Oscillations, travelling fronts and patterns in a supramolecular system

Supramolecular polymers, such as microtubules, operate under non-equilibrium conditions to drive crucial functions in cells, such as motility, division and organelle transport 1 . In vivo and in vitro size oscillations of individual microtubules 2 , 3 (dynamic instabilities) and collective oscillations 4 have been observed. In addition, dynamic spatial structures, like waves and polygons, can form in non-stirred systems 5 . Here we describe an artificial supramolecular polymer made of a perylene diimide derivative that displays oscillations, travelling fronts and centimetre-scale self-organized patterns when pushed far from equilibrium by chemical fuels. Oscillations arise from a positive feedback due to nucleation–elongation–fragmentation, and a negative feedback due to size-dependent depolymerization. Travelling fronts and patterns form due to self-assembly induced density differences that cause system-wide convection. In our system, the species responsible for the nonlinear dynamics and those that self-assemble are one and the same. In contrast, other reported oscillating assemblies formed by vesicles 6 , micelles 7 or particles 8 rely on the combination of a known chemical oscillator and a stimuli-responsive system, either by communication through the solvent (for example, by changing pH 7 – 9 ), or by anchoring one of the species covalently (for example, a Belousov–Zhabotinsky catalyst 6 , 10 ). The design of self-oscillating supramolecular polymers and large-scale dissipative structures brings us closer to the creation of more life-like materials 11 that respond to external stimuli similarly to living cells, or to creating artificial autonomous chemical robots 12 . A perylene diimide derivative shows nonlinear chemical dynamics when chemically fuelled in a semi-batch reactor.