An Overview of Materials with Triply Periodic Minimal Surfaces and Related Geometry: From Biological Structures to Self‐Assembled Systems

Han, Lu; Che, Shunai

doi:10.1002/adma.201705708

Cited by 311 publications

(165 citation statements)

References 209 publications

(299 reference statements)

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“…Only the so-called alternating double-network DG structure,i nw hich the two networks are different and which therefore has the same space group (I4 1 32) as the related single-network structure,h as been reported for ABC triblock copolymers. [14,17] Neither ar elated alternating DD structure,n or the SD structure ( Figure 1e), both with Fd " 3m symmetry,have yet been reported in self-assembled soft matter. Figure 1.…”

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confidence: 96%

A Self‐Assembled Bicontinuous Cubic Phase with a Single‐Diamond Network

et al. 2019

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The first single-diamond cubic phase in al iquid crystal is reported. This skeletal structure with the Fd " 3mspace group is formed by self-assembly of bolaamphiphiles with swallow-tailed lateral chains.I tc onsists of bundles of pconjugated p-terphenyl rods fused into an infinite network by hydrogen-bonded spheres at tetrahedral four-way junctions. We also present aq uantitative model relating molecular architecture to the space-filling requirements of six possible bicontinuous cubic phases,t hat is,t he single-and doublenetwork versions of gyroid, diamond, and "plumber'sn ightmare".Among the most intriguing self-assembled nano-and mesoscale soft-matter structures are the cubic phases formed by lyotropic and thermotropic liquid crystals (LCs), by block copolymers, [1,2] and by nanoparticle arrays. [3][4][5] Tw o classes of cubic phases can be distinguished, the "bicontinuous" and the "micellar" types. [6,7] Them icellar phases represent periodic arrays of spheres on ac ubic lattice, whereas the bicontinuous phases are more complex and usually formed by two networks divided by aminimal surface with aconstant mean curvature.Depending on the symmetry, the double gyroid (DG, Ia " 3d,Q 230 ), the double diamond (DD; Pn " 3m,Q 224 ), and the body-centered plumber'sn ightmare ("double primitive") cubic phases (DP; Im3 m,Q 229 )w ith junction valencies of n = 3, 4, and 6, respectively,c an be distinguished (Figure 1a-c). Figure 6. Models showing a) the micellar Fd " 3m cubic phase [27,28] and b) the new SD bicontinuous cubic phase of compounds 1/18-11/22.

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confidence: 96%

A Self‐Assembled Bicontinuous Cubic Phase with a Single‐Diamond Network

et al. 2019

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“…Therefore, the unit cell parameters of the silica scaffold can go beyond the normal synthesis and are comparable with biological photonic structures [38]. Due to the large amount of THF that occupies space and separates the two interlocking double networks, the double networks shift and adhere each other to form a low-symmetry shifted DD (SDD) structure with the evaporation of the solvent, and this shifted structure introduces the photonic bandgap feature due to decreased crystal symmetry [38,[138][139][140].…”

Section: Artificial Self-assembly Of Amphiphilic Moleculesmentioning

confidence: 99%

Bicontinuous cubic phases in biological and artificial self-assembled systems

2020

Self Cite

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Nature has created innumerable life forms with miraculous hierarchical structures and morphologies that are optimized for different life events through evolution over billions of years. Bicontinuous cubic structures, which are often described by triply periodic minimal surfaces (TPMSs) and their constant mean curvature (CMC)/parallel surface companions, are of special interest to various research fields because of their complex form with unique physical functionalities. This has prompted the scientific community to fully understand the formation, structure, and properties of these materials. In this review, we summarize and discuss the formation mechanism and relationships of the relevant biological structures and the artificial self-assembly systems. These structures can be formed through biological processes with amazing regulation across a great length scales; nevertheless, artificial construction normally produces the structure corresponding to the molecular size and shape. Notably, the block copolymeric system is considered to be an applicable and attractive model system for the study of biological systems due to their versatile design and rich phase behavior. Some of the phenomena found in these two systems are compared and discussed, and this information may provide new ideas for a comprehensive understanding of the relationship between molecular shape and resulting interface curvature and the selfassembly process in living organisms. We argue that the copolymeric system may serve as a model to understand these biological systems and could encourage additional studies of artificial self-assembly and the creation of new functional materials.

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“…Elements are either beam based, such as what we commonly associate with lattice structures [5,6,7], or surface based, such as in Triply Periodic Minimal Surfaces (TPMS) [8]. At a practical level, these three decisions can be used to realize a range of cell shapes, some examples of which are shown in Figure 2, and which is inspired by the design process in the nTopology Element lattice design software [9].…”

Section: Question 1: What Is the Optimum Unit Cell?mentioning

confidence: 99%

Four Questions in Cellular Material Design

Bhate

2019

Materials

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The design of cellular materials has recently undergone a paradigm shift, enabled by developments in Additive Manufacturing and design software. No longer do cellular materials have to be limited to traditional shapes such as honeycomb panels or stochastic foams. With this increase in design freedom comes a significant increase in optionality, which can be overwhelming to the designer. This paper aims to provide a framework for thinking about the four key questions in cellular material design: how to select a unit cell, how to vary cell size spatially, what the optimal parameters are, and finally, how best to integrate a cellular material within the structure at large. These questions are posed with the intent of stimulating further research that can address them individually, as well as integrate them in a systematic methodology for cellular material design. Different state-of-the-art solution approaches are also presented in order to provoke further investigation by the reader.

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An Overview of Materials with Triply Periodic Minimal Surfaces and Related Geometry: From Biological Structures to Self‐Assembled Systems

Cited by 311 publications

References 209 publications

A Self‐Assembled Bicontinuous Cubic Phase with a Single‐Diamond Network

A Self‐Assembled Bicontinuous Cubic Phase with a Single‐Diamond Network

Bicontinuous cubic phases in biological and artificial self-assembled systems

Four Questions in Cellular Material Design

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