Study on the Analysis of Toluene Degradation via Microwave Plasma Based on Density Functional Theory Calculations

Abstract

Volatile Organic Compounds (VOCs) are pervasive environmental pollutants with significant implications for air quality and human health. The development of effective technologies for VOC degradation is essential to mitigate their adverse effects. Microwave plasma technology has emerged as a promising solution for VOC abatement due to its ability to generate highly reactive species at ambient conditions, enabling efficient decomposition of VOCs into harmless byproducts. Concurrently, Density Functional Theory (DFT) has become a critical tool for understanding the molecular-level mechanisms of VOC degradation, providing insights into reaction pathways and energy dynamics. This study explores the integration of microwave plasma experiments with DFT simulations to investigate the degradation mechanisms of VOCs under plasma conditions. DFT calculations of microwave plasma degradation for toluene are performed. The results show that on the one hand, toluene can undergo ring-opening. Then, these active molecules or groups react with active free radicals and are ultimately oxidized into CO₂ and H₂O. On the other hand, VOC gas molecules react with active free radicals (O, OH) generated by background gas (O₂ and H₂O) through oxidation reactions, generating organic intermediates such as benzene, benzyl alcohol, and benzoic acid, respectively, which are finally oxidized into CO₂ and H₂O. Our theoretical research results are expected to provide profound insights into the degradation mechanisms of these aromatic hydrocarbon VOCs through microwave plasma and also contribute to a better understanding of the further degradation mechanisms of air pollutants at the molecular level.

1. Introduction

Volatile Organic Compounds (VOCs) are a class of carbon-based chemicals that readily evaporate at room temperature, contributing to air pollution and posing serious health risks [1,2,3]. Emitted from industrial processes, vehicle exhaust, and household products, VOCs are known to cause respiratory issues, neurological disorders, and even cancer [4,5]. Additionally, they play a significant role in the formation of ground-level ozone and secondary organic aerosols, exacerbating environmental challenges such as smog and climate change [6,7]. As global regulations on the emissions of VOCs become increasingly stringent, there is an urgent need for advanced technologies that can efficiently degrade VOCs.

Plasma technology has gained traction as a highly effective method for VOC abatement. Unlike conventional thermal methods, plasma operates at ambient temperatures and pressures, generating a high-energy environment rich in reactive species such as electrons, ions, and radicals [8,9,10]. These species can break down complex VOC molecules into simpler, non-toxic compounds like CO₂ and H₂O. The non-thermal nature of microwave plasma ensures energy efficiency, making it a sustainable option for large-scale applications [11,12,13,14]. However, the complex chemical reactions involved in microwave plasma-mediated VOC degradation require a deeper understanding to optimize the process and enhance its effectiveness. Compared to the experimental study, theoretical research focusing on the reaction process is a better way to explore the VOCs degradation mechanisms by plasma.

The theoretical method, Density Functional Theory (DFT), has emerged as a powerful computational approach to study the molecular interactions and reaction mechanisms of VOCs [15,16,17]. By simulating the electronic structure and energy dynamics of VOC molecules and their interactions with plasma-generated species, DFT provides a theoretical framework to predict degradation pathways and identify intermediate products [18,19,20].

Volatile Organic Compounds (VOCs) have received much attention in the fields of atmospheric chemistry and environmental health. Among them, toluene, as a typical representative substance, its sources and impacts cannot be ignored. In terms of emission sources, toluene is widely present in human activities such as petroleum processing, transportation, furniture and building material production, and industrial manufacturing [21]. Studies have shown that toluene has a high potential for generating secondary pollutants. It can undergo photochemical reactions with nitrogen oxides (NOx) and be converted into secondary organic aerosols and ozone in the troposphere [22]. This process not only exacerbates air pollution but also causes damage to the balance of the ecosystem and human health [23]. In addition, in the indoor environment, toluene is also one of the important air pollutants. Long-term exposure to an air environment containing toluene may lead to ventricular arrhythmia, dysfunction of the hematopoietic system, respiratory depression, and even uncomfortable symptoms such as nausea [24].

To address the technical bottleneck of traditional experimental methods in capturing transient reaction intermediates, this study employed the Gaussian16 software to construct a quantum chemical model of toluene degradation in a microwave plasma field. The model systematically elucidated the molecular bond cleavage mechanisms under the synergistic action of high-energy electrons and reactive species.

This study reveals the microscopic degradation mechanisms of typical Volatile Organic Compounds (VOCs) from the perspective of quantum chemistry. Toluene is selected for the calculations. The degradation reactions and mechanisms of toluene are analyzed. Moreover, the degradation pathways of toluene are summarized.

2. Model Descriptions and Computational Methods

2.1. Model Descriptions

As shown in Figure 1, microwave plasma dissociates VOCs in chemical industry exhaust gases into CO₂ and H₂O. The operation is carried out under 1 atmosphere pressure. The non-thermal plasma electrons e* are generated via a microwave-induced metal discharge process, a phenomenon that has been elaborately described in our previous research works [25,26]. In the depicted diagram of Figure 1, the black, blue, and red spheres distinctly represent carbon atoms, hydrogen atoms, and oxygen atoms, respectively. The waste gas laden with organic substances enters the electric field through the designated inlet.

It is found in the literature that the discharge phenomenon generates a plasma effect, producing a large number of free electrons, O₃, active free radicals (O, OH, and H), and other particles [27,28]. These active groups can excite VOC gas molecules and promote the degradation of VOCs. Thus, it is simulated and speculated that in the microwave plasma system, the degradation of VOCs mainly involves two processes: direct degradation and indirect degradation, as shown in Figure 1.

As can be seen from Figure 1, in direct degradation, VOC gas molecules undergo inelastic collisions with high-energy electrons generated by discharge, leading to the breakage of chemical bonds in VOC gas molecules. For example, toluene can undergo ring-opening. Then, these active molecules or groups react with active free radicals and are ultimately oxidized into CO₂ and H₂O. In the indirect reaction, when gases such as oxygen and water molecules pass through the plasma region, active free radicals (O, OH) are generated. These active free radicals react with VOC gas molecules through oxidation reactions, generating organic intermediates such as benzene, benzyl alcohol, and benzoic acid, respectively, which are finally oxidized into CO₂ and H₂O.

2.2. Computational Methods

The calculation method is as follows: Gaussian 16 was used to conduct DFT calculations. The classic B3LYP functional was selected, and the 6-311G(d, p) basis set was employed. This basis set offers relatively high calculation accuracy and low time consumption [20,29,30]. The calculation of the reaction potential energy surface was categorized into two cases: one with a transition-state structure and another without a transition-state structure.

For reactions with a transition-state structure, the Intrinsic Reaction Coordinate (IRC) calculation was used to confirm the transition state, which involved the following three steps: First, geometric structure optimization (Optimization, opt) and vibrational frequency analysis (Frequency, freq) of the transition state were performed. Next, the transition state (TS, Transition Structures) was calculated using the opt=TS method to search for the transition state. The keywords used were opt(TS, calcfc, noeigen). Subsequently, IRC calculation was carried out on the optimized transition state (TS) using the keywords IRC(calcfc, lqa). The initial configuration of the oxygen atom adopts the ¹O• (singlet oxygen radical).

For reactions without a transition-state structure, the flexible scanning (Scan) method was employed to investigate the potential energy surface of the system. The keywords opt=modredundant was used, and nosymm was selected simultaneously. Structural optimization and frequency analysis were then performed on the endpoints obtained from the Scan calculation to finally confirm reaction mechanisms, bond dissociation, and other chemical processes.

3. Results and Discussion

3.1. The Initial Step for Toluene Degradation

Direct Degradation Reaction of Toluene

(1)

Toluene cracking reaction

As can be seen from the previous text, in the plasma field generated by microwave plasma, toluene collides with high-energy electrons, which may cause the dissociation of covalent bonds and lead to direct degradation. In the structure of toluene, the C-C bond connecting the methyl group and the benzene ring is much easier to break than the C-C bonds on the benzene ring. Therefore, it is very necessary to study the C-C bond between the α-C and the phenyl group. This section mainly conducts DFT calculations on the cleavage of the C-C bond between the α-C of toluene and the phenyl group. After numerous attempts to search for the transition state with initially guessed structures failed, a flexible scan was carried out on the C₆H₅-CH₃ bond of the most stable state structure, and the scanning results are shown in Figure 2. From the trend in the flexible scanning curve, it can be seen that starting from the initial most stable state structure of toluene with a bond length of 1.50 angstroms, the bond length gradually increases to 6.50 angstroms. During this process, the energy keeps rising. When the distance between C₆H₅-CH₃ is further increased, the energy increase is not significant. This is because when the distance of the C₆H₅-CH₃ bond is 6.50 angstroms, it is already the critical breaking state of the toluene molecular structure, and the chemical bond has been completely broken. Continuing to increase the distance between C₆H₅-CH₃ will only lead to changes in the conformation, and the energy required for the conformational change is much lower than that for the chemical bond. At the same time, as can be seen from Figure 2, there is no derivable saddle point throughout the process, indicating that there may be no transition state in the process of the C₆H₅-CH₃ bond breaking.

Since there is no transition state, it can be considered that the cleavage of the methyl group is determined by the bond dissociation energy of the C₆H₅-CH₃ bond. By optimizing the structures at both ends, the value obtained by subtracting the energy of the leftmost structure from that of the rightmost structure in the figure can be approximately regarded as the bond energy of the C₆H₅-CH₃ bond. The calculation results are shown in

Table 1. Calculated value of the bond energy of toluene.

Structure	Bond Length	Energy	Relative Energy
	(Å)	(Hartree)	(kJ/mol)
C6H5-CH3 (Figure 2A)	1.50	−271.53976	0.0
C6H5CH3 (Figure 2B)	6.50	−271.38969	394.0

. The calculated bond energy is 394.0 kJ/mol, which is basically consistent with the literature result of 391.0 kJ/mol [31]. By comparing the calculated results with the values reported in the literature, it can be considered that the calculation method is reasonable and the calculation results are reliable. This indicates that DFT calculations can be applied to the study of the reaction mechanism of toluene degradation by microwave plasma.

(2)

Oxidation reaction of toluene

In the structure of toluene, it is generally believed that the hydrogen atoms on the methyl group are relatively active, and the methyl α-C is easily attacked by free radicals to undergo an oxidation reaction. As can be seen from Figure 3A, during the degradation of toluene by microwave plasma, toluene can directly undergo an oxidation reaction with free radicals to generate hydrogen-substituted organic products. This section conducts DFT calculations on the oxidation process of toluene, and the calculation results are shown in Figure 3. The contents include the oxidation of toluene to benzyl alcohol (Figure 3A), the oxidation of benzyl alcohol to benzaldehyde (Figure 3B), the oxidation of the benzaldehyde group to benzoic acid (Figure 3C), and the decarboxylation reaction of benzoic acid (Figure 3D). As can be seen from Figure 3A, the process of oxidizing toluene to benzyl alcohol is that under the action of microwave plasma, toluene easily loses a hydrogen atom to generate a benzyl radical. The reaction mechanism of oxidizing benzyl to benzyl alcohol is that the α-C on the side chain is attacked by the hydroxyl group in H₂O, and the H atom on the α-C is substituted by OH. Through the transition state TS, benzyl alcohol and H radicals are generated. The reason is that due to the electron conjugation effect of the benzene ring, the H atom on the α-C of the alkyl group is very active, and the C-H bond is easily broken, which easily causes the toluene group to lose a hydrogen atom to form a benzyl radical and then attract the attack of polar water molecules. The α-C combines with the hydroxyl group OH to undergo an oxidation reaction [31]. When an oxidation reaction occurs in an alkylbenzene, the side-chain alkyl group is oxidized first, and the benzene ring does not participate in the reaction. The potential energy barrier of the reaction is 235.7 kJ/mol, and the heat absorbed is 170.1 kJ/mol.

As can be seen from Figure 3B, in the reaction of oxidizing benzyl alcohol to benzaldehyde, two reaction pathways were investigated: dehydrogenation and oxidation. (1) The reaction mechanism of dehydrogenation is that benzyl alcohol loses the H atom on the α-C to form the transition state TS1 and then loses the H atom on the hydroxyl group to form benzaldehyde and two H atoms. The potential energy barrier of this reaction is 343.4 kJ/mol, and the heat absorbed is 27.1 kJ/mol. (2) The reaction mechanism of oxidation is that benzyl alcohol reacts with the ¹O•. The hydroxyl group loses an H atom to generate the transition state TS2, and the detached H radical combines with the ¹O• to form an OH radical, resulting in the formation of an intermediate, namely the benzyloxy group and the OH radical. The potential energy barrier of this reaction is 18.1 kJ/mol, and the heat released is 189.9 kJ/mol. Then, the intermediate undergoes a decomposition reaction, that is, it loses the H atom on the α-C to generate the transition state TS3. Then, the H radical and the OH radical combine to form H₂O, and the α-C-O bond forms a C=O double bond, thus forming benzaldehyde and H2O. The potential energy barrier of this reaction is 179.8 kJ/mol, and the heat released is 283.0 kJ/mol. From the above analysis, it can be seen that the potential energy barrier during the oxidation reaction process is relatively low, and the reaction is relatively easy. In contrast, for the dehydrogenation reaction from the intermediate through TS1 to benzaldehyde, the required potential energy barrier is relatively high, and the reaction is more difficult.

In the molecular structure of benzaldehyde, due to the conjugation between the benzene ring and the carbonyl group, the hydrogen atom of the aldehyde group is relatively active. Especially in the microwave plasma environment, it is very easy to lose a hydrogen atom to generate a benzaldehyde radical. As can be seen from Figure 3C, the benzaldehyde radical is prone to attract the attack of water molecules (H₂O), forming a transition state TS1. Then, the OH radical and the H atom are simultaneously bonded to the α-C. The C=O double bond in the aldehyde group forms a solid bond and a virtual bond, generating an intermediate. The potential energy barrier of this reaction is 143.8 kJ/mol, and the heat absorbed is 69.5 kJ/mol. The H atom on the α-C of the intermediate is lost again. Through the transition state TS2, benzaldehyde is oxidized to generate benzoic acid and H radicals. The potential energy barrier of this reaction is 37.6 kJ/mol, and the heat released is 16.6 kJ/mol.

As can be seen from Figure 3D, the decarboxylation reaction process of benzoic acid is that the α-C cleaves from the benzene ring, and at the same time, the carboxyl group loses a hydrogen atom. Through the transition state TS, benzene and CO₂ are generated. The potential energy barrier of this reaction is 245.8 kJ/mol, and the heat released is 89.3 kJ/mol.

In conclusion, through DFT calculations, it is found that the reaction of toluene with free radicals such as O and OH can achieve the indirect degradation of toluene, and the main products are benzyl alcohol, benzaldehyde, benzoic acid, and benzene. This is consistent with the organic products detected in the experiment [26,32], thus proving the reaction pathway of the indirect degradation of toluene at the atomic level. Theoretical calculation studies have found that the potential energy barriers of these reactions are relatively low, and there are a large number of active free radicals in the microwave plasma field, making the reactions likely to occur.

3.2. The Subsequent Degradation of Toluene

3.2.1. Direct Degradation Reaction of Organic Intermediates

(1)

Cleavage reaction of the benzene ring

As reported in the literature [33,34], there are mainly two pathways for the cleavage reaction of the benzene ring: (1) The benzene ring undergoes a ring-opening reaction through the breakage of one of its C-C bonds, generating conjugated hexadiene. (2) The dissociation of three C-C bonds occurs simultaneously, and the benzene ring decomposes into three acetylene molecules.

For the calculation of the breaking of a certain C-C bond on the benzene ring, after numerous attempts to search for the transition state with initially guessed structures failed, a flexible scan was carried out on the C1-C6 bond in the most stable benzene ring structure. The scanning results are shown in Figure 4. From the trend in the flexible scanning curve, it can be seen that starting from the initial most stable state structure of the benzene ring with a bond length of 1.39 angstroms, the bond length gradually increases to 5.39 angstroms. During this process, the energy keeps rising. When the distance between C₆H₅ and CH₃ is further increased, the conformation of the benzene ring changes. Therefore, there may be no transition state in the process of the breaking of the C1-C6 bond in the benzene ring structure.

Since there is no transition state, similar to the cracking of toluene in Figure 2, it can be considered that the breaking of a C-C bond in the benzene ring is determined by the dissociation energy of the C-C bond. Therefore, during the calculation, the structures at both ends were optimized, and then the value obtained by subtracting the energies can be approximately regarded as the bond energy of the C1-C6 bond. The calculation results are shown in

Table 2. Calculated value of the bond energy of C1-C6 in benzene.

Structure	Bond Length	Energy	Relative Energy
	(Å)	(Hartree)	(kJ/mol)
C6H6 (Figure 4A)	1.39	−232.23585	0.0
HCCHCHCHCHCH (Figure 4B)	4.39	−231.93215	797.4
HCCCHCHCCH H H (Figure 4C)	5.39	−231.977867	677.3
C2H2 C2H2 C2H2 (Figure 4D)	7.39	−231.925142	815.8

. As can be seen from Table 2, the calculated bond energy is 797.4 kJ/mol, which is higher than the result of 716.9 kJ/mol reported in the literature [33].

There may be a transition state in the reaction of benzene cracking into acetylene. Therefore, the structure of the initially guessed transition state for this reaction was optimized, and frequency calculations were carried out. Additionally, the reactants and products obtained after the IRC (Intrinsic Reaction Coordinate) calculation were optimized and subjected to frequency analysis. It was confirmed that the reactant is benzene and the product is acetylene. The results are shown in Figure 5.

The reaction mechanism is that three C-C bonds (C1-C2, C3-C4, C5-C6) in the stable structure of the benzene ring break simultaneously. After passing through the transition state TS, three acetylene molecules are formed. The potential energy barrier of this reaction is 782.0 kJ/mol, and the heat absorbed is 550.0 kJ/mol. The bond length of the C-C bonds in the stable structure of the benzene ring is 1.39 Å. In the transition state TS, the bond lengths of the breaking C1-C2, C3-C4, and C5-C6 bonds are 2.29 Å, while the bond lengths of the remaining non-breaking bonds are 1.22 Å. Meanwhile, the non-breaking C-C bonds form C≡C triple bonds. From the above analysis, in the ring-opening reaction of the benzene ring, compared with the energy required for the breakage of a single C-C bond, the energy required for the simultaneous breakage of three C-C bonds is lower. Therefore, the reaction of directly obtaining three acetylene molecules through the ring-opening of the benzene ring is more likely to occur.

In conclusion, in the cleavage reaction of the benzene ring, the cleavage of the benzene ring to produce acetylene is one of the theoretically predicted concerted dissociation pathways, which means that the degradation of toluene by microwave plasma may generate acetylene. This is consistent with the experimental results reported in the literature [32,35] and also in line with the reports in the literature that acetylene is produced in the cracking reaction of toluene [36,37]. Compared with the stepwise mechanism (ring-opening reaction), its actual occurrence probability requires further experimental validation in combination with specific plasma parameters.

3.2.2. Free Radical Oxidation Reaction

(1)

Acetylene oxidation reaction

As is known from previous research studies, the benzene ring may undergo a ring-opening reaction to produce acetylene. Meanwhile, due to the presence of high-energy electrons and active free radicals in the plasma formed by the microwave plasma, the oxidation reaction of acetylene can easily proceed.

In the plasma field, acetylene can collide with high-energy electrons to form acetylene radicals, and it can also react with free radicals, eventually generating CO₂ and H₂O. In this section, DFT calculations were carried out for the oxidation reaction of acetylene radicals and the reaction between acetylene and O₃ radicals. The calculation results are shown in Figure 6. Acetylene can easily generate acetylene radicals upon collision with high-energy electrons. Moreover, the acetylene radicals can undergo an oxidation reaction. There are two reaction pathways for its reaction with O₂:

(1)

The terminal carbon of the acetylene radical attracts O₂, as shown in Figure 6A. As can be seen from Figure 6A, when the acetylene radical reacts with O₂, the C atom attracts O₂ to form Intermediate 1. There is no transition state in this reaction process, and the heat released is 233.9 kJ/mol. In Intermediate 1, an O atom transfer reaction occurs. After passing through the transition state TS1, O₂ combines with the middle carbon to form Intermediate 2. The potential energy barrier of this reaction is 227.2 kJ/mol, and the heat released is 185.1 kJ/mol. One of the triple bonds in the alkyne of Intermediate 2 is cleaved. After passing through the transition state TS2, the middle carbon forms a C-O bond to generate Intermediate 3. The potential energy barrier of this reaction is 13.8 kJ/mol, and the heat absorbed is 5.0 kJ/mol. The conformation of the C-O bond in Intermediate 3 changes. After passing through the transition state TS3, an oxygen atom migrates to the terminal carbon atom, forming two C-O bonds to generate Intermediate 4. The potential energy barrier of this reaction is 11.2 kJ/mol, and the heat released is 97.6 kJ/mol. The C-O bond on the middle carbon of Intermediate 4 is very unstable and breaks. After passing through TS4, a terminal carbonyl group is formed, and then Product 1 is generated. The potential energy barrier of this reaction is 66.6 kJ/mol, and the heat absorbed is 92.5 kJ/mol. In addition, Intermediate 1 can also form a terminal carbonyl group through the cleavage of the O-O bond in its molecule after passing through the transition state TS11, thus generating Product 1. The potential energy barrier of this reaction is 72.4 kJ/mol.

(2)

The terminal carbon of the acetylene radical attracts O₂, and there may be other reaction pathways, as shown in Figure 6B. The process of the reactants forming Intermediate 1 is the same as that in Figure 6A mentioned above. Intermediate 1 undergoes an O-transfer reaction. After passing through the transition state TS5, all O atoms are added to the terminal carbon to form Intermediate 5. The potential energy barrier of this reaction is 84.3 kJ/mol, and the heat absorbed is 33.6 kJ/mol. Intermediate 5 isomerizes. After passing through the transition state TS6, Intermediate 6 is formed. The potential energy barrier of this reaction is 38.2 kJ/mol, and the heat released is 463.9 kJ/mol. In addition, Intermediate 1 can directly form Intermediate 6 through an O-transfer reaction after passing through the transition state TS5. The potential energy barrier of this reaction is 84.3 kJ/mol, and the heat released is 430.3 kJ/mol. Intermediate 6 undergoes an adjacent migration of the O atom to the CC position, forming a three-membered-ring transition state TS7. The O atom continues to migrate to generate Intermediate 7. The potential energy barrier of this reaction is 255.7 kJ/mol, and the heat absorbed is 87.3 kJ/mol. Intermediate 7 undergoes an adjacent migration of the H atom to the OC position. After passing through the transition state TS8, Intermediate 8 is formed. The potential energy barrier of this reaction is 278.0 kJ/mol, and the heat absorbed is 175.1 kJ/mol. Intermediate 8 undergoes migrations of the H atom and the O atom. After passing through the transition state TS9, Intermediate 9 is generated. The potential energy barrier of this reaction is 33.8 kJ/mol, and the heat released is 0 kJ/mol. The middle C-O bond in Intermediate 9 is cleaved. After passing through the transition state TS10, Product 2, namely the formyl group and the OH radical, is generated, releasing 273.6 kJ/mol of heat. It is worth noting that the energy of the transition state TS10 is lower than that of Intermediate 9, which is inconsistent with the transition-state theory. A possible reason is that there is no transition state in the last step of the reaction, that is, TS10 does not exist, and Intermediate 9 directly cleaves into the formyl group and the OH radical. In addition, Intermediate 7 undergoes a C-C bond cleavage. After passing through the transition state TS72, Product 2 is generated. The potential energy barrier of this reaction is 34.9 kJ/mol, and the heat released is 98.5 kJ/mol.

As can be seen from the above analysis, compared with Reaction Pathway (1), Reaction Pathway (2) has a higher potential energy barrier, and it is more difficult to generate Product 2. Therefore, it is possible that there are other reaction pathways for the oxidation of acetylene besides these two. Thus, further exploration of the calculation results is shown in Figure 7.

Figure 7 shows the reaction between acetylene and the O₃ radical. As can be seen from this figure, each C atom in acetylene attracts an O atom. After passing through the transition state TS1, two C-O bonds are formed to generate Intermediate 1. The potential energy barrier of this reaction is 28.8 kJ/mol, and the heat released is 242.5 kJ/mol. One of the O atoms in Intermediate 1 attracts an ¹O•. After passing through the transition state TS2, the C-O bond in the structure forms a C=O bond, and finally Intermediate 2 is generated. The potential energy barrier of this reaction is 18 kJ/mol, and the heat released is 119.5 kJ/mol. Intermediate 2 undergoes isomerization. After passing through the transition state TS3, Intermediate 3 is formed. The potential energy barrier of this reaction is 18 kJ/mol, and the heat released is 21.8 kJ/mol. The O atom in Intermediate 3 is transferred. After passing through TS4, Intermediate 4 is formed. The potential energy barrier of this reaction is 90.6 kJ/mol, and the heat absorbed is 43.8 kJ/mol. The C-C bond in Intermediate 4 is cleaved. After passing through the transition state TS5, the C-O bonds on both sides form C=O bonds, and finally acetic anhydride is generated. The potential energy barrier of this reaction is 97.5 kJ/mol, and the heat released is 511.1 kJ/mol.

The calculation of the further oxidation reaction of formic anhydride is shown in Figure 8. Figure 8A shows the oxidation reaction between formic anhydride and the ¹O•. As can be seen from this figure, one of the C-O bonds in the structure of formic anhydride is cleaved to form a formyloxy group and a formyl group. Then, the formyl group combines with the ¹O•. After passing through the transition state TS6, two formyloxy groups are formed. The potential energy barrier of this reaction is 15.5 kJ/mol, and the heat released is 290.8 kJ/mol [38].

Figure 8B illustrates the cleavage reaction of the formyloxy group. As is evident from this figure, an intramolecular H-atom transfer occurs within the formyloxy group structure. Through the transition state TS7, the H atom migrates to the O atom, generating a carboxyl radical, designated as Intermediate 1. This reaction features a potential energy barrier of 105.2 kJ/mol and releases 32.7 kJ/mol of heat. Subsequently, the C-O single bond in Intermediate 1 undergoes a transformation. Through the transition state TS8, a C=O bond is formed, leading to the generation of Intermediate 2. This reaction has a potential energy barrier of 36.0 kJ/mol and absorbs 4.8 kJ/mol of heat. In Intermediate 2, the hydroxyl group dissociates from the C atom. Through the transition state TS9, CO and an OH radical are produced. The potential energy barrier of this reaction is 100.3 kJ/mol, and it absorbs 103.7 kJ/mol of heat. Notably, the energy of the transition state TS9 is lower than that of the products, which contradicts the transition state theory. A plausible explanation is that there is no transition state in the final step; that is, TS9 does not exist, and Intermediate 2 directly dissociates into CO and the OH radical.

DFT calculations were also carried out for the reaction of CO oxidation to CO₂. The reactions of CO with ¹O• and O₃ radicals were investigated separately, and the calculation results are shown in Figure 9. The reaction mechanism of CO with ¹O• is that the C atom attracts the ¹O•. After passing through the transition state TS1, CO₂ is generated. The potential energy barrier of this reaction is 94.9 kJ/mol, and it releases 596.1 kJ/mol of heat. For the reaction of CO with O₃ radicals, the C atom attracts one O atom. After passing through the transition state TS2, CO₂ and O₂ are produced. The potential energy barrier of this reaction is 37.4 kJ/mol, and it releases 336.2 kJ/mol of heat. From the above analysis, compared with O₃ radicals, singlet oxygen radicals have a lower potential energy barrier and release more heat when reacting with CO.

As can be seen from the above analysis, acetylene can be converted into CO and CO₂ under the action of high-energy electrons and active free radicals.

3.3. The Reaction Pathway of Toluene Degradation by Microwave Plasma

In summary, DFT calculations reveal that toluene can not only undergo direct degradation via covalent bond cleavage triggered by collisions with high-energy electrons but also achieve indirect degradation through oxidation reactions with active free radicals. Direct Degradation Pathways of Toluene: Toluene directly collides with high-energy electrons, leading to the rupture of the C-C covalent bond between the methyl group and the benzene ring. As a result, methyl radicals and phenyl radicals are formed. Additionally, toluene can lose a hydrogen atom to generate benzyl radicals. Methyl and phenyl radicals can be further bombarded by high-energy electrons and free radicals. Subsequently, they undergo a series of oxidation reactions with highly reactive free radicals such as O, OH, and O₃, ultimately forming CO₂ and H₂O. Indirect Degradation Pathways of Toluene Toluene reacts with active free radicals like O and OH in the plasma field. Through oxidation, toluene is converted into benzyl alcohol, which is then further oxidized to benzaldehyde and benzoic acid. Benzoic acid undergoes decarboxylation to form benzene. Under the influence of high-energy electrons, the benzene ring may undergo ring-opening cleavage. It continues to react with free radicals, eventually producing CO₂ and H₂O. The process is simulated in Figure 10. This research and analysis provide a clear understanding of the degradation pathways of toluene.

Examination of the calculation results reveals that not only are the organic products generated from theoretical calculations consistent with those detected experimentally, but also the final products of the toluene degradation reaction—CO and CO₂—match the experimental findings. This indicates that DFT calculations can be applied to study the reaction mechanism of toluene degradation by microwave plasma. Moreover, the reliability of the reaction pathways for toluene degradation by microwave plasma has been validated both theoretically through calculations and practically through experiments.

4. Conclusions

In this study, for the toluene degradation reaction, appropriate model compounds were selected. DFT calculations were employed to analyze the geometric structures and reaction potential energy barriers. The impacts of electrons and active free radicals on the degradation of VOCs were investigated at the atomic level, and the reaction mechanism of toluene degradation by microwave plasma was revealed. The main conclusions are as follows:

By integrating the product analysis of experiments, possible reaction pathways of toluene were proposed. During the degradation of toluene by microwave plasma, two types of reactions occur. One is direct degradation, namely, the cracking reaction; the other is indirect degradation, specifically, the oxidation reaction.

DFT calculations were adopted to compute and analyze the degradation reaction pathways of toluene in microwave plasma, thereby obtaining the degradation mechanism of toluene. The results indicate that within the plasma field formed by microwave plasma, toluene can achieve direct degradation through the cleavage of covalent bonds. It can also undergo indirect degradation via oxidation reactions with active free radicals. Reasonable intermediate transition states were identified, and theoretical calculations validated the scientific nature of the hypothesized mechanisms.

DFT calculations demonstrated that the reaction pathways of toluene degradation by microwave plasma were further confirmed. Toluene can collide with high-energy electrons, leading to the cleavage of the C₆H₅-CH₃ bond and thus achieving direct degradation. It can also react with active free radicals in oxidation reactions: toluene is oxidized to benzyl alcohol, benzyl alcohol to benzaldehyde, benzaldehyde to benzoic acid, and benzoic acid undergoes decarboxylation to produce benzene and carbon dioxide. Benzene further undergoes ring-opening cleavage to generate acetylene, which is then oxidized to carbon dioxide. These results are consistent with the organic products detected experimentally. This suggests that DFT calculations can be applied to study the reaction mechanism of toluene degradation by microwave plasma. Moreover, it validates the consistency between the results of theoretical calculations and actual experiments.

By combining experimental results with theoretical models, we aim to elucidate the fundamental processes underlying plasma-VOC interactions. The findings of this study will not only enhance the efficiency of plasma-based VOC abatement but also contribute to the broader field of sustainable pollution control technologies.