Donald P. Poe

Plate height theory for compressible mobile phase fluids and its application to gas, liquid and supercritical fluid chromatography

Abstract General expressions for apparent plate height are derived in terms of temporal and spatial average values of local plate height, solute capacity factor and mobile phase density. The general expressions are applied to the appropriate expressions for gas chromatography, liquid chromatography and supercritical fluid chromatography with open tubular and packed columns. For gas chromatography, the equations reduce to the equations presented earlier by Giddings. For liquid chromatography, the equations reduce to those for local plate height. Predicted results for supercritical fluid chromatography are compared to experimental results reported in the literature.

Effects of pressure drop, particle size and thermal conditions on retention and efficiency in supercritical fluid chromatography.

The effects of particle size and thermal insulation on retention and efficiency in packed-column supercritical fluid chromatography with large pressure drops are described for the separation of a series of model n-alkane solutes. The columns were 2.0mm i.d.x150mm long and were packed with 3, 5, or 10-mum porous octylsilica particles. Separations were performed with pure carbon dioxide at 50 degrees C at average mobile phase densities of 0.47g/mL (107bar) and 0.70g/mL (151bar). The three principal causes of band broadening were the normal dispersion processes described by the van Deemter equation, changes in the retention factor due to the axial density gradient, and radial temperature gradients associated with expansion of the mobile phase. At the lower density the use of thermal insulation resulted in significant improvements in efficiency and decreased retention times at large pressure drops. The effects are attributed to the elimination of radial temperature gradients and the concurrent enhancement of the axial temperature gradient. Thermal insulation had no significant effect on chromatographic performance at the higher density. A simple expression to predict the onset of excess efficiency loss due to the radial temperature gradient is proposed.

Use of the isopycnic plots in designing operations of supercritical fluid chromatography: IV. Pressure and density drops along columns.

The pressure- and the density-drops along a chromatographic column eluted with supercritical fluid carbon dioxide were mapped as a function of the outlet column pressure and the temperature on the P-T diagram of neat CO(2). At low densities, the viscosity of CO(2) is low, which is expected to result into a low pressure drop along the column. However, at these low densities, the volumetric flow rates of the mobile phase at constant mass flow rates are high, which might result into a high pressure drop along the column. These conflicting effects of an adjustment in the mobile phase density on the pressure drop of the mobile phase along the column makes it nearly impossible to develop a simple intuitive understanding of the relationships between the net pressure drops and the operating temperatures and pressures. The development of a similar understanding of their relationships with the density drop along the column is even more complex, because this density drop depends also on the compressibility of the mobile phase, itself a function of the operating pressures and temperatures. Numerical calculations of the pressure and density drops along columns packed with particles of different sizes, under different operating conditions (temperature, outlet pressure, and flow rate), provide important insights regarding the extent of the pressure and density drops under these operating conditions.

Numerical modeling of the elution peak profiles of retained solutes in supercritical fluid chromatography

In supercritical fluid chromatography (SFC), the significant expansion of the mobile phase along the column causes the formation of axial and radial gradients of temperature. Due to these gradients, the mobile phase density, its viscosity, its velocity, its diffusion coefficients, etc. are not constant throughout the column. This results in a nonuniform flow velocity distribution, itself causing a loss of column efficiency in certain cases, even at low flow rates, as they do in HPLC. At high flow rates, an important deformation of the elution profiles of the sample components may occur. The model previously used to account satisfactorily for the retention of an unsorbed solute in SFC is applied to the modeling of the elution peak profiles of retained compounds. The numerical solution of the combined heat and mass balance equations provides the temperature and the pressure profiles inside the column and values of the retention time and the band profiles of retained compounds that are in excellent agreement with independent experimental data for large value of mobile phase reduced density. At low reduced densities, the band profiles can strongly depend on the column axial distribution of porosity.

Use of the isopycnic plots in designing operations of supercritical fluid chromatography. V. Pressure and density drops using mixtures of carbon dioxide and methanol as the mobile phase.

The drops of pressure and density along chromatographic columns of different characteristics, eluted with different mixtures of carbon dioxide and methanol was mapped as functions of the column outlet pressure and the operating temperature. This paper extends an earlier report reporting the extent of the pressure and density drops along chromatographic columns eluted with neat CO(2)[1]. It illustrates the similarities and differences in the pressure and density profiles along columns operated with mixed mobile phases and with neat CO(2). Numerical calculations of the pressure and density drops along columns packed with particles of different sizes, under different operating conditions (temperature, outlet pressure, and flow rate), provide important insights regarding the extent of the pressure and density drops under these operating conditions.

Pressure, temperature and density drops along supercritical fluid chromatography columns. I. Experimental results for neat carbon dioxide and columns packed with 3- and 5-micron particles

The pressure drop and temperature drop on columns packed with 3- and 5-micron particles were measured using neat CO(2) at a flow rate of 5 mL/min, at temperatures from 20°C to 100°C, and outlet pressures from 80 to 300 bar. The density drop was calculated based on the temperature and pressure at the column inlet and outlet. The columns were suspended in a circulating air bath either bare or covered with foam insulation. The results show that the pressure drop depends on the outlet pressure, the operating temperature, and the thermal environment. A temperature drop was observed for all conditions studied. The temperature drop was relatively small (less than 3°C) for combinations of low temperature and high pressure. Larger temperature drops and density drops occurred at higher temperatures and low to moderate pressures. Covering the column with thermal insulation resulted in larger temperature drops and corresponding smaller density drops. At 20°C the temperature drop was never more than a few degrees. The largest temperature drops occurred for both columns when insulated at 80°C and 80 bar, reaching a maximum value of 21°C for the 5-micron column, and 26°C for the 3-micron column. For an adiabatic column, the temperature drop depends on the pressure drop, the thermal expansion coefficient, and the density and the heat capacity of the mobile phase fluid, and can be described by a simple mathematical relationship. For a fixed operating temperature and outlet pressure, the temperature drop increases monotonically with the pressure drop.

Kinetic behaviour in supercritical fluid chromatography with modified mobile phase for 5 μm particle size and varied flow rates.

After much development of stationary phase chemistry, in recent years the focus of many studies in HPLC has shifted to increase the efficiency and analysis speed. Ultra high pressure liquid chromatography (UHPLC) using sub-2 μm particles, and high temperature liquid chromatography (HTLC), using temperatures above 100°C have received much attention. These new approaches allow the use of flow rates higher than those classically used in HPLC, reducing the analysis duration. Due to the low viscosity of supercritical fluids, high velocities, i.e. high flow rates, can be achieved with classical pumping systems typically used in supercritical fluid chromatography (SFC). The effects of the flow rate increase with CO(2)/methanol mobile phase was studied on the inlet pressure, t(0), the retention factor of the compounds, and on the efficiency. Simple comparisons of efficiencies obtained at varied temperature between SFC and HPLC, with a packed column containing 5 μm particles, show the greater kinetic performances achieved with the CO(2)/methanol fluid, and underline specific behaviours of SFC, occurring for high flow rates and sub-ambient temperature. Some values (N/t(0)) are also compared to UHPLC data, showing that good performance can be achieved in SFC without applying drastic analytical conditions. Finally, simple kinetic plots (t(0) vs N) at constant column length are used to select combinations of temperature and flow rate necessary to achieve a required theoretical plate number.

Pressure, temperature and density drops along supercritical fluid chromatography columns in different thermal environments. III. Mixtures of carbon dioxide and methanol as the mobile phase.

The pressure, temperature and density drops along SFC columns eluted with a CO2/methanol mobile phase were measured and compared with theoretical values. For columns packed with 3- and 5-μm particles the pressure and temperature drops were measured using a mobile phase of 95% CO2 and 5% methanol at a flow rate of 5mL/min, at temperatures from 20 to 100°C, and outlet pressures from 80 to 300bar. The density drop was calculated based on the temperature and pressure at the column inlet and outlet. The columns were suspended in a circulating air bath, either bare or covered with foam insulation. The experimental measurements were compared to theoretical results obtained by numerical simulation. For the convective air condition at outlet pressures above 100bar the average difference between the experimental and calculated temperature drops and pressure drops were 0.1°C and 0.7% for the bare 3-μm column, respectively, and were 0.6°C and 4.1% for the insulated column. The observed temperature drops for the insulated columns are consistent with those predicted by the Joule-Thomson coefficients for isenthalpic expansion. The dependence of the temperature and the pressure drops on the Joule-Thomson coefficient and kinematic viscosity are described for carbon dioxide mobile phases containing up to 20% methanol.

Pressure, temperature and density drops along supercritical fluid chromatography columns. II. Theoretical simulation for neat carbon dioxide and columns packed with 3-μm particles

When chromatography is carried out with high-density carbon dioxide as the mobile phase, the required pressure gradient along the column is moderate but this mobile phase is highly compressible so, under certain experimental conditions, its density may decrease significantly along the column. Such an expansion absorbs heat and causes cooling of the column. The resulting heat transfer causes the formation of axial and radial gradients of temperature and density that may become large under certain conditions. In the first part of this series the pressure, temperature, and density drops were measured over a wide range of experimental temperature and pressure conditions, along columns packed with 3- and 5-μm particles. These columns were suspended in a circulating air bath and were either bare or covered with foam insulation. The behavior of these columns was discussed with special attention to their thermal heterogeneity. In this part we scrutinize the application of two heat transfer models to predict the pressure, temperature and density drops. One is a two-dimensional model that takes into account the axial and radial variations of the relevant chromatographic parameters along the column. The other, one-dimensional model ignores the radial variations of these parameters. The numerical solutions of the two-dimensional model are in excellent agreement with independent experimental data. The one-dimensional model can also be applied for the analysis of the behavior of supercritical fluid chromatography (SFC) columns away from the critical conditions.

Efficiency of supercritical fluid chromatography columns in different thermal environments

The efficiency of a packed column eluted with supercritical carbon dioxide at 323K and outlet pressures from 90 to 150bar was studied with the column in two different thermal environments. The 150mm×2.0mm 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 120bar. The efficiency of the same column enclosed in a shell made of foam insulation was restored at low outlet pressures down to 100bar. 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 1mL/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.