Anomalous Sabatier principle on high entropy alloy catalysts

doi:10.21203/rs.3.rs-2756931/v1

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Anomalous Sabatier principle on high entropy alloy catalysts

https://doi.org/10.21203/rs.3.rs-2756931/v1

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published 08 Jan, 2024

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The Sabatier principle is widely explored in heterogeneous catalysis, graphically depicted in volcano plots. The most desirable activity is located at the peak of the volcano, and further advances in activity past this optimum are possible only by designing a catalyst that circumvents the limitations entailed by the Sabatier principle. In this work, by density functional theory calculations, we found that high entropy alloy (HEA) surface with spatially varying adsorption free energy of hydrogen (ΔG_H*), where the active sites with strong adsorption adsorb hydrogen (H*) and other sites with weak adsorption release H* to produce H₂, was against the “just right” (ΔG_H* = 0 eV) in the Sabatier principle of hydrogen evolution reaction (HER). The Gaussian distribution [X ~ N(µ, σ²)] of ΔG_H* on HEA was proposed as a descriptor, deriving an anomalous Sabatier principle, where a larger σ value results with µ = 0 eV results in a higher catalytic activity for HER. As a proof-of-concept, we synthesized a series of alloy systems, the PtFeCoNiCu HEA catalyst has the best catalytic performance for HER with an overpotential of 10.8 mV at -10 mA cm^− 2 and 4.6 times higher intrinsic activity over the state-of-the-art Pt/C. Moreover, the calculated adsorption energy of C*, O*, and N* on HEAs also follows a Gaussian distribution, indicating the anomalous Sabatier principle can be extended to other related catalytic reactions.

Physical sciences/Materials science/Materials for energy and catalysis/Electrocatalysis

Physical sciences/Chemistry/Catalysis/Heterogeneous catalysis

Anomalous Sabatier principle

high entropy alloy catalysts

hydrogen evolution reaction

Gaussian distribution

In the Sabatier principle, the adsorbate should bind neither too weakly (lest reactants fail to activate) nor too strongly (lest products fail to dissociate).^1–2 It provides useful guidance in heterogeneous catalysis and is also held up as a rule or limit to be circumvented when one seeks further to advance catalytic performance.^3–8 The resultant volcano plots have been used to guide catalyst design for the CO₂ reduction reaction (CO₂RR),⁹ nitrogen reduction reaction (NRR),¹⁰ hydrogen evolution reaction (HER),¹¹ and oxygen reduction/evolution reaction (ORR/OER).^12–13 “Just right” adsorption energy is the pursuit of all chemical reactions. However, although we achieve the “just right” adsorption energy, the catalytic activity is just infinitely close to the peak. Further breakthroughs or over the volcano in catalytic activity are almost impossible. For instance, Nørskov et al. applied high-throughput density functional theory (DFT) calculations to screen out BiPt with the optimal adsorption energy of H* among 736 alloy systems. This alloy was synthesized and tested experimentally and showed improved HER performance compared with Pt, however, still below the volcano peak.¹⁴

Circumventing the volcano relationship is plausible to achieve a breakthrough or over the volcano in catalytic activity,¹⁵ and numerous efforts have been focused on this issue.^{8, 16–17} For example, Chen et al. demonstrated that the volcano relationship can be broken by building an interface between transition metals and LiH.¹⁸ Unfortunately, the relatively few active sites have impeded the wide application of interface catalysis.¹⁹ Another strategy of strain effect was proposed by Khorshidi et al., the surface strain has to occur either externally by applying mechanical loading or internally by creating complex core-shell structures or interfaces.⁸ High entropy alloys (HEAs) with huge composition space have complex surface active sites, resulting in spatially varying adsorption of intermediates.²⁰ Some active sites with strong adsorption can be used to activate reactants, while some active sites with weak adsorption are favorable for the formation of products, which circumvents the Sabatier principle if the intermediates can easily diffuse on the HEA surface. It means the HEA catalysts provide new opportunities to achieve a breakthrough over the volcano in catalytic activity.

In this article, we found that HEA surface with spatially varying adsorption free energy of hydrogen circumvent the Sabatier principle of HER. DFT calculations indicate that the adsorption free energy of H* (ΔG_H*) on HEA catalysts follows a Gaussian distribution [X ~ N(µ, σ²), µ: expectation; σ: standard deviation] due to the gradient electron distribution and the diffusion of H* on HEA surface is fairly easy with the small barrier of 0.124 eV. Some sites with strong adsorption (ΔG_H* < µ - σ) are used for H* adsorption, while some sites with weak adsorption (ΔG_H* > µ + σ) are used for H₂ formation. It means that the catalytic activity for HER will be better if the µ is closer to 0 eV and the σ is larger, which is defined as an anomalous Sabatier principle. The µ and σ values could be regulated by the composition, strain effects, and synthesis conditions of HEA catalysts. Guided by these theoretical findings, a PtFeCoNiCu catalyst with electron and composition gradients has been precisely fabricated, exhibiting excellent catalytic performance with an overpotential of 10.8 mV at -10 mA cm^− 2 and more than four times higher intrinsic activity over the state-of-the-art Pt/C. We also show that this anomalous Sabatier principle can be extended to other adsorbents (C*, O*, and N*) on HEA surfaces, indicating potential applications for variety of catalytic reactions.

Dual gradient PtFeCoNiCu HEA model

A PtFeCoNiCu HEA catalyst was originally designed based on the following three aspects: (1) Pt catalyzes HER and is a good choice of the active site for HER;¹⁴ (2) the smaller atomic radii of Fe (1.56 Å), Co (1.52 Å), Ni (1.49 Å), and Cu (1.45 Å) than that of Pt (1.77 Å) would produce compressive strain on the HEA surface, resulting in a weaker H* adsorption on surface Pt sites, which promotes the catalytic performance for HER;^21–22 and (3) the cost of catalysts could be greatly reduced by using non-noble metals.²³

Taking into consideration that (i) some metals (Fe, Co, Ni, Cu) will be corroded away in an acidic electrolyte during the HER process, and (ii) the outer atomic layers will be etched more seriously than the inner layers, a PtFeCoNiCu HEA model with a Pt concentration gradient of 100.0%, 50.0%, 25.0%, 12.5%, and 12.5% for the five layers has been designed, as shown in Fig. 1A. The coordination atoms to surface Pt active sites are diverse due to the nature of HEA, which results in various electron redistributions (electronic gradient), as shown in Fig. 1B. Such an electronic gradient causes different adsorption abilities for H*, where surface Pt sites with strong H* adsorption are active centers for the Volmer reaction (* + H⁺ + e⁻ → H*) while the ones with weak H* adsorption are active centers for the Tafel (H* + H* → H₂) or Heyrovsky reaction (H* + H⁺ + e⁻ → H₂).

Fe, Co, Ni, and Cu with smaller atomic radii than that of Pt will induce a compressive strain on the surface Pt atoms, which further regulates the electron structures of active sites.²¹ Fig. 1C shows that the energy level of d orbitals in surface Pt atoms is gradually away from the Fermi level with increasing compressive strain, indicating the diminished activity. This phenomenon can be further quantified by their d-band center (ε_d) values, where a more negative ε_d value indicates a weaker adsorption ability.²⁴ With the increase of compressive strain, the ε_d values change from − 1.66 eV (HEA without strain) to -1.72, -1.75, -1.89, and − 2.03 eV for 1.4%-HEA (HEA with 1.4% compressive strain), 3.2%-HEA, 5.0%-HEA, and 6.8%-HEA, respectively. The composition-strain-ε_d-activity relation allows for designing HEA catalysts with optimal adsorption energy via composition regulation.²¹

Gaussian distribution of ΔG_H* on PtFeCoNiCu HEA

ΔG_H* is calculated on the designed HEA (111) with different strains (see Fig. 1D). The ΔG_H* distribution roughly conforms to the Gaussian distribution [X ~ N(µ, σ²)]. Herein, µ and σ² determine the location and the variance of ΔG_H*, respectively. As shown in Fig. 1D, the µ value increases with increasing compressive strain. This is consistent with the d-band center theory, where a larger compressive strain brings more negative ε_d, resulting in weaker adsorption.^24–25 The corresponding structure (strain)-property (ε_d)-performance (µ) relation is shown in Figure S1. Note that the compressive strain shows little influence on the σ value. A larger σ value indicates that some adsorption sites have stronger adsorptions while other adsorption sites have weaker adsorptions, which requires a larger electronic gradient on the surface. Above all, the two parameters (µ and σ) in the Gaussian distribution of ΔG_H* could be regulated by the type and number of alloying elements in HEA, which bring various strains and surface electronic gradients.

As is well known, ΔG_H* = 0 eV denotes the optimal catalytic performance of catalysts for HER based on the Sabatier principle.¹¹ However, the active sites of HEA are diverse and their ΔG_H* values follow a Gaussian distribution, rather than a definite value. Hence, the Sabatier principle and the criterion of ΔG_H* = 0 eV are no longer valid for HEA catalysts. In this work, we propose an anomalous Sabatier principle, where the Gaussian distribution of ΔG_H* with a µ value closer to 0 eV and a larger σ value on HEA catalysts could be used as the descriptor of the higher catalytic activity for HER. Theoretically, the sites with ΔG_H* < µ-σ and ΔG_H* > µ + σ serve as the active centers for Volmer and Tafel (or Heyrovsky) reactions (see Figure S2), respectively. The larger σ value indicates that the active center for the Volmer reaction has a stronger H* adsorption while the active center for Tafel (or Heyrovsky) reaction has a weaker H* adsorption (see Figure S3). This means that a larger σ value results in faster Volmer and Tafel (or Heyrovsky) reactions, indicating a higher catalytic activity for HER. Moreover, the symmetry of the Gaussian distribution dictates that these two active centers are guaranteed to be the strongest and the weakest, respectively, only if µ = 0 eV (see Figure S4). Meanwhile, other sites with moderate ΔG_H* (µ-σ < ΔG_H* < µ + σ) are the diffusion region (DR). The diffusion of H* on the HEA surfaces is known as H* spillover, which will be discussed in detail below.

Reaction mechanism of HER on PtFeCoNiCu HEA

The 5.9%-HEA system was used as an example for studying the H* spillover based on the new descriptor of Gaussian distribution of ΔG_H* with the preferable µ = -0.034 eV and σ = 0.041 eV (see Figure S5). The ΔG_H* values on the possible adsorption sites (see Figure S6) of 5.9%-HEA are shown in Fig. 2A, where the green area denotes the DR. The active center for the Volmer reaction has the smallest ΔG_H* of -0.099 eV and the active center for the Tafel or Heyrovsky reaction has the largest ΔG_H* of 0.075 eV.

Both Volmer-Heyrovsky (V-H) and Volmer-Tafel (V-T) mechanisms in HER are considered on Pt (111) and 5.9%-HEA (111), as depicted in Fig. 2B, C. For the V-H mechanism on Pt (111), the potential limiting step (PLS) is the Heyrovsky step with ΔG_Hey = 0.375 eV, an endothermic reaction. However, no PLS exists in the V-H mechanism on 5.9%-HEA (111) when considering the H* spillover. Both the Volmer and Heyrovsky steps are exothermic reactions with ΔG_Vol−1 = -0.099 eV and ΔG_Hey = -0.075 eV, respectively. The adsorbed H* diffuses from Site A to Site B through the DR1 (see Fig. 2D) with the maximum energy barrier of 0.124 eV, which is much smaller than the energy barrier leading to a reaction rate of about 1 site^− 1s^− 1 at room temperature,²⁶ indicating the exceedingly fast diffusion of H*.

For the V-T mechanism, the first two Volmer steps are exothermic reactions (ΔG_Vol−1 = -0.375 eV, ΔG_Vol−2 = -0.201 eV) on Pt (111). They are also exothermic reactions (ΔG_Vol−1 = -0.099 eV, ΔG_Vol−2 = -0.091 eV) on 5.9%-HEA (111). The following Tafel step has a large energy barrier of 1.128 eV on Pt (111). Although the energy barrier decreases to 0.466 eV with increasing H* coverage (see Figure S7), it is still much larger than that on 5.9%-HEA (111) (0.297 eV). For the V-T mechanism, DR2 is involved during the reaction process, as shown in Fig. 2E. The maximum energy barrier in DR2 is 0.232 eV, which is smaller than the rate determining step (RDS) of the Tafel reaction (0.297 eV) on 5.9%-HEA (111). Above all, the H* spillover processes on both DRs wouldn’t be the PLS or RDS during HER on 5.9%-HEA (111).

Moreover, the reaction processes of HER on 5.9%-HEA (111) without H* spillover are also considered, as shown in Figure S8. The corresponding electrocatalytic activity for HER is better than that on Pt (111), while far less than 5.9%-HEA (111) with H* spillover. For instance, the energy barrier of the Tafel step decreases to 0.297 eV (with H* spillover) from 0.519 eV (without H* spillover) on 5.9%-HEA (111). As expected, the designed catalysts should have greatly enhanced catalytic performance than Pt. Note that the adsorption sites considered in DFT calculations are very limited relative to those on the HEA surface. In practice, the active centers for the Volmer (Tafel/Heyrovsky) steps should have stronger (weaker) H* adsorption, respectively, which indicates better catalytic activities of HEAs.

Synthesis and characterization of PtFeCoNiCu HEA

As a proof-of-concept, the PtFeCoNiCu HEA catalysts were synthesized through a solvothermal reaction followed by thermal annealing, as illustrated in Figure S9. Based on different annealing temperatures (300, 400, and 500°C), the synthesized HEA samples are named as HEA-300, HEA-400, and HEA-500, respectively. Figure 3A shows the XRD patterns, where all HEAs present a face-centered cubic structure with three main characteristic peaks corresponding to (111), (200), and (220) planes. The sharp peaks at 15.7° and 16.2° in HEA-300 can be assigned to the transition metal chloride of the precursor, suggesting that 300°C is not high enough to transform the precursor into HEA thoroughly. Compared with the (111) peak position of Pt/C, the HEA-300, HEA-400, and HEA-500 samples show positive shifts of 1.8°, 2.3°, and 2.3°, respectively, implying the existence of compressive strain in the HEAs caused by alloying with Fe, Co, Ni, and Cu.^27–28 Larger compressive strains appear in HEA-400 and HEA-500 than that in HEA-300, demonstrating the influence of annealing temperature on the strain, which results in the regulation of µ value in the Gaussian distribution of ΔG_H*. Based on the DFT results, the PtFeCoNiCu with a larger compressive strain should have a µ value closer to 0 eV, indicating a higher catalytic activity, which is consistent with our experimental results, as shown in Figure S10.

X-ray photoelectron spectroscopy (XPS) analysis (see Figures S11-14) was performed to explore the charge redistribution in HEA catalysts. As shown in Fig. 3B, both Pt⁰ 4f_7/2 and 4f_5/2 peaks in HEA-400 shift negatively compared with that of Pt/C, demonstrating the electron transfer from other components to Pt in HEA, which agrees well with their electronegativity differences (Fe: 1.83, Co: 1.88, Ni: 1.91, Cu: 1.90, and Pt: 2.28).^28–30 After 5000 cycles of cyclic voltammetry (CV) activating, both the Pt⁰ 4f_7/2 and 4f_5/2 peaks in HEA-400-5000 (HEA-400 after 5000-cycle CV activation) shift positively compared with those of HEA-400. This is caused by the corrosion of Fe, Co, Ni, and Cu during the activation process. Therefore, reduced electrons are transferred to the Pt element. The transferred electron amounts between Pt atom and its different neighbors are distinct, leading to a gradient in electron distribution on surface Pt, which is consistent with our proposed DFT model.

The size of the synthesized HEA nanoparticles increases with the annealing temperature, as shown in Figure S15. According to the high-resolution TEM images shown in Figure S16, HEA-300, HEA-400, and HEA-500 have lattice spacings of 0.213, 0.210, and 0.207 nm, corresponding to their (111) planes, respectively. Compared with the Pt (111) plane (0.226 nm, see Figure S17), all HEAs present the compressive strain caused by the alloying of Fe, Co, Ni, and Cu with smaller radii into Pt, which is in accord with the DFT model.

Taking HEA-400 as an example, Pt, Fe, Co, Ni, and Cu elements follow an atomic ratio of 18.8: 19.9: 22.3: 20.2: 18.8, according to inductively coupled plasma optical emission spectroscopy (ICP-OES). The contents of Fe, Co, Ni and Cu in the electrolyte are detected to increase continuously with the CV activation process (see Table S1). Additionally, a small amount of 0.226-nm lattice spacings corresponding to Pt (111) appear after 5000-cycle CV activation while more 0.226-nm lattice spacings expose after 10000-cycle CV activation (see Figure S18). All these findings confirm the corrosion of non-Pt elements during the activation. Correspondingly, the average HEA-400 (111) lattice spacings increase with the activation cycles, which states the increase of Pt component proportion (see Figure S19).

A Pt concentration gradient is generated on the surface of the HEA catalyst, as shown in the high-angle annular dark-field scanning TEM (HAADF-STEM) image of HEA-400-5000 (see Fig. 3C and Figure S20). The (111) plane in HEA-surface has a lattice spacing of 0.226 nm, which is consistent with the Pt (111) spacing, indicating the predominance of Pt in surface layers. The (111) lattice spacing in the core is measured to be 0.210 nm, which is the same as that in HEA-400 before activation (see Figure S16B). Namely, the etching effect only appears in the outermost layers (15 ~ 20 layers) of HEA. A (111) lattice spacing in the transition layer is measured to be 0.217 nm, being between those in Pt (111) and HEA-400 (111), indicating the partial etching of non-Pt elements. The gradually diminished lattice spacings from the outermost layers to the core indicate a Pt concentration gradient (see Fig. 3D). The HAADF-EDS elemental maps demonstrate the homogeneously distributed elements in the nanoparticle (see Fig. 3E). Moreover, the Pt concentration gradient is further confirmed in the near-surface elemental maps (Figures S21-23), where Fe, Co, and Ni are less detected than Cu and Pt, due to the susceptibility to corrosion of Fe, Co, and Ni during the activation process. Furthermore, the HAADF line scan results (see Figure S24) also display the gradually increased degree of the etching of Fe, Co, and Ni from the core to the outermost layers in HEA-400-5000. All these results indicate that the synthesized HEA catalysts are consistent with the designed dual gradient PtFeCoNiCu HEA model.

Catalytic performance of PtFeCoNiCu HEA

The HER performance of the HEA catalysts was measured in 0.5 M H₂SO₄ using a typical three-electrode configuration. Figure 4A shows polarization curves of HEA-400 before and after CV tests. The HEA-400 shows an overpotential of 96.8 mV at -100 mA cm^− 2 in the initial polarization curve. After the 100-cycle CV test, the HEA-400-100 shows a greatly improved HER performance with an overpotential of 37.8 mV at -100 mA cm^− 2. The HER performance of HEA-400 is gradually enhanced with continuous CV tests until the best performance (the overpotential of 30.7 mV at -100 mA cm^− 2) is achieved after 5000 CV cycles. This is caused by the exposure of more Pt elements on the surface. The Pt, Fe, Co, Ni and Cu elements in HEA-400-5000 follow an atomic ratio of 35.0: 12.3: 14.8: 17.3: 20.6 according to ICP-OES results, consistent with our assumption of the dissolution of Fe, Co, Ni, and Cu components on the surface during the CV activation. Further cycling will make excess Fe, Co, Ni, and Cu elements dissolved, resulting in a smaller electron gradient on the HEA surface and thus a smaller σ value. This is the reason that HEA-400-10000 shows an attenuation performance compared with that of HEA-400-5000 (see Figure S25). Even so, the catalytic activity of HEA-400-10000 is still better than that of Pt/C. Besides, the high stability of HEA-400-5000 is verified through the galvanostatic measurement during an 80-h test (see Figure S26). The activation effect of HEA-400 is further demonstrated by the electrochemical double-layer capacitance (C_dl), as shown in Fig. 4B. Consistent with the tendency of HER activity, the C_dl of HEA-400 increases continuously to reach the maximum value of 111.7 mF cm^− 2 after 5000 CV cycles (detailed CV data are provided in Figure S27). This indicates the greatly increased electrochemical surface area (ECSA) brought from the dual gradient formed in HEA. In order to highlight the advantages of HEA catalysts, the HER performances of a ternary PtFeCo alloy and a quaternary PtFeCoNi alloy are compared (see Figures S28-30). As shown in Figure S30, the PtFeCoNiCu catalyst presents better HER performance than those of PtFeCo and PtFeCoNi, demonstrating the benefits of the dual gradient catalytic system in HEA.

The electrochemical activation effect is also observed in HEA-500, as shown in Figure S31. A comparison of HER activity among the activated HEA-400 (HEA-400-5000), activated HEA-500 (HEA-500-2000), and Pt/C is shown in Fig. 4C, where the HEA-400 has the smallest overpotential of 10.8 mV at -10 mA cm^− 2. The corresponding Tafel plots (see the inset in Fig. 4C) indicate that the activated HEA-400 presents the smallest Tafel slope of 28.1 mV dec^− 1, denoting the best HER kinetics, which is further verified by the largest exchange current density (j₀ = 8.99 mA cm^− 2).^31–32 Additionally, when normalized to ECSA (see Figure S32), HEA-400 presents 4.6 times higher specific electrochemical activity (-1.39 mA \({\text{m}}_{\text{ECSA}}^{\text{-2}}\)) than that of Pt/C (-0.30 mA \({\text{m}}_{\text{ECSA}}^{\text{-2}}\), see Fig. 4D) at an overpotential of 20 mV, manifesting the greatly enhanced intrinsic activity brought from the dual gradient structures. Meanwhile, the turnover frequency of HEA-400 (4.36 × 10^− 2 s^− 1) at this potential is also much higher than that of Pt/C (0.98 × 10^− 2 s^− 1), further confirming the excellent intrinsic activity (see Fig. 4E). More detailed electrochemical data are provided in Figures S33-35. Compared with other reported catalysts for HER (see Fig. 4E and Table S2), the designed dual gradient HEA shows the smallest overpotential of 10.8 mV at -10 mA cm^− 2, indicating a breakthrough in the catalytic performance for HER.

Extension to C, O, and N*

The anomalous Sabatier principle is also extended to other adsorbates (C*, O*, and N*) on the designed HEA catalysts. Based on the BEP relation, the strong adsorption leads to a large diffusion barrier for adsorbates. This means that C*, O*, and N* spillover should be difficult due to their stronger adsorptions than that of H*. Herein, the adsorption energies of C*, O*, and N* on the designed 5.9%-HEA were calculated, as shown in Figures S36-38. Their adsorption energy values also roughly follow the Gaussian distribution with µ and σ values of 1.662 and 0.125 eV, 2.072 and 0.135 eV, 2.103 and 0.104 eV, for C*, O*, and N*, respectively. Similar to the adsorption of H*, the designed 5.9%-HEA still has two active centers with strong and weak adsorptions of these adsorbates. The C*, O*, and N* spillovers between the two active centers are shown in Figures S39-41. The diffusion barrier values of their RDS are 0.772, 0.463, and 0.801 eV for C*, O*, and N*, respectively. Although these diffusion barrier values are larger than that of H*, they are still relatively small values, being sufficient for the spillovers of C*, O*, and N* to occur at room temperature.²⁶ Therefore, the proposed anomalous Sabatier principle in this work can be extended to other catalytic reactions associated with these adsorbates, such as CO₂RR, ORR/OER, NRR, etc.

In summary, we found the anomalous Sabatier principle on HEA catalysts for HER. The new descriptors of µ and σ are proposed to indicate the catalytic activity of HEA catalysts for HER based on the Gaussian distribution [X ~ N(µ, σ²)] of ΔG_H*. Mathematically, a larger σ value results with µ = 0 eV results in a higher catalytic activity for HER. Physically, the HEA catalysts with the wider adsorption energy range around 0 eV promoted the adsorption of H* and the formation of H₂ simultaneously. According to the new theoretical insights, a PtFeCoNiCu catalyst with dual-gradient (electronic and composition gradients) is precisely synthesized. The designed HEA catalyst has an excellent catalytic performance for HER with an ovepotential of 10.8 mV at -10 mA cm^− 2 and 4.6 times higher intrinsic activity than that of Pt/C. The anomalous Sabatier principle proved to be applicable to other adsorbents as well. These findings could accelerate the development of HEA catalysts and open avenues to achieve a breakthrough in catalytic performance.

Chemicals

Iron(III) chloride (FeCl₃), Cobalt(II) chloride hexahydrate (CoCl₂·6H₂O), Nickel(II) chloride hexahydrate (NiCl₂·6H₂O), Copper(II) chloride dihydrate (CuCl₂·2H₂O), and Chloroplatinic acid (H₂PtCl₆·6H₂O) were purchased from Sigma Aldrich. All chemicals are of analytical purity and used without further purification.

Synthesis of PtFeCoNiCu HEA catalyst

0.5 mM of FeCl₃, CoCl₂·6H₂O, NiCl₂·6H₂O, CuCl₂·2H₂O, and H₂PtCl₆·6H₂O were added into 40 mL ultrapure water to form a uniform mixture. The mixture was stirred constantly in an oil bath at 80°C until all water evaporated, forming a dark yellow slurry. The HEA-300, HEA-400, and HEA-500 were obtained through annealing the slurry under 5% H₂/Ar atmosphere for 2 h at 300°C, 400°C, and 500°C, respectively.

Synthesis of PtFeCoNi and PtFeCo catalysts

The synthesis method of PtFeCoNi is the same with that of HEA-400, except that the precursor of CuCl₂·2H₂O was not added. The synthesis method of PtFeCo is the same with that of HEA-400, except that the precursors of CuCl₂·2H₂O and NiCl₂·6H₂O were not added.

Material Characterization

For the structural characterization, X-ray diffraction (XRD) was performed on a D/max2500pc diffractometer with a Cu Kα radiation. X-ray photoelectron spectroscopy (XPS) detection was through an ESCALAB 250Xi spectrometer with a monochromatic Al-K source. The morphology characterization was conducted using a JEM-2100F transmission electron microscope (TEM) for TEM images, high-resolution TEM (HRTEM) images and selected area electron diffraction (SAED) patterns. The high angle annular dark field (HAADF) images were obtained through a double-corrected FEI Titan Themis 300 electron microscope. The component analysis was confirmed using an inductively coupled plasma optical emission spectroscopy (ICP-OES).

Electrochemical Measurements

All electrochemical measurements were performed on an Ivium-n-Stat electrochemical workstation under a standard three-electrode system. A graphite electrode, a saturated calomel electrode (SCE) and a rotating disk electrode (RDE) covered with catalyst films were used as the counter electrode, reference electrode, and working electrode, respectively. 3 mg of each catalyst powders distributed into 0.5 mL water-isopropanol solution (4:1, v/v) were used as the catalyst ink. 30 µL of the catalyst ink was taken and dried on the RDE surface for measurement each time. 15 µL Nafion-isopropanol solution (1:19, v/v) was taken and covered on the dried catalyst films as a binder.

The HER performance measurements were conducted in N₂-saturated 0.5 M H₂SO₄. For activating HEA catalysts, cyclic voltammetry (CV) tests were performed at a potential range of 100 ~ 530 mV (vs. reversible hydrogen electrode, RHE) at a scan rate of 400 mV s^-1. Linear sweep voltammetry (LSV) tests were conducted at a scan rate of 5 mV s^-1 with a rotation rate of 2025 rpm. For measuring the double-layer capacitance, CV tests were performed at a potential range of 10 to 20 mV (vs. RHE) at scan rates of 20, 40, 60, 80, and 100 mV s^-1, respectively. Galvanostatic tests were performed at an applied current density of -10 mA cm^-2 for 80 h. Electrochemical impedance measurements were performed at 10 mV (vs. RHE) from 100 kHz to 0.1 Hz. All the measurements were performed at room temperature. All the potentials converted to the RHE were through E_RHE = E_SCE + 0.059 pH + 0.267 V, where E_RHE and E_SCE denote the reversible hydrogen evolution potential and the measured potential, respectively.

Density functional theory calculation

All calculations were performed using the Vienna ab initio simulation package (VASP) based on spin-polarized density function theory (DFT).³³ The projector-augmented wave pseudopotential was applied to treat the core electrons.³⁴ The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof functional (PBE) was adopted in the DFT calculations.³⁵ The kinetic energy cutoff for the wave-function calculations was set to 550 eV. The Fermi smearing function was applied with a smearing width of 0.1 eV. The 4 × 4 supercell with five layers was considered for all systems. The Monkhorst-Pack grid of k-points was 2 × 2 × 1, and a vacuum gap of more than 12 Å was used to avoid interactions between the system and its mirror images. The geometric relaxation was stopped when the incremental changes in total energy and forces were smaller than 1 × 10^− 5 eV and 0.05 eV/Å, respectively. The van der Waals interaction was considered through the DFT-D3 method proposed by Grimme.³⁶ All the transition states were obtained using the climbing image nudged elastic band (CI-NEB) method with a convergence force smaller than 0.05 eV/Å.³⁷

The adsorption energy (ΔE_X*) of adsorbates (X = H, C, O, N) was calculated by the following equation:

ΔE_X* = E_X* – E_cat – E_X (1)

where E_X*, E_cat, and E_X represent the total energy of the catalyst with the adsorbate, isolated catalyst, and the corresponding adsorbate, respectively. Note that the energies of H, C, O, and N refer to the energies of H₂, graphene, H₂O, and NH₃, respectively. The adsorption energy was corrected by considering the zero-point energy and entropy, as shown below:

ΔG_X* = ΔE_X* + ΔZPE – TΔS (2)

where ΔG_X*, ΔZPE, and TΔS denote the adsorption free energy, zero-point energy change, and entropy change, respectively.

Acknowledgments

We wish to thank the financial supports from the National Natural Science Foundation of China (No. 52130101), Science and Technology Development Program of Jilin Province (No. 20230402058GH), Interdisciplinary Integration and Innovation Project of JLU (No. JLUXKJC2021ZY01), the Fundamental Research Funds for the Central Universities, the Nature Science and Engineer Research Council of Canada (NSERC), Hart Professorship and the University of Toronto. We thank Prof. Edward Sargent for the helpful discussions. We also acknowledge Digital Research Alliance of Canada for providing computing resources at the SciNet, CalculQuebec, and Westgrid consortia.

Author Contributions

C. C. Y., C. V. S., and Q. J. conceived the project and oversaw all the research phases. Z. W. C. and J. L. designed the project. Q. J., Z. W. C., and P. O. conceived the theoretical model. C. V. S. and Z. W. C. conducted the theoretical calculations. C. C. Y. and J. L. conducted the experiments. Data collection and analysis were conducted by Z. W. C., J. L., and P. O. All authors discussed the results and commented on the manuscript.

Competing Interests

The authors declare no competing interests.

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Anomalous Sabatier principle on high entropy alloy catalysts

Status:

Journal Publication

Version 1

Abstract

Figures

Introduction

Results And Discussion

Dual gradient PtFeCoNiCu HEA model

Gaussian distribution of ΔG_H* on PtFeCoNiCu HEA

Reaction mechanism of HER on PtFeCoNiCu HEA

Synthesis and characterization of PtFeCoNiCu HEA

Catalytic performance of PtFeCoNiCu HEA

Extension to C, O, and N*

Conclusion

Experimental Section

Chemicals

Synthesis of PtFeCoNiCu HEA catalyst

Synthesis of PtFeCoNi and PtFeCo catalysts

Material Characterization

Electrochemical Measurements

Density functional theory calculation

Declarations

References

Additional Declarations

Supplementary Files

Status:

Journal Publication

Version 1

Anomalous Sabatier principle on high entropy alloy catalysts

Status:

Journal Publication

Version 1

Abstract

Figures

Introduction

Results And Discussion

Dual gradient PtFeCoNiCu HEA model

Gaussian distribution of ΔGH* on PtFeCoNiCu HEA

Reaction mechanism of HER on PtFeCoNiCu HEA

Synthesis and characterization of PtFeCoNiCu HEA

Catalytic performance of PtFeCoNiCu HEA

Extension to C*, O*, and N*

Conclusion

Experimental Section

Chemicals

Synthesis of PtFeCoNiCu HEA catalyst

Synthesis of PtFeCoNi and PtFeCo catalysts

Material Characterization

Electrochemical Measurements

Density functional theory calculation

Declarations

References

Additional Declarations

Supplementary Files

Status:

Journal Publication

Version 1

Gaussian distribution of ΔG_H* on PtFeCoNiCu HEA

Extension to C, O, and N*