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Revealing the Volcano-Shaped Activity Trend of Triiodide Reduction Reaction: A DFT Study Coupled with Microkinetic Analysis Dong Wang, Jun Jiang, Hai Feng Wang, and Peijun Hu ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.5b01714 • Publication Date (Web): 18 Dec 2015 Downloaded from http://pubs.acs.org on December 23, 2015

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Revealing the Volcano-Shaped Activity Trend of Triiodide Reduction Reaction: A DFT Study Coupled with Microkinetic Analysis Dong Wang1,2, Jun Jiang1, Hai-Feng Wang1*, P. Hu1,2* 1

Key Lab of Advanced Materials, Centre for Computational Chemistry and Research Institute of Industrial Catalysis, East China University of Science and Technology, Shanghai 200237, China 2 School of Chemistry and Chemical Engineering, Queen’s University Belfast, Belfast BT9 5AG, UK *Corresponding authors: [email protected]；[email protected]

Abstract Triiodide/iodide (I3−/I−) represents a widely used redox couple and plays an important role in some photovoltaic devices. However, the understanding of the triiodide reduction kinetics occurring at the liquid/electrode is very limiting, which largely hinders the identification of highly efficient electrode material. In this work, by virtue of DFT calculations, we systematically investigated the I3− electroreduction at some acetonitrile/electrode interfaces, and uncovered two new BEP relations for the key elementary steps, i.e. I2 dissociation and I* desorption through one-electron reduction. Furthermore, by utilizing a steady-state microkinetic model, we successfully identified a general volcano-shaped activity trend of triiodide electroreduction as a function of a single descriptor, the adsorption energy of I atom (EadI) at the interface. Our results show that a good catalyst should possess an EadI within the range of 0.3-0.6 eV, while the optimal EadI is 0.43 eV where the surface coverages of free sites and iodine atoms are equal. In particular, the dependences of the volcano shape on the electrochemical conditions (external voltage, temperature, concentration and the transfer coefficient) are quantitatively discussed. Some suggestions for the optimization of experimental conditions and design of better catalysts are also provided. Keywords: triiodide reduction, I3−/I−, dye-sensitized solar cells, BEP relation, microkinetic analysis, volcano curve, electrocatalysis, density functional theory

1 Introduction Efficient conversion of solar power to chemical or electrical energy is a sustainable strategy to solve the energy crisis. Among the current light-to-energy devices, dye-sensitized solar cells (DSSCs) have drawn much attention due to their high efficiency, low cost and easy fabrication.1-3 A typical DSSC has a sandwich-like structure composed of a dye-sensitized photoanode such as TiO2, a counter electrode (CE), and an electrolyte (usually acetonitrile) containing a redox couple. Broadly speaking, the function of anode is to generate electrons upon illumination, leaving photoholes in the dye molecules; whereas the redox couple in the electrolyte is to reduce the oxidized dye molecules and carry the positive charges to CE. The triiodide/iodide (I3−/I−) redox couple is by far the most widely used one in many 1

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electrochemical systems, despite some developed alternatives (e.g. pseudohalogens,4,5 cobalt complexes6,7). As for the CE, its critical role is to collect external electrons and reduce the oxidized redox couple, i.e. catalyzing the triiodide reduction reaction (I3− + 2e- → 3I−). To date, the most commonly used CE is platinized FTO glass with a very high activity towards triiodide reduction. However, the well-known low abundance and high cost of Pt element have seriously restricted the commercialization of DSSCs at large scales. Hence, extensive studies have been performed to replace Pt with other cheaper and abundant substitutes, including carbonaceous materials,8-12 conductive polymers,13-15 inorganic compounds such as sulfides,16-20 nitrides,21-23 carbides,24,25 selenides,26,27 and oxides28,29. Moreover, it is interesting to note that among these active inorganics the metal ions are found to be usually located in some metals (e.g. Fe, Co, Ni, Mo and W) with their valence states varying with the non-metal ligands (i.e. S, N, C, Se and O). Apparently, different combinations of metals and non-metal ligands result in different catalytic activity. Besides, different exposed facets,30 external morphology19 and deposition substrates31 have also demonstrated their significant impacts on catalytic activity. Nevertheless, the fundamental understanding on the whole is very rare. It would be imperative to comprehend the activity variation through some intrinsic properties of a material. As reported in our previous study,28-30 the general mechanism of triiodide electroreduction (I3-(sol) +2e-→3I-(sol)) can be described as follows: I3−(sol) ↔ I2(sol) + I−(sol) (I) I2(sol) + 2* → 2I* (II) − I* + e → I (sol) (III) where * represents the free site on the electrode surface and sol indicates the acetonitrile solution. The solution reaction, I3-(sol) ↔ I2(sol) + I-(sol), has been verified to be usually fast and considered to be in equilibrium.32 Thus, the subsequent iodine reduction reaction (IRR, i.e. steps (II) and (III)) occurring at the liquid/solid interface would determine the overall kinetic activity. Importantly, our previous work has demonstrated that the adsorption energy of I atom (EadI) at the acetonitrile/electrode interface could serve as a good activity descriptor, and an I adsorption energy window from about 0.33 to 1.20 eV, within which good CE materials should locate, was suggested.28 This quantitative window has been well-confirmed and applied to rationally screening catalysts.25,28-30 Although it provides potential candidates with high activity, it is still insufficient to give a direct identification of how high the activity is for a given catalyst. This is because a quantitative establishment on the overall activity trend requires a complete kinetic analysis and in particular the generalization of the Brønsted-Evans-Polanyi (BEP) relation in triiodide electroreduction. However, the current BEP relation is known to be usually obtained for gas/solid reactions,33-35 and it is rarely reported in the electrochemical systems occurring at the liquid/solid interfaces, let alone the case of electro-reductive desorption with electrons involved. As a consequence, there are very few theoretical reports on the kinetic behaviour in such complicated systems, and the influence of electrochemical parameters such as external voltage, temperature and concentration on the general activity remains unclear. In this work, we tackled this problem and uncovered two new kinds of BEP relations for the key steps of triiodide electroreduction, i.e. I2 dissociation and I* desorption through one-electron reduction, at a number of acetonitrile/electrode interfaces. By further combining with a steady-state 2


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microkinetic model, we clearly identified a general activity trend of IRR which mainly varies with EadI. These results represent the first attempt to reveal the volcano-shaped activity trend as well as the rate-determining factor in triiodide electroreduction, and could guide to screen high-efficient non-platinum CE.

2 Computational Methods All the spin-polarized calculations were performed with the Perdew-Burke-Ernzerhof (PBE) functional using the VASP code.36,37 The project-augmented wave (PAW) method was used to represent the core-valence electron interaction. The valence electronic states were expanded in plane wave basis sets with energy cutoff at 450 eV. The occupancy of the one-electron states was calculated using the Gaussian smearing for non-metal compounds and Methfessol-Paxton smearing for Pt surfaces. The ionic degrees of freedom were relaxed using the BFGS minimization scheme until the Hellman-Feynman forces on each ion were less than 0.05 eV/Å. The transition states were searched using a constrained optimization scheme,38,39 and were verified when (i) all forces on atoms vanish; and (ii) the total energy is a maximum along the reaction coordination but a minimum with respect to the rest of the degrees of freedom. The force threshold for the transition state (TS) search was 0.05 eV/Å. The dipole correction was applied throughout the calculations to take the polarization effect into account. With respect to some specific oxides, such as MnO2, Co3O4 and CeO2, the on-site coulomb correction was used to describe the electronic and geometric structure, i.e. the so-called DFT + U method.40 The effective U value was set to 5 eV for Ce, 4 eV for Mn, and 2 eV for Co as suggested in other theoretical works.41-44 For the pseudopotential construction of Sn, Cr, Zr and Mo, the semi-core states are considered, including the 4d10, 3p6, 4s24p6 and 4p6 electrons into the valence states, respectively. In addition, it should be noted that in the optimization of α-Fe2O3 we tested the effect of spin state of 3d electrons in Fe3+, which showed that the high-spin antiferromagnetic arrangement is the most stable state and gives the lowest free energy.45 To calculate the adsorption energy of surface species and the corresponding reaction barrier in the realistic solution, several acetonitrile (CH3CN) layers were explicitly introduced and fully optimized in the surface slab with a density of 0.79 g/cm3 (see calculation details in supporting information and ref. 28, 30). The adsorption energy of I (EadI) is defined as: EadI = E(interface) + 1/2E(I2) – E(I/interface) (1) where E(interface), E(I2) and E(I/interface) are the energies of the liquid/electrode interface, I2 in the gas phase and I adsorbed on the acetonitrile/electrode interface, respectively. The larger EadI is, the more strongly the species I binds on surface. The Gibbs free energy change of IRR, ∆𝐺0 , is difficult to calculate directly with the involvement of electrons, and we achieved it by referencing to the standard hydrogen electrode (SHE) reaction. Namely, we calculated the ∆𝐺 ′ of the following reaction first:   I2(sol)  H2(gas)  2I(sol)  2H(aq)

(2)

and then derive ∆𝐺0 = ∆𝐺 ′ + 2|e|U, where U is the applied voltage relative to SHE. Regarding the calculation of ∆𝐺 ′ , it was indirectly obtained through thermodynamic cycle, and the details can be found in our previous work.28,30 3


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3 Results 3.1 Identification of the transition states at the liquid/solid interfaces 3.1.1 I2 dissociation To understand the trend of kinetic barriers for I2 dissociation (Eadis) and I* desorption resulting from one-electron reduction (Eades), many candidates including metal oxides, carbide, nitride and sulphide were considered, as shown in Table 1. For these materials, the commonly exposed surface of each one in nature was selected with coordinatively unsaturated metal sites exposed, which constitutes the main binding site for I adsorption. For example, the (110) and (012) surfaces were used to represent rutile and corundum oxide, respectively. As a start, the I2 dissociation step at these CH3CN/electrode interfaces was calculated. Figure 1 shows all the optimized TS structures with the corresponding barriers listed in Table 1. One can see from Figure 1 that all the reactions take place at the coordinatively unsaturated surface metal ions (Mcus) and the solvent molecules also hold a certain degree of surface coverage. For the TS of I2 dissociation, we find that on the inert surfaces with very weak EadI (< -0.2 eV), such as MnO2(110), SnO2(110) and La2O3(001), it usually takes more than two sites to split an I2 molecule with the I-I bond distance (dI-ITS) longer than 3.80 Å (2.68 Å for the bond length of gaseous I2 molecule), indicating their incapability in promoting I2 dissociation (the barrier Eadis > 1.40 eV). As EadI becomes stronger, e.g. on the surface of CeO2(110) or ZrO2(100), it changes to a two-site location with a shorter dI-ITS (see Figure 1d-f), corresponding to an evident decrease of the activation energy (Eadis < 0.80 eV). As EadI further increases (EadI > 0.42 eV), the I2 dissociation would turn into a barrierless process. Namely, I2 molecule can readily dissociate into two I* atoms upon adsorption at the interface.

Figure 1 Views of the optimized transition states of I2 dissociation with the elongated I-I bond length (Å) marked occurring at various liquid/solid interfaces. (a-f) correspond to the interface of MnO2(110),

4


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SnO2(110), La2O3(001), Al2O3(012), CeO2(110) and ZrO2(100), respectively. Red and brown balls indicate O and I, while blue, grey and while sticks represent N, C and H atom, respectively.

3.1.2 One-electron reduction of I* and its desorption After I2 dissociation, it forms two I* atoms sitting on the top of surface Mcus, which could proceed the subsequent one-electron reduction and desorb into solution to form solvated I-. The desorption TS structures were examined as illustrated in Figure 2 (except for materials that we have reported before28-30), and all the barriers were summarized in Table 1. From Figure 2, one can see that I* is always surrounded by CH3CN in a stabilized structure above the surface Mcus owing to the Coulomb attraction between I- and H+ and the repulsion from the N-end of the surface-adsorbed CH3CN molecule. The bond length of I-Mcus at the TS (dI-MTS) is always longer than 4 Å, in contrast to ~2.70 Å at the adsorption states. Along with the increase of EadI, dI-MTS generally becomes longer and reveals the growing difficulty in I* desorption, which is contrary to the case of I2 dissociation. Specifically, we notice that at the CH3CN/CeO2(110) interface with a very weak EadI of 0.08 eV, Eades is calculated to be as small as 0.03 eV. Therefore, it could be expected that for materials with very weak EadI, e.g. Al2O3(012), La2O3(001) and SnO2(110), Eades would be very close to zero, while Eadis would become so large to block the I2 dissociation. Hence, it is clear that the conflicting demand on EadI between I2 dissociation and I* desorption would finally give rise to an ideal EadI for IRR where Eades and Eadis compromise, and we will discuss it later.

Figure 2 The optimized transition states of I* desorption through one-electron reduction at the liquid/solid interfaces, in which the optimized I-Mcus bond distances (Å) are also shown. (a-h) correspond to the interface of CeO2(110), ZrO2(100), NiS(100), Co3O4(110), Fe2N(001), MoC(010), WC(010) and Cr2O3(012), respectively.

In addition, we also considered the effect of electrode voltage on the I* desorption 5


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process (written as I* + e- → I-(sol)). Previously, we have systematically studied Pt electrodes (Pt(111), Pt(411) and Pt(100)), showing the variations of both ΔH and Eades as electrode voltage changes28-30. However, herein due to the large number of candidates and the uncertainty of their respective work voltages, it would be unpractical to study the voltage effect one by one. Instead, we introduced a common parameter in electrochemistry, i.e. the transfer coefficient (α) which describes the fraction of potential change for affecting the energy barrier, to investigate the voltage effect on Ea as well as the reaction activity collectively. In other words, when an external voltage Uext is applied under realistic electrochemical conditions, the barrier Ea = Ea0 + αnFU for a cathodic reduction reaction (O + ne- → R) and ΔH can be corrected by |e|U, in which Ea0 is the corresponding barrier in the neutral system under open-circuit conditions (Uext = 0 V). Table 1 Calculated adsorption energies of I atom (EadI) and reaction barriers, as well as the corresponding bond distances (dI-ITS for I2 dissociation; dI-MTS for I* desorption) on the considered materials. All the results are calculated with explicit solvent molecules at the interfaces. The units of energy and bond length are eV and Å, respectively.

Surface

EadI

Eadis

Eades

dI-ITS

dI-MTS

MnO2(110) SnO2(110) La2O3(001) Al2O3(012) CeO2(110) ZrO2(100) Fe2O3(104) Pt(111) Fe2O3(012) NiS(100) RuO2(110) Co3O4(110) Fe2N(001) MoC(010) WC(010) Pt(411) Pt(100) Cr2O3(012)

-0.47 -0.39 -0.22 -0.10 0.08 0.22 0.42 0.52 0.54 0.58 0.59 0.71 0.77 0.91 1.02 1.38 1.56 1.61

2.01 2.00 1.46 1.36 0.73 0.54 0.03 0 0 / 0 0 / / / 0 0 /

/ / / / 0.03 0.14 0.08 0.38 0.18 0.23 0.30 0.31 0.32 0.52 0.59 0.63 0.74 0.73

4.25 3.86 3.80 3.48 3.76 3.40 / / / / / / / / / / / /

/ / / / 4.19 4.04 4.16 4.20 4.12 4.12 4.16 4.07 4.19 4.27 4.28 4.48 4.49 4.36

3.2 BEP relations in triiodide reduction reaction The electronic structure (e.g. the Fermi level, d-band centre) is usually useful to understand the activity tendency, and thus we investigated the possible trends of the Fermi levels, work functions and d-band centres of many materials. It was found that the correlation between the electronic properties and EadI or reaction barriers is inadequate. However, the correlation between EadI and reaction barriers is very good (R2 ≥ 0.9) as shown in Figure 3. Therefore, we focused mainly on the activity descriptor of EadI to reveal the general activity trend in the I3- reduction hereinafter. 6


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3.2.1 I2 dissociation After having calculated Eadis and Eades at the corresponding acetonitrile/electrode interfaces, we correlate them with EadI to examine their variation trends. Figure 3 shows the correlation of Eadis and Eades with respect to EadI in red and black lines respectively. From the red line, one can see that Eadis holds a very good linear relationship with EadI in a sharp negative slope (Eadis = -2.32*EadI +1.00), which is a typical BEP relation33-35,46,47 when substituting EadI with the enthalpy change (ΔH), namely Eadis =1.16*ΔH +1.00. The BEP slope that is close to unity indicates that the TS always has a very FS-like (FS is short for the final state) structure as has been discussed by Nørskov and coworkers33,46 and us48,49, being in accordance with the long dI-ITS shown in Figure 1. It is clear that as EadI goes up, I2 molecule would get increasingly activated on the surface and tends to break its I-I bond more and more easily as a result of the compensation from I-Mcus bond formation. From Figure 3, we can see that as EadI is increased to 0.42 eV, the barrier Eadis would approach zero, indicating that the I2 dissociation would occur spontaneously. For clarity, it is worth noting that Eadis reported here was calculated relative to the state of solvated I2 in acetonitrile at 300 K (experimental condition). By contrast, EadI was calculated by reference to ½ I2 in the gas phase at 0 K, and there thus exists an energy difference of -0.66 eV between these two reference states for Eadis and EadI, as has been evidenced in our previous work.28,30 Therefore, at the point of EadI = 0, Eadis still remains as high as 1 eV, which consists of 0.66 eV originating from the reference energy difference; only until at the turning-point of 0.42 eV (on Fe2O3 (104) surface), I2 molecule can readily dissociate into two I* upon adsorption without an obvious barrier (~0.03 eV). Furthermore, we checked other surfaces such as Pt(111), Fe2O3(012), RuO2(110), Co3O4(110) and Pt(100), and confirmed the barrierless dissociation result which begins from the turning-point. It is consistent with the results of Vojvodic et al., which showed that the barrierless dissociation of I2 totally dominates on reactive materials.46 It should also be noted that Eadis could not keep on increasing toward the negative direction (inert surface), and the maximum barrier would be around 2.28 eV, corresponding to the bond energy of I2 molecule. In addition, being different with the usually reported BEP relations, the relation discovered here is found on the oxide surfaces instead of pure metal.33-35 Generally, it is believed that BEP exists on a series of surfaces with similar atomic configuration. Here considering that it only takes two off-top sites of surface Mcus to accomplish I2 dissociation, most of the oxides possess similar adsorption structures on the surfaces, resulting in the good linear correlation. This finding broadens the understanding on the application scope of BEP relations, and could facilitate deep analyses on more complex systems.

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Figure 3 Illustration of calculated Eadis of I2 dissociation (red dots) and Eades for I* desorption (black squares) in neutral system (Uext = 0 V) as a function of EadI.

3.2.2 I* desorption As shown in the black line in Figure 3, there exists a good linear relationship between des Ea and EadI (Eades = 0.48*EadI - 0.01) by fitting the data from 14 different interfaces. It indicates that, as I* binds to the surface more and more strongly, it would be more and more difficult to desorb into the solution through the one-electron reduction. However, it is worth noting that the slope is moderate (around 0.48), which implies that des Ea could be still surmountable at room temperature under open-circuit conditions (Uext = 0 V) even for a large value of EadI. For instance, EadI on Pt (100) reaches as large as 1.56 eV, but the Pt electrode assembled by (100)-bounded nanocubes still yields a passable efficiency (5.66%) compared with the superior Pt(111) nanooctahedrons (6.91%).30 Another interesting point is that Eades would reach zero near the point of EadI = 0, and thus for the case of weak adsorption (EadI < 0), we treated Eades to be zero at Uext = 0 V during the following micro-kinetic analysis. 3.3 The volcano-shaped activity trend from microkinetic analysis After having obtained the basic BEP relations for I2 dissociation and I* desorption process, we are in a position to evaluate the whole activity trend, aiming to locate the optimum activity. By applying the transition state theory, we can write the rate constant k for each elementary step in IRR (the step II and III in triiodide reduction). Then, following the De Donder relations50,51, the net rate of each step can be written as follows: 𝑟2 = 𝑘2 ∗ 𝐶𝐼2 ∗ 𝜃 2 ∗ (1 − 𝑍2 ); (3) 𝑟3 = 𝑘3 ∗ 𝜃𝐼 ∗ (1 − 𝑍3 ); (4) where θ and θI are the coverage of free sites and adsorbed I* species on the surface, respectively, and Zi is the reversibility of step i (𝑍𝑖 = 𝐽𝑖 /𝐾𝑖𝑒𝑞 ), in which Ji is the concentration 8


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quotient while Kieq is the equilibrium constant determined by the standard Gibbs free energy change (∆𝐺𝑖ɵ ), 𝐾𝑖𝑒𝑞 = exp(−∆𝐺𝑖ɵ /𝑅𝑇). For an irreversible step, Z always approaches zero; while for the quasi-equilibrated one, Z approaches the unity. Under the steady state condition (r=r2=1/2r3), we can solve the kinetic equation together with the condition of θ + θI = 1. Furthermore, the obtained reaction rate (r) can be converted into a common electrochemical parameter, i.e. the current density (i), based on i=nFr/(NAS) (5) where F and NA is the Faraday and Avogadro constant, respectively, and S is the active surface area of the electrode. With respect to the reaction barrier under realistic conditions with external voltage exerted, it has been reported by Fang et al.52 that the surface reaction with a Langmuir-Hinshelwood (LH) mechanism (in the case of step II) is usually insensitive to the potential change (α < 0.1); while reactions with an Eley-Rideal-like (ER-like) mechanism are always strongly dependent on the voltage with a large α usually being around 0.5 (in the case of step III). Therefore, considering the variation of their corresponding working voltages for each material as mentioned above, we applied uniformly an external voltage Uext as 0.54 V, which is the equilibrium voltage (Ueq) of I3−/I− redox couple in solution, and set α = 0 for step II (LH mechanism) and α = 0, 0.5, 1 for step III (ER-like mechanism) to investigate the influence of external voltages. Finally, by utilizing those electrochemical parameters and experimental conditions (CI2=0.03 mol/L; CI-=0.6 mol/L; T=300 K), we can obtain a theoretical activity curve as a function of EadI as shown in Figure 4.

Figure 4 Calculated volcano curves for IRR as a function of EadI under different external voltage Uext (dash: under open-circuit condition, Uext = 0 V; solid: 0.54 V), in which three different transfer coefficients for the I* desorption step are considered (blue: 0; green: 0.5; yellow: 1).

As shown in Figure 4, being different from the common ones, the volcano curves obtained here are composed of few sections with different gradients, which are decided by the behaviours of Eadis and Eades as EadI increases (see Figure 3). Generally, starting from the very 9


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weak EadI, the current rises significantly at the beginning, which is benefited from the sharply decreased Eadis, and it gradually reaches at the maximum at EadI = 0.43 eV. Then, it starts to decline slowly firstly and decreases sharply as EadI continues to increase. The dependence of the volcano shape on the external voltage can be seen from the two blue lines in Figure 4; when Uext is increased from 0 (open-circuit) to 0.54 V, the right branch of the curve shifts parallelly to the left while keeping its middle and left section intact. This is mainly owing to the fact that the I* desorption process becomes different in terms of both kinetics and thermodynamics as a result of the applied voltage. Another interesting result is the effect of transfer coefficient (α), revealing that the top of the volcano curve moves downward and stretches to both the hillsides as α increases from 0 to 1, which can be rationalized by the increased barrier (Ea = Ea0 + αnFU) but unchanged slope of the I* desorption BEP line. Meanwhile, two outermost branches both at the right and left sides (hillsides) keep unchanged, indicating that in these two regions the activities are mainly dependent on I2 dissociation and irrelevant to I* desorption, while the middle part is mainly related to the I* desorption process. Importantly, the peak of volcano curve almost keeps invariant at EadI = 0.43 eV with different α and Uext, although the general shape of the volcano changes considerably. Moreover, it is noteworthy that, for the strongly bound diatomic molecules (such as N2, CO, NO and O2), Nørskov et al.35 has reported that the optimal catalysts usually hold a dissociative chemisorption energy in the range of 1 to 2 eV. Here in the case of I2 with a smaller bond energy of 2.28 eV, the activation of I-I bond would naturally be much easier, and thus it is reasonable that the volcano peak moves towards more noble direction (small dissociative chemisorption energy) at 0.86 eV. In general, among the four representative simulation conditions in Figure 4, the more realistic one is shown in green under the condition of Uext = 0.54 V, α = 0.5. One can see that the ideal catalysts should hold an EadI in the range of 0.3 - 0.6 eV with the volcano peak at 0.43 eV, which enables to rationally screen the efficient electrode materials. For example, α-Fe2O3 with (104) and (012) exposed possesses an EadI of 0.42 and 0.54 eV, respectively, which thus can be expected to give an intrinsically excellent catalytic performance, even better than Pt(111). Our experiment confirmed the high activity of Fe2O3 electrode, which shows a smaller charge-transfer resistance relative to Pt (Rct; 2.3 vs. 3.4 Ω).28 However, it is worth discussing that, in addition to the kinetic activity, the electrode resistance also plays a role in determining the overall efficiency. α-Fe2O3 possesses a larger resistance compared with Pt (Rs; 15.8 vs. 10.5 Ω), resulting in slightly lower overall efficiency than Pt (6.96% vs. 7.32%).28 These results indicate the possible disparities between experimentally detected activities and theoretical one, showing the incompleteness of theoretical estimation which can be of course improved in the future. 3.4 Kinetic analyses on surface coverage and reversibility To shed light on the microscopic picture of IRR and its activity trend as a function of EadI, the following key questions are required to be answered: why is there a valcano-shaped activity trend in IRR? What is the rate-determining step? How does surface species vary with EadI? Taking the most realistic condition (Uext = 0.54 V, α = 0.5) as an example, we did further kinetic analyses in terms of θ, θI, Z2, Z3. Firstly, as shown in Figure 5, the coverage of surface free sites (θ) generally decreases 10


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from the nearly full-coverage on very noble catalysts to a very low coverage (~ 10-10) as EadI increases. On the contrary, θI increases from very low coverage ( 0.9 eV. However, it can be rationalized as follows: too large EadI would result in I* species being overwhelmingly accumulated, leading to the poison of the catalyst and the absence of active sites reversely makes I2 dissociation hardly proceed.

4 General Discussions 4.1 Effects of different experimental conditions In the last section, we have uncovered the volcano-shaped activity and provided an understanding of the trends of both the surface species and rate-determining steps as a function of EadI at a typical experimental condition (CI2=0.03 mol/L; CI-=0.6 mol/L; T=300 K). But what would happen if the experimental conditions were changed? How does one optimize effectively the condition for a given catalyst to make it work at the top capacity? To address these issues, we studied the volcano-shaped activity under different reactant concentration (CI2) and temperature (T) as shown in Figure 6, since these are two common experimental parameters. Firstly, the CI2 effect is shown in Figure 6 (the solid lines). It demonstrates that the whole activities are generally improved as CI2 increases at both the left and right sides, resulting from the fact that I2 dissociation is the main kinetically relevant step (see Equation 6). While in the range from 0.5 to 0.9 eV, the activities almost keep unchanged even though there is an increase in CI2 by the order of 103, owing to that the rate-determining step is the I* desorption in this region rather than I2 dissociation (see Equation 7). Besides, the peak position also shifts slightly towards the left in proportion to the increase in concentration. To understand these results, a simple kinetic analysis was carried out as follows: (i) On the left (right) side of volcano curve, I2 dissociation (I2 + 2* →2I*) is rate-determining as shown above, and I* desorption is in equilibrium. Then the total reaction rate can be derived as Equation 6, indicating the rate being directly proportional with CI2. 𝑟=

𝑘2 𝐶𝐼2 (1−𝑍𝑡𝑜𝑡 ) (1+𝐶𝐼− /𝐾3𝑒𝑞

)2

≈{

𝑘2 𝐶𝐼2 (1 − 𝑍𝑡𝑜𝑡 ) (on the left end, 𝐾3𝑒𝑞 is large) 2 𝑘2 𝐶𝐼2 (𝐾3𝑒𝑞 /𝐶𝐼− ) (1 − 𝑍𝑡𝑜𝑡 ) (on the right end, 𝐾3𝑒𝑞 is small)

(6)

(ii) In the middle, I* desorption (I* + e- → I−) is kinetically more relevant, corresponding to a total rate in Equation 7, which is thus irrelevant to CI2. 𝑟=

𝑘3 𝐶𝐼2 1/2 𝐾2𝑒𝑞 1/2 (1−𝑍𝑡𝑜𝑡 1/2 ) 1+𝐶𝐼2 1/2 𝐾2𝑒𝑞 1/2

≈ 𝑘3 (1 − 𝑍𝑡𝑜𝑡 1/2 )

(middle, 𝐾2𝑒𝑞 is large)

12


(7)

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The temperature effect is shown by the two blue lines in Figure 6. As illustrated by the dash line (T=350 K) in Figure 6, the higher the temperature is, the faster the reaction rate would be. For the peak position, it moves towards the right as T increases, since the entropy effects make both the solvated states of I2 and I- more preferable, which hinders I2 dissociation but promotes I* desorption. In other words, it would result in a relative increase in the coverage of free sites on the surface, thus leaving more room for I* on the surface. In addition, it is interesting to note that T has a small influence on noble catalysts but a significant promotion on catalysts with strong EadI, being contrary with the CI2 effect. Overall, these results can provide us with some constructive guides on the optimization of experimental conditions for a good catalyst (0.3 < EadI < 0.6 eV): If the catalyst possesses a small EadI (< 0.4 eV), it would be better to enlarge CI2 as much as possible as long as I2 would not result in the corrosion of electrode. On the other hand, if it possesses a strong EadI, there is no need to improve CI2, and a typical CI2=0.03 mol/L would be competent enough, while increasing temperature would be a more effective way to enhance the activity.

Figure 6 Variation of volcano curves under different experimental conditions as a function of EadI at Uext = 0.54 V. The influence of CI2 is shown as solid lines (green: 3 mol/L, blue: 0.03 mol/L, red: 0.003 mol/L) at 300 K. The influence of temperature is shown in blue lines (solid: 300K, dash: 350 K).

4.2 General remarks In above, we have applied a two-step model, I2 dissociation and I* desorption, to solve the kinetic equation and understand the activity behaviour qualitatively. However, the I2 dissociation could actually contain two steps on some inert surfaces; I2 adsorption and dissociation, but we treated them as a combined one-step dissociation to facilitate the kinetic analysis. Thus, the coverage of I2 molecule was omitted. Here, taking the I2 adsorption step into consideration, we estimate the surface I2 concentration to be as low as 10-7 in magnitude on the whole. Such a low coverage can be ascribed to the fact that I2 molecules tend to either dissociate easily even at a small EadI (Figure 3) or desorb from the surface. Therefore, it is reasonably believed that the above simplification would hardly affect the activity trend. 13


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Furthermore, it should be mentioned that the coverage effect is not taken in consideration in the quantitative kinetic framework. However, it can be qualitatively understood that it is usually negligible on the surface with weak adsorption towards the intermediates (low coverage), but tends to reduce the bonding strength by the adsorbate-adsorbate interactions at high coverage, which would result in the volcano-peak being somewhat flat in the middle and shifting towards the right-side. Specifically, in the case of IRR, within the active range the rate-determining step is always the I* desorption, and thus the coverage effect would even help to lower the barrier and improve the activity. Lausche et al.53 reported that the coverage effect indeed has a significant influence on the turnover frequency in CO methanation for the material with a high coverage of reactants, and the change in rate can be as large as several orders of magnitude compared with that in the absence of consideration of the adsorbate-adsorbate interactions. Finally, it is worth pointing out that, once we obtain the optimal EadI or adsorption window, we can focus our attention to increase or decrease the adsorption energy of the key intermediate (activity descriptor) by means of changing the ligand elements X (O, C, S, N …), and/or altering the coordination number (MX, M2X3, MX2, MX3 …) and/or even substituting (doping) the metal ions. This strategy is also applicable to other heterogeneous catalysis beyond the scope of triiodide electroreduction, which would provide constructive guides for catalysts design and help to reduce trial-and-error experiments.

5 Conclusions In summary, extensive DFT calculations on some acetonitrile/electrode interfaces were conducted to understand the triiodide electroreduction process, and two new BEP relations for the involved key steps, I2 dissociation and I* desorption through one-electron reduction, were identified. By applying a steady-state microkinetic model, we further described a volcano-shaped activity curve on IRR for the first time, and discussed its kinetic mechanisms in detail. It was found that the optimal catalyst should possess an EadI within the range of 0.3-0.6 eV with the peak at the strength of 0.43 eV, where the surface coverages of free sites and iodine atoms are equal. The rate-determining step within the active range is always the I* desorption, thus underlining that it would be more effective to reasonably reduce the I* desorption barrier rather than I2 dissociation. Moreover, the volcano curves under different experimental conditions were also simulated and discussed, which may help to further optimize the whole catalytic performance. Acknowledgements This work was supported by the Science Fund of Creative Research Group (21421004), National Natural Science Foundation of China (21333003, 21303052), Shanghai Rising-Star Program (14QA1401100) and ChenGuang project (13CG24), the Commission of Science and Technology of Shanghai Municipality (12ZR1442600), Fundamental Research Funds for the Central Universities. D. W. thanks the Chinese Scholarship Council for the abroad living support. Supporting Information 14


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The influence of different solvent configurations on the activity descriptor of EadI. This material is available free of charge via the Internet at http://pubs.acs.org.

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