Bead-Chain Molecular Models

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

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

2021 數感嘉年華 之 挑戰珠立方

Bead-Chain Building Blocks

Contained within the box is a bead chain cube, showcasing an innovative method for building tensile structures. This wooden model utilizes four pre-tensioned linear bead chains interconnected with suitable cross-links. The elastic properties of the bead strings generate tension, causing the beads to repel each other when tightened. This interaction between string tension and bead repulsion ensures the overall self-balancing of the structure.

Bead-Chain Cube (BC-Cube):

Take apart BC-Cube to obtain four chains of five beads each.

Challenge 1: BC-Cube

The first task is to reconstruct the four five-bead chains into a cube structure as depicted in the diagram below. The eight terminal beads of these chains align with the vertices of the cube, while the remaining twelve beads are distributed along the cube's edges.

Challenge 2: Giant Tetrahedron

The next task is to link the same four five-bead chains into a tetrahedral arrangement as shown in the diagram below. Each edge of the tetrahedron consists of four beads, and each triangular face contains a total of ten beads.

Basic Operation

The fundamental process in constructing a bead chain model involves "cross-linking". As illustrated in the figure below with two chains of four beads each, the method entails stretching and crossing these chains over the gap between beads. The pre-stressed elastic strings create tension, causing the beads to snugly tighten and wrap around the crossing point.

Bead-Chain Molecular Models

Bead-chain building blocks enable the construction of valence sphere models for various molecules. In these models, beads symbolize the valence electron pairs of the molecule, while the taut elastic strings provide the necessary attractive force to bind these electron pairs together within the molecule. By carefully balancing tension and compression, bead-chain building blocks effectively simulate the equilibrium structure of numerous molecules.

Cubane, with the chemical formula C₈H₈, features carbon atoms located at the eight vertices of a cube. These carbon atoms are bonded together by twelve carbon-carbon bonds, with the carbon-hydrogen bonds oriented outward from the structure.

See Also

• Chinese(中文)：珠串組合益智積木與珠立方
• Chinese(中文)：2021 數感嘉年華 之 挑戰珠立方 poster

External links

• 2019 Bridges Conference Art Exhibition: BC-Cube and BC-Dodecahedron by Bih-Yaw Jin
• Bih-Yaw Jin, Bead-Chain Construction Set and Interlocking Puzzle Inspired by Polyhedranes, Proceedings of Bridges 2019: Mathematics, Art, Music, Architecture, Education, Culture, 553–556.
• 2024 Bridges Conference Art Exhibition: Polyhedrane with Great Rhombicuboctahedron Skeleton and Bead-Chain Buckyball by Bih-Yaw Jin
• 2020 Bridges Conference Art Exhibition: Octahedral nanodiamond by Bih-Yaw Jin and Chia-Chin Tsoo
• 2021 Bridges Conference Art Exhibition: Bead-Chain Woven Sodalite by Bih-Yaw Jin
• 2022 Bridges Conference Art Exhibition: Interlocked Bead-Chain Model of Zeolite A Structure by Bih-Yaw Jin
• Facebook: 珠璣幾何 GeoBeading