Fig. 2: Synthesis, structural characterization, ORR performance, and statistical analysis of carbon soot catalysts.

a Schematic diagram illustrating the principles of preparing carbon soot of different sizes based on the candle flame combustion process. b HRTEM images of CS-low, CS-middle, and CS-top (from bottom to top). Scale bar: 2.5 nm. c Number density of aromatic rings in three carbon soot samples, with an illustration of the PAH molecules of different sizes, where the black spheres represent carbon atoms. d Raw Raman spectra for CS-low, CS-middle, and CS-top. e, f High-resolution C 1 s and O 1 s XPS spectra, respectively. g RRDE polarization curves (solid lines) and corresponding ring currents (dashed lines) for three carbon soot samples without iR-compensation. Measurements were performed in an O₂-saturated (200 sccm) 0.1 M KOH electrolyte at 25 °C, with a scan rate of 10 mV s⁻¹ and a rotation speed of 1600 r.p.m h Calculated 2e^- selectivity (H₂O₂ selectivity) of three carbon soot samples during the potential sweep. i, j Partial least squares regression (PLSR) bi-plots for H₂O₂ selectivity and onset potential, respectively. The percentages shown on the axes correspond to the variance explained in the predictor variables (X-variables), while the resulting models explain 97% and 96% of the total variance in H₂O₂ selectivity and onset potential, respectively. k F-test results illustrating the statistical significance of various structural descriptors on H₂O₂ selectivity and onset potential (P < 0.05 is considered significant). Source data for (c–k) are provided as a Source Data file.