Theoretical study on NO_x adsorption properties over the α-MnO₂(110) surface

Abstract

Herein, α-MnO₂ was studied as an adsorbent for the removal of NO_x (NO, NO₂) derived from flue gas. First-principles calculations based on the density functional theory (DFT) were performed to investigate the NO_x adsorption properties over the α-MnO₂(110) surface. NO strongly adsorbed over the α-MnO₂(110) surface via chemisorption spontaneously under 550 K. The NO₂ molecules adsorbed over the surface via chemisorption and physisorption when the terminal N- and O atoms approached the surface, respectively. The joint adsorption of NO_x was more stable than the isolated adsorption system. Furthermore, the net charge was transferred from the molecule to the surface. The surface and temperature affected the entropy, enthalpy, NO adsorption and NO₂ desorption in the temperature range of 300–550 K. The equilibrium constants decreased with an increase in temperature, which reduced the conversion rate.

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1. Introduction

More than 90% of the total emissions of nitrogen oxides (NO_x) originate from stationary sources (copper smelter off-gas, power plants, etc.)^1–4 due to the burning of coke under high-temperature combustion conditions. The spread of NO_x in the atmosphere can lead to a global disaster, including ozone depletion, acid rain, photochemical smog and greenhouse effects.^5,6 Thus, the removal of these contaminants in compliance with environmental emission standards is necessary. NO and NO₂ are the main monitoring objects, which typically make up the total emission of NO_x from industries.^7,8 So far, many methods for controlling NO_x contamination, including SCR (selective catalytic reduction) in the gas phase, absorption in the liquid phase and adsorption in the solid phase, have been developed and applied in industries.^9–11 However, the leakage of NH₃ causes air pollution in SCR methods and produces a large amount of wastewater and results in an increase in cost in absorption methods. Comparing the two above-mentioned methods, adsorption is better for the removal of NO_x owing to its excellent characteristics of larger surface area, better selectivity, higher adsorption capacity and rate, better regeneration, and chemical stability. The sorbents CuO, SnO₂, CeO₂, Al₂O₃, TiO₂, and V₂O₅ have been chosen as the ideal materials to remove NO_x in industries.^12–15 However, the high cost of these noble metal oxides limits their application; therefore, there is a need to find inexpensive materials to remove NO_x efficiently. Chen et al. found that α-MnO₂ exhibits the highest adsorption capacity for NO_x among the α-, β-, γ- and σ-MnO₂ phase structures and the abovementioned sorbents.¹⁶ Therefore, α-MnO₂ can act as a suitable sorbent to reduce NO_x emissions. However, very little is known about the NO_x adsorption mechanism over the α-MnO₂ surface. Thus, it is necessary to understand the mechanism with the density functional theory (DFT).

Cockayne et al. computed the atomic, electronic, and magnetic properties of α-MnO₂ crystals using the DMol³ package in Materials Studio to provide quantitative predictions.¹⁷ DFT calculations were performed using the abovementioned package to investigate the α-MnO₂(110) surface by Liu et al., and the hydroxyl α-MnO₂(110) surface was also simulated with reasonable changes from the crystal structure.¹⁸ For oxygen-rich and oxygen-lean α-MnO₂(110) surfaces, Tang et al. explored the surface structure sensitivity of manganese oxides for low-temperature SCR methods to remove NO using the DMol³ package.^19,20 Thus, herein, the DMol³ package in Materials Studio was used to simulate a process of NO_x adsorption over the α-MnO₂(110) surface.

This study was aimed at investigating the adsorption mechanism and fundamental chemical reactivity of NO_x over the α-MnO₂ (110) surface based on DFT. The thermodynamic properties (Gibbs free energy change, enthalpy, entropy and equilibrium constant), adsorption properties (adsorption energy) and electronic transfer properties (Mulliken charge) were evaluated to determine the optimal adsorption site over the (110) surface. Moreover, the potential energy diagrams of the different pathways for NO_x adsorption over the surface were presented and the joint adsorption and analysis temperature effect on the equilibrium constant of NO_x was calculated.

2. Computational method and models

In this research, all calculations were performed with DFT using periodic boundary conditions.^21–24 All DFT calculations were completed using DMol³ with the GGA (generalized gradient approximation) scheme and PBE (Perdew, Burke and Ernzerhof) exchange-correlation functional to describe the exchange-correlation effects.^18,19 Atomic basis sets were applied numerically in terms of the double numerical plus polarization function (DNP) basis set version 3.5 and a global orbital cutoff of 4.7 Å was applied. The geometry optimization convergence tolerances of the energy, gradient, and displacement were 1 × 10⁻⁵ Hartree (Ha), 2 × 10⁻³ Ha Å⁻¹, and 5 × 10⁻³ Å, respectively. The core electrons were modeled using a density functional semi-core pseudopotential (DSPP) method for Mn atoms, and the all-electron method was used for the core electrons of the N and O atoms. For bulk lattice optimization, energies were converged with (3 × 3 × 9) k points in a Monkhorst–Pack grid. The crystal structure of the optimized α-MnO₂ is shown in Fig. 1a, which is a body-centered tetragonal lattice type with the space group I4/m and its optimized unit cell parameters (a = b = 9.815 Å, c = 2.847 Å) within +0.67% and −0.49% error of the experimentally determined lattice constants,²⁵ indicating that the calculation results are reliable.

Fig. 1 (a) Optimized α-MnO₂ crystal structure. (b) α-MnO₂(110) surface configuration. (c) Side view of the α-MnO₂(110) surface with eight layers. (d) Top view of the α-MnO₂(110) surface with different adsorption positions.

The α-MnO₂(110) surface was the most thermodynamically stable bulk termination and catalytically active surface.^21,26 Therefore, the calculation of the thermodynamic properties and adsorption energies was performed using the α-MnO₂(110) surface. The surface slab was cleaved from the optimized structure of α-MnO₂. 8 layers of atoms were extracted. The p(1 × 1) supercell was built with a vacuum region of 15 Å along the z-axis, which is shown in Fig. 1b and c. The Monkhorst–Pack k point sampling was set as 3 × 3 × 1.^18,27 The SCF tolerance and number of cycles were 1.0 × 10⁻⁶ Ha and 1000, respectively. In the region of the surface, there were four different types of coordinative oxygen atoms, where the first layer oxygen atom O_f lies on the top of the surface, the O_s atom lies on the second layer oxygen atom, the O_t atom lies on the fifth layer oxygen atom and the O_h atom lies on the sixth layer oxygen atom. The third- and seventh-layer atoms were Mn atoms, which could be chosen as an adsorption position. They were named Mn_f and Mn_s, respectively. The atoms in the region were all relaxed, as shown in Fig. 1d. All the structures were optimized at the same level of theory.

3. Results and discussion

To investigate the stability of the NO_x molecules adsorbed over the α-MnO₂(110) surface, the adsorption energy (E_ads) was calculated according to eqn (1).

E_ads = E_surf−gas − E_surf − E_gas (1)

where E_surf refers to the total energy of the surface model cleaved after the geometry optimization, E_gas refers to the total energy of each NO_x in the gaseous phase after the geometry optimization, and E_surf–gas refers to the total energy of the surface-gas supersystem build after the geometry optimization. According to this definition, a positive value, corresponding to an exothermic process, means a stable adsorption system.

Moreover, to determine the exothermicity of the adsorption process and to investigate the favorability of the spontaneous reaction as a function of temperature, the equilibrium constant (K_eq),^28–32 Gibbs free energy change, entropy (S) and enthalpy (H) were calculated according to the thermodynamic data from the frequency. The general relationships for the statistical thermodynamic partition functions (translational, rotational, and vibrational partition functions) were introduced.³³ The equilibrium constant (K_eq) can be defined as eqn (2).

ln(K_eq) = −ΔG/RT (2)

where ΔG refers to the Gibbs free energy change, R refers to the ideal gas constant, and T refers to the temperature. According to this definition, the greater the equilibrium constant, the more thorough the reaction.

The Gibbs free energy change during the adsorption process was calculated using eqn (3).

where ΔE_ads refers to the change in adsorption energy, ΔE₀ refers to the change in the zero-point energy, and ΔS_vib and ΔS_trans,rot refer to the changes in the vibrational and translational, rotational entropy during adsorption, respectively.³³ k refers to the Boltzmann constant, and the pressure terms were canceled out because the pressure was constant in this adsorption system. The above equations were used to obtain ΔG and K_eq for NO_x adsorption in the temperature range of 200–1000 K, which covers most experimental relevance for real adsorption systems. According to this definition, a negative value of ΔG means a spontaneous process for NO_x adsorption.

The net charge-transfer (Q) was calculated using eqn (4).

Q = Mulliken charge_after − Mulliken charge_before (4)

where Mulliken charge_after refers to the Mulliken charge of the NO_x molecule in the adsorbed state, and Mulliken charge_before refers to the Mulliken charge of the NO_x molecule in the gaseous phase. According to this definition, a positive value means a loss of electrons from the NO_x molecule.³⁴

The heat (Q) that an adsorption system adsorbs at a specific temperature was calculated using eqn (5).

Q = nC_p,TT (5)

where n refers to the amount of substance. C_p,T refers to the heat capacity at a constant pressure and specified temperature.

The entropy value (S) was calculated using eqn (6).

S = Q/T (6)

The enthalpy value (H) was calculated using eqn (7).

H = U + pV (7)

where U refers to the internal energy, p refers to the pressure and V refers to the volume.

3.1 Adsorption of NO molecule over the α-MnO₂(110) surface

Deshwal et al. found that the major component of NO_x was NO (ca. 90%) in flue gas.³⁵ Also, NO was found to be an intermediate in the industrial production of nitric acid.^36,37 Therefore, it is important to investigate the NO adsorption mechanism over the α-MnO₂(110) surface to remove the vast majority of NO_x as a raw material for the production of nitric acid. Before adsorption, the bond length of the free NO molecule was calculated to be 1.163 Å, which is close to the experimental value (1.17 Å).^38,39 Then, an isolated adsorption system is formed, and the NO molecule adsorbs over the different adsorption positions of the α-MnO₂(110) surface. The optimized models of NO adsorption are presented in Fig. 2. The adsorption energies, bond length, distance and net charge-transfer for NO adsorption over the α-MnO₂(110) surface are shown in Table 1.

Fig. 2 Optimized models of NO adsorption over the α-MnO₂(110) surface.

Table 1 The adsorption energies, bond lengths, distances and net charge-transfer for NO adsorption over the α-MnO₂(110) surface^a

Model	Eads	LN–X	LO–X	dN=O	QNO
a Eads is the adsorption energies (kJ mol^−1); LN–X is the distance between N of the adsorbed NO molecule and closest adsorbate atom (Å); LO–X is the distance between O of the adsorbed NO molecule and closest adsorbate atom (Å); dN=O is the bond length of the adsorbed NO molecule; and QNO is the net-charge transfer of the NO molecule (e).
2A	−53.97	3.014	—	1.131	0.34
2B	−85.05	1.969	2.592	1.127	0.41
2C	−48.65	3.012	—	1.133	0.31
2D	−56.42	3.699	2.863	1.128	0.35
2E	−63.93	2.869	2.928	1.124	0.38
2F	−53.53	3.290	2.727	1.130	0.33

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As shown in Table 1, the adsorption strength for NO adsorption over the surface followed the order of 2C < 2F < 2A<2D < 2E < 2B. This indicates that all the NO adsorption sites exhibited chemisorption, suggesting an exothermic process and a stable adsorption system. The NO molecule adsorbed over the surface is chemisorption, which was modeled by attaching the molecule to the surface by its N atom as well as by its O atom. In the adsorption process, the net charge-transfer based on the Mulliken population analysis was investigated to determine the charge-transfer mechanism between the molecule and surface. The results presented in Table 1 show that the adsorbed NO molecule was positively charged on all the models. This means that electrons transfer from NO to the surface, which indicates that NO acts as a donor to provide electrons. The reason for this that the electronic arrangement of the N and O of NO is 2s²p³ and 2s²2p⁴, respectively, and they form polar covalent bonds via sp hybridization. The hybridization of the atomic orbital of N and O forms a σ bond, a 2-electron π bond and a 3-electron π bond among the polar covalent bonds. There is a lone-pair of electrons in the 2p orbitals of the N atom and also the O atom. Besides, the Mulliken charge was easily affected by the basis set. Hence, there is a lone-pair of electrons from the 2p orbitals with an unpaired electron to be filled in the surface, which is influenced by the basis set. Moreover, the optimized bond lengths of the adsorbed NO molecule in the equilibrium state were all shorter than that in the free case, illustrating that the surface makes the molecule more stable and it is difficult to break the covalent bond after it is adsorbed over the surface. In addition, the optimized distance between the N or O atoms of the adsorbed NO molecule and O or Mn atoms of the surface was probably short enough to form a chemical bond among the NO molecules and the surface. For the six different configurations, it was found that all the distances between the molecule and the surface were less than 3.76 Å,⁴⁰ which showed that our calculation was reasonable.

The most stable model is 1B in Table 1, which lies on the Mn_s top site, but approaches the O_s site with both O and N in the N-down orientation and the distance of 2.592 Å and 1.969 Å, respectively. The adsorption energy was −85.05 kJ mol⁻¹. Combining the bond lengths of NO, the distance between the molecules and the surface was 1.969 Å and 1.127 Å, and thus it can be concluded that the distance between the adsorbed molecules and the surface is due to the formation of chemical bonds. The reason for this that the formed chemical bond will lead to the covalent bond interaction in the adsorbed NO molecule becoming smaller than that in the free NO molecule. This explanation has been already applied to the adsorption of CO molecules on the orthorhombic structure of the LaMnO₃(110) surface.³⁴

Also, the thermodynamic properties (S, H and ΔG) as a function of temperature were calculated and DMol³ was used to plot the thermodynamic properties, as shown in Fig. 3. Furthermore, all the data for NO were demonstrated to be reliable compared to the experimental data.⁴¹ In Fig. 3a, the entropy values of all the configurations increase and their growth rate decrease when NO was almost parallel to the x-axis compared to the other configurations within the range of 44.92 to 56.63 cal mol⁻¹ K as the temperature increased. As calculated using eqn (5) and eqn (6), the blue line in Fig. 3a and c should be parallel, but it is not and also the red line. This is because of the conversion of exergy and heat caused by increasing the temperature in the system. Obviously, exergy has a greater influence on entropy. Due to the stability of the NO molecule in the gaseous phase, it has a stable heat capacity and its covalent bond never breaks in the temperature range of 200–1000 K parallel to the x-axis. Also, the values for the NO adsorption system of Model 2B (S_ads) were higher than that in the other conditions and close to the values of the α-MnO₂(110) surface (S_surf) at the same temperature, and the gap between the surface and the adsorption system increased with an increase in temperature. This indicates that the entropy of the adsorption system is affected more by the surface than by the NO molecule with a change in temperature and makes the molecule unstable to leave the surface. Also, we found that S_ads < S_surf + S_NO and the value of S_ads − S_surf was lower in the range of 33.37–33.95 cal mol⁻¹ K⁻¹ compared to S_NO (44.92–56.63 cal mol⁻¹ K). This indicates that the NO molecule binds on the surface stably and does not undergo desorption and dissociation. In Fig. 3b, the growth rate and enthalpy values of the adsorption system and the surface increase and are close to each other when the free NO molecule is almost parallel to the x-axis with a positive increase in temperature. This indicates that all the configurations are endothermic and the enthalpy of the adsorption system is mainly affected by the surface clearly with an increase in temperature. Besides, the enthalpy was calculated using eqn (7), which is approximately equal to the heat at a constant pressure. Thus, it is influenced by heat, which is a function of temperature, and the heat capacity to cause the rate to increase. Meanwhile, heat in the phase transition does not occur in the adsorption system, as reflected in Fig. 3b by the slight changes in the enthalpy value in the range of 200–1000 K. The phenomenon that the distance between the adsorption system and the surface increases with an increase in temperature reveals that the adsorption system will adsorb more heat than the surface. In Fig. 3d, the plot of ΔG shows an increasing trend with negative values under 550 K and finally becomes positive with an increase in temperature. This indicates that the system functions spontaneously under 550 K and is suitable for laboratory experiments.^42–44 Finally, we calculated the thermodynamic properties at 298.15 K, including H = 293.36 cal mol⁻¹ K, S = 141.86 kcal mol⁻¹, ΔG = −9.25 kcal mol⁻¹, and C_p = 274.14 cal mol⁻¹ K⁻¹. This indicates that at room temperature, the reaction is spontaneous.

Fig. 3 (a) Entropy value. (b) Enthalpy value. (c) Heat capacity value and (d) Gibbs free energy change for NO adsorption system of Model 2B as a function of temperature (kcal mol⁻¹) (the black dashed line represents temperature of 298.15 K, and the red dashed line represents ΔG of 0).

The potential energy diagram for the different pathways of NO adsorption over the (110) surface including the reactants, intermediates and products is shown in Fig. 4. The energies of the optimized structures were relative to the reactants. The desorption of the NO molecule is highly endothermic by 85.05 kJ mol⁻¹, and its dissociation, i.e., N adsorption over the surface and O desorption, is highly endothermic by 384.34 kJ mol⁻¹, 415.42 kJ mol⁻¹ and 379.02 kJ mol⁻¹ for 2A, 2B and 2C, respectively (the adsorption orientation in the N-down mode), while O adsorption over the surface and N desorption are highly endothermic by 718.60 kJ mol⁻¹, 726.12 kJ mol⁻¹ and 715.72 kJ mol⁻¹ for 2D, 2E and 2F, respectively, in the case of the O-down mode. This means that NO prefers to adsorb over the surface rather than dissociate due to the higher energy required to break the covalent bond and lower adsorption energy after geometry optimization of the dissociation model. If an NO molecule was dissociating, it will receive priority in binding N over the surface. Therefore, once NO adsorbs over the surface, it will neither easily desorb nor dissociate from the surface.

Fig. 4 Potential energy diagram for the different pathways for the adsorption of the NO molecule over the α-MnO₂(110) surface.

3.2 Adsorption of NO₂ molecule over the α-MnO₂(110) surface

NO₂ is reddish-brow toxic gas, which can act as a raw material in the nitric acid industry.^45,46 The parameters for the free NO₂ were calculated to be d_N–O = 1.211 Å, d_N=O = 1.211 Å, and θ_NO2 = 132.95°, in good agreement with that by Greenwood et al.⁴⁷ The interactions of NO₂ with different active sites of the α-MnO₂(110) surface were studied. Several possible models of NO₂ molecule adsorption over the α-MnO₂(110) surface were built and then geometry optimization was performed to determine the optimum model. Besides, the adsorption of NO₂ was modeled by attaching the molecule to the surface by its terminal N atom and by its terminal O atom vertically. After geometry optimization, the stable configurations of NO₂ over the α-MnO₂(110) surface are presented in Fig. 5 and Table 2 exhibits the adsorption energies, bond lengths, distance between the NO₂ molecule and the surface, bond angles and net charge-transfer for NO₂ adsorption over the α-MnO₂(110) surface. It was found that the most stable configuration for NO₂ over the surface is 5A, which is on a hollow site that is surrounded by Mn_s and O_h but approaches O_s the closest, and its adsorption energy of −69.74 kJ mol⁻¹ indicates chemisorption via the N-terminal approaching the surface. In contrast, 5D was physisorption with −20.05 kJ mol⁻¹ via the O-terminal approach, with the approach of the closest O_f, which is the most stable model on the Mn_s–O_t bridge site in the physical adsorption process. Also, the angle increases from 132.95° to 135.44° and the bond lengths decrease from 1.211 Å to 1.192 Å in the chemisorption process, while the angle increases to 138.67° and the bond lengths decrease to 1.194 Å and 1.201 Å. This can be influence by the net-charge transfer and adsorption energy. The former indicates that the surface is a receiver of charge from the molecule and that the NO₂ molecule forms covalent bonds with an unpaired electron from the 2p orbitals of O and N.

Fig. 5 Models of NO₂ adsorption over the α-MnO₂(110) surface after optimization.

Table 2 The adsorption energies, bond lengths, bond angles, distances and net charge-transfer for NO₂ adsorption over the α-MnO₂(110) surface^a

Model	Eads	LN–X	LO–X	θNO2	dN–O	dN=O	QNO2
a Eads is the adsorption energy (kJ mol^−1); LN–X is the distance between N of the adsorbed NO2 molecule and closest adsorbate atom (Å); LO–X is the distance between O of the adsorbed NO2 molecule and closest adsorbate atom (Å); dN–O and dN=O are the bond lengths of the NO2 molecule after adsorption (Å); QNO2 is the net-charge transfer of the NO2 molecule (e); and θNO2 is the bond angle of the adsorbed NO2 molecule (°).
5A	−69.74	2.335	—	135.44	1.192	1.192	0.26
5B	−56.81	1.829	—	135.78	1.193	1.195	0.25
5C	−14.98	—	3.355	137.44	1.197	1.200	0.17
5D	−20.05	3.097	3.172	138.67	1.194	1.196	0.21
5E	−13.08	—	3.365	136.98	1.198	1.201	0.15

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It is important to investigate the chemisorption and physisorption for NO₂ adsorption over the surface and determine how to influence the properties of the surface based on analysis of the thermodynamic data. Models 5A and 5D were chosen because they are most stable configurations in the process of chemisorption and physisorption, respectively. The temperature and adsorption energy can influence the thermodynamic data. Thus, the DMol³ thermodynamic properties as a function of temperature was plotted, as shown in Fig. 6. In Fig. 6a, the entropy value increases while its growth rate decreases. Also, with an increase in temperature, the growth rate for chemisorption is higher than that for physisorption initially and lower finally. This indicates that the chemical bond formed during chemisorption between the molecule and the surface changes the reactivity, which is the sensitivity to the desorption of the NO₂ molecule. In Fig. 6b, enthalpy value and its growth rate increases with an increase in temperature and becomes almost parallel for chemisorption and physisorption. This indicates that the adsorption system adsorbs heat with an increase in temperature. Also, the distance between chemisorption and physisorption is caused by the surface activity relative to the adsorption energy. Fig. 6c shows that the Gibbs free energy increases proportionally with respect to temperature for both chemisorption and physisorption. This indicates that ΔG can be influenced by temperature and the adsorption energy. Under 250 K, the physisorption values are higher than 0, while the chemisorption values are lower than 0 at the same temperature. This reveals that the adsorption energy from the surface influences the reaction to be spontaneous or not at low temperature.

Fig. 6 (a) Entropy value, (b) enthalpy value and (c) Gibbs free energy change of 5A and 5D as a function of temperature.

The energy diagram of NO₂ adsorption and possible desorption over the surface including reactants, intermediates and products is shown in Fig. 7. The energies of the optimized structures are related to the reactants. The stability of the surface complex follows the order of 5A>5B > 5D > 5C > 5E. In the chemisorption process, the formation of intermediate 5A and 5D in the physisorption process is highly exothermic, indicating that the surface complexes 5A and 5D are the most likely structures to be formed. In the case of 5A and 5B, they exhibit chemisorption with the formation of a chemical bond between the surface and the molecule. Also, the dissociation of the NO molecule adsorbed over the surface occurs via N-down and O desorption, which are highly endothermic by 447.05 kJ mol⁻¹ and 434.12 kJ mol⁻¹, respectively, indicating that this cannot occur. 5C, 5D and 5E exhibit physisorption. The process of forming intermediates 5C and 5E leads to NO₂ dissociation of the adsorbed NO via O-down and O desorption, which are highly endothermic by 130.54 kJ mol⁻¹ and 128.64 kJ mol⁻¹, respectively. Due to the higher adsorption energy for the formation of 5D, it will lead to O adsorption and NO desorption with 418.48 kJ mol⁻¹.

Fig. 7 Potential energy diagram for the different pathways for the adsorption of the NO₂ molecule over the α-MnO₂(110) surface.

3.3 Joint adsorption and temperature effect on the equilibrium constants of NO_x

The major components of NO_x are NO and NO₂ in flue gas. Hence, it is necessary to determine the mechanism of how NO and NO₂ jointly adsorbed over the surface influence each other that. Previously, the calculated values of E_{ads_NO} = −85.05 kJ mol⁻¹ and E_{ads_NO2} = −69.74 kJ mol⁻¹ showed that NO adsorbs over the surface mainly via the chemisorption mechanism. As seen in Fig. 8, when NO and NO₂ jointly adsorb over the surface, the adsorption energy is −157.36 kJ mol⁻¹, i.e., the chemisorption effect is enhanced. Also, d_N=O = 1.118 Å (in NO) and d_N–O = d_N–O = 1.202 Å (in NO₂). In comparison with the isolated adsorption system, the joint adsorption makes NO more stable and NO₂ more vulnerable. Meanwhile, the distance between O (in NO) and O (in NO₂ from the single bond) is 3.307 Å longer than the bond length of the covalent bond, which cannot form a chemical bond between NO and NO₂ in the joint adsorption system. Besides, the joint adsorption energy is higher than the isolated adsorption energy with a value of −2.57 kJ mol⁻¹. This indicates that the adsorption of both NO and NO₂ over the surface will enhance the adsorption effect and improve their stability.

Fig. 8 Joint adsorption of NO and NO₂ over the α-MnO₂(110) surface.

Temperature can influence the conversion rates relate to the equilibrium constants for NO_x adsorption over the α-MnO₂(110) surface. The equilibrium constants for the adsorption of NO, NO₂ and joint adsorption over the α-MnO₂(110) surface in the temperature range of 200–1000 K are shown in Fig. 9. The results indicate that all the adsorption systems have positive slopes in the studied temperature range and the equilibrium increases as the temperature increase. The joint adsorption has the largest slope, indicating that temperature has the strongest effect on the equilibrium constant for joint adsorption. Also, a negative value was obtained for the isolated adsorption, but not for the joint adsorption, indicating that the isolated adsorption system can desorb from the surface at a high temperature, while the joint adsorption can enhance the stability of NO and NO₂ adsorbed over the surface in the temperature range of 200–1000 K. The equilibrium constants of NO and joint adsorption were reduced by 61.32% and 95.81%, respectively, when the temperature increased from 300 K to 550 K, indicating that the adsorption efficiency of the sorbent of α-MnO₂ can decrease greatly at temperatures above 550 K. Moreover, NO₂ adsorbed over the surface is easier to desorb from the surface because of its lowest equilibrium constant at the same temperature. The joint adsorption energy was higher than that of the isolated adsorption system because of the van der Waals force among the molecules.

Fig. 9 Equilibrium constants for the adsorption of NO, NO₂ and their joint adsorption over the α-MnO₂(110) surface as a function of temperature (the red dashed line represents ln(K_eq) of 0).

4. Conclusion

The detailed adsorption mechanism of NO_x over the α-MnO₂(110) surface was firstly investigated via a systematic density functional theory study. NO strongly adsorbs over the α-MnO₂(110) surface via chemisorption spontaneously. The NO₂ molecule adsorbs over the surface via chemisorption and physisorption when its terminal N- and O atoms approach the surface, respectively. Besides, the adsorption energy of NO (−85.053 kJ mol⁻¹) is higher than of NO₂ (−69.741 kJ mol⁻¹), indicating that NO adsorbs over the surface initially. The joint adsorption of NO_x is more stable than the isolated adsorption system at 200–1000 K according to the analysis of the thermodynamic data of H and S. S can be influenced by exergy and heat. H can be influenced by heat, but heat in the phase transition does not occur in the adsorption system. The values of H and S for NO adsorption over the surface can be influenced greater by the surface rather than NO in the chemisorption process. Besides, the adsorption is spontaneous under 550 K according to the analysis of the thermodynamic data of △G. In the case of NO₂, the different adsorption mechanisms from the analysis of H, S and ΔG can be explained as follows: a chemical bond can be formed during chemisorption to change the sensitivity of the surface and H can be influenced by the temperature and the surface, which influences ΔG. The potential energy diagram for the different pathways for the adsorption of NO and NO₂ over the α-MnO₂(110) surface showed NO adsorption over the surface and NO₂ desorption in the temperature of 300–550 K. Also, joint adsorption maintained a positive value for the equilibrium constants in the temperature range of 200–1000 K, indicating that joint adsorption is beneficial for the adsorption of more contamination at high temperature. Besides, the equilibrium constants of NO and joint adsorption were reduced by 61.32% and 95.81%, respectively, when the temperature increased from 300 K to 550 K, indicating that the adsorption efficiency of the α-MnO₂ sorbent can decrease greatly at temperatures above 550 K. Hence, it is a better approach to regenerate α-MnO₂-based sorbents that have already adsorbed NO, which oxides to NO₂ and then heats the adsorption system. Besides, NO and NO₂ jointly adsorbed over the surface can remove more NO_x at high temperature.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by National Key R&D Program of China (2018YFC0213400), National Natural Science Foundation of China (51708266, 51408282 and 21667015), China Scholarship Council (201808535082) and the Analysis and Testing Foundation of Kunming University of Science and Technology.

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