Fig. 1: Structural characterization, ORR performance, and statistical analysis of GQD catalysts.

a Schematic of size effects for sp² carbon domains, where black and white spheres in the molecular models represent carbon and hydrogen atoms, respectively. Typical TEM images (b–d), the size distribution (e–g), and HRTEM images (h–j) of S-GQDs, M-GQDs, and L-GQDs (from top to bottom). Scale bar: 50 nm for (b–d) and 2 nm for (h–j). k Schematic illustration of the band gap and structure of S-GQDs, M-GQDs, and L-GQDs. l Statistical distribution of the Raman intensities of D bands (I_D) and G bands (I_G) for S-GQDs, M-GQDs, and L-GQDs in multiple point tests. m, n High-resolution C 1 s and N 1 s XPS spectra of L-GQDs, respectively. o RRDE polarization curves (solid lines) and corresponding ring currents (dashed lines) for the three GQD catalysts 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 p Calculated 2e⁻ selectivity (H₂O₂ selectivity) of three GQDs during the potential sweep. q Partial least squares regression (PLSR) bi-plot showing the scores (dots) and loadings (vectors) for ORR selectivity. The percentages on the axes indicate the variance explained in the input features (X-variables), while the model as a whole explains 87% of the total variance in ORR selectivity. r F-test results illustrating the statistical significance of various structural descriptors on H₂O₂ selectivity (P < 0.05 is considered significant). Source data for (l–r) are provided as a Source Data file.