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. Nb 3 Sn), can be seen as arising from two crystallographically equivalent B sites that reside within CN12 distorted icosahedra, while six equivalent face-shared As ites are associated with CN14 polyhedra. Other commonly encountered bimetallic FK phases include the Laves C14 and C15 structures for A 2 B alloys (e.g.MgZn 2 ), and the complex s phase for AB alloys of

Ultra-low molecular weight disaccharide-polyolefin conjugates with cellobiose, lactose and maltose head groups and atactic polypropene tails, such as 1, undergo a series of irreversible thermotropic order-order transitions with increasing temperature to provide nanostructured phases in the sequence: lamellar (L), hexagonal perforated lamellar (HPL), double gyroid (DG) and hexagonal cylindrical (C). The DG phase displays exceptional stability at ambient temperature and features two interpenetrating sugar domain networks having a sub-2-nm strut width and a lattice parameter, a DG , of 13.1 nm. The unique stability of this DG phase extends further within ultrathin films all the way down to the two-dimensional limit of 15 nm in which film thickness, l, is now less than the surface-oriented unit cell height, h DG . In addition to raising the fundamental question of what minimally constitutes a Schoen triply periodic minimal surface and DG lattice, these results serve to establish the class of sugarpolyolefin conjugates as a new material platform for nanoscience and nanotechnology.Scheme 1. Structures of sugar-polyolefin conjugates 1-5.

Incorporation of small amounts of α‐tocopherol (vitamin E) in blends with the cellobiose–triazole‐linked atactic poly(4‐methyl‐1‐pentene) (CB‐aPMP) sugar–polyolefin conjugate can be used to exert external control over thermotropic phase behavior and provide access to non‐canonical soft matter Frank–Kasper A15 and σ phases. These results establish a paradigm that can be used for the further design and development of scalable quantities of soft matter FK phases of increased structural complexity and functional capability.

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. [1-9] 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. Nb 3 Sn), can be seen as arising from two crystallographically equivalent B sites that reside within CN12 distorted icosahedra, while six equivalent face-shared As ites are associated with CN14 polyhedra. Other commonly encountered bimetallic FK phases include the Laves C14 and C15 structures for A 2 B alloys (e.g.MgZn 2), and the complex s phase for AB alloys of

Incorporation of small amounts of α‐tocopherol (vitamin E) in blends with the cellobiose–triazole‐linked atactic poly(4‐methyl‐1‐pentene) (CB‐aPMP) sugar–polyolefin conjugate can be used to exert external control over thermotropic phase behavior and provide access to non‐canonical soft matter Frank–Kasper A15 and σ phases. These results establish a paradigm that can be used for the further design and development of scalable quantities of soft matter FK phases of increased structural complexity and functional capability.