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Kinetic and energetic insights into the dissipative non-equilibrium operation of an autonomous light-powered supramolecular pump


Natural and artificial autonomous molecular machines operate by constantly dissipating energy coming from an external source to maintain a non-equilibrium state. Quantitative thermodynamic characterization of these dissipative states is highly challenging as they exist only as long as energy is provided. Here we report on the detailed physicochemical characterization of the dissipative operation of a supramolecular pump. The pump transduces light energy into chemical energy by bringing self-assembly reactions to non-equilibrium steady states. The composition of the system under light irradiation was followed in real time by 1H NMR for four different irradiation intensities. The experimental composition and photon flow were then fed into a theoretical model describing the non-equilibrium dissipation and the energy storage at the steady state. We quantitatively probed the relationship between the light energy input and the deviation of the dissipative state from thermodynamic equilibrium in this artificial system. Our results provide a testing ground for newly developed theoretical models for photoactivated artificial molecular machines operating away from thermodynamic equilibrium.

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Fig. 1: Simplified energy diagrams of operation of the pump and molecular structures of the components.
Fig. 2: Operative reaction network of the supramolecular pump.
Fig. 3: Time-dependent concentration profiles of complexed Z-2+.
Fig. 4: Dependence of the kinetic and thermodynamic parameters on the photon flow.

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All data needed to evaluate the conclusions are present in the main text and/or the Supplementary Information. Additional data related to this paper may be requested from the corresponding author on reasonable request. Source data are provided with this paper.


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Financial support from the EU (H2020 ERC AdG 692981 and ERC-2015-CoG n. 681456) and the Ministero dell’Università e della Ricerca (PRIN 20173L7W8K and 201732PY3X, FARE R16S9XXKX3) is gratefully acknowledged.

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Authors and Affiliations



S.C. and J.G. synthesized the compounds. M.T.B., S.C., S.S. and M.B. designed and performed the kinetic experiments and analysed the data. S.C. carried out numerical simulations. E.P. and M.E. performed the thermodynamic analysis. A.C. and S.C. wrote the manuscript with input from all authors. All authors discussed the results and commented on the manuscript. A.C. conceived the project and directed the research.

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Correspondence to Alberto Credi.

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Nature Nanotechnology thanks the anonymous reviewers for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Figs. 1–7, Tables 1–8, Discussion and equations.

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Source Data Fig. 3

Mole fractions of Z complex from time-dependent NMR measurements.

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Corra, S., Bakić, M.T., Groppi, J. et al. Kinetic and energetic insights into the dissipative non-equilibrium operation of an autonomous light-powered supramolecular pump. Nat. Nanotechnol. 17, 746–751 (2022).

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