## 3 Results and Discussions
### \({}^{13}\)C NMR Spectra Analysis  
Through the \({}^{13}\)C NMR spectra, the chemical environments of carbon atoms in coal molecules can be understood [29]. Different carbon atoms in coal may exist in various environments, such as aromatic rings, alkyl chains, or oxides. \({}^{13}\)C NMR helps to distinguish these different chemical environments and enables the quantitative analysis of the relative proportions of different types of carbon. To fully understand the carbon structures in LR@1 and LR@2 lignites, PEAK-FIT software (PeakFit v4.12) was used to perform detailed peak fitting on the \({}^{13}\)C NMR spectra of the coal samples, with the fitting results shown in Figure 3. The peak-fitting spectra of the coal samples reveal two distinct carbon peaks: one is the aliphatic carbon peak located at 0-80 ppm, and the other is the aromatic carbon peak located at 100-165 ppm [30]. This indicates that the carbon structures of both lignites are primarily composed of aliphatic and aromatic carbon. Moreover, there are no noticeable peaks corresponding to carbonyl or carboxyl groups (175-200 ppm [31]), suggesting that the carbon-oxygen structures in LR@1 and LR@2 are primarily linked by single bonds.  
Figure 2: Analysis of carbon, oxygen, nitrogen and sulfur fugacity patterns in two lignite structures, LR@1 and LR@2 (**a**) C spectrum of LR@1 (**b**) O spectrum of LR@1 (**c**) N spectrum of LR@1 (**d**) S spectrum of LR@1 (**e**) C spectrum of LR@2 (**f**) O spectrum of LR@2 (**g**) N spectrum of LR@2 (**h**) S spectrum of LR@2.  
Based on the \({}^{13}\)C NMR structural parameters of the coal samples, the forms and contents of aliphatic and aromatic carbons in LR@1 and LR@2 lignites can be quantitatively analyzed. Table 3 presents the macromolecular structural parameters of the coals. From Table 3, it can be observed that aromatic carbon (fa\({}^{\prime}\)) is the dominant component in both LR@1 and LR@2 lignites, with the highest relative content, accounting for 57.69% and 60.68%, respectively. The aliphatic carbon in the coal molecules primarily exists as methyl groups (\(f_{\text{al}}\)\({}^{\text{st}}\), -CH\({}_{3}\)), methylene groups (\(f_{\text{al}}\)\({}^{\text{H}}\), -CH\({}_{2}\), -C-, -CH-), and oxygenated aliphatic carbons (\(f_{\text{al}}\)\({}^{\text{O}}\),O--C). Among these, the highest proportion of aliphatic carbon in both coal molecules is in the form of methylene groups, with relative contents of 27.95% and 20.04%, respectively. This suggests that the aliphatic carbon in the structures of both LR@1 and LR@2 mainly exists as long-side chains. In the coal molecular structure, aromatic carbons mainly include protonated aromatic carbons (\(f_{\text{a}}\)\({}^{\text{H}}\), Ar-H), bridge aromatic carbons (\(f_{\text{a}}\)\({}^{\text{B}}\), C-C), side-chain aromatic carbons (\(f_{\text{a}}\)\({}^{\text{S}}\), Ar-C), oxygen-substituted aromatic carbons (\(f_{\text{a}}\)\({}^{\text{P}}\), Ar-O), and non-protonated aromatic carbons (\(f_{\text{a}}\)\({}^{\text{N}}\)). The aromatic carbon structures in both LR@1 and LR@2 lignites are predominantly protonated aromatic carbons, with relative contents of 28.60% and 27.91%, respectively. The bridge-to-surrounding carbon ratio (\(X_{\text{BP}}\)) reflects the average degree of condensation of aromatic rings. The calculated values for the aromatic bridge carbon to surrounding carbon ratio are 0.295 for LR@1 and 0.266 for LR@2, indicating the degree of aromatic condensation in the two lignites.