**3. Simulation methodologies and procedures**

### **3.1. Static calculations**

These calculations were based upon the DFT [16–18] using the Vienna Ab-initio Simulation Package (VASP). At first, all calculations were performed using the Projector-Augmented Wave (PAW) pseudopotentials [19]. The GGA created by Perdew and co-workers [20, 21] was employed for evaluating the exchange-correlation energy. This methodology was similar to a previous study of optimizing the VPA adsorption geometries on an α-Al<sup>2</sup> O3 (0001) surface [15]. Prior to these calculations, lattice constant, bulk modulus and cohesive energy for a pure aluminum bulk by fitting data of energy versus volume to the Murnaghan Eq. [22] was calculated. A regular Monkhorst-Pack grid [23] of 17 × 17 × 17 was chosen as the best *k*-point sampling, so that the total energy of system was converged within 1–2 meV/atom. The computed lattice constant, *a*<sup>0</sup> '= 4.05(3) Å, see ref. [9].

Then next, calculations of acid adsorptions on the Al (111) surface slab were conducted in a supercell with a periodic four-layer 3*a*<sup>0</sup> '× 3*a*<sup>0</sup> 'units (16 Al ions per layer) in XY directions. A plane-wave cutoff energy, 400 eV, which was primarily required by the "hardest ions (C and O)", was chosen. A regular Monkhorst-Pack grid of a 5×5×1 *k*-point sampling was selected for this orthogonal supercell with three definite orientations: *a*[1 \_ 10] = 2√ \_\_ 2*a*0 ' along the X axis, *b*[11 \_ 2] = √ \_\_ 6*a*0 ' along the Y axis, and *c* [111] = 26.0 Å along the Z axis, plus a vacuum distance of 10.0 Å in *c* direction and with one bottom layer of the Al (111) slab fixed along *c* direction in the supercell. The atomic geometry was optimized through minimizing the Hellman-Feyman forces using a conjugate gradient algorithm [11], until the total force on each ion reduced to 0.05 eV/Å or less.

## **3.2. Dynamic simulations**

**Figure 5** shows distributions of charge density of states (DOS) for three O ions on the VPA and two O ions on the EA, respectively. In **Figure 5**, the *E*lumo represented the energy level corresponding to the lowest unoccupied molecular orbital, i.e., above the *E*lumo the DOS for O ions represented unoccupied states. In **Figure 5**, more portions of the DOS for O ions on the VPA appeared in orbitals above the *E*lumo than those on the EA, implying that VPA may be more

Since Al (111) surface has the lowest surface energy among all surface geometries in aluminum bulk, it is likely to expose in the air during the actual rolling process. So here it is selected as an adsorption slab surface (adsorbent) to react with above adsorbates. **Figure 6** shows three distinguishable adsorption sites in the top layer of Al (111) surface slab. We refer to them as site-1, -2, and -3, respectively. Among these sites, site-1 (S-1) had corners at three Al ions; site-2 (S-2) had corners at three cave points (cross signs); and site-3 (S-3) had corners at three saddle points (ice-star signs). According to past experiences [14], these three sites were more likely to react with adsorbates than others because they allowed O-bases on adsorbates to bond to

These calculations were based upon the DFT [16–18] using the Vienna Ab-initio Simulation Package (VASP). At first, all calculations were performed using the Projector-Augmented Wave (PAW) pseudopotentials [19]. The GGA created by Perdew and co-workers [20, 21] was employed for evaluating the exchange-correlation energy. This methodology was similar to

O3

(0001) surface

a previous study of optimizing the VPA adsorption geometries on an α-Al<sup>2</sup>

reactive with the Al surface than EA by feat of their O ions.

**Figure 6.** Three most favorable adsorption sites in top layer of Al (111) surface slab.

**3. Simulation methodologies and procedures**

**2.2. Adsorbent configurations**

8 Lubrication - Tribology, Lubricants and Additives

surface stronger than other ones.

**3.1. Static calculations**

In this study, all ab-initio molecular dynamics (AIMD) simulations were also based upon the DFT as implemented in the VASP. A Vanderbilt-type ultrasoft pseudopotentials (USP) were utilized for elemental constituents by means of the GGA [24]. In real practice, the GGA usually yielded inaccurate reaction barriers [25–27], while a semilocal-BLYP and hybrid-B3LYP functionals seemed to predict adsorption energies accurately and distinguish adsorption sites correctly. However, for the study of dynamic decomposition, we believed that the GGA was also a reasonable compromise since a highly colliding velocity acting on molecules toward the Al surface slab would likely overwhelm any barrier to the decomposition.

During the AIMD simulation, first of all, lattice constant (*a*<sup>0</sup> ) of pure Al bulk was calculated using the NPT ensemble, which thermally equilibrated one 2*a*<sup>0</sup> × 2*a*<sup>0</sup> × 2*a*<sup>0</sup> unit cell at a room temperature (300 K) plus an ambient pressure of 1.0 bar for about 1500 time steps, a simulation time step of 0.001 ps was selected. A regular gamma-centered grid of 5 × 5 × 5 was chosen as the best *k*-point sampling for the unit cell. Total energy of the system was converged within 1–2 meV/atom. A plane-wave cutoff energy, 400 eV, as dictated by the hardest oxygen pseudopotential, was adopted in all simulations. The computed lattice constant, *a*<sup>0</sup> = 4.05(7) Å, was favorably fitting to other calculations and experimental observations [28].

Besides, for modeling interactions between additive molecules and an Al (111) slab, a Monkhorst-Pack grid of 5 × 5 × 1 was selected for the best *k*-point sampling. A supercell with the entire Al (111) slab consisted of four Al layers (36 ions per layer) of 144 ions. This orthorhombic geometry had three definite orientations: *a*[1 \_ 10] = \_\_3 2√ \_\_ <sup>6</sup> *a*<sup>0</sup> along the X axis, *b*[11 \_ 2] = 3√ \_\_ 2*a*0 along the Y axis, and *c* [111] = 40.0 Å along the Z axis plus a vacuum distance of 24.0 Å in the *c* direction to preclude interactions with periodic images. The bottom layer of the Al (111) slab was fixed along the *c* direction to prevent the whole slab motion during impacts of additive molecules onto the Al slab surface.

In addition, each of isolated molecules was optimized in a same vacuum supercell as used for the Al (111) slab. And then, it was equilibrated at 300 K for about 1500 time steps by re-scaling thermal velocities at each time step [29], the time step = 0.001 ps. Simultaneously, the Al (111) slab were equilibrated in its supercell by the same technique as each isolated molecule. Then next, each isolated molecule was transferred into the simulation supercell containing the Al (111) slab, respectively.

In **Figure 7**, Al─H and Al─O single bonds were formed on Al (111) surface to sustain the

−0.51 eV, respectively. Moreover, VASP calculations indicated that each of adsorption enthalpies would bring additional negative values: −0.26 eV, due to subsequent formation of gas-

were more favorable to those individual H ions adsorbing onto the surface, so molecular main

**Figure 8** shows isosurfaces of charge density for vinyl-phosphonate and acetate on Al (111) surface in their own uni-dentate coordination, respectively. A value of the ELF = 0.67 was chosen because it may provide the best visual difference in charge density on C─O and P─O bonds. In **Figure 8(b)**, a small lobe can be observed on C2─O2 bond, while P─O3 bond in

lent, while O3 ion on P─O3 bond was more ionic. This was expected because P was less electronegative than C (2.1 vs. 2.5), see ref. [32]. Therefore, during these two adsorptions, portions of charge density for O3 on vinyl-phosphonate in **Figure 8(a)** would move more toward the reacting Al ion in surface than that for O2 on acetate in **Figure 8(b)**. Qualitatively, this may

Quantitatively, **Figure 9(a)** shows the modified charge density of states (DOS) for O3 on

**Figure 5(a)**. Comparing this DOS with that in **Figure 5(a)** for O3 on VPA, it may find that

energy band) after VPA adsorption on surface. Similarly, **Figure 9(b)** shows the modified

in **Figure 5(b)**. Comparing O3 on VPA with O2 on EA, we concluded that the DOS for O3

In the following subsections, similar trends of the DOS curves in **Figure 9** can also be observed for O ions on molecular main piece reacting with Al (111) surface in bi-bridged (VPA and EA) and tri-bridged (VPA) coordinations. According to these results, we believed that the VPA should bind stronger than the equivalent EA on Al (111) surface because of its larger number

states evolved into occupied ones (below the *E*<sup>F</sup>

molecule by means of H ions desorbed from Al (111) surface. Therefore, if ignoring

(VPS,EA)

molecule in these final adsorptions

http://dx.doi.org/10.5772/intechopen.72512

Ab-Initio Modeling of Lubricant Reactions with a Metal Al (111) Surface

ion on C2─O2 bond was more cova-

states (around the *E*lumo) in

, the Fermi level on

states (around the *E*lumo)

states for O3 than those for O2 seemed to make

than that for O2 after molecular adsorptions, which made the

= −0.89 and

11

adsorbates. Adsorption enthalpies corresponding to **Figure 7(a)**, **(b)**, <sup>Δ</sup> *Hads*

pieces would be left onto the surface alone in adsorption end, see **Figure 8**.

zero point energy corrections, the formation of gaseous H2

**Figure 8(a)** had no such a character. This meant that O2

the final binding state of VPA stabler than that of EA on the surface.

vinyl-phosphonate as shown in **Figure 8(a)**, corresponding to e<sup>−</sup>

DOS for O2 on acetate as shown in **Figure 8(b)**, corresponding to e<sup>−</sup>

states available for bonding to the surface.

**Figure 7.** Side views of (a) VPA and (b) EA adsorptions on Al (111) surface in uni-dentate coordination.

occur reasonably because more unoccupied e<sup>−</sup>

binding energy of VPA larger than that of EA.

many of unoccupied e<sup>−</sup>

of unoccupied e<sup>−</sup>

would shift more below the *E*<sup>F</sup>

eous H2

After thermal equilibration, all AIMD simulations for interactions between additive molecules and the Al (111) slab were carried out through a constant energy method (NVE) without controlling temperature of system [29]. In real processing works, when steel rollers converged to form bite regions in the metal rolling of Al alloys, pressure gradients in bite regions would draw lubricant additives into conjunction. At this time, translational speeds acting on a single molecule can be estimated to reach as high as 2500 m/s due to kinematics at the tool/Al interface [30]. Hence, a serial approaching velocities, *V*d, based upon this situation, were adopted in the AIMD simulations. Then next, each additive molecule started accelerating toward the Al (111) slab surface once it met a net attraction from the surface. To save computational cost, initial vertical spacing between each additive molecule and Al ions in the surface was set to 2.30 Å, which was slightly larger than Al─O bond length (1.86–1.97 Å) as indicated in ref. [31].
