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Evaluating the Viscosity of Biolubricants via DOSY-NMR
Lucas Queiroz dos Santos
Universidade Federal de Pernambuco - UFPE
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Viscosity(η) is one of the most important properties of (bio)lubricants along with its dependence with temperature and pressure. Many attempts are being made to modify and improve the viscosity of (bio)lubricants. However, standard procedures require a large amount of the sample that hinders the use of high-throughput approaches. Moreover, most common apparatus provides the kinematic viscosity(ν) which requires the mass density(ρ) to provide the viscosity: η=ρν. Therefore, alternative procedures to determine the viscosity are quite relevant. In this context, the diffusion coefficient(D) of a species-i in a fluid is related to the viscosity of the medium, at a given temperature T, through the Stokes-Einstein equation: D=aT/η, with a=k/(cπr), where r the hydrodynamic radius, k is the Boltzmann constant, and c is a factor(c~4-6) related mainly to its shape. Diffusion coefficient can be promptly measured by diffusion-ordered NMR spectroscopy(DOSY), which is simple to measure and requires small amounts of samples. So, we employed 1H-DOSY measurements at temperatures varying from 298 to 338K to provide estimates of the fluid viscosity. The diffusion of large species can be difficult to measure and a small amount of benzene (0.97:0.03mol lubricant/mol benzene) was added to the fluid, so the viscosity could be estimated from the diffusion of benzene. This approach was tested for methyl ricinoleate(MR), because its viscosity is available in a temperature range of 298-358K and can be promptly synthesized from known precursors. Viscosity can be expressed as η(T)=A·exp[Δ‡G/(RT)], where R is the molar gas constant and Δ‡G is the Gibbs free energy of activation. From the Stokes-Einstein equation, the diffusion coefficient of the (bio)lubricant becomes Dlub(T)=A’·T·exp[−Δ‡G/(RT)]. Therefore, plots of ln(η) and of ln(Dlub/T) versus 1/T should be linear and have slopes that yield the same values of Δ‡G. Indeed, from the available viscosity data and the diffusion coefficient of MR from DOSY measurements, these linear relationships were observed and provided 31.2±0.6 and 31.9±1.4kJ/mol for Δ‡G, respectively, with R2=0.996 and 0.989. The excellent agreement, within the uncertainty of the linear fits, indicates that the Stokes-Einstein equation is valid for this fluid. A value of 24.8±0.5kJ/mol for Δ‡G was obtained from ln(Dbenz/T) versus 1/T plot(R2=0.997). Besides, the better fit of benzene data compared to MR suggests that benzene can be an accurate probe for diffusion and viscosity of fluids. Estimates of the viscosity of the binary mixture 0.97:0.03(MR/benz) indicate that at this low mol fraction it does not affect the viscosity of the pure fluid. From the values of Dmr and Dbenz and η of MR, the geometric parameters (cr) were with the Stokes-Einstein equation and their average values over the temperature range of 298 to 328K were 18.35 and 4.26Å, respectively. MR was modified by performing its acetylation, MRA, and benzene diffusion coefficient was measured in the new fluid. Using the values of (cr)benz, the viscosity of MRA was estimated to be 16% smaller than MR at 298K, up to 40% smaller at 318K. This approach was simple and employed small amounts of the products, which can promptly screen suitable modifications.
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