Visualizing Invisible Phase Transitions in Blue Phase Liquid Crystals Using Early Warning Indicators.

Changes in the statistical properties of data as a system approaches a critical transition is studied intensively as early warning signals, but their application to materials science, where phase transitions-a type of critical transition-are of fundamental importance, are limited. Here, a critical transition analysis is applied to time-series data from a microscopic 3D ordered soft material-blue phase liquid crystals (BPLC)-and demonstrates that phase transitions that are invisible under ambient conditions can be visualized through the choice of appropriate early warning indicators. After discussing how a phase transition affects the statistical properties in a system with a Landau-de Gennes type free energy potential, the predicted changes are experimentally observed at the two types of phase transitions that occur in a BPLC: the isotropic to simple cubic, and simple cubic to body-centered cubic transitions. In particular, it is shown that the skewness of the intensity distribution inverts its sign at the phase transition, enabling temporally and spatially resolved mapping of phase transitions. This approach can be easily adapted to a wide variety of material systems and microscopy techniques, providing a powerful tool for studying complex critical transition phenomena.