Arrested coalescence drives helical coiling and networking of filamentous smectic condensates
Liquid-liquid crystal phase separation (LLCPS) occurs in many industrial and biological settings. Interestingly, when smectic phases demix from the homogeneous mixture, they can form filamentous condensates that spontaneously assemble into sparse networks with rich life-like dynamics. Here, we study the underlying process of filament networking. Microscopy reveals that new linkages between filaments are initiated by an adhesive interaction between straight filaments; parallel filaments snap into contact and then rapidly wind into helical coils, despite the absence of molecular chirality or transitions between mesophases. Using polarized optical microscopy, theoretical modeling, and simulation, we show that parallel filaments coalesce, but are arrested in double-barreled ``ribbon'' structures. This arrested coalescence is driven purely by interfacial energy minimization under the constraints of smectic layering. The arrested ribbons spontaneously coil into double helices to further reduce interfacial area, thus driving compaction into networks. We propose a microstructure consistent with this interpretation, which quantitatively predicts the extent of arrested coalescence. In total, these findings suggest a generic pathway for network formation in liquid crystals that provides insight about the formation of condensate networks in other engineered or biological materials.