*2.2. Physicochemical Characterization*

The morphology of the Pd aerogels was characterized using a JEOL JEM-2100F highresolution transmission electron microscope (HR-TEM) with spherical aberration correction and a scanning electron microscope (SEM, Quanta FEG 650 microscopes from FEI). The crystal structures were measured by X-ray diffraction (XRD; D8-advance diffractometer Bruker) equipped with a CuKα X-ray source (λ = 0.1541 nm, 40 kV, 40 mA), using a step size of 0.02◦ 2θ and a scan step time of 5 s. The specific surface area and the pore size distribution were determined by nitrogen adsorption–desorption isotherms at −196 ◦C (Micromeritics ASAP 2020), after an overnight outgassing at 120 ◦C. The electronic structure of elements was measured by X-ray photoelectron spectroscopy (XPS; K-Alpha+ spectrometer equipped with the Avantage Data System from Thermo ScientificTM, Waltham, MA, USA).

## *2.3. Electrochemical Measurements*

#### 2.3.1. Electrocatalytic Activity in Half-Cell Configuration

The electrochemical evaluation of the Pd aerogels was carried out in a Biologic VMP3 Potentiostat/Galvanostat using a conventional three-electrode electrochemical cell in acid media at a scan rate of 20 mV s−1. A glass-carbon electrode (3 mm) was used as the working electrode, Hg/Hg2SO4 electrode as the reference electrode, and Pt wire as the counter electrode. The electrocatalyst ink was prepared using each aerogel sample in a mixture of 500 μL of deionized water and 50 μL of Nafion® (5%) per milligram of catalyst. The ink was sonicated for one hour and then 5 μL were deposited over the electrode surface. A similar ink was prepared using commercial Pd/C (20%, Sigma Aldrich, St. Louis, MI, USA) as catalyst and it was used for comparison. The electrolyte was bubbled with N2 for 30 min before the electrochemical measurement.

The electrochemical profile for each sample was obtained in cyclic voltammetry (CV) experiments in 0.5 M H2SO4 within a potential range of 0–1.4 V vs. RHE, where the faradaic processes were visible in a current (i.e., J) that was tested by mg of catalyst.
