Correction of sideband effects of nuclear magnetic resonance carbon spectrum in coal and its application in coal structure analysis

In the nuclear magnetic resonance (NMR) test of coal, when the spinning frequency of magic‐angle spinning (MAS) is less than the frequency range of chemical shift anisotropy, serious aromatic carbon spinning sidebands will appear. Existing solutions to the sideband effect, such as changing the MAS frequency, inserting total suppression of sidebands (TOSS) pulse sequences, or simply defining the peak after chemical shift of 200 ppm as the sideband peaks generated by aromatic carbon peak, multipling the identified sideband integral by 2 and adding to the main peaks of protonated aromatic carbon and aromatic bridgehead carbon. None of these methods can reasonably correct for the sideband effect and cause errors to accurately quantifying the carbon structure parameters. Compared with 13C nuclear magnetic resonance (13C NMR) spectrum without sideband suppression (13C CP‐MAS NMR) and 13C NMR spectrum under sideband suppression conditions (13C CP‐MAS/TOSS NMR), according to the chemical shifts of the main peaks of four aromatic carbons, namely protonated aromatic carbon, aromatic bridgehead carbon, alkylated aromatic carbon and oxygen‐linked aromatic carbon, combined with the MAS frequency, the first‐ and second‐level sideband peaks generated by four types of aromatic carbons were accurately located and quantified, and they were added to the corresponding aromatic carbon main peaks in 13C CP‐MAS/TOSS NMR spectrum, thus realizing the accurate correction of sideband effect of the solid‐state 13C NMR spectrum of coal samples. The relative area of corrected aliphatic carbon, carbonyl (carboxyl) carbon, and various aromatic carbons were recalculated, and more accurate carbon structure parameters were obtained, which is significant for studying the coal structure from a microscopic perspective.


| INTRODUCTION
Coal is an organic biolith formed by plant remains through long-term complex biochemical, physicochemical, and chemical interactions, which has complexity and heterogeneity. A correct understanding of its structure is of great significance for the efficient and clean utilization of coal. The solid-state 13 C nuclear magnetic resonance ( 13 C NMR) is considered one of the powerful tools for characterizing the structure of natural organic matter, and quantitative information on the distribution of different types of carbon in coal can be obtained by deconvolving the overlapping regions of the NMR spectra. [1][2][3][4] As a technology for rapid and nondestructive observation of the chemical structure of organic matter, solid-state 13 C NMR has been tried to be used in coal research since the 1960s. 5,6 However, due to the low signal-to-noise ratio, low sensitivity, low resolution of 13 C NMR spectra of coal, and the high cost of equipment, it was not until the development of technologies such as cross-polarization (CP) and magic-angle spinning (MAS) that 13 C NMR technology was widely used in the study of coal structure. 7 CP technology is that proton polarization is transferred to carbon, since the gyromagnetic ratio of proton is four times higher than that of carbon, theoretically the 13 C signal intensity can be increased by four times. 8 MAS technology is that the sample spins at magic-angle (54.7°) with the magnetic field direction, which reduces the interactions between molecules and narrows the spectral line, thus providing more accurate information about the coal structure. 9 The combination of CP technology and MAS technology, as well as the use of higher magnetic field, has greatly broadened the capability and application of solid-state NMR, making 13 C CP-MAS NMR technology a common method for characterizing carbon structure. With the help of 13 C CP-MAS NMR technique, Yan et al. 3 studied the structural evolutions during coal metamorphism; Odeh 10 studied the relationship between aromaticity and atomic H/C and O/C; Yoshida et al. 11 studied the relationship between the structural information of coal and the liquefaction product yields; Cao et al. 12 characterized the detailed changes of char structure during heat treatment; Wang et al. 13 comparatively studied the chemical structure of CS 2 /NMP extract and residue of coking coal; Guo et al. 14 studied the influence of tectonic stress on the molecular structure of deformed coal, and discussed the relationship between tectonic coal and gas outburst; Zhou et al. 15 explored the effect of microscopic molecular structure parameters' changes on the wettability of coal dust with the different degrees of metamorphism.
With the deepening of research, researchers have gradually realized that although 13 C CP-MAS NMR technology can solve the problems of spectra line broadening, line asymmetry, and long spin-lattice relaxation time, when the spinning frequency of MAS is less than the frequency range of chemical shift anisotropy, serious aromatic carbon spinning sidebands will appear in the test spectrum. 16 These sideband peaks are mixed with aliphatic carbon peak and carbonyl (carboxyl) carbon peak, which bring nonnegligible errors in quantifying carbon distribution in coal, especially in high-rank coal. 17,18 Liu et al. 19 fitted the 13 C NMR spectrum of Henan anthracite coal (C daf value is 89.03%), and the aromaticity is only 78.56%; Zhang et al. 20 fitted the 13 C NMR spectrum under sideband suppression of Fenghuangshan anthracite coal (C daf value is 89.3% and the mean random vitrinite reflectance is 3.43%), and the calculated aromaticity is 87.9%; Wang et al. 21 fitted the 13 C NMR spectrum of Jincheng anthracite coal (C daf value is 88.04%), the aromaticity is 89.8%. Obviously, due to the influence of sideband effect during test, there is an error between the aromaticity obtained by NMR and the actual aromaticity for these samples.
There are sporadic reports in the literature about the solutions to the sideband effect. (1) Eliminating sideband effects by increasing MAS frequency: Some researchers attempted to remove the aromatic carbon sidebands from the central band region by increasing the MAS frequency, making the effect almost negligible. 9 However, a high spinning frequency will reduce sidebands, but the sample spinning at a sufficiently high frequency, the Hartmann Hahn (HH) match conditions for carbons with narrow HH distributions, such as carboxyl and carbonyl carbons, may have been narrowed to such an extent that their maxima were not being sampled throughout the whole sample, resulting in the decrease of observed carbon signals. 22 To solve this problem, Metz et al. 23 proposed a solution: Ramped amplitude crosspolarization (Ramp-CP). The Ramp-CP changes the amplitude of one of the pulses under the HH condition, so that the frequency range is large enough to cover the sample spinning frequency, which broadens the HH matching condition. However, this method is more suitable for rotating systems with strong abundant-rare dipolar coupling, but coal belongs to a weak abundantrare dipolar coupling system, resulting in significant attenuation of the rare spin signals before reaching the maximum enhancement factor, causing errors in the test. 24 Zhang et al. 25 and Johnson et al. 26 used the multiple-contact CP (multi-CP) method to uniformly enhance the rare spin signals in the sample system through multi-CP, thereby getting rid of the dependence on HH matching conditions, but the method is not applicable when the MAS frequency is fast. 27 Obviously, the above methods tried to use the elimination of the sideband peaks by increasing the MAS frequency, but it caused new errors. (2) Suppressing sidebands by inserting TOSS pulse sequence: Some scholars suppress the sidebands by inserting TOSS pulse sequence to adjust the sideband phase. 28,29 Therefore, the aromatic carbon sidebands no longer appear in the test results, and the aliphatic carbon peaks and carbonyl (carboxyl) carbon peaks in the obtained spectra are no longer mixed with sidebands. The study by Cook et al. 9 concluded that the intensity of aromatic carbon in 13 C NMR spectra should include both the aromatic carbon main peak and the sideband peaks, so the spectra obtained using this method inevitably loses the intensity of the sideband portion of the aromatic carbon. (3) Baysal, 30 Conte, 31 and Okolo 32 attempted to quantify the sideband peaks and correct it. They defined the peak after the chemical shift of 200 ppm as the sideband peaks generated by aromatic carbon peak, and assumed that the aliphatic carbon peak contained a similar sideband peak, multiplied the identified sidebands integral by 2, and added to the central bands of the protonated aromatic carbon and aromatic bridgehead carbon regions. Such a treatment method is not reasonable: first of all, the intensity of the sidebands on the left and right sides of the main aromatic carbon peak is quite different, so it is not conformed with the reality to generally multiply the sidebands integral by 2; in addition, only the sideband effects of protonated aromatic carbon and aromatic bridgehead carbon are considered, while the sidebands contributions of other aromatic carbons are ignored.
It can be seen that none of the existing methods for dealing with NMR sidebands can reasonably correct the sideband effect, and their errors have an unavoidable influence on the proper application of NMR technology in coal. On the basis of comparing the 13 C NMR spectra under the condition of sideband suppression and nonsideband suppression, this paper accurately identifies and quantifies the sideband peaks of various aromatic carbons, namely protonated aromatic carbon, aromatic bridgehead carbon, alkylated aromatic carbon, and oxygen-linked aromatic carbon, removes them from the aliphatic carbon peak and carbonyl carboxyl carbon peak respectively, and accurately superimposes them on the corresponding aromatic carbon contributions, which really realized the reasonable correction of solid-state 13 C NMR spectrum.

| Sample preparation and analysis
This study selected three coal samples with different degrees of metamorphism, which were respectively collected from the No. The proximate analysis, ultimate analysis, and the average maximum vitrinite reflectance of coal samples were performed according to the Chinese national testing standards. [33][34][35] The proximate analysis, ultimate analysis, and the average maximum vitrinite reflectance of the coal samples are presented in Table 1. According to the "Chinese classification of coals" (GB/T 5751-2009), the LL and JC15 # coal samples are classified as bituminous coal and the JC3 # coal sample is anthracite according to dry ash-free basis volatile matter.

| Solid-state 13 C NMR
The solid-state 13 C NMR was tested by Bruker Avance 500 solid-state NMR spectrometer at a frequency of 125.67 MHz for 13 C and a frequency of 500.12 MHz for proton. The dried coal samples were packed into a 4 mm ZrO 2 rotor at a spinning frequency of 8 kHz. At ambient temperature, CP experiments were performed, proton decoupling uses a relaxation or cyclic delay of 3 s. The contact time was 2 ms, the spectral width was 44 kHz and the number of scans was 4000. The 13 C CP-MAS NMR spectra was obtained and the obvious aromatic carbon sideband effect can be observed in the 13 C CP-MAS NMR spectra. TOSS pulse sequence was inserted to obtain 13 C CP-MAS/TOSS NMR spectra in the same experimental condition. Perform a small phase correction of the 13 C NMR spectra using TopSpin software's auto phase correction function to flatten the baseline. The 13 C NMR spectra of the coals are difficult to interpret due to their complicated nature and overlapping bands. According to Okolo et al. 32 and Erdenetsogt et al., 36 the second derivative method has been widely used in curve fitting to separate overlapping peaks in composite spectra, such as NMR spectra of coal and other natural organic materials, and to determine the position and number of each adsorption peak. Therefore, in this paper, we refer to the assignment ranges of different types of carbon in 13 C NMR spectra proposed by the literature 37,38 based on a large number of experiments. The NMR spectra were deconvoluted into individual peaks using Origin software and the positions and number of peaks were determined by the second derivative method, and the peaks were fitted with Gaussian line shapes. The structural parameters were calculated according to the fitting results. 39 3 | RESULTS AND DISCUSSION 3.1 | The 13 C CP-MAS/TOSS NMR and 13 C CP-MAS NMR spectra To facilitate observation, the 13 C CP-MAS/TOSS NMR and 13 C CP-MAS NMR spectra of coal samples were observed in the same coordinate system shown in Figure 1. The peak properties of different chemical shifts in the spectra reflect the composition of different types of functional groups in coal. All of the test spectra under two different conditions were composed of three main peaks for aliphatic carbon (0-90 ppm), aromatic carbon (100-165 ppm), and carbonyl (carboxyl) carbon (165-220 ppm).
It is obvious from Figure 1 that the 13 C CP-MAS NMR and 13 C CP-MAS/TOSS NMR spectra of coal samples LL, JC15 # , and JC3 # exhibit significant differences in the region of aliphatic carbon peaks and carbonyl (carboxyl) carbon peaks. This is because during the 13 C CP-MAS NMR test, the spinning frequency of MAS is less than the frequency range of chemical shift anisotropy, the aromatic carbon peak produce sidebands, and these sidebands are mixed with aliphatic carbon peak and carbonyl (carboxyl) carbon peak, which leads to the false increase of the relative area of aliphatic carbon peak and carbonyl (carboxyl) carbon peak in the whole spectrum, the peak is exhibited even before 0.
The curve-fitted 13 C CP-MAS NMR and 13 C CP-MAS/ TOSS NMR spectra as shown in Figures 2 and 3. The relative areas of each type of carbon in the samples under the two test conditions were determined based on the fitting results. The relative contents of aromatic carbons, carbonyl (carboxyl) carbons, and aliphatic carbons in the samples were calculated using Equations (1)-(3), which were proposed by previous studies. 40,41 These parameters include aromaticity, aliphatic carbon content, and carbonyl (carboxyl) carbon content, which is presented in Table 2.   | 2767 where the f ′ a is the aromaticity, the f a C and f al is the ratio of aliphatic carbon and carbonyl (carboxyl) carbon, respectively, and I 100-165 , I 0-220 , I 165-220 is the area sum of all fitted peaks in the range of 100-165, 0-220, 165-220 ppm, respectively.

| Generation of sideband peaks
During the solid-state 13 C NMR test, the coal sample is subjected to a high-frequency spin in rotor. This phenomenon introduces a time dependence. The "oscillations" due to the refocusing of the magnetization intensity caused by the rotation of the sample can be considered as echoes. The positions of these "oscillations" are related to the sample spinning frequency and are located on both sides of the main peak at distances of one and two times the sample spinning frequency (ω r ). When the free-induced decay is transformed from the time domain to the frequency domain, that is, when the spectrum is generated, these "oscillations" appear as spinning sidebands in the spectrum and are located on both sides of the central isotropic line, the distance is the sample spinning frequency. 9 The sideband in 13 C CP-MAS NMR spectra are generated by the chemical shift anisotropy of four types of aromatic carbons: protonated aromatic carbon, aromatic bridgehead carbon, alkylated aromatic carbon, and oxygen-linked aromatic carbon. The horizontal coordinate value x of the 13 C NMR spectrum represents the chemical shift, and the vertical coordinate value y represents the absorption peak intensity. The experimental parameters of the 13 C CP-MAS NMR spectra and the 13 C CP-MAS/TOSS NMR spectra were set in the same way, and the values of the horizontal coordinates of the two spectra corresponded to one-to-one. Therefore, the 13 C CP-MAS/TOSS NMR spectra can be subtracted from the 13 C CP-MAS NMR spectra, and the result is the sideband spectra of aromatic carbon peaks, as shown in the shaded part of Figure 4.

| The chemical shift of the sideband peaks
According to the intensity and position of the sideband peaks, it can be divided into first-and second-level sidebands. Among them, the first-level sidebands are located on both sides of the aromatic carbon peak, which is closer to the aromatic carbon peak and has higher intensity; the second-level sidebands are far from the aromatic carbon peak, and its intensity is relatively small. Their respective positions are symmetrical to the aromatic carbon peak, and their distances are related to the sample spinning frequency, which can be calculated according to Equations (4) and (5). The distances between the first-and second-level sidebands and the aromatic carbon main peak in this test were calculated to be 63.66 and 127.32 ppm, respectively.
where the L 1 is the distance between the first-level sideband and the main peak and the L 2 is the distance between the second-level sideband and the main peak. The ω r is sample spinning frequency, this test takes the value of 8 kHz and the v is the spectrometer frequency, this test takes the value of 125.67 MHz. Based on the calculated distances between the first-and second-level sidebands and the main peaks of aromatic carbon, the intervals of the first-and second-level sidebands of the four types of aromatic carbon in the spectra were further calculated using Equations (6) and (7), and the results are shown in Table 3.
F I G U R E 4 Aromatic carbon peak sidebands of LL, JC15 # , and JC3 # coal samples. CP, cross-polarization; MAS, magic-angle spinning; NMR, nuclear magnetic resonance; TOSS, total suppression of sideband.
where the δ 1 and δ 2 is the chemical shift of first-and second-level sidebands, respectively. δ MP is the chemical shift of the main peak, according to the literature, is 19,28,37,38 the chemical shifts of the main peaks of four types of aromatic carbons: protonated aromatic carbon, aromatic bridgehead carbon, alkylated aromatic carbon, and oxygen-linked aromatic carbon are 100-129, 129-137, 137-148, and 148-165 ppm, respectively. Figure 5 plots the first-and second-level sideband intervals corresponding to the four types of aromatic carbon, using JC3 # coal as an example.

| Area and correction of sideband peaks
Based on the sideband intervals of protonated aromatic carbon, aromatic bridgehead carbon, alkylated aromatic carbon, and oxygen-linked aromatic carbon listed in Table 3, the left (−27.32 to 100 ppm) and right (165 to 292.32 ppm) sideband spectra of the three coal samples were peak-fitted (Figure 6), and the first-and second-level sideband areas of the four types of aromatic carbon in each sample were calculated and shown in Table 4.   In the curve-fitted results of 13 C CP-MAS/TOSS NMR spectra (Table 2), the peak areas of the aliphatic carbon peak and carbonyl (carboxyl) carbon peak remain unchanged. The peak areas of protonated aromatic carbon, aromatic bridgehead carbon, alkylated aromatic carbon, and oxygen-linked aromatic carbon were correspondingly added with the peak areas of the first-and second-level sidebands of four types of aromatic carbon in Table 4. Further calculate the relative area of aliphatic methyl, aromatic methyl, methylene, quarternary carbon, methine, oxygen-linked aliphatic carbon, protonated aromatic carbon, aromatic bridgehead carbon, alkylated aromatic carbon, oxygen-linked aromatic carbon, carbonyl (carboxyl) carbon. The relative contents of different types of carbon were obtained and completed the correction of solid-state 13 C NMR spectra (Table 5).
3.3 | 13 C NMR structural parameters of JC3 # coal sample before and after correction Table 6 lists the 13 C NMR structural parameters of coal samples obtained according to 13

| 2771
Aromaticity is one of the important indicators of coal maturity. 42 13 C CP-MAS NMR analysis showed that the aromaticity of LL, JC15 # , and JC3 # coal samples were 52.91%, 58.33%, and 54.74%, respectively. Obviously, this set of data cannot accurately reflect the differences in the degree of metamorphism of the three samples. The aromaticity determined by 13 C CP-MAS/TOSS NMR for the three coal samples were 70.71%, 83.59%, and 93.91%, respectively, which are basically consistent with the degree of metamorphism, but this method loses some of the intensity of aromatic carbon, 9 and still has some errors. The aromaticity of the three coal samples after correction were 77.99%, 88.47%, and 96.58%, respectively, which match well with the coal rank law of the three samples.
The studies of Erdenetsogt et al. 36 and He et al. 43 indicate that as the coal rank increases, oxygen is retained mainly as hydroxyl groups on the condensed aromatic ring, with a significant decrease in oxygenlinked aliphatic carbon and carboxyl carbon. The percent oxygen-linked aliphatic carbon content of LL, JC15 # , and JC3 # coal samples obtained by 13 C CP-MAS NMR test were 9.22%, 10.04%, and 13.49%, the percent carboxyl carbon content was 2.41%, 3.24%, and 7.57%, and the percent carbonyl carbon content were 11.95%, 13.64%, and 14.88%, respectively. Apparently, the above data do not match the coal rank variation laws of the three samples, which is due to the fact that the 13 C CP-MAS NMR test was not performed with sideband suppression, and the aliphatic carbon peak and carbonyl (carboxyl) carbon peak were mixed with the sidebands generated by the aromatic carbon peak, resulting in obvious errors in the above parameters. The percent oxygen-linked aliphatic carbon content of LL, JC15 # , and JC3 # coal samples obtained by 13 C CP-MAS/TOSS NMR test were 4.48%, 3.19%, and 1.22%, the percent carboxyl carbon content was 1.47%, 0.00%, and 0.00%, and the percent carbonyl carbon content were 1.36%, 1.17%, and 1.17%, respectively. It can be seen that in the 13 C NMR spectra after the sideband suppression, the obtained three samples with the oxygen-linked aliphatic carbon, carboxyl carbon, and carbonyl carbon contents coincide with the coal rank because the oxygen-linked aliphatic carbon and carbonyl (carboxyl) carbon regions are free from the influence of the aromatic carbon sidebands, but the results still have errors due to the loss of the intensity of the aromatic carbon sideband peaks by this method. The corrected three coal samples showed 3.36%, 2.24%, and 0.69% oxygen-linked aliphatic carbon content, 1.11%, 0.00%, and 0.00% carboxyl carbon content, and 1.02%, 0.83%, and 0.65% carbonyl carbon content, respectively, which showed good consistent with the coal rank laws of the samples. The above data show that the method in this paper can be reasonably corrected for the sideband effect for all coals of different coal ranks.
In addition, the 13 C CP-MAS NMR spectra of LL, JC15 # , and JC3 # coal samples showed that the percentages of the sideband peaks in the aliphatic carbon peak region were 39.13%, 57.15%, and 89.22%, respectively, and the percentages of the sideband peaks in the region of the carbonyl (carboxyl) carbon peaks were 85.76%, 87.08%, and 95.07%, respectively. It shows that as the degree of coal metamorphism increases, the sideband effect produced by the aromatic carbon has a greater effect on the aliphatic carbon peak and the carbonyl (carboxyl) carbon peak.

| CONCLUSION
A method for correcting the sideband effects in coal NMR spectra is proposed based on 13 C CP-MAS NMR and 13 C CP-MAS/TOSS NMR spectra, which could reduce errors caused by the sideband effects. The positions and intervals of the four types of aromatic carbon sidebands were determined based on the principle of sideband peak generation. By conducting peak fitting and area calculation, the sideband peaks were repositioned from the aliphatic carbon peak and carbonyl carbon peak to the main peak of aromatic carbon, achieving the correction of sideband effects in coal NMR spectra. The corrected NMR carbon spectra of three different coal ranks provided the aromaticity, oxygenlinked aliphatic carbon content, carboxyl carbon content, and carbonyl carbon content that are consistent with the respective coal rank laws, indicating that this method is applicable to coal samples of different ranks and provides a new approach for accurately characterizing coal structure.