Phase diagram and snap-off transition for twisted party balloons

Many of us have the experience of inflating balloons and twisting them into different shapes and animals. Snapping the balloon into two separate compartments is a necessary step that bears resemblance to the pinch-off phenomenon when a water droplet detaches from the faucet. In addition to testing whether balloons exhibit the properties of self-similarity and memory effect that are often associated with the latter event, we determine their phase diagram by experiments. It turns out that a common party balloon does not just snap, but can assume five more shapes, i.e., straight, necking, wrinkled, helix, and supercoil, depending on the twist angle and ratio of its length and diameter. Moreover, history also matters due to their prominent hysteresis. One may shift the phase boundary and/or reshuffle the phases by untwisting or lengthening the balloon at different twist angle and initial length. A heuristic minimal model is provided to obtain analytic expressions for the phase boundaries.