Numerical modeling of elution peak profiles in supercritical fluid chromatography. Part I—Elution of an unretained tracer

When chromatography is carried out with high-density carbon dioxide as the main component of the mobile phase (a method generally known as “supercritical fluid chromatography” or SFC), the required pressure gradient along the column is moderate. However, this mobile phase is highly compressible and, under certain experimental conditions, its density may decrease significantly along the column. Such an expansion absorbs heat, cooling the column, which absorbs heat from the outside. The resulting heat transfer causes the formation of axial and radial gradients of temperature that may become large under certain conditions. Due to these gradients, the mobile phase velocity and most physico-chemical parameters of the system (viscosity, diffusion coefficients, etc.) are no longer constant throughout the column, resulting in a loss of column efficiency, even at low flow rates. At high flow rates and in serious cases, systematic variations of the retention factors and the separation factors with increasing flow rates and important deformations of the elution profiles of all sample components may occur. The model previously used to account satisfactorily for the effects of the viscous friction heating of the mobile phase in HPLC is adapted here to account for the expansion cooling of the mobile phase in SFC and is applied to the modeling of the elution peak profiles of an unretained compound in SFC. The numerical solution of the combined heat and mass balance equations provides temperature and pressure profiles inside the column, and values of the retention time and efficiency for elution of this unretained compound that are in excellent agreement with independent experimental data.     

Modeling of thermal processes in high pressure liquid chromatography: I. Low pressure onset of thermal heterogeneity

Heat due to viscous friction is generated in chromatographic columns. When these columns are operated at high flow rates, under a high inlet pressure, this heat causes the formation of significant axial and radial temperature gradients. Consequently, these columns become heterogeneous and several physico-chemical parameters, including the retention factors and the parameters of the mass transfer kinetics of analytes are no longer constant along and across the columns. A robust modeling of the distributions of the physico-chemical parameters allows the analysis of the impact of the heat generated on column performance. We developed a new model of the coupled heat and mass transfers in chromatographic columns, calculated the axial and radial temperature distributions in a column, and derived the distributions of the viscosity and the density of the mobile phase, hence of the axial and radial mobile phase velocities. The coupling of the mass and the heat balances in chromatographic columns was used to model the migration of a compound band under linear conditions. This process yielded the elution band profiles of analytes, hence the column efficiency under two different sets of experimental conditions: (1) the column is operated under natural convection conditions; (2) the column is dipped in a stream of thermostated fluid. The calculated results show that the column efficiency is remarkably lower in the second than in the first case. The inconvenience of maintaining constant the temperature of the column wall (case 2) is that retention factors and mobile phase velocities vary much more significantly across the column than if the column is kept under natural convection conditions (case 1).     

Modeling of thermal processes in very high pressure liquid chromatography for column immersed in a water bath: Application of the selected models

Currently, chromatographic analyses are carried out by operating columns packed with sub-2 μm particles under very high pressure gradients, up to 1200 bar for 5 cm long columns. This provides the high flow rates that are necessary for the achievement of high column efficiencies and short analysis times. However, operating columns at high flow rates under such high pressure gradients generate a large amount of heat due to the viscous friction of the mobile phase stream that percolates through a low permeability bed. The evacuation of this heat causes the formation of significant or even large axial and radial gradients of all the physico-chemical parameters characterizing the packing material and the mobile phase, eventually resulting in a loss of column efficiency. We previously developed and successfully applied a model combining the heat and the mass balances of a chromatographic column operated under very high pressure gradients (VHPLC). The use of this model requires accurate estimates of the dispersion coefficients at each applied mobile phase velocity. This work reports on a modification of the mass balance model such that only one measurement is now necessary to accurately predict elution peak profiles in a wide range of mobile phase velocities. The conditions under which the simple equilibrium-dispersive (ED) and transport-dispersive (TD) models are applicable in VHPLC are also discussed. This work proves that the new combination of the heat transfer and the ED model discussed in this work enables the calculation of accurate profiles for peaks eluted under extreme conditions, like when the column is thermostated in a water bath.     

Density gradients in packed columns: II. Effects of density gradients on efficiency in supercritical fluid separations

To investigate how fluid compressibility affects efficiency in supercritical fluid separations, band dispersion along a packed capillary column was measured from on-column elution rate profiles obtained under solvating gas chromatography (SGC) conditions; this allowed efficiency to be determined with respect to position along the column. Theoretical efficiency was also modeled. The model indicates that the primary cause of band broadening in SGC is high mobile phase velocity near the column outlet. However, the experimental results show that significant band broadening also occurs near the column inlet in a region that corresponds to high elution rates of the analyte. On-column detection also revealed spatial focusing of the analyte as it moves down the column density gradient.     

Structural radial heterogeneity of a silica-based wide-bore monolithic column

The radial distribution of the main characteristics (elution time and standard deviation) of the elution profiles of a flat injected band recorded at the exit of a monolithic column were determined. These distributions provide the radial distributions of the average mobile phase velocity, the elution time and the maximum height of the peak of an analyte, the column efficiency and the analyte concentration. The band profiles were measured at the exit of a 10-mm i.d., 100-mm long silica-based monolithic column. An on-column local electrochemical amperometric detector allowed the recording of the elution profiles at different spatial positions throughout the column cross-section. The local spatial distribution of the mobile phase velocity does not follow a piston-flow behavior but exhibits radial heterogeneity. The local efficiency near the wall is lower than that near the column center. The radial distribution of the maximum concentration of the peaks varies throughout the column exit section, partially due to the radial variations of the column efficiency. These results might explain the rather large value of the A term of the Van Deemter or the Knox equations reported previously for monolithic columns.     

Fundamental chromatographic equations designed for columns packed with very fine particles and operated at very high pressures. Applications to the prediction of elution times and the column efficiencies

The wall temperatures of three Acquity-BEH-C18columns (2.1 mm x 50, 100, and 150 mm) and the temperature of the incoming eluent were maintained constant at 289 K, using a circulating water heat exchanger. The retention times and the band broadening of naphtho[2,3-a]pyrene were measured for each column as a function of the flow rate applied. Pure acetonitrile was used as the eluent. The flow rate dependence of neither elution volumes nor bandwidths can be accounted for by classical models of retention and HETP, respectively, since these models assume columns to be isothermal. Because the heat generated by friction of the eluent against the column bed increases with increasing flow rate, the column bed cannot remain isothermal at high flow rates. This heat is evacuated radially and/or longitudinally by convection, conduction, and radiation. Radial and axial temperature gradients are formed, which are maximum and minimum, respectively, when the temperature of the column wall is kept uniform and constant. The retention times that we measured match well with the values predicted based on the temperature distribution along and across the column, which we calculated and on the temperature dependence of the retention for the same column operated isothermally (i.e., at very low flow rate). The rate of band spreading varies along non-isothermal columns, so the HETP can only be defined locally. It is a function of the axial coordinate. A new contribution is needed to account for the radial thermal heterogeneity of the column, hence the radial distribution of the flow velocities, which warps the elution band. A new model, based on the general dispersion theory of Aris, allows a successful prediction of the unusually large bandwidths observed with columns packed with fine particles, operated at high flow rates, hence high inlet pressures.     

Development of dual gradient column in liquid chromatography

The dual gradient column, in which both the chemical property of the stationary phase and the flow velocity in the mobile phase are heterogeneous longitudinally along the column, is developed to obtain the mobile phase gradient-like elution in an isocratic condition. Here, the step-wise dual gradient columns were prepared by connecting an inlet column (I.D. 50 microm, packed with ODS) serially to an outlet column (I.D. 100-200 microm, packed with the mixture of ODS and C1 [9:1]). The retention behavior of alkylbenzenes was able to be controlled in the dual gradient column depending on the variation in the flow velocity. Moreover, the change in retention behavior induced by the flow velocity variation for the dual gradient columns was quite different from that by the variation in organic modifier content of the mobile phase in isocratic elution for a single gradient column and can induce the similar effect with an ordinary gradient elution in a mobile phase composition.     

Density gradients in packed columns: I. Effects of density gradients on retention and separation speed

Density gradients in packed capillary columns operating under the extreme pressure drops typical for solvating gas chromatography were investigated by on-column spectroscopic measurements and compared to a theoretical model. Laser-induced fluorescence was used to follow the elution of various analytes, and Raman spectroscopy was used to measure the density of the mobile phase, each with respect to column position. Mobile phase linear velocity initially increases gradually, and then rises rapidly near the column outlet. High flow rates near the column outlet are offset by a loss of mobile phase solvating power which ultimately limits the speed of separation. These results represent an extreme case for illuminating factors affecting supercritical fluid separation techniques in general.     

Retention mechanisms in super/subcritical fluid chromatography on packed columns

Whereas the retention rules of achiral compounds are well defined in high-performance liquid chromatography, on the basis of the nature of the stationary phase, some difficulties appear in super/subcritical fluid chromatography on packed columns. This is mainly due to the supposed effect of volatility on retention behaviours in supercritical fluid chromatography (SFC) and to the nature of carbon dioxide, which is not polar, thus SFC is classified as a normal-phase separation technique. Moreover, additional effects are not well known and described. They are mainly related to density changes of the mobile phase or to adsorption of fluid on the stationary phase causing a modification of its surface. It is admitted that pressure or temperature modifications induce variation in the eluotropic strength of the mobile phase, but effects of flow rate or column length on retention factor changes are more surprising. Nevertheless, the retention behaviour in SFC first depends on the stationary phase nature. Working with polar stationary phases induces normal-phase retention behaviour, whereas using non-polar bonded phases induces reversed-phase retention behaviour. These rules are verified for most carbon dioxide-based mobile phases in common use (CO(2)/MeOH, CO(2)/acetonitrile or CO(2)/EtOH). Moreover, the absence of water in the mobile phase favours the interactions between the compounds and the stationary phase, compared to what occurs in hydro-organic liquids. Other stationary phases such as aromatic phases and polymers display intermediate behaviours. In this paper, all these behaviours are discussed, mainly by using log k-log k plots, which allow a simple comparison of stationary phase properties. Some examples are presented to illustrate these retention properties.     

Faster axial band dispersion in a monolithic silica column than in a particle-packed column

The contribution of molecular diffusion to peak broadening was studied in a reversed-phase HPLC system, consisting of a monolithic silica C18 column and methanol-water mobile phase. Study on the band broadening effect of holding a solute in a column or elution at very low linear velocity of mobile phase allowed facile determination of the contribution of the molecular diffusion term. Less obstruction against molecular diffusion, or the faster axial band dispersion in a monolithic silica column than in a particle-packed column, was found both in mobile phase and in stationary phase.     

Prediction of elution bandwidth for purine compounds by a retention model in reversed-phase HPLC with linear-gradient elution

In reversed-phase liquid chromatography, the retention mechanism of solute has been studied under linearly programmed gradient mobile-phase conditions. The separation of a mixture of four purine compounds (purine, theobromine, theophylline, and caffeine) was considered as a practical case in two binary mobile phase systems, water/methanol and water/acetonitrile. The retention model which describes how the retention factor is related to the mobile-phase composition has been developed in various mathematical forms to predict the retention time in both linear and gradient elutions. For a pulse injection of sample, two important factors, the retention time and the bandwidth of solute, might be computable to predict the elution profiles estimated by the distribution function, such as the Gaussian distribution function. In this work, a prediction method based on the analogue of the retention model was proposed to calculate the bandwidth in linear gradient elutions. Band broadening was caused by the different migration velocities of the front and rear ends of the solute band in a chromatographic column. Therefore, the migration behaviors of the front and rear ends of the solute band were explained with the same retention model which had been used to predict the retention time of solute. For the well retained solutes, theophylline and caffeine, the predicted bandwidth and experimentally obtained bandwidth showed good agreement in both isocratic and gradient elutions.     

Analysis of the band profiles of the enantiomers of phenylglycine in liquid chromatography on bonded teicoplanin columns using the stochastic theory of chromatography.

The retention behaviour of the enantiomers of underivatized phenylglycine was studied on a Chirobiotic T column packed with amphoteric glycopeptide teicoplanin covalently bonded to the surface of silica gel. The retention and the selectivity of separation of the enantiomers increase with rising concentration of ethanol or of methanol in aqueous-organic mobile phases. The band profiles of the less retained L-phenylglycine are symmetrical, but the band profiles of the more strongly retained D-phenylglycine are tailing in all mobile phases tested. The band broadening does not diminish even at very low concentrations of phenylglycine, so that it cannot be attributed to possible column overload. The analysis of the band profile using the stochastic theory of chromatography suggests that the broadening can be attributed to at least two additional chiral centres of adsorption in the stationary phase contributing to the retention of the more strongly retained enantiomer in addition to the adsorption of the less retained one. This behaviour can be explained by the complex structure of the teicoplanin chiral stationary phase.     

Efficiency for unretained solutes in packed column supercritical fluid chromatography II. Experimental results for elution of methane using large pressure drops

At near-critical temperatures and pressures, experimental results for elution of methane with neat carbon dioxide on a 150 mm x 2.0 mm I.D. column packed with 5 microm porous silica with a bonded octylsilica stationary phase show much greater efficiency losses than predicted by theory if isothermal conditions are assumed. Experiments with insulated, air- and water-thermostatted columns demonstrate that significant axial and radial temperature gradients are produced by Joule-Thomson cooling of the mobile phase, and that radial temperature gradients can be a major cause of band spreading at low temperatures and pressures. The use of thermal insulation on the column can greatly improve efficiency under these conditions.     

The ultimate band compression factor in gradient elution chromatography

The equations predicting the ultimate time band compression factor, G=(t(R)-t(F))/t(p) in linear gradient elution chromatography, for an infinitely narrow injection (injection time t(p)-->0) were derived for an ideal-model column (dispersionless chromatography, H=0) assuming the Linear Solvent Strength Model for the retention behavior of the analyte. Numerical solutions can readily be obtained when the LSSM model does not apply. The results can be generalized to any retained organic modifier (k'(A)) in the mobile phase. The stronger the retention of the organic modifier, the more effective the band compression. Dispersion in real chromatographic column (H not equal 0) affects the limits that can be reached in linear gradients but poorly in step gradients. Examples based on a conventional HETP of about 12 microm using a 5 microm particle packed column reveal that the best time compression factor that could be expected is twice the one predicted with an ideal column.     

Modeling of thermal processes in high pressure liquid chromatography: II. Thermal heterogeneity at very high pressures

Advanced instruments for liquid chromatography enables the operation of columns packed with sub-2 μm particles at the very high inlet pressures, up to 1000 bar, that are necessary to achieve the high column efficiency and the short analysis times that can be provided by the use of these columns. However, operating rather short columns at high mobile phase velocities, under high pressure gradients causes the production of a large amount of heat due to the viscous friction of the eluent percolating through the column bed. The evacuation of this heat causes the formation of significant axial and radial temperature gradients. Due to these thermal gradients, the retention factors of analytes and the mobile phase velocity are no longer constant throughout the column. The consequence of this heat production is a loss of column efficiency. We previously developed a model combining the heat and mass balance of the column, the equations of flow through porous media, and a linear isotherm model of the analyte. This model was solved and validated for conventional columns operated under moderate pressures. We report here on the results obtained when this model is applied to columns packed with very fine particles, operated under very high pressures. These results prove that our model accounts well for all the experimental results. The same column that elutes symmetrical, nearly Gaussian peaks at low flow rates, under relatively low pressure drops, provides strongly deformed, unsymmetrical peaks when operated at high flow rates, under high pressures, and under different thermal environments. The loss in column efficiency is particularly important when the column wall is kept at constant temperature, by immersing the column in a water bath.     

Pressure drop effects on selectivity and resolution in packed column supercritical fluid chromatography

The influence of pressure drop on retention, selectivity, plate height and resolution was investigated systematically in packed supercritical fluid chromatography (SFC) using pure carbon dioxide as the mobile phase. Numerical methods developed previously which enabled the prediction of pressure gradients, diffusivities, capacity factors, plate heights and resolutions along the length of the column were used for the model calculations. The effects of inlet pressure and supercritical fluid flow rate on selectivity and resolution are studied. In packed column SFC with pure carbon dioxide as the mobile phase, the pressure drop can have a significant effect on resolution. The flow rate is shown to have a larger effect than generally realized. The calculated data are shown to be in good agreement with the experimental results. Finally, the variation of the chromatographic parameters along a 5.5 meter long model SFC column is illustrated. The possibilities and limitations of using long packed columns in SFC are discussed. It is demonstrated that long columns with large plate numbers do not necessarily yield better separations.     

Column radial homogeneity in high-performance liquid chromatography

The radial distribution of analyte molecules within an elution band in HPLC was determined by local, on-column, fluorescence detection at the column outlet. Several optical fiber assemblies were implanted in the exit frit at different points over the column cross-section and the fluorescence of a laser-dye analyte was measured. The individual elements of a diode array were used as independent detectors. The distribution of the mobile phase velocity across the column was measured for a number of standard size analytical HPLC columns of different efficiencies, operated at different mobile phase linear velocities. The dependence of the column efficiency on these profiles is discussed.     

A study of the effects of column porosity on gradient separations of proteins

The type of the stationary phase for reversed-phase liquid chromatography significantly affects the sample elution. Hydrodynamic properties, efficiency and gradient elution of proteins were investigated on five commercial C18 columns with wide-pore totally porous particles, with superficially porous layer particles, non-porous particles and a silica-based monolithic bed. The efficiency in the terms of reduced plate height is higher for low-molecular ethylbenzene than for proteins, but depends on the character of the pores in the individual columns tested. The superficially porous Poroshell and the non-porous Micra columns provide the best efficiency for proteins at high mobile phase flow rates, probably because of similar pore architecture in the stationary phase. The Zorbax column with similar pore architecture as the Poroshell active layer, i.e. narrow pore distribution of wider pores shows better efficiency than the packed column with narrow pores and broad pore distribution. The monolithic column shows lower efficiency for proteins at high flow rates, but it performs better than the broad-pore distribution totally porous particulate columns. Different pore architecture affects also the retention and selectivity for proteins on the individual columns. The retention times on all columns can be predicted using the model for reversed-phase gradient elution developed originally for low-molecular compounds. Consideration of the limited pore volume accessible to the biopolymers has negligible effect on the prediction of retention on the columns packed with non-porous or superficially porous particles, but improves the accuracy of the predicted data for the totally porous columns with broad pore distribution.     

Overview of the retention in subcritical fluid chromatography with varied polarity stationary phases

Retention and separation of achiral compounds in supercritical fluid chromatography (SFC) depend on numerous parameters: some of these parameters are identical to those encountered in HPLC, such as the mobile phase polarity, while others are specific to SFC, as the density changes of the fluid, due to temperature and/or pressure variations. Additional effects are also related to the fluid compressibility, leading to unusual retention changes in SFC, for instance when flow rate or column length is varied. These additional effects can be minimised by working at lower temperatures in the subcritical domain, simplifying the understanding of retention behaviours. In these subcritical conditions, varied modifiers can be mixed to carbon dioxide, from hexane to methanol, allowing tuning the mobile phase polarity. With nonpolar modifiers, polar stationary phases are classically used. These chromatographic conditions are close to the ones of normal-phase LC. The addition of polar modifiers such as methanol or ACN increases the mobile phase polarity, allowing working with less polar stationary phases. In this case, despite the absence of water, retention behaviours generally follow the rules of RP LC. Moreover, because identical mobile phases can be used with all stationary phase types, from polar silica to nonpolar C18-bonded silica, the classical domains, RP and normal-phase, are easily brought together in SFC. A unified classification method based on the solvation parameter model is proposed to compare the stationary phase properties used with the same subcritical mobile phase.     

Quantitative analysis and synthesis of the electrokinetic mass transport and adsorption mechanisms of a charged adsorbate in capillary electrochromatography systems employing charged adsorbent particles.

The dynamic mathematical model of Grimes and Liapis [J. Colloid Interf. Sci. 234 (2001) 223] for capillary electrochromatography (CEC) systems operated under frontal chromatography conditions is extended to accommodate conditions in CEC systems where a positively charged analyte is introduced into a packed capillary column by a pulse injection (analytical mode of operation) in order to determine quantitatively the electroosmotic velocity, electrostatic potential and concentration profiles of the charged species in the double layer and in the electroneutral core region of the fluid in the interstitial channels for bulk flow in the packed chromatographic column as the adsorbate adsorbs onto the negatively charged fixed sites on the surface of the non-porous particles packed in the chromatographic column. Furthermore, certain key parameters are identified for both the frontal and analytical operational modes that characterize the performance of CEC systems. The results obtained from model simulations for CEC systems employing the analytical mode of operation indicate that: (a) for a given mobile liquid phase, the charged particles should have the smallest diameter, d(p), possible that still provides conditions for a plug-flow electroosmotic velocity field in the interstitial channels for bulk flow and a large negative surface charge density, deltao, in order to prevent overloading conditions; (b) sharp, highly resolute adsorption zones can be obtained when the value of the parameter gamma2min, which represents the ratio of the electroosmotic velocity of the mobile liquid phase under unretained conditions to the electrophoretic velocity of the anions (0>gamma2.min>-1), is very close to negative one, but the rate at which the solute band propagates through the column is slow; furthermore, as the solute band propagates across larger axial lengths, the desorption zone becomes more dispersed relative to the adsorption zone especially when the value of the parameter gamma2,max, which represents the ratio of the electroosmotic velocity of the mobile liquid phase under retained conditions to the electrophoretic velocity of the anions (0>gamma2,max>-1), is significantly greater than gamma2,min; (c) when the value of the equilibrium adsorption constant, K(A),3, is low, very sharp, highly resolved adsorption and desorption zones of the solute band can be obtained as well as fast rates of propagation of the solute band through the column; (d) sharp adsorption zones and fast propagation of the solute band can be obtained if the value of the mobility, v3, of the analyte is high and the value of the ratio v1/v3, where v1 represents the mobility of the cation, is low; however, if the magnitude of the mobility, v3, of the analyte is small, dispersed desorption zones are obtained with slower rates of propagation of the solute band through the column; (e) good separation of analyte molecules having similar mobilities and different adsorption affinities can be obtained in short operational times with a very small column length, L, and the resolution can be increased by providing values of gamma2,min and gamma2,max that are very close to negative one; and (f) the change in the magnitude of the axial current density, i(x), across the solute band could serve as a measurement for the rate of propagation of the solute band.