Article pubs.acs.org/EF
Pyrolysis Mechanism of Metal-Ion-Exchanged Lignite: A Combined Reactive Force Field and Density Functional Theory Study Guang-Yue Li,† Quan-An Xie,† Hang Zhang,‡ Rui Guo,† Feng Wang,† and Ying-Hua Liang*,† †
College of Chemical Engineering, and ‡Modern Technology and Education Centre, Hebei United University, Tangshan 063009, People’s Republic of China S Supporting Information *
ABSTRACT: Three-dimensional structural models for lignite and metal-ion-exchanged lignite were constructed to investigate the impact of added metal species on their pyrolysis. The Wender model was used as the structural unit of the two models, and Ca(OH)2 was used as the added metal species. Reactive force field molecular dynamics was employed to simulate the pyrolysis of the two models at 1000−2000 K over a period of 300 ps. Subsequently, cleavage pathways in the pyrolysis of the two models were determined. The characteristics observed in the simulation agree well with the known characteristics of the lignite structure. We found that the initial reactions in the pyrolysis of the two models are mainly decarboxylation and cleavage of the bridged C− O bond. These reactions were further confirmed by density functional theory calculations. Upon addition of Ca(OH)2 to lignite, the carboxyl and phenolic hydroxyl could be deprotonated. Added metal species changed the pathways for both reactions from homolytic cleavage to heterolytic cleavage and decreased the bond dissociation energy and the energy of products, thereby accelerating lignite pyrolysis.
1. INTRODUCTION Lignite, also known as brown coal, is the geologically youngest coal with relatively low heat content. Most of the lignite is now directly burned to generate power, especially in China.1 The process wastes much energy because of its low thermal efficiency, and its exhaust contains soot, which pollutes the environment. Consequently, there is a need for designs that maximize the use of lignite through coal-conversion reactions and, thus, increase its economic value. Pyrolysis is usually the first step for nearly all coal-conversion processes, including combustion, gasification, and liquefaction. Hence, understanding the pyrolysis mechanism is important. However, pyrolysis is a complex process involving numerous reaction pathways that are impossible to detect experimentally.2 Many researchers have added metal species to lignite and other low-rank coals to increase their reactivity.3−6 These metal species include sodium salts (CH3COONa and NaCl),3 potassium salts (KCl),4 calcium species [(CH3COO)2Ca, Ca(NO3)2, CaCl2, Ca(OH)2, and CaCO3],3,4 and species formed with other metals (Mg2+, Fe3+, Al3+, Cu2+, and Ba2+).5 It is thus evident that most of the common metal species could be used as catalysts for coal reactions. However, the catalytic mechanisms for these species are not yet clear; only a few works report the interaction between metal species and lignite.7 The reactive force field (ReaxFF), which was developed by van Duin et al.,8 is an empirical force field for molecular dynamics (MD). It is capable of describing bond-cleavage and cross-linking reactions with a low computational cost and accuracy close to the quantum chemical method. ReaxFF MD has been applied to explore the mechanisms of molecular systems with thousands of atoms.9−11 In particular, this method has been widely used to explore reactions of coal macromolecules in various environments.12−14 Through a ReaxFF method, Salmon et al. reproduced the thermal decomposition © 2014 American Chemical Society
processes of Morwell brown coal in its early maturation, including defunctionalization, depolymerization, and rearrangement of the residual structures. Findings of this study agree well with the experimental results.14 Zheng et al. simulated the pyrolysis reactions of a bituminous coal model of 4976 atoms by using a ReaxFF method.15 The evolution tendency of the product profile and the sequence of gas generation agree well with those obtained experimentally. Furthermore, they developed a graphics processing unit (GPU)-enabled ReaxFF MD program to investigate coal pyrolysis involving atoms with numbers ranging from 1378 to 27 283. This program proved to be much faster than traditional central processing unit (CPU)enabled programs.16,17 These successful applications demonstrate that ReaxFF MD provides a methodology that could explain reaction pathways of coal macromolecules. However, this method does not account for electron motions. Therefore, it cannot be used to calculate accurate energy changes in coal reactions. Density functional theory (DFT), a widely used quantum chemical method, is able to describe the energy changes of a molecular system. Its high accuracy in describing chemical reactions incurs a high computational cost, resulting in its inapplicability to coal macromolecules. On the other hand, DFT could be used to explain local reactions of coal involving small fragments extracted from coal macromolecules. Using benzoic acid and phenol as molecular models, Liu et al. investigated pyrolysis reactions of carboxylic groups in brown coal through DFT calculations.18 Ling et al. used benzenethiol as a molecular model to investigate the migration of sulfur to the products CS, H2S, and thiophene during coal pyrolysis.19 In Received: December 18, 2013 Revised: June 9, 2014 Published: July 2, 2014 5373
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model does not contain functional groups with N and S atoms; therefore, interactions between N- and S-containing functional groups and Wender model molecules could not be considered. Furthermore, because the model is a relatively small, it could lead to a larger ratio of small molecules in the pyrolysis products. Connecting sites in all structural units are saturated with hydrogen atoms. This operation does not change the reactive bonds in the pyrolysis process and has little influence on the pyrolysis mechanism. It also reduces the computational cost in the subsequent DFT calculation. The initial conformation of the structural unit was optimized using the Dreiding force field23 in the LAMMPS program.24,25 Subsequently, 100 structural units were added to a 67.00 × 67.00 × 67.00 Å cell to construct a 3D lignite model (M1, C4200H4600O1300) using the Packmol package.26 To consider the role of the added alkali or salt, we built another 3D model containing 100 structural units, 5 Ca2+ cations, and 10 OH− anions (M2, C4200H4610O1310Ca5) in a cell with the same size to represent metalion-exchanged lignite. Periodic boundary conditions in all directions were applied to the two models. The initial densities of M1 and M2 were low (0.418 and 0.420 g/cm3, respectively), because a low density could prevent overlapping of functional groups. Geometry optimizations were then performed in three steps: (1) an annealing simulation with isothermal−isochoric (NVT) ensemble from 0 to 800 K, (2) compression with the isothermal−isobaric (NPT) ensemble at 10 MPa and decompression at 0.1 MPa at 800 K, and (3) an annealing simulation with NVT ensemble from 800 to 0 K. The simulated densities of M1 and M2 show good agreement with the true density of lignite (1.2−1.4 g/cm3). Thus, the models could properly describe the properties of lignite. 2.2. Convergence Test of ReaxFF Simulation. ReaxFF parameters reported by Pitman and van Duin27 were used in the subsequent MD simulations without any modifications. In the ReaxFF simulations, one trajectory for each simulation could not provide reliable results. To achieve meaningful statistical data, the number of trajectories should be sufficient. Herein, ReaxFF simulations were performed to verify the convergence through a method as reported.28 First, one pre-optimized Wender model molecule was placed in a 40.00 × 40.00 × 40.00 Å periodic cell. We obtained the relationship between the number of molecular fragments that appeared in this unimolecular simulation and the number of computed trajectories at 1500 K (see Figure S1 of the Supporting Information). A lower simulated temperature would produce fewer molecular fragments, which would lead to convergence with fewer trajectories and save the computational cost. However, in that case, the number of trajectories might be insufficient if the simulated temperature is higher. Considering the creditability and the computational cost, a simulated temperature of 1500 K was selected here. The number of molecular fragments increased with the number of trajectories. When the trajectory number was more than 270, the types of total fragments became almost stable. This trend indicates that calculations in simulation of lignite pyrolysis over 270 trajectories could converge. In the simulations of the 3D models of lignite, 100 Wender model molecules are placed in a cubic box. Calculation of one trajectory is equivalent to 100 times the calculations for each molecule. At least three computed trajectories were found to give converged results in the simulations based on the aforementioned unimolecular convergence test. To confirm this estimate, we compared the results of the annealing simulations of one, two, three, four, and five trajectories. The distribution of H2O molecules is shown in Figure S2 of the Supporting Information. Results of calculation for the three trajectories agree well with those for the calculation of four and five trajectories. That is, over three trajectories could give converged results for the subsequent analysis. To improve the accuracy of the sampling, calculations of four trajectories were used in the 3D model simulations. 2.3. ReaxFF Simulation. ReaxFF MD simulations of M1 and M2 were performed with the LAMMPS program. To determine the simulation temperature, we performed annealing ReaxFF simulations of M1 in the temperature range of 500−2500 K at a rate of 5 K/ps. We found that the Wender model molecules began to dissociate at ∼935 K and that all Wender model molecules dissociated at ∼1880 K.
these studies, DFT was used to explain local coal reactions using relatively small molecules as coal models. As mentioned above, computational chemistry methods, such as ReaxFF and DFT, have been proven to be the powerful tools that complement experimental studies. In the present study, the pyrolysis mechanism of metal-ion-exchanged lignite was studied, using a combined ReaxFF and DFT method. We used Ca(OH)2 as the added metal species and the Wender model20 (Figure 1) as the structural unit of the three-
Figure 1. (a) Wender model, where connecting sites are represented by asterisks, and (b) its atom labeling.
dimensional (3D) model to simulate the chemical structure of lignite. First, ReaxFF MD of the models was used to examine the initial decomposition process and to determine the reactive bonds. Subsequently, cleavage reactions of these bonds were further elucidated by DFT calculation. The combined ReaxFF and DFT method could describe not only the reaction pathways of coal macromolecules but also the energy changes involved in local reactions. Very few studies on coal reactions using such a combined method have been published.21 By comparison of the reaction pathways and energies before and after the addition of the metal ions, we could determine the pyrolysis mechanism of the metal-ion-exchanged lignite. We believe that our theoretical work would aid in understanding processes of coal reactions.
2. COMPUTATIONAL METHODS 2.1. Three-Dimensional Model Construction. We selected the Wender model as the structural unit for lignite and Ca(OH)2 as the added metal species. The Wender model contains different types of functional groups with oxygen (hydroxyls, carbonyls, and ethers) and bridge bonds. Because it provides a good chemical representation of lignite, it was used to determine its reactive site and to explain the dissolution behavior of lignite in aqueous KOH.22 Furthermore, it is a relatively small structural model of lignite; it therefore could save computational cost in both ReaxFF and DFT calculations. However, some limitations of the model must be considered in this work. The 5374
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Therefore, the simulation temperature was set to 1000−2000 K. ReaxFF MD simulations using a NVT ensemble in a cube with a periodic boundary of 300 ps with the time step of 0.25 ps were then performed to exploit product distributions of coal pyrolysis at 1000, 1200, 1400, 1600, 1800, and 2000 K. The bond order cutoff was 0.3 Å, and the non-bonded cutoff was 10 Å. In the simulations, all atoms in M1 and M2 were marked and traced. The results were analyzed using a C++ program to determine the hydrogen bonds and possible cleavage reactions through a previously reported method.29−32 Details and source codes are shown in sections 2 and 3 and Figure S3 of the Supporting Information. 2.4. DFT Calculation. All DFT calculations were carried out using the ORCA program.33 Becke’s three-parameter hybrid exchange functional with Lee−Yang−Parr gradient-corrected correlation (B3LYP functional)34−37 provides reasonable agreement with experimental results and is not time-consuming.38,39 Thus, it was used in the DFT method in the subsequent work. Triple-valence quality with one set of polarization functions (TZVP)40 was adopted as the basis set throughout, because it is an appropriate basis set for organic compounds. No constraints for symmetry, bonds, angles, or dihedral angles were applied in the geometry optimization calculations. All of the local minima were confirmed by the absence of an imaginary mode in the vibrational analysis calculations. The bond dissociation energy (BDE) is the energy per mole required to break a given bond of a specific molecule. As shown in Figure 2, it is the energy change for the homolytic reaction X−Y → X•
intermediates, and products were pre-optimized. BDEs were then obtained through a potential-curve scan, with the target bond distance fixed within a series of values by constrained optimizations. The energy of the products could be calculated by geometrical optimization of the products. The cleavage reaction energy (ΔE) was calculated as the energy difference between the fragment products and reactant.
3. RESULTS AND DISCUSSION 3.1. Microstructures of Lignite and Metal-Ion-Exchanged Lignite. Hydrogen bonds of M1 and M2 were rendered in 3D geometries through a program written in C++ code. A hydrogen bond can be conformed if all of the following requirements are satisfied: (1) the O···H···O angle is 150− 180°, and (2) one O···H distance is typically ∼1.10 Å, and the other O···H distance is less than 2.00 Å. Hydrogen bonding is the main intermolecular interaction in lignite.41 As shown in Figure 3a, hydrogen-bond interactions between the units are the dominant intermolecular interactions in M1. Furthermore, there are π−π stacking interactions between the aromatic moieties (Figure 3b). These results agree with the known features of the lignite structure. The optimized structure of M2 shows interactions similar to those in M1. The structural unit in the 3D model contains three types of hydroxyl groups, namely, alcoholic (O3−H, O9−H, O11−H, and O13−H), phenolic (O4− H and O7−H), and carboxyl group (O1−H) hydroxyls. The added hydroxyl anions acted on the hydroxyl groups (Figure 3c), but no Brønsted acid−base reaction occurred because of the non-reactive force field. 3.2. Temperature Effects on Pyrolysis Products. ReaxFF MD simulations of M1 at 1000, 1200, 1400, 1600, 1800, and 2000 K were then performed to investigate the chemical reactions in lignite pyrolysis. A snapshot of the configuration at 1600 K and 300 ps is shown in Figure 4. We observed that radical fragments were generated first. The radicals subsequently attacked the aromatic moieties, resulting in intermolecular cross-linking reactions. Simulations of M1 show agreement with the experimental pyrolysis of low-rank coals.42 ReaxFF simulations of M2 under the same conditions showed similar reactions. The final compound distributions of M1 and M2 within the simulations at 1000−2000 K were analyzed to determine the temperature effect on the pyrolysis products. Products at different temperatures were classified according to mass fractions in ref 15 (Figure 5). Molecules with less than five C atoms, which also include H2O, H2, and O2, were considered as gas. C5−C13 and C14−C40 molecules, with molecular weights ranging from 66.05 (C5H6) to 700.34 (C40H44O11), were
Figure 2. Diagrams of BDE and ΔE calculation for the (a) homolytic reaction and (b) heterolytic reaction. + Y• or the heterolytic reaction X−Y → X: + Y (X and Y are C, O, or H in this paper). It could be calculated from the energy difference between the reactant and the intermediate. In this work, all reactants,
Figure 3. Interaction between units obtained from M1 and M2. Some atoms in the background are omitted. (a) Hydrogen bond in M1, (b) π−π stack in M1, and (c) hydrogen bond between the unit and hydroxyl anion in M2. 5375
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observed that the initial reaction for lignite pyrolysis at any temperature is extremely complex. With higher temperatures, more reactions generally occurred. The initial stage of pyrolysis mainly consists of cleavage of the molecular skeleton (see Figures S4−S9 of the Supporting Information). In particular, cleavage of bridged bonds occurs most frequently. For example, decarboxylation of a unit takes place during 27−29 ps at 1600 K (reaction 1-1 in Figure 6). This reaction in the ReaxFF simulation was observed to have two steps, namely, dissociation of a hydrogen atom and dissociation of carbon dioxide. Because it involves release of a small fragment from the structural unit, this reaction also easily takes precedence. Cleavage of the C10− O5 bond at 58−60 ps at 1800 K was also observed (reaction 1-2 in Figure 6). Bridged C−O bonds in coal easily break via homolytic cleavage, producing free radicals. Initial reactions in the ReaxFF MD trajectories of M2 were also analyzed. We observed deprotonation reactions with Ca(OH)2 in the ReaxFF MD simulation of metal-ionexchanged lignite pyrolysis at 1000−2000 K. Three main sites in the Wender model molecules (O1, O4, and O7; see Table S1 of the Supporting Information) reacted with hydroxyl. Subsequently, the structural units converted into the corresponding anions. In general, cleavage of bridged bonds is not affected if the negative charge is not retained in adjacent conjugated systems. Therefore, some reactions in the pyrolysis of M2 are similar to those in M1 pyrolysis (see Figures S10− S15 of the Supporting Information). However, the mechanisms of other reactions (Figure 7) are altered by the negative charge. Reaction 2-1 shows the decarboxylation of a structural unit with a negatively charged carboxyl group at 25−27 ps and 1600 K. Here, the C1−C2 bond is broken. Carbon dioxide dissociates from the structural unit, leaving a carbanion product. Thus, the two steps of decarboxylation are reduced to only one step. Reaction 2-2 shows the cleavage of the C10−O5 bond at 103− 105 ps at the same temperature. In this reaction, the C10−O5 bond in the structural unit with the negatively charged O4 atom is broken. A neutral molecule and a phenoxide anion, which are more stable than two free radicals, were the products. These results qualitatively explain the primary step of pyrolysis of metal-ion-exchanged lignite. Quantitative descriptions of the cleavage mechanism were investigated by DFT calculation. 3.4. BDEs of the Cleavage Reactions. For the BDE calculations, we optimized the geometries of the structural unit and anions formed by reaction with Ca(OH)2. Seven anions are possible for the structural unit. However, anions formed by deprotonation on O1, O4, and O7 are much more stable than other anions (see Table S2 of the Supporting Information), consistent with the ReaxFF simulation results. The BDE and ΔE for each frequently occurring cleavage reaction found in the ReaxFF simulations of M1 and M2 were calculated through the DFT method. As shown in Table 1, cleavage of the C1−C2 and C10−O5 bonds was affected by the addition of Ca(OH)2. However, Ca(OH)2 had little influence on the cleavage of other bonds. For example, BDEs of the C2−C3 bond in the neutral structural unit and the deprotonated structural unit are 285.5 and 285.9 kJ/mol, respectively. These results show that deprotonation does not obviously change the BDEs of these bonds, because cleavages of these bonds are still homolytic. 3.4.1. Cleavage Pathway of the C1−C2 Bond. Decarboxylation in reaction 1-1 may proceed through two possible pathways (pathways A and B). Pathway A starts with dissociation of the hydrogen atom bonded to O1, followed by elongation of the C1−C2 bond to form the carbon radical and a
Figure 4. Snapshot of M1 at 1600 K and 300 ps in ReaxFF MD.
Figure 5. Composition evolutions in ReaxFF MD at 1000−2000 K for (a) M1 and (b) M2.
considered as constituents of coal tar. Heavier molecules (C40+) were considered as constituents of coal char. C40+ molecules in M1 after 300 ps of simulation are main products and represent 59.72% of the mass at 1000 K. However, only 1.01% of these molecules remained at 1600 K and disappeared at 1800 K. We thus believe that cleavage reactions of C40+ molecules are more likely to happen at higher temperatures. The percentage of C14−C40 molecules increased from 1000 to 1400 K and then decreased from 1400 to 2000 K. The percentage of C5−C13 molecules increased from less than 10% to more than 30% as the temperature increased from 1000 to 2000 K. Simulations of M2 produced similar results. C40+ molecules comprised 49.85% of the products at 1000 K and then disappeared at 1600 K. The ratios of small molecules of M1 increased at the same simulation temperature because of the catalytic metal species. 3.3. Determination of Pyrolysis Pathways in ReaxFF MD. We analyzed the ReaxFF MD trajectories of M1 at various simulation temperatures to determine its reactions. We 5376
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Figure 6. Most frequent cleavage reactions of bridged bonds in M1 obtained by ReaxFF simulation.
Figure 7. Anion-induced cleavage reactions of bridged bonds in anions.
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Table 1. BDE and ΔE Obtained by DFT/B3LYP/TZVP Calculation (kJ/mol) Wender model C10−C5 C1−C2 C2−C3 C15−C18 C18−C19 C27−C28 C41−C42
decarboxylation pathway for reaction 2-1 is the release of CO2 to form the carbon anion and the concomitant proton transfer from O3 to C2. The energy curve shows that BDE of C1−C2 in the reaction 2-1 is 197.6 kJ/mol (Figure 9), which is lower than that of reaction 1-1. Furthermore, the products of reaction 2-1 are a neutral molecule and an anion (with energies amounting to 71.2 kJ/mol), instead of unstable free radicals in the case of reaction 1-1 (267.5 kJ/mol). Therefore, added Ca(OH)2 decreased both BDE and ΔE of C1−C2 bond cleavage. Cleavage of the C1−C2 bond proceeded more easily after the addition of Ca(OH)2. The anion in the products is generated by capture of a proton of the neighboring hydroxyl group by the carbanion. 3.4.2. Cleavage Pathway of the C10−O5 Bond. As seen in Figure 9, reaction 1-3 is also a radical-formation process. The energy curves suggest that the energy along the C10−O5 bond increases. Its reaction mechanism is homolytic cleavage of the C10−O5 bond, producing benzyl and phenol radicals with a BDE of 174.9 kJ/mol. Deprotonation of O4 or O7 changes its cleavage pathway from homolytic cleavage (reaction 1-3) to heterolytic cleavage (reactions 2-2 and 2-3), which has the greatest effect on its BDE. Reaction 2-2 is heterolytic cleavage of the C10−O5 bond to form a neutral unsaturated ketone and a phenoxide anion. The BDE of the C10−O5 bond in reaction 2-2 is 90.0 kJ/mol. Reaction 2-3 is heterolytic cleavage of the C10−
deprotonated Wender model
BDE
ΔE
BDE
ΔE
174.9 357.1/343.1 285.5 361.1 341.2 261.1 308.4
103.3 276.5 205.5 254.6 248.6 168.0 206.0
90.0/85.7 197.6 282.9 356.9 341.5 263.8 312.0
90.0/11.9 71.2 203.3 254.2 248.3 169.3 208.5
CO2 molecule. Pathway B is also a two-step pathway: the first step is the breakdown of the C1−C2 bond, and the second step is dissociation of the hydrogen atom. Examining the potential energy plotted as a function of the broken bond length could help to understand the pathway of the cleavage reaction. Energy diagrams of both pathways are shown in Figure 8. Both pathways are a radical-formation process involving homolytic cleavage of the C1−C2 bond, which is the rate-determining step in both pathways. The BDEs of the C1−C2 bond for pathways A and B are 343.1 and 303.3 kJ/mol, respectively. The DFT results also indicate that deprotonation of the O1 atom greatly affects the cleavage of the C1−C2 bond. The
Figure 8. Energy diagrams of (a) reaction 1-1 (red, pathway A; black, pathway B) and (b) reaction 2-1. 5378
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Figure 9. Energy diagrams of (a) reaction 1-3, (b) reaction 2-2, and (c) reaction 2-3.
ReaxFF MD simulation and DFT calculations. The model system for lignite was built from the classical Wender model, and that for metal-ion-exchanged lignite was built from the Wender model with Ca2+ cations and hydroxyl anions. ReaxFF MD simulation results show the reliability of the simulation in describing lignite pyrolysis and agree with known characteristics of coal. Analysis of trajectories in the ReaxFF MD simulations demonstrated that lignite pyrolysis was mainly initialized by decarboxylation and cleavage of the C−O bridged bond. DFT calculations confirmed that BDEs and ΔE for both of the two reactions were decreased after the addition of Ca(OH)2, hastening lignite pyrolysis. It should be noted that we used Ca(OH)2 in the metal-ionexchanged lignite. Various nitrates, carbonates, or chlorides
O5 bond to form a quinone and a carbanion. Its BDE is 85.7 kJ/mol. At the same time, the proton bonded to O4 is captured by C10 and a phenoxide is generated. Products of the heterolytic reactions 2-2 and 2-3 are more stable than those of the homolytic reaction 1-3. Together with the results of the ReaxFF MD simulation, these results indicate that added Ca(OH)2 could decrease both the BDE and ΔE of the major cleavage reactions, thereby providing favorable conditions for lignite pyrolysis.
4. CONCLUSION We constructed two 3D structural models with periodic boundary conditions to represent lignite and metal-ionexchanged lignite and studied their pyrolysis mechanisms by 5379
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could also increase the pyrolysis reactivity and achieve results similar to those with Ca(OH)2. This similarity is due to the reaction of these salts with carboxyl and phenolic hydroxyl to produce highly volatile CH3COOH, HNO3, CO2, or HCl at the pyrolysis temperature. Thus, the phenomena in other studies could also be theoretically explained by the mechanism that we describe in this paper. In addition, added metal species to large amounts of lignite is not practical or economical for the coal industrial operations. Industrial waste, such as soda residue, may be added to lignite. In this manner, environmental pollution is avoided and the production costs of metal-ionexchanged lignite are reduced.
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ASSOCIATED CONTENT
S Supporting Information *
Section 1, converge test of ReaxFF simulations; section 2, determination of hydrogen bonds; section 3, determination of cleavage reactions; 4, cleavage reactions found in ReaxFF simulation; section 5, deprotonation reactions of M2 by Ca(OH)2 in the ReaxFF simulations; and section 6, BDE and ΔE for the cleavage reactions by DFT calculations. This material is available free of charge via the Internet at http:// pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research was financed by the National Natural Science Foundation of China (U1361212) and the Natural Science Foundation of Hebei Province (B2014209261). The authors thank the Dalian Branch of the Supercomputing Center of the Chinese Academy of Sciences for computing support.
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