Fig. 3.

(A) Histograms of single–H₂ bubble nucleation current, $i_{\text{b}}^{\text{p}}$, on just one SiO₂ nanoparticle as a function of nanoparticle radii. Each distribution contains about 50 independent measurements of bubble formation, and the distributions are fitted by Gaussian function with the mean nucleation current, $\langle i_{\text{b}}^{\text{p}}\rangle$, at –164.1 ± 1.7 nA for smooth glassy carbon surface; –119.2 ± 1.3 nA for 99 nm; –95.0 ± 2.1 nA for 50 nm; –83.9 ± 3.1 nA for 37 nm; –73.2 ± 1.4 nA for 25 nm; –61.1 ± 1.6 nA for 20 nm; –59.8 ± 1.0 nA for 14 nm; –43.9 ± 1.1 nA for 10 nm; –72.0 ± 1.5 nA for 5.3 nm; and –105.3 ± 0.8 nA for 3.4 nm. (B) The Gaussian peak position extracted from A, $\langle i_{\text{b}}^{\text{p}}\rangle$, as a function of SiO₂ nanoparticle radii. (C) The normalized critical local surface H₂ concentration, $C_{{\text{H}}_2}^{*}/C_{{\text{H}}_2}^{*}(\text{bare})$, obtained from the finite element simulation based on measurement results (B) as a function of SiO₂ nanoparticles radii. $C_{{\text{H}}_2}^{*}(\text{bare})$ stands for the local surface H₂ concentration at bubble nucleation in the absence of an SiO₂ nanoparticle, which is 119 mM from SI Appendix, Fig. S24A.