Chia-Chin Tsoo and Bih-Yaw Jin

Researcher and Professor, National Center for High-Performance Computing, Hsinchu, Taiwan; Department of Chemistry, National Taiwan University, Taipei, Taiwan
Mathematical beading is utilized to the construction of bead sculptures of several water cluster architectures based on clathrate hydrates and related Weaire-Phelan’s foam. These nanostructures can be viewed as three-level hierarchical frameworks which are composed of primary tetrahedral hydrogen-bonded water pentamers, secondary cage-like units and final three-dimensional architectures. Here, we show two bead sculptures that represent the most important Type-I and Type-II clathrate hydrates.
Bead model for the Type I clathrate hydrates (Weaire-Phelan structures)
12 x 12 x 16 cm
8mm plastic beads
2014
This sculpture represents a physical model Type-I clathrate hydrates, which is also known as the Weaire-Phelan foam. Type I clathrate hydrate consists of pentagonal dodecahedron and tetrakaidecahedra, which are further stacked in a cubic arrangement. There are 46 water molecules in a unit cell of Type-I hydrates. Typical guest molecules in this type of hydrates are carbon dioxide and methane.
Bead model for the Type II clathrate hydrates
13 x 13 x 13 cm
8mm plastic beads
2014
This sculpture represents a physical model Type-II clathrate hydrates, which contains also two types of polyhedra: the 16-faced hexakaidecahedra together with smaller pentagonal dodecahedra. This sculpture is constructed by focusing on larger hexakaidecahedra which share their hexagonal faces and form a diamond-like three-dimensional network. Each of these hexakaidecahedra is surrounded by twelve pentagonal dodecahedra. There are 136 water molecules in a unit cell. Type-II hydrates are usually formed by guest molecules like oxygen and nitrogen.