Modifications to the ICE 'Polyhedral Model Kit'

Phillip Barak, PhD

Assoc Prof, Dept of Soil Science
Univ of Wisconsin-Madison

21 Jul 2006 (last modified, 21 Nov 2006)

Among the subjects taught in my discipline is the basic crystallography of aluminosilicates, particularly clay minerals, but including other primary minerals that are major constituents of soil. My research involves molecular templating of crystals, and so relies upon inference of a exact level of correspondance between structural units.

As delivered, the Polyhedral Model Kit (PMK)  available from the Institute for Chemical Education consists of:

  1. clear plastic pieces from which tetrahedra and octahedra of equal edge lengths can be assembled,
  2. colored 'pompons' to key to specific elements, and
  3. red 'rubber' (Santoprene 111-45) connectors of two types: 2-prong straight connectors and flat, 'X'-shaped 4-prong connectors.

My difficulty starts with the connectors supplied, since the 2-prong connectors do not match the bond angles of apex-to-apex silica tetrahedra and the 4-prong connectors do not match in bond number or bond angle the edge-to-edge alumina octahedra that bond to apical silica tetrahedra. (The bond number problem can be solved by trimming a connector off the 4-prong connector, but the bond angle problem remains.)

tetrahedra connected apex-to-apex with straight-angle connectorapex-to-apex tetrahedra w/ correct bond angle in connector, permitting basal plane

The connectors are flexible and can bend to make the necessary bonds but to the learner it does not seem that the fit of the structural units is as precise as they are indeed in nature.

Consider the straight, 2-prong connector and the apex-to-apex tetrahedra. As seen in the adjacent figure (left), at rest the connectors to the tetrahedra do not permit a plane of basal silica. Using a connector with the correct bond angle, the tetrahedra arrange themselves in the 'anatomically correct' pose with a basal plane (right).

kaolinite unit_w_modified_connectors

The existing 4-prong connectors bond two octahedra edge-to-edge convincingly using the 90-degree separation, but the third connection to a tetrahedral layer is confusing to the novice because of the improper bond angles, even if the connector is pruned to 3-connectors only. However, when a 3-prong connector is supplied with correct angles (see left), the construction is quite straightforward, the product is pleasingly clear, and the next set of structural units and their orientation is suggested by the connectors.

Kaolinite: PMK w/ supplied connectors (left) and modified connectors (right)

The difference apparent in the 'cleanness' of an assembled model with correct bond angles (right) can be seen in the adjacent photo of kaolinite assembled with connectors as originally supplied (left).

Two prong connector formThree-prong connector form

For the limited purposes of these trials, the connectors supplied were remanufactured in-house by reheating using appropriately designed forms.

paperclips used as forms

A low-tech alternative is to 'bind' the connectors in the proper configuration using paperclips, which can produce bent 2-prong, 3-prong, and 4-prong connectors (the latter shaped to approximate an sp3 orbital and create a tetrahedral orientation of polyhedra around the connector itself.)

[Technical notes: The 2-prong connectors were modified to have a 120° angle, and the 3-prong connector to have a 100° angle between two arms, with the third inclined 30°  above the plane of the first two. Heating the connectors  in the forms for 30-60 minutes, followed by quenching in cool water, was sufficient to make these angles permanent.]