First, I showed the students the fundamental stages of polymer processing (melting, shaping and cooling) using polycaprolactone, which can be melted with boiling water.
To demonstrate processing using a common polymer at real-world polymer processing temperatures, usually much higher than 100 C, I simply used a hot air gun (the type used for paint stripping, like a super-hot hair dryer) on the side of a 1-litre HDPE milk bottle. Within a few seconds the polymer melts, and changes from cloudy to clear.
Milk bottle before heating
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After heating with a heat gun
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If you blow into the neck of the bottle, you can inflate the melted portion into a bubble, which eventually bursts. It's fun! Here's a video of me inflating a bottle:
The polymer in the skin of the bubble cools and freezes very quickly. Take care though, there will still may be some very hot melted polymer around the bottom of the bubble. Here's the finished 'product':
I get the students to feel the bubble - it feels exactly like a supermarket plastic bag. This is because these bags are also made out of HDPE, and also made by inflating molten polymer (in the blown film process). Inflation is also how the milk bottle was made in the first place - by extrusion blow moulding.
I've been doing this demo at the end of a lecture on glass transition temperature. To tie the two ideas together, I dunk the neck of the bottle in liquid nitrogen and smash it with a hammer:
The students have then seen the bottle in three states: solid/glassy, solid/rubbery and melted.