Lubrication Properties of Polyalphaolefin and Polysiloxane Lubricants: Molecular Structure–Tribology Relationships

Abstract

This study investigates the rheological properties, elastohydrodynamic film thickness, and friction coefficients of several commercially available polyalphaolefin (PAO) and polydimethylsiloxane (PDMS)-based lubricants to assess relationships between molecular structure and lubricant performance. Molecular structures and masses were determined by nuclear magnetic resonance spectroscopy and gel permeation chromatography, respectively. Density and viscosity are measured from 303 to 398 K, while elastohydrodynamic lubricant film thickness and friction measurements were made at temperatures, loads, and speeds that are representative of boundary, mixed, and full-film lubrication regimes. The results show that PDMS-based lubricants are thermally and oxidatively more stable than PAOs, while the viscosity of PDMS-based lubricants is generally less temperature sensitive than PAOs, except for highly branched polysiloxanes. In particular, this study provides quantitative insight into the use of PDMS-based lubricants to obtain low friction through the entire lubrication regime (boundary to full film) by optimal tuning of the molecular mass and chain branching.

Appendix: Pressure–Viscosity Indices

A variety of methods have been proposed to approximate the pressure–viscosity indices of different lubricants [41–44]. Pressure–viscosity indices have been calculated from bulk materials properties [41, 45, 46], reference fluids, and film thickness measurements [7, 15, 16, 23, 42], as well as high pressure viscometric data [24, 43, 47–53]. Calculations of pressure–viscosity indices can be a precarious procedure if the influences of fragility [53], dynamic crossover [53, 54], scaling effects [55], compressibility, and non-Newtonian characteristics [16] are not taken into account.

Two pressure–viscosity indices commonly calculated from high pressure data are the isothermal $\alpha_{\text{OT}}$ and reciprocal asymptotic $\alpha^{ * }$indices. The latter is calculated from atmospheric viscosity as well as the integral of viscosity to infinite pressure, and generally correlates with the logarithm of viscosity. The reciprocal asymptotic pressure–viscosity is used in these calculations because it represents a greater portion of the pressure–viscosity curve and reduces the effects of anomalies that give isothermal pressure–viscosity indices unrealistic values [20, 24, 50, 56].

Several researchers have successfully approximated temperature-dependent pressure–viscosity indices using the kinematic viscosity at the temperatures under analysis (Eq. 4) [57–59]. The technique provides accurate approximations for several lubricants when logarithmic viscosity and temperature are linearly related and sufficient data in the proximity of the temperature are available [57–59]. Equation 4 is only used with reference data from high pressure viscometers. In all calculations, the measured viscosity at the test temperatures was used to include the effect of temperature fragility in the approximation of pressure–viscosity indices.

$$ \alpha = b + a \cdot \log \left( \nu \right) $$

(4)

The Hamrock–Dowson equation can be used to approach the pressure–viscosity index of a test fluid $\alpha_{\text{t}}$ from that of a reference fluid $\alpha_{\text{r}}$ by means of the ratio of the measured film thicknesses of the test fluid $h_{\text{t}}$ and the reference fluid h _r [7, 15, 16]. A modification of the aforementioned method from Yokoyama and Spikes [42] was used to calculate the effective pressure–viscosity indices of the PAOs in this study (Eq. 5).

$$ \alpha_{\text{t}} = \alpha_{\text{r}} \cdot \left( {\frac{{h_{\text{t}} }}{{h_{\text{r}} }}} \right)^{1.89} \left( {\frac{{\eta_{\text{r}} }}{{\eta_{\text{t}} }}} \right)^{1.26} $$

(5)

The effective pressure–viscosity index calculated from film thickness can be subjected to errors when scaling effects, compressibility, and non-Newtonian shear-thinning behavior occur. In this study, high pressure viscometric data from Bair and Kottke [60] for PAO B were used in Eq. 4 to calculate the pressure–viscosity indices at different temperatures. Then, the pressure–viscosity indices for other PAOs were calculated at the same temperatures as the reference data by means of Eq. 5. The molecular masses of the PAOs were within the range of Newtonian flow outlined by Liu et al. [20], so the method of Yokoyama and Spikes [42] is applicable (Eq. 5). Table 3 lists the pressure–viscosity coefficients for the lubricants at the temperatures studied.

Table 3 Pressure–viscosity coefficient for PAO, PDMS, and PPMS at 303, 348, and 398 K

Bridgman [47], Winer [49], ASME [48], Jakobsen et al. [50], Kuss [51], King et al. [61], Bair and Qureshi [24], and Liu et al. [20] have reported pressure–viscosity indices for PDMS and PPMS that were measured on high pressure viscometers. The reciprocal asymptotic pressure–viscosity indices from the data of Jakobsen et al. [50] and Winer [49] were used to interpolate the pressure–viscosity indices for PDMS (fluids 12 and 15) and PPMS (fluids 13 and 14), respectively. Table 3 lists the siloxane pressure–viscosity data at three temperatures (303, 348, and 398 K) that are interpolated from four temperature points (297, 311, 372, and 422 K) by means of Eq. 4.

Jakobsen et al. [50], Winer [49], and Kuss [51] correlated the pressure–viscosity characteristics of several siloxanes with the nature of the side radical (branch) and found them to be independent of the degree of polymerization. This observation is used to extrapolate the pressure–viscosity index to other siloxanes of the same species and similar molecular masses.

Two samples of PDMS from Jakobsen et al. [50] were used for the low and high mass PDMS pressure–viscosity index. The low mass PDMS reference sample was intermediate to our low mass group and nearly identical to one sample. The high mass pressure–viscosity data were taken from a sample that is intermediate with respect to our high mass group. The pressure–viscosity indices of the high mass sample were updated to reflect the data more recently reported by Bair and Qureshi [62] for a sample similar to PDMS 1000 (α* = 15 GPa⁻¹ at T = 303 K). The effect of temperature on the pressure–viscosity index is slightly lower than that of the reference sample to reflect the more subtle decrease observed in the bulk of the PDMS data.

The reciprocal asymptotic pressure–viscosity coefficients of the 10 % branched PPMS were calculated from the viscometric measurements of Kuss [51]. For the higher mass, shear-thinning sample, invariance of pressure–viscosity with degree of polymerization was applied as the best approximation from the data at hand. Aderin et al. [16] and Johnston et al. [23] used film thickness to calculate the effective pressure–viscosity index for PDMS and PPMS and noted that it was lower than that measured by Kuss [51]. The discrepancy is attributed to shear thinning.

The pressure–viscosity indices calculated for PPMS 50-125 were obtained from the viscometric measurements of Jakobsen et al. [50] and supported by the measurements of Kuss [51], Bridgman [47], and the ASME pressure–viscosity report [48]. The PPMS 90-500 sample was also based on data from Jakobsen et al. [50]. The authors used the measured viscosity of the high phenyl content siloxanes at each test temperature to include the effect of temperature fragility in the interpolations of the pressure–viscosity indices.

High phenyl contents significantly increase the pressure–viscosity index, but leave it susceptible to greater temperature-dependent viscosity and pressure–viscosity variations. While the pressure–viscosity coefficients of PAO and PDMS were relatively stable over the temperature range investigated, that of PPMS fall nearly 50 % over the temperature range from 303 to 398 K (Table 3). This is in line with the broad correlation between activation energy and pressure–viscosity index observed by Roelands et al. [63], Jakobsen et al. [50], Spikes [64], Aderin et al. [16], and Gunsel et al. [15].