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Updated: Aug 22, 2025

Self-assembling Morphologies Obtained from Helical Polycarbodiimide Copolymers and Their Triazole Derivatives
Published on: February 7, 2017
The first space-filling polyhedrons of polymer cubic cells originated from Weaire-Phelan structure created by
Naofumi Naga1,2, Masumi Jinno3, Yuting Wang4
1Department 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.
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.
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