12
are plotted against methanol concentration in Figure 2a, while the average density in the column, under the same conditions, is plotted in Figure 2b. Clearly, the dramatic decrease in retention with increasing modifi er concentration is not caused by increasing density, since the density often decreases.
Increasing pressure has its greatest effect on retention at low modifi er concentrations, although modifi er concentration is always more important [6]. At 5% MeOH, retention is nearly halved when the BPR pressure is increased from 100 to 300 bar but in both cases, retention is excessive (k ≈ 9-16). However, at higher MeOH concentrations, pressure becomes progressively less important. All this has been partially documented [11] but what about the relationships between density, viscosity, and pressure drops?
The viscosity data of Fekete [3] was used as a basis for quadratic estimation of the viscosities at 100 bar. Then, viscosity values were extrapolated for intervening values of methanol concentration, and the results are presented in Figure 3. The values at 0% were compared to values for pure CO2
from REFPROP and reasonably agreed.
In Figure 4a, the viscosity of the mobile phase, at the pump, using the data in Figure 3, is plotted against the modifi er concentration. In Figure 4b, the pump pressure at the same fl ow rate and temperature, is plotted against the viscosity. Both plots are linear and the calculated increasing viscosities appear to be consistent with increasing system pressure drops, as one would expect.
The calculated viscosity from Figure 3 was plotted against calculated density from Figure 1. The results are presented in Figure 5. At low pressures (100-200 bar), the density initially increases up to ≈ 20-25% methanol, consistent with most users’ perceptions. However, at higher MeOH concentrations, the density then decreases, while viscosity increases. At 300-400 bar, the density actually decreases almost linearly, while viscosity increases with increasing modifi er concentration. Thus, at higher pressures the relation between density and viscosity is actually opposite to the general expectation. All the relationships in Figure 5 are calculated.
The average pressures in Figure 2 were also plotted as density vs viscosity values is presented in Figure 6. The pressures next to the curves were the BPR pressure. The results mirror the results in Figure 5. Thus, the pressure drops in a real column produced similar results.
Conclusions The relationship between density and viscosity of MeOH/CO2
mixtures used in SFC is
complex. In fact, at higher modifi er concentrations, or higher pressures, the relationship is confused or essentially opposite to most users’ perceptions. This makes density less than useless, and, in fact, incorrect in determining retention or pressure drops at higher MeOH concentrations or pressures. This is counter to most of the recent SFC literature recommendations which stress relationships between density and retention. Changes in viscosity, not density, explains both pressure drops and changes in diffusion coeffi cients with pressure and modifi er concentration. Unfortunately, viscosity data are nearly non- existent.
References
1. A. Tarafder, G. Guiochon, ‘Use of isopycnic plots in designing operations of supercritical fl uid chromatography: I. The critical role of density in determining the characteristics of the mobile phase in supercritical fl uid chromatography’, J. Chromatogr. A, 1218 (2011) 4569–4575.
2. E. Lesellier, L. Fougere, D.P. Poe, ‘Kinetic behavior in supercritical fl uid chromatography with modifi ed mobile phase for 5µm particle size and varied fl ow rates’, J. Chromatogr.A, 1218 (2011) 2058-2064.
3. A. Grand-Guillaume Perrenoud, C. Hamman, M. Goel, Jean-Luc Veuthey, D. Guillarme, S. Fekete, ‘“Maximizing kinetic performance in supercritical fl uid chromatography using state-of-the-art instruments’, J. Chromatogr. A, 1314 (2013) 288-297.
4. S. Delahaye, K. Broeckhoven, G. Desmet, F. Lynen, ‘Design and evaluation of various methods for the construction of kinetic performance limit plots for supercritical fl uid chromatography’, J. Chromatogr. A, 1258 (2012) 152-160.
5. A. Tarafder, K. Kaczmarski, D. P. Poe, G. Guiochon, ‘Use of the isopycnic plots in designing operations of supercritical fl uid chromatography. V. Pressure and density drops using mixtures of carbon dioxide and methanol as the mobile phase’, J. Chromatogr. A, 1258 (2012) 136–151.
6. T.A. Berger, J. F. Deye, “Composition and Density Effects Using Methanol/Carbon Dioxide in Packed Column Supercritical Fluid Chromatography” Anal. Chem. 1990, 62, 1181-1185.
7. T.A. Berger, ‘Density of Methanol-Carbon Dioxide Mixtures at Three Temperatures’, J. High Resolut. Chromatogr., 1991, 14, 312-316.
8. E.W. Lemmon, M.L. Huber, M.O. McLinden, NIST Reference Database 23: Ref-erence Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1,National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, MD, 2013.
9. O. Kunz, R. Klimeck, W. Wagner, M. Jaeschke, ‘The GERG-2004 Wide-Range Equation of State for Natural Gases and Other Mixtures GERG Technical Monograph’. Fortschr.-Ber. VDI, VDI-Verlag, Düsseldorf (2007)
10. O. Kunz, W. Wagner, ‘The GERG-2008 wide-range equation of state for natural gases and other mixtures: an expansion of GERG-2004’, J. Chem. Eng. Data, 57 (11) (2012), pp. 3032-3091.
11. T.A. Berger, ‘Effect of density on kinetic performance in supercritical fl uid chromatography with methanol modifi ed carbon dioxide’, Chromatogr. A, 1564, 2018, 188-198.
12. A. Tarafder, G. Guiochon, ‘Use of isopycnic plots in designing operations of supercritical fl uid chromatography: II. The isopycnic plots and the selection of the operating pressure–temperature zone in supercritical fl uid chromatography’, J. Chromatogr., A, 1218 (2011) 4576– 4585.
13.] A. Tarafder, G. Guiochon, ‘Use of isopycnic plots in designing operations of supercritical fl uid chromatography. III: Reason for the low column effi ciency in the critical region’, J. Chromatogr A, 1218 (2011) 7189–7195.
14. R. Sih, F. Dehghani, N. R. Foster, ‘Viscosity measurements on gas expanded liquid systems- Methanol and carbon dioxide’, J. Supercrit. Fluids, 41, 2007, 148-157.
Figure 6. Average viscosity vs density in a 4.6x150mm column packed with 5µm RX-Sil at 3 BPR pressures between 5% and 40% methanol. 2mL/min, 40°C.
15. H. Matsuda, K. Kurihara, K. Tochigi, T. Funazukuri, V.K. Rattan, ‘Estimation of kinematic viscosities for CO2
expanded liquids by ASOG-VISCO model’, Fluid Phase Equilibria 470 (2018) 188-192. Read, Share and Comment on this Article, visit:
www.labmate-online.com/article GCxGC Modulators for Every Challenge
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