Rational strain engineering of single-atom ruthenium on nanoporous MoS2 for highly efficient hydrogen evolution

Maximizing the catalytic activity of single-atom catalysts is vital for the application of single-atom catalysts in industrial water-alkali electrolyzers, yet the modulation of the catalytic properties of single-atom catalysts remains challenging. Here, we construct strain-tunable sulphur vacancies around single-atom Ru sites for accelerating the alkaline hydrogen evolution reaction of single-atom Ru sites based on a nanoporous MoS2-based Ru single-atom catalyst. By altering the strain of this system, the synergistic effect between sulphur vacancies and Ru sites is amplified, thus changing the catalytic behavior of active sites, namely, the increased reactant density in strained sulphur vacancies and the accelerated hydrogen evolution reaction process on Ru sites. The resulting catalyst delivers an overpotential of 30 mV at a current density of 10 mA cm−2, a Tafel slope of 31 mV dec−1, and a long catalytic lifetime. This work provides an effective strategy to improve the activities of single-atom modified transition metal dichalcogenides catalysts by precise strain engineering.

. The as-prepared NPG were washed three times with water to remove the residual acid in the nanopore channels. Afterwards, we use the NPG as a support on which Mo(CO) 6   The Ru content in this work is relatively high compared with the works reported so far (Supplementary Table 2). For the common synthesis strategy of single-atom catalysts, the numbers of defect or anchoring ligand always limit the metal load.
However, the isolated metal atoms are substitutional doped into the MoS 2 in the spontaneous reduction strategy, thus avoiding the limitation of the number of defect or anchoring ligand. This is main responsible for the high metal content in the catalysts prepared by spontaneous reduction strategy. The fitted average oxidation states of Ru from XANES spectra.
In the determining of oxidation state of Ru, we analyzed the absorption energy, which was obtained from the first maximum in the first-order derivative as the electron vacancy. The RuCl 3 (+3) and RuO 2 (+4) were used as the comparison standards.

Supplementary Figure 27. Operando Ru K-edge FT-EXAFS spectra.
The FT-EXAFS spectra of Ru/np-MoS 2 recorded at different applied voltages.

Magnified rising edge XANES regions recorded at the Mo K-edge of np-MoS 2 and
Ru/np-MoS 2 .

Supplementary Figure 29. The device for AP-XPS measurements.
AP-XPS measurements were performed at on the 24A1 beamline of NSRRC. In order to ensure the accuracy of the experiment, we prepared an np-MoS 2 material and cut it into two identical np-MoS 2 films (inset of Supplementary Fig. 29). One of them was used as an undoped sample (np-MoS 2 ) while another one was used as support for Ru doping (Ru/np-MoS 2 ). The Ru/np-MoS 2 film, np-MoS 2 film, and Au foil were directly covered on the carbon conductive adhesive, thus avoiding the influence of carbon conductive adhesive signal.
Then, the sample holder loaded with Ru/np-MoS 2 film, np-MoS 2 film, and Au foil was exposed in the analysis chamber. The AP-XPS analyses were conducted under UHV, a water pressure of 0.01 torr, and a water pressure of 0.1 torr, respectively. The obtained XPS data were corrected by using the Au 4f XPS spectrum of Au foil.

Supplementary Figure 30. AP-XPS measurements.
In order to acquire accurate results, we performed two AP-XPS measurements. Similar results were obtained in the two tests, which further proved the accuracy of the results. It is distinct that the O 1s XPS spectra of Ru/np-MoS 2 display obvious high-energy shifts with the increase of water pressure, resulting from the increase contribution of adsorbed water (Ads. H 2 O) (Fig.   5g). Therefore, it is deduced that Ru/np-MoS 2 own stronger water affinity than np- The unit cell was optimized until the force and total energy were set to be 0.01 eV/Å and 10 −5 eV, respectively. For the application of strain, our preliminary work before this work suggests that the np-MoS 2 experience tensile strain (about 10%) originated from the nanotube-shaped ligament (Ref. 8, 9). Ideally, the uniaxial tensile strain (10%) was applied on the above model. The subsequent HAADF-STEM characterizations show that the value of tensile strain is about 12% (Fig. 2g).
The generally accepted alkaline HER mechanism consists of two steps, with the Volmer step followed by the Tafel step or Heyrovsky step: The free energies of step (1) and step (3) should be the same at equilibrium potential.
Computations on the exact free energy of OHin solutions could be avoided by using computational hydrogen electrode based on the above assumption (Ref. 10).
The free energies (∆G) of steps 1-3 are calculated using the following equation Where h is the Planck constant, v i are the computed vibrational frequencies.
The thermal energy correction is calculated by the following equation: The Where β = 1/κT, {v i } are vibrational modes, κ is the Boltzmann constant, T is the temperature (which is set to 298 K in the present work), respectively. In the present study, the Gibbs free energy is calculated using VASPKIT, and the frequencies below

Supplementary Note 2: The syntheses of Ru/P-MoS 2 and Ru/Lnp-MoS 2
The P-MoS 2 was synthesized by using Au foil as substrates for the chemical vapor CN represents the coordination number; R represents the interatomic distance; σ 2 represents the Debye-Waller factor; ΔE 0 represents the edge-energy shift.