Minimal Twin Surfaces

Chen, Hao

doi:10.1080/10586458.2017.1413455

Cited by 16 publications

(10 citation statements)

References 20 publications

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“…Vignolini et al ( 43 ) briefly noted in 2012 what appeared to be some type of TB in a two-dimensional (2D) scanning electron microscopy (SEM) image of a surface region in their study of a metal network optical metamaterial fabricated from a BCP DG precursor template. In 2019, Chen ( 44 ) addressed the mathematical existence of twins in TPMSs including Schoen’s G surface, and proposed a near-minimal surface model of the shape of a {211} G-surface twin. In 2020, Han et al ( 45 ) proposed a (211) + 0.5 G TB [which is equivalent to the (422) twin that we study] for a mesoporous silica-air sample based on a single transmission electron microscopy (TEM) image and matching this image to a series projected models of the twin structure (for more discussion see SI Appendix , Previous Studies ).…”

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confidence: 99%

Visualizing the double-gyroid twin

Feng

Zhuo

Guo

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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Periodic gyroid network materials have many interesting properties (band gaps, topologically protected modes, superior charge and mass transport, and outstanding mechanical properties) due to the space-group symmetries and their multichannel triply continuous morphology. The three-dimensional structure of a twin boundary in a self-assembled polystyrene-b-polydimethylsiloxane (PS-PDMS) double-gyroid (DG) forming diblock copolymer is directly visualized using dual-beam scanning microscopy. The reconstruction clearly shows that the intermaterial dividing surface (IMDS) is smooth and continuous across the boundary plane as the pairs of chiral PDMS networks suddenly change their handedness. The boundary plane therefore acts as a topological mirror. The morphology of the normally chiral nodes and strut loops within the networks is altered in the twin-boundary plane with the formation of three new types of achiral nodes and the appearance of two new classes of achiral loops. The boundary region shares a very similar surface/volume ratio and distribution of the mean and Gaussian curvatures of the IMDS as the adjacent ordered DG grain regions, suggesting the twin is a low-energy boundary.

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confidence: 99%

Visualizing the double-gyroid twin

Feng

Zhuo

Guo

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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“…Following recent developments in differential geometry, [27] we view D and G TPMSs as consisting of necks among horizontal planes. In both cases, necks in each layer are arranged in a rhombic lattice.…”

Section: Methodsmentioning

confidence: 99%

Self‐Assembly of Single‐Diamond‐Surface Networks

et al. 2021

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Biological scaffolds with hyperbolic surfaces, especially single gyroid and single-diamond structures, have sparked immense interest for creating novel materials due to their extraordinary physical properties. However, the ability of nature to create these unbalanced surfaces has not been achieved in either lyotropic liquid crystals or block copolymer phases due to their thermodynamical instability in these systems. Here, we report the synthesis of a porous silica scaffold with a single-diamond-surface structure fabricated by self-assembly of the poly(ethylene oxide)-b-polystyrene-bpoly(l-lactide) and silica precursors in a mixed solvent of tetrahydrofuran and water. The single-diamond structure with tetrahedral interconnected frameworks was revealed by the electron crystallographic reconstruction. We assume that the formation of single networks is induced by the structural transition and related to the energetic change due to the fluctuations of the Gaussian curvature. This work may provide new insights into these biologically relevant surfaces and related self-assembly systems.

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“…The hexagonal symmetry implies other intersections at x = y = 1/3 and x = y = 2/3, which is the Traizet limit of the H family (non-Meeks). See [Che18] for an analytic proof of the balancedness at the non-trivial intersections.…”

Section: Consider An Embedded Minimal Surfaces S Inside An Axes Paral...mentioning

confidence: 99%

An orthorhombic deformation family of Schwarz' H surfaces

Chen,

Weber

2018

Preprint

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The classical H surfaces of H. A. Schwarz form a 1-parameter family of triply periodic minimal surfaces (TPMS) that are usually described as close relatives to his more famous P surface. However, a crucial distinction between these surfaces is that the P surface belongs to a 5-dimensional smooth family of embedded TPMS of genus three discovered by W. Meeks, while the H surfaces are among the few known examples outside this family. We construct a 2-parameter family of embedded TPMS of genus three that contains the H family and meets the Meeks family. In particular, we prove that H surfaces can be deformed continuously within the space of TPMS of genus three into Meeks surfaces.

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Minimal Twin Surfaces

Cited by 16 publications

References 20 publications

Visualizing the double-gyroid twin

Visualizing the double-gyroid twin

Self‐Assembly of Single‐Diamond‐Surface Networks

An orthorhombic deformation family of Schwarz' H surfaces

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