029 Structures with Bubbles

Expt 029 -- Structures with Bubbles

A variety of geometric frames both large and small can be constructed from relatively inexpensive materials. These may be used to illustrate the various molecular geometries, crystal lattice cell types, packing orientations, as well as cluster configurations -- as in the new and exciting field of fullerene carbon cages. These frames may also be dipped in soapy water to illustrate the tetrahedral configuration.

Chemical Concepts

Molecules have specific shapes in 3-dimensions -- with bond angles and orientations -- all of which can be illustrated with some rather simple geometric models.
Likewise, crystals (metallic, ionic, network covalent, and molecular) have systematic packing arrangements that can also be illustrated with simple geometric models.

Safety

Use scissors for cutting. Use care with the hot glue gun; burns are possible.

Procedure

Cut the wire into 2-3 cm lengths and bend them into V-shapes. The coffee stirrers may be cut to any lengths desired. The wires may then be inserted securely into the stirrers, as demonstrated, to construct just about any geometric shape imaginable -- from a simple cube (for illustrating sodium chloride's unit cell, for example) to a truncated dodecahedron (the supposed shape of the ultra-stable C₆₀ molecule).

!!!Click here to See Movie. Click |> or <| to step the slides forward or back.
!!!Click here to See Picture.
Even large models may be prepared and hung as mobiles.
!!!Click here to See Picture.
For larger rigid models, cut the 1" tubing into 1/2" lengths (rings) and use a hand held hole punch to make 3-4 holes around each ring. The wooden dowels may be inserted into these holes and large models of, for example, the tetrahedron or octahedron, can easily be put together in a matter of minutes.
Very small models may be hot glued together from plastic dust broom straws. Cut broom straws the same length. Glue and hold in place to cool. These models may also be inserted into bubbles formed with the coffee stirrer models.

!!!Click here to See Movie.
The smaller, simpler frames, such as the tetrahedron, triangular prism and cube may be dipped into soapy water to produce some beautiful and fascinating soap film patterns. The tetrahedron, produces a crisp, clean tetrahedral arrangement to illustrate the bonding orientation in the methane molecule (CH₄).

!!!Click here to See Movie. Click |> or <| to step the slides forward or back.
!!!Click here to See Picture.

Variations and Additions

There are several interesting things to do with the soap films just for fun. If a frame is dipped half-way in again, a bubble can be trapped in the center of the film. The bubble assumes a hybrid shape between a sphere and the shape of the frame itself. Thus the tetrahedral frame forms a bubble in the center that is a rounded tetrahedron. You can pop the center bubble without popping the entire film.

!!!Click here to See Movie.
!!!Click here to See Movie.
Dip the coffee stirrer model of a tetrahedron. Insert the smaller broom straw tetrahedron into the center of the bubble. The soap film captures the smaller tetrahedron. You may also pop the sides.

!!!Click here to See Movie.
The triangular prism produces two connected tetrahedral arrangements, for illustrating the bonding in the ethane molecule (C₂H₆). Flexibility of the frame enables you to twist the prism and illustrate the staggered as well as the eclipsed ethane orientations!

!!!Click here to See Movie.
!!!Click here to See Movie. Click |> or <| to step the slides forward or back.
The cube produces four of these tetrahedral arrangements connected in a ring, for illustrating cyclobutane (C₄H₈).

!!!Click here to See Picture.
If this frame is dipped half-way in again, so that a cube-shaped bubble is trapped in the center of the film, you can obtain a model of the elusive cubane (C₈H₈) molecule!

!!!Click here to See Movie.
Just for fun, you can insert your finger into the inner bubble.

!!!Click here to See Movie.
Another way to make the cubane model is to insert a light cube made of broom straws into the bubble. Use a hot glue gun to assemble the straws into a cube. Allow the glue to cool.

!!!Click here to See Picture.
Dip the large cube. Insert the smaller cube into the center of the bubble. The soap film captures the smaller cube. You may also pop the sides. The shape is a little clearer if the faces of the inner cube are popped.

!!!Click here to See Movie.
And just as the cube frame generated the cyclobutane model, so too does a pentagonal prism produce a cyclopentane model!!
Dip a slinky to illustrate hydrophobic and hydrophilic areas in proteins. Support both ends to the slinky. Dip into the soap solution. Lift both ends of the slinky and slowly pull.

!!!Click here to See Movie.

Questions

What dictates the precise shape and configuration of the soap films that form when a given frame is dipped into soapy water?
Why are all free floating soap bubbles spherical? Why are the bubbles that form when the frames are dipped once and a half not spherical?
Sketch the shape assumed by the soap film on the tetrahedral frame. Relate this shape to the predicted shape of methane, CH₄.

Handout Makeup

Name ___________________________ Class ________

Teacher __________________________

BeckerDemos 029 Structures with Bubbles

Watch the movies and answer the questions.

Sketch the shape of cyclobutane.
Sketch the shape of Cubane.

Curriculum-

Or, use this activity when discussing molecular shapes and bonding. Several of the shapes are useful in introducing simple organic structures. Use the shapes when predicting molecular shapes with VSEPR. Also, soap films can be used to illustrate quite dramatically how models can be used for quick efficient problem solving, for problems that involve minimizing surface areas.

Activity-

Demonstration - Student or Teacher

You may simply demonstrate a few shapes in a short time. Making models can be a student project where the models are dipped as a demonstration for the class. Pass the smaller models around for a good look at the shapes.

Safety-

Soapy water may be very slippery. If students are dipping the models, watch for spills. Keep paper towels on hand for them to clean up.
A hot glue gun can cause burns--use care.

Time-

Teacher Preparation: Make soap solution a day ahead if possible. Model construction varies. Most require only a few minutes and may be reused many times.

Class Time: 10 minutes

Materials-

2 liters of 5% detergent solution (100 mL of detergent diluted to 2 liters of solution with water)
plastic coffee stirrers (the double-barreled type)
22 GA insulated hook-up wire, thin insulated telephone wire, or craft-quality pipe cleaners
1/4" wooden dowels (2-3 ft long)
1" diam. clear, pliable tubing
plastic dust-broom straw (2-4 cm in length)
a hot glue gun
paper towels
large basin of soapy water (plastic bucket or dishpan)

Disposal-

The solids may be discarded with ordinary solid trash.

Lab Hints-

For the larger models, the connecting joints are so flexible that a cube is unable to stand up under its own weight! (This illustrates quite effectively the inherent stability of a triangle compared to a square and why engineers always use triangular units in frame-work construction!)
You may want to try dipping the larger frames in soapy water. One way to do this (without a huge tank) is to place some 1 X 2's in a square pattern on the floor, drape a plastic tarp over them and fill the crater in the middle with soapy water. Then simply dip the frame into the puddle one face at a time! Use a dish pan to dip intermediate models one face at a time.
The soapy water recipe is not critical. Use about 1 part dish detergent (Dawn^® or Joy^® work well) to 20-30 parts water. Mix thoroughly, and let stand overnight if possible.
For the coffee-stirrer models, if 22 GA wire is not working, try some of the thin insulated wire available in huge bundles (usually for free) from the telephone company. Cut the lengths a few centimeters longer, and fold over the ends of each "V". These folded ends can usually be inserted snugly into the coffee stirrer holes.

Observations-

Each frame produces a unique, symmetrical and reproducible configuration of soap films. These configurations each represent the best arrangement of surfaces to cover the given frame with the least amount of material. Such minimal surface area patterns can be predicted mathematically, yet the equations and computations become so complicated even for the simplest frames, that high-speed computers might take hours, even days, to solve them. It is remarkable, then, that soap films can solve even the most elaborate minimal surface area problems in a fraction of a second. Essentially when you dip a cube frame, for example, into soapy water, you are posing the question: how can these twelve edges be completely covered and inter-connected with surfaces such that the total surface area is minimal. The soap film arrangement gives the correct answer in less than an eye-blink. Change the problem, by distorting the cube, and the new answer is instantaneously given. Pop the film that extends to one of the twelve edges, and the soap film immediately changes its answer to show the minimal surface solution for covering the remaining eleven edges.
Given that the shortest distance between two points is always a straight line, one might be tempted to assume that these minimal surface area configurations would always be made up of nothing but flat planes. This seems to hold true for many of the patterns, but a surprising number of derived shapes have elaborate and quite beautiful curvilinear surfaces.

Answers-

Q1. What dictates the precise shape and configuration of the soap films that form when a given frame is dipped into soapy water? A1. The soap films achieve their lowest potential energy when the surface area they cover is minimized, for this always allows the greatest degree of hydrogen bonding to occur between adjacent water molecules. Each configuration of films shows the minimum surface area required to cover and interconnect complete frame.
Q2. Why are all free-floating soap bubbles spherical? Why are the bubbles that form when the frames are dipped once and a half not spherical? A2. Free-floating soap bubbles are soap films that are given the problem, not of covering the components of a frame, but of encapsulating a given sample of air using the least amount of surface area. A sphere is always the best solution for this problem, regardless of the shape of the opening through which the bubble was blown. The bubbles caught inside the frames have other requirements imposed. Not only do they need to encapsulate a given sample of air, but they must also connect to the edges of the frame. The cube-sphere hybrid that forms is the compromise solution offering the least total surface area.
Q3. Sketch the shape found for the soap film formed on the tetrahedral frame. Relate this shape to the predicted shape of methane, CH₄. A3. Sketches should show six triangular planes, one extending inward from each of the six edges, and all intersecting at the center of the frame. Their lines of intersection should be the four lines draw in from the four vertices, again intersecting in the center. The six angles formed between these intersecting lines should all be 109.5 degrees. This is the same as the bond angle in a molecule of methane. In other words, the same arrangement that allows a tetrahedral frame with four vertices to be covered with minimal surface area, also allows four atoms of hydrogen to bond to one central atom of carbon with minimal repulsion (maximum distance) between bonding electron pairs.

References-

Acknowledgments:

Many of the ideas described above came to me while reading the wonderful book by C. V. Boys: Soap-bubbles, Their Colours and the Forces Which Mold Them. Dover Publications, Inc., 1959.