30 February / March 2019
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
REFPROP and reasonably agreed.
Figure 4. a. The change in viscosity at the pump with increasing methanol concentration. b. Change in viscosity with pump pressure. Column: 4.6x150mm, 5µm RX-Sil. Other conditions: 100 bar BPR pressure, 40°C.
Results
Density calculations from REFPROP [8-10] for CO2
/MeOH mixtures at 40°C are shown in
Figure 1. These calculations yield densities at Mole%. At low modifi er concentrations and low pressures, density increases dramatically with small increases in methanol concentration, and to a lesser extent with increasing pressure. This is consistent with the general perception of most users. However, at only ≈ 200 bar the density of pure CO2
of 50% methanol in CO2
is about the same as the density . Even 5% MeOH
is denser than 50%. This is completely counter to the general perception about MeOH concentration and density. Above 300 bar, pure CO2
is denser than any mixture of methanol in CO2 ! This has not
been adequately articulated, previously, and indicates that the preoccupation with density as a control variable, by some users, is ill-founded, and counter-productive.
For somewhat polar compounds, such as small drug-like molecules, retention is
usually a strong function of polar modifi er concentration, but it is sometimes suggested that density is also a major control variable. With the data in Figure 1, it is fairly easy to show the effect of the changes in density due to changes in modifi er concentration and pressure on retention. Theobromine was eluted from a 4.6x150mm, 5µm RX-Sil (bare silica) column using various back pressure regulator (BPR) settings and methanol concentrations. The fl ow was set to 2mL/min, with 40°C oven set temperature, which is near the optimum fl ow rate under these conditions.
The pressure drops were modest (≈ 35 bar, mostly in the column) so the average of the pump pressure and the BPR pressure was used as the average column pressure, which in turn, should indicate the approximate average density in the column. The retention factors 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.
Figure 5. Relationship between density and viscosity with changing pressure and methanol concentration. From the left 100 bar, 150 bar, 200 bar, 300 bar, 400 bar. The lowest data point on each curve is 0% methanol. On each curve the % methanol increases in 5% increments up to 50%. 40°C.
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
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.
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