**3. HLH Molecular Model Before and After Modification**

### *3.1. Determination of the Type and Number of Aromatic Ring*

The average molecular formula of HLH is C167N3O27H149 by elemental analysis. The average molecular formula of microwave modified HLH is C148H129N3O20, and that of ultrasonic modified HLH is C155H131O23N23. Combined with XPS and elemental analysis, it is found that S content in HLH lignite is extremely small. S element was added to the macromolecular model, but it was found that the percentage of S atom in the analysis of experimental elements was about 1.5%, which was obviously inconsistent with the actual results. Therefore, a small amount of S content was neglected in the construction of the macromolecular model of HLH.

XBP is calculated by using the twelve structural parameters, which is calculated by 13C NMR. The ratio of aromatic bridge carbon to periphery carbon of HLH raw coal is 0.26, that of microwave modified HLH is 0.29, and that of ultrasonic modified HLH is 0.28. The XBP of naphthalene ring with two rings is 0.25, and that of anthracene ring with three rings is 0.40. Therefore, the aromatic framework of HLH raw coal structure model is mainly composed of benzene ring and naphthalene ring. After HLH with microwave modification model and HLH with ultrasonic modification aromatic framework is mainly composed of naphthalene ring, with anthracene ring and benzene ring supplemented. In order to make the XBP of HLH raw coal and HLH model after microwave and ultrasonic modification close to 0.26, 0.29 and 0.28, the combination number of benzene, naphthalene and anthracene rings in its structural model needs to be adjusted continuously. The type and number of aromatic rings in the three structural models are determined. The results are shown in Table 11.


**Table 11.** Type and quantities of aromatic rings of HLH before and after modification.

Comparing the previous 13C NMR and FTIR spectra, it is found that the proportion of oxygen bonded by carbon-oxygen double bond is much smaller than that bonded by carbon-oxygen single bond, which is consistent with the XPS test results. This shows that the main forms of oxygen in macromolecular structure before and after HLH modification are mostly in the form of ether bond and hydroxyl bond of carbon-oxygen single bond, and the other oxygen-containing structures are in the second place. The final form of oxygen in the structure is determined by constantly adjusting the structure of oxygen.

The main forms of nitrogen in HLH macromolecular structure are pyridine nitrogen and pyrrole nitrogen. According to XPS analysis, the number of nitrogen atoms is always 3 of HLH before and after modification, and the main forms of nitrogen elements were pyridine nitrogen and pyrrole nitrogen the content ratio was 2:1. Therefore, two pyridine rings and one pyrrole ring were added to the HLH structure model before and after modification.

### *3.2. Model Construction*

Wiser coal chemical model is used as the basis, which is widely accepted and considered to be comprehensive and reasonable. Combining with the above calculation results, the existing forms and proportions of each part of the macromolecular structure model before and after modification of HLH are summarized and analyzed. Finally, the two-dimensional molecular model of HLH before and after modification is preliminarily established according to the chemical structure characteristics obtained from the experiments. As shown in Figures 7–9.

**Figure 7.** Final two-dimensional model macromolecular structure diagram of HLH.

**Figure 8.** Final two-dimensional model macromolecular structure of HLH after microwave modification.

**Figure 9.** Final two-dimensional model macromolecular structure of HLH after Ultrasonic modification.

#### *3.3. Verification of Model*

The 13C NMR chemical shifts of the three models were calculated and compared with the experimental 13C NMR chemical shifts. Because of the complexity and diversity of coal's macromolecule structure, it is necessary to constantly adjust the types and quantities of its structural units in the construction process, so as to make its 13C NMR simulation spectra better consistent with the experimental spectra. The comparison of 13C NMR simulation spectra and experimental spectra of the three models is shown in Figure 10.

**Figure 10.** Comparison of 13C NMR computational spectra and experimental spectra of HLH final two-dimensional model before and after modification: (**a**) HLH, (**b**) HLH after microwave modification, (**c**) HLH after Ultrasonic modification.

It can be seen that the 13C NMR simulation spectra of the three models are in good agreement with the experimental spectra. There are some errors between the two spectra due to some uncontrollable factors in the experimental process, but it is considered acceptable and will not affect the characterization of average macromolecular structure of HLH coal samples.

In order to adjust the structure of the model to approximate the experimental data, most researchers adopted the simulation of 13C NMR spectrum, but which cannot avoid the choice of isomers [23,24]. At the same time, the model obtained by this method is only a conceptual structure, which cannot reflect the properties of chemical reactions. By using the main covalent bond concentration instead of

the 13C NMR simulation spectrum, the molecular model can be better corrected. According to the 11 structural parameters (fa, fa H, fa O, fa B, fa S, fa C, fal, falA, falM, falH, falO) obtained from 13C NMB data, nine covalent bond concentrations of HLH lignite (Car-Car, Car-Cal, Cal-Cal, Car-H, Cal-H, Car-O, Cal-O, Cal=O, and O-H.) can be obtained. This covalent concentration method reflects the essence of 13C NMR simulation spectroscopy. By comparing the simulated concentration of the main covalent bond with the experimental results, the preliminary two-dimensional molecular model is modified. The concentrations of nine types covalent bonds in coal can be determined by Equations (7)–(15).

$$con\_{\mathbb{C}\_{4}-\mathbb{C}\_{4}} = \frac{1}{2} \left[ \frac{\mathbb{C}\%}{12} \left( 3f\_{d} - f\_{a}^{H} - f\_{a}^{S} - f\_{a}^{O} \right) \right] \tag{7}$$

$$
tau\_{\rm C\_d - C\_{al}} = \frac{C \%}{12} f\_a^S \tag{8}
$$

$$\begin{array}{ll}\text{con}\_{\mathbb{C}\_{al}\to\mathbb{C}\_{al}} &= \frac{1}{2} \Big[ \frac{\text{C}\_{al}^{\text{e}\_{0}}}{12} \Big( 4f\_{al} + 2f\_{a}^{\text{C}} - f\_{a}^{\text{C}} - f\_{al}^{\text{O}} \Big) - n\_{\mathbb{C}\_{al} - H} \Big] \\ &= -\frac{I\_{a}^{\text{e}\_{0}}}{2} + \frac{I\_{a}^{\text{e}\_{0}}}{16} + \frac{1}{2} \Big[ \frac{\text{C}\_{al}^{\text{e}\_{0}}}{12} \Big( 4f\_{al} + f\_{a}^{\text{H}} - f\_{a}^{\text{S}} - f\_{a}^{\text{O}} - 2f\_{al}^{\text{O}} - f\_{a}^{\text{C}} \Big) \Big] \end{array} \tag{9}$$

$$
tau\_{\mathbb{C}\_4 - H} = \frac{\mathbb{C}\%}{12} f\_a^H \tag{10}
$$

$$\begin{array}{ll}\text{con}\_{\mathbb{C}\_{\text{il}}-H} & = H\%-\text{con}\_{\mathbb{C}-H}-\text{con}\_{\mathbb{C}\_{\text{il}}-H} \\ & = H\%-2\frac{\text{O}\%}{16}+\frac{\text{C}\%}{12}\Big(f\_{a}^{\text{O}}+f\_{a\text{I}}^{\text{O}}+2f\_{a}^{\text{O}}+3f\_{a}^{\text{C}}-f\_{a\text{I}}^{\text{H}}\Big) \end{array} \tag{11}$$

$$
tau\_{\rm C\_{ar}-O} = \frac{\rm C\%}{12} f\_{ar}^{O} \tag{12}
$$

$$
tau\_{C\_{al} - O} = \frac{C \%}{12} \left( f\_{al}^{O} + f\_a^{C} \right) \tag{13}
$$

$$\text{con}\_{\mathbb{C}\_{\text{alv}\sim}} = \frac{\mathbb{C}\%}{12} \Big(f\_a^{\mathbb{C}}\Big) \tag{14}$$

$$\text{Con}\_{O-H} = \frac{2O\%}{16} - \frac{C\%}{12} \left( f\_a^O + f\_{al}^O + 3f\_a^C \right) \tag{15}$$

Based on the formula, the information of covalent bond concentration of the three final planar model structures is calculated and summarized in Table 12, in order to more intuitively compare and analyze the difference between the covalent bond concentration obtained from the experiment and that calculated from the model. Then, the molecular models of the three structures obtained from HLH raw coal, microwave, and ultrasonic upgrading of HLH coal, respectively, were adjusted.

**Table 12.** Covalent bond concentrations of 3 structural models of HLH before and after modification.


According to the covalent bond concentration obtained from the experiment and the concentration calculated by the model, it was found that the concentration of the nine covalent bonds is not different from that calculated by the model, but the difference between the experimental concentration of conCal-Cal and conCar-H and the calculated concentration of the model is relatively large. The reason for this may be that there is a certain difference between the proportion of elements in the model and that in the experimental measurement, which makes the calculation of the nine covalent bonds concentration more intensive.
