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Tribochemical Reaction Dynamics of Phosphoric Ester Lubricant Additive by Using a Hybrid Tight-Binding Quantum Chemical Molecular Dynamics Method Michihisa Koyama,† Jun Hayakawa,† Tasuku Onodera,† Kosuke Ito,‡ Hideyuki Tsuboi,† Akira Endou,† Momoji Kubo,†,§ Carlos A. Del Carpio,† and Akira Miyamoto*,†,| Department of Applied Chemistry, Graduate School of Engineering, Tohoku UniVersity, 6-6-11-1302 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan, Department of Mechanical Systems and Design, Graduate School of Engineering, Tohoku UniVersity, 6-6-01 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan, PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan, and New Industry Creation Hatchery Center, Tohoku UniVersity, 6-6-10 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan ReceiVed: February 25, 2006; In Final Form: June 14, 2006
To study the atomistic behavior of the phosphoric ester molecule on the nascent Fe surface under boundary lubrication conditions, we adopted a hybrid tight-binding quantum chemical molecular dynamics method. First, we investigated chemical interactions between phosphoric ester and the nascent Fe surface. Phosphoric ester was shown to interact with the nascent Fe surface, forming both covalent and ionic bonds. Formation and dissociation dynamics of covalent bonds during tribochemical reaction was clearly observed during the simulation. The effect of friction condition on the tribochemical reaction dynamics was then studied, and it was indicated that friction would influence the formation and the dissociation of covalent bonds. By using a hybrid tight-binding quantum chemical molecular dynamics method, we obtained insights on initial tribochemical reaction processes for the formation of tribofilm from the phosphoric ester molecule on the nascent Fe surface.
Introduction Phosphoric esters are popularly used as a lubricant additive to prevent wear under boundary lubrication.1-3 They prevent wear by the formation of a surface protecting layer. While experimental analyses on the tribofilm formed from phosphoric ester can be found in the literature,1,2 the mechanism for the formation of tribofilm from phosphoric ester as a result of the tribochemical reaction still remains unclear. A probable formation mechanism is summarized in a review on phosphoric estertype oil by Atarashi3 as follows: (1) adsorption of phosphoric ester onto metal surface and subsequent formation of adsorption layer at the surface, (2) formation of the organic iron phosphate layer as the result of decompositions of phosphoric ester, and (3) formation of iron phosphate layer. Atarashi described that further clarification of the mechanism is important while experimental analysis of the mechanism is often difficult due to the complexity of the system. On the other hand, a computational chemistry approach provides electronic and atomistic information and thus has been extensively applied to the study of nanotribology.4-27 Earlier studies are mainly by a classical molecular dynamics method and focused on the dynamic properties.4-21 While some of them provided insightful information on tribochemical reaction dynamics,9 a classical molecular dynamics method in nature cannot deal with electron transfer that is inherently involved in the tribochemical reaction. Therefore, studies based on quantum chemistry, which provides * Corresponding author. Tel.: +81-22-795-7233. Fax: +81-22-7957235. E-mail:
[email protected]. † Department of Applied Chemistry, Tohoku University. ‡ Department of Mechanical Systems and Design, Tohoku University. § PRESTO, Japan Science and Technology Agency. | New Industry Creation Hatchery Center, Tohoku University.
electronic level information, have recently been carried out to study the nature of the tribochemical reaction under boundary lubrication conditions.22-27 Mosey et al. carried out the CarParrinello first-principles molecular dynamics simulation on the triphosphate molecule formed from zinc phosphate lubricant additive and discussed the formation mechanism of anti-wear film under extreme pressure.25,26 While their breakthrough results give an important insight on the tribochemical reaction dynamics, tribochemical reaction between lubricant additive and the nascent metal surface under friction conditions or tribochemical reaction remains to be further studied because no sliding nor metal substrate was introduced in their studies. To study the tribochemical reaction in a more realistic system, development of a new method is favorable because a huge computational cost of the Car-Parrinello first-principles molecular dynamics method used in their studies does not allow one to study the dynamics of a large realistic system with a reasonable computational cost. To realize the tribochemical reaction dynamics of a large-scale system, we have developed a tight-binding quantum chemical molecular dynamics program, Colors, in which electronic structures of systems are selfconsistently solved on the basis of original tight-binding approximation.27-33 To realize the study of a further larger or more complex system, we have developed a hybrid tight-binding quantum chemical molecular dynamics program, HybridColors.34 In Hybrid-Colors, a central part of the tribochemical reaction is calculated by the Colors program, and the remaining part is calculated by the classical molecular dynamics program, thus realizing the study of chemical reaction dynamics for a large complex system.34 In this manuscript, we implemented with the Hybrid-Colors program a function to theoretically study the chemical reaction dynamics under boundary lubrication
10.1021/jp061210m CCC: $33.50 © 2006 American Chemical Society Published on Web 08/11/2006
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Figure 1. Simulation model obtained after equilibration by classical molecular dynamics calculation.
conditions, and we have applied the program to the study of the tribochemical reaction between the phosphoric ester molecule and the nascent Fe surface. Computational Methods Hybrid-Colors program is based on a tight-binding quantum chemical molecular dynamics program, Colors,27-33 and a classical molecular dynamics program, NEW-RYUDO.35-38 Colors is based on the original tight-binding approximation, in which long-range Coulombic interaction is explicitly considered, thus realizing the study of systems including both covalent and ionic interactions. To determine accurate parameters for the Colors program, we used a density functional theory (DFT) program, ADF.39 Generalized gradient approximation with PW91 exchange-correlation functionals40 was adopted for energy calculations. Triple-ζ plus polarization functions were used as basis sets. For the simulation of nonequilibrium simulation under friction conditions, we implemented with Hybrid-Colors34 a function to give an external pressure and/or a sliding velocity to specific atoms in the simulation cell, which worked effectively in the Colors program.32 CVFF potential41 is used for the classical molecular dynamics calculation. We used phosphoric trimethyl for the simulation as the simplest phosphoric ester molecule, and 45 molecules are placed between two Fe substrates. Although the actual working condition is much complex, we included only phosphoric trimethyl molecules and did not include base oil or other lubricant additives in the liquid phase as a first approximation to study the tribochemical reaction of phosphoric ester under boundary lubrication conditions. To obtain a well-equilibrated liquid-state structure of phosphoric trimethyl molecules, a classical molecular dynamics simulation was performed for 50 ps with a pressure of 1 GPa applied vertically to the top layer of the upper Fe substrate. Finally, we obtain the liquid phase structure shown in Figure 1, and the final structure was used for the subsequent simulation by using Hybrid-Colors. We note that a pressure of 100 kPa was applied for the preparation of the equilibrated liquid-state structure for Hybrid-Colors simulation without friction. In the Hybrid-Colors program, atoms that would influence the electron transfer or chemical reactions are specified for quantum chemical calculations. To study the tribochemical reaction dynamics of phosphoric trimethyl with the Fe surface, which was difficult to study by conventional first-principles methods due to the convergence difficulty of open shell transition metal-containing systems, one phosphoric trimethyl molecule and Fe atoms in its vicinity are specified for quantum chemical calculations. Using the function implemented for the simulation under extreme friction conditions,
Figure 2. Radial distribution of electron density for (a) 3s and (b) 3p orbitals of the P atom.
both external pressure and a sliding velocity of 1 GPa and 100 m/s, respectively, are given to the top layer of the upper Fe substrate. On the other hand, the bottom layer of the lower Fe substrate is fixed during the simulation. While we admit that the sliding velocity during the simulation is much higher as compared to typical conditions in the actual system, we believe our simulations under the accelerated sliding condition could provide good insights for the understandings of phenomena under extreme friction conditions. Simulation was carried out under the condition of constant volume and temperature. Temperature was controlled by scaling the velocities of atoms in the system, and the Verlet method was adopted to solve the equation of motion. The hardware configuration for computation in this manuscript is a personal computer with a 1.0 GHz Pentium III CPU and 1 GB memory. Results and Discussion 1. First-Principles Parameterization. In the Colors program used for quantum chemistry calculations in Hybrid-Colors, various parameters, such as those for Slater-type basis sets and orthogonal Hamiltonian term, are used for accelerating computations. To determine the accurate parameters, we determined them on the basis of first-principles DFT calculations via the ADF program. Details of the first-principles parameterization procedure are described elsewhere.28 Figure 2 shows radial distributions of electron density for the 3s and 3p orbitals of the P atom with neutral charge calculated by the Colors and DFT programs. We can see a good agreement between results by Colors and DFT programs for both orbitals, except for the inner electron density that does not influence the chemical interaction with surrounding atoms significantly. Figure 3 shows a charge dependency of the orthogonal Hamiltonian term for the P atom calculated by Colors and DFT programs. Charge dependency of orthogonal Hamiltonian term also shows a good agreement between results by Colors and DFT programs. We then analyzed the charge distribution in the phosphoric trimethyl
Dynamics of Phosphoric Ester Lubricant Additive
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Figure 3. Charge dependency of the orthogonal Hamiltonian term for the P atom: Symbols and solid lines represent results calculated by DFT and Colors programs, respectively. Circles and gray solid line are for the 3s orbital of the P atom, while rectangles and black solid line are for the 3p orbital of the P atom.
TABLE 1: Charge Distribution in Phosphoric Trimethyl Molecule element
charge by Colors (-)
charge by DFT (-)
P OPdO OCH3-O C H
0.43 -0.44 -0.24 0.00 0.08
0.48 -0.36 -0.16 -0.03 0.05
molecule using the determined parameters. Table 1 shows the charge of elements in the phosphoric trimethyl molecule. Only average charges are shown for H and C atoms. Charges of two types of O atoms, that is, O atom of PdO group (OPdO) and O atoms of methoxy group (OCH3-O) in the molecule, are separately shown. The P atom shows a large positive charge, while C and H atoms are almost neutral. OPdO is more negatively charged as compared to OCH3-O. We can confirm that the Colors program well reproduces the results by DFT with our first-principles parameterization method. 2. Chemical Interactions between Phosphoric Trimethyl and the Nascent Fe Surface. To study the tribochemical reaction of phosphoric trimethyl, a hybrid tight-binding quantum chemical molecular dynamics simulation was carried out for phosphoric trimethyl and the nascent Fe surface under boundary lubrication conditions. Simulation temperature was set as 423 K, and the integration time for the simulation was 0.1 fs. First, we analyzed the chemical interaction of phosphoric trimethyl with the nascent Fe surface at the atomistic scale. Figure 4a shows a schematic of interacting structure observed in the simulation. During the simulation, OPdO atom and one of three OCH3-O atoms (OCH3-O,int) were interacting with the Fe surface. Figure 4b shows interatomic distances between OPdO or OCH3-O,int and the nearest Fe atom in the nascent Fe surface. The Fe-OPdO and Fe-OCH3-O,int distances at the initial structure are 3.04 and 3.13 Å, respectively. After 200 fs, the Fe-OPdO distance decreased to the range of 2.31-2.48 Å; on the other hand, the Fe-OPdO distance decreased to the range of 2.452.83 Å. This indicates that chemical bonds are formed between the nascent Fe surface and both OPdO and OCH3-O,int of phosphoric trimethyl and the interaction of OPdO with the nascent Fe surface is stronger than that of OCH3-O,int. To study the nature of these chemical bonds, we analyzed the bond overlap population42 between the nascent Fe surface and OPdO or OCH3-O,int as shown in Figure 5. Bond overlap population, which is an index for covalent bonds, between OPdO and Fe atom increases with simulation time, and after 200 fs the bond population takes a stable value ranging from 0.17 to 0.23. This indicates the formation of a stable covalent bond between them
Figure 4. (a) Schematic structure of phosphoric trimethyl interacting with the nascent Fe surface, and (b) interatomic distances of OPdO and OCH3-O from the nascent Fe surface.
Figure 5. Bond overlap population between OPdO and OCH3-O with the nascent Fe surface.
after 200 fs. On the contrary, bond overlap population between OCH3-O and Fe atom remains zero throughout the simulation, indicating that the covalent bond is not formed. These results mean that the nature of the chemical bond between the OCH3-O,int and Fe atom is not covalent but ionic, while that of the chemical bond between OPdO and Fe atom is covalent. By using the Hybrid-Colors program, it was shown that the phosphoric trimethyl molecule chemically interacts with the nascent Fe surface through the formation of both covalent and ionic bonds. Our results indicate that both OPdO and OCH3-O,int play important roles in the adsorption of phosphoric ester onto the nascent Fe surface, which is reported as a probable first step of the tribofilm formation.3 To further investigate the nature of the chemical bond between OPdO and Fe, we analyzed the density of states for the initial structure and structure at 180 fs when a covalent bond has been formed as shown in Figure 5. Figure 6a shows the density of states for the initial structure. The density of states only for orbitals of Fe and O is shown for clarity. We can see no significant overlap between orbitals of Fe and O at the initial structure. On the contrary, the density of states for the structure at 180 fs shown in Figure 6b clearly shows the overlap between Fe 3d, 4s and O 2p orbitals, which also indicates the formation of a covalent bond. Results shown in both Figures 5 and 6 mean that the covalent bond between OPdO and Fe is formed due to the interaction between Fe 3d, 4s and O 2p orbitals. 3. Tribochemical Reaction Dynamics of Phosphoric Trimethyl with the Nascent Fe Surface. To further study the tribochemical reaction between phosphoric trimethyl and the
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Figure 8. Interatomic distance between OPdO and the nascent Fe surface during simulation without extreme friction.
Figure 6. Density of states for Fe 3d and O 2p orbitals at (a) 0 fs and (b) 180 fs.
Figure 9. Bond overlap population of OPdO and OCH3-O with the nascent Fe surface during simulation without extreme friction.
Figure 7. Bond overlap population between OPdO and P atoms of phosphoric trimethyl molecule.
nascent Fe surface, we analyzed bond overlap population between the OPdO and P atom of phosphoric trimethyl as shown in Figure 7. Bond overlap population between OPdO and the nascent Fe surface is also shown for reference. The bond overlap population between OPdO and P gradually decreases at the beginning of the simulation and becomes almost zero after 200 fs. This corresponds to the time profile of bond overlap population between OPdO and the nascent Fe surface; that is, it gradually increases at the beginning of the simulation and takes a stable value of about 0.2 after 200 fs. This analysis clearly shows the bond dissociation in the phosphoric trimethyl molecule and the formation of a bond between the phosphoric trimethyl molecule and the nascent Fe surface. Simulation by our Hybrid-Colors program indicates that OPdO will play an important role in the initiation of the tribochemical reaction, while both OPdO and OCH3-O,int would be important for the adsorption process of phosphoric ester onto the Fe surface. 4. Influence of Friction Condition on Tribochemical Reaction. To study the influence of friction condition on the tribochemical reaction of the phosphoric trimethyl molecule with the nascent Fe surface, we carried out the simulation under a condition without friction; that is, instead of giving an external high pressure and a sliding velocity, only an atmospheric pressure, 100 kPa, was applied to the top layer of the upper Fe substrate during the simulation. First, we analyzed the interatomic distance between OPdO and the nearest Fe atom in the nascent Fe surface as shown in Figure 8. The result obtained under boundary lubrication conditions is also shown for comparison. During the simulation without friction, the inter-
atomic distance between OPdO and the nascent Fe surface gradually increased after 200 fs and became longer than 4 Å. We then analyzed the bond overlap population between OPdO and the nearest Fe atom in the nascent Fe surface as shown in Figure 9. Although bond overlap population transiently showed a positive value from 80 to 260 fs, that interaction was not stable, and eventually we observed no covalent interaction between OPdO and the nascent Fe surface. These results indicate that OPdO was interacting with the nascent Fe surface only through long-range electrostatic interaction, and not through covalent interaction after 260 fs. Bond overlap population between OPd O and P is also shown in Figure 9. Bond overlap population takes the positive value with the range of 0.11-0.40 throughout the simulation, which means no dissociation of the PdO bond. From this simulation without friction, it was observed that the friction influences the tribochemical reaction of phosphoric trimethyl with the nascent Fe surface. Conclusion In this manuscript, we studied the tribochemical reaction between phosphoric ester and the nascent Fe surface under boundary lubrication conditions by using a hybrid tight-binding quantum chemical molecular dynamics method. Phosphoric trimethyl was found to interact with the nascent Fe surface by forming both covalent and ionic bonds through O atoms of PdO and P-O-CH3, respectively. During the simulation under boundary lubrication conditions, dissociation of the PdO bond was observed, which would be an initial step of the tribochemical reaction to form tribofilm on the nascent Fe surface. From the comparison between the results from simulations under friction and those without friction, we observed that the friction largely influences the tribochemical reaction of phosphoric trimethyl with the nascent Fe surface. References and Notes (1) Najman, M. N.; Kasrai, M.; Bancroft, G. M. Wear 2004, 257, 3240. (2) Najman, M. N.; Kasrai, M.; Bancroft, G. M.; Miller, A. Tribol. Lett. 2002, 13, 209-218.
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