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 microtubules2,3 (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 pH7,8,9), or by anchoring one of the species covalently (for example, a Belousov–Zhabotinsky catalyst6,10). 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.

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Fig. 1: Kinetics of redox-fuelled PDI assembly and disassembly.
Fig. 2: Supramolecular oscillations.
Fig. 3: Supramolecular oscillator model.
Fig. 4: Supramolecular travelling fronts and patterns.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.


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This work was financially supported by the Region Alsace, University of Strasbourg Institute for Advanced Study (USIAS), LabEx grant ‘Suproscill’ (CSC-THE-17) and ERC-2017-STG ‘Life-Cycle’ (757910). M.S. acknowledges an STSM from the CMST COST Action CM1304 Emergence and Evolution of Complex Chemical Systems. We acknowledge T. Ebbesen, C. Genet and M. Seidel for help with the IR-SLS.

Author information




J.L.-I. and T.M.H. designed and performed the experiments, and analysed the data. J.L.-I. performed the synthesis. A.T. performed the static and dynamic light scattering experiments. A.T. and T.A. developed the IR-SLS experiments and interpreted the results. J.L.-I., A.T. and T.A. carried out the IR-SLS experiments. M.S. and T.M.H. performed the modelling and interpretation of the results. J.L.-I. and T.M.H. wrote the paper. All the authors discussed the results and commented on the manuscript. T.M.H. conceived the overall project and supervised the research.

Corresponding author

Correspondence to Thomas M. Hermans.

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Supplementary Information


Supramolecular oscillations in a semi-batch reactor


Propagating front of supramolecular assemblies


The propagating front induces large scale in-plane convection


Control experiment. Seeded front versus non-seeded region


An outward propagating oxidation front induces flow-alignment of PDIassem

Supplementary Information

Supplementary Sections 1–7 and Supplementary Figures 1–17

Supplementary Video 1

Supramolecular oscillations in a semi-batch reactor

Supplementary Video 2

Propagating front of supramolecular assemblies

Supplementary Video 3

The propagating front induces large scale in-plane convection

Supplementary Video 4

Control experiment. Seeded front versus non-seeded region

Supplementary Video 5

An outward propagating oxidation front induces flow-alignment of PDIassem

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Leira-Iglesias, J., Tassoni, A., Adachi, T. et al. Oscillations, travelling fronts and patterns in a supramolecular system. Nature Nanotech 13, 1021–1027 (2018). https://doi.org/10.1038/s41565-018-0270-4

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