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Ind. Eng. Chem. Res. 2003, 42, 1522-1529
Pulsed Field Gradient NMR Spectroscopy: Applications in Determining the Pressure Viscosity Coefficient and Low-Temperature Flow Properties of Lubricant Base Oils Brajendra K. Sharma and Arthur J. Stipanovic* Department of Chemistry, State University of New York-College of Environmental Science and Forestry, One Forestry Drive, 123 E. C. Jahn Laboratory, Syracuse, New York 13210
The pulsed field gradient (PFG) NMR technique was employed to measure the self-diffusion coefficients (D) of hydrocarbon lubricant base fluids under ambient pressure conditions. This parameter was then related to various rheological properties, including the kinematic viscosity and the pressure viscosity coefficient (PVC). The results demonstrate that D varies inversely with the fluid viscosity and PVC. This relationship was then used to predict PVC from D for a series of compositionally diverse base oils, providing an R2 value of 0.86. PFG NMR spectroscopy was also used to study the molecular dynamics of the liquid-solid transitions of the oils at low temperatures ranging from +40 to -40 °C. The self-diffusion coefficient decreased linearly with decreasing temperature to 0 °C and then “leveled off” at lower temperatures. This observation can be explained, using spatially heterogeneous dynamics and other mechanistic models, by the onset of wax crystallization. Introduction
Table 1. API Lubricant Base Stock Categories
The chemical composition of lubricant base oils represents a complex mixture of hydrocarbons ranging in carbon number from 20 to 40 depending on the viscosity grade. Base oils typically contain normal paraffins, branched or isoparaffins, cyclic paraffins (up to 5- or 6-membered rings), aromatic ring structures (mono-, di-, tri-, and polynuclear), and very small quantities of heterocyclic (sulfur, nitrogen, and oxygen) compounds. On the basis of saturates and sulfur contents, the American Petroleum Institute (API) classifies base oils into three main categories plus a class for synthetic oils such as poly(R-olefins), as shown in Table 1. Because the chemical composition of a base oil directly determines its physical and chemical performance characteristics, statistical and neural network modeling methods have been developed that utilize compositional data to predict properties such as oxidation lifetime and engine test performance.1-3 Such structure-property correlations can be used to design better lubricants and to optimize refining processes. The fundamental dynamic properties of fluids, such as rotation, translation, and random diffusion, are related to the viscosities, densities, temperature, and molecular sizes or flexibilities of the constituent molecules. Diffusion is related to the molecular size, temperature (T), and viscosity as shown below, where k is the Boltzmann constant and f is a friction coefficient
D ) kT/f
(1)
In the simple case of a spherical particle with an effective hydrodynamic radius (i.e., Stokes radius) of rs in a solution of viscosity η, the friction factor is given by eq 2, assuming no-slip sticking conditions at the * Corresponding author. E-mail:
[email protected]. Phone: 315-470-6860. Fax: 315 470-4729.
API group
% saturates
% aromatics
VIa
% sulfurb
I II III
90 >90
>10 95%. The PVC values for these base oils ranged from 10 to 15 GPa-1, and their kinematic viscosities at 100 °C ranged from 3 to 12 cSt. Typical spin-echo 1H NMR spectra of a lubricating base oil at 30 °C and ambient pressure obtained using PFGSE 1H NMR spectroscopy are shown in Figure 1 as a function of gradient field strength (G). In the 1H NMR spectra of base oils, sharp signals appearing in the range of 1.0-2.0 ppm can be assigned to -CH2 and -CH protons in n-, iso-, and cycloparaffins, whereas smaller peaks in the range of 0.5-1.0 ppm show the resonances of methyl protons in n- and isoparaffins. These signals become broader at low temperatures because the molecular motion is slow on the 1H NMR time scale (data not shown). The plots of ln(Ig/I0) vs G2 for peaks in the PFGSE 1H NMR (PFG NMR) spectra of lubricating base oils are straight lines with an R2 value of 0.99 (plots not shown). This demonstrates that the self-diffusion of a base oil consists of a single component motion during the observation time. Base oils differing in viscosity or API group exhibit different slopes of intensity decay, and different self-diffusion coefficients values were determined, using eq 4, for the different base oils. Lower values of D indicate that translational motion is more restrained, which is characteristic of more viscous base oils. Self-Diffusion Coefficient vs Viscosity. Through the combination of eqs 1 and 2, Stokes law relates the
D ) kT/Cπηrs
(5)
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Ind. Eng. Chem. Res., Vol. 42, No. 7, 2003 Table 4. Comparison of Neural Network (NN) and Multilinear Regression (MR) for Prediction of PVC Using Self-Diffusion Coefficients and Viscosity Index variables
method
Sa
R2 b
one (D only)
MR NN MR NN
0.50 0.34 (0.33) 0.41 (0.41) 0.25 (0.26)
0.86 0.89 (0.90) 0.91 (0.91) 0.95 (0.94)
two (D + VI)
R2 (adj)c 0.85 0.90 (0.89)
a Residual standard error. b Coefficient of determination. c R2 adjusted for degrees of freedom. Values in parentheses are respective values for cross-validation experiments.
Figure 3. Relationship of PVC and D values measured for various API group I, II, and III base oils using PFG NMR spectroscopy.
T1 relaxation. As the temperature is lowered and viscosity increases, T1 values decrease, pass through a minimum, and increase again, so a simple inverse dependence of T1 on viscosity is expected only for lowviscosity liquids.4,6 Correlation of the Self-Diffusion Coefficient and PVC Using MR and NN Methods. The pressure viscosity coefficient (PVC) is an important parameter for base oils in defining their lubricating capacities because it reflects the extent of “thickening” that occurs under high hydrodynamic loads. Most organic fluids, including lubricant base oils, exhibit a reversible viscosity increase under the application of high pressure as a result of molecular mobility restrictions imposed by the forces being exerted.4,23,29,30 Previous work by So and co-workers showed that an empirical relationship exists relating the PVC to a combination of kinematic viscosity and a term related to the viscosity-temperature properties of a lubricant oil.31 Later, Wu, Klaus, and Duda also determined, using free-volume theory, how the PVC is related to the kinematic viscosity and viscositytemperature characteristics.32 Further confirmation that the PVC is fundamentally related to molecular parameters expressed in the viscosity-temperature properties of a lubricant was provided by Spikes, who utilized a purely thermodynamic approach, assuming that viscosity is a property of state, to demonstrate that a linear relationship exists between the change in viscosity with pressure (at constant temperature) and the change in viscosity with increasing temperature [that is, (δ ln η/δP)T increases as (δ ln η/δT)P increases).33 Spikes also showed that, at similar values of (δ ln η/δT)P/η, naphthenic base oils (containing higher levels of cycloparaffins) have higher values of (δ ln η/δP)T/η than paraffinic base oils (which contain more paraffins than naphthenic oils). This result is consistent with our observation of the relationships between base oil molecular structure and PVC reported earlier.4 In this study, we aim to relate PVCs to aspects of molecular dynamics that contribute directly to the viscosity of a lubricant at high pressures. As shown in Figure 3, an inverse relationship between D, as determined by PFG NMR spectroscopy at 30 °C, and PVC, measured at 100°C, was observed for a series of API group I, II, and III base oils. Combining all data points into one regression analysis provided a R2 value of 0.86. When the repeatability of the PVC measurements is taken into consideration ((0.5 GPa-1), almost all of the points lie on the best-fit regression line, as
illustrated by the error bars in Figure 3. For group II oils, for which sufficient data points exist for an individual regression analysis, an R2 value of 0.91 is observed. Although adequate numbers of data points were not available to demonstrate conclusively that the API group exerts an influence on the slope of the D vs PVC plot, it appears that the differences in chemical structure that differentiate among groups might be important. For group III oils, the observed increase in D with decreasing PVC is more pronounced than those for groups I and II oils possibly because of the greater percentage of branched paraffins in the group III oils. Such molecules potentially have a greater mobilities under high pressure than the multiring cycloparaffin structures more typical of group I and II base stocks. Although diffusion coefficient estimates based on NMR spectroscopy can be used alone to predict PVC values, the inclusion of an additional parameter in the regression analysis, the viscosity index (VI), increases the R2 value to 0.91, as shown in Table 4. The R2 (adj) values also increase, and a reduction is observed in the residual standard error. This observation is consistent with previous empirical and theoretical studies that suggest that the molecular parameters that define the viscosity-temperature relationship for hydrocarbon fluids also influence viscosity-pressure behavior.31-33 An artificial neural network (NN) approach was also used to relate D to PVC. The R2 values obtained using the NN are higher than those obtained obtained for MR models, and similarly, the average error (S) in the predictions is much lower for the NN model than for the MR model (Table 4). The neural net was trained with 12 samples, and its predictability was determined for two sets of unseen samples. The average error value reported in Table 4 is the average of these two values and is comparable to the S values for the whole set. The lower S value and higher R2 value for the case with two variables (D and VI) indicates the better predictive ability of this model. The values in parentheses are for cross-validation experiments and are quite comparable with the actual values, thus confirming that the predicted values for unknown samples will be reliable. Neural network methods do not, however, result in a mathematical equation relating inputs to outputs as obtained from MR models, and the effects of specific individual variable are not always obvious. Variable-Temperature PFG. Although wax molecules (linear n-paraffins) are generally removed from lubricating oils by a solvent or catalytic dewaxing process, small amounts (
