Particle analogs of electrons in colloidal crystals

Abstract

A versatile method for the design of colloidal crystals involves the use of DNA as a particle-directing ligand. With such systems, DNA-nanoparticle conjugates are considered programmable atom equivalents (PAEs), and design rules have been devised to engineer crystallization outcomes. This work shows that when reduced in size and DNA grafting density, PAEs behave as electron equivalents (EEs), roaming through and stabilizing the lattices defined by larger PAEs, as electrons do in metals in the classical picture. This discovery defines a new property of colloidal crystals—metallicity—that is characterized by the extent of EE delocalization and diffusion. As the number of strands increases or the temperature decreases, the EEs localize, which is structurally reminiscent of a metal-insulator transition. Colloidal crystal metallicity, therefore, provides new routes to metallic, intermetallic, and compound phases.

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.

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“…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.…”

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

“…As highlighted with additional selective SAXS data from this same temperature ramp experiment that are reproduced in Figure c, it is interesting to note that within the temperature range of 195 °C to 205 °C, all three phases of 1 were seen to coexist, which is a highly rare phenomenon for the thermotropic phase behavior of soft materials . Finally, the number and pattern of intensities for the scattering peaks observed in the 1D SAXS data for both of the two new phases of 1 are signatures for the cubic FK A15 unit cell structure . Indeed, thirteen peaks at q/q*=√2, √4, √5, √6, √8, √10, √12, √13, √14, √17, √18, √21, √29 were successfully matched to those expected for this particular FK phase at 195 °C, with q*=0.0805 Å −1 for the “transient” phase, A15 t , and q*=0.0823 Å −1 for the final equilibrium structure, A15 e (see Figure c).…”

Small‐Molecule Modulation of Soft‐Matter Frank–Kasper Phases: A Method for Adding Function to Form

“…Thermotropic one-component soft-matter Frank-Kasper (FK) phases are fascinating topologically close-packed (TCP) periodic structures that arise in the condensed state through the reconfiguration and self-sorting of deformable sphere-shaped particles into two or more crystallographically distinct sets with different coordination number, size, or shape. [1][2][3][4][5][6][7][8][9][10][11] On the other hand, the small set of currently known thermotropic FK phases that have now been experimentally established over the past 20 years for a range of different soft materials are largely of structural interest, and with only a few rare examples that can be viewed as coupling form with function. [12] Very recently, we reported that the sugar-polyolefin conjugate, cellobiose-triazole-linked atactic poly(4-methyl-1-pentene) (CB-aPMP) (1), undergoes an irreversible thermotropic order-order transition from an initial hexagonal cylindrical (C) morphology to produce a cubic FK A15 (Pm3 n) phase with the unit cell shown in Figure 1.…”