Volumetric Properties and Internal Pressure of Poly (Î±-olefin) Base Oils

Article pubs.acs.org/IECR

Volumetric Properties and Internal Pressure of Poly(α-olefin) Base Oils Heather E. Grandelli,† James S. Dickmann,† Mark T. Devlin,‡ John C. Hassler,† and Erdogan Kiran*,† †

Department of Chemical Engineering, Virginia Tech, Blacksburg, Virginia 24061, United States Afton Chemical Corporation, Richmond, Virginia 23219, United States

‡

ABSTRACT: This paper describes the high-pressure volumetric properties of three commonly used poly(α-olefin) base oils PAO 2, PAO 4, and PAO 8with nominal 100 °C kinematic viscosities of 2, 4, and 8 cSt. Using a special variable-volume view cell that permits continuous pressure scan and volume measurements, densities were determined at 298, 323, 348, 373, and 398 K at pressures up to 40 MPa. Isothermal compressibilities, isobaric thermal expansivities, thermal pressure coefficients, and internal pressures were then evaluated. At each temperature, density−pressure correlations were developed for the range from 10 to 40 MPa. Density−temperature correlations were developed at 10, 20, 30, and 40 MPa. It is shown that the densities of PAO 2 (which were in the range from 0.7364 to 0.8214 g/cm3) are lower than those of PAO 4 (in the range from 0.7663 to 0.8470 g/ cm3) or PAO 8 (in the range from 0.7664 to 0.8498 g/cm3). The densities of PAO 4 and 8 were essentially the same. Isothermal compressibilities of each base oil were of the same order of magnitude at each temperature (with the range being from 6.8 to 10.2 × 10−4 MPa−1), with PAO 2 showing slightly higher values. Isobaric thermal expansivities were in the range (7.2−9.5) × 10−4 K−1. PAO 2 showed higher expansivity values at all pressures. Thermal pressure coefficients were in the range 0.8−1.2 MPa K−1. The values were higher for PAO 2 at 323 K and higher temperatures. PAO 8, while showing the highest thermal pressure coefficient at 298 K, became lower than that of PAO 2 at 323 K and lower than that of PAO 4 at 348 K and higher temperatures. At 398 K, PAO 4 shows the highest thermal pressure coefficients. The trends observed with the thermal pressure coefficients were also reflected in the internal pressures for the respective oils. The internal pressure values were in the range from 260 to 370 MPa. The internal pressure value in each system was observed to decrease with pressure. These observations were interpreted in terms of the differences in the carbon chain lengths, ease of packing, and relative significance of attractive versus repulsive forces that develop as a function of the pressure or temperature. lubrication efficiency. Compression decreases the film thickness as the lubricant enters the high-pressure contact area, and the more compressible the lubricant, the thinner the film becomes. The pressure dependence of the compressibility of the lubricant and the influence of the pressure on the cohesive and repulsive forces directly affect the dynamics of film formation, the viscosity, and the relaxation behavior of the oil. Indeed, calculation of the film thickness, pressure distribution, and friction in elastohydrodynamic contact and thus assessment of the effectiveness of lubricants rely heavily on the knowledge of their viscosity, compressibility, and density.6−9 To describe variation of the density of lubricants with the pressure, measurements are normally conducted under static conditions by changing the volume.10 Dynamic measurements are also conducted to assess the importance of structural relaxation over short loading times. These measurements employ special techniques such as the split pressure−bar test in which loading pressures up to about 2 GPa are generated for durations of about 100−300 μs.11 The size and shape of the molecules will influence their relaxation behavior. For example, long-chain molecules that make up PAOs are compressible, yet paraffinic mineral oils, which are more molecularly complex, show a stiffer

1. INTRODUCTION Improving the energy efficiency of machines is perhaps the most critical performance property of a lubricant, and it is well-known that reducing the viscosity of a lubricant can result in significant improvements in energy efficiency.1−4 In order to reduce the lubricant viscosity, low-viscosity base oils are being used in the blending of finished lubricants. A majority of lubricants that are currently in use contain petroleum-based mineral oils; however, the use of synthetic lubricants that are based on poly(α-olefins) (PAOs) is increasing. This is due primarily to the fact that lowviscosity PAOs have lower volatilities than low-viscosity mineral base oils.1,5 In many of the applications, lubricants are subjected to high pressures and high shear rates. The pressures may be several gigapascals, and the shear rates may be higher than 105 s−1.6,7 The lubricants typically experience these conditions as a thin film that forms in the confined environment between the contacting surfaces in a cyclic manner with short contact times on the order of 10−4 s. The physical properties of low-viscosity base oils are often studied at high shear rates, but the high-pressure behavior of these base oils is often overlooked. This paper describes the effect of pressure on the density, compressibility, thermal expansivity, thermal pressure coefficient, and internal pressure of three commercial PAO base oils with different kinematic viscosities. Compressibility (or bulk modulus, which is the inverse of compressibility) and viscosity are extremely important physicochemical properties that influence film formation and © 2013 American Chemical Society

Received: Revised: Accepted: Published: 17725

August 12, 2013 November 20, 2013 November 26, 2013 November 26, 2013 dx.doi.org/10.1021/ie402644w | Ind. Eng. Chem. Res. 2013, 52, 17725−17734

Industrial & Engineering Chemistry Research

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(less compressible) behavior.9 It should be noted that the lubricants would appear as if they were less compressible at shorter times because molecules would not have sufficient time to rearrange themselves into their relaxed (equilibrium) conformations, which would be experienced at the prevailing pressures. This type of dynamic behavior becomes especially important when oils are used as hydraulic fluids, where power must be transmitted with greater efficiency. More specifically, low compressibility becomes desirable in hydraulic applications because it translates into fast response time and high-pressure transmission velocity, which, in turn, translate into greater efficiency.8 In general, the energy loss and potential for heat generation are suppressed for lubricants with lower compressibility. Yet, some degree of compressibility is still desirable for hydraulic applications because unwanted pressure surges can then be dampened for smoother operations. The compressibility is significantly affected by the molecular structure, and thus when lubricants or hydraulic fluids are formulated and selected, characterization of the density of the fluid and its dependence on pressure become essential. As has already been noted, in loaded contacts under pressure that involve thin films, the density and compressibility behavior influence the tribological behavior. A recent study reports on the molecular dynamic simulations of three different lubricant fluids, namely, n-heptane (a linear molecule), squalane (a branched molecule), and pentaerythritol tetrakis(2-ethylhexanoate) (PEB8, a spherical molecule), confined to film thicknesses in the range from 3.2 to 9.6 nm.12 Heptane was found to be most compressible, followed by PEB8 and then squalane. This was, however, in contrast to the general expectation that the compressibility decreases with increasing density because PEB8 is denser than squalane yet was found to be more compressible, which was interpreted as arising from the difference in their molecular shape, with PEB8 being spherical and squalane being branched. Another important thermophysical property of lubricants is the “internal pressure”, π, which provides a measure of the consequences of the attractive and repulsive molecular interactions.13−16 The internal pressure is defined in eq 1. ⎡α ⎤ ⎡ ∂U ⎤ ⎡ ∂P ⎤ π = ⎢ ⎥ = T⎢ ⎥ − P = T⎢ P ⎥ − P ⎣ ∂V ⎦T ⎣ ∂T ⎦V ⎣ KT ⎦

conditions, the internal pressure can increase, decrease, go through a maximum, or basically remain insensitive to pressure, thereby providing some insight into the relative role of these factors. In some systems like diethyl ether, it is reported that the internal pressure decreases with increasing pressure and becomes negative,14 which is interpreted as repulsive forces completely dominating the attractive forces at higher pressures. Therefore, exploration of the pressure dependence of the internal pressure can provide valuable insight as to the effect of pressure and the interplay of attractive and repulsive forces and how these differ from one type of oil to another. It is also important to note that even though the correspondence is not exact or strictly valid, because the internal pressure is not viewed as an energy characteristic but as an average force parameter of interactions between the structural units of a liquid system,16 it is considered to be an important alternative to the solubility parameter for complex mixtures like crude oil14 or polymer solutions,18 where measurement of the heat of complete vaporization is not possible. For those systems, the internal pressure provides a good estimate, and eq 2 (where n is a constant) has been proposed.17 π = nδ 2

(2)

A strict relationship between the CED and internal pressure of liquids is given by eq 3, pointing out that they are not simply interchangeable.16,19,20 ⎡ ∂CED ⎤ π = CED + V ⎢ ⎣ ∂V ⎥⎦

(3)

We now report on the volumetric properties of three PAO base oils with nominal 100 °C viscosities of 2, 4, and 8 cSt, which will be referred to as PAO 2, PAO 4, and PAO 8, respectively. The measurements were carried out in a special variable-volume view cell in which the position of a movable piston is recorded continually as a function of the pressure and temperature using a dedicated linear variable differential transformer (LVDT). The piston position is changed using a motorized pressure generator, and the position information is easily transformed into the internal volume and thus the density, thereby allowing the generation of nearly continuous curves describing variation of the density with pressure at any given temperature. The density isotherms are then used to generate information on the isothermal compressibility, isobaric expansivity, thermal pressure coefficients, and internal pressure.

(1)

As shown in eq 1, it is related to the thermal pressure coefficient (∂P∂T)V, which, in turn, is related to the isothermal compressibility, κT, and isobaric coefficient of thermal expansion, αP, which are evaluated from variation of the density with pressure, P, and temperature, T. This quantity provides a measure of the change in the internal energy with an isothermal change in the volume, V. Even though the concepts are different, the internal pressure has been reported to correlate with the solubility parameter δ = [ΔU/V]1/2, which is the square root of the cohesive energy density (CED; evaluated as the molar energy of complete vaporization per unit volume).8,13,14,17 It is noted that CED represents the total molecular cohesion (attractive interactions) per unit volume, but the internal pressure is a change in the internal energy of a liquid as it undergoes a volume change at constant temperature. When the pressure is increased, the intermolecular distance is decreased, leading to changes in both the attractive (i.e., arising from hydrogen-bonding, dipole− dipole, or dispersion interactions) and repulsive forces. As a consequence, depending upon the system and prevailing

2. MATERIALS AND METHODS 2.1. Materials. The base oils PAO 2, PAO 4, and PAO 8 were provided by Afton Chemical Corp. These are liquids with kinematic viscosities of 1.7, 4.0, and 7.9 cSt, respectively, as determined at 100 °C, which were provided by the base oil supplier, determined using the standard procedure ASTM D445. A gas chromatography−mass spectrometry (GC−MS) technique was used to characterize the chemical structure of the PAO base oils. These characterizations were carried out by Triton Analytics (Houston, TX) using the method described in the literature that provides the information on the column, injection details, and heat programs.21 This technique separates chemical species by their degree of unsaturation and carbon number (molecular weight). As expected, the PAOs examined here contain only paraffinic species with no cyclic structures or aromatics, but they differ in their carbon number distributions. They are mostly isoparaffins, with the n-paraffin content being 17726

dx.doi.org/10.1021/ie402644w | Ind. Eng. Chem. Res. 2013, 52, 17725−17734


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less than 0.7% in PAO 2 and less than 0.001% in PAO 4 and PAO 8. As shown in Figure 1, PAO 2 is essentially all C20 paraffins;

PAO 4 consists of equal amounts (50:50) of C30 and C40 paraffins; PAO 8 is mostly (about 55%) C40 but has measurable content (about 10% each) of C30, C32, C34, C36, and C38. Even though the n-paraffin contents are very small, PAO 2 contains C10, C11, C12, C13, C14, C15, C16, C17, C18, C19, C20, and C21 with an average carbon number of 17.2, PAO 4 contains C20 and C21 with an average carbon number of 20.2, and PAO 8 contains C19, C20, C21, C22, C23, C24, C25, C26, C27, C28, and C29 with an average n-paraffin carbon number of 24.7. A typical synthesis of PAO consists of oligomerization of 1decene (C10 alkene), so the presence of C20, C30, and C40 paraffins in PAOs is expected. The paraffins that are detected that are not multiples of C10 could be from the commercial process used to produce the specific samples examined here. PAOs are oligomers of 1-decene and, therefore, normally one expects molecular species that have carbon numbers that are integer multiples of C10 to be detected in these base oils. However, during the commercial process to synthesize and transport (pumping systems) the base oils at the production plant, degradation of higher-molecular-weight species to lowermolecular-weight species may occur, leading to the presence of paraffins that are not multiples of C10, as detected in the present analyses. These oils were investigated as received. Their ambient pressure densities at 25 °C were determined using a 2 mL pycnometer and were found to be to be 0.80, 0.83, and 0.83 g/ cm3 for PAO 2, PAO 4, and PAO 8, respectively. The density values were provided by the supplier at 15 °C as 0.80, 0.82, and 0.83 g/cm3, respectively. Densities at 15 °C would be expected to be slightly higher than densities at 25 °C. However, these differences are not reflected in the values with the 10 °C difference in temperature, with density values that are reported to only two decimal places. The reason for the higher density value

Figure 1. Carbon number distributions of the isoparaffins that make up >99% of the paraffin content of the base oils PAO 2, PAO 4, and PAO 8.

Figure 2. Schematic diagrams of the view-cell system in the upright position: PGN, pressure generator; VVS, variable volume section; TV, transfer vessel; LVDT, linear variable differential transformer; PT/TC, pressure transducer/thermocouple; TLD, transmitted light detector; SW, sapphire windows; OV, outlet valve; IV, inlet valve; Itr, transmitted light intensity; T, temperature; P, pressure; Pos, piston position. 17727



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for PAO 4 measured at 25 °C compared to the value given by the supplier at 15 °C is not clear; however, the pycnometer results obtained in this study are consistent with the high-pressure density results for PAO 4, as will be shown in the following sections. 2.2. Experimental System Description, Operational Procedures, and Data Analysis. Experiments were carried out using a high-pressure variable-volume view cell, which is illustrated in Figure 2. The system was described in our earlier publications.22,23 Briefly, two sapphire windows allow assessment of the phase behavior of the base oil by either visual observations or optical recording of transmitted light intensities. The pressure and temperature in the cell are monitored using a flush-mount Dynisco diaphragm pressure transducer that also incorporates a J-type thermocouple with uncertainties of 0.07 MPa and ±0.5 °C, respectively. The system is fully computer-interfaced, allowing continuous recording of the pressure, temperature, transmitted light intensity, and piston position at 0.5 s intervals. The maximum internal volume of the view cell is 23.0 cm3, which can be reduced by moving the piston inward using a motorized pressure generator to pressurize the fluid (ethanol) on the back side of the piston. The volume changes are recorded with an uncertainty of ±0.1 cm3. From the piston position, the internal volume of the cell is determined, which then allows determination of the densities from the initial mass loading within 1% uncertainty. The typical experimental mass loading of a base oil was maintained in the range of about 14−15 g. The empty cell is first closed to seal before charging the base oil by pumping from a transfer vessel. The amount of base oil charged is determined gravimetrically as the transfer vessel is placed on a high capacity balance (6100 g) with 0.01 g accuracy (Mettler PM6100). After loading, the cell is heated to the desired temperature using four symmetrically positioned heater cartridges, while the solution is mixed with a magnetic stirring bar. Pressure scans are then performed at each temperature (298, 323, 348, 373, and 398 K) by increasing the pressure at a controlled rate up to 40 MPa. The pressure, temperature, piston position, and transmitted light intensity are continuously recorded by a dedicated computer throughout the experiment. The data showing variation of the density, ρ, with pressure at each temperature were correlated as a function of the pressure. The data could be correlated well with a linear function of the form ρ = A + BP, where A and B are empirically derived constants. From these correlations, isothermal compressibilities were generated as a function of the pressure using eq 4, where Vm is the molar volume. κT = −

1 ⎛ ∂Vm ⎞ 1 ⎛ ∂ρ ⎞ ⎜ ⎟ = ⎜ ⎟ Vm ⎝ ∂P ⎠T ρ ⎝ ∂P ⎠T

The isochoric thermal pressure coefficient (γV) was then calculated as a function of the pressure for each base oil using eq 6. γV =

1 ⎛ ∂Vm ⎞ 1 ⎛ ∂ρ ⎞ ⎜ ⎟ =− ⎜ ⎟ ⎝ ⎠ Vm ∂T P ρ ⎝ ∂T ⎠ P

(6)

Finally, the internal pressure (π) was calculated from the isochoric thermal pressure coefficient using eq 7.

π = TγV − P

(7)

In the present study, we report data for up to 40 MPa. As noted earlier, in many applications, lubricants may be exposed to higher pressures, in the gigapascal range. New instrumentation is in development in the author’s laboratory that will allow one to conduct these measurements at pressures up to 400 MPa.

3. RESULTS 3.1. Densities and Their Pressure Dependence. Figure 3 shows a typical recording of the pressure with time during a

Figure 3. Typical pressure-increase scan (left) shown with the corresponding volume reduction profile (center) and calculated density profile (right) for PAO 2 at 398 K.

(4)

To calculate the isobaric expansivity, the density data were processed at selected pressures to describe its variation with temperature. At each pressure, variation of the density with temperature was described with linear functions of the form ρ = C + DT, where C and D are empirically derived constants. Equation 5 was then used to generate isobaric expansivity as a function of the temperature. αP =

⎛ ∂P ⎞ αP ⎜ ⎟ = ⎝ ∂T ⎠V κT

Figure 4. Variation of the density with pressure for PAO base oils at different temperatures.

pressure-increase scan from 1 to 40 MPa conducted with PAO 2 at 398 K. This scan was carried out over 200 s. The scan shows the smooth rate of change in the pressure (about 0.27 MPa/s), which is achievable with the motorized pressure generator.

(5) 17728



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Figure 6. Isothermal compressibilities for base oils in the pressure range 10−40 MPa.

piston positions and potentially eliminate any small density fluctuations that may potentially arise from very small (not measurable) temperature changes.] The internal volume (V, cm3) during pressure-increase scans was calculated using the maximum cell volume (Vmax, cm3) along with the instantaneous piston position from the LVDT reading (x, cm) and the cross-sectional area of the piston (Ax, cm2) as shown in eq 8. Figure 5. Comparative density plots of PAO 2 (blue), PAO 4 (black), and PAO 8 (red) at different temperatures.

V = Vmax − Ax x

The density (ρ, g/cm ) was then easily calculated from the initial mass loading (m, g) to the view cell as ρ = m/V. These are also shown in Figure 3. Similar data were generated for each oil at 298, 323, 348, 373, and 398 K. Comparative results are shown in Figure 4, for each oil for the pressure range from 10 to 40 MPa. As expected, in each oil the densities increase with pressure at a given temperature, and at a given pressure, they decrease with the temperature. Figure 5 shows a comparison of the densities as a function of the pressure at each temperature for the three base oils. PAO 2 has a significantly lower density than PAO 4 and PAO 8 at all temperatures, while PAO 4 and PAO 8 have nearly identical densities at all pressures and temperatures. 3.2. Isothermal Compressibilities. As can be visually assessed from Figure 4, in each oil, variation of the density with pressure is essentially linear. They have been correlated with functional relationships of the form given in Table 1. Correlation coefficients were not much improved with higher-order polynomials, and the linear relationships were preferred because of their simplicity. These correlations for density versus pressure were then used to generate the isothermal compressibilities. They have been plotted as a function of the pressure for each base oil in Figure 6. The compressibilities are in the range of (6.8−10.2) × 10−4 MPa−1. In each oil, as would be expected, compressibilities decrease with increasing pressure and increase with increasing temperature. Even though small, there are differences in the rate

Table 1. Linear Density Correlations for Base Oils in the Pressure Range 10−40 MPa sample

T, K

ρ, g/cm3 = f(P, MPa)

R2 value

PAO 2

298 323 348 373 398 298 323 348 373 398 298 323 348 373 398

ρ = 0.000634P + 0.7960 ρ = 0.000659P + 0.7838 ρ = 0.000667P + 0.7580 ρ = 0.000695P + 0.7421 ρ = 0.000746P + 0.7289 ρ = 0.000650P + 0.8271 ρ = 0.000642P + 0.8095 ρ = 0.000639P + 0.7923 ρ = 0.000683P + 0.7748 ρ = 0.000721P + 0.7591 ρ = 0.000580P + 0.8266 ρ = 0.000600P + 0.8133 ρ = 0.000665P + 0.7908 ρ = 0.000709P + 0.7753 ρ = 0.000764P + 0.7588

0.9848 0.9849 0.9868 0.9879 0.9894 0.9747 0.9812 0.9847 0.9817 0.9840 0.9764 0.9807 0.9885 0.9890 0.9900

PAO 4

PAO 8

(8) 3

Similar pressure scan rates were employed in all of the experiments, which were slow enough not to lead to any observable temperature changes during the scans. These are continuous pressure-increase experiments, with no intermediate stops. [One could, in principle, conduct these scans at much lower rates to further ensure equilibration of the temperature and 17729



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Figure 8. Variation of the density with temperature for base oils at different pressures.

Table 2. Linear Density Correlations for Base Oils in the Temperature Range 298−398 K sample

P, MPa

ρ, g/cm3 = f(T, K)

R2 value

PAO 2

10 20 30 40 10 20 30 40 10 20 30 40

ρ = −0.000693T + 1.0098 ρ = −0.000683T + 1.0129 ρ = −0.000672T + 1.0161 ρ = −0.000662T + 1.0193 ρ = −0.000675T + 1.0343 ρ = −0.000668T + 1.0684 ρ = −0.000661T + 1.0425 ρ = −0.000654T + 1.0467 ρ = −0.000675T + 1.0346 ρ = −0.000656T + 1.0346 ρ = −0.000637T + 1.0346 ρ = −0.000618T + 1.0346

0.9844 0.9828 0.9812 0.9793 0.9993 0.9989 0.9984 0.9978 0.9951 0.9952 0.9953 0.9954

PAO 4

Figure 7. Comparative isothermal compressibilities of base oils PAO 2 (blue), PAO 4 (black), and PAO 8 (red). PAO 8

of change of the compressibility with pressure or temperature in going from PAO 2 to PAO 8. In PAO 4, the compressibilities seem to be very similar at 298, 323, and 348 K and become more distinct at 373 and 398 K. A recent publication on some other mineral and synthetic oils as well as vegetable oils has reported isothermal compressibility values at pressures up to 50 MPa.8 The density determinations were not continuous and were done with 5 MPa intervals over a temperature range from 298 to 373 K using an Anton Paar vibrating densimeter, which uses the dependence of the period oscillations of a fixed U-tube and its mass. The isothermal compressibility values reported are in the same order of magnitude but smaller, with the range being (4.5− 7.5) × 10−4 MPa−1. Another study has reported on the densities and compressibilities of polyol ester based lubricants such as mixtures of pentaerythritol ester lubricants at temperatures 298− 353 K and pressures up to 40 MPa with again 5 MPa intervals. In this study, the densities were determined also using a vibrating tube densimeter. The compressibility values that were reported are in the range of (4.5−9.0) × 10−4 MPa−1.24 Figure 7 shows a comparison of the isothermal compressibilities and their variation with pressure. At 298 K, PAO 8 has the lowest compressibility at all pressures. The compressibilities of PAO 2 and PAO 4 are similar, but with increasing temperature, PAO 2 becomes the most compressible of these oils at any given pressure. The compressibility of PAO 8 increases with the

temperature and becomes higher than that of PAO 4 at 348 K and higher temperatures. In general, oils with lower compressibility would be expected to form thicker films, and in this sense, the temperature sensitivity of PAO 8 that is being observed may alter its tribological performance in applications where the pressures are in the range explored in the present study. As is shown in Figure 5, the densities are almost identical for PAO 4 and PAO 8 and both display values higher than the densities of PAO 2 at all temperatures evaluated. As illustrated in Figure 1, PAO 4 consists of essentially equal amounts (50:50 mixture) of C30 and C40 isoparaffins, while PAO 8 consists of a distribution of C30 to C40 isoparaffins, and PAO 2 is essentially all C20 isoparaffin. Other factors being equal, a lower density would suggest a greater fraction of free volume in PAO 2 and as such may lead to a higher compressibility, which is mostly suggested by the compressibility data shown in Figure 7. Despite the similar densities, the higher compressibility displayed by PAO 8 compared to PAO 4 suggests similar packing densities, yet different chain flexibilities that are sensitive to temperature. In terms of composition, even though both base oils have similar 17730



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Figure 9. Variation of the isobaric expansivity with temperature at different pressures for base oils. Figure 11. Variation of the isochoric thermal pressure coefficient with pressure at different temperatures for each base oil.

have the same opportunities for improved packing and appears to become the least compressible with increasing temperature. 3.3. Densities and Their Temperature Dependence. From the data presented in Figure 4, the density values were determined at selected pressures, namely, 10, 20, 30, and 40 MPa, to show variation of the density with temperature at constant pressure. The results are shown in Figure 8 for each oil. As illustrated, the densities decrease linearly with temperature. The correlation equations are given in Table 2. The data show some deviation from linearity (waviness) for PAO 2 and PAO 8. However, there was no sign of instability with these oils that could reflect itself in a color change or turbidity that would be detected from changes in the transmittance. 3.4. Isobaric Thermal Expansivities. Using the density versus temperature correlations given in Table 2, isobaric expansivities (coefficient of thermal expansion) were generated as a function of the temperature at 10, 20, 30, and 40 MPa. These are shown in Figure 9 for each base oil. The trends at each pressure are compared for different base oils in Figure 10. The expansivity values are in the range (7.2−9.5) × 10−4 K−1. A recent publication has reported the thermal expansivity values for some mineral oils and synthetic oils at 323 K up to 60 MPa. They are in the range (5.5−7.5) × 10−4 K−1, which are in the same order of magnitude but lower than the values for PAO base oils.8 The expansivities for some polyol ester lubricants that are reported in the literature are in the range (6.4−7.8) × 10−4 K−1.24 These measurements were based on density determinations using a vibrating tube densimeter at 5 MPa intervals. Figure 9 shows that the isobaric thermal expansivity increases fairly linearly with increasing temperature (with, however, some tendency for an increased rate of change with the temperature at higher temperatures) and decreases linearly with increasing pressure in the reported pressure range. As shown in Figure 10, at each pressure, PAO 2 was found to have the highest expansivity, while the lowest expansivity values were found for PAO 8, with

Figure 10. Comparative isobaric expansivities of base oils PAO 2 (black), PAO 4 (red), and PAO 8 (blue).

C40 contents (50 vs 55% in PAO 4 vs PAO 8), the remainder in PAO 4 is essentially C30 plus a very small amount of n-paraffins, which are essentially all C20 in PAO 4, while in PAO 8, the remainder consists of about 10% each of C30, C32, C34, C36, and C38 isoparaffins plus a very small amount of n-paraffins from C19 to C29. The presence of a distribution of chain lengths in PAO 8 could potentially be leading to the higher observed compressibilities at higher temperatures for this oil, because with greater thermal motion, the packing arrangements can be improved. PAO 4 being essentially bimodal does not appear to 17731



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Figure 13. Variation of the internal pressure with pressure at different temperatures for each base oil.

small. For PAO 8, the isochoric thermal pressure coefficient appears to be more sensitive to pressure. Figure 12 shows comparisons of the thermal pressure coefficients of the oils at each temperature. The thermal pressure coefficient in PAO 8 decreases and becomes smaller than that of both PAO 2 and PAO 4 with increasing temperature, while the values for PAO 2 and PAO 4 become closer to each other. Figure 13 shows the internal pressure and its variation with pressure at each temperature. These are in the range of 260−370 MPa. They all decrease with pressure. Figure 14 shows comparisons of the internal pressures of the oils at different temperatures. Similar to the trends with thermal pressure coefficients, the internal pressure for PAO 8 decreases and becomes smaller than that for PAO 2 and PAO 4 as the temperature is increased. These differences, even though not very large, are further illustrated in Figure 15, which is a comparison of the internal pressures for each oil as a function of the temperature at 10, 20, 30, and 40 MPa. At a given pressure, the internal pressure for PAO 2 and PAO 4 initially increases with temperature but levels off after 348 K. For PAO 8, the internal pressure does not appear to be as sensitive to the temperature. In the literature, internal pressures have been reported for some polyol ester lubricants.24 The values are in the range 310− 370 MPa for the polyol esters, which are similar to the values for PAO base oils investigated in the present study. At 323 K, the polyol esters show very little sensitivity to pressure. At 20 MPa, they show a reduction with temperature, up to 343 K, that was evaluated. The internal pressures have been reported also for poly(ethylene glycol) dimethyl ether lubricants based on density determinations using a vibrating tube densimeter in 5 MPa intervals from 0.1 to 60 MPa in the temperature range from 298 to 398 K.15 For these lubricants, internal pressure values were somewhat lower, being in the range 300−335 MPa. As discussed earlier, at a given temperature, the internal pressure reflects the consequences of changes in attractive and

Figure 12. Comparative isochoric thermal pressure coefficients of base oils PAO 2 (black), PAO 4 (red), and PAO 8 (blue).

PAO 4 taking on an intermediate value between the other base oils. These trends in the coefficient of thermal expansion are in correspondence with the difference in the molecular weights of hydrocarbon chain lengths in the oils. PAO 8 has the longest chains, which do not expand as readily under pressure as the other base oils. PAO 2 has the shortest carbon chains, permitting a greater degree of expansion under pressure. 3.5. Isochoric Thermal Pressure Coefficients and Internal Pressure. Isochoric thermal pressure coefficients were determined at 298, 323, 348, 373, and 398 K and 10, 20, 30, and 40 MPa for each base oil. The results are shown in Figure 11. It is important to recognize that the derivative data in this figure and also in Figures 12−15 that will follow are not experimental data points but rather derived quantities evaluated at the indicated P and T values. The values are in the range 0.8− 1.2 MPa/K. Thermal pressure coefficients all decrease linearly with increasing pressure. In each oil, the thermal pressure coefficients are observed to decrease with increasing temperature. There seems to be a slight difference in the trend for PAO 4 in the temperature range 298−348 K, but the differences are very 17732



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Figure 15. Variation of the internal pressure of base oils with temperature at 10, 20, 30, and 40 MPa: PAO 2 (black); PAO 4 (red); PAO 8 (blue). (Curves were drawn as a visual aid only and do not represent a fitted equation.)

for example, has a strong influence (such as water, n-propanol, etc.).26 In systems like polyol esters, the decrease in the internal pressure has been interpreted as reflecting the absence of hydrogen bonds, even though there are strong dipole−dipole interactions. In the present systems involving n-paraffins, because there are no associations, one would then expect a decrease in the internal pressure. Here, they, however, appear to be insensitive to temperature above 348 K. The trend below this temperature for PAO 2 and PAO 4, which displays an increase in the internal pressure with temperature, differs from general expectations. These observations point to the importance of giving attention not only to specific (i.e., polar) interactions but also to the architecture of molecules that can influence the packing density and consequently influence the compressibility and expansivity and the other derived quantities such as thermal pressure coefficient and internal pressure. In this context, a recent publication15 provides information on variation of the internal pressure with molar volume for two different poly(propyl glycol) dimethyl ether lubricants, where they report that the internal pressures decrease with increasing molar volume. However, other data reported for pentaerythritol ester lubricants24 indicate that variation with the molar volume may show increasing or decreasing trends, once again pointing to the complexities of these systems.

Figure 14. Comparative internal pressures of base oils PAO 2 (black), PAO 4 (red), and PAO 8 (blue).

repulsive forces as a function of the pressure. As the attractive forces become greater, the value increases, and as the repulsive forces become more dominant, they decrease. For example, in diethyl ether for which internal pressures have been reported over a pressure range from about 50 MPa to 1.1 GPa, the internal pressure decreases from about +300 MPa at about 100 MPa to about -400 MPa at pressures of 1 GPa.14 Even though the pressure range that we have explored is only up to 40 MPa, the observations that the internal pressure is basically decreasing with pressure in all PAO oils investigated would thus suggest that repulsive forces tend to increase, and above 348 K, the repulsive forces appear to be greater in PAO 8 compared to PAO 2 or PAO 4. The trends displayed by the π versus T curves and the sign of the derivative [dπ/dT]P has been discussed in the literature for some other compounds25,26 including polyol ester based lubricants24 and are suggested to be indicative of the structural organization in the fluid. The systems showing a decrease in the internal pressure with temperature, that is, [dπ/dT]P < 0, indicate weakly associating systems (such as n-heptane, n-dodecane, etc.), and those showing an increase in the internal pressure with [dπ/ dT]P > 0 indicate associated fluids in which hydrogen bonding,

4. CONCLUSIONS The PAOs that have been explored in this study, with their welldefined structures, have permitted the documentation and discussion of the effect of the pressure and temperature because they relate to the structure in light of the differences in isoparaffin distributions in the PAOs. There is less than 1% normal paraffins in these base oils and no cycloparaffins or aromatics. At high pressures and temperatures, PAO 2 (which consists almost entirely of C20 isoparaffins) is more compressible than 17733



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dilatation −pressure relationship of lubricants used in elastohydrodynamic lubrication. Proc. Inst. Mech. Eng., Part J 2002, 216, 63−74. (12) Vadakkepatt, A.; Martini, A. Confined fluid compressibility predicted using molecular dynamic simulation. Tribol. Int. 2011, 44, 330−335. (13) Verdier, S.; Anderson, S. I. Internal pressure and solubility parameter as a function of pressure. Fluid Phase Equilib. 2005, 231, 125− 137. (14) Zorebski, E. Internal pressure as a function of pressure. Mol. Quantum Acoust. 2006, 27, 327−336. (15) Fandiño, O.; Lugo, L.; Comuñas, M. J. P.; Lopez, E. R.; Fernandez, J. Temperature and pressure dependence of volumetric properties of two poly(propylene glycol) dimethyl ether lubricants. J. Chem. Thermodyn. 2010, 42, 84−89. (16) Kartsev, V. N.; Shtykov, S. N.; Pankin, K. E.; Batov, D. V. Intermolecular forces and the internal pressure of liquids. J. Struct. Chem. 2010, 53, 1087−1093. (17) Renuncio, J. A. R.; Breedveid, G. J. F.; Prausnitz, J. M. Internal pressures and solubility parameters for carbon disulfide, benzene, and cyclohexane. J. Phys. Chem. 1977, 81, 324−327. (18) Shatamat, M.; Rey, A. D. High pressure miscibility predictions of polyethylene in hexane solutions based on molecular dynamics. Eur. Polym. J. 2013, 49, 471−481. (19) Kartsev, V. N.; Pankin, K. E.; Batov, D. V. On interrelation between the internal pressure and the cohesive energy density. J. Struct. Chem. 2006, 47, 277−84. (20) Kartsev, V. N.; Rodnikova, M. N.; Shtykov, S. N. On internal pressure, its temperature dependence, and the structure of liquid-phase system. J. Struct. Chem. 2004, 45, 96−99. (21) Dzidic, I.; Petersen, H. A.; Wadsworth, P. A.; Hart, H. V. Townsend Discharge Nitric Oxide Chemical Ionization Gas Chromatography/Mass Spectrometry for Hydrocarbon Analysis of the Middle Distillates. Anal. Chem. 1992, 64, 2227. (22) Milanesio, J. M.; Hassler, J. C.; Kiran, E. Volumetric properties of propane, n-octane and their binary mixtures at high pressures. Ind. Eng. Chem. Res. 2013, 52, 6592−6609. (23) Grandelli, H. E.; Kiran, E. High pressure density, miscibility and compressibility of poly(lactide-co-glycolide) solutions in acetone and acetone + CO2 binary fluid mixtures. J. Supercrit. Fluids 2013, 75, 159− 171. (24) Fandiño, O.; Comuñas, M. J. P.; Lugo, L.; Lopez, E. R.; Fernandez, J. Density measurements under pressure for mixtures of pentaerythritol ester lubricants. Analysis of a density−viscosity relationship. J. Chem. Eng. Data 2007, 52, 2429−1436. (25) Kartsev, V. N.; Rodnikova, M. N.; Shtykov, S. N. Inversion of the temperature coefficient of internal pressure and structural organization of liquid phase systems. J. Struct. Chem. 2004, 45, 91−95. (26) Kartsev, V. N. To the understanding of the structural sensitivity of the temperature coefficient of internal pressure. J. Struct. Chem. 2004, 45, 832−837.

higher-viscosity PAOs, PAO 4 (which is an equal mixture of C30 and C40 isoparaffins) and PAO 8 [which is mostly (about 55%) C40 isoparaffins with measurable amounts (about 10% each) of C30, C32, C34, C36, and C38 isoparaffins]. PAO 2 has a higher thermal expansivity than PAO 4 or PAO 8 at all temperatures and pressures evaluated. The present results show that the thermal expansivity is directly related to the molecular weight of the base oils, with a lower molecular weight resulting in higher thermal expansivity, and the compressibility is related to the density and molecular weight distribution of the base oils. The low density of PAO 2 causes it to have the highest compressibility, while the wide distribution of isoparaffins affects the packing of PAO 8 as the pressure and temperature change. The internal pressure, which reflects the effect of attractive and repulsive forces in the fluids, shows that in each base oil, at a given temperature, the values decrease with pressure, suggesting that repulsive forces are increasing. At a given pressure, internal pressure values do not vary significantly with temperature for T > 350 K. At these higher temperatures, at each pressure, internal pressure values are lower for PAO 8, suggesting that repulsive forces become higher in this base oil, which displays a distribution of isoparaffins.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by Afton Chemical Corporation. REFERENCES

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Volumetric Properties and Internal Pressure of Poly (Î±-olefin) Base Oils

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