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Oct 3, 2018 - ABSTRACT: This work presents a new theoretical frame- work to construct volcano relations (VRs) that are capable of predicting and ...
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Energetic Span as Rate-Determining Term for Electrocatalytic Volcanos Junxiang Chen, Yongting Chen, Peng Li, Zhenhai Wen, and Shengli Chen ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.8b03008 • Publication Date (Web): 03 Oct 2018 Downloaded from http://pubs.acs.org on October 3, 2018

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Energetic Span as Rate-Determining Term for Electrocatalytic Volcanos Junxiang Chen1,2, Yongting Chen1, Peng Li1, Zhenhai Wen*,2, Shengli Chen*,1 1. Hubei Key Laboratory of Electrochemical Power Sources, Key Laboratory of Analytical Chemistry for Biology and Medicine (Ministry of Education), Department of Chemistry, Wuhan University, Wuhan 430072, China. 2. CAS Key Laboratory of Design and Assembly of Functional Nanostructures, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian 350002, China

ABSTRACT: This work presents a new theoretical framework to construct volcano relations (VRs) that are capable of predicting and understanding the activity of top electrocatalysts. We propose a thermodynamic form of energetic span (δE) as rate-determining term for electrocatalytic reactions, which allows the essential factors such as the coverage of the stable intermediates and the energetics of the most demanding steps to be included in the rate equations, and therefore overcomes the weakness of the current electrocatalytic VRs derived from kinetic models using the maximum standard free energy (∆G0max) of elementary reaction steps as rate-determining terms. The ∆G0max-based VRs are shown to be applicable only at large overpotentials where the intermediates involved in δE and ∆G0max converge. At small overpotentials where the excellent catalysts function, the ∆G0max-based VRs may give improper prediction by missing the effects of surface phase of stable adsorbates and its evolution with potentials. As well as revealing new features of electrocatalytic VRs and reasonably explaining some recent experiment results about efficient electrocatalysts for the hydrogen and oxygen electrode reactions, the

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δE-based rate models provide rich information about the catalytic mechanism and kinetics, e.g., the evolution surface phases of stable intermediates, rate-determining transition states, and Tafel slopes.

KEYWORDS: electrocatalysis, rate determining term, energetic span, volcano relation, Tafel slopes.

1. Introduction Electrocatalysis plays a vital role in tackling the energy and environment challenges1,2. One of the primary goals in electrocatalysis is to find efficient catalysts for target reactions. First principle-based computation is becoming an essential tool to expedite catalysts searching processes; while volcano relations (VRs), which relate the kinetics of reactions with the computationally accessible adsorption energies of reaction intermediates, serve as a guidance for computation-based catalysts optimization1. Qualitatively, the VRs can be rationalized in terms of the Sabatier principle, which suggests that the best catalyst should have a medium binding ability so that neither the adsorption step nor the desorption step would drag the reaction. To quantify the Sabatier principle into functional VRs for electrocatlytic reactions is not straightforward, because the latter usually involve multiple proton-coupled electron transfer (PCET) steps and multiple intermediates. The electrochemical thermodynamic framework (ETF) developed by Nørskov and Koper et al3,4 has significantly advanced this quantification. In this theoretical framework, a computational hydrogen electrode (CHE) approach is used to avoid the direct computation of solvated protons in electrolytes, and the Brønsted-Evans-Polanyi (BEP) principle5 is used to avoid the direct calculation of activation barriers of PCET steps at electrochemical interfaces. By adopting the concept of rate determining step (rds), it is proposed that the kinetics of an electrocatalytic reaction are limited by the step with the maximum standard reaction free energy (∆G0max), and that the current density can be estimated with ∆G0max according to j≈j0exp(-∆G0max/RT)6, where j0 can be considered as the exchange 2 ACS Paragon Plus Environment

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current density of the reaction at a reference catalyst surface at which all the elementary steps are thermodynamically neutral. They have set the transfer coefficient (β) in the BEP relation for electron transfer to be one here since the model was initially built for the oxygen reduction reaction, which exhibits an apparent β value near 1 at low overpotentials.6 Upon moving from one catalyst to another with different binding ability, the ∆G0max step in a reaction would vary among various elementary steps that may have varied dependence on the binding ability of catalysts. On the other hand, the scaling relationship7 that generally exists among the adsorption energy of different intermediates enables one to formulate the energetics of each step as a function of the adsorption free energy of a single intermediate (∆G0A*). Accordingly, a VR between the activity of catalysts and the ∆G0A* can be established. The ∆G0max-based VRs have shown considerable success in predicting and understanding the general activity trends of various electrocatalytic reactions, for examples, hydrogen evolution/oxidation reactions (HER/HOR)8-10, oxygen evolution reaction (OER) 3,13

11,12

and oxygen reduction reaction (ORR)

, on different types of catalysts, such as transition metals and alloys3,8,13, metal oxides11,12 and

nonprecious metals catalysts14-16. However, the predictions of the ∆G0max-based VRs have been also challenged by some recent experimental observations, for examples, the chlorine evolution reaction (CER) on RuO217,18, ORR on Pt-Cu alloys 19, 20 and stepped Pt (111) surfaces21. Especially, the deviation generally occurs near the top regions of the volcano plots, i.e., for catalysts having ∆G0A* close to the corresponding optimal value, suggesting that the ∆G0max-based VRs have some weakness in accurately predicting the activity trends of highly active catalysts. By building the rate equation merely on the energetics of the most demanding step, the ∆G0max-based VRs neglect the possible accumulation of the stable intermediates, which could greatly impact the rate of a surface reaction by reducing the numbers of reactive sites. Besides, for a reaction on catalysts with relatively optimal binding ability, there might not be an obvious single rds, but rather a few ratecontrolling steps22. Herein, we introduce a new thermodynamic framework to construct eletcrocatlytic 3 ACS Paragon Plus Environment

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VRs that can predict the behaviors of top catalysts. By adopting the recently proposed concept of energetic span 23-25, the approach uses the energetics of intermediates involved in some key steps, rather than in a single step, to build the rate equations, thus allowing the factors such as the coverage of the stable intermediates and the energetics of the most demanding step to be simultaneously included in the rate equations. We apply the approach to construct VRs for the hydrogen and oxygen electrode reactions, and are able to explain some recent experimental results more reasonably than the ∆G0max models. The approach is also shown to provide rich information about the catalytic mechanism and kinetics. 2. Energetic Span-Based Microkinetic Models 2.1 Energetic Span as the rate-determining term for catalytic reactions. The term of energetic span has been proposed on the basis of a full microkinetic analysis on the multi-step and multiintermediate reaction. It was shown by Kozuch et al

23-25

that the turnover frequency (TOF) of a n-step

reaction with standard reaction free energy (∆Gtot0) can be formulated as,

kT TOF = B h

e−∆Gtot n

0

/ RT

−1

[Ti ,i +1 - I j -(1-aij ) ∆Gtot 0 ]/ RT

∑e

i , j =1

(1)

in which Ti,i+1 refers to the molar free energy of the transition state (TS) between the ith and (i+1)th intermediate states (ISs), Ij the molar free energy of the jth IS, aij=0 if i ≥j and aij=1 if i>1 or exp(-∆Gtot0/RT)j). Similarly, we name the Ij and Tvi,i+1 involved in the δEv as the TOFdetermining intermediate (TDI) and the TOF-determining virtual TS (TDTSv), respectively. Accordingly,

δ E v = TTDTS - I TDI v

(6)

In the case when the elementary steps don’t have the same activation free energy under thermodynamically neutral condition, the implementation of the virtual energetic span method would be some complicated. For demonstration purpose, however, we will consider this situation for the hydrogen electrode reactions, which are among the simplest electrocatlytic reactions with only two elementary steps and one intermediate.

Scheme 2 TS-free dual-FED approach to determine δEv.

3. δEv as the rate-determining term for the hydrogen electrode reactions 7 ACS Paragon Plus Environment

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The hydrogen electrode reactions, including hydrogen evolution and oxidation reactions (HER and HOR), may proceed through Tafel-Volmer or Heyrovsky-Volmer pathways.31 For simplicity, we only construct volcano relations based on the Heyrovsky-Volmer pathway (Scheme 3). H++e+*↔H*

Volmer reaction

H++e+H*↔H2+*

Heyrovsky reaction

Scheme 3 The Heyrovsky-Volmer pathway for hydrogen electrode reactions (asterisk denotes the adsorption site). 3.1 Theoretical volcano relations. The Heyrovsky-Volmer pathway could have three different situations, that are, the two steps have similar ∆G0≠, the Volmer step has a much higher ∆G0≠, or the Heyrovsky step has a much a much higher ∆G0≠. Figure 1 displays the schematic dual FEDs for these situations (a, c, e) and the corresponding chromaticity diagrams (b, d, f) of the activities (represented by the value of -δEv= RTlnj/NF) as functions of the electrode potential (U) and the standard adsorption free energy of H* (∆G0H*) which measures the standard reaction free energy of the H2 dissociation reaction of 1/2H2+*↔H*. For each situation, two schematic FEDs are given for negative and positive ∆G0H* values respectively. For the case of equal ∆G0≠, the δEv model gives very similar activity trends to that predicted by the ∆G0max model, with the volcano tops occurring at nearly zero ∆G0H* for both HER and HOR, regardless of electrode potentials (Figure 1b). For unequal ∆G0≠, the VRs are asymmetric, with the optimal ∆G0H* values for volcano tops becoming potential dependent. If the Volmer step is the rds, the optimal ∆G0H* shifts towards more negative value with the electrode potential going negatively (Figure 1d); while the trend is reversed when the Heyrovsky step has much higher activation barrier (Figure 1f).

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Figure 1 (a, c, e) Schematic dual FEDs of Heyrovksy-Volmer pathway, in which the reaction is put in the direction of HER. (b, d, f) The chromaticity diagrams of activities as functions of ∆G0H* and U for the hydrogen electrode reactions. The color variation from blue to red indicates the increase in activity. The ∆G0H* values for the example catalysts Pt, Rh, Pd, Ir and Au are taken from Ref.8, MoS2 from Ref.9. MoP|S from Ref.32. The orange dots in the FEDs indicate the corresponding TDTSv. The different potential dependence of the activity volcanos shown above can be understood mathematically with the corresponding δEv expressions. In the cases when the Volmer or Heyrovsky step has much higher ∆G0≠, δEv have the form of |∆G0H*-eU|/2-|eU|/2 or |∆G0H*+eU|/2-|eU|/2, where the ∆G0H* and eU appear in the same operator in a single absolute function, which makes the δEv-∆G0H* and 9 ACS Paragon Plus Environment

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δEv-U dependence intertwines with each other. This intertwining occurs neither in the δEv expression for the case of equal ∆G0≠ (|∆G0H*|/2-|eU|/2) nor in the ∆G0max expression (|∆G0H*|-|eU|), where the ∆G0H* and eU are included in a different absolute terms. The derivation details for these expressions can be found in Supporting Information (S1). 3.2 Understanding experiments. According to the δEv model for equal ∆G0≠ and the ∆G0max model, the catalyst with good/poor HER activity would be good/poor HOR catalyst too. However, this is not true for many catalyst materials. For examples, the recently reported excellent HER electrocatalysts, such as MoS2 and MoP|S, show rather poor HOR activity33,34. As seen in Figure 1d and 1f, the differed activity for HER and HOR for a single catalyst is well predicted by the δEv-based volcano relations under unequal ∆G0≠. What’s more, the comparison of the theoretical prediction with the experimental observations could help to unveil the reaction mechanism. In the case when the Volmer step is the rds, the δEv-based volcano relations suggest that the MoS2, MoP|S, and Au would have much higher activities for HOR than that for HER (dash lines in figure 1d), which is obviously contradictory with the experimental results33-35. However, the volcano relations for the Heyrovsky rds give the correct prediction (dash lines in Figure 1f), suggesting that the rates of the hydrogen electrode reactions may be generally limited by the Heyrovsky step. On the other hand, the theoretical volcanos in Figure 1f don’t violate the facts that the precious metal catalysts such as Pt, Pd, Rh and Ir have nearly equivalent HER and HOR activities (solid lines)

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. With the Heyrovsky rds, such results seem to implicate catalysts

with better activities for HER than HOR generally have a positive ∆G0H 8,9,32, while an advanced HOR catalyst should have slightly negative ∆G0H*. It should be pointed out that the Volcano relations given in Figure 1 have been deduced under a mean-field approximation, which assumes a Langmuir adsorption of H ad-atoms. In reality, the adsorbed H may have relatively weak interactions which can be described with the Temkin adsorption isotherms31. As shown in Figure S1, the use of Temkin adsorption would result in slight downshift of 10 ACS Paragon Plus Environment

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the optimal ∆G0H* values for volcano tops as comparing to that derived using Langmuir adsorption. Although some quantitative inaccuracy may occur, the Langmuir adsorption isotherm based volcano relations can essentially catch the qualitative activity trends. 4. δEv as the rate-determining term for the oxygen electrode reaction The oxygen electrode reactions, including the oxygen reduction reaction (ORR) and the oxygen evolution reaction (OER), are usually described with the four-PCET-step pathway shown in Scheme 4.13 Due to that multiple oxygenated intermediates are involved, the scaling relations of adsorption free energy among various oxygenated adsorbates on metals-based electrocatalysts for ORR13,20 and that on metal oxides-based electrocatalysts for OER4 are adopted to construct activity models. With these scaling relations, either the δEv or the ∆G0max can be expressed as a function of the adsorption free energy of a single oxygenated adsorbate, e.g., ∆G0O*, and the corresponding volcano relations between the activity and this adsorption free energy can be obtained according to the models described in Section 2. O2+H++e+*↔OOH* OOH*+H++e↔O*+H2O O*+H++e↔OH* OH*+H++e↔ H2O+* Scheme 4 Four-PCET-step pathway for the oxygen electrode reactions.13 4.1 Theoretical volcano relations. Figure 2 displays the theoretical activity of the oxygen electrode reactions as functions of ∆G0O* and electrode potential, derived with the δEv and ∆G0max models respectively. We only consider the situation when the four steps have similar ∆G0≠ values. As indicated by the dash lines in Figure 2a and the plots in Figure 2b, the δEv model predicts optimal ∆G0O values for volcano tops that are very similar to those given by the ∆G0max model at large overpotentials (U1.5 V for the OER on metal oxides), showing negligible potential dependence. As the electrode potential approaches the thermodynamic equilibrium value (1.23 11 ACS Paragon Plus Environment

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V), however, the δEv model gives activity trends varying apparently with electrode potential, while the ∆G0max model remains giving potential insensitive activity trends. Similar results are observed for other types of ORR&OER catalysts14-16,37-39 (Figure S2).

Figure 2 (a) Activity chromaticity map for the oxygen electrode reactions, with the green and black dash lines marking the volcano tops predicted by the ∆G0max and δEv models respectively. (b) Volcano plots of activity as a function of ∆G0O* given by the δEv (black solid lines) and ∆G0max (orange dash lines). The numbers refer to the electrode potentials vs RHE. According to the present δEv model, the potential-dependent volcano relations should be a characteristic feature of the multi-step and multi-intermediate reactions in the low overpotential region, no matter whether the elementary steps have similar ∆G0≠ or not. As seen in Figure 2b, the optimal ∆G0O value for volcano top for the OER shifts negatively with the electrode potential approaching the equilibrium value (upper panel), while that for the ORR shifts positively (lower panel). On this basis, the ∆G0max model would give unreasonable prediction and explanation on the experimental activity trends of multi-intermediate electrocatalytic reactions, especially that on the highly efficient catalysts which exhibit low onset overpotentials. Another important feature of the δEv-based volcano plots for the multi-intermediate electrocatalytical reactions is the relatively flat tops, which implies that there should be a range of catalyst materials which have similarly top activity for a reaction. 4.2 Understanding experiments. To demonstrate the effectiveness of the present δEv model, we take the ORR catalyst of Mo doped Pt3Ni nanocrystals (denoted as Mo-Pt3Ni), which has been recently 12 ACS Paragon Plus Environment

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reported by Huang et al40 having the best activity to date. Such an excellent catalyst should possess abundant surface sites exhibiting ∆G0O* values close to that for the volcano top. According to the theoretical results on the basis of ∆G0max model (orange volcano curve in Figure 3a),40 only the poorly abundant edge sites (labeled with number 3 in Figure 3b) have a relatively optimal ∆G0O* value which is ~0.1 eV away from that for the volcano top and similar to that for the Pt3Ni (111) surface, while the facet sites (labeled with numbers 1 and 2 in Figure 3b) have ∆G0O* values considerably away from the optimal values. On the volcano plot based on the δEv model (black curve in Figure 3a), the excellent ORR activity of Mo-Pt3Ni becomes easily understood. At 0.95 V, three types of surface sites on MoPt3Ni surface (types 1, 2 and 3) fall into the very top region of the volcano plot, with the facet sites 1 and 2 sitting at the top position. In addition, the δEv model suggests that, the Pt3Ni (111) surface also has an excellent ORR activity, but it could be inferior to its Mo-doped nanoparticle counterpart.

δE v Based Activity

(a) 0.0

Pt3Ni(111)

Pt (111)

5

-0.2

3 2 1

4

3

2

4

-0.6

1 5 δ E v on 0.95 V

-0.4

∆G

-0.6

-0.4

1.4

1.6

1.8

-0.8

0 max

2.0

2.2

ΔG0max Based Activity

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0

∆G

/eV O*

Figure 3 (a) Comparison between ∆G0max and δEv in probing activities on the surfaces of the Mo6Pt41Ni178 nano particle, where the ∆G0max and δEv based volcano plots are marked by orange and black lines. The numbers indicate the surface sites, the positions of which on the surface are pictured on (b). All data are taken from Fig.4 in Ref.40. We choose the potential of 0.95 V because it is approximately the experimental half-wave potential for Mo-Pt3Ni.40 5. Discussions. 5.1 Correlation between δEv and ∆G0max. As shown above, the δEv- and ∆G0max-based models give similar results at large overpotentials, whereas their predictions differ significantly as the electrode 13 ACS Paragon Plus Environment

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potential approaches the equilibrium values. The relation between δEv and ∆G0max may be understood with the FEDs of a 4-step reaction (e.g., ORR) illustrated in Scheme 5. In large overpotential region where all the elementary steps have been driven exo-energetic (Scheme 5a), the TDI and TDTSv are also the reactant and virtual transition state of the ∆G0max step. In this case, we have δEv=∆G0max/2, and therefore the ∂∆G0max/∂∆G0O* and ∂δEv/∂∆G0O* follow the similar variation trends. When the overpotential is small (Scheme 5b), the TDI and TDTSv generally appear in different steps which don’t necessarily include the ∆G0max step. In this case, the δEv and ∆G0max are weakly correlated with each other. Thus, the ∆G0max represents an approximation of δEv at large overpotentials.

Scheme 5 Examples of four-step FEDs showing the correlation between ∆G0max and δEv at (a) large and (b) small overpotentials. 5.2 Phase diagrams of surface adsorbates and Tafel slopes from δEv. In addition to acting as a rational rate-determining term in low overpotential region, the δEv could also provide rich information on the multi-step and multi-intermediate electrocatalytical reactions. We demonstrate this with the oxygen electrode reactions. Figure 4 gives the phase diagram of the TDI and TDTSv as functions of ∆G0O* and electrode potential. In the diagram, the “TDI: *” refers to an adsorbate-free surface, and the 14 ACS Paragon Plus Environment

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TDTSv-associated reaction step is given in a simplified form, only showing the adsorbed intermediates involved in it, for instance, the “*→OOH*” represents the OOH* formation step (see Scheme 4). The boundary lines of each phase in Figure 4 are where the transition of TDI and/or TDTSv occur, which would result in change in the slope of volcano curve (∂δEv/∂∆G0O*) and the Tafel slope (∂δEv/∂U). The red dash lines indicate where the volcano tops occur. It can be seen that the formation of a volcano top could be due to the transition of the TDI, or TDTSv, or both. This is to say that the formation of a volcano top not necessarily requires a change in a so-called potential-determining or rate-determining step3,4, but could also be due to the change of surface phase of adsorbate.

Figure 4 Phase diagram of TDI and TDTSv for the oxygen electrode reactions. The red dash line marks the optimal ∆G0O* for volcano top at different electrode potentials. The stable intermediate, i.e., TDI, would accumulate and cover the catalyst surface. Therefore, one can deduce a phase diagram of the major surface adsorbates for the oxygen electrode reactions from Figure 4. Depending on the electrode potential and ∆G0O*, the surface of an ORR and OER catalysts may be free of any adsorbate, mainly covered by OH*, or mainly covered by O* (Figure 5). Using the calculated ∆G0O* values for Pt(111), Au(111) and Ni(111) surface, the evolution of surface adsorbates 15 ACS Paragon Plus Environment

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with electrode potential during the ORR on these electrodes can be plotted (the grey dash-dot lines). These evolution behaviors agree with that obtained through DFT calculation under the O2-free conditions.41 This suggests that the surface phase structures during the ORR process may be estimated through voltammetric measurements in O2-free solutions. Similar conclusion has also been drawn in previous works42,43.

Figure 5 Map of major surface adsorbates for the oxygen electrode reactions on catalysts with different ∆G0O* and at different electrode potentials. The grey dash-dot lines show the transition of the most stable adsorbates with electrode potential on the surface of three typical metal (111) electrodes. As mentioned above, the boundary lines in the TDI/TDTSv phase diagram correspond to the change of Tafel slopes (∂δEv/∂U). On catalysts with a considerable range of ∆G0O* values, as shown in Figure 6, the oxygen electrode reactions exhibit 120 mV/Dec Tafel slope at large overpotentials, which is associated with a single electron transfer step. As the electrode potential approaching the equilibrium value, the Tafel slopes tend to decrease to smaller values, e.g., 24 or 40 mV/Dec. The decrease of Tafel slopes at low overpotentials for the oxygen electrode reactions has been generally observed in experiments.13,19,40,43 According to the present δEv model, the value of Tafel slopes should be 120/(2m+1), with m being the numbers of the elementary steps between the TDI and TDTSv (see the 16 ACS Paragon Plus Environment

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deduction on sec.S2 in supporting information). At large overpotentials, the TDI and TDTSv are in the same elementary step and m=0 (Scheme 5a), therefore a Tafel slope of 120 mV/Dec is obtained. The Tafel slopes of 24 and 40 mV/Dec are the results of m=2 and 1, respectively. According to the ∆G0max model, the Tafel slope of an electrocatalytic reaction should be potential independent and equals to 120 mV/Dec.

Figure 6. Map of Tafel slopes (mV/Dec, indicated by the numbers) as functions of electrode potentials and ∆G0O* for the oxygen electrode reactions derived from the δEv~U dependence. For the ORR on Pt-based catalysts, Tafel slopes of 60-90 mV/Dec are usually observed in low overpotential region (0.85-1.0 V)13, 44, whereas the present δEv model predicts a 40 mV/Dec Tafel slope in this potential region. This should be mainly due to that we have neglected the effect of the adsorbates interaction on ∆G0O*. To precisely predict the voltammetric responses, one should take into account of the adsorbate interaction and the structure ordering of adsorbates (e.g., formation of H2O-OH network)41, 42, 45-48. This, however, should not significantly affect the δEv-based prediction of activity trends of different catalysts. We are developing a self-consistent iteration method to the construct the

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FED for multi-step electrocatalytic reactions so that the adsorbates interaction and surface structure formation can be included in the δEv.

6. Summary and Prospect In summary, a thermodynamic framework has been proposed to build microkinetic models for electrocatalytic reactions. The use of the virtue energetic spans (δEv) as rate-determining terms captures the essential factors that vitally affecting the rates of electrocatalytic reactions at small overpotentials where the excellent electrocatalyts function. The volcano relations (VRs) derived from the δEv-based rate models well explain the electrocatalytic properties of recently reported efficient catalysts for the hydrogen and oxygen electrode reactions. The model results and the comparison with experiments also lead to electrocatalytic knowledge as outlined in the following: (1) The activity trends of various catalysts for the same electrocatalytic reaction could vary with overpotentials, making the optimal adsorption property associated with the volcano top shifts with potentials. An important implication of this feature is that the efficient electrocatalysts identified under relatively low mass transport conditions don’t necessarily function well in practical devises in which the reactions are usually driven to large overpotentials at large current densities. (2) The widely used ∆G0max-based rate models can reasonably predict and understand the activity of various catalysts at large overpotentials, but could give wrong prediction and explanation for the electrocatalytic trends at small overpotentials. (3) The phase behaviors of surface adsorbates play a key role in the electrocatalytic kinetics, especially at small overpotentials. The transformation of surface adsorbate phases is the common reason for the shift of the volcano tops and the potential-dependent Tafel slopes. These features are well described by the δEv-based rate models, but could be missed in the ∆G0max-based rate models.

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(4) The hydrogen electrode reactions at various efficient catalysts such as Pt, Pd, Ir, MoS2, etc. are largely limited by the Heyrovsky reaction. (5) The δEv as rate-determining terms also predicts that the optimized electrocatalysts should have a near zero ∆G0max. When building the volcano plots, we don’t consider the effects of solvation, surface charge density, and pH that are important in the energetics of the adsorption processes at electrochemical interfaces. Taking these effects into account certainly merits future studies. These effects, as well as the adsorbates’s interactions mentioned above, would make the volcano plots established in last sections considerably away from accurate prediction of the kinetic features of electrocatalytic reactions. It is noted that effort has been made to include the solvation energies through explicit49,50 and implicit51 ways in many recent literatures. In recent ab initial molecular dynamic studies, Cheng et al52-54 have shown that the entropy and enthalpy changes associated solvent molecules in electrochemical systems can be considered in a relatively rigorous manner. Recently, Koper et al55 have proposed a method to decouple the PECT into separated proton transfer (PT) and electron transfer (ET) process, which may provide a way to treat the pH effect in PECT reaction. We expect that more realistic prediction would be possible to adopt these progresses in models and computations. ASSOCIATED CONTENT AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] *E-mail: [email protected]. Notes The authors declare no competing financial interests. 19 ACS Paragon Plus Environment

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Supporting Information. Derivation of δEv and ∆G0max expressions for hydrogen electrode reactions, expressions of Tafel slope, supporting Figures. This material is available free of charge via the Internet at http://pubs.acs.org. ACKNOWLEDGMENT We would like to thank the National Natural Science Foundation of China (Grants 21703250 and 21832004), 1000 Plan Professorship for Young Talents, Hundred Talents Program of FuJian Province, and the Fujian Science and Technology Key Project (Item Number. 2016H0043) for financial support. Most of the calculations have been conducted with the facilities in the Supercomputing Center of Wuhan University. REFERENCES (1) She, Z. W.; Kibsgaard, J.; Dickens, C. F.; Chorkendorff, I.; Nørskov, J. K. ; Jaramillo, T. F. Combining theory and experiment in electrocatalysis: Insights into materials design Science. 2017, 355, eaad4998. (2) Montoya, J. H.; Seitz, L. C.; Chakthranont, P.; Vojvodic, A.; Jaramillo, T. F.; Nørskov, J. K. Materials for solar fuels and chemicals. Nat. Mater. 2017, 16, 70-81. (3) Nørskov, J. K.; Rossmeisl, J.; Logadottir, A.; Lindqvist, L.; Kitchin, J. R.; Bligaard, T.; Jonsson, H. Origin of the overpotential for oxygen reduction at a fuel-cell cathode. J. Phys. Chem. B. 2004, 108, 17886-17892. (4) Koper, M. T. Thermodynamic theory of multi-electron transfer reactions: Implications for electrocatalysis. J. Electroanal. Chem. 2011, 660, 254-260. (5) van Santen, R. A.; Neurock, M.; Shetty, S. G. Reactivity theory of transition-metal surfaces: a Brønsted−Evans−Polanyi linear activation energy free-energy analysis. Chem. Rev. 2009, 110, 2005-2048. (6) Rossmeisl, J.; Karlberg, G. S.; Jaramillo, T.; Nørskov, J. K. Steady state oxygen reduction and cyclic voltammetry. Faraday Discuss. 2009,140, 337-346. (7) Abild-Pedersen, F.; Greeley, J.; Studt, F.; Rossmeisl, J.; Munter, T.; Moses, P. G.; Skulason, E.; Bligaard, T.; Nørskov, J. K. Scaling properties of adsorption energies for hydrogen-containing molecules on transition-metal surfaces. Phys. Rev. Lett. 2007, 99, 016105. 20 ACS Paragon Plus Environment

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