Mechanistic investigation of the influence of defects on armchair unburned carbon for PbCl 2 adsorption

Abstract

As the largest consumer of coal energy, coal-fired power plants emit large amounts of PbCl₂ each year, which is of wide concern due to its high toxicity, global migration, and accumulation. Unburned carbon is considered a promising adsorbent for effective PbCl₂ removal. However, there is a problem that the current unburned carbon model cannot show the structure of carbon defects on the actual unburned carbon surface. Therefore, it is important to construct defective unburned carbon models with practical significance. In addition, the adsorption mechanism of PbCl₂ by an unburned model is not studied deeply enough and the reaction mechanism is not clear yet. This has seriously affected the development of effective adsorbents. To reveal the adsorption mechanism of PbCl₂ on unburned carbon, the adsorption mechanism of PbCl₂ on defective unburned carbon surfaces was analyzed by using the density flooding theory to investigate the adsorption process of PbCl₂ on different unburned carbon models. This will provide theoretical guidance for the design and development of adsorbents for the removal of PbCl₂ from coal-fired power plants.

Introduction

Thermal power plants, as representatives of traditional high energy-consuming enterprises, generate large amounts of energy consumption and toxic substances, such as lead (Pb), in their daily operation. Pb mainly exists in coal, municipal solid waste, industrial solid waste and other solid wastes or fuels.^1,2 During the heat treatment or combustion of these solid substances or fuels, a large amount of lead evaporates and is discharged into the atmosphere together with high-temperature flue gas.^3,4 When the smoke cools to a certain point, the lead vapor condenses and partially forms PM1 (lung-accessible particulate matter) and even smaller PM0.1.^5–7 These lung-accessible particles are too small to be captured by existing high-efficiency dust collection equipment. It is reported that the collection efficiency of electrostatic precipitator for PM0.1-1 is about 85.8–98.6% and that of bag filter for PM0.1-1 is 99.54%.^8–10 Once penetrating the dust removal equipment, these heavy metals in high concentrations of PM1 and PM0.1 will become aerosols in the atmosphere, and cause lung and blood vessel diseases after human breathing, even seriously leading to various diseases caused by the oxides produced by heavy metals. ¹¹ Therefore, it is urgent to control Pb and its compounds.

Thermal power plants are considered as one of the major sources of pollutants in the environment due to the large number of pollutants that are emitted into the atmosphere every year. Among the various pollutants, Pb is mainly present in the flue gas in three ways: Pb⁰, PbO, and PbCl₂. To promote the removal of lead contaminants, one way is to enhance the dust removal efficiency of the dust removal equipment, another method is using highly active adsorbents. It was shown that a large amount of lead is present on the surface of unburned carbon, which indicates that unburned carbon in fly ash can adsorb or oxidize lead in the flue gas. ¹² In the experimental phenomenon, unburned carbon has good lead removal performance, but its desorption mechanism is difficult to obtain. Fortunately, quantum chemical calculations can help us study the mechanism of the adsorption of various pollutants on unburned carbon at the micro-level. In the research on the mechanism of PbCl₂ adsorption on carbonaceous surface, Carbonaceous surfaces, such as unburned carbon, are usually modeled as benzene clusters. Shen et al. ¹³ studied the removal of elemental mercury from syngas by loading a porous carbon adsorbent with CuCl₂. Liu et al. ¹⁴ studied the adsorption process of mercury on carbon surface. The results show that the adsorption energies of Zigzag model and Armchair model for mercury are −29.6 kJ/mol and −44.6 kJ/mol, respectively. Shen et al. ¹⁵ studied the effect of hydrogen sulfide on mercury adsorption on the 7-membered benzene ring and obtained good results. Gao et al.^16,17 studied the adsorption mechanism of Pb⁰ and PbO on carbon surfaces and achieved good results. However, there are few studies on the adsorption mechanism of PbCl₂ on carbon surfaces, and the reaction mechanism needs to be further studied. In addition, in the theoretical study of lead adsorption on the unburned carbon surface, Scholars have ignored the true adsorption location of unburned carbon. In fact, unburned carbon is the product of burning coal at high temperatures. The high-temperature environment causes the unburned carbon to produce many adsorption sites with high activity on its surface. Some carbon atoms with high activation energy can overcome the interatomic interactions and separate from the carbonaceous structure under their own frequency vibrations, thus forming a defective carbonaceous surface. Some studies^18–20 show that the existence of defective carbonaceous structure is also proved experimentally. He et al., ¹⁹ only investigated the active site of mercury adsorption with a defective unburned carbon structure, but a consistent and systematic study is still lacking. Therefore, a systematic study of the adsorption sites of PbCl₂ on the surface of unburned carbon would be of great importance. By studying the adsorption mechanism of unburned carbon to capture PbCl₂ and exploring the supplementary adsorption sites, we provide a theoretical basis for the rational development and design of adsorbents.

Density flooding theory (DFT) as an approximation method for dealing with multiparticle systems has been widely used in condensed matter physics, materials science, quantum chemistry, and life sciences.^21,22 Therefore, in this work, DFT is used to calculate the adsorption process of PbCl₂ on a defective carbonaceous surface. A mechanism for the adsorption of PbCl₂ on carbonaceous surfaces is proposed. Firstly, the intensity of six model active sites on unburned carbonaceous surfaces was evaluated with electron localization function (ELF). Secondly, the adsorption energy of PbCl₂ on Armchair intact and defective model surfaces was calculated. The effect of defects on PbCl₂ adsorption was considered. Then, MBO, ELF, and electron density difference maps were used to analyze the interaction between PbCl₂ and unburned carbon for the two configurations with the highest energy. This will provide theoretical guidance for the removal of Pb generated during the combustion of coal energy and the design of adsorbents.

Method

In this work, a quantum chemical approach was used to study the adsorption of PbCl₂ by Armchair-type unburned carbon. B97-3c algorithm is a combination method with acceptable time cost, which adopts pure functional and internal basis set, and also includes DFT-D3^23,24 and SRB correction terms. This applies to both the host and transition metal systems. It has high accuracy and reliability. Therefore, this theoretical level is a reasonable solution and can be done within an acceptable computational cost. All model structures were obtained by geometric optimization. Three spin multiplicities are calculated for each model, and the structure with the lowest energy is selected as the ground state structure. ORCA software package was used for all the calculations. ²⁵ Finally, the Multiwfn program ²⁶ was used to analyze the bonding interactions between PbCl₂ and carbonaceous surfaces. The adsorption energy is an important indicator for the study of the adsorption mechanism. The system energy is mainly calculated by the following equation.

$$E_{ads}=E_{AB}-E_A-E_B$$

E_ads is the adsorption energy, E_AB is the total energy of A adsorbed on the solid surface B, E_A and E_B are the total energy of adsorbent A and solid adsorbent B in the ground state. There are two types of adsorption energy. The adsorption energy of the physical adsorption process is less than −50 kJ/mol. With regard to the adsorption energy greater than −50 kJ/mol, it belongs to the chemical adsorption process. ²⁷

Results and discussion

Research model

Monolayer graphite is commonly used to simulate carbon surfaces, and the simulation results are in good agreement with experimental results. Experimental studies have shown that the carbonaceous surface is usually composed of 3–7 benzene rings. ²⁸ Chen et al. ²⁹ studied six benzene ring models by quantum chemistry method and concluded that the calculated results were in good agreement with the experimental data. Montoya et al. ³⁰ found that the activity of the carbon model did not depend on the size and shape of the edge. In addition, the Armchair model has been applied to simulate carbon surface by numerous scholars.^31–33 Therefore, in this work, six benzoic ring models were selected to simulate carbon surfaces. The C atom at the upper edge of the model is exposed to simulate the adsorption site, and the other atoms at the edge are surrounded by H atoms. Although there are no saturated hydrogen atoms or other hybrid atoms on the carbon surface in the actual reaction, it is still a feasible method to use saturated hydrogen atoms to simulate the adsorption environment. The defective carbonaceous surface is evolved from the nondefective carbonaceous model, including single defect, double defect, and triple defect. The defect model is mainly constructed by removing a carbon atom from the top of the model Armchair to form a five-membered benzene ring. The defective carbon surface obtained through geometric optimization is shown in Figure 1. The other five defective models are derived from Armchair models. The optimized structural parameters are shown in Table 1, and the dihedral angle of the optimized model is 0° or 180°, indicating that the bond lengths and bond angles of these models are consistent with previous studies. ³⁴ The model label naming rules are Armchair representing the complete model and D standing for the defect. For example, Arm-D1-1 indicates that the first case in a single defect is constructed based on the complete model.

Figure 1.

Armchair type and its defects unburned carbon model.

Table 1.

Optimized surface structural parameters of the Armchair model.

	Armchair-PbCl2	Arm-D1-1-PbCl2	Arm-D1-2-PbCl2	Arm-D2-1-PbCl2	Arm-D2-2-PbCl2	Arm-D3-1-PbCl2
C-C(Å)	1.40	1.40	1.40	1.40	1.41	1.40
C-H(Å)	1.09	1.09	1.09	1.09	1.09	1.09
∠C-C-C(deg)	120	120.01	121	121.20	122.22	120
∠C-C-H(deg)	120	120	121.12	123.58	121.22	121.11

ELF is an important tool in the field of quantum chemistry to study electronic structure characteristics. It is very important for the study of the adsorption mechanism. ELF diagrams of the complete Armchair model and its defective model are presented in Figure 2, with color differences representing electron configurations. It can be seen from the figure that the ELF value of the adsorption site of the Armchair model is low, and separate electrons appear in the five-membered ring after the formation of the defect structure, which indicates the existence of defects and separates the complete electrons from the perfectly arranged electronic structure, thus improving the adsorption performance of the active site for air pollutants. In addition, the covalent bonds between C–C atoms are well shown in the figure.

Figure 2.

ELF diagram of the unburned carbon model.

Adsorption of PbCl₂ on the unburned carbon surface

The structures of the Armchair model and its five defect models for PbCl₂ adsorption after geometry optimization as well as frequency validation are shown in Figure 3(a). We added a label (PbCl₂) to the adsorption structure to distinguish the adsorbent label. After observing Arm-D1-1-PbCl₂, Arm-D1-2-PbCl₂, Arm-D2-1-PbCl₂, and Arm-D3-1-PbCl₂, it is found that PbCl₂ tends to be adsorbed by defective point sites (five-membered rings) in these four conformations compared with Armchair-PbCl₂. Arm-D2-2-PbCl₂ conformation also forms a stable structure with the Pb atom at the defective site, even though a six-membered ring is present at the attachment. This suggests that the presence of defective structures makes it easier for PbCl₂ to react with the unburned carbon surface and form stable structures. Figure 3(b) shows the adsorption energies corresponding to the six confirmations. It is obvious from Figure 3(b) that the absolute values of all the adsorption energies are greater than −50 kJ/mol, which can indicate that all the adsorption processes are chemisorption. It is noteworthy that all the defective structures have higher adsorption energy for PbCl₂ than the intact Armchair structure. This is a good indication that the presence of defects can improve the adsorption energy for PbCl₂, and the defective structures are more realistic to reflect the reaction process of unburned carbon with PbCl₂ in practice. The adsorption energies of Arm-D2-1-PbCl₂ and Arm-D3-1-PbCl₂ in the defective carbonaceous configuration exceed −300 kJ/mol. One Pb atom and one Cl atom of Arm-D2-1-PbCl₂ react with the defective sites, which is not available in other structures except for the Arm-D3-1-PbCl₂ configuration. Arm-D3-1-PbCl₂ is adsorbed on the five-membered ring in a complete molecular configuration and is adsorbed by three five-membered rings at the same time, which is the highest adsorption energy and the most stable structure because the carbon atom of this structure forms chemical bonds with two Cl atoms and one Pb atom at the same time. At the same time, an extra Cl atom reacts with the defective site, resulting in higher adsorption energy than the Arm-D2-1-PbCl₂ configuration.

Figure 3.

(a) Adsorption configuration of PbCl₂ on the surface of unburned carbon model and (b) adsorption energy of PbCl₂ on unburned carbon model.

Analysis of bonding mechanism

The Mayer bond level reflects the number of electron pairs shared between two atoms. For single/double/triple bonds, the Mayer bond level should be relatively close to 1.0/2.0/3.0. This is extremely important for our analysis of the bonding mechanism. The MBO values of the C–Cl bond and C–Pb bond during the adsorption of PbCl₂ on the unburned carbon model were calculated using Multiwfn, to explain the adsorption energy difference. The specific MBO values are shown in Table 2. It was found that the MBO values of C–Cl bonds vary roughly between 0.84 and 1.04, which are more stable, indicating that a pair of electrons are shared between carbon and chlorine atoms and a stable chemical single bond is formed, while C–Pb bonds vary between 0.64 and 0.98, which are more variable, thus concluding that C–Pb is the key factor affecting the adsorption energy of PbCl₂ on the surface of unburned carbon.

Table 2.

MBO values between key atoms in the adsorption structure.

Structure	Bonding type	Bond length (Å)	MBO
Armchair-PbCl2	C6-Pb33	2.26	0.66
	C19-Pb33	2.25	0.64
Arm-D1-1-PbCl2	C5-Pb32	2.44	0.71
	C5-Cl34	1.82	0.93
Arm-D1-2-PbCl2	C20-Pb32	2.44	0.71
	C20-Cl33	1.83	0.84
Arm-D2-1-PbCl2	C5-Pb31	2.33	0.83
	C18-Cl33	1.74	1.04
Arm-D2-2-PbCl2	C5-Cl33	1.76	1
	C6-Pb31	2.44	0.73
	C19-Pb31	2.44	0.73
Arm-D3-1-PbCl2	C5-Pb30	2.2	0.98
	C13-Cl32	1.75	1
	C18-Cl31	1.75	1

Since the MBO values fluctuate widely for C–Pb, we made a correlation analysis between the MBO of each adsorption configuration species C–Pb and the corresponding adsorption energy. Considering that Pb is bonded to two C atoms in some of the models, the MBO values of C–Pb in this class of models are averaged. The results are shown in Figure 4(b). The results show that as the MBO value between C–Pb increases, the adsorption energy also increases correspondingly. There is a linear positive correlation between the MBO value of C–Pb and the adsorption energy. Therefore, it can be demonstrated that the adsorption of PbCl₂ using Mayer bond level analysis of the carbon-based model is an effective method. It can be speculated that during the study of the adsorption of heavy metal pollutants by the analytical carbon-based model, the trend of Mayer bond level may be able to predict the magnitude of the adsorption energy of this carbon-based model for pollutants. It provides us a means to reveal the internal mechanism of heavy metal adsorption by carbon base.

Figure 4.

(a) MBO values between C–Pb atoms, (b) correlation of MBO values between C–Pb atoms and adsorption energy.

Due to the high adsorption energies exhibited by the Arm-D2-1-PbCl₂ and Arm-D3-1-PbCl₂ conformations, we analyzed them for the relevant bonding mechanisms. ELF analysis (Figure 5(a)) and electron density difference analysis (Figure 5(b)) were performed on these two structures with high adsorption energy to examine the bonding mechanism of PbCl₂ on the surface of unburned carbon. From Figure 5(a), it can be seen that a region with a higher ELF value appears between C–Cl atoms and C–Pb atoms, indicating that during the adsorption process of PbCl₂ on the carbonaceous surface, a shared electron pair is formed between the C–Cl atoms electricity pair. The electrons between C–Pb are mainly concentrated near the C atoms. This can explain the strong chemical bond between C–Cl and C–Pb. Leading to higher adsorption energy. The electron density difference is the density of system AB in its stable state minus the electron density of system A and system B. It is expressed as a three-dimensional real-space function. The process of forming chemical bonds must be accompanied by the phenomenon of electron transfer and polarization. If one wants to examine this visually, then the best way to do so is to examine the density difference of electrons. Therefore, we analyze the electron density difference for these two structures to analyze their bonding mechanisms. In the electron density difference diagram, the solid line indicates the region of electron increase and the dashed line indicates the region of electron decrease. In Figure 5(b) it is obvious that there is an electron increasing part between C–Cl, it can be concluded that a stable covalent single bond is formed between C–Cl in combination with the MBO value. And the electrons between C–Pb are close to the C atom side, which is the result of the lone pair of electrons gathering here during the formation between C–Pb. However, the MBO values of the Arm-D2-1-PbCl₂ and Arm-D3-1-PbCl₂ structures (0.83 and 0.98) are close or even almost equal to 1, indicating that the presence of the defect makes the bond between C–Pb almost close to that of a covalent bond, even though the diagram does not show the electron aggregation right in the middle of the two atoms. In addition, the Arm-D3-1-PbCl₂ structure has a C–Pb bond of 2.2 Å, which is the shortest C–Pb bond among all structures. This also explains the highest adsorption energy of the Arm-D3-1-PbCl₂ structure. In addition, the Arm-D2-1-PbCl₂ structure has a C–Pb bond of 2.33 Å, which is longer than the Arm-D3-1-PbCl₂ structure and at the same time lower than the other structures. This is also consistent with the adsorption energy data we obtained earlier.

Figure 5.

(a) ELF diagram of Arm-D2-1-PbCl₂ and (b) differential electron density diagram of Arm-D2-1-PbCl₂.

Conclusion

The adsorption energy, MBO, ELF, and electron density difference were calculated using the complete six benzene ring armchair edge unburned carbon models and their five defective armchair edge models for the adsorption of PbCl₂. The results show that the adsorption process of all PbCl₂ on the unburned carbon models belongs to strong chemisorption. The unburned carbon is a promising adsorbent for PbCl₂. For the armchair model and its defective model, the results reflected by the adsorption energy show that the defective structure increases the activity of the model’s active center. The defect sites are the adsorption sites of unburned carbon. The defect model built from the complete model has better adsorption performance and can better model unburned carbon for DFT research. Mayer bonding effectively responds to the magnitude of adsorption energy between the adsorbent and the adsorbate. During the adsorption of PbCl₂ on the surface of unburned carbon, covalent C–Cl bonds, and strong C–Pb chemical bonds are generated. This work provides theoretical guidance for the removal of PbCl₂ generated by coal energy consumption in power plants and the rational optimization of adsorbents.