The first space-filling polyhedrons of polymer cubic cells originated from Weaire-Phelan structure created by polymerization induced phase separation

Naofumi Naga; Masumi Jinno; Yuting Wang; Tamaki Nakano

doi:10.1038/s41598-022-22058-7

The first space-filling polyhedrons of polymer cubic cells originated from Weaire-Phelan structure created by polymerization induced phase separation

Sci Rep. 2022 Nov 9;12(1):19141. doi: 10.1038/s41598-022-22058-7.

Authors

Naofumi Naga^{1

2}, Masumi Jinno³, Yuting Wang⁴, Tamaki Nakano^{5

6}

Affiliations

¹ Department of Applied Chemistry, College of Engineering, Shibaura Institute of Technology, 3-7-5 Toyosu, Koto-ku, Tokyo, 135-8548, Japan. nnaga@sic.shibaura-it.ac.jp.
² Graduate School of Engineering and Science, Shibaura Institute of Technology, 3-7-5 Toyosu, Koto-ku, Tokyo, 135-8548, Japan. nnaga@sic.shibaura-it.ac.jp.
³ Graduate School of Engineering and Science, Shibaura Institute of Technology, 3-7-5 Toyosu, Koto-ku, Tokyo, 135-8548, Japan.
⁴ Institute for Catalysis and Graduate School of Chemical Sciences and Engineering, Hokkaido University, N 21, W 10, Kita-ku Sapporo, 001-0021, Japan.
⁵ Institute for Catalysis and Graduate School of Chemical Sciences and Engineering, Hokkaido University, N 21, W 10, Kita-ku Sapporo, 001-0021, Japan. tamaki.nakano@cat.hokudai.ac.jp.
⁶ Integrated Research Consortium On Chemical Sciences, Institute for Catalysis, Hokkaido University, N 21, W 10, Kita-ku Sapporo, 001-0021, Japan. tamaki.nakano@cat.hokudai.ac.jp.

Abstract

The Weaire-Phelan structure is a three-dimensional structure composed of two different polyhedra having the same volume, i.e., pyritohedron and truncated hexagonal trapezohedron. It was proposed by Weaire and Phelan in 1993 as a solution of the Kelvin problem of filling space with no gaps with cells of minimum surface area and equal volume. It was found in physical systems including liquid foam and a metal alloy while it has never been constructed as organic materials. We report herewith the first polymeric Weaire-Phelan structure constructed through phase-separation of a single polymer species that is synthesized by simple polyaddition between tetrakis(3-mercaptopropionate) and 1,6-diisocyanatohexane. The structure has the order of micrometers and is amorphous unlike reported crystal structures similar to the Weaire-Phelan structure.

Abstract

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