Study on Adsorption Characteristics of Sulfonate Gemini Surfactant on Lignite Surface

: In order to explore the adsorption characteristics of sulfonate gemini surfactants on the surface of lignite, the molecular dynamics simulation method was used, and A kind of sulfonic acid bis sodium salt (S2) and the sodium dodecyl sulfate (SDS) were selected. A binary model of surfactant/lignite adsorption system and a ternary model of water/surfactant/lignite system were constructed, and a series of properties such as adsorption conﬁguration, interaction energy, order parameters, relative concentration distribution, number of hydrogen bonds, etc., were analyzed. The results showed that the adsorption strength of S2 on the surface of lignite was higher than that of SDS. The results indicated that the large-angle molecular chain in S2 tended to become smaller, the small-angle molecular chain tended to become larger, and the angle between the molecular chains and the Z axis tended to be concentrated, making the formed network structure denser during the adsorption process. The number of hydrogen bonds in the water-coal system was 42, and the number of hydrogen bonds in the system after S2 adsorption was 15, which was much lower than the 23 hydrogen bonds in the system after SDS adsorption, and S2 could better adsorb and wrap the oxygen-containing groups on the surface of the lignite. The comparative study of the adsorption characteristics of the two surfactants on the surface of lignite can help us better understand the inﬂuence of the surfactant structure on the adsorption strength. The research results have important theoretical and practical signiﬁcance for developing new surfactants, and enriching and developing the basic theory of coal wettability.


Introduction
Coal is the most abundant fuel on earth, and low-rank coal (LRC) accounts for about half of all coal mines [1].As a low-rank coal, lignite has high oxygen, high moisture, low calorific value and high volatile content, which limits its storage, transportation and utilization in coal seams [2].Therefore, how to use lignite effectively and cleanly becomes more and more important.Lignite contains a large number of oxygen-containing functional groups, resulting in strong hydrophilicity and high moisture content in lignite [3].Many studies have shown that the adsorption of surfactants is a simple and effective method to reduce the hydrophilicity of lignite [4,5].
Surfactants are amphiphilic compounds that contain both hydrophilic and hydrophobic groups [6].This special structure makes it one of the most versatile chemical products [7][8][9] (e.g., in the cosmetics, oil industry, polymer paint, and coal industries).The study on the adsorption characteristics of surfactants is helpful to understand the mechanism of surfactants to change the properties of the interface [10][11][12][13].Gemini surfactants are a series of surfactants formed by linking two single-chain surfactants through a linking group [14][15][16].This special structure makes gemini surfactants have many properties that are superior to traditional single-chain surfactants, such as: lower critical micelle concentration (CMC), higher surface activity, better wetting effect, etc., [17].Study has shown that the CMC of SDS and S2 at 25 • C are 8.0 × 10 −3 mol/L and 4.8 × 10 −5 mol/L, respectively.It can be seen that the CMC of Gemini Surfactant S2 is much lower than the CMC of SDS.Because of these excellent properties, Gemini surfactants have shown great application potential in many fields, but there are still few studies on the adsorption characteristics of sulfonated gemini surfactants on coal surfaces [18].
In the coal industry, surfactants have been widely used in coal flotation and coal dust suppression [19][20][21][22][23].The studies of coal flotation and coal dust suppression rely on the basic theory of coal wettability [24,25].A large number of experiments have shown that the adsorption characteristics of surfactants on the coal surface is an important factor affecting coal wettability [2,[26][27][28].However, the experimental method cannot explain the structure, dynamics, and energy characteristics of the molecular adsorption process on the mineral surface.
Through computer simulation, the microstructure and macroscopic adsorption characteristics of the surfactant system can be linked.In particular, molecular dynamics (MD) simulation has proven to be a very useful tool for studying the structure and adsorption characteristics of surfactants at the molecular level.At present, a large number of MD simulation studies have been carried out on the diffusion of surfactants on the surface of coal [5,29], but the microscopic mechanism of the adsorption of sulfonated gemini surfactants on the surface of coal is still not clear.
In the previous research work of our team, through MD simulations, we explored the microscopic reasons for the different adsorption characteristics of Sodium dodecyl sulfate (SDS) and Sodium dodecyl benzene sulfonate (SDBS) on the coal surface, and concluded that the presence of benzene rings in the surfactant has an important influence on the adsorption characteristics [30].We also studied the adsorption characteristics of the four isomers of the linear alkylbenzene sulfonate family (LAS) on the coal surface, and systematically compared the adsorption characteristics and microscopic adsorption mechanism of the LAS family members on the coal surface [31].
In this paper, sulfonate gemini surfactants (S2) [32] and sodium dodecyl sulfate (SDS) were selected.As seen from Figure 1d, the two have the same hydrophilic head group and similar tail chain length.The biggest difference is that there is a spacer in the S2 molecule.Through the MD simulation of the surfactant/lignite binary system, the adsorption configuration, interaction energy and order parameters of the two surfactants were compared, and the macroscopic conclusion that the gemini surfactant showed the higher adsorption strength on the coal surface was obtained.In order to study the compactness of the layered structure formed by surfactant diffusion, a water layer was added to construct a water/surfactant/lignite ternary system.Through the analysis of the relative concentration distribution and the number of hydrogen bonds, the microscopic reasons for the high adsorption strength of Gemini surfactants were explained from a microscopic point of view.

Methods
The Wender lignite model was selected [33].As shown in Figure 1a, 40 optimized coal molecules were randomly stacked in a cubic unit cell 34 × 34 × 34 Å 3 (X Y Z) through the Amorphous Cell module of Materials Studio 6.0.The NVT ensemble (the constanttemperature, constant-volume ensemble) is used for the annealing operation, the NPT ensemble (the constant-temperature, constant-pressure ensemble) was subjected to 300 ps molecular dynamics simulation, and the unit cell structure was continuously adjusted to realize the relaxation of coal molecules.A 12 nm vacuum layer was added to the surface of the coal model to eliminate the mirror effect.The bottom two-thirds of the model was constrained and fixed, and the top third was free.In a large number of atomic systems, this method will greatly save calculation time.According to the research of Zhang et al. [34], this restrictive method basically has no effect on the calculation results.Figure 1b,c clearly show the top and side views of the surface of the original Wender lignite model.and SDS ions (red is oxygen atom, yellow is sulfur atom, white is hydrogen atom, gray is carbon atom, the black part represents the fixed part).In Figure (c), the white O represents the origin, the red A represents the direction of the X axis, and the green C represents the direction of the Z axis.In the following, the yellow B represents the y-axis direction.

Methods
The Wender lignite model was selected [33].As shown in Figure 1a, 40 optimized coal molecules were randomly stacked in a cubic unit cell 34 × 34 × 34 Å 3 (X Y Z) through the Amorphous Cell module of Materials Studio 6.0.The NVT ensemble (the constanttemperature, constant-volume ensemble) is used for the annealing operation, the NPT ensemble (the constant-temperature, constant-pressure ensemble) was subjected to 300 ps molecular dynamics simulation, and the unit cell structure was continuously adjusted to realize the relaxation of coal molecules.A 12 nm vacuum layer was added to the surface of the coal model to eliminate the mirror effect.The bottom two-thirds of the model was constrained and fixed, and the top third was free.In a large number of atomic systems, this method will greatly save calculation time.According to the research of Zhang et al. [34], this restrictive method basically has no effect on the calculation results.Figure 1b,c clearly show the top and side views of the surface of the original Wender lignite model.
The surfactant layer was a rectangular unit cell containing 8 S2 ions or 16 SDS ions, which was to keep the number of head groups consistent.The unit cell size was the same as the lignite surface model.The water layer was composed of 2000 water molecules.
The polymer uniform force field (PCFF) was used to describe the intermolecular interaction.Before the MD simulation, the Steepest descent algorithm was first used to reduce the energy of the coal surface model, the surfactant cell, and the crystal cell to near the equilibrium.The Conjugate gradient method was then used to reduce the energy to the lowest point, in order to fully eliminate the adverse interaction between atoms.
Subsequently, the water-lignite, surfactant-lignite, and water-surfactant-lignite systems were simulated by molecular dynamics in the NVT ensemble.Nose was used as the thermostat.The temperature was set to 298 K, and the 1000 ps simulation was performed at a step size of 1 fs to make the system reach a fully balanced state.
In all MD simulations, the Ewald algorithm was used to calculate the long-range electrostatic interaction with an accuracy of 0.001 kcal/mol, and the Atom based algorithm was used to calculate the van der Waals interaction with a cut-off distance of 1.25 nm.The above simulations were all carried out in a unit cell with periodic boundary conditions.

Surfactant-Lignite Adsorption System
The initial and final adsorption configurations of the surfactants on the surface of the lignite are shown in Figures 2 and 3, where the surfactant is shown in a line model.When the surfactant layer was placed on the surface of the coal model, the surfactantlignite system becomes thermodynamically unstable.Driven by van der Waals interaction and electrostatic potential, the surfactant diffused to the surface of the coal model and was finally adsorbed.After 1000 ps simulation, a new thermodynamic equilibrium state was reached.
Minerals 2021, 11, x 4 of 14 The surfactant layer was a rectangular unit cell containing 8 S2 ions or 16 SDS ions, which was to keep the number of head groups consistent.The unit cell size was the same as the lignite surface model.The water layer was composed of 2000 water molecules.
The polymer uniform force field (PCFF) was used to describe the intermolecular interaction.Before the MD simulation, the Steepest descent algorithm was first used to reduce the energy of the coal surface model, the surfactant cell, and the crystal cell to near the equilibrium.The Conjugate gradient method was then used to reduce the energy to the lowest point, in order to fully eliminate the adverse interaction between atoms.
Subsequently, the water-lignite, surfactant-lignite, and water-surfactant-lignite systems were simulated by molecular dynamics in the NVT ensemble.Nose was used as the thermostat.The temperature was set to 298 K, and the 1000 ps simulation was performed at a step size of 1 fs to make the system reach a fully balanced state.
In all MD simulations, the Ewald algorithm was used to calculate the long-range electrostatic interaction with an accuracy of 0.001 kcal/mol, and the Atom based algorithm was used to calculate the van der Waals interaction with a cut-off distance of 1.25 nm.The above simulations were all carried out in a unit cell with periodic boundary conditions.

Surfactant-Lignite Adsorption System
The initial and final adsorption configurations of the surfactants on the surface of the lignite are shown in Figures 2 and 3, where the surfactant is shown in a line model.When the surfactant layer was placed on the surface of the coal model, the surfactant-lignite system becomes thermodynamically unstable.Driven by van der Waals interaction and electrostatic potential, the surfactant diffused to the surface of the coal model and was finally adsorbed.After 1000 ps simulation, a new thermodynamic equilibrium state was reached.

Adsorption Configuration
As seen from Figure 4, after the adsorption was completed, the surfactant molecules bent and interwove with each other to form a network structure on the surface of the model, which had the function of preventing contact between water and lignite.The S2 molecules are more interwoven with each other and more densely aggregated, forming a denser network structure on the surface of the lignite, making the hydrophobic ability stronger.

Adsorption Configuration
As seen from Figure 4, after the adsorption was completed, the surfactant molecules bent and interwove with each other to form a network structure on the surface of the model, which had the function of preventing contact between water and lignite.The S2 molecules are more interwoven with each other and more densely aggregated, forming a denser network structure on the surface of the lignite, making the hydrophobic ability stronger.

Interaction Energy
The interaction energy between surfactant and coal after adsorption can be used to evaluate the adsorption strength of the two [35].The more negative the interaction energy, the more energy is released, and the more stable the structure after adsorption.The interaction energy is calculated by the following Equations ( 1)-( 3): where EV represents the van der Waals interaction energy, EL represents the electrostatic interaction energy, E represents the total interaction energy, Etotal is the total energy of (a) (b)

Adsorption Configuration
As seen from Figure 4, after the adsorption was completed, the surfactant molecules bent and interwove with each other to form a network structure on the surface of the model, which had the function of preventing contact between water and lignite.The S2 molecules are more interwoven with each other and more densely aggregated, forming a denser network structure on the surface of the lignite, making the hydrophobic ability stronger.

Interaction Energy
The interaction energy between surfactant and coal after adsorption can be used to evaluate the adsorption strength of the two [35].The more negative the interaction energy, the more energy is released, and the more stable the structure after adsorption.The interaction energy is calculated by the following Equations ( 1)-( 3): where EV represents the van der Waals interaction energy, EL represents the electrostatic interaction energy, E represents the total interaction energy, Etotal is the total energy of (a) (b)

Interaction Energy
The interaction energy between surfactant and coal after adsorption can be used to evaluate the adsorption strength of the two [35].The more negative the interaction energy, the more energy is released, and the more stable the structure after adsorption.The interaction energy is calculated by the following Equations ( 1)-( 3): where EV represents the van der Waals interaction energy, EL represents the electrostatic interaction energy, E represents the total interaction energy, E total is the total energy of surfactant and anthracite, E coal is the anthracite energy, and E surf is the surfactant energy.
The results are presented in Table 1.The van der Waals interaction energy in the two systems wasfar greater than the electrostatic interaction energy, and the van der Waals interaction played a leading role in the adsorption of lignite and surfactants.This was because the surface of lignite wasnegatively charged and repels the anionic head groups of the surfactant.This electrostatic repulsion hindered the adsorption of anionic surfactants on the surface of the lignite, making the van der Waals action the dominant lignite adsorption process.
Comparing the total interaction energy data, the total interaction energy of the S2lignite system was lower, indicating that more energy was released during the adsorption process, the adsorption strength was higher, the formed adsorption system was more stable, and the hydrophobicity was stronger.This was because of the existence of gemini surfactant spacers.The four-atom spacers belong to short-chain spacers.The distance between the two charged head groups in S2 surfactants was stretched compared to singlechain surfactants due to the effect of spacers.At the same time, it also helped to enhance intra-and intermolecular hydrophobic interactions.According to the theory of surfactant stacking parameters, the spontaneous curvature of aggregates formed in the solution at this time was smaller than that of single-chain surfactants, making the layered structure composed of gemini surfactants more compact [36][37][38][39].

Contact Surface Area
The contact surface area (CSA) was introduced to evaluate the intensity of adsorption, A larger contact surface area leads to stronger adsorption intensity.CSA can be calculated using Equation ( 4): where SASA lignite , SASA collector , and SASA complex are the solvent-accessible surface areas (SASA) of the lignite surface model, collector and lignite/collector complex, respectively.In this study, we used a probe with a radius of 1.4 Å to calculate the solvent-accessible surface area.The calculation result is shown in Figure 5.As seen from Figure 5, the CSA of S2 is about 1764 Å 2 , which was greater than 1708 Å 2 of SDS, indicating that the adsorption strength of S2 on the surface of lignite was higher.This was due to the closer interweaving of S2 molecules, which could form a denser network layer that could better cover the surface of coal.This was consistent with the results of interaction energy analysis and adsorption configuration analysis.

Order Parameter
The defined order parameter S and the average order parameter Sp are used to express the order of surfactant molecules [40]; S and Sp are calculated by Equations ( 5) and (6): As seen from Figure 5, the CSA of S2 is about 1764 Å 2 , which was greater than 1708 Å 2 of SDS, indicating that the adsorption strength of S2 on the surface of lignite was higher.This was due to the closer interweaving of S2 molecules, which could form a denser network layer that could better cover the surface of coal.This was consistent with the results of interaction energy analysis and adsorption configuration analysis.

Order Parameter
The defined order parameter S and the average order parameter S p are used to express the order of surfactant molecules [40]; S and S p are calculated by Equations ( 5) and ( 6): where θ is the angle between the line between the head and tail atoms of the surfactant and the interface normal (Z axis).Here, the line between the S atom in the head group and the last carbon atom is used.n is the base number of surfactant heads.When the value of S CD is 1, the molecules are arranged in the vertical direction of the interface.When the value of S CD is −1/2, the molecules are aligned parallel to the interface.The calculation results of sequence parameters are shown in Tables 2 and 3.The average order parameter of Gemini surfactant S2 molecule was −0.27, and the average order parameter of SDS molecule was −0.14.The average angle between SDS molecule and Z axis in the final configuration was smaller, indicating that its order in the Z axis direction was the highest.It tended to "stand" vertically on the surface of the lignite, and the S2 molecule was more inclined to "lie flat" on the surface of the lignite.It was speculated that this was because the S2 gemini surfactant with two ionic head groups had a stronger synergistic effect than single-chain SDS molecules, and the electrostatic repulsion between S2 ionic head groups was weaker due to the existence of short-chain spacers [17,39].The "flat" configuration of S2 was more conducive to cross-linking each other and could cover the coal surface in a larger area.
Figure 6 shows the distribution of the angle between the surfactant molecular chain and the Z axis before and after MD simulation.As shown, 50 represents the angle between the molecular chain and the Z axis is less than 50 • and 60 represents a molecular chain with an angle between 50 • and 60 • .
Minerals 2021, 11, x 9 of 14 made the molecular chains more inclined to the same angle.A more similar angle was conducive to the interweaving of molecular chains to form a denser network structure.
For SDS molecular chains, in the final equilibrium state, the number of molecular chains less than 50° increased significantly, and the number of molecular chains 50°-80° decreased significantly.During the adsorption process, due to the presence of the head group electrostatic repulsion, the molecular chain distribution angle tended to diverge.This trend was not conducive to the linear interweaving of molecular chains, and the formed network structure was relatively loose.

Water-Surfactant-Lignite System
Notably, 2000 water molecules were added on the modified coal to build a watersurfactant-lignite system.After adding the water layer, the system became thermodynamically unstable.After 1000 ps molecular dynamics simulation, the system tended to be stable.The initial and equilibrium configurations of the water-surfactant-lignite system are shown in Figures 7 and 8.The water-lignite system also reached equilibrium after 1000 ps molecular dynamics simulation.For the S2 molecular chain, compared with the initial state, after molecular dynamics equilibrium, the number of molecular chains distributed at 50 • -80 • increased significantly, indicating that the large-angle molecular chains in S2 tended to become smaller during the adsorption process, small-angle molecular chains tended to become larger, and molecular chain distribution angles tended to be concentrated.This was because the spacer in the S2 molecule was a flexible spacer composed of two oxygen atoms and two carbon atoms.This kind of spacer had a greater degree of freedom and could spontaneously adjust the configuration in the aggregate according to the specific system.It also made the molecular chains more inclined to the same angle.A more similar angle was conducive to the interweaving of molecular chains to form a denser network structure.For SDS molecular chains, in the final equilibrium state, the number of molecular chains less than 50 • increased significantly, and the number of molecular chains 50 • -80 • decreased significantly.During the adsorption process, due to the presence of the head group electrostatic repulsion, the molecular chain distribution angle tended to diverge.This trend was not conducive to the linear interweaving of molecular chains, and the formed network structure was relatively loose.

Water-Surfactant-Lignite System
Notably, 2000 water molecules were added on the modified coal to build a watersurfactant-lignite system.After adding the water layer, the system became thermodynamically unstable.After 1000 ps molecular dynamics simulation, the system tended to be stable.The initial and equilibrium configurations of the water-surfactant-lignite system are shown in Figures 7 and 8.The water-lignite system also reached equilibrium after 1000 ps molecular dynamics simulation.Notably, 2000 water molecules were added on the modified coal to build a watersurfactant-lignite system.After adding the water layer, the system became thermodynamically unstable.After 1000 ps molecular dynamics simulation, the system tended to be stable.The initial and equilibrium configurations of the water-surfactant-lignite system are shown in Figures 7 and 8.The water-lignite system also reached equilibrium after 1000 ps molecular dynamics simulation.

Relative Concentration Distribution
The relative concentration distribution along the Z axis can obtain the distribution of the components in the water-lignite and water-surfactant-lignite systems along the Z axis.
Figure 9 shows the relative concentration distribution of water molecules along the Z axis in the three systems.The initial position of the water layer shifts back after the addition of surfactants, indicating that the presence of surfactants enhanced the hydrophobicity of lignite.The starting position of water molecules in the water-S2-lignite system was more rearward, indicating that the Gemini surfactant S2 adsorbed more closely with lignite, and the hydrophobic effect of S2 was better, which was consistent with the above analysis result of the interaction energy.

Relative Concentration Distribution
The relative concentration distribution along the Z axis can obtain the distribution of the components in the water-lignite and water-surfactant-lignite systems along the Z axis.
Figure 9 shows the relative concentration distribution of water molecules along the Z axis in the three systems.The initial position of the water layer shifts back after the addition of surfactants, indicating that the presence of surfactants enhanced the hydrophobicity of lignite.The starting position of water molecules in the water-S2-lignite system was more rearward, indicating that the Gemini surfactant S2 adsorbed more closely with lignite, and the hydrophobic effect of S2 was better, which was consistent with the above analysis result of the interaction energy.
Figure 9 shows the relative concentration distribution of water molecules along the Z axis in the three systems.The initial position of the water layer shifts back after the addition of surfactants, indicating that the presence of surfactants enhanced the hydrophobicity of lignite.The starting position of water molecules in the water-S2-lignite system was more rearward, indicating that the Gemini surfactant S2 adsorbed more closely with lignite, and the hydrophobic effect of S2 was better, which was consistent with the above analysis result of the interaction energy.Figure 10 shows the relative concentration distribution of sulfur atoms in S2 and SDS head groups along the Z axis.The distribution of sulfur atoms in the S2 molecule had three peaks, and the peaks were similar; this phenomenon indicates that part of the S2 molecular head group faced the surface of the lignite, part was parallel to the interface, and part faced the water phase, and the numbers were similar.Such a structure was more helpful for the molecular chains to fill the gaps between each other and formed a denser adsorption layer.The SDS molecule also had three peaks [2], but the height of the third peak was much higher than the first two, indicating that the head group in SDS was more toward the water phase.Combined with the analysis of the above order parameters, the angle between the SDS molecular chain and the Z axis was smaller, and more of the hydrophilic head groups were adsorbed on the surface of the lignite in a way that the hydrophilic head groups face the water phase, which also leaded to a decrease in the hydrophobicity of SDS.

Number of Hydrogen Bonds
The number of hydrogen bonds was calculated to further illustrate the effect of surfactant adsorption on the interaction between water and modified lignite.Geometric criteria were used here to define the existence of hydrogen bonds: the intermolecular hydrogen acceptor distance was less than 2.5Å, and the donor hydrogen acceptor angle was greater than 135 • [41].The calculation results of the number of hydrogen bonds in each system are shown in Table 4. Due to the adsorption of surfactants, the number of hydrogen bonds was significantly reduced, which means a change in surface composition.The oxygen-containing groups of the original lignite were covered by surfactants, which changed the surface of the lignite and weaken the ability to form hydrogen bonds with water.The number of hydrogen bonds in the SDS system was greater than that in the S2 system, which was consistent with the fact that the hydrophilic head groups in SDS were more oriented toward the water phase in the relative concentration distribution analysis.adsorption layer.The SDS molecule also had three peaks [2], but the height of the third peak was much higher than the first two, indicating that the head group in SDS was more toward the water phase.Combined with the analysis of the above order parameters, the angle between the SDS molecular chain and the Z axis was smaller, and more of the hydrophilic head groups were adsorbed on the surface of the lignite in a way that the hydrophilic head groups face the water phase, which also leaded to a decrease in the hydrophobicity of SDS.

Number of Hydrogen Bonds
The number of hydrogen bonds was calculated to further illustrate the effect of surfactant adsorption on the interaction between water and modified lignite.Geometric criteria were used here to define the existence of hydrogen bonds: the intermolecular hydrogen acceptor distance was less than 2.5Å, and the donor hydrogen acceptor angle was greater than 135° [41].The calculation results of the number of hydrogen bonds in each system are shown in Table 4. Due to the adsorption of surfactants, the number of hydrogen bonds was significantly reduced, which means a change in surface composition.The oxygen-containing groups of the original lignite were covered by surfactants, which changed the surface of the lignite and weaken the ability to form hydrogen bonds with water.The number of hydrogen bonds in the SDS system was greater than that in the S2 system, which was consistent with the fact that the hydrophilic head groups in SDS were more oriented toward the water phase in the relative concentration distribution analysis.

System
Number of Hydrogen Bonds Coal-Water 42

Conclusions
The adsorption characteristics of propane-1-sulfonic acid disodium salt and sodium lauryl sulfate on the surface of lignite were studied by molecular dynamics simulation method, and the following conclusions are drawn: (1) By analyzing the interaction energy of the surfactant-lignite system, it was found that the total interaction energy of the S2-lignite system was lower, indicating that S2 had the highest adsorption strength on the lignite surface.(2) Through the analysis of the order parameters of the surfactant-lignite system, it was found that the average included-angle between the SDS molecule and the Z axis was smaller, and the degree of order in the Z axis direction was higher.Further analysis of the angle distribution between the molecular chain and the Z axis before and after the MD simulation showed that during the adsorption process, the large-angle molecular chain in S2 tended to become smaller, the small-angle molecular chain tended to become larger, and the molecular chain distribution angle tended to concentrate.(3) Through the analysis of the relative concentration distribution and the number of hydrogen bonds in the water-surfactant-lignite system, it was found that the gemini surfactant S2 had a better hydrophobic effect, the network layer formed was denser.
In SDS, the head groups were more adsorbed on the surface of lignite in a way that the hydrophilic head groups face the water phase, which also led to the decrease in the hydrophobic ability of SDS.(4) The study on the adsorption characteristics of sulfonate gemini surfactants on the surface of lignite will help to better understand the influence of the surfactant structure on the adsorption strength.The research results have important theoretical and practical significance for developing new surfactants, and enriching and developing the basic theory of coal wettability.

Figure 1 .
Figure 1.(a) Wender lignite molecular structure (b) Top view of lignite 3D structure model (c) Side view of lignite 3D structure model (d) S2 and SDS ions (red is oxygen atom, yellow is sulfur atom, white is hydrogen atom, gray is carbon atom, the black part represents the fixed part).In Figure (c), the white O represents the origin, the red A represents the direction of the X axis, and the green C represents the direction of the Z axis.In the following, the yellow B represents the y-axis direction

Figure 1 .
Figure 1.(a) Wender lignite molecular structure (b) Top view of lignite 3D structure model (c) Side view of lignite 3D structure model (d) S2 and SDS ions (red is oxygen atom, yellow is sulfur atom, white is hydrogen atom, gray is carbon atom, the black part represents the fixed part).In Figure (c), the white O represents the origin, the red A represents the direction of the X axis, and the green C represents the direction of the Z axis.In the following, the yellow B represents the y-axis direction.

Figure 6 .
Figure 6.The distribution of the angle between the surfactant molecular chain and the Z axis before and after MD simulation.

Figure 8 .
Figure 8.The initial (a) and equilibrium (b) configurations of the water-SDS-lignite system.

Figure 9 .
Figure 9. Relative concentration distribution of water molecules along the Z axis.Figure 9. Relative concentration distribution of water molecules along the Z axis.

Figure 9 .
Figure 9. Relative concentration distribution of water molecules along the Z axis.Figure 9. Relative concentration distribution of water molecules along the Z axis.

Figure 10 .
Figure 10.Relative concentration distribution of sulfur atoms along the Z axis.

Figure 10 .
Figure 10.Relative concentration distribution of sulfur atoms along the Z axis.

Table 4 .
Number of hydrogen bonds in water-surfactant-coal models and water-coal model.

Table 1 .
Interaction energy between surfactant and lignite.

Table 2 .
The angle between the S2 molecule and the Z axis and order parameters.

Table 3 .
The angle between the SDS molecule and the Z axis and order parameters.

Table 4 .
Number of hydrogen bonds in water-surfactant-coal models and water-coal model.