Efficiency of supercritical fluid chromatography columns in different thermal environments

• We studied effects of flow rate, outlet pressure and thermal environment on efficiency in SFC.
• We propose two- and one-dimensional models to calculate column efficiency.
• The two-dimensional model correctly predicts the shapes of observed van Deemter plots.
• The one-dimensional model can be applied for modeling of SFC away from the critical conditions.
• The effect of pressure drop on efficiency in SFC is explained.

The efficiency of a packed column eluted with supercritical carbon dioxide at 323 K and outlet pressures from 90 to 150 bar was studied with the column in two different thermal environments. The 150 mm × 2.0 mm ID stainless steel column was packed with spherical 5-μm porous silica particles with a covalently bonded nonpolar stationary phase, and the test solutes were normal alkanes. When operated in a convective air bath the column exhibited severe efficiency losses when its outlet pressure was below 120 bar. The efficiency of the same column enclosed in a shell made of foam insulation was restored at low outlet pressures down to 100 bar. The van Deemter plots showed an abnormal dependence of the plate height (HETP) on the flow rate at low outlet pressures, exhibiting a maximum in the HETP at flow rates around 1 mL/min and a 20-bar pressure drop. The large efficiency losses at low outlet pressures are due to radial temperature gradients associated with enthalpic expansion and cooling of the mobile phase. The separations were simulated by a numerical model that accounts for axial and radial gradients in the temperature and density along the column. The abnormal van Deemter plots arise from competing processes affecting the radial distribution of the solute migration velocity along the column. The negative impact on efficiency is greatest when the density profile of the mobile phase along the column is close to the critical isopycnic line. The efficiency improves at increased flow rates because of increased cooling at larger pressure drops and increased density along the entire length of the column. The model predicts the unusual trends in the van Deemter plots, but the calculated results at low outlet pressures are strongly influenced by small variations in the porosity distribution in the column, limiting the accuracy of the predicted HETP values. In spite of these difficulties, the model has enabled a detailed analysis of the effects of temperature, pressure and flow rate on the thermal properties of the mobile phase, and their impact on the radial distribution of the solute velocities along the column. This work provides a better appreciation of the factors that cause excess efficiency loss at low outlet pressures, a phenomenon that lacked a convincing explanation for over 40 years. Finally, a simplified form of the model, which ignores the radial gradients, provided accurate results only at the highest outlet pressure. Calculations done by the simplified model are much faster, and it can be recommended for simulation of SFC processes at sufficiently high outlet pressures.