Adsorption Behaviors of Straight-Chain Alkanes on a Molybdenite [001]/[100] Surface: A Molecular Dynamics Study

: Straight-chain alkanes (SCA) as collectors can effectively enhance the ﬂoatability of molybdenite. In a previous study, SCA were found to have an excellent adsorption effect on the molybdenite [001] surface (MS001), but they exhibited no adsorption behavior on the molybdenite [100] surface (MS100). However, other studies have shown that SCA could adsorb on MS100. In this paper, the underlying cause of this contradictory conclusion was identiﬁed by molecular dynamics simulation. The results show that SCA could adsorb both MS001 and MS100. However, at low SCA dosages, SCA have a strong interaction with MS001 but desorb quickly on MS100. This leads to the selective adsorption of SCA on MS001. As SCA’s concentration gradually increases, the selective adsorption behavior of SCA on MS001 will be disrupted. Excessive SCA concentration will lead to its adsorption at MS100.


Introduction
Straight-chain alkanes (SCA) are a superior collector of molybdenite [1][2][3][4]. They can enhance the floatability of molybdenite by adsorbing on the surface of molybdenite [4,5]. Some studies have reported that SCA could only adsorb on the surface of molybdenite (001) (MS001) by Van der Waals force, but not on the surface of molybdenite (100) (MS100) [6][7][8] based on the anisotropy of molybdenite [9,10]. It has also been agreed that as the molybdenite's particle size gradually decreases, the proportion of MS100 increases [11,12]. This causes the SCA's effect of enhancing the floatability of molybdenite to become less effective, and the recovery of molybdenite flotation also decreases.
However, it has also been reported that when the amount of SCA increases, the rate of flotation recovery of fine molybdenite gradually increases [13,14]. This indicates that SCA may be adsorbed not only on the MS001 but also on the MS100. This conclusion is contrary to the findings of previous reports. The reason why SCA can adsorb on the MS100 is not yet clear.
In this paper, molecular dynamics simulations were used to obtain the lowest energy conformation of SCA on MS001/MS100, calculate the interaction energy of SCA and MS001/MS100, and analyze the dynamics behavior of SCA on MS001/MS100. The reason why SCA can adsorb on MS100 is explained at the molecular level.

Molecular Dynamics Simulation
Models of the surface of molybdenite and SCA (dodecane representing SCA) were established on the Materials Visualizer module and Amorphous Cell module. Molecular

Molecular Dynamics Simulation
Models of the surface of molybdenite and SCA (dodecane representing SCA) were established on the Materials Visualizer module and Amorphous Cell module. Molecular dynamics simulations were performed under the Universal force field in the Forcite Plus module with the software package Materials Studio 8.0 (Northeastern University, Shenyang, Liao ning, China).

Simulated Detail
Firstly, molybdenite crystal (MS001/MS100) was established and optimized based on the method published in the literature [15] (Figure 1). Secondly, MS001/MS100 were cut at depths of 2 and 4 Å, respectively. They were then extended to 3 × 10-and 10 × 10-unit supercells, respectively, and a vacuum layer of 0 Å was established for combination with SCA boxes.
Thirdly, an MS001/MS100-SCA complex model was optimized to obtain the optimum position in the adsorption equilibrium by using the same method as the optimization of molybdenite crystal ( Figure 2). A cutoff distance for group-based summation was 15.5 Å. The atomic charge was calculated using the QEq charge equilibration method [16]. Secondly, MS001/MS100 were cut at depths of 2 and 4 Å, respectively. They were then extended to 3 × 10-and 10 × 10-unit supercells, respectively, and a vacuum layer of 0 Å was established for combination with SCA boxes.
Thirdly, an MS001/MS100-SCA complex model was optimized to obtain the optimum position in the adsorption equilibrium by using the same method as the optimization of molybdenite crystal ( Figure 2). A cutoff distance for group-based summation was 15.5 Å. The atomic charge was calculated using the QEq charge equilibration method [16].

Molecular Dynamics Simulation
Models of the surface of molybdenite and SCA (dodecane representing SCA) were established on the Materials Visualizer module and Amorphous Cell module. Molecular dynamics simulations were performed under the Universal force field in the Forcite Plus module with the software package Materials Studio 8.0 (Northeastern University, Shenyang, Liao ning, China).

Simulated Detail
Firstly, molybdenite crystal (MS001/MS100) was established and optimized based on the method published in the literature [15] (Figure 1). Secondly, MS001/MS100 were cut at depths of 2 and 4 Å, respectively. They were then extended to 3 × 10-and 10 × 10-unit supercells, respectively, and a vacuum layer of 0 Å was established for combination with SCA boxes.
Thirdly, an MS001/MS100-SCA complex model was optimized to obtain the optimum position in the adsorption equilibrium by using the same method as the optimization of molybdenite crystal ( Figure 2). A cutoff distance for group-based summation was 15.5 Å. The atomic charge was calculated using the QEq charge equilibration method [16].  Finally, molecular dynamics simulations were carried out as follows [15]: (1) The configuration's initial velocity was obtained by the Velocity Scale thermostat of the NVT ensemble. (2) At a time step of 1 fs and a total simulation time of 50 ps, the NVE ensemble carried out annealing molecular dynamics simulations. (3) Molecular dynamics simulations with the NVT ensemble were performed using a Nosé thermostat with a Q ratio of 0.01, at 293 K, a time step of 1 fs, and a total simulation time of 3000 ps.

Interaction Energy Calculation
The interaction energy was calculated based on the configuration with the lowest energy-the optimal adsorption model. The interaction energy was obtained by the following formula [17]: where ∆E is the interaction energy; E total , E MS001/MS100 , and E SCA are the total energy of the complex model, MS001/MS100, and SCA, respectively.

Square Displacement (MSD) Curves
MSD curves were used to analyze the aggregation properties of SCA on the MS001/MS100. In the MSD curves, the mobility of SCA is affected by the properties of MS001/MS100. The relationship between MSD and the diffusion coefficients (D) is based on the related literature, as follows [18,19]: where K MSD is the slope of the MSD curve.

The Adsorption Configuration of SCA on the MS001/MS100
The adsorption configuration of SCA on the MS001/MS100 is shown in Figure 3. Finally, molecular dynamics simulations were carried out as follows [15]: (1) The configuration's initial velocity was obtained by the Velocity Scale thermostat of the NVT ensemble. (2) At a time step of 1 fs and a total simulation time of 50 ps, the NVE ensemble carried out annealing molecular dynamics simulations. (3) Molecular dynamics simulations with the NVT ensemble were performed using a Nosé thermostat with a Q ratio of 0.01, at 293 K, a time step of 1 fs, and a total simulation time of 3000 ps.

Interaction Energy Calculation
The interaction energy was calculated based on the configuration with the lowest energy-the optimal adsorption model. The interaction energy was obtained by the following formula [17]: where ΔE is the interaction energy; Etotal, EMS001/MS100, and ESCA are the total energy of the complex model, MS001/MS100, and SCA, respectively.

Square Displacement (MSD) Curves
MSD curves were used to analyze the aggregation properties of SCA on the MS001/MS100. In the MSD curves, the mobility of SCA is affected by the properties of MS001/MS100. The relationship between MSD and the diffusion coefficients (D) is based on the related literature, as follows [18,19]: (2) where KMSD is the slope of the MSD curve.

The Adsorption Configuration of SCA on the MS001/MS100
The adsorption configuration of SCA on the MS001/MS100 is shown in Figure 3. The results of Figure 3a show that all SCA adsorb in parallel on the MS001, which consists of sulfur atomic planes. Figure 3b shows that SCA also adsorb on the MS100 composed of alternating sulfur and molybdenum atomic planes. They are arranged in The results of Figure 3a show that all SCA adsorb in parallel on the MS001, which consists of sulfur atomic planes. Figure 3b shows that SCA also adsorb on the MS100 composed of alternating sulfur and molybdenum atomic planes. They are arranged in parallel between sulfur atoms and sulfur atoms exposed on the MS100 (containing S-plane). Meanwhile, there is no SCA adsorption above the exposed Mo atom of the Mo plane. This suggests that the exposed sulfur atoms on the MS100 are beneficial to SCA's adsorption, while the exposed Mo atoms can hinder the spreading of SCA. This conclusion can be further explained by relying on the average partial charge of the atomic surface (Table 1). The results of Table 1 show that the averaged partial charges of the surface S/Mo atoms in MS100 are −0.367/+0.734 eV. The averaged partial charges of the surface H atoms in SCA are +0.053 eV. The surface H atoms of SCA and surface S atoms of MS001/MS100 can interact by electrostatic gravitation. The surface H atoms of SCA and surface Mo atoms of MS100 will repel each other. Therefore, the SCA can be adsorbed on the exposed sulfur atoms on the MS100, not on the surface Mo atoms of MS100. Even the surface Mo atoms of MS100 will block the adsorption of SCA.

The Interaction Energy between SCA and the MS001/MS100
To further analyze SCA's adsorption behavior on the surface of molybdenite, SCA's interaction energies with the MS001/MS100 were calculated. The value of interaction energy shows the adsorption system's stability (SCA's interaction strength with the MS001/MS100) [14]. A more negative interaction energy value indicates a more stable adsorption system (favorable interaction). The results are shown in Table 2. The results of Table 2 show that the interaction energy of SCA with the MS001/MS100 is −559.5798/−239.6827 Kcal·mol −1 . The interaction energy between SCA and MS001 is a much more negative value than that of SCA and MS100. Combining the results in Figure 1 shows that SCA's interaction with sulfur atoms on the MS001 is much stronger than its interaction with sulfur atoms on the MS100. Therefore, this can also cause SCA's preferential adsorption on MS001 when there is a low amount of SCA present. This is in agreement with the results of the averaged partial charges of SCA/MS001/MS100.
The results of Table 1 show that the averaged partial charges of the surface S atoms in MS001 are −0.396 eV. The surface H atoms of SCA and surface S atoms of MS001 can also interact by electrostatic gravitation. The interaction force between the surface H atoms of SCA and surface S atoms of MS001 is greater than the interaction force between the surface H atoms of SCA and surface S atoms of MS100. Meanwhile, the repulsive force of MS100 to SCA is stronger than the attraction of MS100 to SCA. Therefore, the MS100 has a repulsive effect on SCA as a whole. However, the MS001 only has an attractive effect on SCA. This further indicates that SCA can be preferentially adsorbed on the MS001.

The Diffusion Coefficients of SCA on the MS001/MS100
MSD curves were used to analyze the stability of SCA on the MS001/MS100. MSD curves of SCA on MS001/MS100 are shown in Figure 4.

The Diffusion Coefficients of SCA on the MS001/MS100
MSD curves were used to analyze the stability of SCA on the MS001/MS100. MSD curves of SCA on MS001/MS100 are shown in Figure 4.  Figure 4 shows that SCA's diffusion coefficients are 3.17 × 10 −5 cm 2 /s and 3.47 × 10 −5 cm 2 /s on MS001 and MS100, respectively. These indicate that the mobility of SCA on the MS001 is slower than that of SCA on the MS100. This is attributed to the fact that the MS001 has a stronger attraction, which limits SCA movement more than it does on the MS100. Therefore, compared with the MS100, it is harder on MS001 to desorb SCA. This will cause more hydrocarbon oil to be retained on the MS001 under the same conditions.

The Relative Concentration of SCA on the MS001/MS100
To further analyze SCA's distribution on the MS001/MS100, the relative concentration of SCA on the MS001/MS100 is shown in Figure 5.  shows that all SCA adsorbed on the MS001 were distributed between 24.19 Å and 25.57 Å. The distance of SCA from the MS001 is approximately 2.71-4.09 Å. The only portion of SCA that is adsorbed on the MS100 is distributed between 11.82 Å and 14.07 Å. The distance of SCA from the MS100 is approximately 2.73-4.98 Å. At a distance of 2.7-5.0 Å from the MS001/MS100, SCA's adsorption on the MS001 is much higher than that of the SCA on the MS100. This is con-  Figure 4 shows that SCA's diffusion coefficients are 3.17 × 10 −5 cm 2 /s and 3.47 × 10 −5 cm 2 /s on MS001 and MS100, respectively. These indicate that the mobility of SCA on the MS001 is slower than that of SCA on the MS100. This is attributed to the fact that the MS001 has a stronger attraction, which limits SCA movement more than it does on the MS100. Therefore, compared with the MS100, it is harder on MS001 to desorb SCA. This will cause more hydrocarbon oil to be retained on the MS001 under the same conditions.

The Relative Concentration of SCA on the MS001/MS100
To further analyze SCA's distribution on the MS001/MS100, the relative concentration of SCA on the MS001/MS100 is shown in Figure 5.

The Diffusion Coefficients of SCA on the MS001/MS100
MSD curves were used to analyze the stability of SCA on the MS001/MS100. MSD curves of SCA on MS001/MS100 are shown in Figure 4.  Figure 4 shows that SCA's diffusion coefficients are 3.17 × 10 −5 cm 2 /s and 3.47 × 10 −5 cm 2 /s on MS001 and MS100, respectively. These indicate that the mobility of SCA on the MS001 is slower than that of SCA on the MS100. This is attributed to the fact that the MS001 has a stronger attraction, which limits SCA movement more than it does on the MS100. Therefore, compared with the MS100, it is harder on MS001 to desorb SCA. This will cause more hydrocarbon oil to be retained on the MS001 under the same conditions.

The Relative Concentration of SCA on the MS001/MS100
To further analyze SCA's distribution on the MS001/MS100, the relative concentration of SCA on the MS001/MS100 is shown in Figure 5.  shows that all SCA adsorbed on the MS001 were distributed between 24.19 Å and 25.57 Å. The distance of SCA from the MS001 is approximately 2.71-4.09 Å. The only portion of SCA that is adsorbed on the MS100 is distributed between 11.82 Å and 14.07 Å. The distance of SCA from the MS100 is approximately 2.73-4.98 Å. At a distance of 2.7-5.0 Å from the MS001/MS100, SCA's adsorption on the MS001 is much higher than that of the SCA on the MS100. This is con-  Figure 5 shows that all SCA adsorbed on the MS001 were distributed between 24.19 Å and 25.57 Å. The distance of SCA from the MS001 is approximately 2.71-4.09 Å. The only portion of SCA that is adsorbed on the MS100 is distributed between 11.82 Å and 14.07 Å. The distance of SCA from the MS100 is approximately 2.73-4.98 Å. At a distance of 2.7-5.0 Å from the MS001/MS100, SCA's adsorption on the MS001 is much higher than that of the SCA on the MS100. This is consistent with the findings in Figure 4, which indicate that adsorption of SCA is more favorable on the MS001.

Discussion
The results of the molecular dynamics simulations explain the reasons for the previous literature's contradictory conclusions. SCA can adsorb on the MS100, despite the low interactions between SCA and the MS100, the easy desorption of SCA on the MS100, and the blocking effect of the exposed molybdenum atoms of the MS100 on hydrocarbon oil. However, when the amount of SCA is low, it can selectively adsorb on the MS001, based on the blocking and strong desorption role of the MS100. At low SCA dosage, SCA can selectively adsorb on the MS001 but not on the MS100, based on the blocking, strong desorption, and weak interaction forces between SCA and the MS100. With the increasing SCA concentration, an excessive amount of SCA will reduce SCA's selectivity for adsorption on the MS001. This will cause a small amount of the SCA to be adsorbed on the MS100. This conclusion is consistent with results concerning oil agglomeration and the flotation of molybdenite [13,14].

Conclusions
Molecular dynamics simulations of SCA's adsorption behaviors on the surface of molybdenite found that SCA can be adsorbed on both MS001 and MS100. At a low SCA dosage, SCA can selectively adsorb on the MS001 but not on the MS100, based on the strong interactions between SCA and the MS001, the easy desorption of SCA on the MS100, and the blocking effect of the exposed molybdenum atoms of the MS100 on SCA. With an increasing SCA concentration, an excessive amount of SCA destroys SCA's selectivity for adsorption on the MS001. This will cause the adsorption of SCA on the MS100 to gradually increase.