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 particless(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).