11
A few approaches have appeared for calculating viscosities, but the results are somewhat inconsistent. Tarafder [5] used REFPROP to generate constant density (isopycnic) lines as a reference, and compared the calculated density of CO2
/MeOH mixtures to old
empirical density measurements and found fairly signifi cant deviations near the critical points but relatively good agreement elsewhere. Tarafder then calculated and plotted all the temperatures and pressures that gave the same density with the same composition.
These plots contain the ratio of ρ/η, where η is dynamic viscosity, and ρ is density. This ratio is proportional to kinematic viscosity. To convert such data to actual values for kinematic viscosity required another estimation, in this case of column porosity, the only non-constant in the differential version of Darcy’s Law [5]. With an estimation of column porosity, values were assigned to each kinematic viscosity curve. Mixtures ranged from 5% to 20%. There are many assumptions, approximations, and estimations in these numbers that make the results questionable.
The pump delivers v/v%. If one knows the density of each fl uid, and the volumetric displacement of each pump vs. time, one then knows the actual Mole%. Conversely, it is fairly easy to convert Mole% to v/v%. With other SFC’s it is more diffi cult due to high heats of compression. With signifi cant pump compression, the temperature of the fl uid is not the temperature of the pump head.
Chemicals
Theobromine was obtained from Sigma-Aldrich, St. Louis MO, USA (> 98%, used as received). The CO2
was beverage grade, from Terry Supply Co., Bradenton, FL, USA, in 50 lb cylinders, without a DIP tube. The HPLC grade MeOH and IPA was purchased from SECO, Aston, PA, USA. The samples were dissolved in methanol. The ‘feed’ solvent used in the autosampler was isopropyl alcohol.
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.
Figure 3. Dynamic viscosity vs methanol concentration in CO2 at 5 pressures. Bottom circles 100 bar; squares, 150 bar; triangles, 200 bar, diamonds, 300 bar; and top circles, 400 bar.
Fekete [3] took a completely different approach in calculating dynamic viscosity of MeOH/ CO2
mixtures where a liquid phase was in contact with a vapor phase at low pressures (<80 bar). He then extended correlations to conditions at higher pressures and temperatures, between 0% and 40% MeOH. Extrapolating the low pressure data to much higher pressures (through the critical points) is a bit of a stretch since there is a poor relationship
mixtures. He used some empirical data [14] on the viscosity/density of CO2
between density and viscosity in fl uids where the modifi er is much less dense than the CO2 at higher pressures. Surprisingly, this is actually a fairly common approach [15] using the same underlying assumptions and similar data. The authors [3] claim to have checked the calculated values with a few measured values with good agreement, without providing details. These results were reported as dynamic viscosity in centi-Poise.
The 2 sets of data don’t quite fi t, but are close, when Fekete’s [3] results are divided by density (to generate kinematic viscosity) or when Tarafder’s [5] data is multiplied by density (to generate dynamic viscosity). The differences are not very large and the curves have the same general shape.
In a recent report, from this laboratory [11], the changes in density, with high modifi er concentrations and high pressures were briefl y characterised with respect to retention, effi ciency, and pressure drops, using density data from REFPROP. A missing link in understanding effi ciency, pressure drops, and optimum fl ow rate has been the lack of accurate viscosity values and the relationship between viscosity, density, and pressure drops at pressures > ≈ 200 bar, and methanol concentrations > ≈ 20%. In the present work, the viscosity results from Fekete [3], which covers a wider range of MeOH concentrations, up to 40%, were extrapolated to lower intermediate concentrations and compared to density data from REFPROP at the same compositions and temperature.
Experimental Equipment
Chromatograms were collected using a Model 4301A 1260 Infi nity II SFC, controlled by a Model C.01.08 (210) Chemstation, all from Agilent Technologies, Waldbronn, DE (Germany). The instrument consists of a SFC conversion module, a binary pump, a Multisampler, thermostated column compartment, and a 120 Hz diode array detector (DAD). Standard 170µm tubing, including 2 heat exchangers was used throughout, except for a 50 cm piece of 120µm tubing serving as the inlet tube of the fl ow cell. The fl ow cell volume was 13µL with a 10mm fl ow path length. The column was 4.6 x 150mm packed with 5µm RX-Sil from Agilent Technologies, Little Falls, DE, USA.
The Agilent SFC is fairly unique in that the binary pump does not compress the CO2 signifi cantly. It is pre-compressed to 8 bar below the delivery pressure by the SFC
binary pump does not compress, there is almost no heat of compression and no ambiguity about the temperature of the CO2
conversion module. The binary pump only meters the fl ow. Since the CO2 and the delivery pressure, one can obtain the density of each pure fl uid from REFPROP. half of the that is being delivered. Knowing the pump temperature,
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.
/MeOH Results Density calculations from REFPROP [8-10] for CO2 /MeOH mixtures at 40°C are shown
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.
is denser than any mixture of methanol in CO2
50%. This is completely counter to the general perception about MeOH concentration and density. Above 300 bar, pure CO2
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 about the same as the density of 50% methanol in CO2
is
. Even 5% MeOH is denser than ! This
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
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