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. 2024 Feb 26;15:1719. doi: 10.1038/s41467-024-46175-1

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© The Author(s) 2024

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 1 — a Reaction pathway Gibbs free energy diagrams and (b) theoretical limiting potential difference of U_L(CO₂)-U_L(H₂) on Ni-N₄ as a function of interfacial electric field strength. c Reaction Gibbs free energy diagrams of ORR on Fe–N₄ under the influence of various electric field strengths. d Contour plot of the ORR limiting potential as a function of ΔG_OH and ΔG_OOH. The values for Fe-SAC are shown with (white triangles) and without (black triangle) the influence of an electric field. e Finite-element numerical method simulation results of the interfacial electric field strength as a function of sphere diameter. See Supplementary Note 1 for more details. f Computed electric field intensity distribution for 4 sphere diameters of 100, 140, 200 and 350 nm with additional results available in Supplementary Fig. 7. Note: the sphere radius rather than diameter is shown in the figure. Source data are provided as a Source Data file.