Evaluation of Methods for Viscosity Simulations of Lubricants at Different Temperatures and Pressures: A Case Study on PAO-2

Abstract

The behavior of lubricants at operational conditions, such as at high pressures, is a topic of great industrial interest. In particular, viscosity and the viscosity-pressure relation are especially important for applications and their determination by computational simulations is very desirable. In this study we evaluate methods to compute these quantities based on fully atomistic molecular dynamics simulations which are computationally demanding but also have the potential to be most accurate. We used the 9,10dimethyloctadecane molecule, main component of PAO-2 base oil as the lubricant for our tests. The methods used for the viscosity simulations are the Green-Kubo equilibrium molecular dynamics (EMD-GK) and non-equilibrium molecular dynamics (NEMD), at pressures of up to 1.0 GPa and various temperatures (40-150 degrees Celsius). We present the theory behind these methods and investigate how the simulation parameters affect the results obtained, to ensure viscosity convergence with respect to the A c c e p t e d M a n u s c r i p t simulation intervals and all other parameters. We show that by using each method in its regime of applicability, we can achieve good agreement between simulated and measured values. NEMD simulations at high pressures captured zero shear viscosity successfully, while at 40 degrees Celsius EMD-GK is only applicable to pressures up to 0.3 GPa, where the viscosity is lower. In NEMD, longer and multiply repeated simulations improve the confidence interval of viscosity, which is essential at lower pressures. Another aspect of these methods is the choice of the utilized force field for the atomic interactions. This was investigated by selecting two different commonly used force fields.

Comparison of Force Fields for the Prediction of Thermophysical Properties of Long Linear and Branched Alkanes

“…Molecular dynamics (MD) simulations have been used often for the prediction of thermophysical bulk properties of lubricants, − wetting, and interfacial properties on solid walls, − as well as for the simulation of tribological contact processes. − Simulations of lubricants usually aim at predicting transport properties, in particular the viscosity, using either equilibrium molecular dynamics (EMD) − or nonequilibrium molecular dynamics (NEMD) simulations. ,− Both methods are challenging: EMD simulations require a large computational effort to compute the viscosity, especially for higher viscosities due to the slow convergence of the autocorrelation function (ACF) . In NEMD simulations, the shear rate has to be small enough to reach the Newtonian regime, which can require very long simulation times due to the bad signal-to-noise ratio at small shear rates .…”

Computing Viscosities of Mixtures of Ester-Based Lubricants at Different Temperatures

“…They show that this coupling increases with the chain length and that the time needed for the Green–Kubo viscosity integral to convergence can be roughly estimated by the rotational relaxation time, which increases with chain length. This finding was also confirmed by other authors. , The effects of temperature, pressure, and other thermodynamic properties on viscosity have been studied by various researchers. − Molecular dynamics was employed on different systems including glass, polyethers, ionic liquids, and biolubricants; − force field impact was also studied. , Lacks et al showed that, if the simulations sample a phase space local minima, it may lead to having a lower or higher shear rate than expected, and that would influence the value of the viscosity and suggest the importance of averaging over multiple trajectories. This provides a simple yet powerful methodology to solve this problem .…”

“… 5 , 6 The effects of temperature, pressure, and other thermodynamic properties on viscosity have been studied by various researchers. 7 − 13 Molecular dynamics was employed on different systems including glass, polyethers, ionic liquids, and biolubricants; 14 − 18 force field impact was also studied. 19 , 20 Lacks et al showed that, if the simulations sample a phase space local minima, it may lead to having a lower or higher shear rate than expected, and that would influence the value of the viscosity and suggest the importance of averaging over multiple trajectories.…”

“…24−26 In our group, we have previously studied the effect of pressure, temperature and force field on an 9,10-dimethyloctadecane system which was studied as a model of PAO-2 lubricant as it is one of the main components. 13 We then decided to focus on more realistic yet simple systems as the mixture of two synthetic esters, di-2-ethylhexyl sebacate (DEHS) (Figure 1a) and di-2-ethylhexyl adipate (DEHA) (Figure 1b). They are industrially relevant lubricants, and their applications involve high temperatures and/or pressures.…”

Review of Molecular Dynamics Simulations of Phosphonium Ionic Liquid Lubricants

“…Of the two EMD approaches, GK is more widely used since it is easy to implement and has been reported to accurately predict viscosity when viscosity is relatively low [64,104]. However, the autocorrelation functions of stress take a long time to converge, especially when the viscosity of the liquids is over 20 mPa•s [105]. In such cases, the Einstein approach is a more computationally efficient and reasonably accurate approach [106,107].…”