This blog post describes
bead-chain models, a novel method for building tensile structures. The models, using interconnected, pre-tensioned bead chains, demonstrate the principles of tension and repulsion in creating self-balancing structures. Examples include building a cube and tetrahedron, and applications extend to modeling molecular structures like cubane, showcasing the potential of bead chains in visualizing complex chemical bonds. The post also highlights the author's related artwork and publications presented at various Bridges conferences.
Podcast: Bead-Chain Molecular Models
Friday, January 3, 2025
The Five-Bead Chain Theorem for Polyhedranes
林映廷, 金必耀, 珠串組合分子模型—多面體烷的五珠串定理, 化學 第七十七卷第四期 405-411 頁 2019.
Ying-Ting Lin and Bih-Yaw Jin, Bead Chain Molecular Models: Five-bead Chain Theorem, CHEMISTRY (Chemical Society Located in Taipei) Vol. 77, No. 4, pp. 405-411, 2019.
DOI: 10.6623/chem.201912_77(4).002
This research paper mathematically proves that any polyhedrane molecule (CnHn) can be constructed using only five-bead chains, where each chain represents specific chemical bonds. The proof utilizes Peterson's perfect matching theorem to demonstrate the existence of resonance structures in fullerene graphs. The authors connect the arrangement of beads in the model to the concept of perfect matchings in graph theory. This innovative molecular model provides a visual representation of molecular structures, including resonance structures. The paper also explores non-uniform chain lengths and Hamilton cycles within the molecular structures.
Podcast: The Five-Bead Chain Theorem for Polyhedranes
Bead Chain Molecular Models of Regular Polyhedranes
金必耀-電子雲價球分子組合模型 化學 第七十七卷第一期 99-109 頁, 2019.
Bih-Yaw Jin, Valence Sphere Models Comprising of One-Dimensional Bead Chains: Polyhedranes as Molecular Assembly Puzzles, CHEMISTRY (Chemical Society Located in Taipei) Vol. 77, No. 1, pp. 99-109, 2019. DOI: 10.6623/chem.201903_77(1).001
This research article details methods for constructing molecular models of polyhedranes—cage-like hydrocarbon molecules—using bead chains. The authors present solutions for building models of tetrahedrane, cubane, and dodecahedrane, transforming the construction problem into a combinatorial puzzle solved via Schlegel diagrams. They propose a conjecture that any C2nH2n hydrocarbon can be built with n five-bead chains. The article includes detailed construction instructions and discusses the mathematical and chemical principles involved. The process is framed as a unique type of puzzle with aesthetically pleasing results.
Podcast: Bead Chain Molecular Models of Regular Polyhedranes
Valence Sphere Models from Bead Chains: Polyhedranes as Molecular Puzzles
金必耀 電子雲價球分子組合模型 化學 第七十七卷第一期 99-109 頁, 2019.
Bih-Yaw Jin, Valence Sphere Models Comprising of One-Dimensional Bead Chains: Polyhedranes as Molecular Assembly Puzzles, CHEMISTRY (Chemical Society Located in Taipei) Vol. 77, No. 1, pp. 99-109, 2019.
DOI: 10.6623/chem.201903_77(1).001
This research article presents a new method for creating valence sphere molecular models using pre-assembled one-dimensional bead chains. The technique allows for the construction of various alkane molecules, including complex polyhedranes, by connecting these chains in specific ways. The process is likened to solving a mathematical puzzle, offering a unique approach to visualizing molecular structures and electron cloud distribution. The method is demonstrated for various molecules and extended to inorganic systems like perovskites. The authors explore the connection between this model and existing valence sphere models and VSEPR theory.
Podcast: Valence Sphere Models from Bead Chains: Polyhedranes as Molecular Puzzles
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