Quantum-Chemical Modeling of the Catalytic Activity of Graphene Doped with Metal Phthalocyanines in ORR

Abstract

The active centers of carbon catalysts doped with cobalt, nickel, copper, manganese, zinc, and chromium were modeled by density functional theory methods. Likewise, the thermodynamics of the oxygen reduction reaction (ORR) on model catalysts were determined. The features of the chemical properties of chromium-containing material, namely its spontaneous oxidation into the hydroxo form, were revealed. In addition, it was established that among the studied catalysts, graphene doped with cobalt showed the best properties.

1. Introduction

In today′s world, mankind is faced with a dilemma: the need for electricity is increasing rapidly and the world’s main present natural energy sources are non-renewable. The efficiency of solar panels and wind turbines is extremely dependent on weather and climatic conditions. Now more than ever, the search for alternative sources of electricity is urgent. Fuel cells seem to be the ideal solution to the energy shortage and tense environmental situation: fuel cells are quiet, highly efficient, and environmentally friendly. However, fuel cells have a disadvantage that has prevented them from becoming widespread—the use of expensive platinum as a catalyst. Finding an alternative to the platinum catalyst will significantly reduce the cost of fuel cells, allowing them to be used more widely.

At the moment, the search for non-platinum catalysts is an urgent aim, and carbon catalysts have shown the greatest promise [1,2,3,4,5]. Theoretical methods, such as quantum chemical modeling using density functional theory (DFT), are used to speed up the process of finding the optimal material [6,7,8]. This approach makes it possible to determine the adsorption properties of the catalyst, as well as the effect of the composition and structure of the material on the kinetics of the catalytic process, and to compare different catalytic materials without resorting to experimental analysis [9,10,11].

Examples of materials described both theoretically and practically are metal-free catalysts based on carbon materials doped with nitrogen, sulfur, and other non-metals. The structure of the carbon framework can be different: carbon nanofibers [12], graphene [13], carbon dots [14], or a nanoporous carbon framework [15] obtained using ionic liquid as a precursor. Metal-containing catalysts with a complex active center structure [16] or multicomponent oxide catalysts [17] are also possible. Such a wide range of possible catalysts allows the material properties to be varied while searching for the most effective catalyst.

In this paper, using quantum-chemical modeling, the properties of carbon materials doped with nitrogen and cobalt, nickel, copper, chromium, manganese, and zinc in ORR, taking into account the solvent and pH of the solution, are investigated.

2. Results and Discussions

Calculations of the optimized structures of intermediates in the ORR (Figure 1) show that oxygen and intermediates during adsorption are localized on the metal atom embedded in the graphene structure.

As a result of the simulation, the ORR energy profiles were obtained for the studied carbon materials, which are presented later in this article.

The energy profile of ORR on CrN₄ (Figure 2) is characterized by the presence of a minimum, which corresponds to the adsorbed hydroxo radical. It can be concluded that such material will spontaneously oxidize to the form Cr(OH)N₄, which is confirmed by the presence of such properties as those in chromium phthalocyanine [18].

Thus, the Cr(OH)N₄ hydroxo form was chosen as the active center of the chromium-containing catalyst, which exhibits catalytic properties. An example of a complex of a catalyst and an intermediate is shown in Figure 3.

The energy profiles on all studied catalysts gradually decrease, which indicates that the choice of the ORR mechanism was made correctly (Figure 4).

According to the calculations presented in

Table 1. Energies of molecular oxygen adsorption.

Catalyst	CuN4	NiN4	MnN4	CoN4	ZnN4	Cr(OH)N4
Gads, eV	0.15	0.23	−0.21	0.12	−0.43	−0.08
dMe-O, Å	2.17	1.94	1.87	2.07	1.99	2.01
dO-O, Å	1.31	1.32	1.32	1.33	1.34	1.32

, ZnN₄ exhibits the highest affinity for oxygen. Moreover, for the CoN₄, CuN₄, and NiN₄ catalysts, an increase in the energy of the system is observed. This suggests that, on these catalysts, energy is spent for adsorption rather than being released, which agrees with the results in [19].

The greatest elongation of the O–O bond during the adsorption of an oxygen molecule occurred on CoN₄ and ZnN₄.

Considering adsorption at individual stages (

Table 2. Relative energies of adsorption intermediates.

Catalyst	CuN4	NiN4	MnN4	CoN4	ZnN4	Cr(OH)N4
Gads OOH, eV	−0.37	0.01	−1.04	−0.60	−1.24	−0.79
Gads O, eV	−1.52	−1.89	−3.58	−3.12	−2.39	−2.74
Gads OH, eV	−1.53	−1.09	−2.30	−1.81	−2.52	−2.02

), it is easy to see that OOH adsorption is characterized by relatively low energy; oxygen atom and hydroxo radical show the highest affinity to the catalyst. The low adsorption energy of the peroxide radical can lead to an increase in the probability of the process proceeding via the undesirable 2-electron mechanism.

Strong adsorption of intermediates can also adversely affect ORR. The energies of each of the stages and overpotential are shown in

Table 3. Free energy release on the elementary reaction stages of ORR (eV).

Catalyst	CuN4	NiN4	MnN4	CoN4	ZnN4	Cr(OH)N4
O2→OOH	0.48	0.18	0.80	0.68	0.77	0.67
OOH→O	1.08	1.83	2.47	2.45	1.08	1.88
O→OH	2.26	1.44	0.96	0.93	2.37	1.52
OH→OH−	1.12	1.57	0.36	0.85	0.14	0.63
Overpotential, V	0.72	1.02	0.84	0.52	1.06	0.56

.

The efficiency of the process is determined by the stage with the least energy release, determining the overpotential on the catalyst, which is calculated by Formula (5). The lower the overpotential, the closer the catalyst properties are to ideal. The catalysts containing cobalt and chrome are characterized by the lowest overpotential (Figure 5). ZnN₄ and MnN₄, which showed the highest affinity for adsorbates, turned out to be inefficient due to the low energy release at the final ORR stage.

The energy profile of the ORR, taking into account the external voltage (U = 1.20 V), changes strongly with a change in the metal in the catalyst structure (Figure 6). Catalysts that include cobalt and chrome are closest to the ideal “zero-point” line.

Separately, it is worth mentioning that cobalt-containing materials are often the subject of practical research [20,21]. On the basis of calculations [22], cobalt is one of the most effective catalysts, second only to iridium and rhodium, which are less promising for commercial use due to their high price.

3. Model and Calculation Methods

Model structures were optimized and energies were calculated using the Gaussian 09 program [23]. The initial model structures and input files were created with the GaussView 6 program, and visualization was performed with the ChemCraft 1.8 program. Modeling was performed using the density functional theory (DFT) method, the B3LYP functional [24,25], and the 6–31G* basis set, which is consistent with previous studies [26]. The influence of the solvent (water) was taken into account in the self-consistent reaction field (SCRF) model [19,27].

The model structure can be described as a metal atom surrounded by four nitrogen atoms (MeN4; Me-Co, Cu, Ni, Cr, Mn, Zn) embedded in the graphene structure represented by 10 aromatic rings (Figure 7). Such porphyrin-like structures can be obtained in practice by using the phthalocyanines of the corresponding metals as the precursor [20].

ORR in an alkaline medium follows two paths (Figure 8)—with the participation of two electrons (path 1) or four electrons (paths 2 and 3)—according to the associative (path 2) and dissociative (path 3) mechanisms [28]. A four-electron associative mechanism was chosen as a model reaction, since it prevails for this type of active centers [21].

The following intermediates were chosen as key points for modeling [29]:

• O₂ + 2 H₂O
• O_2(ads) + 2 H₂O
• OOH_(ads) + H₂O + OH⁻
• O_(ads) + H₂O + 2 OH⁻
• OH_(ads) + 3 OH⁻
• 4 OH⁻

For calculations of energies and the construction of energy dependences, the system energy was taken as being equal to the Gibbs energy calculated as the electron energy corrected for the thermal free energy [23], as shown in the following equation:

G = E_ele + E_ZPE + E_tot + k_BT − TS_tot,

(1)

where E_ele is the total electronic and nuclear repulsion energy at 0 K, E_ZPE is the zero-point vibrational energy, E_tot is the total thermal internal energy, k_B is Boltzmann’s constant, S_tot is the system entropy, and T is the temperature (T = 298.15 K).

E_tot = E_t + E_r + E_v + E_e,

(2)

where E_t is the thermal internal energy due to translation, E_r is the internal energy due to rotational motion, E_v is the internal energy due to vibrational motion, and E_e is the internal energy due to electronic motion. The sum of the energies of the final optimized substances and the catalyst was taken as a zero level.

The adsorption energy was calculated using the following formula [30]:

G_ads = G_system − G_adsorbate − G_catalyst,

(3)

To determine the energy effects of the ongoing processes, the following elementary reactions occurring on the catalyst surface were identified [31]:

• O_2(ads) + H₂O + e⁻ → OOH_(ads) + OH⁻
• OOH_(ads) + e⁻ → O_(ads) + OH⁻
• O_(ads) + H₂O + e⁻ → OH_(ads) + OH⁻
• OH_(ads) + e⁻ → OH⁻

The above reactions correspond to the transitions of intermediates 2→3, 3→4, 4→5, and 5→6, respectively (see Table 1).

The free energy of elementary reactions (used to construct all graphs and tables) was calculated as follows taking into account the pH of the solution and the change in the electrode potential [32]:

ΔG_i = ΔG_s − eU + k_BT·ln10·pH,

(4)

where ΔG_s is the free energy change of the system, eU is the contribution of free energy due to a change in the values of the electrode potential U, and k_BT·ln10·pH is the contribution of free energy, taking into account the pH of the solution.

According to the calculation results, the total change in the free energy in the model reaction is 4.79 eV, which is close to the ideal total change in the Gibbs free energy ORR (4.92 eV) [32].

The overpotential (η_ORR) was calculated as follows [22]:

η_ORR = 1.20 − min{ΔG₁, ΔG₂, ΔG₃, ΔG₄},

(5)

where 1.20 is one-quarter of the total free energy change and ΔG_i is the free energy change for each stage.

4. Conclusions

Based on the work done, it can be concluded that carbon materials doped with nitrogen and metals can exhibit high catalytic activity, and the ability to vary the doping metal makes it possible to select the optimal catalyst composition. Quantum-chemical calculations have shown that the best indicators have cobalt and chromium-based catalysts, and chromium is in the oxidized OH-form.

The obtained data are consistent with the results of other theoretical and experimental studies, in particular, the low overpotential for cobalt-containing materials (~0.5 V).