Effective Viscosity of Confined Hydrocarbons

We present molecular dynamics friction calculations for confined hydrocarbon films with molecular lengths from 20 to 1400 carbon atoms. We find that the logarithm of the effective viscosity ${\eta }_{\mathrm{eff}}$ for nanometer-thin films depends linearly on the logarithm of the shear rate: $\log {\eta }_{\mathrm{eff}}=C-n\log \dot{\gamma }$, where $n$ varies from 1 (solidlike friction) at very low temperatures to 0 (Newtonian liquid) at very high temperatures, following an inverse sigmoidal curve. Only the shortest chain molecules melt, whereas the longer ones only show a softening in the studied temperature interval $0<T<900\mathrm{K}$. The results are important for the frictional properties of very thin (nanometer) films and to estimate their thermal durability.

Figure 1

The logarithm of the effective viscosity as a function of the temperature for (a) ${\mathrm{C}}_{20}{\mathrm{H}}_{42}$, (b) ${\mathrm{C}}_{100}{\mathrm{H}}_{202}$, and (c) ${\mathrm{C}}_{1400}{\mathrm{H}}_{2802}$ system at four sliding velocities: $0.3\mathrm{m}/\mathrm{s}$ (▪), $3\mathrm{m}/\mathrm{s}$ (▴), $10\mathrm{m}/\mathrm{s}$ (⧫◆), and $100\mathrm{m}/\mathrm{s}$ (⬠).

Figure 2

The data points for the logarithm of the effective viscosity as a function of the logarithm of the shear rate at four sliding velocities: 0.3, 3, 10, and $100\mathrm{m}/\mathrm{s}$. The lines represent the linear fits to these data points. The systems are ${\mathrm{C}}_{100}{\mathrm{H}}_{202}$ at 600 K and ${\mathrm{C}}_{1400}{\mathrm{H}}_{2802}$ at 300 K. The values of the slope and the intercept of the ${\mathrm{C}}_{100}{\mathrm{H}}_{202}$ are $-0.520\pm 0.038$ and $2.260\pm 0.351$ and for the ${\mathrm{C}}_{1400}{\mathrm{H}}_{2802}$ system $-0.958\pm 0.024$ and $6.753\pm 0.228$.

Figure 3

Values of the parameter $n$ in Eq. (2) as a function of the temperature for the systems ${\mathrm{C}}_{20}{\mathrm{H}}_{42}$, ${\mathrm{C}}_{100}{\mathrm{H}}_{202}$, and ${\mathrm{C}}_{1400}{\mathrm{H}}_{2802}$. The solid lines are fits to the numerical data using Eq. (3) with the parameters $\alpha$ and $T_c$ given in Table .

Figure 4

The $C$ parameter in Eq. (2) also follows a sigmoidal curve when the temperature is varied. This figure shows the dependence of $C$ on $n$. All three systems ${\mathrm{C}}_{20}{\mathrm{H}}_{42}$, ${\mathrm{C}}_{100}{\mathrm{H}}_{202}$, and ${\mathrm{C}}_{1400}{\mathrm{H}}_{2802}$ are represented.

Figure 5

The polymer film thickness as a function of the temperature. The sliding speed is $10\mathrm{m}/\mathrm{s}$. All three systems ${\mathrm{C}}_{20}{\mathrm{H}}_{42}$, ${\mathrm{C}}_{100}{\mathrm{H}}_{202}$, and ${\mathrm{C}}_{1400}{\mathrm{H}}_{2802}$ are represented.

Figure 6

The relative number of atoms moving at the velocity below $v$, as a function of $v$, at 600 K. It can be seen that the velocity gradient is going from nearly Newtonian in the case of ${\mathrm{C}}_{20}{\mathrm{H}}_{42}$ to solidlike in the ${\mathrm{C}}_{1400}{\mathrm{H}}_{2802}$ case.