Evidence for a C14 Frank–Kasper Phase in One-Size Gold Nanoparticle Superlattices

Abstract

The Frank-Kasper phases were already known in 1982 when quasi-crystals were discovered, but their complex architectures are now considered as making a link between simple close-packed periodic structures and some quasi-periodic ones. These tetrahedrally close packed structures are observed in many materials from elements to intermetallics as well as self-assembled soft materials like micellar systems, dendritric liquid crystals, star polymers, and more recently block copolymers or heated gold nanocrystal superlattices. We report here the existence of a Frank-Kasper phase with hexagonal symmetry (MgZn2 type, also labeled C14) in superlattices of monodisperse hydrophobically coated gold particles at room temperature obtained from suspensions in various solvents. The existence of such a structure in this system is analyzed in terms of geometrical parameters including gold core diameter, ligand length, and grafting density and an energetic approach based on van der Waals attraction. Hydrophobically coated gold nanoparticles is a new system that exhibits a Frank and Kasper phase built by one-size objects. This result opens a route toward a nanoparticle superlattice with complex structures and thus original physical properties.

Stable Frank–Kasper phases of self-assembled, soft matter spheres

“…Once considered anomalous in soft matter systems, the past decade has seen an explosion in the observation of FK lattices in a diverse range of sphere-forming assemblies. These include (A15, σ) liquid-crystalline dendrimers [7,8], linear (σ,A15) tetrablock [9,10], (σ, A15, C14, C15) diblock [11][12][13] and (A15) linear-dendron [14] block copolymer melts, (A15) amphiphilic nanotetrahedra [15,16], (A15, σ, C14, C15) concentrated ionic surfactants [17,18] and (C14) monodisperse, functionalized nanoparticles [19]. The central puzzle surrounding the formation of FK lattices in these diverse systems is understanding why single-components assemble into phases composed of highly heterogeneous molecular environments.…”

Complex Crystals from Size-Disperse Spheres

“…It has been proposed that dynamic dispersity assists the formation of Frank-Kasper (FK) phases [19] and other topologically close-packed complex crystals [20][21][22]. Indeed, the FK phases A15, σ, and Laves C14 and C15 are found with micelles [23][24][25][26][27][28] and soft nanoparticles [29] where shape dispersity and size dispersity are dynamic because micelles and nanocrystal ligand shells can deform and exchange molecules. Topologically closepacked crystals also occur in the elements Mn and U at elevated temperature [30][31][32] where conduction electrons are mobile.…”

An Exceptionally Stable and Scalable Sugar–Polyolefin Frank–Kasper A15 Phase

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One-component" soft material Frank-Kasper (FK) phases are an intriguing structural form of matter that possess periodically ordered structures arising from the self-reconfiguration and close packingo fa ni nitial assembly of identical "deformable" spheres into two or more size-or shape-distinct sets of particles.S ignificant challenges that must still be addressed to advance the field of soft matter FK phases further,h owever,i nclude their rare and unpredictable occurrence,u ncertain mechanisms of solid-state assembly,a nd low thermodynamic stability.H ere we show that ar eadily-accessible sugar-polyolefin conjugate quantitatively produces an exceptionally stable solid-state FK A15 phase through arapid and irreversible thermotropic order-order transition, which contrary to other prevailing proposed mechanisms,d oes not require mass transfer between particles or large structural reorganization in the bulk to establish unit cell non-equivalency.Our results provide the basis for arealistic strategy for obtaining practical and scalable quantities of adiverse range of sugar-polyolefin FK A15 phases with unique intrinsic physical properties and chemical reactivities not previously seen in such systems.Periodically-ordered, "one-component" soft matter Frank-Kasper (FK) phases,w hich arise from the topological close packing (TCP) of "deformable" sphere-shaped particles,have now been experimentally verified for amphiphilic liquid crystals and dendrons,b lock copolymers," giant" molecules and surfactants,a nd colloidal nanoparticles. [1][2][3][4][5][6][7][8][9] Frank and Kasper [10] originally developed the concept of TCP to rationalize how the complex crystal structures of certain intermetallic alloys arise through the packing of asymmetric polyhedra that are associated with different sets of atoms that define ap articular coordination number, CNx, where x = 12,14,15, or 16. Forexample,asshown in Figure 1, the unit cell of the cubic FK A15 (Pm3 n)p hase,w hich is found for some bimetallic alloys with A 3 Bstoichiometry (e.g.

…”

“…Periodically-ordered, "one-component" soft matter Frank-Kasper (FK) phases,w hich arise from the topological close packing (TCP) of "deformable" sphere-shaped particles,have now been experimentally verified for amphiphilic liquid crystals and dendrons,b lock copolymers," giant" molecules and surfactants,a nd colloidal nanoparticles. [1][2][3][4][5][6][7][8][9] Frank and Kasper [10] originally developed the concept of TCP to rationalize how the complex crystal structures of certain intermetallic alloys arise through the packing of asymmetric polyhedra that are associated with different sets of atoms that define ap articular coordination number, CNx, where x = 12,14,15, or 16. Forexample,asshown in Figure 1, the unit cell of the cubic FK A15 (Pm3 n)p hase,w hich is found for some bimetallic alloys with A 3 Bstoichiometry (e.g.…”