Surprising Shrinking Styrofoam Stick: Using the Gas Laws to Get a Square Peg into a Round Hole

Co-Authored by Dean J. Campbell*, Kaitlyn Walls*, Q Ott*, and Zaman Shah*

*Bradley University, Peoria, Illinois

The relationship between an ideal gas temperature and its volume is described by Jacques Charles’s Gas Law.¹ When the temperature of an ideal gas decreases, its volume decreases. To demonstrate this effectively, a sample of gas must have a well-defined boundary on its volume. The boundary can be a balloon, a tire, or even an empty plastic bottle.² Polymer foams can be thought of as many adjacent bubbles of gas, with polymer defining the boundaries of each bubble or cell. Some samples of polystyrene (PS) foam, informally and incorrectly called “styrofoam”,³ can be cooled with liquid nitrogen to decrease their volume.⁴ When the gases in the cells cool, they contract and the foam volume decreases. This idea is the basis of the demonstration described here in which a square-edged stick of polystyrene (PS) foam that cannot fit into a circular hole can be reversibly shrunk with liquid nitrogen to fit into the hole.

Demonstration Setup

A rectangular “stick” of PS foam was obtained from commercial packaging. The piece was long (many tens of cm) relative to its width (about 2 cm x 2.5 cm). Similar pieces could be easily cut from larger sheets of PS foam. The stick was large enough to be readily visible by spectators and wide enough to NOT fit into a target round hole at room temperature (described below), but narrow enough to fit into the target round hole at liquid nitrogen temperature.

One target hole used was a polyethylene terephthalate soda bottle, with a round opening with an internal diameter of about 2 cm. An alternative round target hole for this demonstration was a craft foam sheet cut into a ring shape. This ring could withstand a variety of temperatures without significantly shrinking and was flexible enough to be removed from the PS foam stick. The circular cut in the middle of the ring was designed to be just a little bit smaller than the size of the stick at room temperature, yet sufficiently large so that the shrunken stick could fit into the hole. To aid in manipulating and supporting the ring, a chenille stem, also known as a pipe cleaner, was tied to the ring.

Liquid nitrogen is an effective method to cool the PS foam from roughly 298 K down to 77 K. A container such as a Dewar flask, a polystyrene foam cooler, or a metal can (as seen in Video 1) are all suitable for holding the liquid nitrogen. While convenient, liquid nitrogen is cold enough to create frostbite due to prolonged exposure; therefore, insulated gloves were used to protect skin.

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 Figure 1. (LEFT) Rectangular polystyrene foam stick at room temperature not being able to fit into a round hole. (RIGHT) Shrunken rectangular polystyrene foam stick cooled by liquid nitrogen being able to fit into the round hole.

Demonstration

Before the PS foam stick was dipped into the liquid nitrogen, the stick was placed over the hole to show it would not fit - our “square peg” would not fit into our round hole, Figure 1. Next, one end of the PS stick was dipped into the liquid nitrogen for several seconds. The newly shrunken end was placed into the round hole to show that it now fits, Figure 1. The shrunken end was removed from the hole and allowed to expand back to its original size at room temperature. The attempt was again made to push the square stick into the round hole to again show that the square peg would not fit into the round hole at room temperature. Video 1 shows this demonstration in action.

Video 1. Demonstration of a polystyrene foam stick being cooled with liquid nitrogen to shrink it so it can be placed in the opening of a PET soda bottle. Chem Demos YouTube channel (accessed 11/9/2022).

An alternative approach was explored which allowed the PS foam stick to warm within the round hole. When the stick expanded into the hole, the stick could not be easily removed, demonstrating the expanded PS stick’s larger volume. The problem with this approach is that the hole must be removed carefully (if at all) from the PS stick at room temperature to minimize physically damaging the stick. To remove the hole, it and the end of the PS stick can be exposed to liquid nitrogen so the PS stick will contract and the hole can be removed. This task presents a greater risk of splashing liquid nitrogen around and is not recommended. It is easier to remove the PS stick from the hole before it warms up.

While this demonstration does show gas contraction when temperature decreased, the extent of contraction did not follow the ideal gas law. Cooling the PS sticks to 193 K in a -80°C freezer did not produce any noticeable contraction. Heating the sticks in a drying oven to +80°C did not produce any noticeable expansion. Even when PS sticks were cooled from room temperature to 77 K, they would only contract to 75 % of their original size. By contrast, a sample of ideal gas contracts to 26% of its original volume when cooled over the same temperature range. The discrepancy might be due to rigidity of the PS which prevents the cells from contracting as much as they could. If this indeed the case, the implication would be that the gases in the cells of the PS would be at reduced pressure. Assuming ideal gas behavior and the equation PV = nRT, if temperature (T) decreases and volume (V) does not decrease as much as predicted, then pressure (P) would have to decrease!   

Extensions

Previous blog posts have discussed other chemistry concepts that can be connected to PS, the polymer used for the shrinking foam stick. For example, some of the physical properties of PS are determined by its tacticity, the arrangement of the aromatic ring side groups along the main polymer chain.⁵ Commercial PS is typically atactic, which describes a random alternation of its pendant structures between opposite sides of the main polymer chain.⁶ PS films that have been stretched when warm and then cooled to room temperature will contract when heated to above the polymer glass transition temperature.⁶ Some PS foams have been known to contract irreversibly when heated. This is probably because the PS in the walls between the cells of the foam were stretched as the bubbles grew when the foam was originally produced.

An environmental concern is that PS is not derived from renewable resources and does not biodegrade in the same way food or cellulose does in a compost pile.⁷ Instead, it is petrochemically produced and slowly breaks down, likely forming microplastics along the way.⁸ This spurred the search to find alternative polymer foams that will shrink noticeably when cooled in liquid nitrogen. Alternate polymer foams that did not shrink included petrochemically-derived polyethylene and urethane. We have also explored foams made from polymers that are considered greener in that they can be derived from renewable resources. These polymer-based foams include starch, marshmallows, and cork. As noted in a previous blog post, PS packing peanuts will shrink in liquid nitrogen, but starch packing peanuts retain their size and become brittle.⁸ We also obtained foam samples composed of polylactic acid (PLA) from the Material Sample Shop (Helsingor, Denmark) and the Ricoh Company Ltd. (Tokyo, Japan). Since PLA foams can be produced from biologically-sourced precursors, they are touted as environmentally-friendly alternatives to PS foams, which they resemble in appearance. These PLA foams also did not shrink in liquid nitrogen. Figure 2 shows Raman spectra obtained by our lab of some of our PS and PLA samples.

ps_vs_pla_raman_spectra.jpg

Figure 2. Raman spectra of PS and PLA foam samples, and drawings of their molecular structures.

Why the alternate polymers did not shrink remains an open question. While the successful demonstration with the PS foam stick illustrates gases shrinking as temperature decreases, the polymer foams that did not shrink can still be connected to aspects of polymer foam science. The polymer between the cells of the foam might be too inflexible for the cells to contract in liquid nitrogen. This could be due to the cell walls being too thick to flex or due to the polymer itself becoming less flexible at low temperature. One likely requirement for foam contraction at low temperature is that the foam cells are closed. With closed-cell structures, each cell is completely separated from its neighbors by polymer. Gases do not move readily between the bubbles of a closed-cell foam, so the gases cannot transfer heat by convection. This improves the thermal insulating ability of the polymer.⁹ The gases within the closed cells should be able to contract when cooled without outside gases moving into the cells. Alternatively, polymer foams can have open-cell structures, with gaps in the polymer between the cells that can allow gases or even liquids to move between the void spaces. Some polymer foam samples dipped in liquid nitrogen appear to absorb the liquid. When the foam is lifted out, the liquid nitrogen dribbles back out of the foam. Exploration of foam issues associated with cell wall thickness and open vs. closed cell structures would likely benefit greatly from the use of microscopy.

To produce cell structures of polymer foams, a variety of blowing agents are utilized. Physical blowing agents physically vaporize into the gaseous state within liquid polymers to make many bubbles. Physical blowing agents for PS foam include a wide variety of small alkanes or alkenes bonded to hydrogen, chlorine, and/or fluorine atoms.^9,10 Even pentane or butane, though flammable, can be used.¹¹ These agents vary widely in their environmental impacts if released to the atmosphere. Put simplistically, chlorine from these molecules can damage ozone in the stratosphere and molecules with carbon-fluorine bonds can contribute to climate change; but these carbon-halogen bonds are more resistant to chemical attack than carbon-hydrogen bonds. Some blowing agents contain carbon-hydrogen bonds or carbon-carbon double bonds as reactive sites that enable the molecules to be destroyed before they circulate very far in the atmosphere.^9,10 Chemical blowing agents produce bubbles in liquid polymers by chemically reacting to produce gas bubbles. One advantage of working with chemical blowing agents is that they can be added as solids to physically mix in with solid polymer, so the desired polymer does not have to be liquified with extra energy before the blowing agent is added.¹² An example of a chemical blowing agent is azodicarbonamide, which can be thermally decomposed to produce dinitrogen, carbon monoxide, carbon dioxide, and ammonia gases.^12,13 A variety of chemical processes are used to produce carbon dioxide in baked goods, which can have foam-like structures containing polymers such as starch. It is doubtful that the composition of the blowing agents will prevent the polymer foams from contracting in liquid nitrogen, but the use of polymer foams in a classroom setting provides the opportunity to bring up the chemistry and environmental considerations of what makes the polymer into a foam in the first place.

Some polystyrene foam sticks will contract sufficiently in contact with liquid nitrogen to produce a simple demonstration of Charles’s Law. The failure of many other polymer foams to contract in a similar manner still provides many opportunities to discuss and explore their structure and chemistry.

Safety: The very cold temperatures of liquid nitrogen can produce frostbite, so do not handle the cold surfaces with bare skin – use tongs or the appropriate insulating gloves. Goggles are also recommended. 

Acknowledgements: This work was supported by Bradley University and the Mund-Lagowski Department of Chemistry and Biochemistry with additional support from the Illinois Heartland Section of the American Chemical Society. The material contained in this document is based upon work supported by a National Aeronautics and Space Administration (NASA) grant or cooperative agreement. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of NASA. This work was supported through a NASA grant awarded to the Illinois/NASA Space Grant Consortium.

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