28 February / March 2019
Clarifying the Relationship Between Density and Viscosity of Methanol/ Carbon Dioxide Mixtures used in Supercritical Fluid Chromatography
by Terry A. Berger, SFC Solutions, Inc. Email:
tabergersfc@aol.com The effect of viscosity and the relationship between viscosity and density is characterised for MeOH/C02 mixtures at 40°C. It appears that most
SFC users equate higher pressure drops with higher density, which is often NOT true. At higher modifier concentrations (> ≈ 20%) and pressures (> ≈ 200 bar), the density of MeOH/CO2
mixtures actually decreases compared to lower MeOH concentrations at lower pressures. At the same
time, pressure drops increase, indicating that the viscosity increases. Thus, the relationship between density, and viscosity is still poorly understood at many typical conditions used in SFC. There are no measured values for viscosity under the conditions used in SFC. There are 2 approaches published in the literature to calculate viscosity under SFC conditions, one producing dynamic viscosity and the other kinematic viscosity, but neither is clearly superior or more accurate. Correcting for differences in density they disagree only slightly, which is good. Here, data from one of the approaches is used to characterise the relationship between density and viscosity. The results indicate that density is a very poor indicator of retention, or pressure drops when modifier concentration is changed significantly. This is in clear contradiction to mainstream teaching where density is indicated as the primary control variable for retention. Changes in viscosity, not density, explains both pressure drops and changes in diffusion coefficients with pressure and modifier concentration.
Introduction
A great deal has been written in recent years on the effect of density on retention under isocratic conditions in supercritical fl uid chromatography (SFC) [1-5]. Such reports suggest that density is a major control variable. In fact, it is sometimes characterised as the most important control variable. This is a serious distortion. With polar solutes, changes in modifi er concentration always have a much larger impact on retention [6], and effi ciency, compared to changes in density.
Relatively high modifi er concentrations (>20%) are often used, along with gradient elution. In addition, there is increasing use of sub-2µm particles which generate much higher system pressures. A common perception is that increasing modifi er concentration always results in increasing density, along with increasing pressure drops.
The physio-chemical properties of MeOH/ CO2
mixtures have not been signifi cantly studied at such high MeOH concentrations and higher pressures. The relationship between density and viscosity remain poorly
understood. The few empirical density measurements available for such mobile phases [7], are quite old and support this perception. When such reports were published, the modifi er concentrations used in the literature seldom exceeded 10-20% and pressure was seldom > 200 bar. Not surprisingly, published density data only covers relatively low MeOH concentrations and low pressures. However, some pure modifi ers, such as MeOH, are signifi cantly less dense than CO2
at high pressures. At
some intermediate MeOH concentrations and pressures, the density of CO2
/MeOH
mixtures should begin to decrease. Unfortunately, there are no published experimental data for density at such higher concentrations and pressures.
It has only been in the last few years that reasonably accurate values could be calculated for the density of CO2
/MeOH
mixtures. The REFPROP program [8-10] from NIST is reasonably accurate for calculating the density of CO2
/MeOH mixtures. The
results have not been widely accessible, although a small number of reports have appeared [5,11-13].
Viscosity is a much bigger problem. No Figure 1. The density of CO2 /MeOH mixtures
between 0% and 50% in 5% increments at 40°C (Mole%). At the right margin the top curve represents 0% methanol. The bottom curve represents 50%.
empirical viscosity measurements exist for mixtures of CO2
with polar modifi ers used
in SFC, and any experimental approach is daunting. With increasing modifi er concentration, pressure drops continue to increase, due to increasing molecular closeness, and subsequently, increasing viscosity. Unfortunately, REFPROP cannot generate accurate transport properties, such as viscosity, for such mixtures of a non-polar main fl uid with a polar modifi er.
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