Anomalous Sabatier principle on high entropy alloy catalysts

Anomalous Sabatier principle on high entropy alloy catalysts | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Anomalous Sabatier principle on high entropy alloy catalysts Chandra Veer Singh, Zhi-Wen Chen, Jian Li, Pengfei Ou, Jianan Erick Huang, and 6 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2756931/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 08 Jan, 2024 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract 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 (Δ G H* ), where the active sites with strong adsorption adsorb hydrogen (H*) and other sites with weak adsorption release H* to produce H 2 , was against the “just right” (Δ G H* = 0 eV) in the Sabatier principle of hydrogen evolution reaction (HER). The Gaussian distribution [ X ~ N (µ, σ 2 )] of Δ G 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 Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction 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 CO 2 reduction reaction (CO 2 RR), 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* (Δ G H* ) on HEA catalysts follows a Gaussian distribution [ X ~ N (µ, σ 2 ), 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 (Δ G H* µ + σ ) are used for H 2 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. Results And Discussion 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. 1 A. 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. 1 B. 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* → H 2 ) or Heyrovsky reaction (H* + H + + e − → H 2 ). 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. 1 C 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 Δ G H* is calculated on the designed HEA (111) with different strains (see Fig. 1 D). The Δ G H* distribution roughly conforms to the Gaussian distribution [ X ~ N (µ, σ 2 )]. Herein, µ and σ 2 determine the location and the variance of Δ G H* , respectively. As shown in Fig. 1 D, 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 Δ G 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, Δ G 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 Δ G H* values follow a Gaussian distribution, rather than a definite value. Hence, the Sabatier principle and the criterion of Δ G H* = 0 eV are no longer valid for HEA catalysts. In this work, we propose an anomalous Sabatier principle, where the Gaussian distribution of Δ G 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 Δ G 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 Δ G H* (µ-σ < Δ G 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 Δ G H* with the preferable µ = -0.034 eV and σ = 0.041 eV (see Figure S5 ). The Δ G H* values on the possible adsorption sites (see Figure S6 ) of 5.9%-HEA are shown in Fig. 2 A, where the green area denotes the DR. The active center for the Volmer reaction has the smallest Δ G H* of -0.099 eV and the active center for the Tafel or Heyrovsky reaction has the largest Δ G 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. 2 B, C. For the V-H mechanism on Pt (111), the potential limiting step (PLS) is the Heyrovsky step with Δ G 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 Δ G Vol−1 = -0.099 eV and Δ G Hey = -0.075 eV, respectively. The adsorbed H* diffuses from Site A to Site B through the DR1 (see Fig. 2 D) 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 − 1 s − 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 (Δ G Vol−1 = -0.375 eV, Δ G Vol−2 = -0.201 eV) on Pt (111). They are also exothermic reactions (Δ G Vol−1 = -0.099 eV, Δ G 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. 2 E. 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 3 A 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 Δ G 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. 3 B, both Pt 0 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 Pt 0 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. 3 C 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 S16 B). 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. 3 D). The HAADF-EDS elemental maps demonstrate the homogeneously distributed elements in the nanoparticle (see Fig. 3 E). 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 H 2 SO 4 using a typical three-electrode configuration. Figure 4 A 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. 4 B. 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. 4 C, 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. 4 C) 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 ( j 0 = 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. 4 D) 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. 4 E). More detailed electrochemical data are provided in Figures S33-35 . Compared with other reported catalysts for HER (see Fig. 4 E 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 CO 2 RR, ORR/OER, NRR, etc. Conclusion 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, σ 2 )] of Δ G 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 H 2 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. Experimental Section Chemicals Iron(III) chloride (FeCl 3 ), Cobalt(II) chloride hexahydrate (CoCl 2 ·6H 2 O), Nickel(II) chloride hexahydrate (NiCl 2 ·6H 2 O), Copper(II) chloride dihydrate (CuCl 2 ·2H 2 O), and Chloroplatinic acid (H 2 PtCl 6 ·6H 2 O) 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 FeCl 3 , CoCl 2 ·6H 2 O, NiCl 2 ·6H 2 O, CuCl 2 ·2H 2 O, and H 2 PtCl 6 ·6H 2 O 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% H 2 /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 CuCl 2 ·2H 2 O was not added. The synthesis method of PtFeCo is the same with that of HEA-400, except that the precursors of CuCl 2 ·2H 2 O and NiCl 2 ·6H 2 O 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 N 2 -saturated 0.5 M H 2 SO 4 . 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 (Δ E X* ) of adsorbates (X = H, C, O, N) was calculated by the following equation: Δ E 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 H 2 , graphene, H 2 O, and NH 3 , respectively. The adsorption energy was corrected by considering the zero-point energy and entropy, as shown below: Δ G X* = Δ E X* + Δ ZPE – T Δ S (2) where Δ G X* , Δ ZPE , and T Δ S denote the adsorption free energy, zero-point energy change, and entropy change, respectively. Declarations 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. 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Commun. 12, 6261. Shi, Y. and Zhang, B. (2016). Recent advances in transition metal phosphide nanomaterials: synthesis and applications in hydrogen evolution reaction. Chem. Soc. Rev. 45, 1529-1541. Huang, Z.P., Chen, Z.Z., Chen, Z.B., Lv, C.C., Humphrey, M.G. and Zhang, C. (2014). Cobalt phosphide nanorods as an efficient electrocatalyst for the hydrogen evolution reaction. Nano Energy 9, 373-382. Kresse, G. and Furthmuller, J. (1996). Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169. Blochl, P.E. (1994). Projector augmented-wave method. Phys. Rev. B 50, 17953-17979. Perdew, J.P., Burke, K. and Ernzerhof, M. (1996). Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865. Grimme, S., Antony, J., Ehrlich, S. and Krieg, H. (2010). A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104. Henkelman, G., Uberuaga, B.P. and Jonsson, H. (2000). A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys. 113, 9901-9904. Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryMaterials.docx Supplementary Materials Cite Share Download PDF Status: Published Journal Publication published 08 Jan, 2024 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2756931","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":189665349,"identity":"26f704f3-aff4-419b-9152-ed3e942c4dad","order_by":0,"name":"Chandra Veer 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University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Qing","middleName":"","lastName":"Jiang","suffix":""}],"badges":[],"createdAt":"2023-03-30 13:55:49","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2756931/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2756931/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-023-44261-4","type":"published","date":"2024-01-08T05:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":35465332,"identity":"3e586500-383a-48ee-9944-9aab73210f87","added_by":"auto","created_at":"2023-04-07 20:19:21","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1553922,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDFT calculation of PtFeCoNiCu HEA model.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e(A) The HEA (111) structure with Pt concentration gradient. (B) The electron localization function (ELF) contour for HEA (111) plane. The red areas represent rich electron distributions. (C) Partial density of states (PDOS) of \u003cem\u003ed\u003c/em\u003e-band on surface Pt atoms in HEAs with different strains. The Fermi level is set to be 0 and the vertical dashed line is the \u003cem\u003ed\u003c/em\u003e-band center (\u003cem\u003eε\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e). (D) Gaussian distribution of adsorption free energy of H* (Δ\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e) with the corresponding μ and σ on HEAs with different strains.\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2756931/v1/148d9d6821049b1c6f5f6807.jpeg"},{"id":35465898,"identity":"d43c1c49-22ee-4d5c-b1a4-30b737f8aa80","added_by":"auto","created_at":"2023-04-07 20:27:21","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1501925,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eReaction mechanism studies by DFT calculations.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e(A) The distribution of Δ\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e on HEA with 5.9% compressive strain (5.9%-HEA), including different adsorption sites (hcp hollow site, fcc hollow site, and bridge site). The red dashed circles indicate the active centers for Volmer and Heyrovsky (or Tafel) steps, respectively. The green area represents the diffusion region (DR) for the adsorbed H*. (B) Volmer-Heyrovsky mechanism of HER on 5.9%-HEA (111) and Pt (111). (C) Volmer-Tafel mechanism of HER on 5.9%-HEA (111) and Pt (111). (D) The H* spillover on DR1 for 5.9%-HEA (111). (E) The H* spillover on DR2 for 5.9%-HEA (111).\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2756931/v1/fe6ab79ea663caec8594e9b4.jpeg"},{"id":35465335,"identity":"9ff8bd8a-b65b-4ea9-81f2-7d6f34be7ac4","added_by":"auto","created_at":"2023-04-07 20:19:22","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":5308439,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eStructural characterization of HEA catalysts.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e(A) XRD patterns of HEA-300, HEA-400, and HEA-500. (B) Pt 4f high-resolution XPS spectra of Pt/C, HEA-400, and HEA-400-5000. (C) HAADF-STEM image of HEA-400-5000. (D) Intensity line profile from the surface to the core in HEA-400-5000 as framed in (C). (E) HAADF-EDS elemental maps of HEA-400-5000.\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2756931/v1/d05102cde276752488aba231.jpeg"},{"id":35465334,"identity":"21a9b21b-0238-4549-a61e-012e2c81a7c4","added_by":"auto","created_at":"2023-04-07 20:19:22","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":993711,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eElectrochemical performance.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e(A) Polarization curves of HEA-400 before and after cyclic voltammetry (CV) activation. (B) Plots of capacitive currents with various scan rates for HEA-400 before and after CV activation. (C) Polarization curves of activated HEA-400, activated HEA-500, and Pt/C. The corresponding Tafel plots and exchange current density (\u003cem\u003ej\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e) are described in the inset. (D) Specific activities of activated HEA-400, activated HEA-500, and Pt/C at \u003cem\u003eη\u003c/em\u003e = 20 mV. (E) TOFs of activated HEA-400, activated HEA-500, and Pt/C at \u003cem\u003eη\u003c/em\u003e = 20 mV. (F) Comparison of HER performance for HEA-400 with other reported catalysts in 0.5 M H\u003csub\u003e2\u003c/sub\u003eSO\u003csub\u003e4\u003c/sub\u003e (see Table S2 for more details).\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2756931/v1/98a8f0c84e05b5abe4be4174.jpeg"},{"id":49355801,"identity":"6831e01a-0fee-44c6-b713-e0db78639b4d","added_by":"auto","created_at":"2024-01-09 08:12:30","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1217007,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2756931/v1/f493dae2-38c8-4bc9-b76d-82d294dfb0ea.pdf"},{"id":35465336,"identity":"9dda1c1f-3224-4976-ba27-d0acaf0d24e7","added_by":"auto","created_at":"2023-04-07 20:19:22","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":15824749,"visible":true,"origin":"","legend":"\u003cp\u003eSupplementary Materials\u003c/p\u003e","description":"","filename":"SupplementaryMaterials.docx","url":"https://assets-eu.researchsquare.com/files/rs-2756931/v1/53b765abc45e1b47e577b176.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Anomalous Sabatier principle on high entropy alloy catalysts","fulltext":[{"header":"Introduction","content":"\u003cp\u003eIn the Sabatier principle, the adsorbate should bind neither too weakly (lest reactants fail to activate) nor too strongly (lest products fail to dissociate).\u003csup\u003e1\u0026ndash;2\u003c/sup\u003e 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.\u003csup\u003e3\u0026ndash;8\u003c/sup\u003e The resultant volcano plots have been used to guide catalyst design for the CO\u003csub\u003e2\u003c/sub\u003e reduction reaction (CO\u003csub\u003e2\u003c/sub\u003eRR),\u003csup\u003e9\u003c/sup\u003e nitrogen reduction reaction (NRR),\u003csup\u003e10\u003c/sup\u003e hydrogen evolution reaction (HER),\u003csup\u003e11\u003c/sup\u003e and oxygen reduction/evolution reaction (ORR/OER).\u003csup\u003e12\u0026ndash;13\u003c/sup\u003e \u0026ldquo;Just right\u0026rdquo; adsorption energy is the pursuit of all chemical reactions. However, although we achieve the \u0026ldquo;just right\u0026rdquo; 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, N\u0026oslash;rskov \u003cem\u003eet al.\u003c/em\u003e 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.\u003csup\u003e14\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eCircumventing the volcano relationship is plausible to achieve a breakthrough or over the volcano in catalytic activity,\u003csup\u003e15\u003c/sup\u003e and numerous efforts have been focused on this issue.\u003csup\u003e8, 16\u0026ndash;17\u003c/sup\u003e For example, Chen \u003cem\u003eet al.\u003c/em\u003e demonstrated that the volcano relationship can be broken by building an interface between transition metals and LiH.\u003csup\u003e18\u003c/sup\u003e Unfortunately, the relatively few active sites have impeded the wide application of interface catalysis.\u003csup\u003e19\u003c/sup\u003e Another strategy of strain effect was proposed by Khorshidi \u003cem\u003eet al.\u003c/em\u003e, the surface strain has to occur either externally by applying mechanical loading or internally by creating complex core-shell structures or interfaces.\u003csup\u003e8\u003c/sup\u003e High entropy alloys (HEAs) with huge composition space have complex surface active sites, resulting in spatially varying adsorption of intermediates.\u003csup\u003e20\u003c/sup\u003e 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.\u003c/p\u003e \u003cp\u003eIn 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* (Δ\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e) on HEA catalysts follows a Gaussian distribution [\u003cem\u003eX\u003c/em\u003e\u0026thinsp;~\u0026thinsp;\u003cem\u003eN\u003c/em\u003e(\u0026micro;, σ\u003csup\u003e2\u003c/sup\u003e), \u003cem\u003e\u0026micro;\u003c/em\u003e: expectation; \u003cem\u003eσ\u003c/em\u003e: 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 (Δ\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;\u003cem\u003e\u0026micro;\u003c/em\u003e - \u003cem\u003eσ\u003c/em\u003e) are used for H* adsorption, while some sites with weak adsorption (Δ\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;\u003cem\u003e\u0026micro;\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eσ\u003c/em\u003e) are used for H\u003csub\u003e2\u003c/sub\u003e formation. It means that the catalytic activity for HER will be better if the \u003cem\u003e\u0026micro;\u003c/em\u003e is closer to 0 eV and the \u003cem\u003eσ\u003c/em\u003e is larger, which is defined as an anomalous Sabatier principle. The \u003cem\u003e\u0026micro;\u003c/em\u003e and \u003cem\u003eσ\u003c/em\u003e 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\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e 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.\u003c/p\u003e"},{"header":"Results And Discussion","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n\u003ch2\u003eDual gradient PtFeCoNiCu HEA model\u003c/h2\u003e\n\u003cp\u003eA 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;\u003csup\u003e14\u003c/sup\u003e (2) the smaller atomic radii of Fe (1.56 \u0026Aring;), Co (1.52 \u0026Aring;), Ni (1.49 \u0026Aring;), and Cu (1.45 \u0026Aring;) than that of Pt (1.77 \u0026Aring;) 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;\u003csup\u003e21\u0026ndash;22\u003c/sup\u003e and (3) the cost of catalysts could be greatly reduced by using non-noble metals.\u003csup\u003e23\u003c/sup\u003e\u003c/p\u003e\n\u003cp\u003eTaking 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.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eA. 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.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eB. 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\u003csup\u003e+\u003c/sup\u003e + e\u003csup\u003e\u0026minus;\u003c/sup\u003e \u0026rarr; H*) while the ones with weak H* adsorption are active centers for the Tafel (H* + H* \u0026rarr; H\u003csub\u003e2\u003c/sub\u003e) or Heyrovsky reaction (H* + H\u003csup\u003e+\u003c/sup\u003e + e\u003csup\u003e\u0026minus;\u003c/sup\u003e \u0026rarr; H\u003csub\u003e2\u003c/sub\u003e).\u003c/p\u003e\n\u003cp\u003eFe, 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.\u003csup\u003e21\u003c/sup\u003e Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eC shows that the energy level of \u003cem\u003ed\u003c/em\u003e 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 \u003cem\u003ed\u003c/em\u003e-band center (\u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e) values, where a more negative \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e value indicates a weaker adsorption ability.\u003csup\u003e24\u003c/sup\u003e With the increase of compressive strain, the \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e values change from \u0026minus;\u0026thinsp;1.66 eV (HEA without strain) to -1.72, -1.75, -1.89, and \u0026minus;\u0026thinsp;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-\u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e-activity relation allows for designing HEA catalysts with optimal adsorption energy via composition regulation.\u003csup\u003e21\u003c/sup\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n\u003ch2\u003eGaussian distribution of \u0026Delta;G\u003csub\u003eH*\u003c/sub\u003e on PtFeCoNiCu HEA\u003c/h2\u003e\n\u003cp\u003e\u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e is calculated on the designed HEA (111) with different strains (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eD). The \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e distribution roughly conforms to the Gaussian distribution [\u003cem\u003eX\u003c/em\u003e\u0026thinsp;~\u0026thinsp;\u003cem\u003eN\u003c/em\u003e(\u0026micro;, \u0026sigma;\u003csup\u003e2\u003c/sup\u003e)]. Herein, \u0026micro; and \u0026sigma;\u003csup\u003e2\u003c/sup\u003e determine the location and the variance of \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e, respectively. As shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eD, the \u0026micro; value increases with increasing compressive strain. This is consistent with the \u003cem\u003ed\u003c/em\u003e-band center theory, where a larger compressive strain brings more negative \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e, resulting in weaker adsorption.\u003csup\u003e24\u0026ndash;25\u003c/sup\u003e The corresponding structure (strain)-property (\u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e)-performance (\u003cem\u003e\u0026micro;\u003c/em\u003e) relation is shown in \u003cstrong\u003eFigure \u003cspan class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/strong\u003e. Note that the compressive strain shows little influence on the \u003cem\u003e\u0026sigma;\u003c/em\u003e value. A larger \u003cem\u003e\u0026sigma;\u003c/em\u003e 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 (\u003cem\u003e\u0026micro;\u003c/em\u003e and \u003cem\u003e\u0026sigma;\u003c/em\u003e) in the Gaussian distribution of \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e could be regulated by the type and number of alloying elements in HEA, which bring various strains and surface electronic gradients.\u003c/p\u003e\n\u003cp\u003eAs is well known, \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e = 0 eV denotes the optimal catalytic performance of catalysts for HER based on the Sabatier principle.\u003csup\u003e11\u003c/sup\u003e However, the active sites of HEA are diverse and their \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e values follow a Gaussian distribution, rather than a definite value. Hence, the Sabatier principle and the criterion of \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e = 0 eV are no longer valid for HEA catalysts. In this work, we propose an anomalous Sabatier principle, where the Gaussian distribution of \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e with a \u003cem\u003e\u0026micro;\u003c/em\u003e value closer to 0 eV and a larger \u003cem\u003e\u0026sigma;\u003c/em\u003e value on HEA catalysts could be used as the descriptor of the higher catalytic activity for HER. Theoretically, the sites with \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;\u0026micro;-\u0026sigma; and \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;\u0026micro;\u0026thinsp;+\u0026thinsp;\u0026sigma; serve as the active centers for Volmer and Tafel (or Heyrovsky) reactions (see \u003cstrong\u003eFigure S2\u003c/strong\u003e), respectively. The larger \u0026sigma; 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 \u003cstrong\u003eFigure S3\u003c/strong\u003e). This means that a larger \u0026sigma; 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 \u003cem\u003e\u0026micro;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0 eV (see \u003cstrong\u003eFigure S4\u003c/strong\u003e). Meanwhile, other sites with moderate \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e (\u0026micro;-\u0026sigma;\u0026thinsp;\u0026lt;\u0026thinsp;\u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;\u0026micro;\u0026thinsp;+\u0026thinsp;\u0026sigma;) 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.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n\u003ch2\u003eReaction mechanism of HER on PtFeCoNiCu HEA\u003c/h2\u003e\n\u003cp\u003eThe 5.9%-HEA system was used as an example for studying the H* spillover based on the new descriptor of Gaussian distribution of \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e with the preferable \u003cem\u003e\u0026micro;\u003c/em\u003e = -0.034 eV and \u003cem\u003e\u0026sigma;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.041 eV (see \u003cstrong\u003eFigure S5\u003c/strong\u003e). The \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e values on the possible adsorption sites (see \u003cstrong\u003eFigure S6\u003c/strong\u003e) of 5.9%-HEA are shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eA, where the green area denotes the DR. The active center for the Volmer reaction has the smallest \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e of -0.099 eV and the active center for the Tafel or Heyrovsky reaction has the largest \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e of 0.075 eV.\u003c/p\u003e\n\u003cp\u003eBoth 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.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eB, C. For the V-H mechanism on Pt (111), the potential limiting step (PLS) is the Heyrovsky step with \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eHey\u003c/sub\u003e = 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 \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eVol\u0026minus;1\u003c/sub\u003e = -0.099 eV and \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eHey\u003c/sub\u003e = -0.075 eV, respectively. The adsorbed H* diffuses from Site A to Site B through the DR1 (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eD) 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\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003es\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e at room temperature,\u003csup\u003e26\u003c/sup\u003e indicating the exceedingly fast diffusion of H*.\u003c/p\u003e\n\u003cp\u003eFor the V-T mechanism, the first two Volmer steps are exothermic reactions (\u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eVol\u0026minus;1\u003c/sub\u003e = -0.375 eV, \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eVol\u0026minus;2\u003c/sub\u003e = -0.201 eV) on Pt (111). They are also exothermic reactions (\u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eVol\u0026minus;1\u003c/sub\u003e = -0.099 eV, \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eVol\u0026minus;2\u003c/sub\u003e = -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 \u003cstrong\u003eFigure S7\u003c/strong\u003e), 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.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eE. 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\u0026rsquo;t be the PLS or RDS during HER on 5.9%-HEA (111).\u003c/p\u003e\n\u003cp\u003eMoreover, the reaction processes of HER on 5.9%-HEA (111) without H* spillover are also considered, as shown in \u003cstrong\u003eFigure S8\u003c/strong\u003e. 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.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n\u003ch2\u003eSynthesis and characterization of PtFeCoNiCu HEA\u003c/h2\u003e\n\u003cp\u003eAs a proof-of-concept, the PtFeCoNiCu HEA catalysts were synthesized through a solvothermal reaction followed by thermal annealing, as illustrated in \u003cstrong\u003eFigure S9\u003c/strong\u003e. Based on different annealing temperatures (300, 400, and 500\u0026deg;C), the synthesized HEA samples are named as HEA-300, HEA-400, and HEA-500, respectively. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eA 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\u0026deg; and 16.2\u0026deg; in HEA-300 can be assigned to the transition metal chloride of the precursor, suggesting that 300\u0026deg;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\u0026deg;, 2.3\u0026deg;, and 2.3\u0026deg;, respectively, implying the existence of compressive strain in the HEAs caused by alloying with Fe, Co, Ni, and Cu.\u003csup\u003e27\u0026ndash;28\u003c/sup\u003e 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 \u003cem\u003e\u0026micro;\u003c/em\u003e value in the Gaussian distribution of \u0026Delta;\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e. Based on the DFT results, the PtFeCoNiCu with a larger compressive strain should have a \u003cem\u003e\u0026micro;\u003c/em\u003e value closer to 0 eV, indicating a higher catalytic activity, which is consistent with our experimental results, as shown in \u003cstrong\u003eFigure S10\u003c/strong\u003e.\u003c/p\u003e\n\u003cp\u003eX-ray photoelectron spectroscopy (XPS) analysis (see \u003cstrong\u003eFigures S11-14\u003c/strong\u003e) was performed to explore the charge redistribution in HEA catalysts. As shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eB, both Pt\u003csup\u003e0\u003c/sup\u003e 4f\u003csub\u003e7/2\u003c/sub\u003e and 4f\u003csub\u003e5/2\u003c/sub\u003e 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).\u003csup\u003e28\u0026ndash;30\u003c/sup\u003e After 5000 cycles of cyclic voltammetry (CV) activating, both the Pt\u003csup\u003e0\u003c/sup\u003e 4f\u003csub\u003e7/2\u003c/sub\u003e and 4f\u003csub\u003e5/2\u003c/sub\u003e 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.\u003c/p\u003e\n\u003cp\u003eThe size of the synthesized HEA nanoparticles increases with the annealing temperature, as shown in \u003cstrong\u003eFigure S15.\u003c/strong\u003e According to the high-resolution TEM images shown in \u003cstrong\u003eFigure S16\u003c/strong\u003e, 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 \u003cstrong\u003eFigure S17\u003c/strong\u003e), 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.\u003c/p\u003e\n\u003cp\u003eTaking 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 \u003cstrong\u003eTable \u003cspan class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/strong\u003e). 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 \u003cstrong\u003eFigure S18\u003c/strong\u003e). 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 \u003cstrong\u003eFigure S19\u003c/strong\u003e).\u003c/p\u003e\n\u003cp\u003eA 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.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eC and \u003cstrong\u003eFigure S20\u003c/strong\u003e). 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 \u003cstrong\u003eFigure S16\u003c/strong\u003eB). Namely, the etching effect only appears in the outermost layers (15\u0026thinsp;~\u0026thinsp;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.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eD). The HAADF-EDS elemental maps demonstrate the homogeneously distributed elements in the nanoparticle (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eE). Moreover, the Pt concentration gradient is further confirmed in the near-surface elemental maps (\u003cstrong\u003eFigures S21-23\u003c/strong\u003e), 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 \u003cstrong\u003eFigure S24\u003c/strong\u003e) 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.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n\u003ch2\u003eCatalytic performance of PtFeCoNiCu HEA\u003c/h2\u003e\n\u003cp\u003eThe HER performance of the HEA catalysts was measured in 0.5 M H\u003csub\u003e2\u003c/sub\u003eSO\u003csub\u003e4\u003c/sub\u003e using a typical three-electrode configuration. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eA 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\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e 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\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e. 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\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e) 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 \u0026sigma; value. This is the reason that HEA-400-10000 shows an attenuation performance compared with that of HEA-400-5000 (see \u003cstrong\u003eFigure S25\u003c/strong\u003e). 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 \u003cstrong\u003eFigure S26\u003c/strong\u003e). The activation effect of HEA-400 is further demonstrated by the electrochemical double-layer capacitance (C\u003csub\u003edl\u003c/sub\u003e), as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eB. Consistent with the tendency of HER activity, the C\u003csub\u003edl\u003c/sub\u003e of HEA-400 increases continuously to reach the maximum value of 111.7 mF cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e after 5000 CV cycles (detailed CV data are provided in \u003cstrong\u003eFigure S27\u003c/strong\u003e). 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 \u003cstrong\u003eFigures S28-30\u003c/strong\u003e). 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.\u003c/p\u003e\n\u003cp\u003eThe electrochemical activation effect is also observed in HEA-500, as shown in \u003cstrong\u003eFigure S31\u003c/strong\u003e. 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.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eC, where the HEA-400 has the smallest overpotential of 10.8 mV at -10 mA cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e. The corresponding Tafel plots (see the inset in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eC) indicate that the activated HEA-400 presents the smallest Tafel slope of 28.1 mV dec\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, denoting the best HER kinetics, which is further verified by the largest exchange current density (\u003cem\u003ej\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;8.99 mA cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e).\u003csup\u003e31\u0026ndash;32\u003c/sup\u003e Additionally, when normalized to ECSA (see \u003cstrong\u003eFigure S32\u003c/strong\u003e), HEA-400 presents 4.6 times higher specific electrochemical activity (-1.39 mA \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{m}}_{\\text{ECSA}}^{\\text{-2}}\\)\u003c/span\u003e\u003c/span\u003e) than that of Pt/C (-0.30 mA \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{m}}_{\\text{ECSA}}^{\\text{-2}}\\)\u003c/span\u003e\u003c/span\u003e, see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eD) 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 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) at this potential is also much higher than that of Pt/C (0.98 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e), further confirming the excellent intrinsic activity (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eE). More detailed electrochemical data are provided in \u003cstrong\u003eFigures S33-35\u003c/strong\u003e. Compared with other reported catalysts for HER (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eE and \u003cstrong\u003eTable S2\u003c/strong\u003e), the designed dual gradient HEA shows the smallest overpotential of 10.8 mV at -10 mA cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, indicating a breakthrough in the catalytic performance for HER.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n\u003ch2\u003eExtension to C*, O*, and N*\u003c/h2\u003e\n\u003cp\u003eThe 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 \u003cstrong\u003eFigures S36-38\u003c/strong\u003e. Their adsorption energy values also roughly follow the Gaussian distribution with \u0026micro; and \u0026sigma; 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 \u003cstrong\u003eFigures S39-41\u003c/strong\u003e. 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.\u003csup\u003e26\u003c/sup\u003e Therefore, the proposed anomalous Sabatier principle in this work can be extended to other catalytic reactions associated with these adsorbates, such as CO\u003csub\u003e2\u003c/sub\u003eRR, ORR/OER, NRR, etc.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eIn summary, we found the anomalous Sabatier principle on HEA catalysts for HER. The new descriptors of \u003cem\u003e\u0026micro;\u003c/em\u003e and \u003cem\u003eσ\u003c/em\u003e are proposed to indicate the catalytic activity of HEA catalysts for HER based on the Gaussian distribution [\u003cem\u003eX\u003c/em\u003e\u0026thinsp;~\u0026thinsp;\u003cem\u003eN\u003c/em\u003e(\u0026micro;, σ\u003csup\u003e2\u003c/sup\u003e)] of Δ\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e. Mathematically, a larger σ value results with \u0026micro;\u0026thinsp;=\u0026thinsp;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 H\u003csub\u003e2\u003c/sub\u003e 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\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e 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.\u003c/p\u003e"},{"header":"Experimental Section","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eChemicals\u003c/h2\u003e \u003cp\u003eIron(III) chloride (FeCl\u003csub\u003e3\u003c/sub\u003e), Cobalt(II) chloride hexahydrate (CoCl\u003csub\u003e2\u003c/sub\u003e\u0026middot;6H\u003csub\u003e2\u003c/sub\u003eO), Nickel(II) chloride hexahydrate (NiCl\u003csub\u003e2\u003c/sub\u003e\u0026middot;6H\u003csub\u003e2\u003c/sub\u003eO), Copper(II) chloride dihydrate (CuCl\u003csub\u003e2\u003c/sub\u003e\u0026middot;2H\u003csub\u003e2\u003c/sub\u003eO), and Chloroplatinic acid (H\u003csub\u003e2\u003c/sub\u003ePtCl\u003csub\u003e6\u003c/sub\u003e\u0026middot;6H\u003csub\u003e2\u003c/sub\u003eO) were purchased from Sigma Aldrich. All chemicals are of analytical purity and used without further purification.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eSynthesis of PtFeCoNiCu HEA catalyst\u003c/h2\u003e \u003cp\u003e0.5 mM of FeCl\u003csub\u003e3\u003c/sub\u003e, CoCl\u003csub\u003e2\u003c/sub\u003e\u0026middot;6H\u003csub\u003e2\u003c/sub\u003eO, NiCl\u003csub\u003e2\u003c/sub\u003e\u0026middot;6H\u003csub\u003e2\u003c/sub\u003eO, CuCl\u003csub\u003e2\u003c/sub\u003e\u0026middot;2H\u003csub\u003e2\u003c/sub\u003eO, and H\u003csub\u003e2\u003c/sub\u003ePtCl\u003csub\u003e6\u003c/sub\u003e\u0026middot;6H\u003csub\u003e2\u003c/sub\u003eO were added into 40 mL ultrapure water to form a uniform mixture. The mixture was stirred constantly in an oil bath at 80\u0026deg;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% H\u003csub\u003e2\u003c/sub\u003e/Ar atmosphere for 2 h at 300\u0026deg;C, 400\u0026deg;C, and 500\u0026deg;C, respectively.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eSynthesis of PtFeCoNi and PtFeCo catalysts\u003c/h2\u003e \u003cp\u003eThe synthesis method of PtFeCoNi is the same with that of HEA-400, except that the precursor of CuCl\u003csub\u003e2\u003c/sub\u003e\u0026middot;2H\u003csub\u003e2\u003c/sub\u003eO was not added. The synthesis method of PtFeCo is the same with that of HEA-400, except that the precursors of CuCl\u003csub\u003e2\u003c/sub\u003e\u0026middot;2H\u003csub\u003e2\u003c/sub\u003eO and NiCl\u003csub\u003e2\u003c/sub\u003e\u0026middot;6H\u003csub\u003e2\u003c/sub\u003eO were not added.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eMaterial Characterization\u003c/h2\u003e \u003cp\u003eFor 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).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eElectrochemical Measurements\u003c/h2\u003e \u003cp\u003eAll 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 \u0026micro;L of the catalyst ink was taken and dried on the RDE surface for measurement each time. 15 \u0026micro;L Nafion-isopropanol solution (1:19, v/v) was taken and covered on the dried catalyst films as a binder.\u003c/p\u003e \u003cp\u003eThe HER performance measurements were conducted in N\u003csub\u003e2\u003c/sub\u003e-saturated 0.5 M H\u003csub\u003e2\u003c/sub\u003eSO\u003csub\u003e4\u003c/sub\u003e. For activating HEA catalysts, cyclic voltammetry (CV) tests were performed at a potential range of 100\u0026thinsp;~\u0026thinsp;530 mV (\u003cem\u003evs.\u003c/em\u003e reversible hydrogen electrode, RHE) at a scan rate of 400 mV s\u003csup\u003e-1\u003c/sup\u003e. Linear sweep voltammetry (LSV) tests were conducted at a scan rate of 5 mV s\u003csup\u003e-1\u003c/sup\u003e 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 (\u003cem\u003evs.\u003c/em\u003e RHE) at scan rates of 20, 40, 60, 80, and 100 mV s\u003csup\u003e-1\u003c/sup\u003e, respectively. Galvanostatic tests were performed at an applied current density of -10 mA cm\u003csup\u003e-2\u003c/sup\u003e for 80 h. Electrochemical impedance measurements were performed at 10 mV (\u003cem\u003evs.\u003c/em\u003e 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 \u003cem\u003eE\u003c/em\u003e\u003csub\u003eRHE\u003c/sub\u003e = \u003cem\u003eE\u003c/em\u003e\u003csub\u003eSCE\u003c/sub\u003e + 0.059 pH\u0026thinsp;+\u0026thinsp;0.267 V, where \u003cem\u003eE\u003c/em\u003e\u003csub\u003eRHE\u003c/sub\u003e and \u003cem\u003eE\u003c/em\u003e\u003csub\u003eSCE\u003c/sub\u003e denote the reversible hydrogen evolution potential and the measured potential, respectively.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003eDensity functional theory calculation\u003c/h2\u003e \u003cp\u003eAll calculations were performed using the Vienna ab initio simulation package (VASP) based on spin-polarized density function theory (DFT).\u003csup\u003e33\u003c/sup\u003e The projector-augmented wave pseudopotential was applied to treat the core electrons.\u003csup\u003e34\u003c/sup\u003e The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof functional (PBE) was adopted in the DFT calculations.\u003csup\u003e35\u003c/sup\u003e 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 \u0026times; 4 supercell with five layers was considered for all systems. The Monkhorst-Pack grid of k-points was 2 \u0026times; 2 \u0026times; 1, and a vacuum gap of more than 12 \u0026Aring; 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 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e eV and 0.05 eV/\u0026Aring;, respectively. The van der Waals interaction was considered through the DFT-D3 method proposed by Grimme.\u003csup\u003e36\u003c/sup\u003e 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/\u0026Aring;.\u003csup\u003e37\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eThe adsorption energy (Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eX*\u003c/sub\u003e) of adsorbates (X\u0026thinsp;=\u0026thinsp;H, C, O, N) was calculated by the following equation:\u003c/p\u003e \u003cp\u003eΔ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eX*\u003c/sub\u003e = \u003cem\u003eE\u003c/em\u003e\u003csub\u003eX*\u003c/sub\u003e \u0026ndash; \u003cem\u003eE\u003c/em\u003e\u003csub\u003ecat\u003c/sub\u003e \u0026ndash; \u003cem\u003eE\u003c/em\u003e\u003csub\u003eX\u003c/sub\u003e (1)\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eE\u003c/em\u003e\u003csub\u003eX*\u003c/sub\u003e, \u003cem\u003eE\u003c/em\u003e\u003csub\u003ecat\u003c/sub\u003e, and \u003cem\u003eE\u003c/em\u003e\u003csub\u003eX\u003c/sub\u003e 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 H\u003csub\u003e2\u003c/sub\u003e, graphene, H\u003csub\u003e2\u003c/sub\u003eO, and NH\u003csub\u003e3\u003c/sub\u003e, respectively. The adsorption energy was corrected by considering the zero-point energy and entropy, as shown below:\u003c/p\u003e \u003cp\u003eΔ\u003cem\u003eG\u003c/em\u003e\u003csub\u003eX*\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eX*\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;Δ\u003cem\u003eZPE\u003c/em\u003e \u0026ndash; \u003cem\u003eT\u003c/em\u003eΔ\u003cem\u003eS\u003c/em\u003e (2)\u003c/p\u003e \u003cp\u003ewhere Δ\u003cem\u003eG\u003c/em\u003e\u003csub\u003eX*\u003c/sub\u003e, Δ\u003cem\u003eZPE\u003c/em\u003e, and \u003cem\u003eT\u003c/em\u003eΔ\u003cem\u003eS\u003c/em\u003e denote the adsorption free energy, zero-point energy change, and entropy change, respectively.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003eAcknowledgments\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe 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.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eAuthor Contributions\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eC. 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.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eCompeting Interests\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003eReceived: ((will be filled in by the editorial staff))\u003c/p\u003e\n\u003cp\u003eRevised: ((will be filled in by the editorial staff))\u003c/p\u003e\n\u003cp\u003eAccepted: ((will be filled in by the editorial staff))\u003c/p\u003e\n\u003cp\u003ePublished: ((will be filled in by the editorial staff))\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eSabatier, P. (1920). La catalyse en chimie organique. Berauge, Paris, 48-57.\u003c/li\u003e\n\u003cli\u003eN\u0026oslash;rskov, J.K., Bligaard, T., Logadottir, A., Bahn, S., Hansen, L.B., Bollinger, M., Bengaard, H., Hammer, B., Sljivancanin, Z., Mavrikakis, M., Xu, Y., Dahl, S. and Jacobsen, C.J. (2002). 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Phys. 113, 9901-9904.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Anomalous Sabatier principle, high entropy alloy catalysts, hydrogen evolution reaction, Gaussian distribution","lastPublishedDoi":"10.21203/rs.3.rs-2756931/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2756931/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe 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 (Δ\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e), where the active sites with strong adsorption adsorb hydrogen (H*) and other sites with weak adsorption release H* to produce H\u003csub\u003e2\u003c/sub\u003e, was against the \u0026ldquo;just right\u0026rdquo; (Δ\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e = 0 eV) in the Sabatier principle of hydrogen evolution reaction (HER). The Gaussian distribution [\u003cem\u003eX\u003c/em\u003e\u0026thinsp;~\u0026thinsp;\u003cem\u003eN\u003c/em\u003e(\u0026micro;, σ\u003csup\u003e2\u003c/sup\u003e)] of Δ\u003cem\u003eG\u003c/em\u003e\u003csub\u003eH*\u003c/sub\u003e on HEA was proposed as a descriptor, deriving an anomalous Sabatier principle, where a larger σ value results with \u0026micro;\u0026thinsp;=\u0026thinsp;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\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e 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.\u003c/p\u003e","manuscriptTitle":"Anomalous Sabatier principle on high entropy alloy catalysts","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-04-07 20:19:17","doi":"10.21203/rs.3.rs-2756931/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"ec1193d0-c956-42e0-a141-340dc1170640","owner":[],"postedDate":"April 7th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":20507536,"name":"Physical sciences/Materials science/Materials for energy and catalysis/Electrocatalysis"},{"id":20507537,"name":"Physical sciences/Chemistry/Catalysis/Heterogeneous catalysis"}],"tags":[],"updatedAt":"2024-01-09T08:12:25+00:00","versionOfRecord":{"articleIdentity":"rs-2756931","link":"https://doi.org/10.1038/s41467-023-44261-4","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2024-01-08 05:00:00","publishedOnDateReadable":"January 8th, 2024"},"versionCreatedAt":"2023-04-07 20:19:17","video":"","vorDoi":"10.1038/s41467-023-44261-4","vorDoiUrl":"https://doi.org/10.1038/s41467-023-44261-4","workflowStages":[]},"version":"v1","identity":"rs-2756931","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2756931","identity":"rs-2756931","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}