First-principles theoretical study on dry reforming of methane over perfect and boron-vacancy-containing h-BN sheet-supported Ni catalysts

Abstract

The entire reaction mechanism of the dry reforming of methane (DRM) as well as the competition processes over perfect and boron-vacancy-containing h-BN sheet-supported Ni-catalysts (labeled Ni₂/h-BN and Ni₂/h-BN-B–D) was studied by density functional theory calculations in the present work. Our calculation results show that B-defected h-BN strongly binds to the Ni₂ active sites (i.e., shows a strong metal-support interaction (SMSI) character) due to the better electron transfer between Ni₂ sites and the support. It was found that CH₄ is easier to activate than molecular CO₂. The activation of CO₂ occurs on the surface of Ni₂/h-BN through a direct route, whereas it is prone to follow a hydrogen-assisted path for Ni₂/h-BN-B–D via the COOH* intermediate, and the results show that the oxidant O* is easily formed on the surface of Ni₂/h-BN-B–D. It was also found that O* is the main oxidant agent for CH_x* intermediates through the CH₃–O oxidation mechanism. The reaction kinetic analysis indicated that the reverse water gas shift reaction (RWGS) is much more favorable than DRM (1.30 vs. 1.72 eV) over the Ni₂/h-BN system, whereas the RWGS and DRM are comparable on Ni₂/h-BN-B–D (1.77 vs. 1.66 eV), suggesting a high DRM activity on Ni₂/h-BN-B–D. Moreover, neither methane cracking nor a Boudouard reaction to form C* species is thermodynamically and kinetically unfavorable over Ni₂/h-BN-B–D; hence, Ni₂/h-BN-B–D has strong resistance to carbon deposition. Compared to Ni(111), both Ni₂/h-BN-B–D and Ni₂/h-BN show strong resistance to carbon deposition. Our results provide a further mechanistic understanding of the DRM over an Ni-based catalyst through the SMSI characteristic and the SMSI favors strong resistance to carbon deposition.

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1. Introduction

The greenhouse effect caused by greenhouse gas emissions has great impact on the ecological environment. Statistics from the Intergovernmental Panel on Climate Change (IPCC) show that carbon dioxide and methane are the main components of greenhouse gases. With respect to reducing emissions, developing methods to efficiently convert greenhouse gases into usable energy is a win-win option. In recent decades, research on the dry reforming (DRM) of methane (CH₄(g) + CO₂(g) ⇌ 2CO(g) + H₂(g)) has received extensive attention,^1–6 as this process can simultaneously convert both greenhouse gases CO₂ and CH₄ into two clean fuel gases: carbon monoxide and hydrogen. Moreover, compared with the syngas produced by other methods such as steam reforming (SRM)^7,8 (CH₄(g) + H₂O(g) ⇌ CO(g) + 3H₂(g)), the synthesis gas produced by DRM has a lower H₂/CO ratio (1 : 1),⁹ suitable for further use in the Fischer–Tropsch synthesis of long-chain hydrocarbons.^10–14 From the perspectives of economy and the environment, DRM has a broad application space and research value.

However, there are still many problems to be solved to realize the industrialization of the DRM reaction. The occurrence of side reactions is one of the important factors that affect the reactivity of DRM. During the DRM process, the OH* produced by hydrogen-assisted CO₂ dissociation and the H* produced by the CH₄ dissociation, or the reaction between the O* produced by CO₂ dissociation and the H* produced by the CH₄ dissociation, produce H₂O. As long as H₂O is formed during the DRM process, steam reforming may also contribute to the formation of carbon monoxide and H₂. Therefore, SRM can affect DRM by changing the ratio of H₂ and CO. Due to the high endothermic properties of DRM (ΔH = 247.4 kJ mol⁻¹), the reverse water shift reaction (RWGS) (CH₂(g) + H₂(g) ⇌ CO(g) + H₂O(g)) (ΔH = 41.1 kJ mol⁻¹) is enhanced compared to DRM at lower temperatures.^15–17 RWGS can affect DRM by decreasing the ratio of H₂ and CO. In addition, the formation of C* is the main cause of DRM catalyst deactivation. During the process, the formation of carbon mainly comes from the cracking of methane (CH₄(g) ⇌ C(s) + 2H₂(g)) and the Boudouard reaction (2CO(g) ⇌ C(s) + CO₂(g)).^18,19

The lack of a highly active and stable catalyst is also one of the factors restricting the industrialization of DRM reactions. Although the theoretical and experimental research on DRM catalysts has been very rich, it is still necessary to have a further basic understanding of the reaction in order to rationally design a highly active and coke-resistant catalyst. An important aspect is to understand the preferred reaction path, since it controls the DRM activity as well as the extent of the abovementioned competitive reactions. In general, the mechanism of the methane dry gas reforming reaction is analyzed in the following aspects. The first is the activation mode of carbon dioxide (direct dissociation or hydrogen-assisted CO₂ dissociation). A theoretical study by Foppa et al.¹⁹ found that direct CO₂ dissociation is preferred on Ni; the hydrogen-assisted path presents a similar free energy span for Pd and Pt compared to direct CO₂ dissociation. In the DRM reaction, carbon dioxide is generally regarded as an oxidant, because the dissociation of carbon dioxide can generate O*. In addition to O* as oxidant, OH* is also used as an oxidant in some catalytic systems.²⁰ Last but not least, CH_x* can couple with O*/OH* to form CH_xO*/CH_xOH*. When DRM occurs in many catalytic systems, CH₄ decomposes to CH* or C* and then oxidizes to CHO* or CO*.^19,21–23 It is worth noting that Akri et al. propose that CH₃* is oxidized more than it is decomposed on atomically dispersed Ni single atoms.²⁴ Moreover, a recent report on DRM over Ni₄ clusters identified the oxidation of CH₃* to CH₃O* as an alternative route to CO following the initial methane activation,²⁵ as also proposed for Ni₁–Ru₁/CeO₂.²⁶

Nearly three decades of research have found that a nickel-based catalyst is the most competitive catalyst for DRM due to its low cost and its high catalytic activity comparable to noble metal catalysts such as Pd, Rh and Pt.^15,27–29 However, the biggest factor restricting the industrialization of Ni-based catalysts for DRM processes is that they suffer from deactivation because of carbon deposition.^30–32 To avoid such a problem, many methods have been developed, such as alloying with other less active metals,^33–36 making a strong metal-support interaction (SMSI) system by choosing a special reduced metal oxide support to make oxygen defects³⁷ or controlling the size of active sites.³⁸ In fact, a previous study showed that anatase defective TiO₂-supported Rh catalyst favors stronger carbon deposition resistance than rutile defective TiO₂-supported Rh catalysts for the partial oxidation of methane due to the SMSI properties of the former.³⁹ Moreover, it was also found that a smaller sized active site is much more favorable for carbon deposition resistance, implying a strong size effect.^40–42

Very recent experimental results found that Ni nanoparticles embedded on the vacancy defects of hexagonal boron anitride nanosheets (h-BN) show high coke-resistance behavior in the DRM compared to that of perfect h-BN sheets, suggesting the importance of vacancy defects.⁴³ The existence of defects makes the interaction between the metal and the support stronger and the Ni atoms on the surface are more dispersed and not easily aggregated. To shed light on the vacancy defect effect on coke-resistance in the DRM processes, a systemic theoretical study was performed on the detailed reaction mechanism of DRM catalyzed by perfect and defected-h-BN supported Ni catalysts in this work and it was shown that the vacancy defects lead to SMSI and thus high catalytic DRM activity and resistance to carbon deposition.

2. Computational methods and model

2.1. Methods

All the density functional theory (DFT) calculations were performed using the Vienna ab initio simulation package (VASP).^44–46 Potentials within the projector augmented wave method (PAW)^47,48 were used to represent the core–valence electron interaction; the Perdew–Burke–Ernzerhof (PBE)⁴⁹ functional within the generalized gradient approximation (GGA) was employed to calculate the exchange and correlation energies. The valence electronic states were expanded in plane wave basis sets with a kinetic cutoff energy of 400 eV and the surface Brillouin zone sampling was carried out using a 3 × 3 × 1 Monkhorst–Pack⁵⁰k-point mesh for better calculation accuracy. During configuration optimization, the self-consistent field calculation was repeated until the absolute force of each field is less than 0.035 eV Å⁻¹. The climbing image nudged elastic band (CI-NEB) method⁵¹ was employed to locate the transition states (TSs). A further frequency analysis was carried out to confirm the located TSs; during the frequency calculation, all catalyst atoms remained stationary. Spin-polarized effects were considered for the case of Ni. It is worth mentioning that Tanaka et al.^52,53 proposed the scheme about the spin effect on the reaction barrier to improve calculation accuracy.

The adsorption energy (E_ads), reaction energies (ΔE) and activation energy (E_a) were calculated as follows: E_ads= E_system− E_substrate− E_absorbate; ΔE = E_FS− E_IS; E_a= E_TS− E_IS. Here, E_system, E_substrate, E_adsorbate, E_IS, E_TS, and E_FS represent the energies of the adsorption system, substrate, adsorbate, initial state (IS), transition state (TS), and final state (FS), respectively.

In order to compare the calculation results with the experimental conditions more accurately, the Gibbs adsorption free energy and the Gibbs free energy of the whole reaction were further considered. The Gibbs free energy (G) of a gas-phase species is estimated by considering the contributions of the translation, rotation and vibration of the distribution function and is directly derived from the experimental data. For substances with weaker molecular adsorption, such as methane, we carried out dispersion correction (DFT-D2) and, assuming that they maintain the full rotation and vibration modes of their gas phase materials, the adsorption entropy was calculated using the following formula.⁵⁴

S_ads(T) = 0.7S_gas(T) − 3.3R (1)

Here, R is the ideal gas constant, S_gas is the entropy of the corresponding gas phase material obtained from the thermodynamic database (see Table S1, ESI†) and S_ads is the entropy of the adsorbate. For the strongly chemically adsorbed species like CO, we assume that the most important contribution comes from translational entropy and its adsorption entropy change was estimated by using the following formula:^55,56

S(T) = 1.5R ln(2ΠMkT) − 3R ln h + R ln(kT/P) + 2.5R (2)

Here k, T, P, h, R and M represent the Boltzmann constant, temperature, pressure, Planck constant, ideal gas constant, and molecular mass, respectively.

According to the activation energy and reaction energy of each basic reaction, the free energy curve of the reaction can be obtained.¹⁹ In this work, we define the total free energy span as the difference between the free energy of the starting reactant and the free energy of the highest transition state. Assuming that the reaction proceeds step by step, the free energy span corresponds to the activation energy of the reaction and can be used to measure the difficulty of the reaction.

2.2. Models

The calculated lattice constant of h-BN is 2.51 Å (the experimental lattice constant is approximately 0.25 nm)⁵⁷ and the h-BNNS is represented by a single layer slab with a 7 × 7 element of h-BN with a vacuum separation of 15 Å between successive slabs. Periodic boundary conditions were used for all systems. The B-defected h-BN was modeled by removing one B atom from the perfect h-BN (labeled as h-BN-B–D) (see Fig. 1).

Fig. 1 Perfect (left) and B-defected (right) h-BN surfaces.

3. Results and discussion

3.1. Optimization and electronic analysis of perfect and B-defected h-BN supported Ni₂ catalysts

The perfect and B-defected h-BN surfaces are shown in Fig. 1. We first examined sites for Ni–Ni adsorption on the perfect h-BN surface. Two top sites for B and N were considered. One bridge site (B–N) and one hollow site were also examined. The most energetically preferred structures are presented in Fig. 2 and the corresponding adsorption energy is −4.28 eV. For B-defected h-BN supported Ni catalysts, we also optimized to find the most stable structure (see Fig. 2) and the corresponding adsorption energy is −8.70 eV. As shown in Fig. 2, when introducing B defects, the distances between Ni atoms and h-BN are shorter than in perfect h-BN, indicating that the introduction of B-defects enhances the interaction between Ni atoms and the carrier. It is worth noting that the defects strongly affect the charge transfer between h-BN and Ni₂. The Bader charge analysis^58,59 shows that 0.18–0.24 electrons are transferred from the adsorbed Ni₂ to pristine h-BN, while the defects in h-BN highly enhance the charge transfer (0.44–1.62 e); it is also apparent that the introduction of B-defects enhances the interaction between Ni atoms and the carrier. The partial densities of states (DOS) of Ni₂/h-BN and Ni₂/h-BN-BD were also calculated and are shown in supporting Fig. S1 (ESI†). The figure shows that the magnetic moment of Ni₂ on the perfect h-BN surface is 1.529 μ_B and the magnetic moment of Ni₂ on the B-defect h-BN surface at the equilibrium lattice constant is 0.75 μ_B; these results are consistent with the calculated value. On the surface of the B-defect h-BN, the decrease of Ni₂ magnetic moment indicates that Ni₂ transfers more electrons to the surface, thus showing a strong metal-support interaction character.

Fig. 2 Top and side views of Ni₂ adsorption configurations on perfect (left) and B-defected (right) h-BN.

It is worth mentioning that we also considered the adsorption of a single Ni on h-BN (see Fig. S2, ESI†). We found that the activation of methane and carbon dioxide on the Ni₁/h-BN and Ni₁/h-BN-B–D surfaces becomes more difficult (see Table S2, ESI†). Since the reaction tends to proceed on metallic Ni, there are fewer reactive sites when there is only a single Ni atom on the h-BN surface, which does not match the experimental conditions. Therefore, we did not consider this catalyst configuration. We will conduct a detailed study regarding the effect of Ni cluster size on DRM reactivity in the next work.

3.2. Adsorption configurations and stability of key species involved in DRM

As the adsorption process is the initial step and important for the whole reaction process, it is worth investigating the adsorption strength of reactants like CH₄ (CO₂) as well as key intermediate species related to DRM.

The adsorption energies are shown in Fig. 3 and Table S3 (ESI†) and the corresponding adsorption configurations are displayed in Fig. S4 and S5 (ESI†). First, oxygen and hydroxyl interact strongly with the catalyst; as the proposed hydrocarbon oxidants in the methane reforming reaction, the stabilities of O* and OH* on this Ni₂/h-BN-B–D surface are reduced by at least 1 eV compared to those on Ni₂/h-BN. Second, the adsorption strengths of methane cracking products CH_x* and C* increase in the order Ni₂/h-BN-B–D < Ni₂/h-BN, so favorable carbon deposition resistance on Ni₂/h-BN-B–D can be expected. From Table S3 (ESI†), one can find that most species bind strongly to perfect h-BN supported Ni₂ catalyst, generally following the trend Ni₂/h-BN > Ni₂/h-BN-B–D > Ni(111). The stronger adsorption ability on Ni₂-based catalyst may lead to the more facile activation of CH₄ and CO₂ compared to that on Ni(111) and thus to higher catalytic activity for DRM.

Fig. 3 Adsorption energies of key species on Ni₂/h-BN-B–D (red) and Ni₂/h-BN (blue).

3.3. CH₄ and CO₂ activation

The activation of methane and carbon dioxide is the starting step of the DRM process, so it is critical to the entire process. We first examine CH₄ activation steps on the different catalysts.

3.3.1. CH₄ activation. Fig. 4 shows the energetics of CH₄ activation on Ni₂/h-BN and Ni₂/h-BN-B–D. CH₄ is first physically adsorbed on the catalysts and dissociates into CH₃* and H*; the positions of adsorption and reaction are at the top of the Ni atom (see Fig. S4 and S5, ESI†). We also considered the adsorption of CH₄ on h-BN (see Fig. S6, ESI†) and found that the adsorption strength was significantly reduced. This shows that the catalytically active sites on these two surfaces are Ni₂ rather than the h-BN support. In the TSs, the C–H bond breaking distances on Ni₂/h-BN and Ni₂/h-BN-B–D are 1.52 Å and 1.82 Å, respectively. The CH₄ dissociation energy barriers are 0.36 eV and 0.11 eV on Ni₂/h-BN-B–D and Ni₂/h-BN, respectively. The CH₄ dissociation reaction standard free energy (ΔrG⁰) at 973.15 K is endothermic and increases in the order Ni₂/h-BN-B–D (0.39 eV) < Ni₂/h-BN-B–D (0.50 eV). It should be noted that 973.15 K is a temperature commonly used in DRM reactions and is consistent with the experimental temperature.⁴⁰ The results show that Ni₂/h-BN is more likely to activate CH₄ than is Ni₂/h-BN-B–D due to the dissociation products CH₃* and H* being more stable on Ni₂/h-BN. The free energy barrier of CH₄ dissociation is higher on Ni(111),²⁰ which indicates that CH₄ is more easily activated on these two catalysts than on Ni(111).

Fig. 4 Free energy profiles of CH₄ dissociation on the Ni₂/h-BN (red) and Ni₂/h-BN-B–D (black) surfaces at 973.15 K.

3.3.2. CO₂ activation. We analyze the breakage of C–O in carbon dioxide through two distinct routes. The first route is the direct decomposition of CO₂ into CO* and O* and the second is H-assisted CO₂ dissociation. The mechanism of hydrogen-assisted CO₂ dissociation is as follows: CO₂* + H* → COOH* → CO* + OH* → CO* + O* + H*. In the DRM reaction involving Ni-based catalysts, another H-assisted carbon dioxide dissociation path has also been extensively studied:²¹ CO₂* + H* → HCOO* → HCO* + O* → CO* + O* + H*. However, on the surface of the two catalysts studied in this work, the CO₂* + H* → HCOO* → HCO* + O* reaction is strongly endothermic and needs to overcome a high activation energy barrier (see Table 1), so this path will not be discussed in detail in the present study.

Table 1 Calculated energy barriers (E_a) and reaction energies (ΔE) for all elementary reactions involved in dry reforming of methane

	Reaction	Ni2/h-BN		Ni2/h-BN-B–D
		E a (eV)	ΔE (eV)	E a (eV)	ΔE (eV)
1	CH4* → CH3* + H*	0.11	−0.04	0.36	0.35
2	CH3* → CH2* + H*	0.95	0.79	0.95	0.94
3	CH2* → CH* + H*	1.00	0.87	1.20	1.15
4	CH* → C* + H*	1.17	0.75	1.33	1.24
5	CO2* → CO* + O*	1.11	0.22	1.42	0.24
6	CO2* + H* → COOH*	1.56	0.65	0.50	−0.05
7	CO2* + H* → HCOO*	0.97	−0.34	0.85	−0.62
8	COOH* → CO* + OH*	0.76	−1.14	0.96	−1.25
9	HCOO* → HCO* + O*	2.91	2.83	2.36	1.65
10	OH* → O* + H*	1.41	1.02	1.44	1.25
11	CH3* + O* → CH3O*	1.29	0.17	0.85	0.12
12	CH3* + OH* → CH3OH*	1.73	1.5	1.14	0.20
13	CH3O* → CH2O* + H*	0.16	0.06	0.08	−0.19
14	CH2* + O* → CH2O*	0.47	−1.33	0.46	−1.35
15	CH2* + OH* → CH2OH*	1.05	0.39	1.06	0.45
16	CH* + O* → CHO*	0.80	−2.00	0.57	−2.38
17	CH2O* → CHO* + H*	0.21	−2.88	0.37	−1.75
18	CHO* → CO* + H*	0.71	−0.04	0.08	−0.74
19	2H* → H2*	0.27	0.20	0.38	−1.00
20	C* + O* → CO*	1.23	−3.00	0.39	−4.00
21	OH* + H* → H2O*	1.07	0.71	0.58	0.12
22	2OH* → H2O* + O*	0.83	0.06	1.12	1.00

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Different from methane activation, on these two catalysts there is a significant difference between the activation mechanism of CO₂ and the energy barrier required by the reaction. Fig. 5 shows two different routes of CO₂ activation. In the case of direct decomposition of CO₂, the free energy barriers reduce when going from Ni₂/h-BN-B–D (1.68 eV) to Ni₂/h-BN (1.31 eV). This result is consistent with the adsorption trend where both reactants (CO₂) and dissociation products (CO* and O*) are more stable on Ni₂/h-BN than Ni₂/h-BN-B–D. From the transition state structure in direct CO₂ cracking (Fig. S7, ESI†), the C–O fracture bond distances are equal to 1.66 Å on Ni₂/h-BN-B–D and 2.01 Å on Ni₂/h-BN.

Fig. 5 Free energy profiles of CO₂ activation on Ni₂/h-BN (red) and Ni₂/h-BN-B–D (black) surfaces at 973.15 K: (a) direct route and (b) hydrogen-assisted via COOH* intermediate route.

The hydrogen-assisted path presents different free energy spans for Ni₂/h-BN (1.75 eV) and Ni₂/h-BN-B–D (1.13 eV) compared to those for direct CO₂ dissociation (1.31 eV and 1.68 eV, respectively). These results indicate that the C–O activation pathway is more energetically likely to be a COOH* path on Ni₂/h-BN-B–D, but direct CO₂ decomposition is preferred on Ni₂/h-BN. Due to the introduction of B-defects, the interaction between the support and the metal is enhanced, so the adsorption energy of CO₂ on Ni₂/h-BN-B–D is less than that on Ni₂/h-BN. This reaction of carbon dioxide and hydrogen atoms combining to form COOH* intermediates is easier on Ni₂/h-BN-B–D because of the low affinity of this surface for CO₂* and H*.

Since the activation of methane is easier than that of carbon dioxide on these two surfaces, we investigated the dissociation of carbon dioxide in the presence of CH₃*. IS and TS configurations of CO₂ direct activation on Ni₂/h-BN in the presence of CH₃* are shown in Fig. S3 (ESI†). We found that methane tends to adsorb on the top positions of Ni atoms, while the most stable configuration of carbon dioxide is two-position adsorption between two Ni atoms, so methane and carbon dioxide can be adsorbed simultaneously on the same Ni₂ metal cluster. In the presence of CH₃*, the reaction energy barrier for direct activation of CO₂ is 1.16 eV, which is not significantly different from that in the absence of CH₃* (1.11 eV). For the Ni₂/h-BN-B–D surface, like the Ni₂/h-BN surface, methane and carbon dioxide can be simultaneously adsorbed on the different positions of Ni atoms. The previous calculation results show that, on the Ni₂/h-BN-B–D surface, CO₂ tends toward H-assisted dissociation, so H atoms are generated after methane activation and the reaction between CO₂ and H* can proceed smoothly. Therefore, for these two surfaces, the activation of methane and carbon dioxide can be performed in situ on the Ni dimer. Regarding the influence of the surface coverage of intermediate species on the reaction, we will use kinetic Monte Carlo method in future work to further explain the reaction mechanism and phenomenon.

The comparison between the C–H and C–O activation curves shows that, under the conditions considered, the activation of CO₂ is easier on Ni₂/h-BN-B–D (1.13 eV) than on Ni₂/h-BN (1.31 eV), but CH₄ activation is more likely to occur on Ni₂/h-BN. This result shows that, compared with the Ni₂/h-BN surface, the Ni₂/h-BN-B–D surface is more likely to produce O*, but C* is more difficult to generate, showing that the Ni₂/h-BN-B–D surface has the potential to resist carbon deposition.

3.4. DRM reaction mechanism

Table 1 shows the activation free energy values of all the steps in the DRM and the competitive reactions network. There are many elementary reactions in DRM. Generally, we consider the reaction process from two major aspects. The first is the activation mode of CO₂: (a) direct disintegration of CO₂ into CO* and O* or (b) hydrogen-assisted CO₂ dissociation (here, the CO₂* + H* → COOH* → CO* + OH* → CO* + O* + H* route is considered). The second aspect is the formation of the C–O bond. The continued dissociation of alkanes (CH_X*) or the formation of oxides by O* or OH* depends on the competition of the two reactions: CH_X* → CH_X−1* + H* and CH_X* + O*→ CH_XO* or CH_X* + OH* → CH_XOH*.

We constructed the free energy curves of the DRM reactions completed through different paths according to the activation energy of each basic reaction. First, we consider the situation of direct dissociation of CO₂. There are many paths for the formation of the C–O bond, like CH₃, CH₂, CH, or C oxidation by O*. As the formations of CH* and C* each have a high energy barrier (see Table 1), the paths of CH* and C* oxidation by O* can be ignored. On these two catalysts, CH₃* species are relatively easy to generate, but CH₃* → CH₂* → CH* is thermodynamically unfavorable, with a high activation barrier. Therefore, we think that the CH₃* may be oxidized by O* instead of continuing to decompose. Even though the decomposition of CH₃* is a strong endothermic reaction, its reaction activation barrier is lower than the activation energy of CO₂ direct decomposition. For the comprehensiveness of the work, we studied the activation pathway of CH₂ oxidized by O*. At 973.15 K, the DRM reaction is endothermic and the standard free energy is 1.54 eV. We chose the activation of CH₄ instead of CO₂ as the starting step of DRM based on which has the lower activation energy.

Fig. 6 shows the different ways of forming C–O bonds on the surfaces of these two catalysts. Fig. 6(a) and (b) respectively show the free energy profiles of the DRM through the CH₃–O and CH₂–O pathways when CO₂ is directly dissociated. On the Ni₂/h-BN-B–D surface, the overall free energy spans of DRM through the CH₃–O and CH₂–O routes are 2.19 eV and 3.13 eV. The results clearly show that DRM on Ni₂/h-BN-B–D tends to occur through the CH₃–O pathway. On Ni₂/h-BN, the overall free energy spans by the CH₃–O and CH₂–O routes are 1.72 eV and 2.07 eV, respectively; unlike on the Ni₂/h-BN-B–D, there is no obvious difference in the overall free energy span of the two paths. Therefore, these two paths have a competitive relationship on the surface of Ni₂/h-BN-B–D. This may be because the first step of CH₄ activation is faster on Ni₂/h-BN than on Ni₂/h-BN-B–D (0.11 eV vs. 0.36 eV).

Fig. 6 Free energy profiles of DRM on Ni₂/h-BN (red) and Ni₂/h-BN-B–D (black) surfaces at 973.15 K. (a) CO₂ direct dissociation with CH₃–O oxidation and (b) CO₂ direct dissociation with CH₂–O oxidation.

Secondly, we considered the overall free energy span in the case of the H-assisted CO₂ dissociation path and the results are shown in Fig. 7. It should be noted that on the surface of Ni₂/h-BN, the activation energy barrier of CO₂* + H* → COOH* is much higher than that of the decomposition of CH₃*. Therefore, we consider that, on the surface of Ni₂/h-BN, CH₂–O is the main path of DRM in the case of H-assisted CO₂ dissociation via COOH*. Fig. 7(a) shows that the overall free energy span of DRM on Ni₂/h-BN is 2.51 eV by H-assisted CO₂ dissociation via COOH*, higher than that of CO₂ direct dissociation. Consistent with the above analysis, this result shows that the path of CO₂ direct dissociation on the surface of Ni₂/h-BN is more likely to occur. Fig. 7(b) shows that the overall free energy span of DRM on Ni₂/h-BN-B–D is 1.66 eV by H-assisted CO₂ dissociation via COOH*, which is significantly lower than the direct dissociation of CO₂. This is because, on the surface of Ni₂/h-BN-B–D, the activation of CO₂ prefers the path of H-assisted dissociation. It is worth mentioning that although OH* was produced in this process (COOH* → CO* + OH*), we did not take OH* as the main oxidant because CH_x* + OH* → CH_xOH* is a strong endothermic reaction and has a high activation energy barrier (see Table 1).

Fig. 7 Free energy profiles of DRM by H-assisted CO₂ dissociation via COOH* on Ni₂/h-BN (red) and Ni₂/h-BN-B–D (black) surfaces at 973.15 K.

On both surfaces, the decomposition of CH₄ is the initial step of the reaction. On the surface of Ni₂/h-BN, the activation of CO₂ tends to be direct decomposition. However, on the surface of Ni₂/h-BN-B–D, H-assisted dissociation of CO₂ becomes the main method. The oxidation of alkanes mainly occurs through the CH₃–O pathway even though there is a competitive relationship on the Ni₂/h-BN. On the Ni₂/h-BN-B–D, the overall free energy span is lower but there is no significant difference between the two surfaces.

3.5. Reverse water gas shift (RWGS) reaction mechanism

RWGS is a major side reaction during the DRM reaction. When methane cracks to produce H₂, it reacts with CO₂ in the raw material to produce H₂O and CO. Even if the reaction produces CO, by-products (H₂O) are also introduced and reduce the ratio of H₂ to CO. Therefore, when studying the DRM process, the RWGS reaction should be considered.

The standard free energy of the reverse water gas shift reaction at 973.15 K (ΔrG⁰) is 0.41 eV. The initial step of the RWGS reaction is the activation of carbon dioxide. As in DRM, carbon dioxide may be dissociated directly or through H-assisted dissociation on Ni₂/h-BN and Ni₂/h-BN-B–D. Fig. 8 shows the free energy profiles of the RWGS calculated for Ni₂/h-BN and Ni₂/h-BN-B–D. On these two surfaces, there are obvious differences in the pathways of carbon dioxide dissociation. RWGS via direct C–O activation route is preferred on Ni₂/h-BN, whereas the reaction proceeds preferentially via the COOH* intermediate on Ni₂/h-BN-B–D. The overall free energy span of the RWGS reaction is lower for Ni₂/h-BN (1.30 eV) than for Ni₂/h-BN-B–D (1.77 eV).

Fig. 8 Free energy profiles of RWGS reaction on Ni₂/h-BN (red) and Ni₂/h-BN-B–D (black) surfaces at 973.15 K: CO₂ direct decomposition path (a) and hydrogen-assisted CO₂ dissociation path (b).

As seen in Fig. 8, regardless of the difference in the catalyst and the cracking mechanism of C–O, breaking the C–O bond requires a higher energy barrier than the formation of water; this shows that the cleavage of the C–O bond is the key step that affects the RWGS reaction. Since OH* and O* on Ni₂/h-BN-B–D are less stable than on Ni₂/h-BN (Fig. 3), it is easier to form water from OH* and H* on the surface of Ni₂/h-BN-B–D. Therefore, in the case of Ni₂/h-BN-B–D, the H-assisted CO₂ activation route, with OH* and H* then forming water, can promote the entire RWGS reaction. It is worth mentioning that the H-assisted C–O cracking pathway on Ni₂/h-BN-B–D can significantly reduce the free energy span by 0.52 eV compared to the pathway via direct CO₂ activation.

3.6. Steam reforming of methane (SRM) mechanism

The steam reforming reaction must also be considered when evaluating the dry gas reforming reaction. When dry reforming conditions or the reverse water gas shift reaction generates water molecules, methane will react with the water to form CO and H₂.

Fig. 9 displays the calculated energy profiles for steam reforming of methane on Ni₂/h-BN and Ni₂/h-BN-B–D. The overall free energy spans of SRM are 3.31 eV and 2.83 eV for the Ni₂/h-BN and Ni₂/h-BN-B–D surfaces, respectively. Like that of the DRM reaction, the free energy profile for steam reforming is higher in energy on Ni₂/h-BN than on Ni₂/h-BN-B–D. In steam reforming reactions, lower activation energies are required for the dissociation of H₂O on both surfaces (0.37 eV and 0.47 eV for Ni₂/h-BN and Ni₂/h-BN-B–D). O–H bond breaking reactions occurring in the SRM mechanism display similar free energy barriers on both surfaces. The higher activation energy required on Ni₂/h-BN-B–D than Ni₂/h-BN is due to the lower affinity of OH* for this surface. From the energy profile (Fig. 9), the combination of CH₃* and O* is the rate-limiting step of the steam reforming reaction on Ni₂/h-BN; the formation of CH₃O* requires higher activation energy on Ni₂/h-BN than on Ni₂/h-BN-B–D because CH₃* and O* are more stable on Ni₂/h-BN than on Ni₂/h-BN-B–D. It is interesting that the overall energy span of SRM occurring on these two surfaces is higher than that of DRM.

Fig. 9 Free energy profiles of steam reforming of methane on Ni₂/h-BN (red) and Ni₂/h-BN-B–D (black) surfaces at 973.15 K.

3.7. Coke formation

The ability of the catalyst to resist carbon deposition is an important indicator to measure the stability of the catalyst in the dry and steam reforming reactions. Reforming reactions usually occur at very high temperatures, so the material must resist coke formation and should not sinter at the strict working temperatures. Once coke is formed on the catalyst surface, the activity of the catalyst will be decreased or even deactivated. The ability to resist carbon deposition is an important indicator to measure the Ni-based catalyst in the DRM reaction.

There are two main ways to form C* on the catalyst surface: (i) methane cracking (CH₄ → C* + 2H₂) and (ii) the Boudouard reaction (2CO → C* + CO₂). The energy profile of the methane cracking reaction is presented in Fig. 10. Methane cracking requires higher energy on Ni₂/h-BN-B–D. In addition to the lower activation energy barrier of methane in the first step, the subsequent decomposition (CH₃* → CH₂* → CH* → C) energy gradually increases, with an overall free energy span up to 3.85 eV. Less energy is required on the Ni₂/h-BN and the overall free energy span is still as high as 3.13 eV.

Fig. 10 Free energy profiles of the CH₄ cracking (a) and Boudouard reaction (b) on Ni₂/h-BN (red) and Ni₂/h-BN-B–D (black) surfaces at 973.15 K.

C* can also be formed from CO by the Boudouard reaction (as shown in Fig. 10(b)). It is worth noting that the Boudouard reaction (2CO* → CO₂* + C*) is not completed in one step, but in two. First, CO* dissociates into C* and O* (CO* → O* + C*), then O* reacts with another CO* to produce CO₂* (O* + CO* → CO₂*). For Ni₂/h-BN and Ni₂/h-BN-B–D, the overall free energy spans are 3.10 eV and 4.54 eV, respectively. The free energy span of the Boudouard reaction on Ni₂/h-BN is lower than that of methane cracking, which demonstrates that carbon is preferentially formed from CO on this surface. On the Ni₂/h-BN-B–D surface, however, cracking of methane is more likely to occur than the Boudouard reaction.

In addition to the reactions that produce carbon deposits, the coupling capacity of C* and the oxidation of C* are also factors that measure the catalyst's ability to resist carbon deposits. The kinetics of carbon deposition on the surface of Ni₂/h-BN and Ni₂/h-BN-B–D were further studied. We calculated the potential barrier of the surface C-coupling mechanism (C–C coupling) and the potential barrier of forming CO* on the two surfaces.

On Ni₂/h-BN, we find that when the catalyst surface is covered with carbon atoms, they tend to form clusters spontaneously. Regardless of the position of the two coupled C atoms in the initial form, a C–C coupling structure is always spontaneously formed after optimization. But for the formation of CO*, the energy barrier of the reaction is 1.26 eV (Table 1), indicating the surface coupling mechanism on this surface is kinetically favored. On Ni₂/h-BN-B–D, the barrier for C–C coupling (0.28 eV) is similar to that of CO* formation (0.38 eV), indicating that CO formation and C–C coupling might be kinetically favored on this surface. But we need to pay attention to the fact that the above calculation results show that the formation of C* is more difficult than the formation of O*. Overall, the above results suggest that carbon deposition is preferred on Ni₂/h-BN over Ni₂/h-BN-B–D.

An experimental study⁴³ found that the Ni content in the defected h-BN catalyst is significantly lower than that of the perfect h-BN catalyst, which further indicates that Ni can be highly dispersed through the introduction of controllable vacancy defects (this has been further confirmed by our recent study on the Pt_n/TiO₂ system, where it was reported that both the support and defect against thermal sintering of Pt atoms in fact⁶⁰). Therefore, it is necessary to consider that Ni has a tendency to aggregate on a perfect surface. Here, we constructed the most stable configuration of Ni₄/h-BN catalyst to study the effect of Ni accumulation on the resistance to carbon deposition (see Fig. S8, ESI†). The energy span profiles of the methane cracking reaction are presented in Fig. 11, in which the Ni₄/h-BN catalyzed cracking reaction presents a much lower energy profile compared to that of Ni₂/h-BN (free energy span of 1.43 eV). On the surface of Ni₄/h-BN, once methane is activated, C* species are relatively easy to form. As a result, when the amount of nickel at a single site on the h-BN surface increased, the rate of methane decomposition accelerated and C* species were more likely to form on the surface. We studied the kinetics between the deposition and removal of surface carbon on Ni₄/h-BN; the results are shown in Fig. 12. On Ni₄/h-BN, the barrier for C–C coupling (1.05 eV) is lower than that for CO* formation (1.72 eV), indicating the surface coupling mechanism is kinetically favored on this surface. Therefore, when Ni accumulates on the h-BN surface, the formation of C* becomes easier.

Fig. 11 Free energy profiles of CH₄ cracking over Ni₂/h-BN (red) and Ni₄/h-BN (blue) surfaces at 973.15 K.

Fig. 12 Energy profiles of carbon oxidation to CO (black) and carbon–carbon coupling (red) on Ni₄/h-BN.

3.8. Comparisons of DRM activity for Ni₂/h-BN, Ni₂/h-BN-B–D and Ni(111)

Fig. 13 shows the free energy spans of DRM and the competitive reactions on the Ni₂/h-BN and Ni₂/h-BN-B–D surfaces at 973.15 K and P = 1 bar. Compared with Ni(111),¹⁹ the overall free energy span of the DRM reaction on the Ni₂/h-BN and Ni₂/h-BN-B–D surfaces is significantly reduced. Also, unlike Ni(111), on Ni₂/h-BN and Ni₂/h-BN-B–D, methane activation is easier than carbon dioxide activation. On the Ni(111) and Ni₂/h-BN surfaces, the RWGS reaction is the reaction with the smallest span of free energy among these reactions, which shows that RWGS easily occurs with the DRM reaction on these two catalysts. Moreover, both Ni₂/h-BN and Ni₂/h-BN-B–D have significantly improved abilities to resist carbon deposition.

Fig. 13 Comparison of free energy spans of DRM and competitive reactions on Ni₂/h-BN (red) and Ni₂/h-BN-B–D (blue) at 973.15 K and P = 1 bar.

Comparing the reaction paths, on Ni(111) and Ni₂/h-BN, CO₂ activation tends to be direct dissociation; for the Ni₂/h-BN-B–D surface, the overall free energy span required by H-assisted carbon dioxide dissociation is lower. On these three surfaces, O* is the most potent oxide. The difference is that on the Ni(111) surface, the CH-O path has priority, while on the Ni₂/h-BN-B–D and Ni₂/h-BN surfaces, the free energy span required for CH₃–O to occur is lower. Overall, compared with Ni(111), the DRM reaction is more likely to occur on Ni₂/h-BN-B–D and Ni₂/h-BN and the ability to resist carbon deposition was improved, with the trend being Ni₂/h-BN-B–D > Ni₂/h-BN > Ni(111). This indicated that a good catalyst for DRM can be rationally designed by performing size and defect engineering through the SMSI properties.

In this work, turnover frequency (TOF) (expressed as the number of cycles performed per unit of time) was used to further measure the efficiency of the Ni-base catalyst for DRM. The TOF can be calculated as follows:^61,62

where k_B is the Boltzmann constant, h is the Planck constant, T is temperature, ΔE is the total free energy span, and R is the ideal gas constant. Accordingly, the TOFs for DRM on Ni₂/h-BN and Ni₂/h-BN-B–D are 25.30 s⁻¹ and 51.72 s⁻¹, respectively. It is obvious that the presence of B-defects can reduce the apparent activation energies and improve the catalytic activity of catalysts for DRM.

4. Discussion

In this work, we studied the dry reforming of methane (DRM) and a series of competitive reactions over perfect and boron-vacancy-containing h-BN sheet supported Ni-catalysts (Ni₂/h-BN and Ni₂/h-BN-B–D) using density functional theory calculations and comparison to metallic Ni(111).

Compared with the perfect h-BN surface, the introduction of B-defects makes the interaction force between Ni and the surface stronger and thus less binding to adsorbed species like O*, OH*, and CH_x (x = 0–3) than Ni₂/h-BN. For this reason, DRM reactions involving decomposition reactions, such as the decomposition of carbon dioxide and methane, are more likely to occur on Ni₂/h-BN. Recombination reactions (such as oxidation of CH_x* species) are more likely to occur on Ni₂/h-BN-B–D.

Comparing the activation of DRM reactants on the surface, we find that CH₄ is easier to activate than molecular CO₂ on both the Ni₂/h-BN and Ni₂/h-BN-B–D surfaces. The activation of CO₂ occurs on the surface of Ni₂/h-BN through a direct route, but is prone to following a hydrogen-assisted path on Ni₂/h-BN-B–D via the COOH* intermediate. On these two surfaces, O* is the main oxide and the main reaction path is CH₃* being oxidized to form CH₃–O.

Moreover, comparing the free energy span of DRM on these two catalysts, we found that Ni₂/h-BN-B–D is more favorable than Ni₂/h-BN (1.66 vs. 1.72 eV). The trend is the same in the SRM reaction. It is worth noting that on the surface of Ni₂/h-BN, the trend is the same as that of metal Ni(111) and the RWGS reaction has the smallest free energy span among these reactions. But on the Ni₂/h-BN-B–D, DRM has the highest priority.

The calculation results show that on the surface of Ni₂/h-BN-B–D, the ability to resist carbon deposition is greatly enhanced. C* formation by Boudouard reaction has a higher energy span than the methane cracking reaction on Ni₂/h-BN-B–D, while the latter requires more energy on Ni₂/h-BN. From the Ni₂/h-BN surface to the Ni₂/h-BN-B–D surface, the free energy span formed by C* species increases significantly. And C–C coupling is easier than C–O formation on the Ni₂/h-BN surface because the force between Ni and the carrier on the perfect surface is relatively small and Ni tends to aggregate on the surface. When the concentration of Ni increases on the catalytically active sites on the surface, the ability to resist carbon deposition is significantly reduced. Not only is carbon formation easier, but the tendency to form C–C on the catalyst surface is significantly enhanced.

This study analyzed the factors that affect DRM activity from multiple angles. With the introduction of defects on the catalyst, we found that the activity and selectivity of DRM were enhanced and, most importantly, the ability to deposit carbon was greatly improved. It provides theoretical guidance and support for the application of an Ni-based catalyst in the DRM reaction via its SMSI character.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants No. 21973048, 21773123, 91545106).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0cp04732e

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