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 transport¹. In vivo and in vitro size oscillations of individual microtubules^2,3 (dynamic instabilities) and collective oscillations⁴ have been observed. In addition, dynamic spatial structures, like waves and polygons, can form in non-stirred systems⁵. 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 vesicles⁶, micelles⁷ or particles⁸ 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 materials¹¹ that respond to external stimuli similarly to living cells, or to creating artificial autonomous chemical robots¹².