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Probing far-from-equilibrium dynamics of electrical double layers

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  • Article
  • Published:
  • Yu-Chen Cai  ORCID: orcid.org/0009-0005-0924-03981 na1,
  • Zhao-Dong Meng  ORCID: orcid.org/0000-0003-0821-59141,
  • Ze-Tong Jia1,
  • Yu-Chen Sun  ORCID: orcid.org/0009-0003-4695-11271,
  • Jin-Yu Ye  ORCID: orcid.org/0000-0003-0521-633X1,
  • Na Tian  ORCID: orcid.org/0000-0002-8654-68181,
  • Zhi-You Zhou  ORCID: orcid.org/0000-0001-5181-06421,
  • Jun Huang  ORCID: orcid.org/0000-0002-1668-53612,3,
  • Junxiang Chen  ORCID: orcid.org/0000-0003-3047-00304,
  • Shi-Gang Sun  ORCID: orcid.org/0000-0003-2327-40901 &
  • …
  • Tao Wang  ORCID: orcid.org/0000-0002-3013-19471 

Nature (2026) Cite this article

Abstract

Electrified solid–liquid interfaces are central to energy and matter conversion in biological1 and electrochemical systems2,3,4, in which intense local electric fields govern reaction kinetics5,6,7,8,9. Yet, under realistic electrocatalytic conditions involving rapid charge transfer and far-from-equilibrium dynamics, the molecular structure and evolution of the electrical double layer (EDL) remain poorly understood. Classical EDL models, derived under equilibrium and non-reactive conditions, cannot capture the interfacial processes emerging at reactive interfaces10,11,12,13,14,15,16. Here we develop an integrated experimental–computational framework to directly resolve EDL dynamics under the hydrogen evolution reaction (HER). Chemically stable nanostructured Pt film electrodes enable high-sensitivity, time-resolved surface-enhanced infrared absorption spectroscopy (SEIRAS) at increased overpotentials, whereas machine-learning molecular dynamics (MLMD) captures interfacial charge fluctuations and solvent dynamics over nanosecond timescales. This combined approach reveals a nonlinear, two-phase evolution of the inner layer that intensifies the local electric field. Time-resolved spectra further uncover irreversible restructuring of interfacial water during cyclic potential modulation. These findings show that ions and interfacial water respond asynchronously under the condition far from equilibrium, establishing a quantitative molecular framework for understanding electrostatic potential variations, interfacial electrostriction of ions17,18,19, electrolyte effects20,21,22,23,24 and rational electrolyte design for energy conversion technologies.

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Data availability

All data are available in the main text and its Supplementary Information. Source data are provided with this paper. Extra data are available from the corresponding authors on request.

Code availability

The code and database for DPχ construction used in this study are available at GitHub (https://github.com/cjxxjc729/DPx-preview).

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Funding

This work was supported by the National Natural Science Foundation of China (22322202, 22288102, 22021001 and 22272134) and the National Key Research and Development Program of China (2023YFA1508300). This work was also supported by the Fundamental Research Funds for the Central Universities (20720250005). J.H. is supported by the European Research Council (ERC) (starting grant no. 101163405 ‘MESO-CAT’) and the Initiative and Networking Fund of the Helmholtz Association (no. VH-NG-1709).

Author information

Author notes

  1. These authors contributed equally: Xiao-Yu Li, Yu-Chen Cai

Authors and Affiliations

  1. State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM (Collaborative Innovation Center of Chemistry for Energy Materials), College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, China

    Xiao-Yu Li, Yu-Chen Cai, Zhao-Dong Meng, Ze-Tong Jia, Yu-Chen Sun, Jin-Yu Ye, Na Tian, Zhi-You Zhou, Shi-Gang Sun & Tao Wang

  2. Institute of Energy Technologies, IET-13: Theory and Computation of Energy Materials, Forschungszentrum Jülich GmbH, Jülich, Germany

    Jun Huang

  3. Theory of Electrocatalytic Interfaces, Faculty of Georesources and Materials Engineering, RWTH Aachen University, Aachen, Germany

    Jun Huang

  4. CAS Key Laboratory of Design and Assembly of Functional Nanostructures, Fujian Provincial Key Laboratory of Nanomaterials, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, China

    Junxiang Chen

Authors

  1. Xiao-Yu Li
  2. Yu-Chen Cai
  3. Zhao-Dong Meng
  4. Ze-Tong Jia
  5. Yu-Chen Sun
  6. Jin-Yu Ye
  7. Na Tian
  8. Zhi-You Zhou
  9. Jun Huang
  10. Junxiang Chen
  11. Shi-Gang Sun
  12. Tao Wang

Contributions

T.W., J.H., J.C. and X.-Y.L. conceived the idea and designed the experiments. X.-Y.L. and Z.-Y.Z. performed and analysed infrared experiments and electrochemical measurements. J.C. developed the MLMD method and performed the simulations. Y.-C.C. performed the ab initio MD simulations and analysis. J.H. constructed the continuum model of the EDL. Z.-D.M., Z.-T.J., Y.-C.S., J.-Y.Y., N.T. and S.-G.S. participated in the discussion and interpretation of experimental and theoretical data. Z.-Y.Z. supervised this work. X.-Y.L., T.W., J.H. and J.C. wrote the manuscript. All authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Zhi-You Zhou, Jun Huang, Junxiang Chen or Tao Wang.

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Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature thanks Victor Climent and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data figures and tables

Extended Data Fig. 1 Large enhancement factor for square-wave electrodeposited Pt black.

a, The enhancement factors of the square-wave electrodeposited Pt black (used in SEIRAS measurements) and the directly electrodeposited Pt black are compared. The spectra were obtained by subtracting the profile of saturated CO on clean Pt surfaces from that on Pt nanofilm electrodes at an electrode potential of 0.37 V. b,c, Scanning electron microscope images evidence that the uniform nanoparticles of the square-wave electrodeposited Pt electrode (c) contribute to a much higher enhancement factor, whereas the directly electrodeposited Pt electrode (b) exhibits an uneven morphology.

Source data

Extended Data Fig. 2 The contraction process of the inner layer and the appearance of Eigen protons at potentials below −0.79 V.

The fitted infrared spectra collected in a solution of 0.1 mol l−1 H2SO4 + 0.2 mol l−1 K2SO4 at an ES of −0.075 V (upper spectrum) and −1.07 V (lower spectrum), with ER = 0.37 V. The fitted peaks are colour-coded for clarity: blue represents the interfacial water signal, pink indicates the Eigen proton signal, grey and gradient grey denote weakly hydrogen-bonded water.

Source data

Extended Data Fig. 3 Training and inference workflow for DPχ-based MD run.

a, Active-learning workflow for constructing the DPχ potential. Candidate models (DP1–DP4; four replicas for DP3) propagate exploratory MD; newly encountered configurations are annotated by DFT and fed back and the loop is iterated to convergence. b, Data flow for training (top) and inference (bottom). c, Three-electrode cell used for inference. The WE and auxiliary electrode carry equal and opposite charge; the WE potential is computed by the reference electrode (RE) as UWE = (χWE − χRE)/K + Upzc. Adapated with permission from ref. 31, American Chemical Society.

Extended Data Fig. 4 Regional computational spectra of K+ solution from MLMD.

Computational spectra of water in different regions of the EDL in K+ solution. a, Inner layer. b, Outer layer. c, Inner layer and around K+. d, Outer layer and around K+. e, Inner layer and not around K+. f, Outer layer and outside the K+ hydration shell. The computational spectra in these regions indicate that the experimentally observed changes in EDL structure under HER conditions can be explained by the synchronous changes of the inner layer and the outer layer of the EDL.

Source data

Extended Data Fig. 5 EDL structural variation under HER conditions detected by time-resolved SEIRAS.

a, Time-resolved SEIRAS spectra with a time resolution of 62.5 ms, obtained at ER = 0.37 V and ES = −1.04 V. b, Time-resolved SEIRAS spectra obtained at ER = 0.37 V and ES = −0.25 V. c, Time-resolved SEIRAS spectra collected during electrode potential shifts from −1.04 V to 0.37 V. d, Time-resolved SEIRAS spectra collected during electrode potential shifts from −0.25 V to 0.37 V.

Source data

Extended Data Fig. 6 Repeated measurements of infrared spectra in a solution of 0.1 mol l−1 D2SO4 + 0.2 mol l−1 K2SO4 (D2O).

a–c, Three sets of parallel SEIRAS measurements performed in a solution of 0.1 mol l−1 D2SO4 + 0.2 mol l−1 K2SO4 (D2O) with an ER of 0.37 V. d–f, Potential-dependent wavenumbers of Pt–D stretching in a solution of 0.1 mol l−1 D2SO4 + 0.2 mol l−1 K2SO4 (D2O) that are extracted from a–c, respectively. g–i, Potential-dependent wavenumbers of Pt–D stretching in a solution of 0.1 mol l−1 D2SO4 + 0.2 mol l−1 K2SO4 (D2O), carefully corrected with the solution resistance.

Source data

Extended Data Fig. 7 Comparison of structural changes of the EDL at two potentials.

a,b, Time-resolved SEIRAS in a solution of 0.1 mol l−1 D2SO4 + 0.2 mol l−1 K2SO4 (D2O), obtained at an ES of −0.27 V (a) and −1.02 V (b), respectively.

Source data

Extended Data Fig. 8 Excluding the pH effect on the substantial decrease in Pt–D frequencies.

a,b, CV curves of the Pt nanofilm electrode collected in 1 mol l−1 PBS solution (pH = 7.2) (a) and 0.2 mol l−1 K2SO4 solution (pH = 5.82) (b), referenced to the RHE scale. c, Potential-dependent infrared spectra of Pt–D stretching obtained in 0.2 mol l−1 K2SO4 solution (pH = 5.82). d, Potential-dependent Pt–D frequencies collected in various electrolytes, including 0.2 mol l−1 K2SO4 solution (pH = 5.82), referenced to the SHE scale.

Source data

Extended Data Fig. 9 Comparison of the compressible EDL model and the classical EDL model.

a,b, Schematic diagram of the compressible EDL model (a) and the classical GCS model (b), characterized by two parameters: the distance (δ) between the electrode and the centre of a K+ ion and the volume ratio (γ) of a hydrated K+ ion referenced to a water molecule. c, Both parameters decrease as the electrode potential becomes more negative, indicating dehydration of K+ and their approach towards the electrode surface. d, Schematic diagram of the classical GCS model, in which δ and γ remain constant despite shifts in potential. e, Simulated values of δ and γ using both the compressible EDL model (solid line) and the classical GCS model (broken line). f, Simulated concentrations of K+ at the outer layer and the surface charge densities, as predicted by the compressible EDL model (solid line) and classical GCS model (broken line).

Source data

Extended Data Fig. 10 The maximum K+ coverage.

a, Simulated K+ concentration and surface charge density in the potential range from 0 V to −1.2 V, showing that K+ reaches its maximum coverage on the electrode surface at −1.16 V. b,c, The simulated values of δ and γ (b) and the electric field intensity (c) using the compressible EDL model in the potential range from 0 V to −1.2 V. d, The measured potential-dependent Pt–D frequencies, which level off at electrode potentials below −1.2 V.

Source data

Supplementary information

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Li, XY., Cai, YC., Meng, ZD. et al. Probing far-from-equilibrium dynamics of electrical double layers. Nature (2026). https://doi.org/10.1038/s41586-026-10986-7

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