Electrochemical chlorine evolution at rutile oxide (110) surfaces

Abstract

Based on density functional theory (DFT) calculations we study the electrochemical chlorine evolution reaction on rutile (110) oxide surfaces. First we construct the Pourbaix surface diagram for IrO₂ and RuO₂, and from this we find the chlorine evolution reaction intermediates and identify the lowest overpotential at which all elementary reaction steps in the chlorine evolution reaction are downhill in free energy. This condition is then used as a measure for catalytic activity. Linear scaling relations between the binding energies of the intermediates and the oxygen binding energies at cus-sites are established for MO₂ (M being Ir, Ru, Pt, Ti). The linear relations form the basis for constructing a generalized surface phase diagram where two parameters, the potential and the binding energy of oxygen, are needed to determine the surface composition. We calculate the catalytic activity as function of the oxygen binding energy, giving rise to a Sabatier volcano. By combining the surface phase diagram and the volcano describing the catalytic activity, we find that the reaction mechanism differs depending on catalyst material. The flexibility in reaction path means that the chlorine evolution activity is high for a wide range of oxygen binding energies. We find that the required overpotential for chlorine evolution is lower than the overpotential necessary for oxygen evolution.

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Introduction

Chlorine is an essential product for the global chemical industry – approximately 50% of the total turnover of the chemical industry depends on chlorine and caustic soda.¹ Chlorine production by chlor-alkali processes is one of the largest current technological applications of electrochemistry.²

The most active anode catalysts are usually based on RuO₂, however, RuO₂ is barely stable at the high potentials. Therefore RuO₂ is mixed with IrO₂ and additives such as TiO₂ and SnO₂, in order to improve the stability. The most commonly used electrocatalyst in industrial chlorine processes is the so-called Dimensionally Stable Anodes (DSA^®) which is named according to its improved lifetime compared with earlier used electrocatalysts.³

The equilibrium potential for Cl₂ evolution is 1.36 V at room temperature and standard conditions, which is slightly larger than the equilibrium potential for oxygen evolution, which is 1.23 V under the same conditions. This means that under chlorine evolution the simultaneous evolution of oxygen tends to occur as a parasitic side reaction, especially at high current densities. However, depending on the employed catalyst, oxygen evolution usually requires a somewhat larger overpotential than chlorine evolution. Unfortunately, RuO₂ is known to be a good catalyst for oxygen evolution as well as for chlorine evolution. This suggests an overlap of the activity volcanoes for the two reactions, and it has in fact been suggested that high catalytic activity for chlorine evolution is fundamentally linked with high oxygen evolution activity.²

Anodic chlorine evolution at oxide electrodes, and especially chlorine evolution on RuO₂, has been widely studied experimentally. A variety of different reaction mechanisms have been suggested based on indirect experimental quantities such as Tafel slopes and reaction orders.⁴ Among the possible reactions are the Volmer–Tafel reaction⁵

2* + 2Cl⁻ → 2Cl* + 2e⁻ → 2* + Cl₂ + 2e⁻, (1)

the Volmer–Heyvrosky reaction⁶

* +2Cl⁻ → Cl* + e⁻ + Cl⁻ → * +Cl₂ + 2e⁻, (2)

and the Khrishtalik reaction^7,8

* +2Cl⁻ → Cl* + e⁻ + Cl⁻ → (Cl*)⁺ + 2e⁻ + Cl⁻ → * + Cl₂ + 2e⁻. (3)

Here, * is an active site, which may be a surface oxygen or a metal atom.⁸

Very little is known about the reaction mechanism for chlorine evolution and about the atomic-scale structure of the surface, which depends strongly on catalyst material, electrostatic potential, and electrolyte. Recent developments within density functional theory analysis of electrochemical reactions have opened up the possibilities to study these reactions at the atomic scale.⁹ In particular, investigations of fuel cell catalysis such as oxygen reduction^10–13 and methanol oxidation^14–17 have deepened the insight into reaction mechanisms and surface composition under electrocatalytic reaction conditions. In a previous study the oxygen evolution reaction was investigated.¹⁸ There it was established that it is possible to describe the trends in the oxygen evolving activity using one single descriptor: the adsorption energy of O-atoms on the surfaces. RuO₂ was determined to be the most active rutile (110) surface, which is in good agreement with the experiments. Recently, theoretical studies have addressed heterogeneously catalyzed chlorine production by the so-called Deacon process.^19,20 However, in spite of the significant importance of electrochemical chlorine evolution, detailed electronic structure studies of this process have not appeared in the literature.

The aim of the present study is to analyze the surface structure and the activity trends underlying electrochemical chlorine evolution over rutile oxides. We start by analyzing IrO₂ and RuO₂ and we construct surface phase diagrams of the rutile (110) surfaces. This allows us to derive plausible mechanisms of the electrochemical chlorine evolution based on the reaction intermediates. We determine the lowest potential where Cl evolution is possible. Applying adsorption energy correlations, we can determine a reduced set of key energetic descriptors for the surface reactions involved, and generalize the analysis of IrO₂ and RuO₂ to a trend study where all the material dependence is included in a single descriptor, in this case the oxygen binding energy.

Methods

Calculation details

All electronic structure calculations have been carried out using density functional theory (DFT), with the RPBE functional for exchange and correlation.²¹ A periodically repeated 4-layer slab is chosen for the rutile (110) surfaces of RuO₂, IrO₂, TiO₂, and PtO₂. A vacuum layer of 16 Å is used to separate the slab from its periodically repeated images. We use a 2 × 1 surface unit cell and 4 × 4 × 1 Monkhorst–Pack type k-point sampling for slab calculations.²² The Kohn–Sham equations are solved using a plane wave basis with a cutoff of 350 eV for the eigenstates, and the densities are described using a cutoff corresponding to 500 eV. Vanderbilt ultrasoft pseudopotentials are used to deal with the ion cores.²³ A Fermi smearing of 0.1 eV is used, and energies are extrapolated to an electronic temperature of 0 K. The two bottom layers of the slab are fixed in their bulk structure, while the two top layers as well as possible adsorbates on it are relaxed until the sum of the absolute forces is less than 0.05 eV Å⁻¹. All calculations are performed using the Dacapo and ASE simulation package.²⁴

The surface of the unit cell contains two bridge and two cus sites, which means that the total coverage at each type site varies between 50% and 100%. We consider all relevant combinations of adsorption site and adsorbates. We find that adsorbates bind stronger at bridge sites than on cus sites and bridge sites are therefore occupied with oxygen for a large range of conditions. We therefore focus on cus sites throughout this paper. Mixed phases where different kinds of adsorbates are mutually present at the cus sites may exist, however, we find that they are in general only stable in very narrow windows of conditions.

We consider the adsorption of Cl^c, OH^c and O^c at a cus site, ^c, as well as the formation of O₂^cc and Cl(O^c)₂ adsorbed at two cus sites. The adsorption energy of chlorine is calculated using:

ΔE(Cl^c) = E(Cl^c) − E(^c) − ½E(Cl₂). (4)

For oxygen the energy is calculated relative to water

ΔE(O^c) = E(O^c) − E(^c) − E(H₂O) + E(H₂) (5)

and for ClO^c we apply the combined reference energy states from above

ΔE(ClO^c) = E(ClO^c) − E(^c) − ½E(Cl₂) − E(H₂O) + E(H₂). (6)

The adsorption energy of O₂^cc is defined with reference to water and hydrogen

ΔE (O₂^cc) = E(O₂^cc) − E(2^c) − 2E(H₂O) + 2E(H₂), (7)

and the adsorption energy of Cl(O^c)₂ is defined by

ΔE(Cl(O^c)₂) = E(Cl(O^c)₂) − E(2^c) − 2E(H₂O) + 2E(H₂). − ½E(Cl₂). (8)

The changes in the interaction between the liquid electrolyte and the surface upon adsorption of molecules are expected to be small as long as all hydrogen bonds are saturated. It has previously been shown that the O and OH adsorption energies at the cus site is changed by less than 0.05 eV by the presence of water at the surface on RuO₂.¹⁸ These interactions are therefore neglected in the present study.

Furthermore, the effect of the local field in the Helmholtz layer is not accounted for. Previously, it has been shown that for metal surfaces the effect of the field is negligible for adsorbates with small dipole moments perpendicular to the surface.²⁵ For RuO₂ we find that applying a homogeneous external field up to −0.53 V Å⁻¹, corresponding to a 1.6 V potential drop across a 3 Å thick Helmholtz layer, changes the relative adsorption energies by less than 0.11 eV.

The above simplifications are expected to be independent on the catalyst material, and therefore the resulting trends in catalytic activity should only be weakly affected by them. Variations in the adsorption energy of e.g. oxygen on the (110) surfaces are several eV between e.g. IrO₂ and TiO₂, while differences in water interaction and field effects are at least an order of magnitude smaller, and therefore vanish on the adsorption energy scale.

Surface phase diagram

There are four parameters determining the surface composition: the potential, the pH, the concentration of Cl⁻, and the electrode material. Only the latter is directly available in the simulations, and the other three parameters can be included analytically as described below. By applying the computational standard hydrogen electrode,⁹ it is possible to construct surface Pourbaix diagrams, and identify the most stable structure of the catalyst surface at a range of potentials and pH values.²⁶ At conditions where oxygen and chlorine evolution are negligible, the structure of the catalyst surface is determined by the equilibrium with water, protons and chloride ions. The oxidation of water may lead to the formation of OH^c or O^c through

H₂O(l) + ^c ⇌ HO^c + H⁺(aq) + e⁻ ⇌ O^c + 2H⁺(aq) + 2e⁻ (9)

Chloride ions may be exchanged with the surface via

Cl⁻(aq) + ^c ⇌ Cl^c + e⁻ (10)

ClO^c may be formed by first having O^c adsorbed on the surface followed by Cl⁻ adsorption on top of O^c. At potentials where evolution of Cl₂ or O₂ is appreciable, the surface structure is, however, controlled by the steady-state reaction.

At standard conditions (zero pH), H⁺(aq) + e⁻ is in equilibrium with ½H₂(g) at zero potential vs. the standard hydrogen electrode. At finite pH and potential the chemical potential of a proton and an electron is:

μ(H⁺(aq)) + μ(e⁻) = ½μ_H2(g) − eU_SHE + k_BT ln(10)pH. (11)

Similarly, Cl⁻(aq) is in equilibrium with ½Cl₂ + e⁻ under standard conditions at the potential of standard chlorine electrode,

Cl⁻(aq) ⇌ ½Cl₂ + e⁻ @U_SHE = 1.36 V. (12)

For an arbitrary potential and activity we therefore obtain

μ(Cl⁻(aq)) − μ(e⁻) = ½μ_Cl2(g) − e(U_SHE − 1.36 V) + k_BT lna_Cl−. (13)

Eqns (11) and (13) allow us to calculate the free energies of O^c, OH^c, Cl^c, and ClO^c adsorbed at a surface site in the electrochemical environment, based on calculations of the gas-phase molecules rather than the solvated ions.

The free energy of adsorption for a surface with an adsorbate at U_SHE = 0 V is given by

ΔG = ΔE + ΔZPE − TΔS + ΔG_ref, (14)

where ΔZPE is the change in zero point energy, T is the temperature, ΔS is the change in entropy upon absorption, and ΔE is the DFT-calculated adsorption energy. The zero-point energy contribution and the entropy for the adsorbed species are obtained from harmonic vibrational analysis and from tables of thermodynamic properties in the case of gas-phase species. The numbers for ΔZPE and −TΔS are listed in the ESI† (in Table S1). The correction ΔG_ref is 1.36 eV for Cl^c, ClO^c and Cl(O^c)₂ and zero for HO^c and O^c, and is related to the reversible potentials of the chlorine and hydrogen electrodes, respectively (see ESI for details†).

To obtain a measure of the activity we apply a simplified estimate: the chlorine evolution reaction is considered possible if and only if all the involved reaction steps are neutral or downhill in free energy. For a given reaction we can determine the lowest potential for which this is the case. Due to the significant challenges in treating reaction barriers for electrochemical processes, we do not include reaction barriers in the present study, and can therefore not directly compare e.g. the relative rates of the Volmer–Tafel and the Volmer–Heyvrosky reactions. Our approach can thus be viewed as a “lower-bound overpotential analysis” of the chlorine evolution activity. Since barriers of surface reactions²⁷ as well as barriers for proton transfer reactions²⁸ are known to often be linearly dependent on the reaction energy, we expect that the trends are conserved even when barriers are included.

Results and discussion

Surface phase diagram for IrO₂

Fig. 1 shows the interesting part of the phase diagram of IrO₂. At pH = 7 the surface sites are covered by OH and O at most potentials. At low potential, the surface is covered by OH groups (not shown). Increasing the potential oxidizes OH to O first at the bridge sites and then at the cus sites. Eventually formation of OOH becomes thermodynamically favored. When this happens, we expect oxygen evolution to become appreciable,¹⁸ and the surface structure is then determined by the kinetics of the steady-state evolution of oxygen. The formation of chlorine adsorbates directly at the cus sites requires pH < −3. Formation of Cl at the bridge sites requires even lower pH.

Fig. 1 Surface phase diagram for IrO₂ (110) in equilibrium with Cl⁻, H⁺ and H₂O at 298.15 K and a_Cl⁻ = 1. The regions where we expect chlorine or oxygen evolution to become significant have been marked. ^c and ^b denote cus site and bridge sites, respectively. The adsorbate phases are shown in the insets. Ir atoms are cyan, O atoms are red, H atoms are white and Cl atoms are green.

We would expect that for a good catalyst the formation of the Cl intermediate has ΔG ∼ 0 eV near 1.36 V and that there are free sites available for the formation of this intermediate. A mechanism involving Cl adsorbed directly at an Ir cation, does not fulfill any of these requirements. Instead we see from the phase diagram that a ClO^c intermediate is thermodynamically favored for U > 1.5 V in the pH range from 0 to 3.

This suggests the following sequence of intermediates on IrO₂

O^c + 2Cl⁻(aq) → ClO^c + Cl⁻(aq) + e⁻ → O^c + Cl₂(g) + 2e⁻ (15)

as both steps have |ΔG| = 0.14 eV at U = 1.36 V, and a significant amount of O^c sites exist at U > 1.36 V. The reaction is written here as a Volmer–Heyvrosky mechanism. However, as we only consider the stability of the adsorbed intermediate, we cannot compare the relative rates of the Tafel, Heyvrosky and Khrishtalik steps.

Surface phase diagram for RuO₂

The phase diagram for RuO₂ (110) turns out to be a bit more complicated (see Fig. 2). At pH = 7, the surface is dominated by species formed by the oxidation of water. At low potential, only the bridge sites are covered by OH. When the potential is increased, OH is formed at the cus sites, before OH is oxidized to O. We find that oxygen association at the cus sites

2O^c → O₂^cc (16)

is exothermic by 0.71 eV for the fully O-covered surface. The association barrier is only 0.18 eV, while desorption of O₂^cc is endothermic by 1.16 eV. O₂^cc will therefore most likely be present at the surface rather than O^c. Oxygen evolution could happen by further oxidation of the surface

H₂O + O₂^cc → O₂^c + ^c + H₂O → O₂^c + OH^c + H⁺ + e⁻. (17)

The stability of the O₂^c + OH^c structure relative to H₂O and H⁺ is indicated in Fig. 3. Desorption of O₂ from this surface has ΔG = −0.1 eV, however, so when O₂^c + OH^c starts to form, we expect oxygen evolution to become important. Additional barriers could exist, but we will not go further into the details of oxygen evolution.

Fig. 2 Surface phase diagram for RuO₂ (110) in equilibrium with Cl⁻, H⁺ and H₂O at 298.15 K and a_Cl⁻ = 1. The regions where we expect chlorine or oxygen evolution to become significant have been marked. ^c and ^b denote cus site and bridge sites, respectively.

Fig. 3 The adsorption energies of chlorine at cus (black): ΔE(Cl^c) = 0.59 ΔE(O^c) −2.26 eV (■ – vacant neighboring cus-sites, ▲ – Cl neighbor, ● – O neighbor), the adsorption energy of ClO (red) at cus: ΔE(ClO^c) = 0.52 ΔE(O^c) + 0.62 eV ( – vacant neighboring cus sites, – O neighbor, – average adsorption energy of ClO for the fully covered surface vs. average adsorption energy for O for fully covered surface), adsorption energy of Cl atop O at cus (blue): ΔE(Cl^c) = −0.48 ΔE(O^c) + 0.68 eV ( – Cl atop O vs. O with vacant neighboring cus sites, —Cl atop O vs. O with O neighbors, – Cl atop O vs. O with ClO neighbors, – average adsorption energy of Cl atop O for fully covered surface on vs. average adsorption energy of O for fully covered surface), the adsorption energy of O₂^ccvs. the average adsorption energy of O^c (yellow): ΔE(O₂^cc) = 0.94 ΔE(O^c) + 1.96 eV, and the adsorption energy of Cl(O^c)₂vs. the average adsorption energy of O^c (green): ΔE(Cl(O^c)₂ = 0.56 ΔE(O^c) + 2.51 eV. The mean absolute error of the fits are below 0.21 eV.

On RuO₂–chlorine species formed at pH < 1.3, however, oxygen is still the most stable adsorbate near U = 1.36 V. We find that the 2O^b + O^c + OCl^c intermediate is metastable relative to a 2O^b + Cl(O^c)₂ structure. The latter structure forms at U > 1.5 V, and we expect this to be the intermediate on RuO₂ (110).

O₂^cc + 2Cl⁻(aq) → Cl(O^c)₂ + Cl⁻(aq) + e⁻ → O^c + Cl₂(g) + 2e⁻. (18)

Adsorption of oxygen at the cus sites leads to an increase in the work function. This is consistent with negatively charged O₂^cc adsorbates. Subsequent formation of Cl(O^c)₂ leads to a decrease in the work function. This is consistent with Cl(O^c)₂ being more positively charged than O₂^cc, as has been suggested for the Khrishtalik mechanism.

We note in passing that the formation of O₂^cc and Cl(O^c)₂ depend on the presence of pairs of Ru cus sites at the surface, and it may not be relevant for alloys of e.g. TiO₂ and RuO₂. Neglecting the formation of O₂^cc and Cl(O^c)₂ and considering the IrO₂ reaction path eqn (15), we find that at U = 1.36 V each step has |ΔG| = 0.05–0.12 eV, depending on whether there is O^c or OCl^c adsorbed at the other cus site in the (2 × 1) unit cell. The trend in the change of the function upon formation of O^c and ClO^c is similar to the change of the work function upon formation of O₂^cc and Cl(O^c)₂.

Scaling relations. As mentioned above, it is possible to construct the surface phase diagram and reaction intermediate as function of pH, potential and the Cl⁻ concentration for a given material. The aim is now to generalize the analysis, not studying a single or a few oxide surfaces but rather determining a descriptor which will be a continuous material variable. The starting point of our analysis is to establish correlations between adsorption energies of intermediates on various (110) rutile oxide surfaces. Such relations can be useful in establishing simplified models describing the surface activity and composition, and can be suitable for subsequent screening purposes.²⁹ In Fig. 3 the adsorption energies of Cl^c and ClO^c as defined above are plotted against the O binding at the cus-site with the same environment at the surface. The plot clearly shows that the Cl and O adsorption energies are linearly correlated. Such linear energy relations between adsorption energies of hydrogenated species (CH_x, OH, SH, and NH_x) and the adsorption of the corresponding unhydrogenated atoms: (C, O, S, and N) have previously been shown for transition metals^30,31 and transition metal compounds including oxides.^18,32 The scaling of Cl with respect to O is very similar to the scaling of OH with respect to O. This reflects the fact that Cl has a valency of one like the oxygen atom in OH. ClO^c thus also scales as OH (and similar to HOO^c). The present results suggest that the oxygen adsorption energy is a general measure (a so-called “descriptor”) for the reactivity of oxides which has also been suggested for the case of cations in oxides by Pankratiev.³³

Adsorption of Cl atop O^c is determined by:

ΔE = E(ClO^c) − E(O^c) − ½E(Cl₂) = ΔE(ClO^c) − ΔE(O^c) (19)

The linear scaling relations established above makes it possible to analyze the reaction, not only for a specific metal oxide surface, but for potential metal oxide catalyst surfaces with continuously varying reactivity as measured by the adsorption energy of oxygen at the cus-site. The obtained reactivity curves will then be continuous in the oxygen adsorption energy, whereas specific oxides (e.g. RuO₂, IrO₂, PtO₂, and TiO₂) will show up as discrete points. The descriptor approach provides a fast overview of the “phase-space” of materials, but leaves the problem of how to find specific materials with the desired descriptor properties unanswered.

Generalized phase diagram

Since the binding energy of all intermediates at the cus sites scales directly with ΔE(O^c), it is possible to construct a generalized phase diagram showing the most stable phase at potential U as function of the material-dependent descriptor, ΔE(O^c).

We choose the electrolytic conditions such that when increasing the potential the most stable form of chlorine goes directly from Cl⁻ to Cl₂, which means that the pH value should be between −1 and 3. HCl(aq) is more stable than Cl⁻ at pH values below ∼−1, whereas HClO(aq) becomes stable at pH values higher than ∼3. We keep the electrolyte pH and Cl⁻ concentration fixed (pH = 0, a_Cl⁻ = 1) and investigate the surface phase diagram as a function of ΔE(O^c ) and potential. This approach is not a limitation of the method, since other electrolyte conditions can be treated just by changing the free energies accordingly.

This is shown in Fig. 4. In the limit of weak binding, oxygen association becomes exothermic and barrierless, so phases like ClO^c and Cl(O^c)₂ cannot form. From the linear relations we find that

O₂^cc → O₂(g) + 2^c (20)

has |ΔG| < 0 for ΔE(O^c) > 2.97 eV. We therefore chose to consider only OH^c and Cl^c for ΔE(O^c) > 2.97 eV. The free energies of OH^c and Cl^c are within 0.01–0.27 eV depending on the oxide, and we expect some coexistence in these regions of phase space. The range of ΔE(O^c) for some rutile oxides is seen in Fig. 5. For IrO₂ and RuO₂ the line at lowest ΔE(O^c) marks the adsorption energy with free neighboring cus sites, and the line at highest ΔE(O^c) marks the adsorption energy with O^c neighbors as calculated in the (2 × 1) unit cell. For PtO₂ and TiO₂ the line at weakest binding marks the binding energy at high O^c coverage. The variation in adsorption energy with coverage may be seen as an uncertainty arising from neglecting adsorbate–adsorbate interactions. For the considered oxides ΔE(O^c) is more affected by changing the oxide than changing the O^c coverage. The change of the most stable adsorbate when the potential is increased is qualitatively reproduced for RuO₂ and IrO₂.

Fig. 4 The most stable surface at pH = 0 and a_Cl⁻ = 1 as a function of potential, U, and the surface reactivity descriptor, ΔE(O^c). Metal ions are blue, O atoms red, hydrogen atoms white, and chlorine atoms are green. The regions in the figure are determined by the most stable surface configuration at the given potential. The phase borders are defined by the equilibrium point of the reactions. So for example, the border between the surface with O^c on the surface and the surface with ClO^c is defined by: O^c + Cl⁻(aq) ⇌ ClO^c + e⁻, ΔG(O^c) − ΔG(ClO^c) − eU_SHE = 0.

Fig. 5 Sabatier volcanoes (black dotted) for the considered reaction paths involving ClO^c, Cl(O^c)₂ and Cl^c (from left to right). The domains of the most stable surface structure as function of potential and oxygen binding energy is marked by gray. To be truly active, the intermediate should form at sites that are stable, as this makes the active site abundant. The solid black line shows the combined Sabatier volcano taking into account the stability of the active sites for a given mechanism. The Sabatier volcano for oxygen evolution¹⁸ (dashed blue line) shows OER always requires a higher potential than ClER. The activity of IrO₂ and RuO₂ are indicated with error bars derived from the variation of the O^c adsorption energy with varying O^c coverage.

Chlorine evolution activity. Firstly, we investigate the mechanism involving ClO^c

O^c + 2Cl⁻(aq) → ClO^c + Cl⁻(aq) + e⁻ → O^c + Cl₂(g) + 2e⁻. (21)

The potential at which all steps are neutral or downhill is:

U = U^eq + |ΔG(ClO^c) − ΔG(O^c)|/e, (22)

where U^eq is the equilibrium potential for chlorine evolution, in this case 1.36 V_SHE. Secondly, we investigate the mechanism involving Cl(O^c)₂:

O₂^cc + 2Cl⁻(aq) → Cl(O^c)₂ + Cl⁻(aq) + e⁻ → O^c + Cl₂(g) + 2e⁻. (23)

The potential at which all steps are neutral or downhill is:

U = U^eq + |ΔG(Cl(O^c)₂) − ΔG(O₂^cc)|/e. (24)

Thirdly we consider a mechanism involving Cl^c adsorbed directly at the metal cus site.

2Cl⁻(aq) + ^c → Cl⁻(aq) + Cl^c + e⁻ → Cl₂(g) + ^c + 2e⁻. (25)

This mechanism could be relevant for oxides with weaker adsorption energy at the cus site than RuO₂. However, our calculations suggest that this mechanism will be somewhat poisoned by OH^c formation at the cus sites. The potential where all steps are neutral or downhill is:

U = U^eq + |ΔG(Cl^c)|/e, (26)

RuO₂ and PtO₂ have |ΔG(Cl^c)| < 0.05 eV for high and low coverage of Cl^c, respectively, and could in principle work as good catalysts following this path; however, for RuO₂ we find the cus sites to be blocked by O₂^cc.

Since the different chlorine evolution potentials all are functions of ΔE(O^c), the potentials can be plotted directly on the phase diagram as shown in Fig. 5. This is similar to the Sabatier activity volcano curves known from heterogeneous catalysis.³⁴ To have the surface phase diagram in the same plot as the potential volcano directly assures that the activity volcano and the stable surface configuration agree. In other words, the different activity plots are relevant in different areas of the phase diagram, which are easily obtained by looking at Fig. 5. The thick black line marks the volcanoes, where the mechanism involves one of the most stable surfaces as an intermediate at the potential where all steps are neutral or downhill in free energy. We note that the surface composition during oxygen and chlorine evolution is not determined by equilibrium, but rather by a steady state. However, it seems plausible that the surface composition determined by equilibrium is one of the intermediates during the reaction. Fig. 5 also shows the activity of IrO₂ and RuO₂ based on O^c adsorption energy, with the error bars corresponding to the variation of the O^c adsorption energy when going from low to high O^c coverage.

If the accuracy of the linear relations are taken into account, the three investigated mechanisms form a single volcano with a broad plateau for ΔE(O^c) from 1.5 eV to 3.5 eV. Deviations from the linear relations could be important in this area. The agreement between the detailed analysis for IrO₂ and RuO₂ and the linear relations is therefore surprisingly good.

We find RuO₂ to be at the top of the volcano, whereas IrO₂ binds Cl on top O^c too weakly. TiO₂ does not show up on this activity scale. To our knowledge, only a few studies of the relative activity of rutile oxides have been carried out. Kuhn and Mortimer found IrO₂ and RuO₂ to have similar activities and to be more active than TiO₂. Mixtures of TiO₂ with Ir and Ru are more active than mixtures of TiO₂ with Cr, Co, or Pt.³⁵ Arikado et al. found the overpotential to increase in the order RuO₂ < Ti/PtO₂ < IrO₂.³⁶ Kelly et al. found the specific activity of Ru sites at Ru_xTi_1−xO₂ to be 45% more active than the Ir sites at Ir_xTi_1−xO₂. ^4,37 We note the discrepancy between the relative activity of RuO₂, IrO₂, and PtO₂ could be because different preparation methods may lead to different surface roughness factors and different concentrations of residual chlorine in thermally prepared oxides.⁴ The high activity of RuO₂ and IrO₂ relative to TiO₂ is in agreement with experiments. The rutile crystal structure of PtO₂ is not the most stable structure for PtO₂. It is however possible that some PtO₂ may be found in the rutile crystal phase if PtO₂ is mixed with oxides that do form the rutile crystal phase.

For comparison the potential for oxygen evolution is also shown in Fig. 5. It is seen that the potential for chlorine evolution is lower than the potential for oxygen evolution in spite of the lower equilibrium potential for oxygen evolution. This is the reason why electrochemical chlorine evolution is possible. It is also seen that a good oxygen evolution catalyst is also a good chlorine evolution catalyst. A comparison of the experimental potentials for OER and ClER has suggested that the selectivity of oxides does not depend appreciably on the catalyst material.² The potential of chlorine evolution changes with the potential of oxygen evolution with a slope of 1. Interestingly, one of the biggest outliers in the comparison above was a Pt/MnO₂ catalyst in acid where the potential for oxygen evolution was 0.3 eV higher than the potential of chlorine evolution. MnO₂ has an oxygen binding energy around 3.2 eV.³⁸ Based on Fig. 5 we would therefore expect the potential for chlorine evolution to be 0.4 V lower than the potential for oxygen evolution. We note that at other pH values the competition between chlorine and oxygen evolution will change; see Fig. 1 and Fig. 2.

Single-crystal experiments on RuO₂ show that the (110) surface is less active for Cl₂ evolution than the (101) and the (320) surfaces.^8,39 On polycrystalline RuO₂,⁴⁰ mixed RuO₂ + TiO₂,⁴¹ and RuO₂ (320)³⁹ the activity depends on pH, whereas the activity of RuO₂ (110) is independent on pH. The variation of activity with pH has been explained by the reaction

OH^c ⇌ O^c + H⁺(aq) + e⁻ (22)

determining the availability of active O^c sites.^7,39,40,42 This clearly requires O^c and OH^c to be near equilibrium at the reaction conditions for Cl₂ evolution. Since the bridge sites and cus-sites on the (110) surface of rutile oxides fulfill the same scaling relations between O and OH adsorption as perovskites,³² it is reasonable to assume the scaling relations are identical for all rutile oxide surfaces. In this case Fig. 5 applies for any rutile oxide surface, but with the oxygen adsorption energy depending on the specific surface facet. It has been argued that the binding energy on the stepped (320) surface is stronger than on the (110) surface.³⁹ If it is assumed the O₂^cc and Cl(O^c)₂ intermediates form at the (320) surface as well, Fig. 5 shows that as ΔE(O^c) is decreased from ca. 2.6 eV, the OH^c–O₂^cc equilibrium shifts to higher potential, which leads to increased blocking of the active sites by OH^c at a fixed overpotential. We note the overpotential at constant current is found to be 80 meV lower on the (320) surface than on the (110) surface,³⁹ and thus within the vertical error bars indicated in Fig. 5.

Conclusion

Based on DFT calculations, we have established linear scaling relations between Cl, ClO, and O adsorption energies at the cus-sites of rutile oxides. These linear energy relations enable the construction of a generalized surface phase diagram where potential and binding of oxygen are the descriptors determining the surface composition. By applying an electrochemical–thermodynamic approach we can make the first simple theoretical analysis of the electrocatalytic chlorine evolution reaction based on the free energies of the reaction intermediates. A lower-bound to the overpotential required for driving the reaction is thereby determined as function of the oxygen adsorption energy. This approach is an electrochemical analogue to the Sabatier analysis used in heterogeneous catalysis. Combining the surface phase diagram and the Sabatier volcano, one obtains a qualified suggestion for the surface structure during reaction condition. The analysis shows that ClO or Cl(O^c)₂ will form spontaneously on the cus-sites of IrO₂ and RuO₂ at the potential required for chlorine evolution. This indicates that the Cl₂ evolution occurs through these intermediates on IrO₂ and RuO₂. The potential necessary for Cl₂ evolution is always smaller than the potential for oxygen evolution for oxides exhibiting certain oxygen adsorption energies. A simple explanation is that the oxide evolution reaction involves three intermediates, and since the bindings of these intermediates to the catalyst are linearly related, there cannot be found a material that binds all of them to the surface with exactly the right binding strength. This is the reason for the high overpotential even at the top of the oxygen evolution volcano. The chlorine evolution reaction, on the other hand, involves only a single intermediate, and a material that optimizes this bond could in principle exist. This difference in overpotential is consistent with experiments² and rationalizes experimental findings.

Acknowledgements

The authors thank Prof. M. T. M. Koper for useful discussions. The Center for Atomic-scale Materials Design is funded by the Lundbeck Foundation. This work was supported by the Danish Center for Scientific Computing through Grant No. HDW-1103-06, the European Commission (Marie Curie Research Training Network MRTNCT-2006-032474) and The Danish Council for Strategic Research though the HyCycle Center (No. 2104-07-0041).

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Footnote

† Electronic supplementary information (ESI) available: Details regarding construction of the phase diagrams; Tables S1–S5, and linear relations. See DOI: 10.1039/b917459a

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