**4.1. Static calculations**

To better understand adsorption mechanisms of VPA and EA on Al (111) surface, several combined adsorbate/slab systems were selected for the investigation. The adsorption enthalpy (the binding energy or the binding strength), <sup>Δ</sup> *Hads* (m) , was defined as the difference between the total energy of the combined adsorbate plus slab (adsorbent), and the total energy of the separated adsorbate and, the separated slab, which was given by

$$
\Delta H\_{\text{ads}}^{\text{(m)}} = E(\text{adsorstate \& slab)} - \left[ E(\text{adsorstate}) + E(\text{slab}) \right] \tag{1}
$$

where the superscript (m) indicated one reaction type. A negative <sup>Δ</sup> *Hads* (m) value corresponded to a favorable adsorption on surface, while a positive one represented an unlikely reaction on surface.

Preliminary investigation of the VPA adsorption on Al (111) surface indicated that, its standing geometries at S-2 and S-3 always shifted to S-1 on the surface when using the energy minimization. Similar results can be obtained for the EA adsorption at S-2 and S-3 on Al (111) surface. Therefore, S-1 was regarded as the most favorable adsorption site for these adsorbates. According to this, we would only focus on the S-1 for the VPA and the EA adsorptions on Al (111) surface.

### *4.1.1. Uni-dentate configurations*

**Figure 7** shows side views of VPA and EA adsorptions on Al(111) surface in their own uni-dentate coordination with one of their oxygen ions and one H ion (dissociated from this oxygen ion) bonding onto the surface, respectively. Molecular binding sites on the surface were both at S-1.

In **Figure 7**, Al─H and Al─O single bonds were formed on Al (111) surface to sustain the adsorbates. Adsorption enthalpies corresponding to **Figure 7(a)**, **(b)**, <sup>Δ</sup> *Hads* (VPS,EA) = −0.89 and −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 gaseous H2 molecule by means of H ions desorbed from Al (111) surface. Therefore, if ignoring zero point energy corrections, the formation of gaseous H2 molecule in these final adsorptions were more favorable to those individual H ions adsorbing onto the surface, so molecular main pieces would be left onto the surface alone in adsorption end, see **Figure 8**.

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

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].

To better understand adsorption mechanisms of VPA and EA on Al (111) surface, several combined adsorbate/slab systems were selected for the investigation. The adsorption enthalpy

the total energy of the combined adsorbate plus slab (adsorbent), and the total energy of the

favorable adsorption on surface, while a positive one represented an unlikely reaction on surface. Preliminary investigation of the VPA adsorption on Al (111) surface indicated that, its standing geometries at S-2 and S-3 always shifted to S-1 on the surface when using the energy minimization. Similar results can be obtained for the EA adsorption at S-2 and S-3 on Al (111) surface. Therefore, S-1 was regarded as the most favorable adsorption site for these adsorbates. According to this, we would only focus on the S-1 for the VPA and the EA adsorptions

**Figure 7** shows side views of VPA and EA adsorptions on Al(111) surface in their own uni-dentate coordination with one of their oxygen ions and one H ion (dissociated from this oxygen ion) bonding onto the surface, respectively. Molecular binding sites on the surface were both at S-1.

(m)

(m) = *E*(adsorbate & slab) − [*E*(adsorbate) + *E*(slab)] (1)

, was defined as the difference between

value corresponded to a

(m)

(111) slab, respectively.

10 Lubrication - Tribology, Lubricants and Additives

**4. Results and discussions**

(the binding energy or the binding strength), <sup>Δ</sup> *Hads*

separated adsorbate and, the separated slab, which was given by

where the superscript (m) indicated one reaction type. A negative <sup>Δ</sup> *Hads*

**4.1. Static calculations**

Δ *Hads*

on Al (111) surface.

*4.1.1. Uni-dentate configurations*

**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 **Figure 8(a)** had no such a character. This meant that O2 ion on C2─O2 bond was more covalent, 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 occur reasonably because more unoccupied e<sup>−</sup> states for O3 than those for O2 seemed to make the final binding state of VPA stabler than that of EA on the surface.

Quantitatively, **Figure 9(a)** shows the modified charge density of states (DOS) for O3 on vinyl-phosphonate as shown in **Figure 8(a)**, corresponding to e<sup>−</sup> states (around the *E*lumo) in **Figure 5(a)**. Comparing this DOS with that in **Figure 5(a)** for O3 on VPA, it may find that many of unoccupied e<sup>−</sup> states evolved into occupied ones (below the *E*<sup>F</sup> , the Fermi level on energy band) after VPA adsorption on surface. Similarly, **Figure 9(b)** shows the modified DOS for O2 on acetate as shown in **Figure 8(b)**, corresponding to e<sup>−</sup> states (around the *E*lumo) in **Figure 5(b)**. Comparing O3 on VPA with O2 on EA, we concluded that the DOS for O3 would shift more below the *E*<sup>F</sup> than that for O2 after molecular adsorptions, which made the binding energy of VPA larger than that of EA.

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 of unoccupied 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.

*4.1.3. Tri-bridged configurations*

*4.1.4. Other adsorption geometries*

unfavorable in the adsorption.

Δ *Hads* (VPA)

respectively.

the CH3

**Figure 11** shows a side view of VPA adsorption on Al (111) surface in tri-bridged coordination. In **Figure 11**, 2 H ions liberated from the VPA main piece through the condensing reaction and were adsorbed on the surface. Adsorption enthalpy corresponding to **Figure 11**,

**Figure 10.** Side views of (a) vinyl-phosphonate and (b) acetate adsorptions on Al (111) surface in bi-bridged coordination,

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

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

13

ions desorbed from Al (111) surface would bring additional negative values for this enthalpy: −0.51 eV, indicating that vinyl-phosphonate bonding to Al (111) surface alone in its own tri-

When rotating initial configurations of adsorbates by some clockwise angels (e.g., 120° or 180° etc) toward Al (111) surface rather than their functional groups facing the surface, i.e., with

surface would indicate positive values, meaning that such kinds of reacting geometries were

**Figure 11.** A side view of vinyl-phosphonate adsorption on Al (111) surface in tri-bridged coordination.

end directly pointing toward the surface, the binding energies of adsorbates on the

molecule by means of H

<sup>=</sup> −2.61 eV. Moreover, subsequent formation of gaseous H<sup>2</sup>

bridged coordination, would be more favorable in final adsorption.

**Figure 8.** Isosurfaces of charge density at the ELF = 0.67 for (a) VPA and for (b) EA adsorptions on Al (111) surface in their own uni-dentate coordination.

**Figure 9.** The modified DOS for (a) O3 ion on vinyl-phosphonate and (b) O2 ion on acetate.

#### *4.1.2. Bi-bridged configurations*

**Figure 10** shows side views of vinyl-phosphonate and acetate adsorptions on Al (111) surface in their own bi-bridged coordination, respectively, with H ions liberating from molecular main piece and bonding to the surface. In these two adsorptions, adsorption enthalpies corresponding to **Figure 10(a)**, **(b)**, <sup>Δ</sup> *Hads* (VPA,EA) = −1.32 and −1.52 eV, respectively. Moreover, subsequent formation of gaseous H2 molecule by means of H ions desorbed from Al (111) surface would bring additional negative values for these enthalpies: −0.51 and −0.26 eV, respectively, indicating that both vinyl-phosphonate and acetate bonding to Al (111) surface alone in their own bi-bridged coordination, respectively, would be more favorable in final adsorptions.

**Figure 10.** Side views of (a) vinyl-phosphonate and (b) acetate adsorptions on Al (111) surface in bi-bridged coordination, respectively.

#### *4.1.3. Tri-bridged configurations*

**Figure 11** shows a side view of VPA adsorption on Al (111) surface in tri-bridged coordination. In **Figure 11**, 2 H ions liberated from the VPA main piece through the condensing reaction and were adsorbed on the surface. Adsorption enthalpy corresponding to **Figure 11**, Δ *Hads* (VPA) <sup>=</sup> −2.61 eV. Moreover, subsequent formation of gaseous H<sup>2</sup> molecule by means of H ions desorbed from Al (111) surface would bring additional negative values for this enthalpy: −0.51 eV, indicating that vinyl-phosphonate bonding to Al (111) surface alone in its own tribridged coordination, would be more favorable in final adsorption.

#### *4.1.4. Other adsorption geometries*

*4.1.2. Bi-bridged configurations*

their own uni-dentate coordination.

12 Lubrication - Tribology, Lubricants and Additives

responding to **Figure 10(a)**, **(b)**, <sup>Δ</sup> *Hads*

quent formation of gaseous H2

**Figure 10** shows side views of vinyl-phosphonate and acetate adsorptions on Al (111) surface in their own bi-bridged coordination, respectively, with H ions liberating from molecular main piece and bonding to the surface. In these two adsorptions, adsorption enthalpies cor-

**Figure 8.** Isosurfaces of charge density at the ELF = 0.67 for (a) VPA and for (b) EA adsorptions on Al (111) surface in

would bring additional negative values for these enthalpies: −0.51 and −0.26 eV, respectively, indicating that both vinyl-phosphonate and acetate bonding to Al (111) surface alone in their own bi-bridged coordination, respectively, would be more favorable in final adsorptions.

= −1.32 and −1.52 eV, respectively. Moreover, subse-

molecule by means of H ions desorbed from Al (111) surface

(VPA,EA)

**Figure 9.** The modified DOS for (a) O3 ion on vinyl-phosphonate and (b) O2 ion on acetate.

When rotating initial configurations of adsorbates by some clockwise angels (e.g., 120° or 180° etc) toward Al (111) surface rather than their functional groups facing the surface, i.e., with the CH3 end directly pointing toward the surface, the binding energies of adsorbates on the surface would indicate positive values, meaning that such kinds of reacting geometries were unfavorable in the adsorption.

**Figure 11.** A side view of vinyl-phosphonate adsorption on Al (111) surface in tri-bridged coordination.
