Hierarchical self-assembly of a striped gyroid formed by threaded chiral mesoscale networks

Abstract

Numerical simulations reveal a family of hierarchical and chiral multicontinuous network structures self-assembled from a melt blend of Y-shaped ABC and ABD three-miktoarm star terpolymers, constrained to have equal-sized A/B and C/D chains, respectively. The C and D majority domains within these patterns form a pair of chiral enantiomeric gyroid labyrinths (srs nets) over a broad range of compositions. The minority A and B components together define a hyperbolic film whose midsurface follows the gyroid minimal surface. A second level of assembly is found within the film, with the minority components also forming labyrinthine domains whose geometry and topology changes systematically as a function of composition. These smaller labyrinths are well described by a family of patterns that tile the hyperbolic plane by regular degree-three trees mapped onto the gyroid. The labyrinths within the gyroid film are densely packed and contain either graphitic hcb nets (chicken wire) or srs nets, forming convoluted intergrowths of multiple nets. Furthermore, each net is ideally a single chiral enantiomer, induced by the gyroid architecture. However, the numerical simulations result in defect-ridden achiral patterns, containing domains of either hand, due to the achiral terpolymeric starting molecules. These mesostructures are among the most topologically complex morphologies identified to date and represent an example of hierarchical ordering within a hyperbolic pattern, a unique mode of soft-matter self-assembly. chirality | liquid crystals | entanglement | hyperbolic tilings | miktoarm copolymers L iquid crystals formed by molecular self-assembly provide fascinating examples of complicated space partitions in softmaterial science. Relatively complex examples are the bicontinuous mesostructures found ubiquitously in both natural and synthetic soft matter, including lipid-water systems and block copolymer melts, namely the double diamond (symmetry Pn3m), the primitive ðIm3mÞ, and, particularly, the gyroid ðIa3dÞ mesophases. The structure of these mesophases can be described by a molecular membrane folded onto one of the three simplest triply periodic minimal surfaces (TPMS), namely the D, P, and G(yroid) surfaces, named by Schoen in the 1960s (1). From a 3D perspective, these structures are characterized by the nets describing the pair of mutually threaded labyrinths carved out of space by the convoluted hyperbolic architecture of the TPMS. For the gyroid, this is a racemic mixture of two chiral srs nets, one left-and the other right-handed [the three-letter nomenclature follows the Reticular Chemistry Structure Resource naming convention for 3D nets (2)]. This leads to an overall achiral structure when the two nets are chemically identical, which is the case in most experimentally identified gyroid liquidcrystal structures. One such structure recently reported is a gyroid assembly found in an ABC three-miktoarm star terpolymer melt (3). In this structure, the majority C component constitutes the two labyrinth nets while the...

Highly sensitive, reproducible and uniform SERS substrates with a high density of three-dimensionally distributed hotspots: gyroid-structured Au periodic metallic materials

“…9,24,43 More importantly, the mechanism presented here can act as a guideline for the future design and selection of SPR substrates. The existence of several other bicontinuous interconnected structures has been confirmed in various biological systems and self-assembly systems, such as the diamond structure found in the brilliantly green weevil Lamprocyphus augustus 25 and the double-gyroid, 44 stripedgyroid 26 and double-diamond 45 structures in block polymer systems. Figure 8 depicts the nanogap distribution in the two-dimensional For the gyroid and diamond structures, note that the value of t varies in the range between − 1.5 and 1.5, and that the nanogaps originate from the approaching of one network by increasing its VF.…”

“…Moreover, the mechanism deduced here will provide insight into the future design and selection of novel SPR substrates, as many other bicontinuous interconnected systems are available. [25][26][27] EXPERIMENTAL PROCEDURES Fabrication of GAPMMs The fabrication of GAPMMs using a biotemplate involves three steps as follows: (1) amination of the biotemplate: butterfly wings were first immersed in ethanol for 30 min to preliminarily clean the surface of the wings. Afterwards, the wings were aminated by immersion in dilute 8 vol% nitric acid for 2 h and then in an ethanol solution of ethanediamine (25 vol%) for 6 h. (2) Nanoseed growth: the aminated wings were immersed for 4 h in a mixed solution of HAuCl 4 (0.2 wt %), which was prepared by dissolving HAuCl 4 in equal weights of ethanol and deionized water.…”

Chirality Induction through Nano‐Phase Separation: Alternating Network Gyroid Phase by Thermotropic Self‐Assembly of X‐Shaped Bolapolyphiles

“…In conclusion, we present the first I4 1 32 alternating double network gyroid cubic LC.The work demonstrates anovel way of inducing chirality through phase separation in chemically non-chiral systems.T he network segments reported here are on the scale of only af ew nm between junctions,w hich is of great potential in nano-templating, [12d] for example as enantiomer-specific membranes [8c] for use in enantiomer separation and production and manipulation of circularly polarized light, chirality switching through thermally,c hemically or light-induced mesophase transitions. [23] Moreover,the present study shows how the principle of self-assembled multicolor tiling can be extended from two dimensions (columnar) to three dimensions (cubic), [13,24] providing an ew way to fabricate complex nano-architectures.…”

Rational design of nanomaterials from assembly and reconfigurability of polymer-tethered nanoparticles

“…[72][73][74][75] As the spacing and characteristics of individual domains can be tuned in a reliable manner, it is possible to propose new and previously inaccessible structures, as well as create complex and hierarchical morphologies. [76][77][78][79][80][81][82][83] Finally, the solvent selectivity is important to the kinds of morphologies that will assemble, and has been found to dramatically affect the nature of self-assembled structures allowing for a wide variety of tunable micellar structures. [84] As the complexity of static assemblies has grown over the past decade, so too has the desire to incorporate these assemblies into devices and other applications.…”