Anomalous thermomechanical actuation of liquid crystal elastomer balloons

Elastomeric balloons are widely studied in various soft actuation systems owing to their simplicity and versatility. Recently, balloons made of liquid crystal elastomers (LCEs) stand out with their unconventional, thermal-responsive inflation behaviors due to the intrinsic coupling between directionally ordered liquid crystal mesogens and stretchable polymer networks, offering an attractive way for fast, large, reversible, and stimuli-responsive actuation. However, this thermomechanical coupling, together with their resultant actuation and instability in LCE balloons, remains poorly understood. Here we show the anomalous thermomechanical actuation of a spherical LCE balloon by solving a boundary-value problem based on the well-established quasi-convex elastic energy for polydomain LCE. We modify the elastic energy to ensure its consistency with the classical model by Bladon, Warner, and Terentjev based on freely jointed chains. We predict the thermally modulated pressure-volume response of the LCE balloon, where the peak pressure for snap-through instability depends non-monotonically on temperature. This nonmonotonic dependence originates from the competing temperature-dependent effects of the mesogen order and the network elasticity, which also govern the modulus of the LCE in the nematic phase. Finally, by extending the free energy to a Gent-like model, we quantify the detailed temperature-dependent snap-through behavior, compare multiple performance metrics of spherical and cylindrical balloons, and analyze an envisioned thermally modulated fluid pump across a wide range of operating temperatures.