constituents, block polymers (1), giant shape amphiphiles (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 structures, and 3D packings of spherical particles. Columnar and spherical phases are useful as templates for mesoporous heterogeneous catalysts (6) and as microscale photonic bandgap materials (7). Manipulating supramolecular self-assembly to achieve specific materials morphologies and functions requires a fundamental understanding of the interplay between the structure and symmetry of the constituents and their multibody interactions.Although the packing of spherical objects (e.g., oranges and billiard balls) seems intuitively simple, point particles form a dizzying array of periodic crystals, quasicrystals (QCs), and structurally disordered glasses. Metallic elements typically form high-symmetry body-centered cubic (BCC), hexagonally closest-packed, and facecentered cubic (FCC) structures, due to the isotropy of metallic cohesion mediated by itinerant electrons (8). A few pure elements (e.g., Mn and U) form low-symmetry crystals with large and complex unit cells that maximize metallic cohesion against local constraints, such as maximization of Fermi surface sphericity (9).Sphere-forming soft mater...

show abstract

Section: Discussionmentioning

confidence: 88%

Low-symmetry sphere packings of simple surfactant micelles induced by ionic sphericity

Kim

Jeong

Yethiraj

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

118

137

View full text Add to dashboard Cite

show abstract

“…This contrasts with the single local coordination environment of the particles, one per lattice site, associated with the BCC structure. The σ phase is a periodic approximant to an aperiodic dodecagonal quasicrystal structure; reports of the DDQC in soft materials often coincide with the observation of the σ phase (3)(4)(5)8). We have proposed that the spontaneous symmetry breaking associated with the formation of the low-symmetry σ phase in diblock copolymers, which requires a redistribution of mass between particles to accommodate the five Significance Spherical objects ranging in size from metal atoms to micron-scale colloidal particles to billiard balls tend to form regular close packed arrays with three-dimensional translational symmetry.…”

mentioning

confidence: 87%

“…More recently, quasicrystalline order has been found in an expanding variety of soft materials including self-assembling wedge-shaped dendrimers, mixtures of ligand coated nanoparticles, concentrated solutions of surfactant and block polymer micelles, multicomponent polymer blends containing ABC-type miktoarm star polymers, and an ABA′C-type linear multiblock polymer (3)(4)(5)(6)(7)(8). The underlying principles that govern the formation of quasicrystals in soft materials remain largely unresolved.…”

mentioning

confidence: 99%

Dodecagonal quasicrystalline order in a diblock copolymer melt

Gillard

Lee

Bates

2016

Proc. Natl. Acad. Sci. U.S.A.

182

264

View full text Add to dashboard Cite

We report the discovery of a dodecagonal quasicrystalline state (DDQC) in a sphere (micelle) forming poly(isoprene-b-lactide) (IL) diblock copolymer melt, investigated as a function of time following rapid cooling from above the order-disorder transition temperature (T ODT = 66°C) using small-angle X-ray scattering (SAXS) measurements. Between T ODT and the order-order transition temperature T OOT = 42°C, an equilibrium body-centered cubic (BCC) structure forms, whereas below T OOT the Frank-Kasper σ phase is the stable morphology. At T < 40°C the supercooled disordered state evolves into a metastable DDQC that transforms with time to the σ phase. The times required to form the DDQC and σ phases are strongly temperature dependent, requiring several hours and about 2 d at 35°C and more than 10 and 200 d at 25°C, respectively. Remarkably, the DDQC forms only from the supercooled disordered state, whereas the σ phase grows directly when the BCC phase is cooled below T OOT and vice versa upon heating. A transition in the rapidly supercooled disordered material, from an ergodic liquid-like arrangement of particles to a nonergodic soft glassy-like solid, occurs below ∼40°C, coincident with the temperature associated with the formation of the DDQC. We speculate that this stiffening reflects the development of particle clusters with local tetrahedral or icosahedral symmetry that seed growth of the temporally transient DDQC state. This work highlights extraordinary opportunities to uncover the origins and stability of aperiodic order in condensed matter using model block polymers.quasicrystals | Frank-Kasper phases | block polymers T he discovery of aperiodic order, today referred to as quasicrystalline order, in rapidly cooled Al-Mn alloys by Shechtman and coworkers in 1984 heralded a paradigm shift in the understanding of what constitutes long-range order in matter (1, 2). More recently, quasicrystalline order has been found in an expanding variety of soft materials including self-assembling wedge-shaped dendrimers, mixtures of ligand coated nanoparticles, concentrated solutions of surfactant and block polymer micelles, multicomponent polymer blends containing ABC-type miktoarm star polymers, and an ABA′C-type linear multiblock polymer (3-8). The underlying principles that govern the formation of quasicrystals in soft materials remain largely unresolved.Block polymers are uniquely tunable self-assembling soft materials in which the nanoscale morphology, characteristic length scale, chemical and physical properties, and dynamics can be precisely controlled through the judicious choice of block repeat unit chemistries, block molecular weights, and molecular architecture (9, 10). Such exquisite control over structure, and the associated dynamics, makes block polymers ideal model materials for fundamental inquiries into the formation and stability of soft quasicrystals. In this article, we report the discovery of a long-lived metastable dodecagonal quasicrystalline phase (DDQC) in a (nominally) single-component poly(1,4-is...

show abstract

“…The vast majority of the QCs discovered so far are metallic alloys (e.g., Al/Mn or Cd/Ca). However, QCs have recently been found in nanoparticles [2], mesoporous silica [3], and soft matter [4] systems. The latter include micellar melts [5,6] formed, e.g., from linear, dendrimer or star block copolymers.…”

mentioning

confidence: 99%

Three-Dimensional Icosahedral Phase Field Quasicrystal

et al. 2016

View full text Add to dashboard Cite

We investigate the formation and stability of icosahedral quasicrystalline structures using a dynamic phase field crystal model. Nonlinear interactions between density waves at two length scales stabilize threedimensional quasicrystals. We determine the phase diagram and parameter values required for the quasicrystal to be the global minimum free energy state. We demonstrate that traits that promote the formation of two-dimensional quasicrystals are extant in three dimensions, and highlight the characteristics required for three-dimensional soft matter quasicrystal formation. DOI: 10.1103/PhysRevLett.117.075501 Periodic crystals form ordered arrangements of atoms or molecules with rotation and translation symmetries, and possess discrete x-ray diffraction patterns, or equivalently, discrete spatial Fourier spectra. In contrast, quasicrystals (QCs) lack the translational symmetries of periodic crystals, yet also display discrete spatial Fourier spectra. QCs made from metal alloys were discovered in 1982 [1] and attracted the Nobel prize for chemistry in 2011. QCs can be quasiperiodic in all three dimensions (e.g., with icosahedral symmetry), or can be quasiperiodic in two (or one) directions while being periodic in one (or two). The vast majority of the QCs discovered so far are metallic alloys (e.g., Al/Mn or Cd/Ca). However, QCs have recently been found in nanoparticles [2], mesoporous silica [3], and soft matter [4] systems. The latter include micellar melts [5,6] formed, e.g., from linear, dendrimer or star block copolymers. Recently, three-dimensional (3D) icosahedral QCs have been found in molecular dynamics simulations of particles interacting via a three-well pair potential [7].In recent years, model systems in two dimensions (2D) have been studied in order to understand soft matter QC formation and stability [8][9][10][11][12]. Phase field crystal models have been employed to simulate the growth of 2D QCs [13] and the adsorption properties on a quasicrystalline substrate [14]. The ingredients for 2D quasipattern formation are, first, a propensity towards periodic density modulations with two characteristic wave numbers k 1 and k 2 [15-18]. The ratio k 2 =k 1 must be close to certain special values; e.g., for dodecagonal QCs the value is 2 cosðπ=12Þ. Second, strong reinforcing (i.e., resonant) nonlinear interactions between these two characteristic density waves are required [17,19,20]. Earlier work on quasipatterns observed in Faraday wave experiments reveals similar requirements [19,[21][22][23]. We demonstrate here, following Mermin and Troian [24], that these same requirements suffice to stabilize icosahedral QCs in 3D. In contrast, nonlinear resonant interactions between density waves at a single wavelength are important in stabilizing simple crystal structures, such as body-centered cubic (bcc) crystals [25] although, with the right coupling, QCs can also be stabilized [26].We consider a 3D phase field crystal (PFC) model, appropriate for soft matter systems, that generates modulations with two l...

show abstract

Dodecagonal tiling in mesoporous silica

Cited by 155 publications

References 24 publications

Low-symmetry sphere packings of simple surfactant micelles induced by ionic sphericity

Low-symmetry sphere packings of simple surfactant micelles induced by ionic sphericity

Dodecagonal quasicrystalline order in a diblock copolymer melt

Three-Dimensional Icosahedral Phase Field Quasicrystal

Contact Info

Product

Resources

About