Coarse-Grained Molecular Dynamics Simulations of Boundary Lubrication on Nanostructured Metal Surfaces

Abstract

Coarse-grained molecular dynamics simulations were carried out to investigate the frictional properties of lubricant molecules on nanostructured metal surfaces. The simulation cell consists of a lubricant film enclosed between two metal surfaces. The attractive potential of specific iron atoms on the surface was modified such that the lubricant molecule adsorb preferentially on these atoms. These particular iron atoms were arranged to reproduce a grain boundary surface nanostructure. It is found that below the critical normal stress, the strength of the interaction between Fe and the lubricant molecule has little effect on the friction coefficient. However, the behavior of the lubricant film on the metal surface is sensitive to the interaction strength. Large attraction forces increase the adherence of the lubricant film.

Appendices

Appendix: Coarse-Grained Modeling for the Iron-Lubricant System

Although CG potential parameters for the CH₂–CH₂, CH₂–COOH, and COOH–COOH interactions are available (see Table 2), no CG model for the Fe–CH₂ and Fe–COOH interactions has been developed so far.

To address this need, we developed a coarse-grained potential function for the Fe-${{\hbox{CH}}_2}$ interaction based on the all-atom (AA) potential model for the Fe–C–H system. Details are given in section A1.1. In section A1.2, we show how the CG potential parameters for the Fe–CH₂ interaction can be derived from a simple relationship.

${\hbox{Fe}}{\rm{-}}{{\hbox{CH}}_2}$ interaction

Figure 9 is a schematic illustration of the atomistic structure used for CG modeling. The system consists of an ${\hbox{Fe}}$ surface (bcc {110} plane) and a ${\hbox{CH}}_{4}$ (methane) molecule. An equivalent model for AA and CG simulation was prepared as shown in Fig. 9a, b, respectively. The distance (d) between the ${\hbox{Fe}}$ surface and the ${\hbox{CH}}_{4}$ molecule was varied between 4 Å and 12 Å and the total potential energy of the system E was evaluated as a function of d. The CG potential parameters $\alpha_{{\text{Fe-CH}}_{2}}$ and $\beta_{{\text{Fe-CH}}_{2}}$ in the Lennard–Jones potential function (Eq. 1) were determined to reproduce the potential curve E(d) of the ${\hbox{CH}}_{4}$ molecule on the bcc ${\hbox{Fe}}$ {110} surface. We employed the AA models developed in Ref. [42] for the bonding interaction of a ${\hbox{CH}}_{4}$ molecule and Ref. [43] for the non-bond interaction of ${\hbox{Fe}}-{\hbox{H}}$ and ${\hbox{Fe}}-\hbox {C}$. Since there are only two CG potential parameters to be optimized, they were adjusted manually by comparing the CG result (with provisional potential parameter sets) to the AA result. Thermal fluctuations were not considered for the ${\hbox{Fe}}$, $\hbox {C}$ and ${\hbox{CH}}_{4}$ particles. The dynamics of ${\hbox{H}}$ atoms was controlled by a Nose–Hoover thermostat to keep the temperature constant $(T = 300\,{\rm K})$. Note that this CG simulation is static because there is no degree of freedom to allow thermal fluctuations.

Fig. 9

Schematic illustration of the model used in studying the interaction between a ${\hbox{CH}}_{4}$ molecule and an Fe surface for a the AA method and b the CG method

Figure 10 shows the energy profile as a function of d obtained by the AA model and by the optimized CG model. The optimized CG parameters are as follows: $\alpha _\mathrm{Fe-CH2} =$ 0.2499 kcal/mol and $\beta _\mathrm{Fe-CH2} = 4.2999$ Å. We confirmed that the optimized CG model reproduces successfully the potential curve obtained from the AA model. The interaction between ${{\hbox{Fe}}^{\mathrm{SP}}}$ and ${{\hbox{CH}}_2}$ was regarded as identical to the ${{\hbox{Fe}}^{\mathrm{SP}}}$-${{\hbox{CH}}_2}$ interaction.

Fig. 10

Potential energy of the ${\hbox{Fe}}-{\hbox{CH}}_{4}$ system as a function of the separation distance d obtained by the AA model and the optimized CG model. Note that the result from the AA model was shifted vertically to satisfy $E(d\rightarrow \infty ) \rightarrow 0$

1.1 ${\hbox{Fe}}{\rm{-}}{\hbox{COOH}}$ Interaction

To estimate the CG potential parameters $\alpha _{\mathrm{Fe-COOH}}$ and

$\beta _{\mathrm{Fe-COOH}}$, we use the geometric mean:

$$\begin{aligned} \alpha _{A\textit{-}B}= & {} \sqrt{\alpha _{A\textit{-}A}\alpha _{B\textit{-}B}} \end{aligned}$$

(2)

$$\begin{aligned} \beta _{A\textit{-}B}= & {} \sqrt{\beta _{A\textit{-}A}\beta _{B\textit{-}B}} \end{aligned}$$

(3)

where A and B denote the types of particles (i.e., ${{\hbox{CH}}_2}$, ${\hbox{COOH}}$, ${\hbox{Fe}}$ and ${{\hbox{Fe}}^{\mathrm{SP}}}$). To derive $\alpha _{\mathrm{Fe-COOH}}$, we consider two equations as follows:

$$\begin{aligned} \alpha _{\mathrm{Fe-COOH}}= & {} \sqrt{\alpha _{\mathrm{Fe-Fe}}\alpha _{\mathrm{COOH-COOH}}} \end{aligned}$$

(4)

$$\alpha_{{\text{Fe-CH}}_{2}}= \sqrt{\alpha _{{\text{Fe-CH}}}\alpha_{{\text{CH}_{2}}-{\text{CH}}_{2}}}$$

(5)

From these equations, we obtain:

$$\alpha_{\text{Fe-COOH}}= \alpha_{\text{Fe-CH}_{2}} \sqrt{\frac{\alpha _{\text{COOH-COOH}}}{\alpha_{\text{CH}_{2}-{\text{CH}}_{2}}}}$$

(6)

Here, all the parameters on the right side of the equation are known, and thus $\alpha _{\mathrm{Fe-COOH}}$ can be evaluated.

In a similar way, we obtain:

$$\beta _{\text{Fe-COOH}}= \beta_{\text{Fe-CH}_{2}} \sqrt{\frac{\beta_{\text{COOH-COOH}}}{\beta_{\text{CH}_{2}-{\text{CH}}_{2}}}}$$

(7)

The evaluation of the aforementioned equations is easily carried out and leads to $\alpha _{\mathrm{Fe-COOH}} = 0.3658$ kcal/mol and $\beta _{\mathrm{Fe-COOH}} = 4.5675$ Å. The parameter $\beta_{\text{Fe}^{\text{SP}}{-}{\text{COOH}}}$ was set to 4.5675 Å as well.